JP2014032714A - Equalizer device for holographic memory and hologram reproduction device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain an equalizer device for a high-performance holographic memory and a hologram reproduction deice which can perform high-speed processing with a small amount of operation and obtaining low Raw BER.SOLUTION: A hologram reproduction device 1 for acquiring reproduction light of page data from a recording medium 9 by an image sensor 5 to perform data reproduction includes a multistage equalizer 7 for recovering a reproduction signal of the page data from the image sensor 5. The multistage equalizer 7 comprises a first equalizer 71 made of a sharpening FIR filter, and a second equalizer 72 made of a segment linear interpolation filter, the number of segments being six, for approximating a sinc function by a plurality of linear functions.

Description

  The present invention relates to an equalizer device and a hologram reproducing device for a holographic memory, and in particular, when reproducing page data (for example, large-capacity archive data for storage) recorded on a hologram recording medium, data reproducing light is used. The present invention relates to an equalizer device for a holographic memory and a hologram reproducing device suitable for restoring a reproduction signal from a read image sensor.

  In an information recording / reproducing apparatus using a holographic memory, that is, a hologram (see, for example, Patent Document 1 below), generally, a laser beam is light that is later carried by a beam splitter or the like (hereinafter referred to as “signal carrier” as appropriate). Light and a reference light, and the separated signal carrying light is spatially converted using a spatial light modulator (SLM) such as a liquid crystal panel or DMD (Digital Mirror Device). The signal to be recorded is superimposed on the signal carrying light to obtain signal light. The signal light on which the signal to be recorded is superimposed is guided so as to intersect with the reference light, and the recording medium disposed at the intersecting position is irradiated simultaneously with the reference light. Due to this irradiation, interference fringes, that is, holograms are refracted. It is recorded and held by a recording medium in the form of a rate distribution or the like.

  A pattern for spatial intensity modulation to be superimposed on the signal light is called page data or a data page. In general, this is image data in which white / black binary pixels are arranged in a two-dimensional array. When configuring page data, first, an error correction code is added to information to be recorded, and further converted into another bit string (one-dimensional or two-dimensional bit array) by a modulation code. For example, 5: 9 code (for example, refer to Patent Document 2 below), 2: 4 code, and the like are used as modulation codes. Are converted into a 2 × 2 two-dimensional bit array. By arranging these sequentially, page data is configured.

  By changing the reference light conditions such as wavefront, wavelength, and irradiation angle to the recording medium, different page data can be multiplexed and recorded at the same location on the recording medium, and these page data can be read out separately during playback. A recording / reproducing apparatus using a hologram is expected to be capable of recording / reproducing high-density and large-capacity information. Furthermore, since page data having an information amount of about 1 megabit can be recorded or reproduced with a single light irradiation, an increase in data transfer speed can be expected.

  On the other hand, when reproducing the recorded page data, only the reference light is irradiated to the recording medium. When the reference light is irradiated, diffracted light is generated from the hologram recorded on the recording medium, and this is acquired as an image by an image sensor such as a CCD image sensor or a CMOS image sensor. It is possible to restore the original information by specifying a data area from the acquired image areas, demodulating the data in the reverse order of the page data, and then performing error correction.

  Reproduction signal equalization is indispensable for reconstructing and demodulating page data after specifying a data area from an image acquired by an image sensor. A reproduction signal used for information communication, an optical disk, a magnetic disk, or the like is a voltage value or a current value with respect to a time axis, and these are one-dimensional signal forms. On the other hand, the holographic memory handles page data which is a two-dimensional signal form. Therefore, even if the reproduction equalizer that has been applied to the one-dimensional signal is directly applied to the two-dimensional signal, the performance is not guaranteed.

  In signal equalization when demodulating page data as a two-dimensional signal reproduced by a holographic memory, each page data image (hereinafter referred to as “imaged page data image” as appropriate) captured by an image sensor is used. Correspondence between the coordinate points and the position coordinates of each component (pixel) in the original page data array (hereinafter referred to as “original page data array” as appropriate) is obtained.

  Conventionally, after an L-shaped marker image is arranged outside the data area in the original page data array (see, for example, Patent Document 3 below), after the marker position is specified by a template matching method or the like in the captured page data image A method of calculating the coordinates of the four corners of the data area (captured page data image) (the positional relationship between the marker position and the coordinates of the four corners in the original page data array is known at the time of recording) is known.

