Free-space multi-channel interferometer

Abstract

Described herein are devices, systems, and methods for implementing free-space multi-channel optical interferometers. Such interferometers may include a beam-splitting device or assembly that performs the various beam-splitting and beam-combining functions, and multiple collimator devices configured in pairs that map light for the multiple optical channels along the interferometer paths between sets of waveguide cores. The interferometer may include one or more of the following features: high-precision collimator assemblies constructed from a waveguide array and two collimator lenses whose distance is carefully set to achieve a desired focal length, a transparent plate or set of plates with selective beam-splitting surface coatings serving as the beam-splitting device, and a planar light circuit (PLC) free-space-coupled to an optical fiber to split light from the optical fiber between multiple waveguide cores for the multiple optical channels, optionally with a polarization controller or modulator inserted between optical fiber and PLC for polarization-diverse interferometry.

Description

Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 FREE-SPACE MULTI-CHANNEL INTERFEROMETER CLAIM OR PRIORITY

[0001] This application claims the benefit of priority to U.S. Provisional Patent Application Serial No. 63 / 659,815, filed on June 13, 2024, which is incorporated by reference herein in its entirety. BACKGROUND

[0002] Optical fibers can be used as distributed sensors, e.g., for strain or temperature sensing along the fiber. Multicore fibers, moreover, enable shape sensing based on the reconstruction of the fiber shape from simultaneously measured strain signals along the multiple fiber cores. Fiber-optic sensing generally involves interrogating the sensing fiber core(s) interferometrically. For example, in optical frequency domain reflectometry (OFDR), frequency- swept laser light is coupled into each sensing fiber core via a measurement arm of an interferometer, and light reflected or scattered along the fiber core is recombined with light that has traversed a reference arm; the resulting interference signal is measured as a function of time, e.g., with a polarization- diverse detector, and then processed to extract the strain-dependent reflection spectrum as a function of position along the fiber. Fiber-optic shape sensing utilizes multiple channels of interferometric sensing, one for each of the simultaneously measured fiber cores.

[0003] Conventional OFDR systems are typically constructed using discrete optical fiber components, such as fiber-optic couplers, polarizing beam splitters, polarization controllers, connectors, fanout assemblies, etc. As the number of channels increases, such OFDR systems become more complex, costly, and space-consuming because for each additional core, another set of discrete optical fiber components is added. Improved interferometer system designs are desirable.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 SUMMARY

[0004] Described herein are devices, systems, and methods for implementing multi-channel optical interferometers at least partially in free space. In the free- space portions of the interferometer, as the term “free space” is herein understood, light is not guided in optical fiber or other waveguide structures; instead, light is directed without lateral confinement through bulk-optic components and the space between them. An interferometer including such free- space portions is herein referred to as a “free-space interferometer.” (Notwithstanding the phrase “free-space interferometer,” the interferometer may also include one or more optical waveguide components.)

[0005] The bulk-optic components are used in place of fiber optics to provide various system functions, and can be shared between multiple optical channels. This approach can avoid much of the replication of components from which conventional, fiber-optic multi-channel systems suffer, and can as such reduce or even eliminate the added cost and complexity associated with increasing the number of channels As a result, in some instances, the overall cost, complexity, and number of optical components are reduced, as compared with conventional systems. The shared bulk-optic component or multi- component assembly providing the beam-splitting and / or beam-combining functions of the interferometer is herein also referred to as a “beam-splitting device,” “beam-splitting assembly” (if it includes multiple components), or “beam-splitting optic.”

[0006] In accordance with various embodiments, the inputs and outputs along one or more interferometric paths for the multiple channels through the beam-splitting optic are still provided by respective input and output sets of fiber cores or other waveguide cores (hereinafter also simply “cores” or “waveguides”), and suitable coupling assemblies are used to help ensure that light is mapped precisely and coupled efficiently between input-output pairs of such sets of cores. (Although an “input set” of cores may be structurally separate from an “output set” of cores, the designation of a set of cores as an “input set” here does not mean core(s) of that “input set” cannot also be part of an “output set.” Similarly, a set of cores identified as an “output set” may contain core(s) that are part of an “input set.” For example, in some instances, the same set of cores may serve as the input set of cores for one interferometricIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 path and as the output set of cores for another path.) The coupling assemblies, which generally collimate light that is emitted by the input cores before the light enters the beam-splitting optic and, conversely, focus light that exits the beam- splitting optic onto the output cores, are herein also referred to as “collimator assemblies” or “collimator devices.”

[0007] In an example application of the principles discussed herein, the interferometer system is an OFDR system whose measurement branch is coupled bidirectionally to a multicore sensing fiber and whose interferometer output is split between two mutually orthogonal polarizations for polarization-diverse detection. Such a system can be implemented using a (bulk-optic) beam- splitting device or a beam-splitting assembly, configured to redirect probe light from a set of probe input cores into the sensing cores of the multicore sensing fiber (or associated with the multicore sensing fiber), combine reflected light received from the sensing cores with reference light received from a set of reference input cores, and split the combined light polarization-dependently between two sets of output cores. In this example, light is coupled along five interferometer paths between respective input-output pairs of the sets of cores: from the set of probe input cores to the set of sensing cores, from the set of sensing cores to each of the two sets of output cores, and from the set of reference input cores to each of the two sets of output cores. Note that the term “sensing cores,” as used herein, may refer to the fiber cores of the sensing fiber itself if light is coupled directly between the beam-splitting device and the sensing fiber, or otherwise to a set of cores that are, in turn, connected to the sensing fiber cores of the sensing fiber.

[0008] Various interrelated aspects of the disclosed subject matter pertain to collimator assemblies, constituting sub-assemblies of the interferometer system at large, for coupling light between an input set of cores and an output set of cores efficiently, that is, with low optical losses. In some embodiments, such a collimator assembly is constructed with a pair of lenses mounted, along with a linear waveguide array (e.g., implemented by single-core fibers retained in a v- groove assembly or by a planar light chip), to a collimator base. During assembly, the distance between the two lenses is set or adjusted based on the individual focal lengths of the lenses to achieve a specified effective focal length of the compound two-lens system; beneficially, using this approach, the effectiveIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 focal length can be controlled with much higher precision than the individual focal lengths (e.g., within 0.1% rather than 1% tolerances). High-precision collimator assemblies are useful, in particular, to couple light between linear arrays of single-core fibers, whose larger core spacings as compared with multicore fibers render them more susceptible to optical losses resulting from magnification errors due to focal-length deviations from their nominal values. Using verified collimator assemblies (that is, collimator assemblies whose effective focal length has been measured and confirmed to be within specified tolerance margins prior to integration of the collimator assembly into the interferometer system) increases the yield of the manufacturing process and as such contributes to lower cost.

[0009] The collimator assemblies are mounted (with their bases) to a substrate carrying the interferometer system at large. The bonding surfaces of the collimator assemblies, which are generally planar, may be joined with a thin layer of adhesive (e.g., epoxy). Alternatively, in some embodiments, the bonding surface are instead joined by welding (e.g., glass-to-glass welding when the components are made of glass). Glass-to-glass welding can increase the range of operating conditions (e.g., including temperature ranges), and improve reliability. Optionally, an additional weakly focusing lens for each collimator assembly can be mounted on the substrate to compensate for any small errors in the placement of the collimator assembly. To reduce or minimize optical coupling losses, the collimator assemblies may be configured telecentrically, meaning that the distances between pairs of collimator assemblies are all equal to the sum of the effective focal lengths of each pair, and thus to each other if the collimator assemblies share the same effective focal length. Further, to render the system as a whole more robust to thermal expansion, the collimator assemblies may be mounted on their side (that is, with side surfaces of their bases contacting the substrate) and with pairs of collimator assemblies being 180° rotated copies of each other in the plane of the substrate, which effects a mutual compensation between the two collimator assemblies in any thermally induced changes in the beam direction. “Beam” is generally used herein to refer to a beam of light. Reducing the sensitivity of the system to temperature changes by design in this manner facilitates the use of molded glass lenses inIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 place of fused-silica lenses, whose smaller thermal expansion comes at significantly higher manufacturing cost.

[0010] In some embodiments, assembling the collimator devices involves alignment operations performed in a suitable fixture, including operations to help ensure that the beam exiting the collimator assembly is parallel to the surface of the collimator base that is going to be bonded to the substrate, which in turn will result in a beam parallel to the substrate surface once the collimator assembly has been bounded to the substrate. These alignment operations include, first, aligning the collimator base surface parallel to an alignment beam and recording the location of the alignment beam on the image sensor of a camera focused at infinity, and then, without moving the collimator base relative to the camera, configuring the collimator device components, and in particular positioning the waveguide array relative to the collimator lens pair, such that the collimated beam leaving the collimator device is focused on the image sensor at the same coordinate(s) as the alignment beam. The alignment between the collimator base surface and the alignment beam in the first step can be accomplished using a transmission grating to split the alignment beam of light into zeroth and two first diffraction orders, reflecting one of the first diffraction orders off the collimator base surface, and orienting the collimator base such that the two first-order beams are focused onto the same location on the image sensor; this coincidence of the first-order beams guarantees that the zeroth-order beam is parallel to the collimator base surface. In addition to ensuring parallelism between the collimator base surface and the collimated beam, the alignment operations performed in the fixture may also include setting the distance between the two lenses to achieve the desired effective focal length, corresponding to the desired angular separation between collimated light beams originating from different cores of the linear waveguide array, e.g., as measured based on the distance of these beams on the image sensor of the camera focused at infinity. Further, the alignment operations may include adjusting the distance of the waveguide array from the pair of lenses to achieve acceptable (or to optimize) collimation of the light from any individual core, e.g., by ensuring the spot size of the beam on the image sensor of the camera is no larger than a defined size that corresponds with the acceptable collimation (or is minimized when optimizing collimation).Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1

[0011] In some embodiments, as part of the assembly of the interferometer system at large, the collimator subassemblies are aligned pairwise in a sequential process aided by a retroreflector and a camera focused at infinity. To align a given pair of collimator assemblies, light is injected simultaneously into both collimator assemblies, resulting in two collimator output beams, portions of which are counterpropagating through the beams-splitting optic from one collimator assembly to the other, and other portions of which are branched off at the various beams-splitting surfaces of the beam-splitting optic. The retroreflector is strategically placed into the path of a branched-off portion of one of the collimator output beams such that the associated beam-splitting surface will direct the retroreflected portion along the same path and in the same direction as the other collimator output beam. The resulting co-propagating beams are imaged onto the camera, which is for that purpose likewise placed strategically relative to the beam-splitting optic. The collimator output beams can then be adjusted, in position and / or orientation, to cause the beam images on the camera to coincide, which helps to ensure that the counterpropagating portions are accurately mapped between the two collimator assemblies. The adjustments may involve positioning a weakly focused lens between the waveguide array and the collimator lenses of the collimator assembly.

[0012] Another aspect of the disclosed subject matter pertains to the beam- splitting optic. Instead of using an assembly of beam-splitting prisms that include various beam-splitting interior surfaces, a single transparent plate, e.g., of glass or other material, may be configured with functional optical surface coatings selectively applied to various surface regions to create non-polarizing and polarizing surfaces that are functionally equivalent to the interior surfaces of the beam-splitting prism. Multiple such coated-plate beam-splitting optics can be manufactured simultaneously and cost-efficiently by patterning and coating a larger plate, and then dicing it into individually devices. As an alternative to a single coated plate, an arrangement of multiple transparent plates (or other optical components), e.g., having surface coatings extending over the entire faces, which eliminates or reduces the need for patterning during manufacture, may also be employed as the beam-splitting optic. As used herein, “transparent” is used with a component to indicate transparency to the wavelength(s) of lightIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 with which the component is designed to interact, and the component may or may not be transparent to other wavelengths.

[0013] Yet another aspect of the disclosed subject matter relates to the interferometer system as a whole, and involves the use of planar light circuits (PLCs) in place of optical fiber arrays to split probe light into multiple probe beams and reference light into multiple reference beams. Light from a single input fiber along each interferometer branch may be free-space-coupled into the PLC input, allowing for the insertion of free-space (rather than fiber-based) polarization controllers or modulators in the measurement and reference branches preceding the PLC, which obviates the need to modulate the polarization of probe or reference light in each channel individually.

[0014] These and other aspects and features will be discussed in more detail in, and will become more readily understood from, the following detailed description, in particular, when taken in conjunction with the accompanying drawings. The foregoing summary is not intended as a comprehensive list of all relevant aspects, features, and embodiments, but serves merely to introduce, at a high level, certain terms used and various concepts and principles explained more fully below. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] FIG. 1 is a schematic diagram of an example fiber-optic multi- channel OFDR system.

[0016] FIG. 2 is a conceptual drawing of a beam-splitting assembly and associated input and output sets of optical fibers of an example free-space multi- channel interferometer, in accordance with various embodiments.

[0017] FIG. 3 is a conceptual drawing of a beam-splitting assembly and associated collimator assemblies of an example free-space multi-channel interferometer, in accordance with various embodiments.

[0018] FIG. 4 is a conceptual drawing illustrating a simple camera focused at infinity, as may be used for beam alignment of a collimator assembly, in accordance with some embodiments.

[0019] FIG. 5 is a conceptual drawing illustrating a long-period transmission grating, as may be used for beam alignment of a collimator assembly, in accordance with some embodiments.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1

[0020] FIGS. 6A and 6B are conceptual drawings illustrating a fixture and method for aligning a selected surface parallel to an alignment beam, in accordance with some embodiments.

[0021] FIG. 7A and 7B are conceptual drawings illustrating, in side view and top view, respectively, the alignment of the side surfaces of the collimator base parallel to an alignment beam within the fixture of FIGS. 6A and 6B, in accordance with some embodiments.

[0022] FIG. 8 is a conceptual drawing illustrating the alignment of the collimator assembly within the fixture of FIGS. 6A-7B such that the collimator output beam is parallel to the top and side surfaces of the collimator base, in accordance with some embodiments.

[0023] FIG. 9 is a conceptual drawing illustrating calibration of the effective focal length of the collimator assembly using the fixture of FIGS. 6A-8, in accordance with some embodiments.

[0024] FIG. 10A is a conceptual drawing of a pair of v-groove fiber arrays with slightly different core spacings as may be used in a pair of respective collimator assemblies, and FIG. 10B is a conceptual drawing illustrating how the configuration of a collimator assembly can be adjusted to accommodate the different core spacings, in accordance with some embodiments.

[0025] FIG. 11 is a flowchart of a method of constructing and aligning a collimator assembly, in accordance with various embodiments.

[0026] FIGS. 12A-12C are conceptual drawings illustrating the use of a compensating lens to correct for misalignments of the collimator output beam that are introduced by the beam-splitting optic, in accordance with various embodiments.

[0027] FIGS. 13A and 13B are conceptual drawings illustrating the misalignment and alignment, respectively, between a pair of waveguide cores that are imaged onto each other by associated collimator lenses.

[0028] FIGS. 14A and 14B are conceptual drawings illustrating the misalignment and alignment, respectively, between a pair of waveguide cores on both sides of a beam-splitting device, using a retroreflector and camera focused at infinity to aid in the alignment process, in accordance with various embodiments.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1

[0029] FIG. 15 is a conceptual drawing illustrating the alignment of a pair of collimator assemblies relative to each other and to a beam-splitting assembly with the help of a retroreflector and camera focused at infinity, in accordance with various embodiments.

[0030] FIGS. 16A-16G are conceptual drawings illustrating the step-wise alignment of the five collimator assemblies of the interferometer system of FIG. 3, in accordance with one embodiment.

[0031] FIG. 17 is a conceptual drawing of a beam-splitting optic implemented by a transparent plate with various surface coatings, in accordance with one embodiment.

[0032] FIG. 18 is a conceptual drawing of an example free-space multi- channel interferometer including a coated-plate beam-splitting optic surrounded by five collimator assemblies, in accordance with various embodiments.

[0033] FIGS. 19A and 19B are conceptual drawings illustrating, in perspective views, a method of manufacturing multiple beam-splitting optics as shown in FIG. 17 from a single transparent plate, in accordance with various embodiments.

[0034] FIG. 20 is a conceptual drawing of an example free-space multi- channel interferometer including a beam-splitting assembly comprising multiple coated plates, surrounded by five collimator assemblies, in accordance with various embodiments.

[0035] FIG. 21A is a conceptual drawing illustrating a PLC configured as an optical splitter to divide light from an input optical fiber between eight output optical fibers of a v-groove array, in accordance with various embodiments.

[0036] FIG. 21B is a conceptual drawing illustrating the PLC and v-groove fiber array of FIG. 21A in top view alongside side views of their respective end- faces.

[0037] FIG. 22 is a conceptual drawing illustrating a PLC optical splitter that is free-space coupled to an input optical fiber and eight output optical fibers, in accordance with various embodiments.

[0038] FIG. 23 is a schematic diagram of an example polarization-diverse free-space multi-channel OFDR system that utilizes free-space-coupled PLCs to divide probe and reference input light between multiple channels, in accordance with various embodiments.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1

[0039] FIG. 24 is a perspective drawing of an example polarization controller, in accordance with one embodiment, as may be used in an OFDR system as shown in FIG. 23.

[0040] FIG. 25 is a schematic diagram of an example polarization-diverse free-space multi-channel OFDR system that utilizes free-space-coupled PLCs to divide probe and reference input light between multiple channels and further includes a free-space polarization modulator for modulating the probe input light before it is coupled into the PLC, in accordance with various embodiments.

[0041] FIG. 26 is a perspective drawing of an example polarization modulator that includes two polarization controllers each including a polarization-modulating crystal, in accordance with one embodiment.

[0042] FIG. 27 is a perspective drawing of an example polarization modulator that utilizes a polarization controller with a polarization-modulating crystal in conjunction with a half-wave plate, in accordance with another embodiment. DESCRIPTION

[0043] Various principles, aspects, and features of free-space multi-channel optical interferometers will, in the following, be explained in the context of OFDR systems, with the general understanding that at least some of the described embodiments are not limited to OFDR, but may find broader application. Before turning to the description of free-space multi-channel interferometers, it may be instructive, for purposes of comparison, to first consider a conventional fiber-optic OFDR system.

