Background correction for birefringence measurements

Abstract

One example provides a computer-implemented method for reading data stored as birefringence values ​​in a storage medium. The method includes: acquiring an image of a voxel in the storage medium; applying a first low-pass filter having a first cutoff frequency to the voxel image to obtain a first background image; applying a second low-pass filter having a second cutoff frequency to the voxel image to obtain a second background image, the second cutoff frequency being different from the first cutoff frequency; determining an enhancement background image from the first and second background images; determining birefringence values ​​for the enhancement background image; determining birefringence values ​​for the voxel image; and correcting the birefringence values ​​of the voxel image based on the birefringence values ​​of the enhancement background image.

Description

Background Technology

[0001] Over the past decade, much of the world's data has moved to the cloud. To meet this growing demand, cloud providers rely on a variety of data storage technologies. These technologies include non-volatile memory (NVM), flash memory, hard disk drives (HDDs), magnetic tape, and optical discs. These storage technologies differ in terms of cost, latency, throughput, storage density, failure rate, and media lifetime. Summary of the Invention

[0002] This summary is provided to introduce some concepts in a simplified form, which will be further described in the detailed description below. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to limit the scope of the claimed subject matter. Furthermore, the claimed subject matter is not limited to embodiments that address any or all of the shortcomings pointed out in any part of this disclosure.

[0003] A promising technique for storing data is to encode data as localized birefringent voxels within a storage medium. This data can be stored at high density, and the storage medium can have a long lifespan compared to magnetic and other storage media. Reading birefringent voxels involves probing the voxel with polarized light and detecting the polarization change of the light generated by the voxel. However, polarization changes can also originate from background sources both external to and internal to the storage medium. While external background effects can be corrected by acquiring measurements in the absence of the storage medium, such background correction methods cannot correct for background polarization changes generated by the storage medium itself. Furthermore, acquiring background measurements in the absence of the storage medium requires additional measurements, thus increasing the amount of time required for data reading. Therefore, aspects of the techniques disclosed herein use the same image of the storage medium to correct for background generated by sources external to the storage medium and by the storage medium itself.

[0004] One aspect provides a computer-implemented method for reading data stored as birefringence values ​​in a storage medium. The method includes acquiring an image of a voxel in the storage medium; applying a first low-pass filter having a first cutoff frequency to the voxel image to obtain a first background image; applying a second low-pass filter having a second cutoff frequency to the voxel image to obtain a second background image, the second cutoff frequency being different from the first cutoff frequency; determining an enhanced background image from the first and second background images; determining birefringence values ​​for the enhanced background image; determining birefringence values ​​for the voxel image; and correcting the birefringence values ​​of the voxel image based on the birefringence values ​​of the enhanced background image. The first background image may represent more localized background features, such as birefringence noise generated by other voxels in the storage medium, while the second background image may represent more global background features. The first bandpass filter serves to remove high-frequency data representing more detailed features of the focused voxel, thus leaving less detailed features of other voxels that are out of focus during the reading process. In this aspect, images of birefringence samples can be used to correct background from both the storage medium itself and external sources, without requiring separate background measurements in the absence of a storage medium. Attached Figure Description

[0005] Figure 1 The reading of birefringent voxels in a storage medium is illustrated schematically.

[0006] Figure 2 A storage medium comprising data encoded as birefringent voxels is schematically described.

[0007] Figure 3 The Poincaré sphere is shown, representing the polarization state as the position on the sphere.

[0008] Figure 4 A flowchart is shown describing an example method for determining birefringence values ​​based on the maximum value determined for the likelihood function.

[0009] Figure 5 This shows an example of a polarization state used to measure birefringence values.

[0010] Figure 6 Example solutions based on birefringence values ​​based on two measurements and one measurement are shown.

[0011] Figure 7 A flowchart is shown illustrating an example method for obtaining birefringence measurements using wavelength multiplexing.

[0012] Figure 8 A block diagram of an example system for reading birefringent data using wavelength multiplexing is shown.

[0013] Figure 9An example system for wavelength multiplexing of light with different polarization states using light from the same image source is shown.

[0014] Figures 10A-10B A flowchart is shown to illustrate an example method for measuring birefringent voxels by wavelength multiplexing.

[0015] Figure 11 Shows a flowchart describing an example method for performing background correction of birefringence values.

[0016] Figure 12 A block diagram of an example computing system is shown. Detailed Implementation

[0017] As described above, a promising cloud data storage technology involves optically writing data onto a solid dielectric substrate, such as glass, using high-power, short-pulse laser irradiation. The irradiance induces localized birefringence at its focal point, which can then be read back using polarization imaging. The term "voxel" here refers to any discrete volume of the substrate in which a single data value (i.e., a symbol) can be stored. The data stored in the voxel can take various forms. In principle, any Mueller matrix coefficient of the substrate lattice can be manipulated to encode the data. In the example using a silica glass substrate, the lattice perturbation from focused polarized irradiation takes the form of intrigued birefringence at the focal point. Thus, each voxel of the substrate can be modeled as a very small waveplate with a hysteresis amplitude and an azimuth angle. These model parameters can be manipulated independently to write the desired symbol into a given voxel. Here, the polarization angle of the beam determines the azimuth angle of the voxel, while various other factors (pulse amplitude, duration, energy, number, and / or interval between pulses) determine the hysteresis of the voxel.

[0018] By dividing the continuous space of achievable azimuth angles and / or hysteresis magnitudes into discrete intervals, and by writing the birefringence of the voxel into one of these discrete intervals, multi-bit data values ​​can be encoded into each voxel. Furthermore, in some examples, multiple parallel voxel structure layers can be written onto the same substrate by focusing laser irradiance to a specific depth below the substrate irradiation surface. These features, individually or in combination, allow large amounts of data to be written into a single medium. In some examples, the storage medium comprises a solid, plate-like structure. In other examples, the storage medium comprises 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.

[0019] A birefringent voxel exhibits anisotropy as light passes through it because different polarization states of light travel through the sample at different speeds. When light passes through or is reflected from a birefringent voxel, its polarization state changes in a specific way, depending on the sample's azimuth and hysteresis. Therefore, information about the voxel's azimuth and hysteresis can be obtained by measuring the polarization state of the polarized light interacting with the birefringent voxel.

[0020] Some methods for measuring polarization states (and therefore voxel angles and hysteresis) involve a series of measurements using different input or output (or both) polarizations. Figure 1 The illustration schematically depicts the reading of birefringent data stored in storage medium 100. Light from light source 102 passes through polarization state generator (PSG) 104, whose output polarized light has a polarization angle determined by the PSG. This light source may include an LED, a laser, or other light source.

