Spatially multiplexed diffractive lens with extended depth of field via phase correction

Abstract

To introduce a phrase correction concept to improve performance of a spatially multiplexed optical system.SOLUTION: In a specific example, an optical system is a diffractive lens. A phase offset is added to extend the depth of field of the diffractive lens and increase its focusing intensity. This can result in increased signal-to-noise ratio. These diffractive lenses may be used for imaging, focusing, and / or delivering light to an area of interest. They may be used to realize a miniaturized medical image based on different imaging modalities such as optical coherence tomography, Raman spectroscopy, and fluorescence microscopy. They may also be used for different purposes and applications, for example laser ablation.SELECTED DRAWING: Figure 1A

Description

[Technical field]

[0001] The present disclosure relates generally to spatially multiplexed optical systems employing phase correction concepts, such as may be used in miniaturized optical imaging, illumination, and navigation systems. [Background technology]

[0002] Accurate diagnosis and treatment of diseases in internal organs such as the lung airways, coronary arteries, and gastrointestinal tract is challenging due to the lack of easy access to the affected areas. This is the main driving force behind the miniaturization of optical imaging, illumination (for therapeutic purposes), and navigation (to guide biopsy needles and surgical instruments) systems. Miniaturization often comes at the cost of reduced functionality. For example, it is difficult to cascade multiple components or incorporate electrical or mechanical actuators to achieve smaller form factor imaging systems. This limits the capabilities of the imaging system, such as the depth of field, which determines the signal-to-noise ratio in imaging applications.

[0003] Spatial multiplexing is an approach to multiplexing an optical element. In spatial multiplexing, different regions of the optical system are used for different functions. However, these can interfere with each other, reducing the overall performance of the optical system. Summary of the Invention [Means for solving the problem]

[0004] According to some embodiments, the concept of phase correction is introduced to improve the performance of spatially multiplexed optical systems. In a specific example, the optical system is a diffractive lens. A phase offset is added to increase the depth of field of the diffractive lens and to increase the light collection intensity. This can improve the signal-to-noise ratio. Such diffractive lenses can be used for imaging, light collection, and / or light illumination of an area of ​​interest. Diffractive lenses can be used to realize miniaturized medical imaging based on different imaging modalities such as optical coherence tomography, Raman spectroscopy, and fluorescence microscopy. They can also be used for various purposes and applications such as laser ablation.

[0005] In one aspect, a method for designing a spatially multiplexing optical system is implemented in a computer system. The optical system has two or more sub-apertures with corresponding optical functions. Complex amplitude profiles of the sub-apertures are determined based on the achievement of the corresponding optical functions of the sub-apertures. A merit function is selected. The function is indicative of the optical performance of the spatially multiplexing optical system. A constant phase offset is added to one or more of the complex amplitude profiles based on the improvement of the merit function.

[0006] In a particular example, the spatially multiplexing optical system is a multifocal lens, such as may be used in an endoscope. Sub-apertures of the multifocal lens focus at different focal points. The complex amplitude profile is a phase profile, and the phase profile of the sub-apertures is determined based on the focusing at different focal points. The merit function describes the focusing produced by the multifocal lens. For example, it may describe the depth of field of the focus or the strength of the focus.

[0007] Other aspects include components, devices, systems, improvements, methods, processes, applications, computer readable media, and other technologies relating to any of the above. [Brief description of the drawings]

[0008] The accompanying drawings presented in this disclosure constitute a part of this disclosure and illustrate different embodiments of the present invention. Furthermore, the drawings may include captions and / or text that may describe specific embodiments of the present disclosure. These texts and captions are included for non-limiting illustrative / illustrative purposes of the specific embodiments described in this disclosure.

