Efficient Reading of Birefringence Data

Abstract

One example provides a system (800) for reading birefringence data. The system includes one or more light sources (802, 804), a first polarization state generator (808) positioned to generate a first polarization from light of a first wavelength band output by the one or more light sources, a second polarization state generator (810) positioned to generate a second polarization from light of a second wavelength band output by the one or more light sources, an image sensor (822) configured to acquire images of a sample area (814) via the first polarization and the second polarization, a polarization state analyzer (824) positioned between the sample area and the image sensor, a first bandpass filter configured to pass light of the first wavelength band to reach the image sensor, and a second bandpass filter configured to pass light of the second wavelength band to reach the image sensor.

Description

Background Art

[0001] Background

[0001] Over the past decade, the majority of the world's data has moved to the cloud. To meet the increasing demand, cloud providers rely on various data storage technologies. These storage technologies include non-volatile memory (NVM), flash, hard disk drives (HDDs), magnetic tapes, and optical disks. These storage technologies differ from each other in terms of cost, latency, throughput, storage density, failure rate, and media lifespan.

Summary of the Invention

[0002] Summary

[0002] This summary is provided to introduce various concepts in a simplified form, and further explanations are provided in the following detailed description. This summary is not intended to identify the key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. Moreover, the claimed subject matter is not limited to implementations that solve any or all of the disadvantages described in any part of this disclosure.

[0003]

[0003] A promising technique for storing data is to encode the data as local birefringence voxels in a dielectric memory medium. Such data can be stored at high density, and the memory medium can have a long lifespan compared to magnetic and other memory media. However, reading the local birefringence to decode the data involves performing a number of optical measurements in different polarization states. Each additional measurement increases the time required to read the medium. Thus, aspects of the techniques disclosed herein are useful in reducing the time utilized to read data stored as local birefringence.

[0004]

[0004] One aspect provides a system for reading birefringence data. The system includes one or more light sources, a first polarization state generator positioned to generate a first polarization from light in a first wavelength band output by the one or more light sources, a second polarization state generator positioned to generate a second polarization from light in a second wavelength band output by the one or more light sources, an image sensor configured to acquire an image of a sample region through which the first polarization and the second polarization pass, a polarization state analyzer optically disposed between the sample region and the image sensor, a first bandpass filter optically disposed between the polarization state analyzer and the image sensor and configured to pass light in the first wavelength band, and a second bandpass filter optically disposed between the polarization state analyzer and the image sensor and configured to pass light in the second wavelength band. In some examples, three or more polarization state generators can be used to generate three or more different polarization states using light in three or more wavelength bands, and three or more corresponding bandpass filters can be used between the polarization state analyzer and the image sensor. Using this aspect, multiple wavelength multiplexed measurements of voxels can be performed in a temporally overlapping manner, thereby reducing the amount of time utilized for reading birefringence data compared to the use of sequential measurements without wavelength multiplexing.

[0005]

[0005] Another aspect provides a method that includes inducing light including one or more predetermined polarization states through a birefringent voxel on a computing device and receiving the light at an image sensor to obtain measurement data for the birefringent voxel; determining, based on the measurement data, two points on the surface of the Poincaré sphere corresponding to two possible birefringent states of the birefringent voxel, each state including a respective set of birefringence values including an azimuth angle and a retardance; applying constraints to determine the azimuth angle and the retardance; and outputting the determined birefringence values including the determined azimuth angle and retardance. Using this aspect, by applying constraints to determine the azimuth angle and the retardance, the birefringence values of the voxel can be determined with fewer measurements than would be possible without the application of the constraints.

Brief Description of the Drawings

[0006] Brief Description of the Drawings

Figure 1

[0006] Schematically shows the reading of a birefringent voxel of a storage medium.

Figure 2

[0007] Shows a schematic depiction of a storage medium including data encoded as a birefringent voxel.

Figure 3

[0008] Shows a Poincaré sphere representing polarization states as locations on the sphere.

Figure 4

[0009] Shows a flowchart depicting an exemplary method for determining birefringence values based on a maximum value determined for a likelihood function.

Figure 5

[0010] Shows examples of polarization states for measuring birefringence values.

Figure 6

[0011] Shows exemplary solutions for birefringence values based on two measurements and based on one measurement.

Figure 7

[0012] Shows a flowchart depicting an exemplary method for obtaining birefringence measurements using wavelength multiplexing.

Figure 8

[0013] A block diagram of an exemplary system for reading birefringence data using wavelength multiplexing is shown.

Figure 9

[0014] An exemplary system for wavelength multiplexing light of different polarization states using light from the same image source is shown.

Figure 10A

[0015] A flowchart depicting an exemplary method for measuring birefringent voxels via wavelength multiplexing is shown.

Figure 10B

[0015] A flowchart depicting an exemplary method for measuring birefringent voxels via wavelength multiplexing is shown.

Figure 11

[0016] A flowchart depicting an exemplary method for performing background correction on birefringence values is shown.

Figure 12

[0017] A block diagram of an exemplary computing system is shown.

Best Mode for Carrying Out the Invention

[0007] Detailed Description

[0018] As mentioned above, one promising technology for cloud data storage involves the use of high-power short-pulse laser irradiation to optically write data onto a dielectric solid substrate such as glass. The irradiation induces local birefringence at its focus that can later be read using polarization imaging. The term "voxel" is used herein to refer to any discrete volume of the substrate that can store an individual data value (i.e., symbol). The data stored in a voxel can take various forms. In principle, any of the Mueller matrix coefficients of the substrate lattice can be manipulated to encode data. In an example using a fused silica substrate, the lattice perturbation from focused polarized irradiation takes the form of non-natural birefringence localized at the focus. Accordingly, each voxel of the substrate can be modeled as a very small waveplate having a retardance magnitude and azimuth angle. These model parameters can be independently manipulated to write a desired symbol to a given voxel. Here, the polarization angle of the beam determines the azimuth angle of the voxel, and various other factors (pulse amplitude, duration, energy, number and / or spacing between pulses) determine the retardance of the voxel.

[0008]

[0019] By dividing the continuous space of achievable azimuth angles and / or retardance magnitudes into discrete intervals and writing the birefringence of that voxel into one of the discrete intervals, multi-bit data values can be encoded and embedded in each voxel. Further, in some examples, multiple parallel layers of voxel structures can be written to the same substrate by focusing the laser irradiation at a specified depth below the irradiated surface of the substrate. These features allow large amounts of data to be written to a single medium, either individually or in combination. In some examples, the storage medium includes a solid plate-like configuration. In other examples, the storage medium includes a thin layer formed on another substrate. In further examples, the storage medium can have any other suitable configuration, such as a prism or cylinder.