  If the coordinates of the four corners of the captured page data image can be specified, each coordinate point on the captured page data image corresponding to the position coordinates of an arbitrary component (element point) in the original page data array can be calculated. . Specifically, as shown in FIG. 3, when an arbitrary element point R (i, j) in the original page data array corresponds to a point Q (x, y) on the imaged page data image, imaging is performed. Based on the positions A, B, C, and D of the four corners of the page data image, the coordinates of the point Q (x, y) can be obtained by the following equation (1).

  In general, the coordinates of the point Q are not integer values (when the center position of each pixel constituting the captured page data image is an integer value). Therefore, an interpolation process for obtaining a density value corresponding to the point Q based on density values (pixel values) of pixels around the point Q on the captured page data image is required. 2. Description of the Related Art Conventionally, there is known a hologram reproducing apparatus that uses an interpolation filter having such an interpolation processing function as an equalizer when reconstructing an original page data array from a captured page data image.

  The simplest equalizer uses an interpolation filter based on the nearest neighbor method. For example, the coordinate value (x, y) of the point Q on the captured page data image corresponding to the element point R of the original page data array to be obtained is converted into an integer value by the following equation (2) (coordinate value) Rounded off to the first decimal place, and the pixel value of the pixel located at the integer coordinate point (the pixel closest to the point Q (x, y)) is reconstructed into the element point R in the original page data array. This is a method of setting the pixel value of (i, j).

  Although this method requires a small amount of calculation, it can be processed at high speed.However, since the image quality is likely to deteriorate due to the lack of detailed information in the reconstructed image, a highly accurate decoding result is desired. difficult.

  There is also known a method of obtaining a pixel value of an element point R (i, j) by performing linear interpolation (bilinear interpolation) based on a distance ratio from four pixels around the point Q (x, y) (for example, (See Patent Document 4). Bilinear interpolation for determining the pixel value of the element point R (i, j) in the original page data array using the four pixel values on the image sensor is expressed by, for example, the following expressions (3) and (4).

  This bilinear interpolation can be considered as a piecewise linear interpolation in which the number of sections is two, excluding the sections that do not act (1 ≦ | t |). As described in paragraph (0009) of Patent Document 4 below, according to bilinear interpolation, the image quality is smooth, but the sharpness is lowered, and there is a possibility that minute bit information in the original page data array is lost. is there.

  Cubic convolution interpolation is known as an interpolation that can maintain sharpness more than bilinear interpolation. For example, Non-Patent Document 1 below discloses a technique that uses an equalizer that uses a neural network together with bilinear interpolation and cubic convolution interpolation. The cubic convolution interpolation is expressed by, for example, the following expressions (5) and (6).

  In cubic convolution interpolation, sharpness is maintained as compared with bilinear interpolation, and fine bit information is missing in the original page data array, so a low Raw BER (bit error rate before error correction processing) can be obtained.

  However, since cubic convolution interpolation uses many power operations as shown in the above equation (6), when using FPGA (Field-programmable gate array) with a limited number of multipliers, There is a possibility that the number of parallelization is restricted, and as a result, throughput is reduced. There is also a problem that even if the coefficient α in the cubic function shown in the above equation (6) is changed, it does not necessarily match the characteristics of the page data reproduced from the holographic memory.

  Patent Document 5 below discloses that a finite impulse response (FIR) filter in which the number of taps is set to 3 in both the vertical and horizontal directions is used as an adaptive equalizer that adaptively obtains tap coefficients. Yes. An FIR filter in which the number of taps is set to 3 both vertically and horizontally is represented by, for example, the following expressions (7) and (8).

  As described above, since the coordinates of the point Q in the above equation (1) generally do not become an integer value, only the FIR filter represented by the above equations (7) and (8) has a pixel value corresponding to the point R. Cannot be determined. For this reason, it is necessary to use an interpolation filter by the above-mentioned nearest neighbor method, bilinear interpolation, cubic convolution interpolation, or the like.

JP 2006-154163 A Japanese Patent No. 4863947 Japanese Patent No. 4809756 Japanese Patent No. 3720741 Special table 2008-536158 gazette

H. Osawa et al. `` Neural Network Equalization for Holographic DataStorage '' Technical Digest of International Symposium on Optical Memory (ISOM'06), Th-I-40 (2006)

  In general, in the holographic memory, the more multiplexed recording is performed, that is, the higher the density is recorded, the more noise is generated in the reproduced page data. In other words, if it is possible to reduce the raw BER in the reproduced page data by using an equalizer with higher performance than the conventional equalizer, the holographic memory can be further increased in density / The capacity can be increased.