[0044] FIG. 1 is a schematic diagram of an example fiber-optic multi- channel OFDR system 100. The depicted system 100 implements six interferometric channels configured to interrogate a six-core sensing fiber, but can readily be adjusted for any number of channels and sensing fiber cores. The system 100 includes a frequency tunable laser 102, controlled by a controller and data processor (also “processor” or “controller”) 104. The processor 104 may be implemented using any suitable combination of processing hardware and software, such as, without limitation, a general-purpose computer including memory storing and one or more hardware processors (e.g., CPUs) executing software programs, applications specific integrated circuitry (ASIC), one orIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 more digital signal processors (DSPs), or other electronic circuitry. Frequency- swept light emitted by the laser 102 is split, e.g., with 90 / 10 coupler 106, between a laser monitor interferometer 108 and a measurement interferometer 110.

[0045] In the laser monitor interferometer 108, the light is split by a coupler 112 between three paths. The first path goes to a photodetector 114 to monitor laser power. The second path passes through a hydrogen cyanide (HCN) gas cell 116 to a photodetector 118 to provide an absolute wavelength reference. The third path goes through an isolator 120 to an interferometer for measuring the change in optical frequency of the swept laser light, using two Faraday rotator mirrors (FRM) 122 having a known delay difference in conjunction with a pair of photodetectors 124 for measuring a quadrature detection signal from which the optical frequency change can be inferred. The detectors 114, 118, 124 of all three paths may be implemented as part of a data acquisition unit 126 of the system 100.

[0046] The light going into the measurement interferometer 110 is split by a 90 / 10 coupler 130 between a reference branch and a measurement branch of the interferometer 110. In the reference branch, the light is further split, by cascaded couplers 132, between six reference paths 133 for the six interferometric channels. The light in the measurement branch passes through an isolator 134 and then through a fiber amplifier implemented by a length of erbium-doped fiber 136 pumped with light from a pump laser 138 that couples in through a Wavelength Division Multiplexed (WDM) coupler 140 and is controlled by the processor 104. The amplified light passes through another isolator 142, followed by a polarization controller 144 that is controlled by the processor 104 and flips the light between two orthogonal (or nearly orthogonal) polarization states on subsequent frequency scans. The polarized light is split by cascading couplers 146 between six measurement paths 147 for the six interferometric channels. Six associated couplers 148 couple the light, via a fanout assembly 150 that couples six single-core fibers 152 to six cores for a multicore fiber 154, from the measurement paths 147 into respective cores of a multicore sensing fiber 160, and couple the reflected light returning from the multicore sensing fiber 160 via the fanout assembly 150 back into the six measurement paths 147. The light in the measurement paths 147 and theIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 reference paths is 133 is combined by couplers 162 (only one being labeled). The resulting six interference light signals then pass through polarization beam splitters (PBSs) 164, which are controlled by the processor 104, to respective pairs of photodetectors 166 (measuring the S- and P-polarized components, respectively) in the data acquisition unit 126 for polarization-diverse detection of the interference signal in each channel. In this manner, the light reflected in the six cores of the multicore sensing fiber 160 can be interferometrically measured.

[0047] The data processor 104, in addition to controlling the tunable laser 102, pump laser 138, polarization controller 144, and polarization beam splitters 164, acquires and processes the electronic output signals from photodetectors 114, 118, 124, 166 in the data acquisition unit 126. The electronic signals from the photodetectors 166 reflect the amplitude of the measured interference signals in all channels as a function of time, and thus as a function of optical frequency of the laser 102, for two polarization states, S and P. The processor 104 linearizes this recorded data with respect to optical frequency, using the data from the laser monitor interferometer, to represent the amplitude in equal increments of optical frequency. The linearized data is Fourier-transformed into the time domain to represent the amplitude and phase of the reflected light as a function of optical delay along each fiber core. The S and P data from two sequential orthogonal polarization scans are combined to compensate for birefringence in the fiber cores and form a scalar measure of the amplitude and phase of the reflected light from each core. This combined complex signal (including amplitude and phase) is compared with interferometric data recorded in a reference scan, and the resulting phase difference or change for each core is the measured signal that is used to compute the current shape of the sensing fiber 160. The derivatives of the measured phase changes are proportional to the strains in each core. The bends in two dimensions, the twist, the strain, and the temperature in the sensing fiber may be determined from the derivatives of the measured phase changes.

[0048] As can be seen from FIG. 1, the optical fiber components of the measurement interferometer 110, including the couplers 148, 162, polarization beam splitters 164, and optical fiber implementing the measurement and reference paths, are replicated six-fold to provide six interferometric channels. This large amount of hardware, which increases with increasing number ofIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 channels, contributes significantly to the cost and complexity of interferometer systems like OFDR system 100. It is desirable, therefore, to perform the functions of the discrete optical fiber components by a shared optical assembly or device.

[0049] FIG. 2 is a conceptual drawing of a beam-splitting assembly 200 and associated input and output sets of optical fibers of an example free-space multi- channel interferometer, in accordance with various embodiments. For simplicity of illustration, two cores are depicted in each of the sensing fiber 202, in the set of probe input fibers 204, in the set of reference input fibers 206, and in each of the two sets of output fibers 208, 210 for the S and P components of the interference signal. However, it will be apparent that larger numbers of cores and fibers may be used, without change to the general configuration, to implement multi-channel interferometers with more than two channels. As an example, for a system that is configured for a six-core sensing fiber, the beam- splitting assembly 200 is configured with corresponding sets of six single-core input fibers and six single-core output fibers; such a six-core beam-splitting assembly 200 can be substituted in the OFDR system 100 for the optical fiber components inside the framed portion 180 of the system to implement the measurement and reference branches for the most part in free space. (In other examples, the system may be configured for sensing fibers having a different number of optical cores, such as a single optical core, four optical cores, seven optical cores, etc.) Note that, in the depicted example, the sets of probe input cores, reference input cores, and output cores for both polarizations are all implemented by respective sets of single-core fibers; this is consistent with replacing portion 180 of the OFDR system 100 with the beam-splitting assembly 200. The beam-splitting assembly 200 can, however, also be used in conjunction with multicore fibers or PLCs providing the various sets of cores. In the context of the OFDR system 100, this would entail some system modification, such as the addition of suitable interfaces of the multicore fibers or PLCs to respective sets of single-core fibers.

[0050] As illustrated, the beam-splitting assembly 200 is a contiguous, transparent bulk-optic component that provides, inside its volume, first and second partially reflective, partially transmissive polarization-independent beam- splitting surfaces 212, 214 (e.g., 50 / 50 surfaces, which evenly split incomingIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 light between reflected and transmitted beams) and a polarization-dependent beam-splitting (or “polarization-splitting”) surface 216 to split incoming light into two orthogonally polarized beams of roughly equal power. Such a bulk- optic component may be assembled from suitable beam-splitting prisms joined at their exterior surfaces. For example, two 50 / 50 cube beam splitters may be used to provide the polarization-independent beam-splitting surfaces 212, 214, and a Wollaston prism or other birefringent, polarization-splitting prism may provide the polarization-splitting surface 216. Alternatives to cube beam splitters include “Swiss cheese” splitters, plate splitters, and pellicle beam splitters; alternatives to the Wollaston prism include Nicol, Glan-Taylor, Rochon, Senarmont, and Nomarski prisms. The beam-splitting assembly 200 may further include, as shown, lenses 218 bonded to select exterior surfaces of the various beam-splitting prisms to collimate light received from the sets of input fibers 204, 206 and / or the sensing fiber 202 and, conversely, focus light onto the sensing fiber 202 and the sets of output fibers 208, 210.

[0051] In the illustrated configuration, the optical fibers are placed relative to the beam-splitting assembly 200 such that probe light 220 from the set of probe input fibers 204 is reflected off the first beam-splitting surface 212, and thereby redirected into the multicore sensing fiber 202. Further in this example, reference light 222 from the set of reference input fibers 206 is reflected off the second beam-splitting surface 214, and thereby combined with reflected light 224 (or “sensor light”) returned from the sensing fiber 202 and transmitted through the first and second beam-splitting surfaces 212, 214. Finally in this example, the combined light 226 is split, at the polarization-splitting surface 216, into S-polarized and P-polarized components 228, 230, which are coupled into the sets of output fiber 208, 210, respectively. Alternative configurations that achieve the same function can be devised by those of ordinary skill in the art without undue experimentation. For example, the sensing fiber 202 may be placed to receive light transmitted through, rather than reflected off, the first beam-splitting surface 212, which then serves to redirect the sensor light towards the second beam-splitting surface 214. As another example, the second beam- splitting surface 214 may reflect sensor light and transmit reference light to create the combined light; in this case, the beam-splitting assembly 200 downstream of the second beam-splitting surface 214 is reconfigured such thatIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 the combined light still passes to the polarization-splitting surface 216. Regardless of the particular configuration, light from multiple cores (often all cores) of any of the input set of cores, output sets of cores, or the sensing fiber passes through the beam-splitting assembly 200 along the same general path. As such, the beam-splitting assembly 200 is shared among the multiple interferometric channels, providing beneficial reductions in cost and complexity as compared with a fiber-optic multi-channel interferometer, e.g., as shown in FIG. 1.

[0052] Various aspects that provide further improvements and benefits for free-space multi-channel interferometers are described in the following sections. Broadly, these aspects fall into three general categories pertaining to different sub-systems of an interferometer system: (i) collimator assemblies at the interface between the input / output cores and the beam-splitting optic for low- loss coupling of light between input cores and output cores, along with assembly and alignment methods; (ii) alternative shared beam-splitting optics that provide the beam-splitting functions by exterior surface coatings rather than at interior surfaces, along with methods of their manufacture; and (iii) light-splitting devices and configurations for creating multiple channels of polarization- controlled input from a single laser input. In general, the various aspects can be used separately and independently, or in conjunction with one another. For example, the disclosed collimator assemblies can be used both with beam- splitting assemblies as described with reference to FIG. 2 and with the alternative beam-splitting optics described below, and conversely, the alternative beam-splitting optics may be used with or without the collimator assemblies. Similarly, the disclosed light-splitting devices and configurations may be used with either type of beam-splitting optic, and may be, but need not necessarily be combined with the collimator assemblies. Collimator assemblies

[0053] In the free-space multi-channel interferometer configuration of FIG. 2, light is directly coupled from the input cores (including the sensing cores) into the bulk-optic beam-splitting assembly 200 and from the beam-splitting assembly into the output cores (including the sensing cores). At the interface of each set of input or output cores with the beam-splitting assembly, a single lensIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 218 formed integrally with the beam-splitting assembly 200 is used to collimate the light in one direction and focus it in the other direction. This configuration provides reasonably high coupling efficiencies (e.g., between 50% and 90% coupling, corresponding to a 3 dB to 0.5 dB loss) if the cores within each set are relatively closely spaced (e.g., with distances between pairs of cores of less than 100 m), as is the case, for instance, in a seven-core multicore fiber with six cores helixed (at a same radius from a neutral axis of the fiber) around a central core located at the neutral axis, having a fiber diameter of 125 m, and with a 35 m spacing between neighboring cores. However, if the cores are farther apart, e.g., if seven single-core fibers are arranged in a standard v-groove fiber assembly with 127 m spacing between neighboring cores (or in a standard PLC designed to match the spacing of the v-groove assembly), small errors can have a significant effect on the accuracy of mapping light from an input core to an associated output core, causing coupling inefficiencies. For example, small errors in the focal length of the collimating lenses can cause non-negligible coupling inefficiencies. This issue is addressed, in accordance with various embodiments, by the addition of high-precision collimator assemblies between the cores and the beam-splitting optic.

[0054] FIG. 3 is a conceptual drawing of a beam-splitting optic 300 and associated collimator assemblies 302, 304, 306, 308, 310 of an example free- space multi-channel interferometer, in accordance with various embodiments. The beam-splitting optic 300 and collimator assemblies 302, 304, 306, 308, 310 are bonded, or otherwise mounted, to a shared substrate 311 (e.g., made of fused silica), which is in FIG. 3 depicted in a top view. The beam-splitting optic 300 may be a prism assembly, such as the beam-splitting assembly 200 shown in FIG. 2. Example dimensions of such a prism assembly, in accordance with some embodiments, are in the range from a few millimeters to tens of millimeters. Alternatively, a component or set of components with suitable beam-splitting surface coatings, as described below with reference to FIGS. 17-20 may serve as the beam-splitting optic 300. For example, a transparent plate or set of transparent plates (e.g., of glass or other transparent material) with suitable coatings may serve as the beam-splitting optic 300 for the example system described above, with some adjustments in the placement and orientation of the collimator assemblies 302, 304, 306, 308, 310 (see FIG. 18). Such a plate mayIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 have lateral dimensions on the order of millimeters, and a thickness of a few hundred micrometers, for instance. In general, the structure and function of the collimator assemblies and the principles discussed in this section are independent of the particular choice of beam-splitting optic, and those of ordinary skill in the art given the benefit of the present disclosure will know how to integrate the collimator assemblies with beam-splitting optics of various types into free-space interferometers.

[0055] Further, in the depicted example, the interferometer includes five collimator assemblies 302, 304, 306, 308, 310, one for each of the set of probe input cores, the set of sensing cores, the set of reference input cores, and the two sets of output cores. The interferometer and these collimator assemblies can be employed, for example, in OFDR systems. However, the collimator assemblies are not limited to this particular interferometer configuration, but may also be used in smaller or greater numbers in other types of interferometers. For example, in applications that do not require polarization-diverse detection, an interferometer for interrogating a sensing fiber may utilize a beam-splitting optic without a polarizing-splitting surface in conjunction with only four sets of cores (including a single set of output cores). In any case, the depicted collimator assemblies are configured in pairs, where one collimator assembly provides the set of input cores and the other collimator assembly provides the set of output cores. The pairs of collimator assemblies are generally not disjoint (i.e., are “non-disjoint”), meaning that they may overlap in one of the collimator assemblies. For example, the collimator assembly 304 for the set of sensing cores is paired with each of the collimator assemblies 302, 308, 310 for the sets of probe input cores and the two sets of output cores. Overall, the depicted interferometer includes five pairs of collimator assemblies.

[0056] Each of the collimator assemblies 302, 304, 306, 308, 310 includes a waveguide array assembly and a pair of lenses 320 mounted to a collimator base 322. The collimator base 322 may be or comprise a rectangular plate with planar surfaces, e.g., with a thickness of several hundred micrometers and lateral dimensions of its top and bottom surfaces of a few millimeters. Each waveguide array assembly includes a linear waveguide array 323, corresponding to one of the sets of cores, implemented using, e.g., an optical PLC chip 324 with a linear array of waveguide cores at its output face, or alternatively a linear array ofIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 single-core fibers in a fused-silica v-groove assembly 326. As shown, different ones of the collimator assemblies may use different types of linear waveguide arrays 323; for instance, the probe and reference input cores may be provided by PLC chips 324, and the sensing cores and output cores may be implemented with v-groove assemblies 326. The waveguide array 323 may have a width of between a few hundred micrometers and a few millimeters, and the lenses 320 may have slightly larger diameters, e.g., of several millimeters.

[0057] For a given pair of collimator assemblies whose linear waveguide arrays serve as a set of input cores and a set of output cores, the associated pairs of lenses 320 are configured to image light from the input cores onto the output cores by achieving a magnification equal to the ratio of the core spacing between the output cores and the input cores. While the magnification can, in principle, take any value, various embodiments use the same spacing between cores (within specified error margins) for all sets of cores, with a corresponding magnification equal to one, which tends to provide for a simpler design and lower cost.

[0058] The magnification achieved by a pair of collimator assemblies is the ratio of the (effective) focal lengths of their respective collimating lens systems. Lenses may be manufactured to have focal lengths within a margin of error of about 1% of their nominal values. With such a manufacturing tolerance, if one lens is used to collimate the light from a set of input cores and another lens is used to focus the light into a set of output cores, there could be a magnification error of 2%. As the waveguide cores become farther apart, such errors in magnification begin to matter. For example, for seven cores in a linear array with 127 m spacing, the error in the imaged position of the outer cores could be as large as 7.6 m. With cores that are only 9 m in diameter, such an error will induce substantial loss (around 9 dB). This problem could be addressed, in principle, by requiring that the lens be manufactured with tighter tolerances (e.g., 0.1%) in the focal lengths of the individual lenses or by sorting the lenses into matching pairs (or, for the depicted interferometer, matching sets of five). Both approaches generally would increase the cost of the lenses and decrease yield.

[0059] As an alternative that can provide advantages such as lower cost, greater availability, and higher manufacturing yield, the collimator assemblies 302, 304, 306, 308, 310 used in accordance with various embodiments eachIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 include a two-lens optical system. In this optical system, two lenses 320 are aligned along a common optical axis 328, with the distance 330 (indicated for collimator assembly 308) between the lenses 320 set during manufacturing of the collimator assembly to achieve a specified target effective focal length of the compound lens system, within a specified margin of error. The distance 330 for a particular system is dependent on the focal lengths of the individual lenses 320.The effective focal lengthfeffof a system of two thin lenses spaced a distance sapart and having focal lenses f1and f2is given by the equation: 1 / feff= 1 / f1+1 / f2-s / (f1·f2).The mutual distance 330 between the lenses 320 may be set based on the individual focal lengths by explicitly calculating its value from measured values of the individual focal lengths in conjunction with the target effective focal length. Alternatively, the value of the mutual distance 330 may be set implicitly by adjusting the positions of the lenses 320 until the target effective focal length is achieved. Thus, the distance between the two lenses may be used as an adjustable parameter to compensate for deviations of the individual focal lengths from their nominal values. This adjustability enables controlling the effective focal length of the compound lens system within significantly tighter margins, e.g., 0.1% of the focal length (meaning that the actual effective focal length deviates from the target effective focal length by no more than 0.1%). The use of a pair of lenses 320 can provide the additional benefit of reducing aberrations present in the imaging of the outer cores, providing further reductions in coupling losses.