[0009]

[0020] Birefringent voxels behave anisotropically when light passes through them because different polarization states of light travel through the sample at different speeds. When light travels through or is reflected off a birefringent voxel, its polarization state changes in a specific way that depends on the azimuthal angle and retardance of the sample. Therefore, information about the azimuthal angle and retardance of a voxel can be obtained by measuring the polarization state of polarized light that has interacted with the birefringent voxel.

[0010]

[0021] Some methods for measuring the polarization state (and thus the angle and retardance of a voxel) involve performing a series of measurements using different input or output (or both) polarizations. Figure 1 shows a schematic of reading birefringence data stored in a storage medium 100. Light from a light source 102 passes through a polarization state generator (PSG) 104, which outputs polarized light with a polarization angle determined by the PSG. The light source may include an LED, a laser, or other light source.

[0011]

[0022] After passing through storage medium 100, the light from light source 102 and PSG 104 passes through one or more voxels of storage medium 105, passes through polarization state analyzer (PSA) 106, and then reaches detector 108. The settings of PSA 106 and PSG 104 determine the intensity m of the measurements, as described in more detail below. k defines a polarization state k for . Detector 108 may include, for example, a CMOS image sensor (e.g., a high resolution / high frame rate sensor) or other suitable photodetector array capable of imaging an entire focal plane positioned within storage medium 105, thereby imaging a large number of arranged voxels into the same image. In other examples, a point detector or small detector array, such as, for example, a photodiode, phototransistor, or SPAD (single photon avalanche diode), may be used to build up an image point by point). While FIG. 1 shows light rays passing through the storage medium to reach the image sensor, in other examples, light rays may reflect off the storage medium to reach the image sensor.

[0012]

[0023] In an example where data is read from multiple layers of the memory medium 105, the variable focus optical system 110 can be used to adjust the focal plane of the detector 108 so that the voxels in the focal plane are read while the other voxels are out of focus. In other examples, changing the focus can be achieved by moving the sample. FIG. 2 schematically shows an exemplary memory medium 200 including voxels of multiple layers, two of which are indicated at 202 and 204.

[0013]

[0024] To explain the voxel measurements being performed, a commonly used structure is the Poincaré sphere shown at 300 in FIG. 3. The Poincaré sphere 300 is used to represent the polarization state of light by mapping the last three components of the 4D Stokes vector to a 3D Cartesian coordinate system. In the case of complete polarization, a particular measurement state is explained by a particular position on the surface of the sphere, which represents a particular polarization state of the light. Partial polarization is represented by a point inside the surface of the Poincaré sphere. The north pole represents RCP (right circular polarization). The south pole represents LCP (left circular polarization). The states on the equator are linearly polarized with an angle defined by the azimuth angle on the sphere. A general point on the sphere is elliptically polarized with an ellipticity determined by the angle between that state and the poles and an azimuth angle defined by the angle around the sphere. An exemplary polarization state is shown at 302 on the sphere. The black dashed curve is a circle of constant latitude and thus of constant retardance. The term "swing" refers to the angle 304 of the measurement state with respect to the poles of the sphere. The horizontal angle is the azimuth angle 306. The azimuth angle and retardance of the voxel can also be represented as a point on the surface of the sphere, as they result in the output state of the polarization of the probe light.

[0014]

[0025] Current methods for determining the birefringence value for voxels of a memory medium involve three or more (typically four) measurements of the voxels performed with different polarization states of the probe light. The multiple measurements are used because four degrees of freedom (voxel retardance, voxel azimuth, measurement scale, and measurement offset) are required for the determination. The four-measurement method determines all of these four values for each read process. Shribak and Oldenbourg (M. Shribak and R. Oldenbourg, “Techniques for Fast and Sensitive Measurements of Two-Dimensional Birefringence Distributions” in Applied Optics, Volume 42, Issue 16, 2003, published by the Optical Society of America (see also https: / / www.osapublishing.org / ao / abstract.cfm?uri=ao-42-16-3009 and https: / / doi.org / 10.1364 / AO.42.003009)) have described a three-measurement method that assumes the offset is zero and solves for the other three parameters through three measurements. However, the use of three or four measurements affects the speed at which data can be retrieved from the memory device due to the number of measurements being made.

[0015]

[0026] Accordingly, disclosed herein is an exemplary measurement process that can be used to determine the azimuth angle and retardance value for a birefringent voxel using fewer than three measurements. Briefly, the disclosed method takes advantage of constraints on the retardance value based on prior knowledge of the retardance so that the retardance and azimuth angle values can be determined with two measurements or even one measurement. Also, the disclosed method can be used with three measurements and offers advantages over previous three-measurement methods, such as the advantage that it is not necessary to assume the offset is zero as long as it is known before the measurement, and the advantage that relative retardance and angles can be determined. Since the scale and offset do not vary much spatially or temporally in the context of reading data encoded as birefringence in a memory medium, the scale and offset can be determined once or periodically using four (or more) measurement techniques, and then the determined scale and offset values can be used for subsequent retardance and angle determinations using fewer than four measurements. Further, as will be described below, the scale and offset can be determined via numerical optimization techniques when unknown.