[0009] [Figure 1A] FIG. 1 is a side view of a multifocal diffractive lens. [Figure 1B] FIG. 1B is a diagram showing spatial multiplexing of the multifocal diffractive lens of FIG. 1A. [Figure 2A] FIG. 1 is a side view of a bifocal highly diffractive lens. [Figure 2B] 1 is a plot of phase error as a function of phase offset C1. [Figure 2C] 1 is a two-dimensional map of phase error when phase offset C1 is the minimum phase error. [Figure 2D] 1 is a two-dimensional map of phase error when phase offset C1 is the maximum phase error. [Figure 2E] 2D intensity maps for different phase offsets C1. [Figure 2F] 13 is a plot of intensity as a function of axial position z for different phase offsets C1. [Figure 2G] 1 is a plot of normalized intensity integral and maximum intensity as a function of phase error. [Figure 3A] 1 is a plot of phase error as a function of phase offsets C1 and C3. [Figure 3B] 2D intensity maps for different phase offsets C1 and C3. [Figure 3C] 13 is a plot of intensity as a function of axial position z for different phase offsets C1 and C3. [Figure 3D] 1 is a plot of normalized intensity integral and maximum intensity as a function of phase error. [Figure 4A] FIG. 1 is a side view of a four-focal polarization dependent highly diffractive lens. [Figure 4B]2D intensity maps for different phase offsets C1 and C2. [Figure 4C] 1 is a plot of intensity as a function of axial position z. [Figure 5A] FIG. 1 is a side view of a reflective highly diffractive lens. [Figure 5B] This is a two-dimensional intensity map when the phase error is minimal. [Figure 5C] 2D intensity map without phase correction. [Figure 6A] FIG. 1 is a side view of a highly diffractive lens within a housing. [Figure 6B] 2D intensity maps for different phase offsets. [Figure 7] FIG. 1 illustrates the use of a highly diffractive lens in an endoscopic probe. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] The figures and the following description relate to preferred embodiments for illustrative purposes only. It should be noted from the following discussion that alternative embodiments of the structures and methods disclosed herein are readily recognized as viable alternatives that may be adopted without departing from the principles of what is claimed. Although embodiments of the present disclosure are more fully described below with reference to the accompanying drawings, alternative configurations and embodiments are also possible without departing from the scope of the present disclosure. Thus, the present disclosure should not be construed as being limited to the embodiments expressly set forth herein. Rather, the illustrated and described embodiments are provided as examples to convey the scope of the present disclosure to those skilled in the art. In the drawings, the sizes and relative sizes of layers and regions may be exaggerated for clarity.

[0011] In certain aspects, the spatially multiplexed optical system includes different sub-apertures. Each sub-aperture is designed for a different function. However, because the optical system is spatially multiplexed, the different sub-apertures may operate simultaneously and interfere with each other. In order to control the relative phase between the different sub-apertures with a controller, a phase offset is added to the sub-apertures. This can improve the interference effect between the different sub-apertures and improve the overall performance of the spatially multiplexed optical system.

[0012] The following disclosure begins with some specific examples of spatially multiplexing diffractive lenses, and then the principles are generalized to other types of spatially multiplexing optical systems and other types of functions of these optical systems.

[0013] (Highly diffractive lens that uses phase offset to extend depth of field (DOF)) FIG. 1A-B shows a point light source focused at multiple focal points F 1 , F 2 , ..., F m FIG. 1A shows a diffractive lens 100 that focuses light to a desired m-th focus. For the purposes of the phase concepts described herein, this is referred to as a highly diffractive lens (ADL). FIG. 1A shows the focusing geometry to multiple focuses. The phase profile that achieves diffraction-limited focusing at the desired m-th focus for a point source 103 is:

[0014]

number

[0015] Here, (x, y) are the plane coordinates on the ADL surface, λ is the wavelength, n is the refractive index of the medium, and z 0 is the reference position z 0 = 0, L is the distance between the point light source 103 and the center of the ADL, and f m is the m-th focal length. (x ps ,y ps ,z ps ) is the position of the point light source 103, (x fm ,y fm ,z fm) is the mth focal spot (F m ) position. In the case shown in FIG. 1A, for simplicity, the on-axis transmission ADL (x ps =y ps =x fm =y fm =0).