  The present invention has been made in view of such circumstances, and provides a high-performance holographic memory equalizer device and a hologram reproducing device that can perform high-speed processing with a small amount of calculation and that can obtain a low raw BER. The purpose is to do.

The equalizer device for a holographic memory of the present invention comprises:
In a hologram reproduction apparatus for reproducing information by reproducing information reproduction light from a hologram recording medium on which page data information arranged in a two-dimensional array is recorded, to reproduce a reproduction signal from the image pickup element An equalizer device for a holographic memory used in
At least one equalizer, wherein one of the equalizers is configured by a piecewise linear interpolation filter having a number of pieces of three or more, which approximates a sinc function by a plurality of linear functions. .

  In the equalizer device for a holographic memory according to the present invention, the equalizer is arranged in two or more stages, and one of the equalizers is configured by the piecewise linear interpolation filter. One may be composed of a finite impulse response filter for image sharpening.

  The equalizer is arranged in a two-stage configuration, the first-stage equalizer is configured by the finite impulse response filter, and the second-stage equalizer is configured by the piecewise linear interpolation filter. It is preferable that

  The piecewise linear interpolation filter may be a filter represented by the following expressions (A) and (B).

  Further, the coefficient β in the above formula (B) is preferably set to a negative value.

Further, the finite impulse response filter is a filter represented by the following formula (C) and the following formula (D) in which the number of taps is set to 3 in both the vertical direction and the horizontal direction, and in the following formula (D) The tap coefficients of w ₁₂ , w ₂₁ , w ₂₃ , and w ₃₂ are set to values of −0.26 or more and −0.2 or less, and the tap coefficients of w ₁₁ , w ₁₃ , w ₃₁ , and w ₃₃ are − The value can be set to 0.04 or more and +0.04 or less.

  A hologram reproducing apparatus according to the present invention includes the equalizer device for a holographic memory according to the present invention.

  In the equalizer device and the hologram reproducing device of the present invention, one equalizer is constituted by a piecewise linear interpolation filter having a number of pieces of three or more, which approximates a sinc function by a plurality of linear functions. doing.

  This piecewise linear interpolation filter, like the conventional cubic convolution interpolation filter, can obtain a low raw BER, while interpolating as compared with a cubic convolution interpolation filter using a cubic function as a function for approximation. Since the amount of computation required for processing is greatly reduced, high-speed processing is possible.

  Therefore, according to the equalizer device for hologram memory and the hologram reproducing device according to the present invention, it is possible to perform high-speed processing with a small amount of calculation and obtain a low raw BER.

It is the schematic which shows the structure of the hologram recording / reproducing apparatus (hologram reproducing | regenerating apparatus) which concerns on one Embodiment of this invention, and a multistage equalizer apparatus (equalizer apparatus for holographic memories). It is a figure which shows typically the picked-up page data image on an image sensor. It is a figure which shows the correspondence of a captured page data image (a) and an original page data arrangement | sequence (b). It is a figure explaining the effect | action of the 1st equalizer and 2nd equalizer which are shown in FIG. It is a figure which shows the graph of the function which approximates a sinc function by a piecewise linear interpolation filter. It is the schematic which shows the structure of the equalizer apparatus (equalizer apparatus for holographic memories) which concerns on other embodiment of this invention. It is a figure which shows the captured page data image used for performance evaluation. The relationship between the first values of C1 and Raw BER tap coefficients sharpening FIR filter in the equalizer _{(w 21, w 12, w} 32, w 23) shown in FIG. 1, a diagram shown with comparative examples is there. The relationship between the first values of C2 and Raw BER tap coefficients sharpening FIR filter in the equalizer _{(w 11, w 31, w} 13, w 33) shown in FIG. 1, a diagram shown with comparative examples is there. It is a figure which shows the relationship between the value of coefficient (beta) of the piecewise linear interpolation filter in the 2nd equalizer shown in FIG. 1, and the value of Raw BER.

  Hereinafter, embodiments of an equalizer device and a hologram reproducing device for a holographic memory according to the present invention will be described in detail with reference to the drawings.

  A hologram recording / reproducing apparatus 1 shown in FIG. 1 constitutes one embodiment of a hologram reproducing apparatus according to the present invention, and includes a hologram optical system 3 for recording / reproducing holograms on a recording medium (hologram recording medium) 9. The image sensor 5 which consists of a CCD image sensor, a CMOS image sensor, etc. which images the reproduced hologram, and the multistage equalizer device 7 which restores the hologram imaged by the image sensor 5 are provided. The recording medium 9 used is composed of a photopolymer material having a thickness of about 1 mm sandwiched between two glass plates.