[0016]

[0027] FIG. 4 shows a flowchart illustrating an exemplary method 400 for determining a birefringence value. Method 400 is an example of a technique that can be used to determine scale and offset values for use in subsequent determinations using a smaller number of measurements, and offers an advantage over current methods in that determinations can be made using any probe light polarization state rather than a given state that is difficult to implement with physical devices. Method 400 first includes, at 402, obtaining four or more measurements of the voxel in different polarization states, where each measurement value is the observed intensity m at a measurement state k defined by a measurement polarization state having a swing χ k and an angle θ k . kincludes. Method 400 further includes, at 404, determining a likelihood function for the measured values of the voxels, where the likelihood function represents the likelihood of the measured values of the voxels generated by each set of birefringence values for a number of sets of birefringence values. The likelihood is determined as a function of the angle and retardance using assumptions of the noise model and the data model. Any suitable data model and noise model can be used, including Gaussian, Poisson, and combinations of Gaussian and Poisson. As an example, using a Gaussian noise model (shown at 406), given the measurement state k, the likelihood for measuring the intensity m k is given by Equation (1). [Number] In Equation (1), I k = a(1 - cosχ k cosδ + sinχ k sinδ sin(2φ - 2θ)) + b, where I k is the expected measured value taken for the polarization state k, δ is the sample retardance, φ is the sample angle, a is the scale parameter, b is the offset, and σ is the noise. The term "set of birefringence values" refers to a set of values of {a, b, δ, φ}. Using this representation, the likelihood function for determining the likelihood of the set of measured values is [Number] and thus [Number] can be expressed as. L is computed for a number of sets of birefringence values, and as shown at 408, a maximum value is determined for the likelihood function. Then, at 410, using the maximum value of the likelihood function, the most probable set of birefringence values for the set of measured values of the voxels is determined based on the set that produced the maximum determined value. This can be mathematically expressed as Equation (2). {a, b, δ, φ} = argmax(L(a, b, δ, φ)) (2)

[0017]

[0028] The determined scale and offset can be used in a determination using three or fewer measurements. It should be understood that the term "maximum determined value" and similar terms used herein are not intended to indicate the actual global maximum of the likelihood function, but rather are intended to represent the maximum observed value for all parameter sets utilized. Further, in other examples, it will be understood that any other suitable method can be used to determine the birefringence value including the scale and offset. For example, according to Bayes' theorem, it is also possible to include prior knowledge about the angle or retardance distribution, and instead of calculating the likelihood of the parameters, the posterior probability can be calculated. In this case, the values of the parameters that maximize the posterior probability (which is often called MAP (maximum a posteriori)) can be found. In such examples, the parameter values can be determined, for example, by finding the expected value of the posterior probability or by using other statistical measures.

[0018]

[0029] As mentioned above, the advantage provided by the use of the maximum likelihood determination method for determining the birefringence value for a voxel is that the polarization state used for the measurement is arbitrary rather than being a predefined one. Nevertheless, in some examples, some configurations of the polarization state can provide a more effective use of the available signal than other configurations. Two examples of such configurations are as follows. Referring again to the Poincaré sphere of FIG. 3, a first example of a set of polarization states for determining the birefringence value for a voxel includes a circularly polarized input state (such as set by the PSG) having a certain chirality and an elliptically polarized output state (such as set by the PSA) having a chirality opposite to that of the input state, having equal ellipticity with each other, but having equally spaced varying azimuth angles over half or the whole of a circle at equal latitudes on the Poincaré sphere, such as {0, 45, 90, 135} degrees or {0, 22.5, 45, 67.5} degrees. A second example of a set of polarization states includes a circularly polarized output state having a certain chirality and an elliptically polarized input state having a chirality opposite to that of the output state, having equal ellipticity with each other, but having a varying azimuth angle, and the azimuth angles are equally spaced over half or the whole of a circle on the surface of the Poincaré sphere. FIG. 5 depicts examples of such three polarization state configurations, and each configuration is indicated by having a symbol different from other configurations. In FIG. 5, the view of the Poincaré sphere is along the polar axis of the sphere, the dashed circles correspond to the selected latitudes including the polarization states, and the outer boundary line corresponds to the equator of the sphere.

[0019]

[0030] When the measurement is configured in this way, the azimuth angle of the voxel can be determined as follows.

Number

[0020]

[0031] Here, φ is the measurement angle, the subscript k indicates the number of measurements, m k is the intensity of the k-th measurement, 2θ kis the angle of the k-th measurement state on the Poincaré sphere. To find the retardance, one appropriate method involves numerically optimizing the likelihood of the data given the measurements, as described above with respect to FIG. 4.

[0021]

[0032] As mentioned above, prior knowledge of the scale and offset parameters can be used to reduce the number of measurements to determine the azimuth angle and retardance of the voxel. For example, the azimuth angle of the voxel can be determined by using Equation (4) in addition to three measurements and using a known offset value.

Number

[0022]

[0033] If some prior information about the retardance is known but the retardance value itself is not known, a two-measurement method can be used to determine the birefringence value of the voxel. In some examples, the two-measurement method also utilizes prior knowledge of the scale and offset, while in other examples, the scale and offset are determined by numerical optimization as mentioned above.

[0023]

[0034] When using two measurements, even if one has knowledge of the offset and scale, there are two possible solutions for the sample retardance and angle. This is because each measurement restricts the solution to lie on a 2D plane of the 3D space of the Poincaré sphere. Thus, two measurements define a line in 3D. FIG. 6 shows an example of a two-measurement determination for a hypothetical voxel on the Poincaré sphere 602. In this example, the line 604 defined by the two measurements of the voxel intersects the surface of the sphere at two points 606, 608.

[0024]

[0035] To determine which of the two points corresponds to the actual birefringence value of the measured voxel, a constraint is applied to select the point with the lower retardance as corresponding to the state of the voxel. This is because it can be mathematically shown that the other solution is at least approximately the same magnitude as the effective retardance of the measurement state. For example, considering the two measurements on the Poincaré sphere 602, since point 606 represents a lower retardance value than point 608, point 606 will be selected. This constraint based on prior information can be used in any system where it is known that the effective measurement retardance is different (greater or smaller) from the measurement retardance. This constraint narrows down the solution to one point on the sphere, thereby enabling the determination of the sample retardance and azimuth angle.

[0025]

[0036] A more detailed mathematical explanation of the exemplary two-measurement method is as follows. Note that the method can be performed by using the scale and offset values initially determined using more (e.g., four) measurements and then applying them to the two-measurement determination, or by determining the scale and offset values using a numerical optimization method. When the scale and offset values are determined first, any suitable method, including the maximum likelihood example described above with respect to FIG. 4, can be used to determine these parameters.

[0026]

[0037] After obtaining the measured values, an exemplary two-measurement method involves first solving the following set of simultaneous equations (5, 6, 7) for the retardance δ. m1 = a(1 - cosχ1cosδ + sinχ1sinδsin(2φ - 2θ1)) + b (5) m2 = a(1 - cosχ2cosδ + sinχ2sinδsin(2φ - 2θ2)) + b (6) (sinδsin(2φ - 2θ1)) 2 +(sinδsin(2φ - 2θ2)) 2 +cos 2 δ = 1 (7) Since there are two possible solutions for δ, the smaller value is selected as described above. Next, using equation (8),

Number

Number

[0027]

[0038] If known values of scale and offset are used in this determination, the determination is complete at this stage. On the other hand, if assumed scale and offset values are used, a and b can be adjusted using prior information. For example, if the angular distribution is uniform (such as in the case of birefringence data when the data writing process is known), the angular distribution can be calculated, and equations (5) - (7), (8) can be repeatedly determined while adjusting a and b until the measured angle histogram is sufficiently similar to the expected one.