[0060] To construct the collimator assemblies 302, 304, 306, 308, 310, the pair of lenses 320 is bonded, once their relative spacing has been determined, to a surface 332 (indicated for collimator assembly 302) of the collimator base 322 hereinafter referred to as the “top surface” or “first surface.” The waveguide array assembly is configured and likewise bonded to the top surface 332 of the collimator base 322 in a manner such that the optical axis of its linear waveguide array 323 (defined as an axis in a direction of the emitted light through a center point of the linear array) coincides with the optical axis 328 of the lenses 320. The waveguide array assembly may, for example, include a pedestal 334 that is bonded to collimator base 322, and to which the PLC chip 324 or v-grooveIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 assembly 326 is, in turn, bonded. The PLC chip 324 or v-groove assembly 326 may be mounted on top of the pedestal 334, with the height of the pedestal 334 being selected or adjusted (e.g., by grinding down the initial pedestal block) such that the center of the linear waveguide array 323 is at the same height above the top surface 332 of the collimator base as the centers of the lenses 320. Alternatively, the PLC chip 324 or groove assembly 326 may be bonded to a side surface of the pedestal 334 at the desired vertical height. The pedestal 334 is bonded to the collimator base 322 at a position such that the center of the linear waveguide array 323 aligns with the optical axis 328 of the lenses 320. In other words, the waveguide array 323 and the two lenses 320 are aligned along a shared optical axis parallel to the surface of the collimator base 322 to which they are bonded.

[0061] In various embodiments, the collimator base 322 and pedestal 334, as well as the v-groove assembly 326 or PLC chip 324, are made of fused silica. The lenses 320 may likewise be made of fused silica. Beneficially, with all fused-silica optical components, temperature-dependent dimensional changes are kept to a minimum. However, fused-silica lenses can be expensive. In some embodiments, the lenses 320 are instead made by a glass molding process whose associated melting temperature is significantly below the melting point of fused silica. Such molded glass lenses can be much lower in cost and easier to manufacture. The resulting molded glass lenses increase in size by a small, but non-negligible amount when the temperature increases. These increases in size can cause a shift of the optical axis 328 (of the molded glass lenses) relative to the collimator base 322 and the linear waveguide array 323. This shift can result in a nonzero angle of light emitted by the waveguide array 323 relative to the top surface 332.

[0062] To accommodate such temperature-induced dimensional changes and help maintain alignment of the collimator assemblies 302, 304, 306, 308, 310 despite temperature variations, the collimator assemblies are, in accordance with various embodiments, mounted to the substrate 311 of the free-space interferometer on their side. This side-mounting is illustrated in FIG. 3. In FIG. 3, the surface of the collimator base 322 that is bonded to the substrate is not the bottom surface 336 (i.e., not the surface opposite of and parallel to the top surface 332). Instead, as depicted in FIG. 3, one of the side surfacesIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 perpendicular to the top surface 332 and bottom surface 336, and parallel to the optical axis 328 of the lenses 320, is bonded to the substrate. These side surfaces are hereinafter also referred to as the “left surface” and “right surface” (referencing left and right relative to a viewing direction from the waveguide array 323 towards the lenses 320) or the “second surfaces.” With the collimator assemblies thus flipped over onto their side (or, in other words, rotated by around 90° or exactly 90° about the viewing direction in the clockwise direction for bonding at the right surface or in the counterclockwise direction for bonding at the left surface), temperature-dependent dimensional changes of the lenses 320 have little or no effect on the height of their optical axis 328 above the substrate 311, or on the angle of the collimated light beam relative to the plane of the substrate 311. Instead, such dimensional changes of the lenses 320 can change the distance of their optical axis from the top surface 332 of the collimator base 322. This distance change from the top surface 332 can change the angle of the collimated light beam within a plane parallel to the substrate surface, and cause lateral misalignment between pairs of collimator assemblies corresponding to a pair of sets of input and output cores.

[0063] To compensate for such misalignments, each pair of collimator assemblies may be configured such that the effects of the displacements of their respective optical axes mutually cancel out. Such cancelation is achieved if the two collimator assemblies are rotated about their respective optical axes appropriately relative to the viewing direction defined from the waveguide array 323 to the lenses 320: in the same direction (e.g., both onto the left surface or both onto the right surface) if light is reflected an even number of times along the path from one collimator assembly to another, and in opposite directions (i.e., one onto the left surface and one onto the right surface) if the light is reflected an odd number of times along the path. In the example of FIG. 3, the collimator assemblies 304, 310 that provide the sensing cores and the output cores on opposite side of the beam-splitting optic 300 are both rotated onto their right surfaces, whereas the collimator assemblies 302, 306, 308 providing the probe and reference input cores and the second set of output cores are rotated onto their left surfaces. The pair of collimator assemblies 302, 304 providing the probe input cores and the sensing cores, for instance, are rotated in differentIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 directions, in accordance with light undergoing a single reflection on the path between them.

[0064] In the assembly of the collimator assemblies 302, 304, 306, 308, 310 and of the interferometer more generally, the planar bonding surfaces allow for thin adhesive bond-lines. Example adhesives include epoxy. Example planar bonding surfaces include that between the pedestal 334 or lenses 320 and the top surface 332 of the collimator base 322, or between the side surface of the collimator base 322 and the substrate 311. Thin bond-lines reduce the temperature dependence of the system induced by changes of the adhesive with temperature. Alternatively to bonding with adhesive, laser welding may be employed to join the various parts at their bonding surfaces (e.g., by welding glass to glass). Beneficially, laser welding can reduce or eliminate the use of adhesives (e.g., epoxies) and plastic materials, can increase the reliability, manufacturability, and yield in production of the optical devices, and can increase the allowable range of storage and operating temperatures of the optical part, which generally correlates with increased reliability during use.

[0065] In various embodiments, the interferometer is telecentric, meaning that the collimator assemblies are positioned such that the path length (that is, the distance along the optical path) from one collimator assembly to the other collimator assembly within each pair is equal to the sum of the effective focal lengths of the two collimator assemblies. This can reduce or minimize optical coupling losses. Although the collimator assemblies 302, 304, 306, 308, 310 can in principle be of different types and configurations, in various embodiments they are all of the same type and configuration. Where they are all of the same type and configuration, they have the same effective focal length, and the path lengths between the collimator assemblies of each pair are, accordingly, all equal. In FIG. 3, the telecentric configuration with equal path lengths between the five pairs of collimator assemblies is illustrated in the larger distances from the beam-splitting optic of the collimator assemblies 302, 306 associated with the probe input and reference input cores, as compared with the distances of the three collimator assemblies 304, 308, 310 associated with the sensing and output cores.

[0066] A free-space interferometer as described above, e.g., with prefabricated and verified high-precision collimator assemblies mounted on theirIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 sides in a telecentric configuration, can provide efficient optical coupling between the associated sets of cores. However, errors in positioning of the prefabricated collimator assemblies on the substrate during assembly of the interferometer, even if quite small (e.g., as small as 1 m,) can introduce significant coupling losses. Achieving the tight tolerances specified for efficient coupling can pose a challenge to developing high-yield manufacturing processes. This problem is addressed, in accordance with various embodiments, by adding for each collimator assembly a third, compensating lens 340 that can be positioned and oriented independently to correct for positioning errors of the collimator assembly. This third lens (compensating lens 340) is a weak lens, which as understood herein means that its focal length is significantly longer than (e.g., at least five times or at least ten times as long as) the effective focal length of the collimator assembly. Due to the longer focal length of the third lens (the compensating lens 340), fine adjustments to the location of the core images can be made with relatively coarse adjustments to the location of the third lens. For example, in some embodiments, the focal length of the weak compensating lens 340 is ten times the effective focal length of the compound lens system of the collimator assembly, which facilitates placing the core images with a precision of 1 m, using coarse 10 m movements of the weak compensating lens 340. The weak compensating lens 340 may be mounted on a pedestal 342, allowing its height above the substrate 311 to be adjusted via the height of the pedestal 342 (e.g., by grinding down the pedestal to the desired height). The pedestal 342 can also be moved within the plane of the substrate 311, as well as rotated about an axis perpendicular to the substrate 311 and / or tilted with respect to that axis by grinding down the top or bottom surface of the pedestal 342 at an angle. Using a pedestal 342, thus, provides three degrees of positional freedom and two degrees of angular (orientational) freedom for the placement of the weak compensating lens 340. While the compensating lens 340 cannot be rotated about its optical axis, such rotation would be without effect due to the rotational symmetry of the lens about the axis.

[0067] The compensating lens 340 can compensate for some error in the placement of the interferometer parts on the interferometer substrate 311. However, careful initial placement of the parts is still desirable. In particular, it is desirable to help ensure that the beam coming out of the collimator assemblyIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 is parallel to the surface of the interferometer substrate, e.g., in some embodiments, within an angular tolerance of about 0.0005 radians or 0.03 degrees, which cannot be achieved with standard machining processes. Generally, without additional optical components, the angle of the beam with respect to the plane of the substrate cannot be changed once the collimator assembly has been placed on the substrate. Thus, achieving parallelism between the collimated beam and the substrate prior to mounting the collimator assembly to the substrate is desirable. This parallelism is achieved, in some implementations, by ensuring that the beam exiting the collimator assembly is parallel to the surface of the collimator base 322 that is going to be bonded to the substrate. In some embodiments, the surface to be bonded is the bottom surface 336 or, in accordance with the side-mounted embodiment of FIG. 3, the surface to be bonded is the left-side surface or right-side side surface. Due to the intimate planar contact of that surface with the surface of the substrate upon bonding, parallelism between the collimated beam and the bonded surface is used as a proxy for ensuring that the collimated beam is also parallel to the surface of the substrate in various embodiments. Further, since parallelism between two surfaces of a component can be held to tight tolerances, the two side surfaces of the collimator base may be assumed to be parallel in such embodiments, such that aligning the beam in parallel with one of the side surfaces (e.g., the left one) also helps to ensure parallelism with the other side surface (e.g., the right one).

[0068] The following figures illustrate methods and fixtures for achieving beam alignment parallel to the bonded side surface, in accordance with various embodiments. An alignment fixture may include a calibrated camera focused at infinity, a long-period transmission grating, and a light source that produces a well-collimated alignment beam.

[0069] FIG. 4 is a conceptual drawing illustrating a simple camera focused at infinity, as may be used for beam alignment of a collimator assembly, in accordance with some embodiments. A camera focused at infinity has its image sensor 400 (e.g., a CCD or CMOS array) placed at the back focal plane of the imaging optic(s) 402, which is, in the depicted example, a single lens, although more complex imaging optics, such as compound lenses, may also be used alternatively. Such a camera converts the incident angle of light into a positionIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1f on the image sensor 400, where f is the focal length of the imaging optic 402,which is in this case equal to the distance between the imaging optic and the image sensor. Thus, collimated light (that is, parallel light, which propagates at a single angle relative to the optical axis 403) is focused to a single point on the image sensor 400 within the diffraction limit (e.g., point 404 for a beam parallel to the optical or point 406 for a beam at a non-zero angle relative to the optical axis 403). The camera used in the beam alignment fixture may be a standard, standalone camera configured to focus at infinity, or a custom camera constructed from separate components providing the image sensor and imaging optics.

[0070] FIG. 5 is a conceptual drawing illustrating a long-period transmission grating 500, as may be used for beam alignment of a collimator assembly, in accordance with some embodiments. The long period of the transmission grating 500 means that the diffraction angles are small, e.g., < 10°, and can be approximated by the sine of the diffraction angle expressed in radians. The transmission grating 500 is used, in the beam alignment fixture, to divide a single collimated alignment beam generated by a light source into three beams corresponding to the zeroth and first diffraction orders. Denoting the diffraction order as m, the wavelength of light as , and the period of the grating as p, the relationship between the incident angleiand the diffraction angled(both measured relative to an axis normal to the transmission grating) is given by the diffraction equation: m= p (sin i – sin d).The diffraction orders m = 0 and m = ±1 correspond to a central beamtransmitted without any angular deflection (that is, i = d) and diffracted first-order beams on both sides of the central beam. If the incident beam is normal tothe grating (i= 0), the first-order beams propagate at angles= sin-1(m / p) relative to the central beam.

[0071] For small angles, the sine of the angle can be replaced with the angle expressed in radians, resulting in the approximate relation: m= p ( i – d),Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 or after solving for the diffraction angle: d= i – m / p.The angles relative to the central beam are approximately:d–i–m / p. If the transmission grating is tipped by a small angle relative to itsnominal orientation, this angle is added to both the incident angle and the diffraction angles (decreasing the absolute value of the angle for the +1 order and increasing the absolute value of the angle for the -1 order by , and as a result, the difference remains the same (as does the direction of the central beam, which is transmitted through the grating without deflection). Accordingly, as illustrated in FIG. 5, the tip of the grating 500 with respect to the incident beam does not, to first order, affect the angles of the diffracted beams relative to the incident beam. Thus, if there is a small misalignment between the incident beam and the grating 500, the diffracted orders and the zero order will still propagate at the same angles as in the case of perfect alignment, providedthat the angles are small enough that sin within the desired angularresolution.

[0072] In accordance with various embodiments, the principles illustrated in FIGS. 4 and 5 are used during construction of a collimator assembly 302, 304, 306, 308, 310 to help ensure that the beam output by the center core of the waveguide array, when coming out of the collimator assembly, is parallel to the top and / or side surfaces of the collimator base 322. The collimated center-core output is hereinafter also referred to as the “collimator output beam.” For each surface to be aligned in these examples, the alignment process involves orienting the collimator base 322 such that the relevant surface is parallel to a collimated alignment beam, and then adjusting the position of the waveguide array assembly and lenses on the collimator base such that the collimator output beam is imaged onto the same spot as the alignment beam.

[0073] FIGS. 6A and 6B are conceptual diagrams illustrating a fixture and method for aligning a selected surface 600 parallel to an alignment beam, in accordance with some embodiments. The selected surface may be any of the surfaces of the collimator base 322, but the technique works, of course, for the alignment of surfaces of any other device as well. The fixture may be orientedIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 such that FIGS. 6A and 6B represent top views of the depicted components arranged on a horizontal fixture substrate parallel to the plane of the figure (labeled the x-z-plane). For illustration and ease of explanation, a Cartesian coordinate system is often used herein to describe directions or orientations. However, any appropriate coordinate system may be used with the described technology. In this orientation, the collimator base 322 contacts the fixture substrate with a surface perpendicular to the selected surface 600, and the selected surface 600 extends vertically from the fixture substrate (in a direction out of the plane of the figure, labeled as the y-direction). Alternatively, the fixture may be oriented such that FIGS. 6A and 6B represent side views with the y-z-plane corresponding to a horizontal plane. In general, the orientation of the fixture in space is not essential to its functioning.

[0074] The fixture uses an alignment collimator 602 to generate a well- collimated alignment beam 603 (as depicted, in the z-direction) from light supplied by a monochromatic light source (not shown), such as a laser, which may be part of the fixture, but may also be an external light source, for instance, the same light source as will be employed in the interferometer system. Further, the fixture includes a long-period transmission grating 500, as described in FIG. 5, to split the alignment beam 603 into a zeroth-order central beam 604 (also “central alignment beam” or “zeroth-order alignment beam”) and two (±) first- order diffracted beams 606, 608 (also “first-order beams”) diverging (asdepicted, in the x-direction) at angles ± relative to the central beam. Thecollimator base 322 is placed in the fixture at a position and orientation such that one of the first-order beams, 606, is reflected off the selected surface 600. The reflected first-order beam 607, along with the other first-order beam 608 and the central beam 604, are imaged by an imaging optic 402 onto an image sensor 400, which may both be oriented approximately parallel to the grating 500. The imaging optic 402 and image sensor 400 together are configured as a camera focused at infinity, as described with reference to FIG. 4. With the camera focused at infinity, parallel light is focused at a position on the image sensor 400 that depends on the angle of the light relative to the optical axes. Thus, the central beam 604 is focused at a different location (in the x-direction) as the first-order beams 606, 608.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1

[0075] Denote the angles at which the first-order beams 606 propagaterelative to the central beam 604 by – and + , respectively. If the reflectingselected surface 600 of the collimator base 322 is aligned in parallel with the central beam 604, as shown in FIG. 6A, the first-order beam 606 will be incident on the selected surface 600 at angle 90°– such that the reflected first-orderbeam 607 propagates at angle + relative to the central beam 604, and thuspropagates parallel to the other first-order beam 608. As a result, the two first- order beams 606a, 608 will be imaged onto the same location 610 on the sensor 400. By contrast, as shown in FIG. 6B, if the reflecting selected surface 600 is oriented at an angle relative to the central beam 604, the incidence angle of thefirst-order beam 606 is now 90°– ( , and the reflected first-order beam607b travels at angleto the central beam 604. Consequently, theimages of the two first-order beams 607b, 608 in FIG. 6B no longer coincide on the image sensor 400. By adjusting the orientation of the collimator base 322 until the reflected first-order beam 607 is parallel to the first-order beam 608 and imaged onto the same location 610 in the image plane, the selected surface 600 can be aligned parallel to the central beam 604. The location 612 of the imaged central beam 604 on the image sensor 400 is recorded for use in the next step.

[0076] The alignment of the selected surface 600 parallel to the central beam 604 determines the central beam location 612 on the image sensor 400 in one dimension, namely in the direction along which the diffraction orders generated by the grating 500 fan out. This fan out direction is shown as the x-direction in FIG. 6A. In accordance with some embodiments, to facilitate aligning the collimator output beam in parallel with both the top / bottom surfaces and the side surfaces of the collimator base 322, the selected surface alignment to the central alignment beam is performed along two dimensions. For this purpose, two orientations of the grating 500, or two separate gratings that are differently oriented (optionally each with its own associated alignment beam) are used to determine the respective central beam locations in both dimensions of the plane of the image sensor 400, that is, in both the x-direction and the y-direction (where a Cartesian coordinate system is used).