  In the hologram optical system 3, the light beam emitted from the laser light source 11 is guided to the spatial filter 13 (comprised of a plurality of lenses and a pinhole plate) by opening the shutter 12, and this spatial filter 13 removes spatial noise and enlarges the beam diameter. The used laser light source 11 is a green laser having an output wavelength of 532 nm.

  At the time of signal recording, the light beam from the spatial filter 13 is adjusted to a desired polarization ratio by the half-wave plate 15 via the mirror 14, and then the polarized light separated by the PBS (polarization beam splitter) 16. For example, the longitudinal polarization component (S polarization component) is used as reference light, and the lateral polarization component (P polarization component) is used as signal carrying light that carries a signal (page data) later.

  After the beam diameter is expanded to the size of the original page data array described later by the lenses 17 and 18, the signal carrying light is transmitted through the PBS 20 by opening the shutter 19, and is then subjected to SLM (Spatial Light Modulator: (Spatial light modulator) 21 is irradiated. At this time, the original page data array is displayed on the SLM 21, whereby the signal carrying light is spatially modulated to become signal light. The SLM 21 is a reflective liquid crystal panel having 1408 × 1058 pixels and a pixel pitch of 10.4 μm, and the original page data array has a size of 1260 × 1044.

  Information is stored in the original page data array by, for example, the method disclosed in Patent Document 2 described above. That is, an information string to be recorded is extracted 5 bits at a time and converted into a 3 × 3 array using a predetermined conversion table (see FIG. 9 of the above-mentioned Patent Document 2). Store sequentially in the direction. When storage to the right end is completed, the process proceeds to the next line in order, and storage continues in the same manner. In this embodiment, in order to evaluate Raw BER, no error correction code is added to the information sequence to be recorded.

  Only the longitudinal polarization component of the signal light is reflected by the PBS 20 toward an FTL (Fourier Transform Lens) 22. The reflected signal light (longitudinal polarization component) is optically Fourier transformed by passing through the FTL 22, and then only the 0th-order diffracted light is received by the rectangular aperture of the light shielding aperture plate 23 disposed on the Fourier transform plane. Passing is allowed, and the recording medium 9 is irradiated via the relay lens 24. Note that the length of one side of the rectangular opening was 2.0 times the Nyquist spatial frequency. If the length of one side is shortened, the recording density increases, but it causes signal deterioration such as waveform dullness.

  On the other hand, the reference light passes through the half-wave plate 31 in a vertically polarized state. The reference light that has passed through the half-wave plate 31 is incident on the diaphragm 33 via the mirror 32, and after the diameter of the light beam is reduced, the reference light is reflected at right angles as reference light at the time of recording in the PBS 34, and the mirror 35, the galvanometer mirror 36, and the relay The recording medium 9 is irradiated through the lens 37 at a predetermined angle.

  A light interference fringe, that is, light brightness and darkness occurs at a portion where the reference light and the signal light intersect at the time of recording, and because the recording medium 9 is arranged at this position, a place where the light is strong on the recording surface of the recording medium 9 While the polymerization reaction proceeds, the polymerization reaction does not proceed so much in weak areas. As a result, a refractive index distribution is formed on the recording surface of the recording medium 9, and the recording operation of one hologram is completed. Note that angle multiplex recording in which a plurality of holograms are recorded in the same region of the recording medium 9 can be performed by changing the angle of incidence of the reference light on the recording medium 9 by changing the angle of the galvanometer mirror 36.

  At the time of signal reproduction, the light beam from the spatial filter 13 is completely vertically polarized (S-polarized) by the half-wave plate 15 and reflected by the PBS 16 at a right angle. Thereafter, it is completely laterally polarized (P-polarized) by the half-wave plate 31, so that the PBS 34 is transmitted as reference light during reproduction and recorded from the back side through the mirror 38, the galvanometer mirror 39 and the relay lens 40. The medium 9 is irradiated. This is a known reproduction method called phase conjugate reproduction. In this case, reproduction light is emitted from the recording medium 9 to the FTL 22 side and passes through the FTL 22. Since the reproduction light at this time is laterally polarized light, it then passes through the PBS 20 and enters the image sensor 5. The image sensor 5 was a CMOS image sensor having a pixel count of 1696 × 1710 and a pixel pitch of 8.0 μm. From the pixel pitch ratio with the SLM 21, the oversampling rate is approximately 1.3.