[0028]

[0039] When the retardance of the voxels is known (or when the birefringence writing characteristics are known depending on the situation), the birefringence value can be determined via a single measurement, also in this case, using known or assumed values of the scale and offset parameters. When assumed values are used, the values can be numerically optimized. Based on the known or assumed scale and offset values, a single measurement 612, referring to the Poincaré sphere 610 in FIG. 6, defines a two-dimensional plane in three-dimensional space. This two-dimensional plane intersects the surface of the sphere along a circle 614, and the circle represents a continuous range of possible sample angles and retardance values. If the sample retardance (represented by angle 616) is exactly known, the angle can be determined to be the one inside of one of two values (represented by points 620, 622, i.e., where the retardance plane 618 intersects the measurement circle 614). In comparison, the two-measurement example described above utilizes less detailed prior information (i.e., retardance smaller than the swing). If it is known that the angle is in a range that spreads only half of all available angles (e.g., 0 to 90 degrees, 45 to 135 degrees, or any other 90-degree range), these two points are limited to one, thereby determining the retardance and angle of the sample. Mathematically, the operations for performing the exemplary one-measurement determination disclosed are represented by equations (9) and (10).

Number

[0029]

[0040] FIG. 7 shows a flowchart depicting an exemplary method 700 for determining the birefringence value of a voxel using two or fewer measurements. As described above, the method of FIG. 7 can utilize the scale and offset parameters determined via the method of FIG. 4, or can first assume these parameters and then numerically optimize them. Method 700 includes, at 702, inducing probe light including one or more predetermined polarization states through the birefringent voxel and receiving the light at an image sensor to obtain measurement data for the birefringent voxel. In some examples, as shown at 704, the measurement data can include measurement data obtained using light in a first polarization state and measurement data obtained using light in a second, different polarization state. In other examples, the measurement data can include data from a single measurement, as shown at 706.

[0030]

[0041] Continuing, method 700 includes, at 708, determining, based on the measurement data, two points on the surface of the Poincare sphere corresponding to two possible birefringence states of the birefringent voxel, each state including one set of birefringence values, and applying constraints to determine the birefringence value of the voxel. For example, when the measurements are made in two polarization states, there are two azimuthal angle solutions to equations (5)-(7) above. In this example, method 700 includes, at 710, applying a constraint specifying that the set of birefringence values having the lower retardance value is the correct set. By selecting the point on the Poincare sphere representing the lower retardance, the azimuthal angle can be solved using equation (8) above, thereby providing the determined set of birefringence values for the voxel.

[0031]

[0042] When a single measurement is used, method 700 includes, at 712, determining a circle on the surface of the Poincare sphere based on the measurement, the circle including two locations where it intersects a plane representing the known retardance of the voxel. Then, at 714, a point representing the birefringence value of the voxel can be selected based on the azimuth angles of points within the expected range of angles, and the birefringence value can be determined using equations (9) and (10) above. Method 700 further includes, at 716, optionally numerically optimizing a likelihood function based on the determined azimuth angles and retardance values to determine these values in an example where the scale and offset values are initially unknown. Method 700 further includes, at 718, outputting the birefringence value of the voxel.

[0032]

[0043] The examples described above can be useful in reducing the time and computational resources consumed when reading the birefringent voxels of a storage medium compared to methods using four or more measurements. As an alternative or in addition thereto, other processes can also be used to provide an efficient reading of the birefringent voxels. For example, wavelength multiplexing can be used to reduce the number of individual images acquired during the reading process.

[0033]

[0044] FIG. 8 shows a schematic depiction of an exemplary system 800 for reading a birefringent storage medium. System 800 utilizes wavelength multiplexing in which N different wavelength bands of light having different polarization states are multiplexed to obtain N measurements in a temporally overlapping manner. System 800 includes N light sources, shown as a first light source 802, a second light source 804, and an Nth light source 806, each configured to output light in a different wavelength band (e.g., red, green, and blue). Each light source directs light to a corresponding PSG (shown as PSG 808, PSG 810, PSG 812 for light sources 802, 804, 806, respectively) so that a different polarization state can be set for each wavelength band. In other examples, a system for performing two temporally overlapping measurements can have two light sources and corresponding PSGs.

[0034]

[0045] Light from each PSG is directed toward a storage medium 814 disposed in a sample region of the system for reading the storage medium. The term "sample region" is used herein to denote the location where the storage medium is disposed for reading. In the example depicted, N-1 beam combiners (shown as beam combiner 1 816 and beam combiner N-1 818) are used to combine the light from each PSG into a beam for probing the sample medium.

[0035]

[0046] In the embodiment depicted, an optical system in the form of a condenser lens 820 directs light through the storage medium, and an objective lens 817 focuses the light onto a detector in the form of an image sensor 822 that images the entire data layer in the storage medium 814 frame by frame. An achromatic PSA 824 is positioned between the storage medium and the image sensor 822. The image sensor 822 includes a number of integrated wavelength-selective bandpass filters such that light in different wavelength bands passes through different filters and reaches different areas of the pixels of the image sensor 822. In this way, the intensity of each wavelength band of light (each having a different polarization setting) can be measured in the same image frame.

[0036]

[0047] In some examples, one or more physical masks can be used for the pupil design to help improve the quality of the signal used to read the birefringence encoded data of the memory medium. Examples of masks that can be used are schematically shown as intensity mask 825 and phase mask 826. The pupil design may depend on the layout of the voxels of the memory medium (e.g., x, y, z spatial distribution). For example, a ring-shaped intensity mask applied to the pupil of a lens generates a Bessel beam rather than a conventional Gaussian beam. Also, the phase mask can be applied to design the polarization field in the sample plane to optimize the pupil profile for the intended type of birefringence distribution of the sample. Thus, if a particular measurement light probe is desired, the signal that can be used as an input to these methods can be adjusted by designing the shape of the input light to match the purpose of improving the quality of the measurement.