[0021] After passing through storage medium 100, light from light source 102 and PSG 104 passes through one or more voxels of storage medium 105, through polarization state analyzer (PSA) 106, and then to detector 108. The settings of PSA 106 and PSG 104 define the intensity used for measurement. m k polarization state k As described in more detail below. Detector 108 may include, for example, a CMOS image sensor (e.g., a high-resolution / high-frame-rate sensor) or other suitable photodetector array that can image the entire focal plane located within storage medium 105, thereby imaging multiple array voxels in the same image. In other examples, a point detector or a small detector array, such as a photodiode, phototransistor, or SPAD (single-photon avalanche diode), may be used to build the image point by point. Although Figure 1 The diagram illustrates the process of light passing through the storage medium and reaching the image sensor, but in other examples, light may reach the image sensor through reflection from the storage medium.

[0022] In an example where data needs to be read from multiple layers of storage medium 105, variable focal length optics 110 can be used to adjust the focal plane of detector 108 so that voxels on the focal plane are read while other voxels are not in the focal range. In other examples, changing the focus can be achieved by moving the sample. Figure 2 An example of a storage medium 200 comprising multiple voxels is schematically shown, with two layers illustrated at 202 and 204.

[0023] To describe the measurement of voxels, a commonly used structure is the Poincaré sphere, in Figure 3The Poincaré sphere 300 is shown at position 300. It represents the polarization state of light by mapping the last three components of a four-dimensional Stokes vector onto a three-dimensional Cartesian coordinate system. For fully polarized light, a particular measurement state is described by a specific location on the surface of the sphere, representing a particular polarization state of the light. Partially polarized light is represented by points originating from within the surface of the Poincaré sphere. The North Pole represents RCP, i.e., right circularly polarized light. The South Pole represents LCP, i.e., left circularly polarized light. The state at the equator is linearly polarized, with the angle defined by the azimuth angle on the sphere. A general point on the sphere is elliptically polarized, with the ellipticity determined by the angle between the state and the pole, and the azimuth angle defined by the angle around the sphere. An example of a polarization state is shown at position 302 on the sphere. The black dashed line is a circle of constant latitude, and therefore also constant hysteresis. The term "oscillation" refers to the angle 304 of the measurement state relative to the pole of the sphere. This horizontal angle is the azimuth angle 306. Since the azimuth and hysteresis of the voxel affect the polarization output state of the probe light, the azimuth and hysteresis of the voxel can also be represented as a point on the surface of a sphere.

[0024] Current methods for determining the birefringence of voxels in storage media involve three or more (usually four) measurements of the voxel under different probe light polarization states. Multiple measurements are used because the determination method involves four degrees of freedom—voxel hysteresis, voxel azimuth, measurement scale, and measurement offset. Four measurement methods determine all four values ​​for each readout. Shribak and Oldenbourg (M. Shribak and R. Oldenbourg, “Techniques for Fast and Sensitive Measurements of Two-Dimensional Birefringence Distributions”, Applied Optics, Vol. 42, No. 16, Optical Society of America, 2003 (https: / / www.osapublishing.org / ao / abstract.cfm?uri=ao-42-16-3009; see also https: / / doi.org / 10.1364 / AO.42.003009) describe a three-measurement method that assumes zero offset and resolves the other three parameters through three measurements. However, due to the number of measurements, using three or four measurements can affect the speed of retrieving data from storage.

[0025] Therefore, this paper discloses an example measurement procedure for determining the azimuth and hysteresis values ​​of birefringent voxels using fewer than three measurements. In short, the disclosed method utilizes constraints on the hysteresis value based on prior knowledge of the hysteresis, allowing the determination of hysteresis and azimuth values ​​with two or even one measurement. The disclosed method can also be used for three measurements, with the advantage that, compared to previous three-measurement methods, it does not need to assume the offset to be zero as long as it is known before the measurement, and the relative hysteresis and angle can be determined. Since the scale and offset do not change significantly in space and time when reading data encoded as birefringent in the storage medium, the scale and offset can be determined once or periodically using a four- (or more) measurement technique, and then the determined scale and offset values ​​can be used for subsequent hysteresis and angle determination using a measurement method with fewer than four measurements. Furthermore, as described below, when the scale and offset are unknown, they can be determined using digital optimization techniques.

[0026] Figure 4 A flowchart illustrating an example method 400 for determining birefringence values ​​is shown. Method 400 is an example of a technique that can be used to determine scale and offset values ​​for subsequent determinations using fewer measurements and offers the advantage over current methods that determination can be performed using arbitrary probe light polarization states, rather than predetermined states that may be difficult to achieve with physical instruments. Method 400 first includes, at 402, acquiring four or more measurements of a voxel in different polarization states, wherein each measurement includes a measurement state. k The intensity of observation below The measurement state is determined by the oscillation. and angle The measurement polarization state is defined. Method 400 further includes: at 404, determining a likelihood function for voxel measurement, wherein for each of a plurality of birefringence value sets, the likelihood function represents the likelihood of the voxel measurement arising from the birefringence value set. This likelihood is determined using assumptions from a noise model and a data model, based on angle and hysteresis. 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 (represented at 406), given a measurement state... k Measurement intensity The likelihood is given by formula (1).

[0027] (1)

[0028] In formula (1), ,in For polarization state k The expected measurements to be taken It's a sample delay. It's from the perspective of the sample. It is a proportional parameter. b It's an offset. It's noise. The term "birefringence value" indicates... A set of numerical values. Using this expression, the likelihood function for determining the probability of a set of measurements can be represented as: As Calculations for multiple birefringence value sets L And a maximum value is determined for the likelihood function, as shown at 408. Then at 410, the maximum value of the likelihood function is used to determine the most likely set of birefringence values ​​for the set of voxel measurements that produce the maximum value. This can be mathematically expressed as Equation (2).

[0029] (2)

[0030] A determined scale and offset can be used for determination using three or fewer measurements. It is understood that the term maximum determined value, and similar terms used herein, do not imply an actual global maximum value for the likelihood function, but rather the maximum observed value across all utilized parameter sets. It is further understood that in other examples, any other suitable method can be used to determine the birefringence value, including the scale and offset. For example, prior knowledge about the angle or hysteresis distribution can be included, according to Bayes' theorem, instead of calculating the likelihood of the parameters, the posterior can be calculated. In this case, one can find the parameter value that maximizes the posterior value (this is often referred to as MAP, i.e., maximum a posteriori). In such examples, the parameter value can be determined, for example, by finding the expected value of the posterior or using other statistical measures.