  By acquiring (capturing) the reproduction light incident on the image sensor 5 with the image sensor 5, it is possible to generate a reproduction image (captured page data image) of the original page data array. FIG. 2 schematically shows a captured page data image formed on the image sensor 5. In FIG. 2, a rectangular area indicated by black is an imageable area of the image sensor 5, and a rectangular area indicated by the background of the geometric pattern is an area of a captured page data image formed on the image sensor 5. In addition, L-shaped marker images are formed near the four corners of the captured page data image. This marker is displayed together when the original page data array is displayed on the SLM 21, and the positional relationship between the marker position and the coordinates of the four corners in the original page data array is a known value determined at the time of recording. It has become a thing.

  Since the captured page data image formed on the image sensor 5 is affected by signal noise or the like, it does not accurately reproduce the original page data array. FIG. 3 shows the relationship between the captured page data image and the original page data array. As described above, in the captured page data image, the coordinates of the four corners of the captured page data image can be calculated after specifying the marker position by the template matching method or the like.

  If the coordinates of the four corners of the captured page data image can be specified, each coordinate point on the captured page data image corresponding to the position coordinates of an arbitrary component (element point) in the original page data array can be calculated. . Referring to FIG. 3, when an arbitrary element point R (i, j) in the original page data array corresponds to a point Q (x, y) on the captured page data image, the captured page data image Based on the four corner positions A, B, C, and D, the coordinates of the point Q (x, y) can be obtained by the above-described equation (1) (reproduced below).

  Here, NX and NY are the sizes of the original page data array (in this embodiment, NX = 1260, NY = 1044). I and j are integer values corresponding to the element points of the original page data array, and satisfy the relationship of 0 ≦ i ≦ NX−1 and 0 ≦ j ≦ NY−1.

  A multistage equalizer device 7 shown in FIG. 1 constitutes an embodiment of an equalizer device for a holographic memory according to the present invention, and the original page data is obtained from the captured page data image captured by the image sensor 5. It has a function to reconstruct (restore) the array.

  The multistage equalizer device 7 includes a first equalizer 71 and a second equalizer 72 arranged in a two-stage configuration. The first equalizer 71 arranged in the first stage is configured by a finite impulse response (FIR) filter for image sharpening (for reducing intersymbol interference) (hereinafter referred to as “sharpening FIR filter” as appropriate). The second equalizer 72 arranged in the second stage approximates the sinc function by a plurality of linear functions, and has a piecewise linear interpolation with a number of pieces of 3 or more (in this embodiment, “6”). It is composed of filters.

  FIG. 4 schematically shows the operation of the first equalizer 71 and the second equalizer 72. The first equalizer 71 arranged in the first stage has the pixel values of the 9 × 3 pixels of the captured page data image (the pixel values of the pixels at the center of the 9 pixels are represented by Q (X, Y), one pixel value P (U, V) is obtained from the following equation (E) and the following equation (F).

  The above equation (E) corresponds to the above-described equation (C) in which R (i, j) is replaced with P (U, V) and Q (x, y) is replaced with Q (X, Y). Formula (F) corresponds to the above-described formula (D). In addition, X, Y, U, and V in the above formula (E) take integer values corresponding to the pixel arrangement positions of the image sensor 5. (X, Y) and (U, V) take different values when the origin positions in the respective coordinate systems are different from each other (general case), but the origin positions in the respective coordinate systems are different from each other. When they are aligned and matched, (X, Y) = (U, V) may be obtained.

  The second equalizer 72 arranged in the second stage uses each pixel value of 4 × 4 16 pixels in the captured page data image (the pixel value of one of the 16 pixels is P ( U, V)), the pixel value R (i, j) of one element point in the original page data array is obtained and is expressed by the following equation (G) and the following equation (H).

  The above expression (G) corresponds to the above-described expression (A) in which Q (X, Y) is replaced with P (U, V), and the above expression (H) corresponds to the above-described expression (B). To do. Further, X, Y, U, and V in the above equation (G) take integer values corresponding to the pixel arrangement positions of the image sensor 5 as in the above equation (E). (U, v) is the coordinate value of the point P corresponding to the coordinate value (i, j) (i, j is an integer value) of one element point R in the original page data array. Don't be.

  The above equation (G) is piecewise linear interpolation in which a plurality of sections are set and linear interpolation is performed in each section as shown in the above expression (H). In this example, the number of sections is 6 except for sections that do not act (2 ≦ | t |).