[0037]

[0048] In some examples, the adjustable focus optical system can be moved to selectively focus on the voxels of a particular layer within the volume of the memory medium 814, thereby enabling reading of different layers. In other examples, the memory medium can be moved to focus on the voxels of different layers. The image sensor depicted includes an integrated bandpass filter, but in other examples, the bandpass filter can be included elsewhere in the system. For example, the system can be utilized in combination with a number of PSGs and wavelength multiplexing with a rotating bandpass filter (e.g., a color wheel) to enable sequential acquisition of images in different polarization states.

[0038]

[0049] As mentioned above, in some examples, fewer light sources can be used to generate more wavelength bands having different polarization states. FIG. 9 shows an exemplary light source configuration in which light from a single light source 902 is split into two beams 906, 908 of different wavelength bands via a dichroic beam splitter 904. Beams 906, 908 are directed through respective PSGs 912, 914 using any suitable optics (such as mirrors 916, 918 in the example depicted), and PSGs 912, 914 set different polarization states for beams 906, 908. After passing through the PSGs, beams 906, 908 are combined by a dichroic beam combiner 920 to probe the memory medium. In other examples, light from a suitable light source can be split into three or more different wavelength bands.

[0039]

[0050] FIGS. 10A and 10B show flow diagrams depicting an exemplary method 1000 for obtaining a number of temporally overlapping measurements via wavelength multiplexing. First, referring to FIG. 10A, method 1000 includes, at 1002, generating a first polarization of a first wavelength band, the first polarization including a first polarization state, and generating a second polarization of a second wavelength band different from the first wavelength band, the second polarization including a second polarization state different from the first polarization state. In some examples, as shown at 1004, light of the first wavelength band is output via a first light source and light of the second wavelength band is output by a second light source. In other examples, as shown at 1006, light can be output from fewer light sources and then split into more beams of different wavelength bands. Further, it will be appreciated that more than two additional wavelength bands can be used. Thus, method 1000 can include, at 1008, outputting light of three or more different wavelength bands having different polarization states to generate a third polarization and potentially additional other polarized beams.

[0040]

[0051] Continuing, method 1000 includes, at 1010, passing a first polarization and a second polarization through a voxel of a storage medium, thereby changing a first polarization state of the first polarization to a first modified polarization state and changing a second polarization state of the second polarization to a second modified polarization state. Passing the first polarization and the second polarization through a voxel of the storage medium may include, at 1012, combining the first polarization and the second polarization via a beam combiner before passing the first and second polarizations through the storage medium. Further, process 1010 may also include, at 1014, combining a third polarization and any additional wavelength band of polarization with the first and second polarizations before passing the light through the storage medium. In some examples, one or more masks can be used to implement a designed pupil. Accordingly, method 1000 may include, at 1016, passing the polarization through an intensity mask before passing the polarization through a voxel of the storage medium. As an alternative or in addition thereto, method 1000 may include, at 1018, passing the polarization through a phase mask before passing the polarization through a voxel of the storage medium.

[0041]

[0052] Next, referring to FIG. 10B, method 1000 includes, at 1022, passing the first polarization, the second polarization, and any additional wavelength band of polarization through a polarization state analyzer after passing the polarization through a voxel of the storage medium, the analyzer attenuating the intensity of the light compared to the state of the analyzer based on the polarization state of the light. Then, at 1024, method 1000 includes passing the first polarization through a first bandpass filter to reach an image sensor and passing the second polarization through a second bandpass filter to reach the image sensor, the first bandpass filter selectively passing a first wavelength band and the second bandpass filter selectively passing a second wavelength band. Further, as shown at 1026, polarizations of additional wavelength bands having different polarization states can pass through corresponding additional bandpass filters. In this way, the intensities of the first wavelength band, the second wavelength band, and any additional wavelength band are imaged separately.

[0042]

[0053] In some examples, the first band-pass filter, the second band-pass filter, and any additional band-pass filters are integrated with the image sensor as spatially separate filters integrated with the pixels of the image sensor. In such examples, method 1000, at 1028, includes passing a first polarization to reach a first region of the image sensor, passing a second polarization to reach a second region of the image sensor, and passing the polarization of any additional wavelength band to reach the image sensor. In this method, images for each polarization state can be separately acquired in the same image frame. In other examples, different band-pass filters can be applied by a time-division multiplexing method, such as by a color wheel. In such examples, different image frames are acquired for each wavelength band. After acquiring measurements using different wavelength bands for different polarization settings, method 1000, at 1030, includes determining the birefringence value of a voxel based on the first polarization received at the image sensor through the first band-pass filter, the second polarization received at the image sensor through the second band-pass filter, and any additional wavelength multiplexed polarization. The birefringence value can be determined using the exemplary methods disclosed above or any other suitable method.

[0043]

[0054] Using any of the methods described above, the system and medium through which the probe light passes when probing a voxel can impart additional rotation and / or retardance to the polarization used to probe the voxel. For example, by reading a layer of voxels of a data storage medium including a three-dimensional array of voxels, a situation can occur in which the polarization probe light is rotated in the reading process by passing through other out-of-focus layers of voxels. Also, system imperfections can lead to background noise. Thus, it is often of interest to measure the birefringence characteristics of a sample, such as a data storage medium, in relation to system and storage medium imperfections (e.g., the presence of other unread voxels in the optical path). This is referred to as background removal.

[0044]

[0055] The current method involves removing the background signal, which is done by capturing the image set {b k} in addition to the measurement set {m k} and calculating the background angle and retardance. {b k} is captured using the same device with the same set of polarization states as {m k}. {b k} is captured simply by removing the actual sample from the field of view. Also, for example, by performing a blurring operation, it is possible to estimate {b k} from {m k}. Blurring can be achieved by a simple low-pass filter. However, such methods cannot properly correct for both system imperfections and sample imperfections (such as other voxels).