[0016] To generate multiple foci along the same axis as shown in FIG. 1A, the ADL required phase at each coordinate (x, y) is formulated as follows:

[0017]

number

[0018] where M is the total number of foci, φ m is the phase profile of the mth focus. Each phase profile φ m generates a spherical wave that is focused at the mth focus. m (x,y) is a binary matrix that implements spatial multiplexing, which assigns each ADL unit cell 102 (FIG. 1B) to a different focal spot.

[0019] FIG. 1B is a schematic diagram of the ADL 100 and its spatially multiplexed phase implementation. The aperture of the lens 100 is divided into M subapertures, each having a focal point F m In this example, the lens 100 is divided into an array of supercells 101. Each supercell has a focal point F 1 , F 2 , ..., F m φ corresponding to 1 , φ 2 , ..., φ m and a pattern of unit cells 102 including a phase profile of m The sub-aperture for the phase profile φ m A collection of unit cells 102 having a C mis a constant phase offset that is independent of different focal spots and can be set from -π to π. The constant phase offset does not affect the DOF of a single focal lens design, but it does affect the interaction from different subapertures in a spatially multiplexed design.

[0020] One of the factors that determines the diffraction of light along the focal axis is the phase mismatch error E m This is defined as follows:

[0021]

number

[0022] where φ(x,y) is the spatially multiplexed phase profile generated by all the subapertures, and φ m (x,y) is the ideal phase profile for focusing at the mth focal position in the absence of spatial multiplexing. E m (x,y) is the phase mismatch error profile for the mth phase specified at the mth focal position. Since the phase error is modulo 2π, the phase error is defined as the absolute value of the minimum phase difference. For example, a phase difference of -0.1π is not a phase error of -0.1π or +1.9π, but a phase error of |-0.1π|=+0.1π. To quantify the total error, the phase error mismatch can be evaluated for all desired phases defined as errors.

[0023]

number

[0024] Different phase φ m For (x,y) the phase constant C m By choosing the value of , we can design the evolution of the diffraction profile of the light along the optical axis and significantly increase the DOF and intensity of the focal spot, both of which improve the imaging performance. In the following example, the error E mean Based on the reduction in C mBy appropriately setting , longer degrees of freedom and higher integrated intensity are achieved. Other merit functions describing the light collection by a multifocal lens can also be used, such as the Strehl ratio and / or the Modulation Transfer Function (MTF).

[0025] (Bifocal transmissive highly diffractive lens) Consider a two-focal ADL. The multiple phases of the ADL are as follows:

[0026]

number

[0027] And the phase error is defined as follows:

[0028]

number

[0029] Here, A 1 (x,y) and A 2 (x,y) is a binary matrix, and C 1 and C. 2 is the error E mean is a constant phase offset that is adjusted from -π to π to minimize and extend the DOF. Without loss of generality, C 2 =0.

[0030] 2A-F show the case of a bifocal ADL with extended DOF. As shown in FIG. 2A, the ADL 200 focuses light from a point source 203 into two focal spots F with focal lengths of 1.5 mm and 2 mm, respectively. 1 and F 2 Here, the two desired phases are multiplexed. The ADL has the supercell / unit cell structure of Figure 1B. The supercell has two unit cells. Each unit cell is designed to focus the light to a corresponding focused spot. One unit cell (unit cell #1) is F 1 The other unit cell #2 is F 2The error comes from the unit cells not being designed for the other focal spot. For example, unit cell #1 is F 1 It is designed to focus the light at F 2 The phase of unit cell #1 and the phase of F 2 The difference between the phase required for focusing on the target and the phase error is the phase error.

[0031] Figure 2B shows the phase offset C 1 Phase error E as a function of mean This is a plot of the phase offset C 1 By adjusting E mean Using equation (1), we calculate the phase required for the dual-focal ADL200 for both focal spots, C 1 E as a function of mean Since point 212 is a situation where no phase offset is introduced, C 1 = 0. Point 214 is the point of maximum phase error and point 216 is the point of minimum phase error. As shown in FIG. 2B, at point 216, the phase offset C 1 If we set it to 2.136, the error E mean can be minimized.