[0077] For illustration, assume that FIG. 6A is a side view, with x extending in the vertical direction, that depicts the alignment of the top surface 332 of the collimator base 322 parallel to the zeroth order of a first alignment beam 603,Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 using a reflection of a first order off the top surface 332. This alignment can be achieved by adjusting, if needed, the orientation of the collimator base 322 or of the incoming alignment beam 603 in the x-z-plane (about the y-axis). Assume further, without loss of generality, that following this alignment step, the top surface 332 and central beam 604 are parallel to the y-z-plane, and the corresponding x-coordinate of the central beam on the image sensor 400 has been determined. A second alignment beam split into zeroth and first orders along the y-direction with a 90° rotated grating can then be employed to align a side surface of the collimator base 322 with the zeroth order of the second alignment beam. This second alignment beam with the rotated grating facilitates adjusting the orientation of the collimator base 322 within the y-z-plane about the x-axis. Rotating the collimator base within the y-z plane does not affect the previous alignment of the top surface relative to the zeroth order of the first alignment beam. The 90° rotated grating used with the second alignment beam may be a separate second grating, or may be the same grating 500, rotated by 90°.

[0078] FIG. 7A and 7B are conceptual side and top view, respectively, illustrating the alignment of the side surfaces of the collimator base 322 parallel to an alignment beam 700 within the fixture of FIGS. 6A and 6B, in accordance with some embodiments. Since the grating 702 is oriented to divide the alignment beam 700 along the-y direction, all diffraction orders coincide in the side view of FIG. 7A, and are imaged onto the same x-coordinate on the image sensor 400 (corresponding to the location 612 if the alignment beam 700 is parallel to the top surface 332). In the top view of FIG. 7B, the individual diffraction orders can be seen. The collimator base 322 is oriented within the plane of FIG. 7B (i.e., the y-z-plane) until the two first order beams, one of which is reflected off one of the polished side surfaces 704 of the collimator base 322, coincide with each other on the image sensor 400. This coincidence of the two first order beams signifies that the central alignment beam 706 is parallel to the side surfaces 704. The central beam location 708 on the image sensor 400 in the y-direction is recorded for subsequent use.

[0079] FIG. 8 is a conceptual drawing illustrating the alignment of the collimator assembly within the fixture of FIGS. 6A-7B such that the collimator output beam 800 is parallel to both the top surface 332 and side surface 704 ofIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 the collimator base 322, in accordance with some embodiments. The collimator base 322 and fixture are, once again, shown in a side view, and the coordinate axes are labeled consistently with FIGS. 6A-7B. In this assembly step, the collimator base 322 remains fixed at the orientation that renders, simultaneously, the top surface 332 (in FIG. 6A) and the side surfaces 704 (in FIG. 7B) parallel to the zeroth order of the respective alignment beam 603, 700 in the preceding alignment step. The collimator assembly is constructed such that the collimator output beam 800 (originating from the center core of the waveguide array 323) is imaged onto a location 802 on the image sensor 400. The coordinates of location 802 in the x- and y-direction correspond to the recorded locations 612, 708 of the respective central alignment beams 604, 706. The collimator assembly is constructed to achieve this effect by positioning and orientation of the waveguide array assembly and lenses.

[0080] In particular, to align the collimator output beam 800 parallel to the top surface 332 of the collimator base 322, the following is done: The center of the waveguide array 323 (e.g., of PLC chip 324 or v-groove assembly 326) and the centers of the lenses 320 are set to the same height above the top surface 332 while limiting or avoiding any tilt of the optical axes of the waveguide array 323 and lenses 320 relative to the top surface 332, that is, while keeping the optical axes parallel to the top surface 332. (Note that the term “height,” in this context, indicates the distance from the top surface 332, as measured in the x-direction, regardless of the orientation of the collimator base 322 and fixture in space.) In various embodiments, the height of the lenses 320 above the top surface 332 is fixed, and relative height adjustments between the lenses 320 and waveguide array 323 are made by setting the height of the waveguide array 323. The height of the waveguide array 323 can be set, e.g., by adjusting the pedestal 334 until it has the desired height, by mounting the PLC chip 324 or v-groove assembly 326 at the appropriate height to a side surface of the pedestal 334, etc. When the collimator output beam 800 is parallel to the top surface 332, its image on the image sensor 400 is at the recorded location 612 of the central alignment beam 604 in the x-direction.

[0081] Further, to align the collimator output beam 800 parallel to the side surface 704 of the collimator base 322, the following is done: The relative locations of the waveguide array 323 and lenses 320 in a direction perpendicularIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 to the side surface 704 (i.e., in the y-direction) and their orientations about the vertical axis (i.e., the x-axis) are adjusted until the image of the collimator output beam 800 on the image sensor 400 coincides with the recorded location 708. The recorded location 708 is of the central alignment beam 706 in the y- direction. This alignment, taken together with the alignment in height above the top surface 332 and reduction (or elimination) of tilt relative to the top surface 332, helps to ensure that the waveguide array 323 and lenses 320 are aligned along a shared optical axis parallel to the top surface 332 and side surface 704.

[0082] As described, the relative orientations and lateral positions of the waveguide array 323 and lenses 320 can be adjusted to help ensure a zero angle of the collimator output beam 800 with respect to the surfaces of the collimator base 322. (“Lateral” is used here for motion in a plane perpendicular to the optical axis.) In addition, the distance of the waveguide array 323 from the lenses 320 along the shared optical axis (that is, in the z-direction) may be adjusted to render the collimator output beam 800 well collimated. The degree of collimation may, e.g., be measured by a shear plate or be based on the spot size of the beam 800 on the image sensor 400. Since the imaging optic 402, for a camera focused at infinity, maps parallel light onto the same location on the image sensor 400, collimation can be improved by reducing the spot size, and optimized by minimizing the spot size. For example, collimation sufficient to meet a defined specification may be achieved by ensuring that the spot size is no bigger than a defined size corresponding to the specification. Collimation of light from any of the waveguide cores is achieved when the waveguide array 323 is placed at the focal plane of the system of lenses 320.

[0083] Note that, in various embodiments where the collimator assemblies are to be used in a free-space interferometer system that incorporates weak compensating lenses 340, as shown in FIG. 3, the alignment fixture includes a placeholder compensating lens 804, as shown in FIG. 8. This placeholder compensating lens is of known optical characteristics, and may be configured to match the weak compensating lens 340 in all material respects (including, for example, focal length). In this manner, the effect that the weak compensating lenses 804 will have on the light beams in the assembled interferometer system is largely taken into account during collimator assembly.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1

[0084] As described, the alignment fixture facilitates the alignment of the collimator output beam 800 parallel to the surfaces of the collimator base 322, and the adjustment of the distance between the waveguide array 323 and the lens system to create a well-collimated output. In addition, the alignment fixture may also serve to set the spacing between the two lenses 320 of the collimator to achieve the desired effective focal length. With the collimator output beam 800 of light generated by the center core defining an optical axis of the collimator assembly, the light that is output by any non-center core leaves the collimator assembly at an angle relative to the optical axis whose tangent is equal to the ratio of core’s distance from the center core and the effective focal length of the system of lenses 320. For example, denoting the width of the waveguide array 323 as x and the effective focal length as feff, the angle between the collimated beams of one of the outermost cores and the center core is given by:tan x / (2feff). Accordingly, the effective focal length of the lenses 320 of thecollimator assembly can be determined from a measurement of the angle between beams from different cores. The alignment fixture enables such angle measurements: with knowledge of the wavelength of the light and of the period of the diffraction grating, the scale of the camera focused at infinity for a given angular separation between the beams (e.g., the zeroth-order and first-order beams) can be calibrated. The scale of the camera focused at infinity is observable as the distance between beam spots on the image sensor (e.g., as measured in terms of the number of pixels). If the period of the diffraction grating is, for instance, known to within 1 part in 10,000, then the angle associated with the first diffraction order can be determined to within about 0.01 degrees. Once the angle per pixel (or unit distance on the image sensor) is known, the angle between the beams from two cores can be computed from their distance on the image sensor 400.

[0085] FIG. 9 is a conceptual drawing illustrating calibration of the effective focal length of the collimator assembly using the fixture of FIGS. 6A-8, in accordance with various embodiments. In this example, beams 900, 902 originating from the center core and one of the outermost cores, respectively, are focused with the imaging optic 402 onto the image sensor 400 at locations 904, 906. Based on a preceding calibration of the scale of the camera, the distance 908 between these image locations 904, 906 on the sensor 400 can beIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 straightforwardly converted to an angular separation between the two beams 900, 902. Assuming the spacing between cores in the waveguide array 323 is known with high accuracy, the angular distance between the beams 900, 902 that is associated with a given effective focal length of the lens pair of the collimator assembly is also known with high accuracy. Then, the effective focal length can be accurately set by adjusting the distance 910 between the lenses 320 to achieve the associated corresponding angular separation between the beams 900, 902. Note that the calibration of the effective focal length of the collimator assembly in accordance with various embodiments, is performed with a placeholder compensating lens 804 in the fixture. The placeholder compensation lens 804 is positioned between the waveguide array 323 and the collimator lenses 320. The use of this placeholder compensation lens 804 is analogous to the use with the alignment of the collimator output beam parallel to the collimator base surface. Including this placeholder compensating lens 804 is useful since the placeholder compensation lens 804 does affect the overall focal length of the three-lens system formed by the compensating lens 804 and collimator lenses 320 together.

[0086] In various embodiments, the collimator assemblies 302, 304, 306, 308, 310 use waveguide arrays 323 designed to all share the same spacing between cores. Accordingly, to couple light between an input set of cores and an output set of cores, the associated lenses are configured to image the input cores onto the output cores with a magnification of -1. However, while core spacings can generally be held to tight tolerances, the tolerances are not infinitely tight. In practice, slight differences between the core spacings of different waveguide arrays may occur. To improve optical coupling between sets of input and output cores that exhibit a small difference in core spacings, the effective focal lengths of the associated lens pairs may be adjusted to achieve a magnification that is slightly different from -1.

[0087] FIG. 10A is a conceptual drawing of a pair of v-groove fiber arrays 1000, 1002 with slightly different core spacings as may be used in a pair of respective collimator assemblies, in accordance with some embodiments. FIG. 10B is a conceptual drawing illustrating how the configuration of a collimator assembly can be adjusted to accommodate the different core spacings, in accordance with some embodiments. The width of the fiber arrays is an integer multiple of the core spacing (seven times the core spacing in the depicted eight-Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 core example). As can be seen in FIG. 10A, the width of the fiber arrays differs between the nominal width X in v-groove fiber array 1000 (resulting from a nominal core spacing) and a slightly larger width X + d in v-groove fiber array 1002 (resulting from a slightly larger core spacing). The cores can be properly mapped from one array to the other array, despite that difference in core spacings, by setting the spacing between the two lenses of the collimator assembly appropriately. In this case, this spacing is not set to achieve a fixed effective focal length shared among all collimator assemblies, and instead is set to achieve a particular angular spacing between the collimated beams exiting thearray of cores (e.g., as indicated in FIG. 10B, an angular spacing 2 between thetwo outer-core beams). Denoting the target effective focal length for a waveguide array of width X (that is, an array having core spacings equal to thenominal value) asf0, the effective focal lengthfdthat achieves the same angularbeam spacing for a waveguide array of width X + d is given by: fd = f0 (1 + d / X).The effective focal length of the two-lens system depends on the individual focal lengths and the distance between the lenses. Thus, that distance between thelenses (labeledsdin FIG. 10B), like the effective focal lengthfdachieving thespecified angular beam spacing, depends on the deviation d of the width of the array from the nominal width. In practice, the distance between the lenses 320 can be adjusted until the desired angular separation between the beams from different cores of the waveguide array 323 (e.g., the pair of outmost cores) is achieved. This can be measured using the distance between the beam images on the image sensor 400 of the calibrated camera. Implicitly, setting the angular separation in this manner also sets the associated effective focal length of the two-lens system of the collimator assembly.

[0088] FIG. 11 is a flowchart summarizing a method 1100 of constructing and aligning a collimator assembly using the fixture of FIGS. 6A-9, in accordance with various embodiments. The method 1100 may involve calibrating (at 1102), in preparation for later configuration of the effective focal length of the collimator lenses 320, the scale of the camera focused to infinity in terms of a change in the angle of incidence of a light beam incident upon the imaging optic per change in position of the beam image on the image sensorIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 (e.g., measured in degrees per pixel). As explained with reference to FIG. 9, this calibration may be based on a measurement of the distance on the image sensor between two beams and knowledge of the angle included between the two beams. For example, the two beams may correspond to two diffraction orders created by a transmission grating of the fixture, and the knowledge of the included angle can be derived from knowledge of the wavelength of the light and the grating period of the grating. The calibration can be performed separately for two dimensions of the image sensor (e.g., rows and columns of the pixelated sensors array). For a square pixel array, and assuming the imaging optic is radially symmetric, a single calibration can suffice.

[0089] To construct the collimator assembly, the collimator base is first positioned and oriented within the alignment fixture such that one or more of its surfaces are aligned parallel to respective zeroth-order alignment beams (at 1104). The surface alignment parallel to a zeroth-order alignment beam can be determined, as explained with reference to FIGS. 6A-7B, based on the coincidence of the associated pair of first diffraction orders on the image sensor. In various instances, the alignment process is performed at least for the surface of the collimator base that will be bonded to the interferometer substrate. (As described earlier, the surface to be bonded may be the bottom surface of the collimator base or one of the side surfaces, depending on the particular embodiment.) It is assumed that the top and bottom surfaces are parallel to each other to a high degree of precision, and that the pair of side surfaces are likewise parallel to each other to a high degree of precision. With these assumptions, alignment of the top surface implies alignment of the bottom surface parallel to the zeroth-order alignment beam, and alignment of one side surface implies alignment of the other side surface parallel to the zeroth-order alignment beam. In some embodiments, both the top / bottom and the side surfaces of the collimator base are aligned, using separate alignment beams diffracted along different dimensions. The different dimensions can comprise mutually perpendicular dimensions. For example, the collimator base may be placed bottom-side down onto the substrate of the alignment fixture. In this bottom- side-down placement, the top surface may be aligned with a first alignment beam diffracted into multiple orders within a vertical plane, while a side surface is aligned with a second alignment beam diffracted within a horizontal plane.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 Once the collimator base is oriented with its surface(s) parallel to the zeroth- order alignment beam(s), the corresponding location(s) of the beam(s) on the image sensor are recorded (at 1106) for subsequent use. Without further moving the collimator base inside the fixture, the optical components of the collimator assembly, including the waveguide array assembly and pair of lenses, are then arranged on, and ultimately affixed to, the collimator base. For purposes of these alignment and assembly steps, light beam originating from one or more cores of the waveguide array are focused onto the image sensor of the camera.

[0090] In some embodiments, positioning the optical components on the collimator base involves the following: First, the distance between the two collimator lenses is set to achieve the desired effective focal length, which may be accomplished by achieving the desired angular separation between beams from different cores of the waveguide array (at 1108). This focal-length adjustment can be achieved, as explained with reference to FIG. 9, using the distance between the locations on the image sensor onto which the beams from at least two different cores (e.g., the two outer cores, or the central core and one outer core) are focused, along with the calibrated scale of the camera. When the effective focal length has been properly set, the lenses may be affixed, e.g., by welding or bonding with an adhesive, to the top surface of the collimator base (at 1110).

[0091] Next, the waveguide array assembly is positioned and oriented on the collimator base. The height of the waveguide array above the top surface of the collimator base may first be set (at 1112) to focus the collimator output beam on the recorded location (in the vertical direction) of the first zeroth-order alignment beam. This helps ensure that the collimator output beam is parallel to the top surface of the collimator base. The output beam can be the beam originating from the central core of the waveguide array. To adjust the height of the waveguide array above the top surface of the collimator base, the height of the pedestal or the height along a side surface of the pedestal to which the PLC chip or v-groove assembly is bound can be adjusted, for example. Simultaneously with, or separately from, the height of the waveguide array, the tilt of the waveguide array relative to top surface in both dimensions may also be adjusted. For this purpose, the beams from two cores may be used to help ensure that all beams propagate at the same height above the top surface. OnceIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 the focused collimator output beam is parallel to the top surface of the collimator base, the waveguide array is affixed to the pedestal (at 1114). As examples, the waveguide array may be implemented in a PLC, v-groove assembly, etc., and the affixing may be done by techniques such as welding, gluing, etc. The position of the waveguide array assembly may then be adjusted within a plane parallel to the top surface, both in a direction towards or away from the collimator lenses and laterally to the collimator lenses. This is to align the collimator output beam parallel to side surfaces of the collimator base and to help optimize its collimation (at 1116). Alignment parallel to the side surface is achieved when the lateral position of the waveguide array relative to the lenses, along with the orientation of the waveguide array about a vertical axis, are such that the collimator output beam coincides on the image sensor horizontally with the recorded location of the second zeroth-order alignment beam. The beam is collimated when the distance of the waveguide array from the lenses minimizes its focal spot size on the image sensor. As noted earlier, depending on the implementation, sufficient collimation may occur when the focal spot size is not at its minimum, but is sufficiently small (e.g., smaller than a defined size). With the position and orientation of the waveguide array thus determined in all dimensions, the pedestal of the waveguide array assembly is affixed (e.g., welded or glued) to the collimator base (at 1118).