[0045]

[0056] Therefore, based on a two-step process, {b k} is estimated from {m kExamples related to estimating {} are disclosed. In the two-step process, two low-pass versions of the measured intensity are calculated and combined using a multiplication constant to form an improved background image. In this method, both the local background intensity and the overall background intensity are estimated, so that the large-scale background can compensate for an imperfect system and the small-scale background can compensate for the three-dimensional nature of the storage medium, thus representing a more accurate estimate of the background intensity at both large and small scales. The filter parameters and the multiplication constant can be derived, for example, by minimizing the error between the retardance of a known sample and the calculated retardance distribution. Such a background correction method can be more efficient than separately acquiring the background image for the system (e.g., with no data storage medium in the sample area), because fewer physical measurement processes are performed, thereby saving the time and resources used for separate physical background measurements. As a more specific example, in the case of a sample where known data is encoded and embedded in glass and an image frame set is acquired, initial filter parameters and a multiplication constant are set and the encoded data is decoded. This is repeated using the updated filter parameters and multiplication constant. Then, the parameters and multiplication constant that provide the minimum error determined in the decoding are selected. The process of updating the filter parameters can be, in various examples, a brute search or a gradient method in the parameter space.

[0046]

[0057] Figure 11 shows a flowchart depicting an exemplary method 1100 for correcting birefringence values using a number of low-pass filters. Method 1100 includes, at 1102, obtaining an intensity image of the voxels of a storage medium. To measure the birefringence of the voxels, as shown at 1104, a plurality of images of the voxels are obtained in different polarization states. In some examples, the images can be of a number of voxels arranged in an image plane within the storage medium, as shown at 1106. The images of the voxels include high-frequency image information resulting from the birefringence state of the voxels and low-frequency image information resulting from one or more birefringent regions of the storage medium other than the voxels.

[0047]

[0058] At 1108, method 1100 includes applying a first low-pass filter to the image of the voxels to obtain a first background image and applying a second low-pass filter to the image of the voxels to obtain a second background image. As described above, the first low-pass filter and the second low-pass filter have different cut-off frequencies, such that the first background image represents more local background characteristics (birefringence noise arising from other voxels of the storage medium), and the second background image has a lower cut-off frequency than the first low-pass filter and can represent more global background characteristics. The effect of the more local low-pass filter can be to remove high-frequency data representing more detailed features of the focused voxel during the read process, leaving less detailed features from other unfocused voxels. As shown at 1110, the first and second low-pass filters are applied to each measurement image obtained for the voxels to form the background images of each measurement image.

[0048]

[0059] Continuing, method 1100 includes, at 1112, determining an improved background image from a first background image and a second background image. The improved background image can be determined in any suitable manner. In some examples, the improved background image can be determined by combining the first background image and the second background image using a multiplicative constant, as shown at 1114. A more specific example utilizes the following equation. b k =α(low pass 1(m k ) - low pass 2(m k )) + low pass 2(m k ) (11) where the measured intensity = m k and the local background intensity is represented by low pass 1(m k ), the overall background intensity is represented by low pass 2(m k ), α is a multiplicative constant used as a scale factor, and b k is the improved background image.

[0049]

[0060] Method 1100 further includes, at 1116, determining a birefringence value for the improved background image and, at 1118, determining a birefringence value for the voxel's image. Each set of birefringence values includes a retardance value and an azimuthal angle value and can be determined using the examples described above or any other suitable method.

[0050]

[0061] Method 1100 further includes, at 1120, correcting the birefringence value for the voxel's image based on the birefringence value for the improved background image. At 1122, correcting the birefringence value for the image can include, for example, determining the relative angle and relative retardance of the birefringence value for the voxel's image compared to the birefringence value for the improved background image. In one example, for instance, using any of the methods described above or other suitable methods, the measured retardance δm and the angle θ m is determined from {m k}, and the background retardance δ b and the angle θ b is determined from {b k}. The relative angle θ r and the retardance δ r are determined by the following equations.

Equation

[0051]

[0062] In some embodiments, the methods and processes described herein may relate to a computing system of one or more computing devices. Specifically, such methods and processes can be implemented as a computer application program or service, an application programming interface (API), a library, and / or other computer program products.

[0052]

[0063] FIG. 12 schematically shows a non-limiting embodiment of a computing system 1200 that can execute one or more of the methods and processes described above. The computing system 1200 is shown in a simplified form. The computing system 1200 can take the form of one or more personal computers, server computers, tablet computers, home entertainment computers, network computing devices, gaming devices, mobile computing devices, mobile communication devices (e.g., smartphones), and / or other computing devices.

[0053]

[0064] Computing system 1200 includes a logical subsystem 1202 and a memory subsystem 1204. Computing system 1200 may optionally include a display subsystem 1206, an input subsystem 1208, a communication subsystem 1210, and / or other components not shown in FIG. 12.

[0054]

[0065] The logical subsystem 1202 includes one or more physical devices configured to execute instructions. For example, the logical subsystem may be configured to execute instructions that are part of one or more applications, services, programs, routines, libraries, objects, components, data structures, or other logical constructs. Such instructions can be implemented to perform a task, implement a data type, transform the state of one or more components, achieve a technical effect, or reach a desired result.

[0055]

[0066] The logical subsystem may include one or more processors configured to execute software instructions. In addition or in the alternative, the logical subsystem may include one or more hardware or firmware logical subsystems configured to execute hardware or firmware instructions. The processors of the logical subsystem may be single-core or multi-core, and the instructions executed on the processors may be configured to perform sequential, parallel, and / or distributed processing. The individual components of the logical subsystem may optionally be remotely located and / or distributed among two or more separate devices configured to perform cooperative processing. Aspects of the logical subsystem can be virtualized and executed by a remotely accessible network-connected computing device configured in a cloud computing configuration.

[0056]

[0067] Memory subsystem 1204 includes one or more physical devices configured to hold instructions executable by a logical subsystem to implement the methods and processes described herein. When such methods and processes are implemented, the state of memory subsystem 1204 may be transformed, for example, to hold different data.

[0057]

[0068] Memory subsystem 1204 may include removable and / or built-in devices. Memory subsystem 1204 may include, among other things, optical memory (e.g., CD, DVD, HD-DVD, Blu-ray disk, etc.), semiconductor memory (e.g., RAM, EPROM, EEPROM, etc.) and / or magnetic memory (e.g., hard disk drive, floppy disk drive, tape drive, MRAM, etc.). Memory subsystem 1204 may include volatile, non-volatile, dynamic, static, read / write, read-only, random access, sequential access, location addressable, file addressable and / or content addressable devices.

[0058]

[0069] It will be appreciated that memory subsystem 1204 includes one or more physical devices. However, aspects of the instructions described herein may alternatively be propagated by a communication medium (e.g., electromagnetic signal, optical signal, etc.) that is not held by a physical device for a finite period of time.