[0032] FIG. 2C is a two-dimensional map of the phase error. The top left of FIG. 2C and the top right of FIG. 2C are C 1 Phase error map of the ADL200 at E = 2.136 1 and E 2 This is point 216 in FIG. 2B, where the phase error is minimized. 1 The checkerboard pattern is the result of spatial multiplexing. The phase error E m is zero. Only the other unit cells have non-zero phase errors. In this example, M=2, resulting in a checkerboard pattern. 1 = 2.136 (minimum phase error), C in the lower right of Figure 2C 1 = 2.136 (no phase correction, reference) mean) are shown.

[0033] Figure 2D shows the same phase map, but with 1 =-1.005 (point 214 in FIG. 2B). mean C where is the maximum 1 The value of the constant C 1 By appropriately adjusting = 2.136, the average phase error (E mean ) decreases. There is a big difference between the phase error maps in the lower left of Figure 2C and the lower left of Figure 2D.

[0034] To further evaluate the effectiveness of this phase correction method, 1 We calculate the point spread function (using scalar diffraction theory) of the ADL with different values ​​of E. mean = 1.29 minimum, no phase correction (E mean =171), E mean = 1.844, which corresponds to the maximum value of C 1 4 shows the point spread functions of ADL200A, ADL200B, and ADL200C with phase offsets equal to 2.136, 0, and −1.005, respectively. mean The DOF with the smallest phase offset (Figure 2E, top) shows a continuous electric field distribution with enhanced intensity along the optical axis. The DOFs for the other phase offsets are much worse.

[0035] FIG. 2F plots the intensity along the z-axis at (x,y)=(0,0) for the same phase offsets shown in FIG. 2E. As shown in FIG. 2F, E mean Optimized ADL200A(C 1 = 2.136), when no phase correction is performed (C 1 =0), the maximum strength increases by 1.5 times and the DOF increases by 3.9 times.

[0036] To better understand how the phase error contributes to the DOF, we calculate the relationship between the light distribution along the z-axis (x = 0) and the phase error. Figure 2G shows the phase offset C 1Various intensity measurements are plotted as a function of phase error for different values ​​of . The y-axis on the left is the normalized intensity integral along the z-axis, plotted with circles. This intensity metric shows the expansion of the DOF along the propagation direction. The y-axis on the right is the highest intensity along the z-axis, plotted with stars. This intensity metric shows the confinement of the focus along the principal axis. By minimizing the phase error, the normalized intensity integral can be increased by 50%, improving the highest intensity by a factor of 2 compared to the maximum phase error.

[0037] (Trifocal transmissive highly diffractive lens) For a trifocal design, the spatial multiplexing phase of the ADL is:

[0038]

number

[0039] Here, A 1 , A 2 , A 3 is a binary matrix, and C 1 and C. 3 can be independently adjusted in the range of -π to π. For simplicity, 2 = 0. φ 1 , φ 2 , φ 3 f 1 <f 2 <f 3 In this case, the focal length is assigned according to the following: Since the continuity of DOF is the most important, only the phase error between two adjacent foci is considered. That is, φ 1 and φ 2 Between and φ 2 and φ 3 (φ 1 and φ 3 Therefore, we divide the phase error into two parts and use the phase offset C 1 and C. 3 can be optimized individually.

[0040]

number

[0041] C 1 (C 3 ) can be adjusted appropriately to mean,1 (E mean,2 ) and minimize f 1 and f 2 (f 2 and f 3 ) can be optimized.

[0042] Figure 3A-D shows the design of the three-focal ADL (f 1 = 1.2 mm, f 2 = 1.5 mm, f 3 = 2.0 mm), where f 1 and f 2 , and f 2 and f 3 Figure 3A shows how the phase error of both C(C 1 Or C 3 Average total phase error (E mean ) plot. The solid line is the 1 Phase error E as a function of mean,1 3. Points 312, 314, and 316 are points of no phase offset, maximum phase error, and minimum phase error, respectively. The dotted lines indicate 3 Phase error E as a function of mean,2 3 is a plot of the phase offset, maximum phase error, and minimum phase error, respectively.