[0031] As mentioned above, one advantage of using the maximum deterministic likelihood method to determine the birefringence value of a voxel is that the polarization state used for measurement can be arbitrary, rather than predetermined. However, in some cases, certain polarization state configurations may utilize the available signal better than others. Two examples of such configurations are as follows. (See again...) Figure 3For a Poincaré sphere, the first example of a set of polarization states used to determine the birefringence values ​​of voxels includes a circularly polarized input state (set by the PSG) with chirality and an elliptically polarized output state (set by the PSA) with opposite chirality to the input state and equal ellipticity to each other, but with different azimuth angles, which are equidistantly distributed on a semicircle or full circle of equal latitude on the Poincaré sphere, for example {0, 45, 90, 135} degrees or {0, 22.5, 45, 67.5} degrees. The second set of polarization states includes a circularly polarized output state with chirality and an elliptically polarized input state with opposite ellipticity to the output state, which have equal ellipticity to each other but with different azimuth angles, wherein the azimuth angles are equidistantly distributed on a half or full circle on the surface of the Poincaré sphere. Figure 5 Three examples of such polarization state configurations are described, each represented by a point with a different sign than the others. Figure 5 In the diagram, the view of the Poincaré sphere is along the polar axis of the sphere, with dashed circles corresponding to selected latitudes that include the polarization state, and the outer boundary corresponding to the equator of the sphere.

[0032] When measurements are configured in this manner, the azimuth angle of the voxel can be determined as follows:

[0033] (3)

[0034] here It is the angle of measurement, index. k Indicates the measurement number. It is the first k The intensity of each measurement, and It is the first k The angle of a measured state on the Poincaré sphere. To find the hysteresis, a suitable method involves numerically optimizing the probabilities of the given measurement data, as discussed above. Figure 4 The description.

[0035] As mentioned above, prior knowledge of the scale and offset parameters can be used to determine the azimuth angle and the hysteresis of voxels using fewer measurements. For example, the azimuth angle of a voxel can be determined using three measurements plus a known offset value by using formula (4).

[0036] (4)

[0037] For example, hysteresis can be found by numerically maximizing the likelihood function described above. Furthermore, even when the scale and offset are initially unknown, numerical optimization techniques can be used to determine them. In such cases, where information about the expected distribution of the angle is known, the scale and offset can be determined (as might be the case with birefringent voxels as previously discussed). With prior knowledge of the expected angular distribution, the scale and offset can be adjusted through calculations until a suitable approximation of the expected distribution is achieved.

[0038] If some prior information about the hysteresis is known, but the hysteresis value itself is unknown, a two-measurement method can be used to determine the birefringence value of the voxel. In some cases, the two-measurement method also utilizes prior knowledge of the scale and offset, while in others, as mentioned above, the scale and offset are determined through numerical optimization.

[0039] When using two measurements, even knowing the offset and scale, there are still two possible solutions for the hysteresis and angle of the sample. This is because each measurement restricts the solution to a two-dimensional plane within the three-dimensional space of the Poincaré sphere. Therefore, the two measurements define a line in three-dimensional space. Figure 6 An example is shown where two measurements of a hypothetical voxel on a Poincaré sphere 602 determine the position of the voxel. In this example, the line 604, defined by the two measurements of the voxel, intersects the surface of the sphere at points 606 and 608.

[0040] 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 hysteresis as the state corresponding to the voxel, since it can be mathematically proven that the other solution is at least as large as the effective hysteresis of the measured state. For example, given two measurements in Poincaré sphere 602, point 606 would be selected because it represents a lower hysteresis value compared to point 608. This constraint, based on prior information, can be used for any system where the known effective measurement hysteresis differs from the measured hysteresis (either large or small). This constraint narrows the solution down to a single point on the sphere, allowing the determination of the sample's hysteresis and azimuth.

[0041] Below is a mathematical description of a more detailed example of a two-measurement method. It's important to note that this method can be performed by applying the scale and offset values ​​initially determined using more measurements (e.g., four) to the determination of the two measurements, or by determining the scale and offset values ​​using a numerical optimization method. In the case of initially determining the scale and offset values, any suitable method can be used to determine these parameters, including those mentioned above. Figure 4 Maximum likelihood example.

[0042] After obtaining the measurement results, the dual measurement method in the example first involves solving a set of simultaneous equations (5, 6, 7) concerning the hysteresis δ.

[0043] (5)

[0044] (6)

[0045] (7)

[0046] Since there are two possible solutions for δ, as mentioned above, the smaller value is chosen. Next, the azimuth angle can be calculated using formula (8).

[0047] when hour,

[0048] (8)

[0049] If known proportions and offset values ​​are used in the determination, then the determination is completed at this stage. For example, if the distribution of angles will be uniform (as in the case of birefringence data, where the data writing process is known), then the distribution of angles can be calculated, and equations (5)-(7) and (8) can be determined iteratively, while adjusting a and b, until the measured angle histogram is sufficiently similar to the expected one.

[0050] If the hysteresis of the voxel is known (as in the case where the writing properties of birefringence are known), the birefringence value can be determined by a single measurement, again using known or assumed values ​​of scale and offset parameters. When using assumed values, these values ​​can be numerically optimized. Based on known or assumed scale and offset values, a single measurement 612 defines a two-dimensional plane in three-dimensional space, referencing... Figure 6 The Poincaré sphere 610. This two-dimensional plane intersects the surface of the sphere along a circle 614, where the circle represents a continuous range of possible sample angles and hysteresis values. If the hysteresis of the sample (represented by angle 616) is known precisely, then the angle can be determined at one of two values ​​(represented by points 620 and 622), where the hysteresis plane 618 intersects the measurement circle 614. In contrast, the two measurement examples described above utilize less detailed prior information, namely that the hysteresis is less than the oscillation. If the angle is known to be within a range that spans only half of the total available angles, such as between 0 and 90 degrees, or between 45 and 135 degrees (or any other 90-degree range), then these two points can be constrained to one, which determines the hysteresis and angle of the sample. Mathematically, the calculations determined by performing a single measurement of the disclosed examples are expressed by formulas (9) and (10).