[0059]

[0070] Aspects of logical subsystem 1202 and memory subsystem 1204 may be integrated together into one or more hardware logic components. Such hardware logic components may include, for example, field programmable gate arrays (FPGA), application specific integrated circuits (PASIC / ASIC) for programs and applications, application specific standard products (PSSP / ASSP) for programs and applications, system on a chip (SOC), and combined programmable logic circuits (CPLD).

[0060]

[0071] The term "program" can be used to describe an aspect of the computing system 1200 implemented to perform a particular function. In some cases, a program can be instantiated by the logical subsystem 1202 executing instructions held by the memory subsystem 1204. It will be understood that different programs can be instantiated from the same application, service, code block, object, library, routine, API, function, etc. Similarly, the same program can be instantiated from different applications, services, code blocks, objects, routines, APIs, functions, etc. The term "program" can encompass individual or groups of executable files, data files, libraries, drivers, scripts, database records, etc.

[0061]

[0072] A "service", as used herein, will be understood to be an application program executable over multiple user sessions. A service can be available to one or more system components, programs and / or other services. In some implementations, a service can be run on one or more server computing devices.

[0062]

[0073] The display subsystem 1206, if included, can be used to present a visual display of data held by the memory subsystem 1204. This visual display can take the form of a graphical user interface (GUI). The methods and processes described herein change the data held by the memory subsystem and thus transform the state of the memory subsystem. Accordingly, the state of the display subsystem 1206 is similarly transformed to visually represent the underlying data changes. The display subsystem 1206 can include one or more display devices that utilize virtually any type of technology. Such display devices can be combined with the logical subsystem 1202 and / or the memory subsystem 1204 in a shared enclosure, or such display devices can be peripheral display devices.

[0063]

[0074] The input subsystem 1208, if included, can include or interface with one or more user input devices such as a keyboard, mouse, touch screen, or game controller. In some embodiments, the input subsystem can include or interface with a selected natural user input (NUI) component. Such components can be integrated or peripheral, and the introduction and / or processing of the input actions can be handled on-board or off-board. Exemplary NUI components can include a microphone for voice and / or voiceprint authentication, infrared, color, stereo, and / or depth cameras for machine vision and / or gesture recognition, head trackers, eye trackers, accelerometers, and / or gyroscopes for motion detection and / or intent recognition, and electric field sensing components for evaluating brain activity.

[0064]

[0075] When included, the communication subsystem 1210 can be configured to communicatively couple the computing system 1200 to one or more other computing devices. The communication subsystem 1210 can include wired and / or wireless communication devices that are compatible with one or more different communication protocols. By way of non-limiting example, the communication subsystem can be configured to communicate via a cellular telephone network or via a wired or wireless local or wide area network. In some embodiments, the communication subsystem can enable the computing system 1200 to send messages to and / or receive messages from other devices via a network such as the Internet.

[0065]

[0076] Another example is a system for reading birefringence data, comprising one or more light sources, a first polarization state generator positioned to generate a first polarization from light in a first wavelength band output by the one or more light sources, a second polarization state generator positioned to generate a second polarization from light in a second wavelength band output by the one or more light sources, an image sensor configured to acquire an image of a sample region through which the first polarization and the second polarization pass, a polarization state analyzer optically disposed between the sample region and the image sensor, a first band-pass filter optically disposed between the polarization state analyzer and the image sensor and configured to pass light in the first wavelength band, and a second band-pass filter optically disposed between the polarization state analyzer and the image sensor and configured to pass light in the second wavelength band. In some such examples, the system further comprises a third polarization state generator positioned to generate a third polarization from light in a third wavelength band output by the one or more light sources, wherein the third wavelength band is different from the first wavelength band and the second wavelength band, and a third band-pass filter optically disposed between the polarization state analyzer and the image sensor and configured to pass light in the third wavelength band. In some such examples, the system further comprises a beam combiner configured to combine the first polarization and the second polarization optically upstream of the sample region. In some such examples, the first band-pass filter and the second band-pass filter of the system can be integrated with the pixels of the image sensor. In some such examples, the one or more light sources include a first light source configured to output light in the first wavelength band and a second light source configured to output light in the second wavelength band.In some such examples, the system further includes a computing system including instructions executable to determine a birefringence value of a voxel of a storage medium disposed in a sample region based on light received at an image sensor via a first band-pass filter and light received at the image sensor via a second band-pass filter. In some such examples, the system further includes one or more of an intensity mask and a phase mask optically positioned upstream of the sample region.

[0066]

[0077] Another example is a method for performing birefringence measurement, which includes generating a first polarization from light in a first wavelength band output by one or more light sources, where the first polarization includes a first polarization state; generating a second polarization from light in a second wavelength band output by one or more light sources, where the second wavelength band is different from the first wavelength band and the second polarization includes a second polarization state different from the first polarization state; passing the first polarization and the second polarization through voxels of a storage medium, thereby changing the first polarization state to a first modified polarization state and changing the second polarization state to a second modified polarization state; passing the first polarization and the second polarization through the voxels of the storage medium and then passing the first polarization and the second polarization through a polarization state analyzer; passing the first polarization through a first bandpass filter to reach a first region of an image sensor; and passing the second polarization through a second bandpass filter to reach a second region of the image sensor. In some such examples, the method further includes generating a third polarization from light in a third wavelength band output by one or more light sources, where the third wavelength band is different from the first wavelength band and the second wavelength band and the third polarization includes a third polarization state different from the first polarization state and the second polarization state; and passing the third polarization through a third bandpass filter optically disposed between the polarization state analyzer and the image sensor, where the third bandpass filter is configured to pass light in the third wavelength band. In some such examples, the method further includes combining the first polarization and the second polarization via a beam combiner before passing the first polarization and the second polarization through the voxels of the storage medium. In some such examples, the method further includes outputting light in the first wavelength band via a first light source and outputting light in the second wavelength band via a second light source. In some such examples, the method further includes determining a birefringence value of a voxel of the storage medium based on the first polarization received by the image sensor via the first bandpass filter and the second polarization received by the image sensor via the second bandpass filter.In some such examples, the method further includes passing a first polarization and a second polarization through one or more of an intensity mask and a phase mask prior to the voxel of the storage medium.