[0043] Figure 3B shows the minimum E mean , no phase correction, max E mean 10A, 10B, and 10C are 2D intensity maps showing the point spread functions of ADL300A, ADL300B, and ADL300C, respectively, where the minimum E mean is the minimum E mean,1 and minimum E mean,2 Both are the minimum E meanThe point spread function of the ADL300A in (top of FIG. 3B) shows a continuous electric field distribution (long DOF) with enhanced intensity along the optical axis compared to the other cases (middle and bottom of FIG. 3B). For the optimized ADL300A, E mean is minimized, so without phase correction (C 1 =C 3 = 0), the DOF increases by about four times.

[0044] Figure 3C plots the intensity along the z-axis for (x,y)=(0,0) for the same case as in Figure 3B, highlighting how minimizing the phase error can extend the DOF and increase the maximum intensity.

[0045] To better understand how the phase error contributes to the DOF, we plotted the light distribution along the z-axis (x = 0) versus the phase error (E mean,1 +E mean,2 ) relationship. The left y-axis is the normalized intensity integral along the z-axis, plotted with circles. The right y-axis is the maximum intensity along the z-axis, plotted with stars. By minimizing the phase error, the normalized intensity integral can be increased by a factor of 3.33 and the maximum intensity can be increased by a factor of 2.7 compared to the case with maximum phase error.

[0046] So far, we have demonstrated that in the bifocal and trifocal cases, a smaller phase error results in more concentrated light along the main optical axis, resulting in higher maximum intensity and longer DOF. This method can also be extended to increase the number of foci to M>3. The focal length f 1 <f 2 <f 3 <... <f M Then, equation (9) holds.

[0047]

number

[0048] Here, each Cm can be optimized to minimize each Emean,m (1 ≤ m ≤ M-1) and obtain the desired depth of focus. In this approach, only adjacent foci are considered so that each phase offset Cm can be optimized individually. Alternatively, multiple foci can be considered and the phase offsets Cm can be optimized together, not just adjacent foci.

[0049] (4-focal transmissive highly diffractive lens with multiple polarization) Spatial multiplexing is one method to increase the number of focal points in the design of an ADL. It is also possible to combine other multiplexing techniques with spatial multiplexing. The following example shows a 4-focal polarization-dependent highly diffractive lens (PADL) design with extended DOF, combining polarization multiplexing (2 channels) and bifocal spatial multiplexing (2 channels). The schematic design of the 4-focal PADL is shown in Figure 4A. When the input light is TE (TM) polarized, f 1 and f 2 (f 3 and f 4 ) has a spatially multiplexed phase distribution. The spatially multiplexed phase of each polarization is as follows:

[0050]

number

[0051] Here, A j (x,y) is a binary matrix that implements spatial multiplexing. In this example, the TE focal length f 1 and TM focal length f 3 share the same subaperture and have a TE focal length f 3 and TM focal length f 4 The focal point f 2 and f 4 The phase offset of is set to zero. The remaining phase offset C 1 and C. 2can be individually optimized to minimize the phase error. Because the diffracted light intensities from the TE and TM are independent, the two intensities can be simply added together to quantify the light intensity in the propagation axis.

[0052]

number

[0053] where |E| is the amplitude of the light field, not the phase error. By using a polarization-dependent subwavelength phase shifter as a unit cell and independently designing the phase structures for TE and TM polarizations, we can design a PADL.

[0054] FIG. 4B is a two-dimensional intensity map of the four-focal PADL design. As shown at the top of FIG. 4B, a constant phase offset (C 1 =C 2 =2.0944) is optimized to obtain the result without phase correction (C 1 =C 2 = 0) (Figure 4B, bottom), not only can the DOF be expanded but also the strength can be improved.

[0055] Figure 4C shows the intensity distribution along the z-axis (x,y = 0). The top of Figure 4C shows the intensity distribution of a tetrafocal PADL, and the bottom of Figure 4C shows the intensity distribution of four monofocal lenses with different focal lengths for comparison. It is noteworthy that the DOF is expanded in the case of the PADL compared to the monofocal lens design. Monofocal lenses have a limited DOF limited by their numerical aperture.