[0051] (9)

[0052] (10)

[0053] Figure 7 A flowchart illustrating an example method 700 for determining the birefringence value of a voxel using two or fewer measurements is shown. As described above, Figure 7 The method can be used through Figure 4 The scaling and offset parameters are determined by the method, or these parameters can be initially assumed and then numerically optimized. Method 700 includes, at 702, acquiring measurement data of the birefringent voxel by guiding probe light comprising one or more predetermined polarization states through the birefringent voxel and receiving the light at an image sensor. In some examples, as shown at 704, the measurement data may include measurement data obtained using light with a first polarization state, and measurement data obtained using light with a different second polarization state. In other examples, the measurement data may include data from a single measurement, as shown at 706.

[0054] Continuing, method 700 includes, at 708, determining, based on the measurement data, two points on the surface of the Poincaré sphere corresponding to two possible birefringence states of a birefringence voxel, each state comprising a set of birefringence values, and applying constraints to determine the birefringence value of the voxel. For example, when measurements are taken in two polarization states, the above equations (5)-(7) have solutions for two azimuth angles. In this case, method 700 includes, at 710, applying constraints specifying that the set of birefringence values ​​with lower hysteresis values ​​is the correct set. By selecting the point on the Poincaré sphere representing the lower hysteresis value, the azimuth angle can be solved using the above formula (8), thereby providing a determined set of birefringence values ​​for the voxel.

[0055] In the case of using a single measurement, method 700 includes, at 712, determining a circle on the surface of the Poincaré sphere based on the measurement, the circle including two locations intersecting with a plane representing a known hysteresis of a voxel. Then, at 714, the point representing the birefringence value of the voxel can be selected based on the azimuth of the point being within a desired angular range, and the birefringence value can be determined using the above formulas (9) and (10). Method 700 further optionally includes, at 716, numerically optimizing the likelihood function based on the determined azimuth and hysteresis values ​​to determine the scale and offset values ​​when these values ​​are initially unknown. Method 700 further includes, at 718, outputting the birefringence value of the voxel.

[0056] Compared to methods using four or more measurements, the embodiments described above may help reduce the time and computational resources consumed when reading birefringent voxels from a storage medium. Other processes may also be used alternatively or additionally to provide efficient reading of birefringent voxels. For example, wavelength multiplexing can be used to reduce the number of individual images obtained during the reading process.

[0057] Figure 8 A schematic description of an example system 800 for reading birefringent storage media is shown. System 800 utilizes wavelength multiplexing, in which N light bands of different wavelengths with different polarization states are multiplexed to obtain N measurements in a temporally overlapping manner. System 800 includes N light sources, illustrated 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 into a corresponding PSG, shown as PSG 808, PSG 810, and PSG 812 for light sources 802, 804, and 806, respectively, to allow setting different polarization states for each wavelength band. In other examples, a system performing two temporally overlapping measurements may have two light sources and corresponding PSGs.

[0058] Light from each PSG is directed to storage medium 814, which is placed in the system's sample region for reading. The term "sample region" is used here to refer to the location where the storage medium is placed for reading. In the described example, an N-1 combiner (illustrated as combiner 1 816 and combiner N-1 818) is used to combine the light from each PSG into a single beam for probing the sample medium.

[0059] In the described embodiment, an optics device in the form of a condenser lens 820 guides light through the storage medium, while an objective lens 817 focuses the light onto a detector in the form of an image sensor 822, which images the entire data layer within the storage medium 814 in each image frame. An achromatic PSA 824 is disposed between the storage medium and the image sensor 822. The image sensor 822 includes multiple integrated wavelength-selective bandpass filters, allowing light of different wavelengths to pass through different filters and illuminate different areas of a pixel in the image sensor 822. In this way, the intensity of light in each wavelength band (where each wavelength band has a different polarization setting) can be measured in the same image frame.

[0060] In some examples, one or more physical masks can be used for pupil engineering to help improve the quality of the signal used to read birefringent encoded data from the storage medium. Example masks that can be used are schematically illustrated as intensity mask 825 and phase mask 826. Pupil engineering may depend on the voxel layout in the storage medium (e.g., x, y, z spatial distribution). For example, an annular intensity mask added to the pupil of a lens will produce a Bessel beam instead of a conventional Gaussian beam. Phase masks can also be used to design the polarization field of the sample plane to optimize the pupil profile for the birefringent distribution of the sample. Therefore, if a particular measurement optics probe is desirable, the signal that can be used as input to these methods can be customized by engineering the shape of the input light to improve the quality of the measurement.

[0061] In some examples, the adjustable-focus optics can be moved to selectively focus voxels onto specific layers within the volume of storage medium 814, thereby allowing the reading of different layers. In other examples, the storage medium can be moved to focus voxels on different layers. While the described image sensor includes an integrated bandpass filter, in other examples, the bandpass filter may be included elsewhere in the system. For example, the system may utilize multiple PSGs and wavelength multiplexing combined with a rotating bandpass filter (e.g., a color wheel) to allow the sequential acquisition of images with different polarization states.

[0062] As mentioned above, in some cases, a smaller number of light sources can be used to generate a larger number of wavebands with different polarization states. Figure 9 An example of a light source configuration is shown, in which light from a single light source 902 is split into two beams 906 and 908 of different wavelengths by a dichroic beam splitter 904. Beams 906 and 908 are guided through respective polarization gates (PSGs) 912 and 914 using any suitable optics (such as mirrors 916 and 918 in the described example), and PSGs 912 and 914 are configured with different polarization states for beams 906 and 908. After passing through the PSGs, beams 906 and 908 are combined by a dichroic beam combiner 920 for probing the storage medium. In other examples, light from a suitable light source can be split into three or more different wavelengths.

[0063] Figures 10A-10B A flowchart illustrating an example method 1000 for acquiring multiple temporally overlapping measurements via wavelength multiplexing is shown. First, refer to... Figure 10AMethod 1000 includes, at 1002, generating first polarized light in a first wavelength band, the first polarized light including a first polarization state, and generating second polarized light in a second wavelength band different from the first wavelength band, the second polarized light including a second polarization state different from the first polarization state. In some examples, light in the first wavelength band is output via a first light source, and light in the second wavelength band is output via a second light source, as shown at 1004. In other examples, light can be output from a smaller number of light sources and then split into a larger number of beams of different wavelength bands, as shown at 1006. Furthermore, it is understood that more than two additional wavelength bands can be used. Therefore, method 1000 may include, at 1008, outputting light in three or more different wavelength bands with different polarization states to generate third polarized light and potentially other polarized beams.