[0092] In various embodiments, the positioning and orientation of the collimator base in the fixture and of the various optical components relative to the collimator base is accomplished using a suitable robotic assembly system with fine motor control to hold and manipulate (e.g., move translationally or rotate) the base and components. Such systems are already available and in commercial use in the manufacture of optical and other systems; an example robotic system is Mecademic Model: MC500-1412. To implement the described alignment procedure, the robotic assembly system may be integrated with the fixture disclosed herein to use the images produced by the camera as feedback during the assembly process. In some embodiments, automated measurements (e.g., using software-based image processing) of degrees of misalignment, e.g., as reflected in displacements of the collimator output beam from recorded locations of the zeroth-order alignment beam or in the beam spot size, are directly provided as input to control software operating the robotic assemblyIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 system and commanding its movements. The control software may be stored on a non-transitory computer-readable medium and executed by a computer processor of suitable processing system. In other embodiments, a human system operator may view the images and use them to guide the robotic assembly system.

[0093] Once the collimator assemblies 302, 304, 306, 308, 310 have been built and aligned with their collimator output beams parallel to the surface(s) of the collimator base, the collimator assemblies can be placed on the interferometer substrate along with the beam-splitting optic 300. Due to imperfections (e.g., in surface orientations) of this beam-splitting optic 300, the propagating beam may be deflected off the plane parallel to the surface of the interferometer substrate. A compensating lens 340 may be used to redirect the beam so that it exits the beam-splitting optic parallel to the substrate surface.

[0094] FIGS. 12A-12C are conceptual drawings illustrating the use of a compensating lens 340 to correct for misalignments of the collimator output beam 800 introduced by the beam-splitting optic 300, in accordance with various embodiments. For ease of illustration, the collimator assemblies are depicted as bonded bottom-side down onto the interferometer substrate 1200. However, the principles now discussed apply equally to side-mounted collimator assemblies. As shown in FIG. 12A, a collimator output beam 800, as a result of its alignment in parallel to the collimator base surface bonded to the substrate, propagates parallel to the substrate 1200 before entering the beam-splitting optic 300. The collimator output beam 800 may be refracted at one or both of the surfaces through which it enters and exits the beam-splitting optic 300. This results in a direction of propagation at an angle relative to the plane of the substrate 1200 upon exit from the beam-splitting optic 300. Using the same fixture as employed to align the individual collimator assemblies, this angle can be quantified by focusing the beam 800 onto the image sensor 400 of the camera focused at infinity and measuring its distance, on the image sensor 400, from a recorded location 1202 of a beam parallel to the substrate surface. For purposes of determining that location 1202, an alignment beam may be aligned parallel to the surface of the substrate 1200 using a diffraction grating 500 to create zeroth- order and first-order beams, reflecting one of the first-order beams off theIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 substrate 1200, and adjusting the beam orientation relative to the substate to achieve coincidence between the two first-order beams on the image sensor, in the same manner as described with reference to FIG. 6A.

[0095] FIG. 12B shows the addition of a compensating lens 340, e.g., placed between the waveguide array 323 and the pair of collimator lenses 320, to correct for the beam deflection at the surface(s) of the beam-splitting optic 300. The position of the compensating lens 340 relative to the optical axis defined by the pair of lenses 320 is adjusted to redirect the collimator output beam 800 prior to its entry into the beam-splitting optic 300. Specifically, the beam 800 is redirected prior to entry into the beam-splitting optic 300 such that it is, upon exit from the beam-splitting optic 300, parallel to the surface of the substrate and, accordingly, focused onto the recorded location 1202 on the image sensor 400. Redirecting the beam 800 with the compensating lens 340 will change the position of the beam 800 in the optical system, resulting in imperfect overlap between the beam from a given core of the input set of cores and the corresponding core of the output set of cores onto which it is mapped. However, if the angular adjustments are small and the beam diameters are large, the offset in position remains small over reasonable distances between an input set of cores and an output set of cores. For example, in some embodiments, the angular adjustments are less than 0.2° and the beam propagates over a distance of about 20 mm, resulting in an offset in position of less than 70 m; and the beam diameter is about 3 mm. Since a maximum 70 m offset is small compared with the beam diameter, the optical loss due to the imperfect overlap is negligible in many applications.

[0096] FIG. 12C shows the interferometer with a pair of collimator assemblies configured on the substrate 1200. A first collimator assembly 1204 includes the input set of cores that generate the beams input into the beam- splitting optic 300, and a second collimator assembly 1206 includes the output set of cores that receive the beams output from the beam-splitting optic 300. When the second collimator assembly 1206 is placed, only small adjustments are needed to correct for imperfections in the placement of the second collimator assembly 1206.

[0097] Aligning the collimator assemblies on the substrate 1200 can be a time-consuming and difficult process. One way of aligning a pair of collimatorIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 assemblies relative to each other and the beam-splitting optic is to inject light into at least one input core of one collimator assembly of the pair, and then adjusting the configuration until light is detected on a corresponding output core of the other collimator assembly. Using this process, no signal is detected until the images of the two cores overlap, which is the case only over a very small range. Further, while misalignment will result in failure to detect any light at the output, other problems, such as a broken input fiber, can cause the same lack of detected light.

[0098] FIGS. 13A and 13B are conceptual drawings illustrating the misalignment and alignment, respectively, between a pair of waveguide cores 1300, 1302 that are imaged onto each other by associated collimator lenses 1304, 1306. The waveguide cores 1300, 1302 may constitute an input-output pair of cores of the waveguide arrays 323 of a pair of collimator assemblies, and the collimator lenses 1304, 1306 may each represent a system of lenses including a pair of lenses 320 and, optionally, a weak compensating lens 340. As can be seen in FIG. 13A, when the beam of light emitted by a core 1300 (or 1302) deviates in its direction slightly from its direction in the aligned state, its image will be displaced relative to the other core 1302 (or 1300). This can hinder or prevent the beam of light from being coupled into the other core 1302 (or 1300).

[0099] As can be seen from FIGS. 13A and 13B, collimator assemblies may be aligned in pairs by injecting light into an input core at one collimator assembly and detecting it at an output core of the other collimator assembly. However, in various alternative embodiments, aligning the collimator assemblies in pairs instead involves injecting light into both of the cores that are to be optically coupled, and imaging the two cores onto a shared camera focused at infinity. For the purpose of directing the light beams from both cores onto the same camera for detection, a partially reflective beam-splitting surface is positioned between the collimator assemblies in the path where their beams overlap. Further, a retroreflector, e.g., implemented by a 90-degree corner cube, is placed to intercept one of the beams and reflect it back along the same path in the opposite direction. A retroflector reverses the direction of an impinging beam, regardless of the retroreflector’s orientation relative to the beam (as long as the beam hits the reflective surface). This reduces or obviates the need for precise alignment of the retroreflector relative to the beam. When the twoIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 collimators are aligned, the two beams are imaged onto the same spot on the camera. In case of any misalignment, within limits such that both beams are still detected on the camera, the distance between the beam spots provides a quantitative measurement of the correction to be applied to bring the beams into alignment.

[0100] FIGS. 14A and 14B are conceptual drawings illustrating the misalignment and alignment, respectively, between a pair of waveguide cores 1300, 1302 on opposite sides of a beam-splitting surface 1400. In this example, a corner cube retroreflector 1402 and a camera 1404 focused at infinity are used to aid in the alignment process, in accordance with various embodiments. In the depicted configuration, light from the first core 1300 is in part reflected at the beam-splitting surface 1400 towards the corner cube retroreflector 1402. On its return trip from the retroreflector 1402, this light passes through the beam- splitting surface 1400 to be detected on the image sensor of the camera 1404. Light from the second core 1302, which is placed on the opposite side of the beam-splitting surface 1400 as the first core 1300, is in part reflected by the beam-splitting surface 1400 directly onto the camera 1404. In FIG. 14A, the two beams from cores 1300, 1302 are focused onto slightly different locations on the image sensor, resulting from slightly different angles of incidence on the beam- splitting surface 1400. As shown, this misalignment on the camera sensor also means that light from one core that is transmitted through the beam-splitting surface is not accurately imaged onto the other core. By contrast, in FIG. 14B, the two beams from the cores 1300, 1302 are aligned along the path through the beam-splitting surface 1400 such that the light from one of the cores is focused onto and coupled into the other one of the cores. This alignment is reflected in the collocation of the two imaged beams on the camera 1404.

[0101] In FIGS. 14A and 14B, the beam-splitting surface 1400 is provided by a stand-alone cube beam splitter (e.g., a 50 / 50 beam splitter). In practice, the beam-splitting surface is usually part of the interferometer system (or, more generally, optical network) under construction, obviating the need for an additional beam-splitting surface. Instead, the camera and retroreflector may simply be strategically positioned to facilitate alignment in the manner described. Further, in FIGS. 14A and 14B, the two cores to be optically coupled are positioned on opposite sides of the beam-splitting surface. However, otherIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 arrangements are also possible, including arrangements in which the two cores are oriented to direct light at the beam-splitting surface along two mutually perpendicular directions, such that light from one core is reflected at the beam- splitting surface towards the other core. In this case, the camera will be opposite to one of the cores, and the retroreflector will be opposite to the other core.

[0102] FIG. 15 is a conceptual drawing illustrating the alignment of a pair of collimator assemblies 1500, 1502 relative to each other and to a beam-splitting optic 1504. A corner cube retroreflector 1402 and camera 1404 focused at infinity are used, in accordance with various embodiments. The depicted beam- splitting optic 1504 is a transparent plate (e.g., a glass plate) with a beam- splitting surface coating in a region where the mutually perpendicular beams from the two collimator assemblies 1500, 1502 are incident, as described further below with reference to FIGS. 17-18. To align the collimator assemblies 1500, 1502, the following is done: Light from one collimator assembly 1500 is transmitted through this beam-splitting surface and the transparent plate and detected by the camera 1404, while light from the other collimator assembly 1502 is transmitted through the beam-splitting surface and the transparent plate, reflected back from the retroreflector 1402, transmitted back through the transparent plate, reflected at the beam-splitting surface, transmitted once more through the transparent plate, and finally detected at the camera 1404.

[0103] For an interferometer system including three or more collimator assemblies to be aligned in pairs, the method illustrated in FIGS. 14A-15 can be repeated for each pair, and retroreflector 1402 and / or the camera 1404 are repositioned as needed for each alignment. Due to spatial constraints imposed by the collimator assemblies themselves, the alignment process may involve building and aligning the system gradually, e.g., as a part of such alignment process, adding one collimator assembly at a time in an order that facilitates sequentially aligning the various pairs of collimator assemblies.

[0104] FIGS. 16A-16G are conceptual drawings illustrating the step-wise alignment of the five collimator assemblies 302, 304, 306, 308, 310 of the interferometer system of FIG. 3, in accordance with one embodiment. The process begins, as depicted in FIG. 16A, with the positioning of the camera 1404 on an axis perpendicular to the optical axis of the collimator assembly that will be used for the detection of p-polarized light, herein also “p-output collimatorIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 assembly” 310. For this step, light is injected into the waveguide array of the collimator assembly, and the collimator output beam is redirected by ninety degrees with the aid of a penta prism (that is, a ninety-degree reflector) 1600. Once the camera 1404 has been positioned to detect the redirected beam, the penta prism 1600 is removed, and the beam-splitting optic 300 is put in the path of the collimator output beam 1610. In this example, the beam-splitting optic 300is composed of three cube beam splitters providing three parallel beam- splitting surfaces 1602, 1604, 1606. The beam-splitting optic 300 is positioned and oriented, as shown in FIG. 16B, such that the collimator output beam 1610 is incident upon the second (center) beam-splitting surface 1604 at a 45° angle and reflected off the surface 1604 in a direction away from the camera 1404. The corner cube retroreflector 1402 is then placed in the reflected beam to reflect the beam back through the beam-splitting surface 1604 and onto the camera 1404.

[0105] With retroreflector 1402 and camera 1404 thus in place, the collimator assembly that includes the sensing cores (which are those cores that will be coupled to the sensing fiber), herein “sensor collimator assembly” 304, can then be placed into the system. The sensor collimator assembly 304 is placed on the opposite side of the beam-splitting optic 300 as the p-output collimator assembly 310, as shown in FIG. 16C. The two collimator assemblies 310, 304 can be aligned by injecting light into both of them and ensuring that the two collimator output beams 1610, 1612 are imaged onto the same spot on the image sensor of the camera 1404. As shown in FIG. 16C, the first and second collimator output beams 1610, 1612 are initially counterpropagating and are then redirected onto the camera 1404, with one of them via the retroreflector 1402. In this alignment step, fine adjustments of the beam propagation directions can be achieved with the help of the weak compensating lenses 340 added to the collimator assemblies 310, 304.

[0106] After the position and orientation of the sensor collimator assembly 304 and of the compensating lenses 340 of both collimator assemblies 310, 304 have been fixed, a third collimator assembly is added. For example, the collimator assembly to be used for the detection of s-polarized light, herein “s- output collimator assembly” 308, is added to the system adjacent to the third beam-splitting surface 1606, and oriented perpendicularly to the p-outputIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 collimator assembly 310, as shown in FIG. 16D. Without moving the retroreflector 1402 and camera 1404, the pair of collimator assemblies including the newly added s-output collimator assembly 308 and the sensor collimator assembly 304 are aligned relative to each other using the following technique: Light is injected into both the s-output collimator assembly 308 and the sensor collimator assembly 304 and the collimator output beam 1614 of the s-output collimator assembly 308 is brought into overlap with the beam 1612 from the sensor collimator assembly 304 by adjusting the position and orientation of the detector collimator assembly 308 and its associated weak compensating lens 340, as needed. As shown in FIG. 16D, the collimator output beam 1614 is reflected at both the third beam-splitting surface 1606 and the second beam- splitting surface 1604, before being directed back towards the camera 1404 by the retroreflector 1402.

[0107] Next, the collimator assembly that will provide the probe input light, herein “probe input collimator assembly” 302, is placed adjacent to the first beam-splitting surface 1602 and oriented perpendicularly to the sensor collimator assembly 304, as shown in FIG. 16E. The probe input collimator assembly 302 and its associated weak compensating lens 340 are adjusted in position and orientation to align the corresponding collimator output beam 1616 with the collimator output beam 1612 of the sensor collimator assembly 304. For this purpose, the retroreflector 1402 is repositioned to reflect light from the probe input collimator assembly 302 that is transmitted through the first beam- splitting surface1602; the returning light is reflected by the first and second beam-splitting surfaces 1602, 1604 to be ultimately directed at the camera 1404.

[0108] Lastly, the collimator assembly that will provide the reference input light, herein “reference input collimator assembly” 306, is placed into the system and aligned with the p-output collimator assembly 310 (which implies alignment with the s-output collimator assembly 308 as well) by causing the corresponding collimator output beams 1618, 1620 to coincide on the camera, as shown in FIG. 16F. For this purpose, the retroreflector 1402 remains in the same position as in the preceding step, but now serves to reflect the beam 1620 from the p-output collimator assembly 310. The return beam is twice reflected, at the first and second beam-splitting surfaces 1602, 1604, before being detected at the camera 1404. The beam from the reference input collimator assembly 306 is directedIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 through the second beam-splitting surface 1604 directly at the camera. Following this alignment of all five collimator assemblies 302, 304, 306, 308, 310, the retroreflector 1402 is removed. As shown in FIG. 16G, a polarization modulator may be incorporated into the reference path preceding the reference input collimator assembly 306 to facilitate balancing the power of the reference light between the s and p detectors associated with the s- and p-output collimator assemblies 308, 310, regardless of the input state of polarization. Beam-splitting optics

[0109] The beam-splitting assemblies depicted in FIGS. 3 and 16B-16G are constructed from three cube beam splitters each formed of a pair of right-angle triangular prisms. These right-angle triangular prisms may be made of glass, and may be joined at their hypotenuse lateral faces to form an interior diagonal surface that provides the beam-splitting function. To achieve polarization- independent and polarization-dependent beam-splitting surfaces, different optical coatings are applied to the interior surfaces of different cubes. Most or all outer surfaces are generally provided with antireflection coatings. To create a contiguous optical component, the separate cubes are then bonded together, which can be technically demanding and expensive. In various embodiments, the functionality of the multiple beam-splitting surfaces of an assembly of cube beam splitters is instead provided by a single plate. This single plate may be made of glass (e.g., fused silica) or another material (e.g., chalcogenide glass, sapphire, zinc selenide, calcium fluoride, silicon, silicone, poly-carbonate, plastic, etc.) that is transparent over the range of operating wavelengths of the interferometer (e.g., between about 1400 and 1600, about 1450 and 1550 nm, etc.), with specialized, functional optical coatings applied over different surface regions of the plate.

[0110] FIG. 17 is a conceptual drawing of a beam-splitting optic implemented by a transparent plate 1700 with various surface coatings, in accordance with one embodiment. In this example, the plate 1700 is a glass plate. However, plates made of other transparent materials can also be used. The plate 1700 is shown in a cross section that coincides with the plane of propagation of light. The plate 1700 defines a pair of parallel surfaces 1702, 1704, separated by a distance t that defines the thickness 1705 of the plate 1700.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 These surfaces 1702, 1704 are configured to provide different beam-splitting functions in different regions. Note that, while FIG. 17 represents light beams symbolically by a single light ray for each beam, in reality, the light beams have a spatial extent (e.g., with an intensity falling off according to a Gaussian or similar profile centered along the depicted representative ray).

[0111] On the first surface 1702, a first region is covered by a non-polarizing beam-splitting coating 1706. Light incident on the coated first region is in part reflected and in part refracted at the surface 1702 and transmitted into the plate 1700. To implement an interferometer system for interrogating a sensing fiber, a probe beam 1708 of light may be directed at the first region at a 45° angle to the surface normal 1712, as shown. A sensing core 1710 (of the sensing fiber itself or connected to the sensing fiber) may be positioned and oriented to point at the first region at a 45° angle on the other side of the surface normal 1712, so as to receive the portion of the probe light that is reflected by the coating 1706 applied in the first region (herein the “reflected probe beam” 1714). Light reflected along the sensing core 1710 (forming a “sensor beam” 1716) is once again incident upon the coating 1706 in the first region, where a portion of the sensor beam 1716 is refracted to propagate (as a “refracted sensor beam” 1718) through the plate 1700 towards the second surface 1704. The angle of refraction, , depends on the angle of incidence (in this case 45°) and the refractive indices of the plate 1700 and surrounding medium, and can be computed according to Snell’s law, as: =arcsinIf the plate has a refractive indexglass= 1.44 and is surrounded by air withrefractive index air = 1.00, the angle is = 29.4°.