  Further, as shown in FIG. 5, the above equation (H) is set so as to approximate the sinc function as a whole (in FIG. 5, the coefficient β of the above equation (H) is set to −0.2. ing). The cubic convolution interpolation filter also performs interpolation using a function that approximates a sinc function by a cubic function (shown in FIG. 5 as a comparison), but is defined by the above formulas (G) and (H). Unlike the cubic convolution interpolation filter, the linear interpolation filter does not use exponentiation, so that the amount of calculation is small and the implementation is easy even when the circuit scale is limited.

  In addition, the coefficient β in the above formula (H) is calculated when the distance from the data array element to be obtained exceeds one element and is calculated (1 ≦ | t | <2). It has been experimentally confirmed that it is desirable to set a negative value. There is an optimum value for β. This optimum value will be described later. Note that the piecewise linear interpolation can change the characteristics in various ways by allowing the coefficient β to have various values, both positive and negative.

  Next, another embodiment of the equalizer device for a holographic memory according to the present invention will be described. An equalizer device 8 shown in FIG. 6 is used to reconstruct (restore) the original page data array from the captured page data image captured by the image sensor 5, instead of the multistage equalizer device 7 described above. And is provided with one equalizer 81. This equalizer 81 is similar to the second equalizer 72 described above, and each pixel value (one of the 16 pixels) of 4 × 4 16 pixels in the first captured page data image. The pixel value R (i, j) of one element point in the original page data array is obtained from the pixel value of the pixel Q (X, Y), and the above-described equations (A) and (B ) (Reproduced below).

  The above expression (A) corresponds to the above-described expression (G) in which P (U, V) is replaced with Q (X, Y), and the above expression (B) corresponds to the above-described expression (H). To do. Further, (x, y) in the above formula (A) is the coordinate value of the point Q corresponding to the coordinate value (i, j) (i, j is an integer value) of one element point R in the original page data array. In general, it is not an integer value.

  Since the performance evaluation of the equalizer device for a holographic memory according to the present invention was performed, the evaluation result will be described below. In the performance evaluation, a captured page data image acquired by the image sensor 5 shown in FIG. 7 is used.

  Table 1 below shows Raw BER values when the original page data array is restored from the captured page data image shown in FIG. 7 using an equalizer having a one-stage configuration including various interpolation filters. In Table 1, “partition linear interpolation” is described when the equalizer device 8 shown in FIG. 6 is used. As a comparative example, the Raw BER value was similarly obtained for an equalizer based on the nearest neighbor method, bilinear interpolation, and cubic convolution interpolation. Note that the coefficient α (see the above equation (6)) in the cubic convolution interpolation is −0.6, and the coefficient β (see the above equation (B)) in the piecewise linear interpolation is −0.2.

  As shown in Table 1, according to the equalizer based on the piecewise linear interpolation according to the present invention, the Raw BER is the lowest value compared with the case where other equalizers are used. You can see that

Next, the evaluation result of the multistage equalizer apparatus 7 shown in FIG. 1 will be described. FIG. 8 shows a tap coefficient of the sharpening FIR filter (in FIG. 8, simply described as “FIR”) in the first equalizer 71 arranged in the first stage (see the above formula (F)). ), The value of w ₂₂ is set to 1, and the values of w ₁₁ , w ₁₃ , w ₃₁ , and w ₃₃ are all set to 0, and this is set to 0, and w ₂₁ , w ₁₂ , w ₃₂ , w The relationship between the value of C1 and the value of Raw BER when the value of ₂₃ is C1 is shown.

  For comparison, an equalizer using a sharpened FIR filter is provided in the first stage in the same manner as the first equalizer 71, and the nearest neighbor method, bilinear interpolation or cubic convolution interpolation is used in the second stage. The relationship between the set value of C1 and the Raw BER value when an equalizer is provided is also shown. Note that the coefficient α (see the above equation (6)) in the cubic convolution interpolation is −0.6, and the coefficient β (see the above equation (B)) in the piecewise linear interpolation is −0.2.