[0067]

[0078] Another example is a method for determining the birefringence values of the birefringent voxels of a storage medium on a computing device, the method including: inducing light including one or more predetermined polarization states through the birefringent voxels and receiving the light in an image sensor to obtain measurement data for the birefringent voxels; determining, based on the measurement data, two points on the surface of the Poincaré sphere corresponding to two possible birefringence states of the birefringent voxels, each state including a set of birefringence values including an azimuth angle and a retardance; applying constraints to determine the azimuth angle and the retardance; and outputting the determined birefringence values including the determined azimuth angle and retardance. In some such examples, the measurement data includes measurement data from a first measurement using light in a first polarization state and measurement data from a second measurement using light in a second polarization state. In some such examples, the two points on the Poincaré sphere are determined based on the measurement data from the first measurement and the measurement data from the second measurement, and applying the constraints includes selecting, from the two points on the Poincaré sphere, a point representing a set of birefringence values having a lower retardance value. In some such examples, the method further includes multiplexing light in a first wavelength band having a first polarization state with light in a second wavelength having a second polarization state to obtain the first measurement and the second measurement. In some such examples, the measurement data includes measurement data from a single measurement. In some such examples, determining the two points on the Poincaré sphere includes determining a circle on the Poincaré sphere based on the measurement, the two points including where the circle intersects a plane representing a known retardance of the voxel, and applying the constraints includes selecting, from the two points, a point representing a set of birefringence values having an azimuth angle within an expected angular range. In some such examples, the method further includes determining an offset parameter and a scale parameter via numerical optimization after determining the azimuth angle.

[0068]

[0079] Another example is a method for reading data stored as birefringence values in a storage medium on a computing device, the method comprising using light in a polarization state k to obtain a measurement value including the intensity m of an image of a voxel of the storage medium k and determining a likelihood function for the image of the voxel, the likelihood function representing the likelihood of the intensity of the voxel generated by a set of birefringence values for each of a number of possible sets of birefringence values, the determining being based on a selected data model and a selected noise model, determining a maximum value of the likelihood function, and determining a most probable set of birefringence values for the voxel based on the set of birefringence values that generates the maximum value of the likelihood function. In some such examples, the noise model includes a Gaussian noise model. In some such examples, the likelihood of measuring the intensity m of the image of the voxel for a measurement state k k is given by

Number

Number

Mathematics

[0069]

[0080] Since many modifications are possible, it should be understood that the configurations and / or techniques described herein are essentially illustrative and that these specific embodiments or examples should not be considered in a limiting sense. The particular routines or methods described herein may represent one or more of any number of processing strategies. Accordingly, the various acts shown and / or described may be performed in other orders, in parallel, or omitted, in the order shown and / or described. Similarly, the order of the processes described above can be changed.

[0070]

[0081] The subject matter of the present disclosure includes all novel and non-obvious combinations and sub-combinations of various processes, systems, and configurations, other features, functions, acts, and / or properties disclosed herein, and any and all of their equivalents.

Claims

A system for reading a birefringence value including an azimuth angle and a retardance magnitude recorded in voxels of a memory medium, comprising: one or more light sources; a first polarization state generator positioned to generate a first polarization from light in a first wavelength band output by the one or more light sources; a second polarization state generator positioned to generate a second polarization from light in a second wavelength band output by the one or more light sources, wherein the second wavelength band is different from the first wavelength band; an image sensor configured to acquire an image of the voxels of the memory medium through which the first polarization and the second polarization pass; a beam combiner configured to combine the first polarization and the second polarization optically upstream of a sample region in which the memory medium is disposed; a polarization state analyzer optically disposed between the sample region and the image sensor; a first band-pass filter optically disposed between the polarization state analyzer and the image sensor and configured to pass light in the first wavelength band; a second band-pass filter optically disposed between the polarization state analyzer and the image sensor and configured to pass light in the second wavelength band; a computing system including instructions executable to determine a birefringence value of the voxels of the memory medium based on light received by the image sensor through the first band-pass filter and light received by the image sensor through the second band-pass filter The system comprising. Claim 2 A third polarization state generator positioned to generate a third polarization from light in a third wavelength band output by the one or more light sources, wherein the third wavelength band is different from the first wavelength band and the second wavelength band; a third band-pass filter optically disposed between the polarization state analyzer and the image sensor and configured to pass light in the third wavelength band The system according to claim 1, further comprising. Claim 3 The system according to claim 1, wherein the first band-pass filter and the second band-pass filter are integrated with pixels of the image sensor.

4. The system according to claim 1, wherein the one or more light sources include a first light source configured to output light in the first wavelength band and a second light source configured to output light in the second wavelength band.

5. The system according to claim 1, wherein the storage medium includes a fused silica medium.

6. The system according to claim 1, further comprising one or more of an intensity mask and a phase mask optically positioned upstream of the sample region.

7. A method for determining a birefringence value including an azimuth angle and a retardance magnitude recorded in a voxel of a storage medium, generating a first polarization from light in a first wavelength band output by one or more light sources, the first polarization including a first polarization state; generating a second polarization from light in a second wavelength band output by the one or more light sources, the second wavelength band being different from the first wavelength band, the second polarization including a second polarization state different from the first polarization state; combining the first polarization and the second polarization via a beam combiner; passing the first polarization and the second polarization through a voxel of the storage medium, thereby changing the first polarization state to a first modified polarization state and changing the second polarization state to a second modified polarization state; after passing the first polarization and the second polarization through the voxel of the storage medium, passing the first polarization and the second polarization through a polarization state analyzer; passing the first polarization through a first band-pass filter to reach a first region of an image sensor; passing the second polarization through a second band-pass filter to reach a second region of the image sensor; determining a birefringence value of the voxel of the storage medium based on the first polarization received by the image sensor via the first band-pass filter and the second polarization received by the image sensor via the second band-pass filter comprising the method.

8. generating a third polarization from light in a third wavelength band output by the one or more light sources, wherein the third wavelength band is different from the first wavelength band and the second wavelength band, and the third polarization includes a third polarization state different from the first polarization state and the second polarization state; passing the third polarization through a third bandpass filter optically disposed between the polarization state analyzer and the image sensor, wherein the third bandpass filter is configured to pass light in the third wavelength band; The method according to claim 7, further comprising.

9. The method according to claim 7, further comprising outputting light in the first wavelength band via a first light source and outputting light in the second wavelength band via a second light source.

10. The method according to claim 7, further comprising passing the first polarization and the second polarization through one or more of an intensity mask and a phase mask in front of the voxel of the storage medium.

11. The method according to claim 7, wherein the storage medium includes fused silica.

Images