[0056] (Bifocal reflective highly diffractive lens) As another example, in this section, we designed an off-axis reflective ADL 500 as shown in FIG. ps ,y ps ,z ps ) and the focal position (x fm ,y fm ,z fm) should be entered as follows:

[0057]

number

[0058] where L is the distance between the light point source 503 and the center (0,0,0) of the ADL 500, and α is the tilt angle of the ADL, as shown in FIG. 5A. Here we consider α=42.5°, but it can be any value without changing the approach. After calculating the phase φm for each focal point m, we follow the same approach as described above (expanding the DOF and increasing the collected light intensity) to optimize the performance of the ADL.

[0059] Figure 5B-C shows the reflective bifocal ADL (f 1 = 1.5mm and f 2 5C. Two-dimensional intensity maps of the ADL with minimized phase error in the x'z plane (left in FIG. 5B) and yz plane (right in FIG. 5B), where the x'z plane is the xz plane that intersects the optical axis of the ADL 500. Similarly, the point spread function of the ADL without phase correction is shown for the x'z plane (left in FIG. 5C) and yz plane (right in FIG. 5C). Comparing FIG. 5B and FIG. 5C, the phase correction approach increases the DOF by a factor of 2.4 and the maximum intensity by 72%.

[0060] (4-focal transmissive highly diffractive lens covered with flexible tube) Imaging systems may be enclosed in a housing in medical applications to keep them clean or to avoid contact with tissue. Figure 6A shows the ADL 600 placed in a housing 610, such as a plastic tube. The tube is cylindrical. Figure 6A shows a cross section. The rectangles at the top and bottom of Figure 6A are the walls of the cylinder. Mirror 620 reflects the light (received from point source 603) towards the ADL 600. Thus, the ADL 600 now focuses the light radially. The mirror itself is mounted on a holder 622. The ADL 600 and substrate 601 are also mounted on the holder 622. The quad-focal ADL 600 has four foci (F 1 , F 2 , F 3 ) with working distances of 0.4 mm, 0.6 mm, 1 mm, and 1.5 mm, respectively. 1 -F 4 The working distance is defined as the distance from the focal point to the outer surface of the plastic tube (the outer surface of the tube faces the focal point).

[0061] Figure 6B shows the point spread functions of three ADL designs with minimum phase error (left in Figure 6B), no phase correction (middle in Figure 6B), and maximum phase error (right in Figure 6B). By minimizing the phase error, the DOF can be increased by a factor of 3.5 compared to the case without phase correction.

[0062] Figure 7 shows one example of how an ADL can be used to construct an endoscopic probe 750. Figure 7 shows a cross section of the tip region of the probe. The outer portion 710 comprises a tube. Inside the probe, a fiber 702 is connected to a ferrule 704. The ADL 700 is attached to the ferrule by a holder 701. The components are surrounded by a tube 710. The tube can be plastic, polymer, glass, or other flexible or rigid material.

[0063] Other examples of endoscopic equipment suitable for use with ADL are described in U.S. Patent Application No. 18 / 269709, entitled "Methods and Systems for Multi-Functional Miniaturized Endoscopic Imaging and Illumination," filed December 27, 2021, and International Patent Application No. PCT / US2022 / 029301, entitled "Methods and Apparatus for Reconfigurable Optical Endoscopic Catheter," filed May 13, 2022, both of which are incorporated by reference in their entireties.

[0064] Although the detailed description contains many specific examples, these should not be construed as limiting the scope of the invention, but merely as illustrating different examples, and it should be understood that the scope of the disclosure includes other embodiments not described in detail above.

[0065] For example, an embodiment may include two or more ADLs. In some cases, two ADLs provide additional degrees of freedom to reduce phase errors. ADLs may be stacked on top of one another with space between them. ADLs may also be cascaded with other optical components such as polarizers and color / spectral filters to add functionality to the system such as polarization resolved imaging or hyperspectral imaging. ADLs may also be used with other light gathering components such as reflective lenses or liquid crystals. Some instruments may also use multiple fibers. One fiber may deliver light to the site (e.g., tissue) and another fiber may collect light from the site.