[0112] The second surface 1704 of the plate 1700 is covered by a non- polarizing beam-splitting coating 1720 (e.g., of the same material as the coating 1706 of the first region or a different material) in a second region that is located where the refracted sensor beam 1718 is incident. As can be seen, the coated second region on the second surface 1704 is offset relative to the coated first region on the first surface 1702 in a direction parallel to the first and second surfaces and within the plane of the light beams 1708, 1714, 1716, 1718 (herein the “offset direction”). The offset distance 1722, d, between the first and secondIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 regions (e.g., the distance between their center points) may be equal to the product of the tangent of the angle of refraction, , and the thickness 1705 of the plate 1700, t. With this configuration, a probe beam 1708 centered at a center point of the first region will result in a refracted sensor beam 1718 centered at a center point of the second region. A reference beam 1724 of light may be directed from outside at the coated second region at a 45° angle. The portion of the reference beam 1724 that is refracted into the plate 1700 and the portion of the refracted sensor beam 1718 that is internally reflected by the coating 1720 in the second region are then combined along a shared optical path, forming an interference beam 1726 that propagates back towards the first surface 1702.

[0113] On the first surface 1702, a third region located where the interference beam 1726 is incident, is covered by a polarizing beam-splitting coating 1728. The coated third region may be offset, in the offset direction, by the offset distance d relative to the second region and thus by twice the offset distance, 2d, relative to the first region, to help ensure that the interference beam 1726 is centered in the third region. The polarizing beam-splitting coating 1728 divides the incoming interference beam 1726 based on the direction of polarization into a first polarized beam (e.g., of p-polarized light) and second a polarized beam (e.g., of s-polarized light). The portion of light that is transmitted through and refracted at the coating 1728 forms the first polarized beam, which constitutes a first output beam 1730 to be detected. The portion of light that is reflected back into the plate 1700 towards the second surface 1704 forms the second polarized beam 1732. At least a portion of the second polarized beam is refracted at the second surface 1704, where it exits the plate 1700 as a second output beam 1734 to be detected. Optionally, to help ensure that the majority of the light of the second polarized beam 1732 is transmitted through, rather than reflected at, the second surface 1704, a fourth region located on the second surface 1704 where the second polarized beam 1732 impinges may be coated with an antireflection coating 1736. That fourth region may be offset, in the offset direction, by the offset distance d relative to the third region.

[0114] For purposes of discussing the offsets between the surface regions, it is assumed that the coated first, second, third, and fourth regions of the surfaces 1702, 1704 are about as wide as, but not much wider than, the respective incident beams as projected onto the surface. Then, if the beams are centered onIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 the respective regions, substantially all of the beam intensity (allowing for some marginal losses that are inevitable if the intensity profile goes to zero asymptotically) will fall within, and thus be refracted or reflected at, the respective surface region. Laterally offsetting the regions by a distance =tan( ) helps to guarantee that, if the probe beam 1708 is centered on the firstregion, the refracted probe beam 1718 will be centered on the second region. Further, if the reference beam 1724 is also centered on the second region, the interference beam 1726 will be centered on the third region and the second polarized beam 1732 will be centered on the fourth region. The distance =tan( ) corresponds to the distance that the beams travel in the offsetdirection between the first and second surfaces. The surface portions of the plate 1700 that are outside the first, second, third, and fourth regions are not relevant to the optical function discussed herein of the beam-splitting optic, and may therefore be coated arbitrarily or not at all, depending, e.g., on convenience or other practical manufacturing considerations. If used for other optical purposes, such as for other light beams, the surface portions of the plate 1700 that are outside the first, second, third, and fourth regions can be coated appropriately for those other optical purposes. This flexibility allows, for example, setting the widths of the four regions equal to the offset distance, such that the first region is directly adjacent to the third region and the fourth region is directly adjacent to the second region without gaps as shown in FIG. 17; this, however, need not be the case. Rather, there may be gaps between the first and third and between the second and fourth regions, such as where the projected beam widths on the surfaces are narrower than twice the offset distance. (The “width” of a coated region is herein understood as its spatial extent, measured in units of length or distance, in the offset direction, which is parallel to both the plane of light propagation and the surface of the plate. Use of the term “width” is not intended to imply that the spatial extent of the coated region in the offset direction is necessarily smaller than the spatial extent in a direction perpendicular to the offset direction.) Further, the arbitrariness of the surface coatings outside the regions where the beams impinge allows extending the surface coatings beyond those regions. Such surface coating extensions may potentially be only to one side or be generally asymmetric, which would move the center point of the resulting larger contiguously coated region, without affecting the beam-splittingIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 function in any way. When referring to the offset distance, therefore, these added portions, which do not affect the beams, are not deemed included in the first, second, third, and fourth regions.

[0115] The various coatings 1706, 1720, 1728, 1736 may be made from various different materials and using various coating techniques. With physical vapor deposition (PVD) such as sputtering or evaporation, layers of different materials are deposited on the plate (serving as the substrate) to create a stack of thin films with varying refractive indices that, together, control the optical filter properties of the coating. Similarly, with chemical vapor deposition (CVD), vapor-phase chemicals are deposited on the plate to react with the surface and form a solid material on the surface. Optical draw techniques sandwich refractive materials (e.g., glass, plastics, and others) with alternating indices of refraction to achieve optical interference effects. In ion beam sputtering (IBS), an ion beam is directed at a target material, causing atoms to be ejected and deposited on the substrate. Atomic layer deposition (ALD), used for ultra-thin coatings and atomic-level thickness control, involves the sequential use of gas- phase chemical processes to deposit conformal thin films, which is beneficial for creating very specific optical filter properties. Magnetron sputtering, which uses magnetic fields to trap electrons close to a target material and thereby enhance the sputtering efficiency, is effective for producing optically uniform and stable thin-film coatings, e.g., of materials such as zin oxide, tin oxide, or titanium dioxide. Dielectric coatings made from non-metallic materials such as oxides, nitrides or sulfides (e.g., silicon dioxide, tantalum pentoxide, magnesium fluoride, zinc sulfide, or titanium dioxide) may be used to create coatings with high damage thresholds and good optical properties for high-power light. Soft lithography and nanoimprint lithography may be used to pattern the coatings on the nanoscale, e.g., to create complex filter designs based on structural patterns that beyond simple layer stacks. Sol-gel processes, which involve the transition of a solution into a gel to form materials at low temperatures, may be used to make optical coatings on substrates with complex shapes or on larger scales. Electron-beam PVD , which uses an electron beam to evaporate materials which then condense on the substrate (e.g., plate) to from thin films, are useful to make optical interference filters.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1

[0116] In some embodiments, the beam-splitting coatings 1706, 1720, and 1728 divide incoming light about evenly between reflected and transmitted beams (e.g., reflecting between 47% and 53% of the light), and are nominally 50 / 50 beam splitters. Such beam-splitting coatings are readily available. Also, beneficially, a non-polarizing 50 / 50 beam splitter in the first region helps to maximize the optical power (or intensity) of the refracted sensor beam 1718. A polarizing 50 / 50 beam splitter in the third region, in conjunction with a highly transmissive antireflection coating 1736, can help to ensure good optical power balance between the two output beams 1730, 1734. Unequal split ratios can generally be compensated for by adjusting the relative optical power of the input beam(s), relative amplification of the output beams 1730, 1734, and / or amplification or computational scaling factors applied to the detected signals. In some embodiments, uneven split ratios are deliberately used for one or more of the beam-splitting coatings. For example, the non-polarization coating 1720 in the second region may be configured, based on the noise level at the detectors and the amount of input reference power that can be provided in the given system, to achieve a split ratio resulting in a reference power on the detectors that is about ten times the noise level of the detectors. Further, while it is usually convenient to configure the system for 45° incidence at the exterior surfaces, other incidence angles can in principle also be used. Beneficially, 45° incidence provides the shortest optical path, which can serve to achieve good or optimal coupling.

[0117] FIG. 18 is a conceptual drawing of an example free-space multi- channel interferometer 1800 including a coated-plate beam-splitting optic (as shown in FIG. 17) surrounded by five collimator assemblies 302, 304, 306, 308, 310, in accordance with various embodiments. The probe input collimator assembly 302, whose waveguide array serves as the probe light source, is positioned and oriented to direct the probe beam 1708 at the non-polarizing beam-splitting coating 1706 in the first region 1706, such that at least part of the probe beam 1708 is reflected at the coating 1706 to create the reflected probe beam 1714. The sensor collimator assembly 304 provides the sensor connection to a multicore sensing fiber (also herein the “optical sensor”); it is positioned and oriented relative to the probe light source and the coated first region to receive the reflected probe beam 1714 and to direct the sensor beam 1716 back onto theIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 first region. The sensor beam 1716 is created by reflection of light of the reflected probe beam 1714 along the optical sensor when the optical sensor is optically coupled with the sensor connection. At the beam-spitting coating 1706 in the first region, the sensor beam 1716 is partially transmitted to create the refracted sensor beam 1718. The reference input collimator assembly 306, whose waveguide array serves as the reference light source, is positioned and oriented to direct the reference beam 1724 at the non-polarizing beam splitting coating 1720 in the second region. The second region is disposed relative to the first region, the reference light source, and the third region to reflect the refracted sensor beam 1718 and transmit the reference beam 1724 so as to combine the two beams into an interference beam 1726 directed at the polarizing beam-splitting coating 1728 in the third region. This polarizing beam-splitting coating 1728 is configured to partially transmit the interference beam 1726 to form a first polarized beam 1730 and to partially reflect the interference beam to form a second polarized beam 1732. The detector collimator assemblies 308, 310, whose waveguide arrays serves as detector connections configured to optically couple with first and second detectors, are positioned and oriented relative to the third region to receive the first and second polarized beams 1730, 1732, respectively.

[0118] Unlike FIG. 17, FIG. 18 illustrates the lateral extent of the various beams of light. Each depicted beam may correspond to a superposition of multiple beams, resulting from probe and reference light originating from different cores of the waveguide arrays of the collimator assemblies 302, 306 that is collimated by the respective lenses into beams having slightly different angles of divergence in a direction out of the plane of the drawing; this divergence can be accommodated by extending the plate 1700 in the out-of- plane direction. In the context of discussing the beam-splitting optics (e.g., in conjunction with FIGS. 18 and 20), reference to a beam (e.g., probe beam, reference beam, etc.) in the singular is intended to also encompass sets of superposed beams that essentially co-propagate along the same path (with the noted slight divergence).

[0119] FIG. 18 also shows beams that are not being used in the interferometric measurements, but are dumped. In particular, as can be seen, the portion of the probe beam 1708 that is not reflected in the first region towardsIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 the sensor collimator assembly 304, but is transmitted into the plate 1700, will exit the plate at the opposite surface as a dumped probe light beam 1802. Further, the portion of the reference beam 1124 that is reflected, rather than being transmitted into the plate 1700 (along with the generally much lower- intensity portion of the refracted sensor beam 1718 that is not reflected in the second region back into the plate 1700), occurs as dumped light beam 1804. Since the antireflection coating in the fourth region is 1736 is not 100% reflective, there will generally also be a reflected portion (not shown) of the second polarized beam 1732 that is transmitted back through the plate 1700 and is ultimately dumped. The dumped probe light beam 1802 and dumped light beam 1804 generally have a lot of power, e.g., roughly half of the power of the incoming probe and reference beams 1708, 1724, and are therefore deliberately handled, e.g., to prevent from coupling into the waveguide cores of the collimator assemblies or other system components and perturb the signals.

[0120] FIGS. 19A and 19B are conceptual drawings illustrating, in perspective views, a method of manufacturing multiple beam-splitting optics as shown in FIG. 17 from a single plate 1900, in accordance with various embodiments. (In this example, plate 1900 is made of glass. However, in other examples the plate 1900 may be made from another transparent material.) The method involves applying polarizing and non-polarizing beam-splitting coatings (for the reflection of probe light towards the sensor and for the separation of the interference light into two polarization components, respectively) on one surface 1902 of the plate 1900. The method also involves applying non-polarizing beam-splitting and, optionally, antireflection coatings (for the combination of sensor light with reference light and to avoid reflection of one of the polarized output beams) on the other, opposite surface 1904 of the plate 1900. The method further involves dicing the plate 1900 into multiple individual beam- splitting optics.

[0121] In more detail, as can be seen in FIG.19A, the multiple coatings may be applied to surface regions that form parallel strips extending in a first direction parallel to the first surface, labeled the y-direction. Surface regions of each surface that are coated with the same material may be created simultaneously, e.g., by a film deposition processes such as the ones described above with reference to FIG. 17., while the remaining portion of the surface isIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 masked. Thus, to create one or more first regions 1906 covered by a non- polarizing beam-splitting surface coating, a masking layer is first deposited on the first surface 1902 of the plate 1900 and patterned. This patterning is to define the first regions 1906, and may be achieved by selective removal of the mask in the first regions 1906. After patterning, the non-polarizing beam- splitting surface coating is then applied over the surface. After removal of the remnant masking layer, a new masking layer can be created and patterned to expose one or more third regions 1908 to be covered by a polarizing beam- splitting coating. Second regions of non-polarizing beam-splitting coatings and fourth regions with antireflection coatings may be formed on the second surface 1904 in a similar manner. The various regions are spatially organized in sets of regions, where each set includes a first region, a second region, a third region, and an optional fourth region. These regions are offset relative to each other, as described with reference to FIG. 17, in a second direction that is parallel to the surfaces 1902, 1904 and perpendicular to the first direction (labeled the x- direction). In FIG. 19A, only two sets of regions 1910, 1912 are shown. It is to be understood that, in general, any number of sets of regions (including, in one example, just one set), arranged in parallel strips, may be created on the surfaces of the plate 1900.

[0122] The coated plate 1900 may be cut along the second (x-) direction, or in between sets of regions along the first direction, or both, as shown in FIG. 19B, to create multiple beam-splitting optics or devices 1920. In this manner, many beam-splitting devices can be created simultaneously, reducing the cost of manufacture per device substantially. While ten individual beam-splitting devices 1920 are shown in FIG. 19B, it will be understood that, in practice, the number of simultaneously created beam-splitting devices 1920 may be much larger.

[0123] The beam-splitting optic described in FIGS. 17 and 18 is implemented as a single part, and can help to simplify the assembly of the interferometer network, the tracking of parts in inventory, and reduce cost. On the other hand, manufacturing the part involves masking during the deposition of the various specialized optical coatings, which can complicate and drive up the cost of the process. As an alternative to using a single plate with multiple coated surface regions on each side, a beam-splitting optic can be constructed, inIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 accordance with various embodiments, from multiple plates, e.g., two plates, with only a single coating on each side. While this approach entails mounting two (or more) parts on the interferometer substrate, it can still be simpler than using bonded cube beam splitters.

[0124] FIG. 20 is a conceptual drawing of a beam-splitting assembly 2000 comprising two coated plates 2002, 2004, in accordance with various embodiments. Collectively, the two plates 2002, 2004 provide the same optical functionality as the single-plate beam-splitting optic of FIGS. 17 and 18. In the assembly 2000, the first plate 2002 serves to redirect a probe beam 2010 into the sensor, and to combine the resulting sensor beam 2012 with a reference beam 2014. (As noted, each “beam” may, in fact, include multiple beams for multiple optical channels.) For that purpose, non-polarizing beam-splitting coatings are applied to the two parallel, opposing surfaces 2006, 2008 of the first plate 2002. The probe beam 2010 is in part reflected off the first surface 2006, and coupled via a sensor connection into a sensing fiber. Light reflected along the sensing fiber returns, via the sensor connection, as sensor beam 2012, which is in part transmitted through the first surface 2006 and the plate 2002 to impinge internally on the second surface 2008. The reference beam 2014 is directed at the second surface 2008 in the region of incidence of the (refracted) sensor beam 2012. At the second surface 2008, the transmitted portion of the sensor beam 2012 and the reflected portion of the reference beam 2014 combine into an interference beam 2016 that now propagates outside the first plate 2002. Note that the depicted configuration of the probe, sensor, reference, and interference beams 2010, 2012, 2014, 2016 is achieved via the placement and orientation of the probe and reference light sources and the sensor connection (which are not directly shown in FIG. 20, but whose locations are indicated at 2018, 2020, and 2022, respectively) relative to each other and to the beam-splitting plate 2002. The probe and reference light sources may correspond, e.g., to the waveguide arrays of the collimator assemblies that receive probe and reference light from, ultimately, the same light source.

[0125] The second plate 2004 serves to split the interference beam 2016 into polarized beams with mutually orthogonal polarization, e.g., a first, s-polarized beam 2024 and a second, p-polarized beam 2026. For this purpose, a polarizing beam-splitting coating is applied to one of the two parallel, opposing surfacesIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 2028, 2030 of the second plate 2004. As depicted, the second plate may be oriented perpendicularly to the first plate 2002. Further, the second plate may be configured such that the interference beam 2016, before being split by the polarizing beam-splitting coating on the first surface 2028, is first transmitted through the second surface 2030 and the plate 2004 to be incident internally on the first surface 2028. At the polarizing beam-splitting coating on the first surface 2028, the light is split into a reflected portion and a transmitted portion. The reflected portion propagates back through the plate 2004, and eventually exits the plate at the second surface 2030 as the first polarized beam 2024. The transmitted portion leaves the plate 2004 at the first surface 2028 as the second polarized beam 2026. The second surface 2030 of the plate may be covered by an antireflection coating to allow all or most of the first polarized beam 2024 to pass without further reflections. The first and second polarized beams are focused onto respective waveguides or waveguide arrays (e.g., of collimator assemblies 308, 310, not shown, at locations indicated at 2032, 2034, respectively), which couple the light into respective first and second sets of detectors (not shown).