As shown in FIG. 8, according to the present invention, the first stage is composed of a first equalizer 71 using a sharpened FIR filter, and the second stage is composed of a second equalizer 72 using a piecewise linear interpolation filter. According to the multistage equalizer device 7, it can be seen that the Raw BER is the lowest value when the value of C1 is set to the optimum value as compared with the case where the sharpening FIR filter and another interpolation filter are combined. . In particular, as compared with the case where the cubic convolution interpolation filter is used, it can be seen that the multistage equalizer device 7 according to the present invention obtains a low Raw BER value despite a small amount of calculation. In addition, according to the evaluation result shown in FIG. 8, the values C1 of the tap coefficients w ₂₁ , w ₁₂ , w ₃₂ , and w ₂₃ of the sharpened FIR filter are in the range of −0.26 or more and −0.2 or less. It can be seen that it is preferable to set a numerical value.

After the optimum value of the sharpening FIR tap coefficients of the filter _{w 21, w 12, w 32} , the value C1 of _{w 23} is determined, the optimum value C2 of the other tap coefficients _{w 11, w 13, w 31} , w 33 The value was determined. FIG. 9 shows a tap coefficient of the sharpening FIR filter (simply indicated as “FIR” in FIG. 9) in the first equalizer 71 in the first stage of the multistage equalizer device 7 (the above formula ( F))), the value of w ₂₂ is set to 1, and the values of w ₂₁ , w ₁₂ , w ₃₂ , and w ₂₃ are all set to C1, and these are set to optimum values, and w ₁₁ , w ₁₃ , W ₃₁ , w ₃₃ are C2, and the relationship between the set value of C2 and the Raw BER value is shown.

  For comparison, an equalizer using a sharpened FIR filter is provided in the first stage in the same manner as the first equalizer 71, and the nearest neighbor method, bilinear interpolation or cubic convolution interpolation is used in the second stage. The relationship between the set value of C2 and the value of Raw BER when an equalizer is provided is also shown. The coefficient α in cubic convolution interpolation (see the above equation (6)) is −0.6, and the coefficient β in piecewise linear interpolation (see the above equation (B)) is −0.2. Is the same as in FIG.

As shown in FIG. 9, according to the multistage equalizer device 7 according to the present invention, the Raw value when the value of C2 is set to the optimum value as compared with the case where the sharpening FIR filter and another interpolation filter are combined is shown. It can be seen that the BER is the lowest value. According to the evaluation results shown in FIG. 9, the values C2 of the tap coefficients w ₁₁ , w ₁₃ , w ₃₁ , and w ₃₃ of the sharpened FIR filter are values in the range of −0.04 or more and +0.04 or less. It can be seen that C2 = 0.01 is the optimum value.

  Next, the optimum value of the coefficient β (see the above formula (B)) of the piecewise linear interpolation filter in the second equalizer 72 installed in the second stage of the multistage equalizer device 7 was obtained. FIG. 10 shows the relationship between the set value of the coefficient β of the piecewise linear interpolation filter and the Raw BER value in the second equalizer 71 in the second stage of the multistage equalizer device 7. According to the evaluation result shown in FIG. 10, it can be seen that the optimum value of the coefficient β of the piecewise linear interpolation filter is −0.2.

  Although the equalizer (second equalizer 72, equalizer 81) configured by the piecewise linear interpolation filter having six pieces has been described above, the number of pieces of the piecewise linear interpolation filter is limited to six. is not. For example, in the case of an equalizer configured by a piecewise linear interpolation filter having four pieces, the above equation (B) or the above equation (H) can be realized by simplifying to the following equation (I). it can.

  The above formula (I) is a form obtained by further approximating the approximation function by the piecewise linear interpolation filter having the number of pieces 6 shown in FIG. Since the piecewise linear interpolation filter having the number of sections of 4 has a smaller number of case divisions than that of the section having the number of sections of 6, the arithmetic processing can be performed at higher speed.

  The optimum values of C1, C2, and β obtained in the above description and preferable numerical ranges are the conditions of the recording medium to be used, the configuration of the optical system, the fill factor of the SLM and the image sensor, the pixel pitch, the oversampling rate, Since it is expected to vary depending on various conditions such as a modulation code, it is desirable to obtain an optimum value according to the system conditions. Further, in order to dynamically obtain the optimum values of C1, C2, and β, a method of adaptively deriving them can be considered. Even in this case, it is possible to use the configuration of the equalizer for a holographic memory according to the present invention, and even in this case, a low Raw BER can be obtained.

  As mentioned above, although embodiment of this invention was described, this invention is not limited to embodiment mentioned above, A various aspect can be changed. Hereinafter, the modified mode will be considered using mathematical expressions.

  In FIG. 4, one pixel value P (U, V) is obtained from each pixel value of 9 pixels of 3 × 3 of the captured page data image (the pixel value of the central pixel is Q (X, Y)). The operation of the first equalizer 71 (sharpening FIR filter) is expressed by the following equation (J) when coordinate values (U, V) = (X, Y) are used for the sake of simplicity.