[0064] Continuing, method 1000 includes, at 1010, passing first polarized light and second polarized light through a voxel of the storage medium, thereby changing the first polarization state of the first polarized light to a first modified polarization state and changing the second polarization state of the second polarized light to a second modified polarization state. Passing the first polarized light and second polarized light through the voxel of the storage medium may include, at 1012, combining the first polarized light and second polarized light by a beam combiner before passing the first and second polarized light through the storage medium. Furthermore, process 1010 may also include, at 1014, combining third polarized light and any additional bands of polarized light with the first and second polarized light, thereby passing the light through the storage medium. In some examples, one or more masks may be used to implement the engineered pupil. Therefore, method 1000 may include, at 1016, passing the polarized light through an intensity mask before passing the polarized light through the voxel of the storage medium. Alternatively or additionally, method 1000 may include, at 1018, passing the polarized light through a phase mask before passing the polarized light through the voxel of the storage medium.

[0065] Next reference Figure 10B Method 1000 includes, at 1022, after passing polarized light through a voxel of a storage medium, passing the first polarized light, the second polarized light, and any additional bands of polarized light through a polarization state analyzer, wherein the analyzer attenuates the intensity of the light based on the polarization state of the light compared to the state of the analyzer. Then, at 1024, method 1000 includes passing the first polarized light through a first bandpass filter to an image sensor, and passing the second polarized light through a second bandpass filter to the image sensor, wherein the first bandpass filter selectively passes through a first wavelength band, and the second bandpass filter selectively passes through a second band. Furthermore, as shown at 1026, additional bands of polarized light with different polarization states can pass through corresponding additional bandpass filters. In this way, the intensities of the first wavelength band, the second band, and any additional bands are imaged separately.

[0066] In some instances, the first bandpass filter, the second bandpass filter, and any additional bandpass filters are integrated with the image sensor as spatially independent filters integrated with the pixels of the image sensor. In such an example, method 1000 includes, at 1028, transmitting first polarized light to a first region of the image sensor, transmitting second polarized light to a second region of the image sensor, and transmitting the band of any additional polarized light to the image sensor. In this way, images of each polarization state can be acquired separately in the same image frame. In other instances, different bandpass filters can be applied in a time-multiplexed manner, for example, via a color wheel. In such an example, different image frames are acquired for each band. After acquiring measurement results using different bands with different polarization settings, method 1000 includes, at 1030, determining the birefringence value of the voxel based on the first polarized light received at the image sensor via the first bandpass filter and the second polarized light received at the image sensor via the second bandpass filter, as well as any additional wavelength-multiplexed polarized light. The birefringence value can be determined using the example methods disclosed above, or in any other suitable manner.

[0067] By any of the methods described above, the system and medium through which the probe light passes when probing voxels can impart additional rotation and / or hysteresis to the polarized light used for voxel probing. For example, reading a layer of voxels in a data storage medium composed of a three-dimensional voxel array may cause the polarized probe light to rotate as it passes through other defocused voxel layers during the reading process. System imperfections can also lead to background noise. Therefore, the birefringence properties of the measured sample (such as the data storage medium) are often significant relative to defects in the system and storage medium (e.g., the presence of other unread voxels in the optical path). This is known as background subtraction.

[0068] The current approach is to use a measurement set Capture a set of images To eliminate background signals and calculate the background angle and hysteresis. They were taken with the same instrument, and They have the same polarization state. Capture can be achieved simply by removing the actual sample from the field of view. It can also be achieved, for example, by performing a blurring operation. estimate Blurring can be achieved using a simple low-pass filter. However, such a method may not adequately correct for system defects and sample defects, such as those found in other voxels.

[0069] Therefore, the disclosed examples involve a two-step process from estimate The measurement intensities of two low-pass versions are calculated and combined using a multiplication constant to form an enhanced background image. In this way, both localized and global background intensities are estimated, representing more accurate estimates of both large-scale and small-scale background intensities, as large-scale backgrounds can compensate for imperfections in the system, while small-scale backgrounds can compensate for the three-dimensional properties of the storage medium. The filter parameters and multiplication constant can be derived, for example, by minimizing the error between the known hysteresis of the specimen and the calculated hysteresis distribution. Such a background correction method is more efficient than acquiring a background image of the system separately (e.g., in the absence of a data storage medium in the sample area) because fewer physical measurement processes are performed, saving time and resources for separate physical background measurements. As a more concrete example, for a sample where known data is encoded into glass and a set of image frames has been acquired, initial filter parameters and multiplication constants are set, and the encoded data is decoded. This is repeated using updated filter parameters and multiplication constants. The parameters and multiplication constants that produce the lowest error during decoding are then selected. The process of updating filter parameters can be either a forced search in the parameter space or a gradient method in various examples.

[0070] Figure 11 A flowchart is shown illustrating an example method 1100 for correcting birefringence values ​​using multiple low-pass filters. Method 1100 includes, at 1102, acquiring intensity images of voxels in the storage medium. To measure the birefringence of the voxels, multiple images of the voxels are acquired at different polarization states, as shown at 1104. In some examples, the images may be multiple voxels arranged on an image plane within the storage medium, as shown at 1106. The voxel images include higher-frequency image information generated by the birefringence state of the voxel and lower-frequency image information generated by one or more birefringent regions of the storage medium outside the voxel.

[0071] At 1108, method 1100 includes applying a first low-pass filter to an 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 and second low-pass filters have different cutoff frequencies, such that the first background image can represent more localized background features, such as birefringence noise generated by other voxels in the storage medium, while the second background image can have a lower cutoff frequency than the first low-pass filter, representing more global background features. The effect of the more localized low-pass filter may be to remove high-frequency data representing more detailed features of the focused voxels, thereby leaving less detailed features of other voxels that are out of focus during readout. As shown at 1110, the first and second low-pass filters are applied to each measurement image acquired for the voxels to form a background image for each measurement image.

[0072] Continuing, method 1100 includes, at 1112, determining an enhanced background image from the first background image and the second background image. The enhanced background image can be determined in any suitable manner. In some examples, the enhanced background image can be determined by combining the first and second background images using a multiplication constant, as shown at 1114. A more specific example utilizes the following formula:

[0073] , (11)

[0074] Where the measured intensity = The intensity of localization background is represented as The global background intensity is represented as , It is a multiplication constant that acts as a scaling factor. It enhances the background image.

[0075] Method 1100 further includes, at 1116, determining the birefringence values ​​of the enhanced background image, and at 118, determining the birefringence values ​​of the voxel image. Each set of birefringence values ​​includes a hysteresis value and an azimuth angle, which can be determined using the examples described above or in any other suitable manner.