[0126] Beneficially, in the two-plate beam-splitting assembly 2000, only one functional optical coating is applied to each of the paired surfaces 2006, 2008, 2028, 2030. This allows the surfaces 2006, 2008, 2028, 2030 to be coated in their entirety, reducing or eliminating the need for masking during manufacture.

[0127] The configuration of the two plates perpendicular to one another is convenient for the placement of the various collimator assemblies surrounding the beam-splitting assembly 2000, but is not necessary for the underlying principle of operation. Other, functionally equivalent arrangements will occur to those of ordinary skill in the art. For example, the two plates may alternatively be arranged parallel to one another, spaced apart and / or laterally shifted relative to each other such that the interference beam generated at the first plate, upon reflection off the polarizing beam-splitting surface of the second plate, is not blocked by the first plate, but can proceed to the waveguide array associated with the first set of detectors. Also, as will be appreciated, in both perpendicular and parallel configurations (or, indeed, any other relative orientation of the two plates), the polarizing beam-splitting coating may alternatively be disposed on the surface of the second plate that the interference beam first encounters, andIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 the polarized beam that is transmitted through that surface will then propagate through and exit the plate on the other side. The arrangement of the plates relative to each other and to the other components of the interferometer system will often be determined based on spatial constraints.

[0128] In general, beam-splitting optics and assemblies including one or more transparent optical components with functional optical coatings (whether covering only portions of the faces of the components or being coextensive with them) may find application in various interferometric systems—including, but not limited to OFDR systems as described herein—as substitutes for or in conjunction with conventional beam-splitting prisms assemblies or the like. The number and shapes of the individual components and the overall configuration of the beam-splitting assembly may vary depending on the application, the associated number and type of specialized optical surface regions, and related considerations. Light-splitting devices and polarization control

[0129] In free-space multi-channel optical interferometers as described herein, the multiple optical channels are implemented with sets of multiple beams that largely overlap, with some slight divergence, along the various shared interferometric paths. Creating the input sets of beams that provide the probe and reference light for the multiple channels, preferably with evenly distributed optical power between channels, can be challenging. In various embodiments, this challenge is met by using a PLC to divide probe light received from a single probe input optical fiber between multiple outputs of the PLC, and another PLC to divide reference light received from a single reference input optical fiber between multiple outputs of the second PLC. PLCs that can divide light evenly between multiple PLC cores at low losses are widely available, including with PLC output core spacings that match the fiber core spacing of commercially available v-groove fiber arrays (e.g., a spacing of 127 m between neighboring cores), which allows the PLC outputs to be coupled directly to a corresponding v-groove fiber array.

[0130] FIG. 21A is a conceptual drawing illustrating a PLC 2100 configured as an optical splitter to divide light from an input optical fiber 2102 between eight output optical fibers 2104 of a v-groove fiber array 2106, in accordanceIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 with various embodiments. FIG. 21B is a conceptual drawing illustrating the PLC 2100 and v-groove fiber array 2106 of FIG. 21A in top view alongside side views of their respective end-faces. The chip 2101 in which the PLC 2100 is implemented has a single-core end-face serving as the input face 2108, end a multi-core (eight-core) end-face serving as the output face 2110. The number of output optical fibers 2104 and corresponding output cores 2111 of the PLC 2100 can, of course, vary in different embodiments. As shown in FIG. 21A, the input optical fiber 2102 can be butted against, and be “butt-coupled” to the single input core 2112 of the PLC 2100 at the input face 2108. The output cores 2111 of the PLC 2100 at the output face 2110 can be butt-coupled to the input ends of the output optical fibers 2104 at the end-face (or input face) 2116 of the fiber array 2106. In various embodiments, the input ends of the output optical fibers 2104 and the output face 2110 of the PLC chip 2101 are angle-polished to suppress reflections of light back into the waveguide cores of the PLC 2100. Similarly, the output end of the input optical fiber 2102 and the input face of the PLC chip 2101 may be angle-polished to avoid reflections back into the input fiber. The end-faces of the PLC chip 2101 (e.g., input face 2108 and output face 2110) may also be coated with an antireflection coating to reduce coupling losses due to reflections.

[0131] Instead of being butt-coupled, the waveguide cores of the PLC 2100 and respective optical fibers (e.g., input and output optical fibers 2102, 2104) can also be coupled together by imaging the PLC cores and fiber cores onto one another with free-space optics. Consequently, instead of coupling light from the output cores 2111 of the PLC 2100 into an optical fiber array 2106 that then generates a set of probe beams or reference beams, the output face 2110 of the PLC chip 2101 may be used directly, as part of a collimator assembly, to generate probe beams or reference beams. These probe beams or reference beams can then be focused, after propagating through the beam-splitting optic, onto the sensing cores (in the case of the probe beams) or output cores (in the case of reference beams) of the receiving collimator assembly of a given pair of collimator assemblies. On the input side of the PLC 2100, free-space coupling to the input optical fiber 2102 provides an opportunity to insert polarization controllers and modulators into the optical path to generate polarization-Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 controlled input to the beams-splitting optic, as explained with reference to FIGS. 23 and 25 below.

[0132] FIG. 22 is a conceptual drawing illustrating a PLC 2100 that is free- space coupled to an input optical fiber 2102 and eight (output) optical fibers 2104, in accordance with various embodiments. Preceding the PLC 2100, a pair of collimating lenses 2202, 2204 images the input optical fiber 2102 onto the input core of the PLC 2100. That is, the diverging light output by the input optical fiber 2102 is collimated, by the first lens 2202 of the pair of collimating lenses, to collimate the light, and the second lens 2204 then focuses the collimated beam onto the input core 2112 of the PLC 2100. In the collimated space 2208 between the lenses 2202, 2204, free-space optical components can be inserted. At the output end of the PLC 2100, another pair of collimating lenses 2210, 2212 is used to first collimate the diverging light beams emitted by the eight output cores 2111, and then refocusing the light onto the inputs of the output optical fibers 2104. In the collimated space 2214, the beams associated with different output cores 2111 of the PLC 2100 propagate with slightly different angles. Free-space optics may be placed in this space 2214 between the pair of collimating lenses 2212. Such free-space optics may be or include, for example, a beam-splitting optic 300, 1700 or the like; in this case, the (output) optical fibers 2104 constitute the fiber arrays of collimator assemblies that receive the light. Note that each of the depicted lenses 2204, 2206, 2210, 2212 in FIG. 22 may be implemented as a single lens, or as a system of multiple lenses, such as a pair of lenses 320 as used in the high-precision collimator assemblies discussed with reference to FIG. 3. Also, the fiber array 2106 may be replaced by an array of waveguide cores of another PLC, in some embodiments.

[0133] FIG. 23 is a schematic diagram of an example polarization-diverse free-space multi-channel OFDR system 2300 that utilizes free-space-coupled PLCs to divide probe and reference input light between multiple channels, in accordance with various embodiments. The system 2300 includes a beam- splitting optic 2302 and five collimator assemblies 302, 304, 306, 308, 310 (as described with reference to FIG. 3) mounted on a common interferometer substrate 311. While the beam-splitting optic 2302 is depicted as a transparent plate 1700 with non-polarizing and polarizing beam-splitting surface coatings, asIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 described in detail with reference to FIG. 17, a beam-splitting optic constructed from cube beam splitters or similar optical prism assembly (e.g., as depicted in FIGS. 2, 3, and 16B-16G) can be substituted for the coated plate 1700 with some incidental rearrangements of the collimator assemblies 302, 304, 306, 308, 310, without otherwise affecting the configuration of the system 2300.

[0134] The system 2300 receives input light from a tunable laser (not shown), e.g., via an input optical fiber 2304. An optical splitter 2306 (e.g., implemented by a fiber-optic 1x2 coupler) divides the input light between measurement and reference branches of the interferometer, implemented by first and second input fibers 2308, 2310, respectively. The first input fiber 2308 delivers probe light to the input of collimator assembly 302, which generates the probe beams, and the second input fiber 2310 delivers reference light to the input of collimator assembly 306, which generates the reference beams. The two collimator assemblies 302, 306 each include a PLC to split the received light between multiple waveguide cores, which output respective probe and reference beams for the multiple optical channels. The remaining collimator assemblies 304, 308, 310 are, in the depicted embodiment, implemented with optical fiber arrays (e.g., in v-groove assemblies 326), but may, alternatively, likewise use PLCs. The optical fibers of the collimator assembly 304 may be routed, e.g., as a multi-fiber ribbon, to a fanout assembly 2312 that couples each of the fibers to a corresponding core of a multicore sensing fiber 2314. The optical fibers of the collimator assemblies 308, 310 may route the detected s-polarized and p- polarized output light to respective first and second sets of detectors 2316, 2318.

[0135] At times, large optical delays (e.g., on the order of tens of nanoseconds) are added in the reference path for path matching between the reference and measurement branches. These delays are usually implemented using a fiber-optic delay line, e.g., a loop of single-mode optical fiber, in the second (i.e., reference) optical input fiber 2310. Optical fiber, however, moves the polarization state of the light in unpredictable ways. Therefore, in order to balance the power of the reference light between the two sets of detectors 2316, 2318, the system 2300 includes a polarization controller 2320 in the reference branch, preceding the collimator assembly 306. As shown, the polarization controller 2320 is placed in the collimator space between a pair of lenses (or lens systems) that image the output of the second optical input fiber 2310 onto theIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 input of the PLC of the collimator assembly 306, as explained with reference to FIG. 22. Since polarization states are deterministic in free-space optics, one polarization adjustment preceding the PLC optical splitter suffices to balance the power of the reference light between vertical and horizontal polarization states on all of the optical channels. To achieve this balance in a fiber-optic network instead, a polarization adjustment would be applied separately for each optical channel.

[0136] FIG. 24 is a perspective drawing of an example polarization controller 2400, in accordance with one embodiment, as may be used in an OFDR system as shown in FIG. 23. The polarization controller 2400 includes a polarization-modulating crystal 2402, such as a lithium niobate, barium titanate, beta-barium borate, monopotassium phosphate, or other crystal. The polarization-modulation crystal 2402 is placed between a pair of electrodes configured to generate an electric field at a 45° angle relative to the polarization- splitting axis (oriented, in this example, normal to the plane of the substrate) of the polarizing beam-splitting surface. The electrodes 2404, 2406 may be metal parts that simultaneously serve as the mechanical mounts for the crystal 2402. By controlling the voltage applied between the electrodes 2404, 2406, the relative phase between the polarization component parallel to the electric field of a beam of light (such as, reference light in FIG. 23) propagating through the crystal 2402 and the polarization component orthogonal to the electric field of the beam of light can be shifted by a controllable amount. It can be shown that there is power on the two sets of detectors 2316, 2318.

[0137] While a single polarization-modulating crystal 2402 can be used to adjust the light in the reference path to achieve power balance of the reference light on the detectors, polarization-diverse detection usually also utilizes a means of modulating the polarization of the probe light between two non-parallel (e.g., orthogonal states) to enable fully characterizing the polarization response of the system. For this purposes, the system 2300 of FIG. 23 includes a fiber-based polarization modulator 2322 in the of the measurement arm. In accordance with various embodiments, this fiber-based polarization modulator 2322 is replaced by a free-space polarization modulator.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1

[0138] FIG. 25 is a schematic diagram of an example polarization-diverse free-space multi-channel OFDR system 2500 that utilizes free-space-coupled PLCs to divide probe and reference input light between multiple channels, and further includes a free-space polarization modulator 2502 for modulating the probe input light, in accordance with various embodiments. The polarization modulator 2502, which is a two-component device, is placed in the collimator space between the two lenses used to couple probe light via free space from the first input optical fiber 2308 into the input of the PLC 2100 of the collimator assembly 302. Since the polarization modulation takes place before the probe light is split into multiple probe beams, it is applied simultaneously to all channels.

[0139] FIG. 26 is a perspective drawing of an example polarization modulator 2600 that includes two polarization controllers 2602, 2604 each including a polarization-modulating crystal, in accordance with one embodiment. The electrode pairs associated with the two crystals two generate respective controllable electric fields are oriented at a 45° angle relative to one another. This configuration allows modulating the polarization between two orthogonal polarization states for any polarization state of the incoming light, which is useful since the light has propagated through optical fiber and thus comes in with arbitrary polarization. The first modulator is used to get the polarization into a state that has equal amplitude components in the principle states of the second modulator. The second modulator can then quickly switch the polarization state between two orthogonal states.

[0140] FIG. 27 is a perspective drawing of an example polarization modulator 2700 that utilizes a polarization controller 2702 with a polarization- modulating crystal 2703 in conjunction with a half-wave plate 2704, in accordance with another embodiment. A half-wave plate phase-shifts one polarization component, measured against the optical axis of the half-wave plate, relative to the other, which rotates the polarization direction. Here, the half- wave plate 2704 is inserted into the beam path at a 22.5° angle relative to the direction of the electric field applied across the polarization-modulating crystal of the polarization controller 2702, which effectively rotates the polarization by 45°. The polarization-splitting axes of the crystal 2703 are parallel and perpendicular to the substrate surface, respectively. Thus, if the incoming lightIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 is linearly polarized parallel or perpendicular to the substrate, the crystal 2703 will not be able to change the polarization state, but the half-wave plate 2704 will rotate the polarization by 45° degrees and thereby balance the power between the perpendicular and parallel states. If the light is polarized at 45° degrees relative to the substrate, then the half-wave plate 2704 will rotate the light to be parallel to the substrate. Because the light is not on the axis of the polarization-modulating crystal 2703, the crystal 2703 will be able to adjust the state of the light such that the half-wave plate 2704 will produce light with equal powers in the polarization parallel and perpendicular to the substrate.

[0141] Various aspects of multi-channel free-space interferometer systems, including high-precision collimator assemblies and associated methods for assembly and alignment, inexpensive beam-splitting optics utilizing exterior surface coatings, and configurations for beam splitting and polarization control, have been described.

[0142] The various embodiments and examples described herein are intended as illustrative and not as limiting. Various modifications, additional combinations of features, and further applications may occur to those of ordinary skill in the art. What is claimed is:

Claims

Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 Claims 1. A beam-splitting optic comprising: a transparent plate comprising a first surface and a second surface, the second surface being parallel and opposite to the first surface; a first non-polarizing beam-splitting coating covering a first region on the first surface; a second non-polarizing beam-splitting coating covering a second region on the second surface; and a polarizing beam-splitting coating covering a third region on the first surface; wherein the second region is offset relative to the first region by an offset distance in an offset direction that is parallel to the first surface; and wherein the third region is offset relative to the second region by the offset distance in the offset direction.

2. The beam-splitting optic of claim 1, further comprising: an antireflection coating covering a fourth region on the second surface, wherein the fourth region is offset relative to the third region by the offset distance in the offset direction.

3. The beam-splitting optic of claim 2, wherein the third region is adjacent to the first region and the fourth region is adjacent to the second region.

4. The beam-splitting optic of claim 2, wherein the first, second, and third regions are equal in a width in the offset direction.

5. The beam-splitting optic of any of claims 1 to 3, wherein the offset distance is equal to a product of a thickness and a tangent, the thickness being of the plate between the first and second surfaces, and the tangent being of an angle of refraction of light transmitted into the plate upon incidence at a 45° angle.

6. The beam-splitting optic of any of claims 1 to 3, wherein the polarizing and non-polarizing beam-splitting coatings are between 47% and 53% reflective.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 7. The beam-splitting optic of any of claims 1 to 3, wherein the first non- polarizing beam-splitting coating and the second non-polarizing beam-splitting coating are of a same material.

8. A method of manufacturing beam-splitting optics, the method comprising: applying a first non-polarizing beam-splitting coating over one or more first regions on a first surface of a transparent plate, the transparent plate comprising the first surface and a second surface, the second surface being parallel and opposite to the first surface; applying a second non-polarizing beam-splitting coating over one or more second regions on the second surface; and applying a polarizing beam-splitting coating over one or more third regions on the first surface; wherein the one or more first regions, one or more second regions, and one or more third regions form parallel strips extending in a first direction parallel to the first surface; wherein the one or more first regions, one or more second regions, and one or more third regions form one or more region sets, each region set comprising a corresponding first region, a corresponding second region, and a corresponding third region; wherein, for each region set of the one or more region sets, the corresponding second region is offset by an offset distance relative to corresponding first region in a second direction, the corresponding third region is offset relative to the corresponding second region by the offset distance in the second direction, the second direction is parallel to the first surface, and the second direction is perpendicular to the first direction; and wherein the method further comprises: cutting the plate along the second direction into multiple beam-splitting optics.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 9. The method of claim 8, further comprising: applying an antireflection coating over one or more fourth regions on the second surface; wherein the one or more fourth regions form one or more strips extending in the first direction; wherein each region set of the one or more region sets further comprises a corresponding fourth region of the one or more fourth regions; and wherein, for each region set of the one or more region sets, the corresponding fourth region is offset relative to the corresponding third region by the offset distance in the second direction.

10. The method of claim 9, wherein: the one or more region sets comprise multiple region sets; for each set of the multiple region sets, the corresponding third region is adjacent to the corresponding first region and the corresponding fourth region is adjacent to the corresponding second region; and the method further comprises: cutting the plate along the first direction in between the multiple region sets.

11. The method of any of claims 8 to 10, wherein: the first, second, and third regions are equal in width in the offset direction; or the offset distance is equal to a product of a thickness of the plate between the first and second surfaces and an tangent of an angle of refraction of light transmitted into the plate upon incidence at a 45° angle.