[0066] The concepts of phase correction described herein can be applied beyond lenses and focusing. For example, spatially multiplexing optics can be designed for other purposes or to achieve other wavefront shaping, such as the generation of Bessel beams. In such cases, the effect of different sub-apertures in a spatially multiplexing optic can be modeled using a complex amplitude profile, which includes amplitude effects in addition to phase effects. Adding a constant phase offset does not change the optical function of the individual sub-apertures, but can be used to control the interference between different sub-apertures.

[0067] Various other modifications, changes, and variations in the arrangement, operation, and details of the methods and apparatus disclosed herein, which are apparent to those skilled in the art, may be made without departing from the spirit and scope as defined in the appended claims. Accordingly, the scope of the present invention should be determined by the appended claims and their legal equivalents.

Claims

1. 1. A method implemented on a computer system for designing a spatially multiplexed optical system having two or more sub-apertures with corresponding optical functions, comprising: determining a complex amplitude profile of the subaperture based on achieving the corresponding optical function for the subaperture; selecting a merit function indicative of the optical performance of the spatial multiplexing optical system; adding a constant phase offset to one or more of the complex amplitude profiles based on an improvement of the merit function; A method comprising:

2. the spatially multiplying optical system is a multifocal lens, the sub-apertures of the multifocal lens focusing light at different focal points; the complex amplitude profile is a phase profile, and determining the phase profile for the subaperture is based on focusing the light onto the different focal points; The merit function describes the concentration of light produced by the multifocal lens. The method of claim 1.

3. 3. The method of claim 2, wherein the merit function comprises a phase mismatch error between (a) a phase profile for focusing light at a focal point for one of the subapertures and (b) a phase profile produced by a different subaperture.

4. The method of claim 2 , wherein the multifocal lens has three or more sub-apertures that focus at different focal points, and the merit function includes only phase mismatch errors between sub-apertures at adjacent focal points.

5. The method of claim 2 , wherein the multifocal lens has M sub-apertures that focus light at different focal points, and a constant phase offset is added to (M−1) of the phase profiles.

6. The method of claim 2 , wherein the merit function is a measure of the depth of field of the multifocal lens.

7. The method of claim 2 , wherein the phase profile for the sub-apertures produces spherical waves that focus at the different focal points.

8. 3. The method of claim 2, wherein the multifocal lens has M subapertures that focus light to different focal points, and the multifocal lens comprises an array of supercells, each supercell comprising the same pattern of M unit cells, one unit cell for each of the M subapertures.

9. The method of claim 2 , wherein the multifocal lens is polarization multiplexed, and sub-apertures of the multifocal lens focus light of different polarizations to different focal points.

10. A spatially multiplexed multifocal optical system having two or more sub-apertures that focus light at different focal points, the sub-apertures being characterized by phase profiles determined by the focal points, at least one phase profile including a constant phase offset that improves the multifocal performance of the multifocal optical system.

11. The multifocal optical system of claim 10 , wherein the multifocal optical system is polarization multiplexed.

12. The multifocal optical system of claim 10 , wherein the multifocal optical system is a reflective lens.

13. The multifocal optical system of claim 10 , wherein the multifocal optical system is a diffractive lens.

14. The multifocal optical system of claim 10 , wherein the multifocal optical system has a longer depth of field compared to when the constant phase offset is zero.

15. The multifocal optical system of claim 10 , wherein the multifocal optical system has a higher normalized intensity integral compared to when the constant phase offset is zero.

16. The multifocal optical system of claim 10 , wherein the multifocal optical system has a higher maximum intensity compared to when the constant phase offset is zero.

17. 1. An optical system for an endoscope, comprising: a substrate having at least one planar surface; an input aperture configured to receive light from an optical fiber within the endoscope, the received light propagating along an axial direction of the substrate; and an optical routing structure comprising at least one flat optical component supported by the planar surface of the substrate; A spatially multiplexed multifocal lens with two or more sub-apertures focusing at different focal points, the sub-apertures being characterized by phase profiles determined by the focal points, at least one phase profile including a constant phase offset that improves the multifocal performance of the multifocal lens; An optical system comprising:

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