[0076] Method 1100 further includes, at 1120, correcting the birefringence value of the voxel image based on the birefringence value of the enhanced background image. At 1122, correcting the birefringence value of the image may include, for example, determining, a relative angle and relative hysteresis between the birefringence value of the voxel image and the birefringence value of the enhanced background image. In one example, the hysteresis is measured. and angle From The background is sluggish. and angle From For example, by using any of the methods described above or other appropriate methods to determine the relative angle. and hysteresis It is determined by the following formula.

[0077] (12)

[0078] (13)

[0079] (14)

[0080] (15)

[0081] In some embodiments, the methods and processes described herein may be associated with a computing system of one or more computing devices. In particular, these methods and processes may be implemented as computer applications or services, application programming interfaces (APIs), libraries, and / or other computer program products.

[0082] Figure 12 A non-limiting embodiment of computing system 1200 is illustrated schematically, which may implement one or more of the methods and processes described above. Computing system 1200 is shown in a simplified form. Computing system 1200 may 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.

[0083] The computing system 1200 includes a logic subsystem 1202 and a storage subsystem 1204. The computing system 1200 may optionally include a display subsystem 1206, an input subsystem 1208, a communication subsystem 1210, and / or... Figure 12 Other components not shown.

[0084] The logic subsystem 1202 includes one or more physical devices configured to execute instructions. For example, the logic subsystem may be configured to execute instructions belonging to one or more applications, services, programs, routines, libraries, objects, components, data structures, or other logical constructs. Such instructions may be implemented to perform tasks, implement data types, transform the state of one or more components, achieve technical effects, or otherwise achieve desired results.

[0085] A logical subsystem may include one or more processors configured to execute software instructions. Alternatively, a logical subsystem may include one or more hardware or firmware logical subsystems configured to execute hardware or firmware instructions. The processor of the logical subsystem may be single-core or multi-core, and the instructions executed thereon may be configured for sequential, parallel, and / or distributed processing. Individual components of the logical subsystem may optionally be distributed across two or more independent devices that may be remotely located and / or configured for coordinated processing. Various aspects of the logical subsystem may be virtualized and executed by remotely accessed, networked computing devices configured in a cloud computing configuration.

[0086] Storage 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 storage subsystem 1204 can be transformed—for example, to hold different data.

[0087] Storage subsystem 1204 may include removable and / or built-in devices. Storage subsystem 1204 may include optical memory (e.g., CD, DVD, HD-DVD, Blu-ray disc, etc.), semiconductor memory (e.g., RAM, EPROM, EEPROM, etc.), and / or magnetic memory (e.g., hard disk drive, floppy disk drive, magnetic tape drive, MRAM, etc.), etc. Storage subsystem 1204 may include volatile, non-volatile, dynamic, static, read / write, read-only, random access, sequential access, addressable, file-addressable, and / or content-addressable means.

[0088] It will be understood that the storage subsystem 1204 includes one or more physical devices. However, the various aspects of the instructions described herein may alternatively be propagated by a communication medium (e.g., electromagnetic signals, optical signals, etc.) that is not held by the physical devices for a finite period of time.

[0089] Various aspects of the logic subsystem 1202 and the storage subsystem 1204 can be integrated together into one or more hardware-logic components. For example, such hardware-logic components may include field-programmable gate arrays (FPGAs), application-specific integrated circuits (PASICs / ASICs), application-specific standard products (PSSPs / ASSPs), system-on-a-chip (SOCs), and complex programmable logic devices (CPLDs).

[0090] The term "program" can be used to describe one aspect of the computing system 1200 that performs a specific function. In some cases, a program can be instantiated through the logical subsystem 1202 to execute instructions held by the storage subsystem 1204. It is 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 modules, objects, routines, APIs, functions, etc. The term "program" may include single or group executable files, data files, libraries, drivers, scripts, database records, etc.

[0091] As used herein, a "service" is an application that can be executed across multiple user sessions. A service may be available to one or more system components, programs, and / or other services. In some implementations, a service may run on one or more server computing devices.

[0092] Display subsystem 1206 can be used to display a visual representation of the data stored in storage subsystem 1204. This visualization can take the form of a graphical user interface (GUI). Since the methods and procedures described herein change the data held by the storage subsystem, thereby altering the state of the storage subsystem, the state of display subsystem 1206 can also be transformed to visually represent changes in the underlying data. Display subsystem 1206 may include one or more display devices using virtually any type of technology. Such display devices may be combined with logical subsystem 1202 and / or storage subsystem 1204 in a shared cabinet, or such display devices may be peripheral display devices.

[0093] When included, the input subsystem 1208 may include, or interface with, one or more user input devices, such as a keyboard, mouse, touchscreen, or game controller. In some embodiments, the input subsystem may include or interface with selected Natural User Input (NUI) components. These components may be integrated or peripheral, and the transduction and / or processing of input actions may be performed onboard or offboard. Example NUI components may include microphones for speech and / or speech recognition; 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 assessing brain activity.

[0094] When included, the communication subsystem 1210 may be configured to communicatively couple the computing system 1200 to one or more other computing devices. The communication subsystem 1210 may include wired and / or wireless communication devices compatible with one or more different communication protocols. As a non-limiting example, the communication subsystem may be configured to communicate via a wireless telephone network or a wired or wireless local area network or wide area network. In some embodiments, the communication subsystem may allow the computing system 1200 to send and / or receive messages from other devices via a network (such as the Internet).

[0095] Another example provides a computer-implemented method for reading data stored as birefringence values ​​in a storage medium. The method includes acquiring an image of a voxel in the storage medium, the image including higher-frequency image information from the birefringence state of the voxel and lower-frequency image information from one or more birefringence regions in the storage medium other than the voxel; applying a first low-pass filter having a first cutoff frequency to the voxel image to obtain a first background image; applying a second low-pass filter having a second cutoff frequency different from the first cutoff frequency to the voxel image to obtain a second background image; determining an enhanced background image from the first and second background images; determining birefringence values ​​for the enhanced background image; determining birefringence values ​​for the voxel image; and correcting the birefringence values ​​of the voxel image based on the birefringence values ​​of the enhanced background image. In some such examples, acquiring an image of a voxel in the storage medium includes acquiring multiple images of the voxel at different polarization states, and wherein applying the first and second low-pass filters to the voxel images includes applying the first and second low-pass filters to each of the multiple images of the voxel. In some such examples, determining the enhanced background image includes combining the first and second background images with a multiplication constant. In some such cases, in polarization state k Images of voxels obtained below m k The enhanced background image is represented as b k And determined in the following ways.