12. An interferometer system comprising: a beam-splitting optic comprising: one or more transparent optical components comprising a set of surfaces, and on the set of surfaces, a first non-polarizing beam-splitting coating covering the set of surfaces in a first region, a second non- polarizing beam-splitting coating covering the set of surfaces in a secondIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 region, and a polarizing beam-splitting coating covering the set of surfaces in a third region; a probe light source configured to direct a probe beam at the first region, such that at least part of the probe beam is reflected by the first non-polarizing beam-splitting coating as a reflected probe beam; a sensor connection configured to optically couple with an optical sensor, the sensor connection positioned and oriented relative to the probe light source and the first region to receive the reflected probe beam and to direct a sensor beam back onto the first region, the sensor beam being created by reflecting light of the reflected probe beam along the optical sensor when the optical sensor is optically coupled with the sensor connection, the first non-polarizing beam- splitting coating configured to partially transmit the sensor beam to create a refracted sensor beam; a reference light source positioned and oriented to direct a reference beam at the second region, the second region being disposed relative to the first region, the reference light source, and the third region to combine the refracted sensor beam and the reference beam into an interference beam directed at the third region, the polarizing beam-splitting coating configured to partially transmit the interference beam to form a first polarized beam and to partially reflect the interference beam to form a second polarized beam; a first detector connection configured to optically couple with a first detector, the first detector connection positioned and oriented relative to the third region to receive the first polarized beam; and a second detector connection configured to optically couple with a second detector, the second detector connection positioned and oriented relative to the third region to receive the second polarized beam.

13. The interferometer system of claim 12, wherein the beam-splitting optic further comprises: an antireflection coating covering a fourth region on the set of surfaces.

14. The interferometer system of claim 13, wherein: the one or more transparent optical components comprise a transparent plate;Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 the set of surfaces comprises: first and second surfaces of the transparent plate, the first surface being parallel and opposite to the second surface; the first and third regions are on the first surface; and the second and fourth regions are on the second surface.

15. The interferometer system of claim 13, wherein: the one or more transparent components comprise first and second transparent plates; the set of surfaces comprises first and second surfaces of the first transparent plate and third and fourth surfaces of the second transparent plate, the first surface being parallel and opposite to the second surface, and the third surface being parallel and opposite to the fourth surface; the first region is on the first surface, the second region is on the second surface; and the third region is on the third surface, and the fourth region is on the fourth surface.

16. The interferometer system of claim 15, wherein the first plate is perpendicular to the second plate.

17. The interferometer system of claim 16, wherein the interference beam is transmitted through the fourth region prior to reaching the third region.

18. The interferometer system of claim 15, wherein the first plate is parallel to the second plate.

19. The interferometer system of claim 15, wherein: the first region is coextensive with an entirety of the first surface; or the second region is coextensive with an entirety of the second surface; or the third region is coextensive with an entirety of the third surface; or the fourth region is coextensive with an entirety of the fourth surface.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 20. The interferometer system of any of claims 12 to 19, wherein: the probe light source comprises one or more output surfaces of optical fibers or waveguides configured to carry light; or the reference light source comprises one or more output surfaces of optical fibers or waveguides configured to carry light.

21. A collimator assembly comprising: a collimator base; a waveguide array assembly bonded to a surface of the collimator base; and a compound lens system bonded to a surface of the collimator base, the compound lens system comprising first and second lenses; wherein a waveguide array of the waveguide array assembly and the first and second lenses are aligned along an axis parallel to the surface; and wherein the first and second lenses are placed at a mutual distance, dependent on focal lengths of the first and second lenses, that achieves a target effective focal length of the compound lens system within a specified margin of error.

22. The collimator assembly of claim 21, wherein the specified margin of error is no more than 0.1%.

23. The collimator assembly of claim 21, wherein the first lens is a molded glass lens, and wherein the second lenses is a molded glass lens.

24. The collimator assembly of any of claims 21 to 23, wherein the waveguide array comprises: a linear array of waveguide cores in a planar light circuit (PLC) chip; or a linear array of single-core fibers retained in a v-groove assembly.

25. A free-space interferometer comprising: a substrate; a beam-splitting optic mounted to the substrate; and multiple collimator assemblies mounted to the substrate;Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 wherein each collimator assembly comprises: a collimator base, and a waveguide array assembly, the waveguide array assembly bonded to a surface of the collimator base, and the waveguide array assembly comprising a waveguide array and a compound lens system, the compound lens system comprising first and second lenses; wherein the multiple collimator assemblies are configured in one or more non-disjoint pairs, each non-disjoint pair of the one or more non-disjoint pairs comprising a first corresponding collimator assembly and a second corresponding collimator assembly; and wherein, for each pair of the one or more non-disjoint pairs, the first and second corresponding collimator assemblies are positioned and oriented relative to the beam-splitting optic such that light emitted from the waveguide array of the first corresponding collimator assembly is coupled, via the beam-splitting optic, into the waveguide array of the second corresponding collimator assembly.

26. The free-space interferometer of claim 25, wherein, in each collimator assembly of the multiple collimator assemblies: the waveguide array and the first and second lenses are aligned along an axis parallel to the surface of the collimator base; and the first and second lenses are placed at a mutual distance, dependent on focal lengths of the first and second lenses, that achieves a target effective focal length of the compound lens system within a specified margin of error.

27. The free-space interferometer of claim 25, wherein: for each collimator assembly of the multiple collimator assemblies, the waveguide array assembly and the first and second lenses are bonded to a top surface of the collimator base, and the collimator base is rotated about its optical axis to be mounted to the substrate at one of a pair of side surfaces of the collimator base, the side surfaces being perpendicular to the top surface and parallel to an optical axis of the collimator assembly; andIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 for each pair of the one or more non-disjoint pairs of collimator assemblies, the first and second corresponding collimator assemblies are rotated in a same direction about their optical axes if there is an even number of reflections along a path from the first corresponding collimator assembly to the second corresponding collimator assembly, and in opposite directions about their optical axes if there is an odd number of reflections along the path from the first collimator assembly to the second collimator assembly.

28. The free-space interferometer of claim 25, further comprising: for each collimator assembly of the multiple collimator assemblies, a third lens mounted to at least one of the collimator base or the substrate, the third lens having a focal length that is at least five times an effective focal length of the compound lens system.

29. The free-space interferometer of claim 25, wherein in each pair of the one or more non-disjoint pairs, a path length between the first corresponding collimator assembly and the second corresponding collimator assembly is equal to a sum of effective focal lengths of the first and second corresponding collimator assemblies.

30. The free-space interferometer of any of claims 25 to 29, wherein the multiple collimator assemblies comprise at least three collimator assemblies configured in at least two non-disjoint pairs of the one or more non-disjoint pairs.

31. The free-space interferometer of any of claims 25 to 30, wherein: the free-space interferometer is configured to couple to an optical sensor comprising a set of sensing cores; the multiple collimator assemblies comprise: a first collimator assembly associated with a set of probe input cores, a second collimator assembly associated with the set of sensing cores,Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 a third collimator assembly associated with a set of reference input cores, a fourth collimator assembly associated with a first set of output cores for a first polarization, and a fifth collimator assembly associated with a second set of output cores for a second polarization; and the beam-splitting optic comprises: a first polarization-independent beam-splitting surface to couple probe light from the set of probe input cores into the set of sensing cores and to transmit light returned from the set of sensing cores, a second polarization-independent beam-splitting surface to combine the returned light from the set of sensing cores with reference light from the set of reference input cores to create combined light, and a polarization-splitting surface to split the combined light into light of the first polarization and light of the second polarization and to couple the light of the first polarization into the first set of output cores and the light of the second polarization into the second set of output cores.

32. The free-space interferometer of any of claims 25 to 31, wherein the beam-splitting optic comprises a glass plate with beam-splitting surface coatings.

33. A method of assembling, using a fixture comprising an imaging optic and an image sensor placed at a back focal plane of the imaging optic, a collimator device comprising a collimator base and optical components, the method comprising: while the collimator base is in the fixture with a first surface of the collimator base parallel to a zeroth diffraction order of an alignment beam, imaging the zeroth diffraction order of the alignment beam with the imaging optic onto the image sensor to produce an image and determining an associated alignment location of the zeroth diffraction order of the alignment beam on the image sensor; andIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 positioning and orienting the optical components relative to the collimator base to generate a collimator output beam parallel to the first surface by: imaging the collimator output beam with the imaging optic onto the image sensor, and positioning and orienting the optical components relative to the collimator base such that a location of the collimator output beam on the image sensor is aligned with the alignment location of the zeroth diffraction order of the alignment beam on the image sensor at least along a direction normal to the first surface.

34. The method of claim 33, further comprising: aligning the collimator base in the fixture with the first surface parallel to the zeroth diffraction order of the alignment beam by: dividing the alignment beam with a long-period transmission grating into the zeroth diffraction order and two first diffraction orders; positioning the collimator base such that one of the two first diffraction orders reflects off the first surface of the collimator base; imaging the first diffraction orders of the alignment beam along with the zeroth diffraction order onto the image sensor; and orienting the collimator base such that the two first diffraction orders coincide on the image sensor.

35. The method of claim 33, further comprising: while the collimator base is in the fixture with a second surface of the collimator base parallel to a zeroth diffraction order of a second alignment beam, the second surface being perpendicular to the first surface, determining an alignment location of the zeroth diffraction order of the second alignment beam on the image sensor; and positioning and orienting the optical components relative to the collimator base to generate a collimator output beam parallel to the second surface by: imaging the collimator output beam with the imaging optic onto the image sensor, andIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 positioning and orienting the optical components relative to collimator base such that the location of the collimator output beam on the image sensor is aligned with the alignment location of the zeroth diffraction order of the second alignment beam on the image sensor at least along a direction normal to the second surface.

36. The method of claim 35, further comprising: affixing the optical components to the first surface.

37. The method of claim 36, wherein: the optical components comprise a waveguide array and one or more lenses; and positioning and orienting the optical components relative to the collimator base such that the location of the collimator output beam is aligned with the location of the zeroth diffraction order of the alignment beam on the image sensor at least along the direction normal to the first surface comprises: adjusting a height of the waveguide array above the first surface, or adjusting a position of the one or more lenses relative to the waveguide array in the direction normal to the second surface.

38. The method of claim 33, wherein the optical components comprise a waveguide array and one or more lenses, and wherein positioning and orienting the optical components relative to the collimator base such that the location of the collimator output beam on the image sensor is aligned with the location of the zeroth diffraction order of the alignment beam on the image sensor comprises: setting a distance between the one or more lenses and the waveguide array based on a spot size of the collimator output beam on the image sensor.

39. The method of claim 38, wherein setting the distance between the one or more lenses and the waveguide array based on the spot size comprises: minimizing the spot size.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 40. The method of claim 33, wherein the optical components comprise a waveguide array and two lenses, the method further comprising: setting a distance between the two lenses to achieve a specified effective focal length; and affixing the two lenses to the first surface after the distance has been set.

41. The method of any of claims 33 to 40, wherein the positioning and orienting are performed by a robotic assembly system operating under control of a processing system, and wherein positioning and orienting comprises: commanding the assembly system to position or orient the optical components 42. A method of assembling an interferometer system comprising a beam- splitting optic and a plurality of collimator devices generating respective collimator output beams, the method comprising: injecting light into a first collimator device to generate a first collimator output beam; injecting light into a second collimator device to generate a second collimator output beam; using the beam-splitting optic to split, at a beam-splitting surface of the beam-splitting optic, each output beam of the first and second collimator output beams into first and second portions, with the first portion of the first collimator output beam counterpropagating to the first portion of the second collimator output beam between the first and second collimator devices; and aligning the first and second collimator devices by: using a retroflector in a path of the second portion of one of the first or second collimator output beams to reflect that second portion back onto the beam-splitting surface, the beam-splitting surface combining the reflected second portion with the second portion of the other one of the first or second collimator output beams; orienting at least one of the first collimator output beam or the second collimator output beam such that the second portions of the first and second collimator output beams coincide on an image sensor of aIntuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 camera, the camera focused at infinity and in a path of the combined second portions.

43. The method of claim 42, wherein orienting the at least one of the first collimator output beam or the second collimator output beam comprises: adjusting a position or orientation of the first collimator device, or of the second collimator device, or of both the first and second collimator devices.

44. The method of claim 42 or 43, wherein orienting the at least one of the first collimator output beam or the second collimator output beam comprises: adjusting a position or orientation of a weak compensating lens placed in the first collimator device or in the second collimator device.

45. The method of any of claims 42 to 44, wherein the orienting step is performed by a robotic assembly system operating under control of a processing system.

46. A polarization-diverse, multi-channel, free-space interferometer comprising: a beam-splitting optic comprising a first non-polarizing beam-splitting surface, a second non-polarizing beam-splitting surface, and a polarizing beam- splitting surface; a first collimator assembly comprising a first planar light circuit (PLC) configured to split light received at an input of the first PLC between multiple outputs of the first PLC to generate probe beams for multiple optical channels, the first collimator assembly configured to direct the probe beams at the first non-polarizing beam-splitting surface; a second collimator assembly configured to receive the probe beams via the first non-polarizing beam-splitting surface, couple the probe beams into multiple sensing cores associated with the multiple optical channels, generate sensor beams of reflected light for the multiple optical channels, and direct the sensor beams via the first non-polarizing beam-splitting surface at the second non-polarizing beam-splitting surface;Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 a third collimator assembly comprising a second PLC configured to split light received at an input of the second PLC between multiple outputs of the second PLC to generate reference beams of light for the multiple optical channels, the third collimator assembly configured to direct the reference beams at the second non-polarizing beam-splitting surface, wherein the second non-polarizing beam-splitting surface is configured to combine the sensor beams and the reference beams into interference beams for the multiple channels and to direct the interference beams at the polarizing beam-splitting surface, and wherein the polarizing beam-splitting surface is configured to split the interference beams into first polarized beams for the multiple channels and second polarized beams for the multiple channels; a fourth collimator assembly configured to receive the first polarized beams and couple them into multiple first output cores for detection at respective first detectors; a fifth collimator assembly configured to receive the second polarized beams and couple them into multiple second output cores for detection at respective second detectors; and at least one polarization modulator coupled in a free-space manner between at least one of the input of the first PLC and a first optical input fiber providing probe light or the input of the second PLC and a second optical input fiber providing reference light.

47. The interferometer of claim 46, wherein the at least one polarization modulator comprises a polarization modulator coupled in a free-space manner between the input of the second PLC and the second optical input fiber.

48. The interferometer of claim 47, wherein: the polarization modulator comprises: a polarization-modulating crystal disposed between a pair of electrodes that generate an electric field oriented at 45 degrees relative to a polarization-splitting axis of the polarizing beam- splitting surface.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 49. The interferometer of claim 47, wherein the input of the first PLC is one of free-space-coupled or butt-coupled to the first optical input fiber, the interferometer further comprising a fiber-based polarization modulator in the first optical fiber.

50. The interferometer of claim 46, wherein the at least one polarization modulator comprises: a pair of polarization modulators coupled in a free-space manner between the input of the first PLC and the first optical input fiber, the pair of polarization modulators configured to modulate a polarization of the probe beam between two polarization states.

51. The interferometer of claim 50, wherein the pair of polarization modulators comprises a pair of polarization-modulating crystals disposed between respective pairs of electrodes that generate respective electric fields oriented at 45° relative to each other.

52. The interferometer of claim 46, wherein: the at least one polarization modulator comprises: a polarization modulator and a half-wave plate coupled in a free-space manner between the input of the first PLC and the first optical input fiber; the polarization modulator comprises a polarization-modulating crystal oriented with its axis parallel to a plane of the interferometer, the polarization- modulating crystal disposed between a pair of electrodes that, when driven, generates an electric field oriented perpendicular to a plane of the interferometer; and the half-wave plate is oriented with its axis at 22.5 degrees relative to an axis normal to the plane of the interferometer.

53. The interferometer of claim 46, further comprising: the first optical input fiber; the second optical input fiber;Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 an optical splitter configured to split input light received from a light source between the first and second optical input fibers; and the light source, wherein the light source comprises a tunable laser.

54. The interferometer of claim 53, wherein the second optical input fiber comprises a fiber-optic delay line.

55. The interferometer of claim 46, wherein the second, fourth, and fifth collimator assemblies each comprise a v-groove fiber array, and wherein: the sensing cores are retained in the v-groove fiber array of the second collimator assembly and are coupled to respective fiber cores of a multi-core sensing fiber; or a core spacing in the v-groove fiber arrays matches a core spacing at the outputs of the first and second PLCs.

56. The interferometer of any of claims 46 to 55, wherein each collimator assembly of the first, second, third, fourth, and fifth collimator assemblies comprises first and second lenses, and wherein: the first and second lenses of the first collimator assembly are configured to collimate the probe beams; the first and second lenses of the second collimator assembly are configured to focus the probe beams onto the sensing cores and to collimate the sensor beams; the first and second lenses of the third collimator assembly are configured to collimate the reference beams; the first and second lenses of the fourth collimator assembly are configured to focus the first polarized beams onto the first output cores; and the first and second lenses of the fifth collimator assembly are configured to focus the second polarized beams onto the second output cores.Intuitive Ref. No. P06746-WO / Attorney Ref. No. 3948.249WO1 57. The interferometer of any of claims 46 to 55, wherein each collimator assembly of the first, second, third, fourth, and fifth collimator assemblies comprises a first lens and a second lens, the first and second lenses being placed at a mutual distance, dependent on focal lengths of the first and second lenses, that achieves a target effective focal length within a specified margin of error.

58. The interferometer of any of claims 46 to 55, wherein the beam-splitting optic comprises: an optical prism assembly, wherein the first non-polarizing beam- splitting surface, the second non-polarizing beam-splitting surface, and the polarizing beam-splitting surface are interior surfaces of the prism assembly; or a transparent plate with beam-splitting surface coatings comprising the first non-polarizing beam-splitting surface in a first region, the second non- polarizing beam-splitting surface in a second region, and the polarizing beam- splitting surface in a third region; or first and second transparent plates, the first transparent plate comprising parallel opposing first and second surfaces, the second transparent plate comprising parallel opposing third and fourth surfaces, the first surface comprising the first non-polarizing beam-splitting surface, the second surface comprising the second non-polarizing beam-splitting surface, the third surface comprising the polarizing beam-splitting surface, and the fourth surface comprising an antireflection coating.

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