[0096]

[0097] The first low-pass filter is LowPass1, the second low-pass filter is LowPass2, and α is a multiplication constant. In some such examples, the birefringence value of the enhanced background image includes values ​​from... b k Determined background hysteresis and background angle The birefringence values ​​of the voxel image include those from... m k Determined measurement hysteresis and measuring angle The method further includes determining a relative angle. and relative hysteresis To correct the birefringence value.

[0098]

[0099] ,

[0100] , as well as

[0101] .

[0102] In some such examples, the method further includes determining the error between the optimized known hysteresis of the sample and the calculated hysteresis distribution. α In some such examples, acquiring an image of a voxel includes acquiring an image of an array of voxels within an image plane, and wherein one or more birefringent regions of the storage medium outside the voxels include one or more other voxels outside the image plane.

[0103] Another example provides a computer system including a logic subsystem and a storage subsystem. The storage subsystem includes instructions executable by the logic subsystem to read birefringence data from the storage medium by receiving an image of a voxel, the image including higher-frequency image information generated by the birefringence state of the voxel and lower-frequency image information generated by one or more birefringence regions in the storage medium other than the voxel. The instructions apply a first low-pass filter with a first cutoff frequency to the voxel image to obtain a first background image. A second low-pass filter with a second cutoff frequency, different from the first cutoff frequency, is applied to the voxel image to obtain a second background image. An enhanced background image is determined from the first and second background images. A birefringence value is determined for the enhanced background image. A birefringence value is determined for the voxel image. The instructions then correct the birefringence value of the voxel image based on the birefringence value of the enhanced background image. In some such examples, the executable instructions are used to acquire voxel images of the storage medium to acquire multiple images of voxels in different polarization states and to apply the first and second low-pass filters to each of the multiple images of the voxels. In some such examples, executable instructions for determining an enhanced background image include executable instructions for combining a first background image and a second background image with a multiplication constant. In some such examples, the image of a voxel is acquired at polarization state k. The enhanced background image is represented as b k The executable instructions can be determined in the following ways. b k

[0104]

[0105] In this context, the first low-pass filter is LowPass1, the second low-pass filter is LowPass2, and α is a multiplication constant. In some such examples, the birefringence values ​​used to enhance the background image include those from... b k Determined background hysteresis and background angle The birefringence values ​​used for the voxel image include those from... m k Determined measurement hysteresis and measuring angle And the instructions therein can be executed to determine the relative angle and relative hysteresis To correct the birefringence value.

[0106]

[0107] , as well as

[0108] , as well as .

[0109] In some such examples, the instructions can be further executed to determine α by optimizing the error between the hysteresis of a known specimen and the calculated hysteresis distribution. In some such examples, the instructions are executable to acquire an image of a voxel by acquiring an image of an array of voxels in an image plane, and wherein one or more birefringent regions of the storage medium outside the voxels include one or more other voxels outside the image plane. Another example provides a computer-readable storage device including instructions executable by a computing system to read birefringent data from the storage medium by receiving an image of a voxel in the storage medium, the image including higher-frequency image information generated by the birefringence state of the voxels and lower-frequency image information generated by one or more birefringent regions in the storage medium other than the voxels; apply a first low-pass filter having a first cutoff frequency to the image of the voxels to obtain a first background image; apply a second low-pass filter having a second cutoff frequency different from the first cutoff frequency to the image of the voxels to obtain a second background image; determine an enhanced background image from the first background image and the second background image; determine birefringence values ​​for the enhanced background image; determine birefringence values ​​for the voxel image; and correct the birefringence values ​​of the voxel image based on the birefringence values ​​of the enhanced background image. In some such examples, executable instructions are used to acquire voxel images of the storage medium to acquire multiple images of voxels under different polarization states, and to apply a first low-pass filter and a second low-pass filter to each of the multiple images of the voxels. In some such examples, executable instructions for determining an enhanced background image include executable instructions for combining the first background image and the second background image with a multiplication constant. In some such examples, in polarization states... k Voxel images obtained below m k The enhanced background image is represented as And the instructions therein are executable to determine b in the following way k .

[0110]

[0111] In this context, the first low-pass filter is LowPass1, the second low-pass filter is LowPass2, and α is a multiplication constant. In some such examples, the birefringence value for enhancing the background image includes... b k Determined background hysteresis and background angle The birefringence values ​​of the voxel image include those from... m k Determined measurement hysteresis and measuring angle And the instructions therein can be executed to determine the relative angle The birefringence value is corrected by relative hysteresis, which is given below.

[0112]

[0113] ,

[0114] , as well as

[0115] .

[0116] In some such examples, the instructions are executable to acquire an image of a voxel by acquiring an image of an array of voxels within an image plane, and wherein one or more birefringent regions of a storage medium outside the voxels include one or more other voxels outside the image plane.

[0117] Another example provides a method for reading data stored as birefringence values ​​in a storage medium on a computing device, the method comprising acquiring the intensity of a voxel of the storage medium including light using a polarization state k. m k Image measurement involves determining a likelihood function for the voxel image. This likelihood function represents the likelihood of the voxel intensity produced by each of a plurality of possible sets of birefringence values, based on a selected data model and a selected noise model. The maximum value of the likelihood function is determined, and the most probable set of birefringence values ​​for the voxel is determined based on the set of birefringence values ​​that produces the maximum value. In some such examples, the noise model includes a Gaussian noise model. In some such examples, for measurement state k, the image intensity of a voxel is measured. m k The possibilities are given in the following ways.

[0118]

[0119] Among them, polarization state k Including swing and angle .

[0120] in It is for polarization state k The expected measurement obtained,

[0121] Where δ is the hysteresis of the voxel in the storage medium.

[0122] in It is the azimuth angle of the storage medium voxel.

[0123] in a It is a proportional parameter.

[0124] in b It is the offset, and

[0125] in σ It represents noise.

[0126] In some such examples, for a set of measurements The likelihood function is denoted by L, and is derived from... Given, and wherein the method includes... a , b , δ and Calculate L for each of the multiple values ​​in the set, and determine the most likely set of birefringence values. .

[0127] It is understood that the configurations and / or methods described herein are exemplary in nature, and these specific implementations or examples should not be considered limiting, as many variations are possible. The specific routines or methods described herein may represent one or more of any number of processing strategies. Therefore, the various behaviors illustrated and / or described may be performed in the order illustrated and / or described, or in a different order, or in parallel, or omitted. Similarly, the order of the above processing may also be changed.

[0128] The subject matter of this disclosure includes all novel and non-obvious combinations and sub-combinations of the various processes, systems and configurations disclosed herein, as well as any and all equivalents thereof.

Claims

1. A computer-implemented method for reading data stored as birefringence values ​​in a storage medium, the method comprising: Acquire an image of a voxel of the storage medium, the image of the voxel including higher frequency image information generated by the birefringence state of the voxel and lower frequency image information generated by one or more birefringence regions of the storage medium other than the voxel; A first low-pass filter with a first cutoff frequency is applied to the image of the voxel to obtain a first background image; A second low-pass filter with a second cutoff frequency is applied to the image of the voxel to obtain a second background image, wherein the second cutoff frequency is different from the first cutoff frequency; An enhanced background image is determined from the first background image and the second background image; Determine the birefringence value used for the enhanced background image; Determine the birefringence value of the image used for the voxel; as well as The birefringence value of the image of the voxel is corrected based on the birefringence value used for the enhanced background image.

2. The method of claim 1, wherein acquiring the image of the voxel of the storage medium comprises acquiring a plurality of images of the voxel under different polarization states, and wherein applying the first low-pass filter and the second low-pass filter to the image of the voxel comprises applying the first low-pass filter and the second low-pass filter to each of the plurality of images of the voxel.

3. The method of claim 1, wherein determining the enhanced background image comprises combining the first background image and the second background image with a multiplication constant.

4. The method of claim 3, wherein the enhanced background image of the image of the voxel acquired at polarization state k is represented as k and determined as follows: b k The first low-pass filter is LowPass1, the second low-pass filter is LowPass2, and α is the multiplication constant.

5. The method of claim 4, wherein the birefringence value for the enhanced background image comprises from... b k Determined background hysteresis and background angle The birefringence value of the image used for the voxel includes values ​​from... m k Determined measurement hysteresis and measuring angle And the method further includes determining the relative angle by: and relative lag To correct the birefringence value: ， ， ,as well as 。 6. The method of claim 4, further comprising determining based on the error between the optimized known hysteresis of the sample and the calculated hysteresis distribution. α .

7. The method of claim 1, wherein acquiring the image of the voxel comprises acquiring an image of a voxel array in an image plane, and wherein the one or more birefringent regions of the storage medium other than the voxel include one or more other voxels outside the image plane.

8. A computer system, comprising: Logical subsystem; as well as A storage subsystem includes instructions executable by the logic subsystem to read birefringent data from a storage medium in the following manner: Acquire an image of a voxel of the storage medium, the image of the voxel including higher frequency image information generated by the birefringence state of the voxel and lower frequency image information generated by one or more birefringence regions of the storage medium other than the voxel; A first low-pass filter with a first cutoff frequency is applied to the image of the voxel to obtain a first background image; A second low-pass filter with a second cutoff frequency is applied to the image of the voxel to obtain a second background image, wherein the second cutoff frequency is different from the first cutoff frequency; An enhanced background image is determined from the first background image and the second background image; Determine the birefringence value used for the enhanced background image; Determine the birefringence value of the image used for the voxel; as well as The birefringence value of the image of the voxel is corrected based on the birefringence value used for the enhanced background image.

9. The computer system of claim 8, wherein the instructions for executing to acquire the image of the voxel of the storage medium are executable to acquire a plurality of images of the voxel in different polarization states, and the first low-pass filter and the second low-pass filter are applied to each of the plurality of images of the voxel.

10. The computer system of claim 9, wherein the instructions executable to determine the enhanced background image include instructions executable to combine the first background image and the second background image with a multiplication constant.

11. The computer system of claim 10, wherein the polarization state is... k Image of the voxel obtained at the location The enhanced background image is represented as b k And is determined as follows: The first low-pass filter is LowPass1, the second low-pass filter is LowPass2, and α is the multiplication constant.

12. The computer system of claim 11, wherein the birefringence value for the enhanced background image comprises from... b k Determined background hysteresis and background angle The birefringence value of the image used for the voxel includes values ​​from... m k Determined measurement hysteresis and measuring angle And wherein the execution is executable to determine the relative angle by means of the following: and relative lag To correct the birefringence value: ， ， ,as well as 。 13. The computer system of claim 11, wherein the instructions are further executable to determine by optimizing the error between the known hysteresis of the sample and the calculated hysteresis distribution. α .

14. The computer system of claim 8, wherein the instructions are executable to acquire the image of the voxels by acquiring an image of an array of voxels in an image plane, and wherein the one or more birefringent regions of the storage medium other than the voxels include one or more other voxels outside the image plane.

15. A computer-readable storage device comprising instructions executable by a computing system to read birefringence values ​​from a storage medium in such a way as: Acquire an image of a voxel of the storage medium, the image of the voxel including higher frequency image information generated by the birefringence state of the voxel and lower frequency image information generated by one or more birefringence regions of the storage medium other than the voxel; A first low-pass filter with a first cutoff frequency is applied to the image of the voxel to obtain a first background image; A second low-pass filter with a second cutoff frequency is applied to the image of the voxel to obtain a second background image, wherein the second cutoff frequency is different from the first cutoff frequency; An enhanced background image is determined from the first background image and the second background image; Determine the birefringence value used for the enhanced background image; Determine the birefringence value of the image used for the voxel; as well as The birefringence value of the image of the voxel is corrected based on the birefringence value used for the enhanced background image.

16. The storage device of claim 15, wherein the instructions for executing to acquire the image of the voxel of the storage medium are executable to acquire a plurality of images of the voxel in different polarization states, and the first low-pass filter and the second low-pass filter are applied to each of the plurality of images of the voxel.

17. The storage device of claim 15, wherein the instructions for determining the enhanced background image include instructions for combining the first background image and the second background image with a multiplication constant.

18. The storage device of claim 17, wherein the polarization state is... k Image of the voxel obtained at the location The enhanced background image is represented as b k And is determined as follows: The first low-pass filter is LowPass1, the second low-pass filter is LowPass2, and α is the multiplication constant.

19. The storage device of claim 17, wherein the birefringence value for the enhanced background image comprises from... b k Determined background hysteresis and background angle The birefringence value of the image used for the voxel includes values ​​from... m k Determined measurement hysteresis and measuring angle And wherein the execution is executable to determine the relative angle by means of the following: and relative lag To correct the birefringence value: ， ， ,as well as 。 20. The storage device of claim 15, wherein the instructions are executable to acquire the image of the voxels by acquiring an image of an array of voxels in an image plane, and wherein the one or more birefringent regions of the storage medium other than the voxels include one or more other voxels outside the image plane.

Images