  At this time, in FIG. 4, from each pixel value of 4 × 4 16 pixels in the captured page data image (a pixel value of one of the 16 pixels is P (U, V)), The action of the second equalizer 72 (piecewise linear interpolation filter) for obtaining the pixel value R (i, j) of one element point in the original page data array is expressed by the following equation (K).

  Here, when the formula (J) is substituted into the formula (K), the following formula (L) is obtained.

  However, U, V, s, and t are integer values, the parentheses represent the action of the first equalizer 71 in the first stage, and the parts outside the parentheses are those of the second equalizer 72 in the second stage. Represents the action. If the position of the parenthesis of the above formula (L) is changed, the following formula (M) is obtained.

  In the above formula (M), if the parenthesis represents the action of the first-stage equalizer and the outside of the parenthesis represents the action of the second-stage equalizer, This means that a piecewise linear interpolation filter (which may be a cubic convolution filter) may be applied and a sharpening FIR filter may be applied in the second stage.

  Moreover, when the parenthesis of the above formula (M) is removed, it can be transformed as the following formula (N).

  Here, f is a function having x, y, U, V, s, and t as arguments, and this is a tap coefficient of a convolution filter in which the number of taps is 6 in both the vertical and horizontal directions (not multistage). It can be seen as a function to determine.

  That is, in the above equation (N), the pixel value R of one element point of the original page data array in FIG. 4 is not multistage from the pixel values of 36 pixels of 6 × 6 of the captured page data image. It means that it is derived by using a convolution filter, and the two-stage equalizer according to the present invention can be considered to provide a method for determining the tap coefficient of the convolution filter. .

  From such consideration, as a modification of the equalizer device for a holographic memory according to the present invention, a piecewise linear interpolation filter (hereinafter referred to as “ (referred to as a sinc function approximation piecewise linear interpolation filter)). A two-stage configuration in which an equalizer composed of a sharpened FIR filter is arranged in the second stage. Can be mentioned. As another modification of the two-stage configuration, a sinc function approximation piecewise linear interpolation filter is arranged in the first and second stages, and a sinc function approximation piecewise linear interpolation filter is arranged in the first stage. In the second stage, another interpolation filter different from the sinc function approximation piecewise linear interpolation filter is arranged, and in the first stage, another interpolation filter different from the sinc function approximation piecewise linear interpolation filter is arranged. An example in which a sinc function approximate piecewise linear interpolation filter is arranged at the stage.

  In addition, the equalizer device for a holographic memory according to the present invention includes three or more equalizers including three or more stages including an equalizer configured by a sinc function approximation piecewise linear interpolation filter. It is also possible to adopt an arrangement mode.

  In the above-described embodiment, a hologram recording / reproducing apparatus having both a hologram recording function and a reproducing function has been described as an aspect of the hologram reproducing apparatus. However, the present invention provides only a hologram reproducing function. The present invention can also be applied to the provided hologram reproducing apparatus.

DESCRIPTION OF SYMBOLS 1 Hologram recording / reproducing apparatus 3 Hologram optical system 5 Image sensor 7 Multistage equalizer apparatus 8 Equalizer apparatus 9 Recording medium 11 Laser light source 12, 19 Shutter 15, 31 Half-wave plate 16, 20, 34 PBS
21 SLM
22 FTL
36, 39 Galvanometer mirror 71 First equalizer 72 Second equalizer 81 Equalizer

Claims (7)

In a hologram reproduction apparatus for reproducing information by reproducing information reproduction light from a hologram recording medium on which page data information arranged in a two-dimensional array is recorded, to reproduce a reproduction signal from the image pickup element An equalizer device for a holographic memory used in
At least one equalizer, wherein one of the equalizers is configured by a piecewise linear interpolation filter having a number of pieces of three or more, which approximates a sinc function by a plurality of linear functions. Equalizer device for holographic memory.   The equalizers are arranged in two or more stages, one of the equalizers is constituted by the piecewise linear interpolation filter, and another one of the equalizers is constituted by a finite impulse response filter for image sharpening. The equalizer device for a holographic memory according to claim 1, wherein the equalizer device is a holographic memory equalizer.   The equalizer is arranged in a two-stage configuration, the first-stage equalizer is configured by the finite impulse response filter, and the second-stage equalizer is configured by the piecewise linear interpolation filter. The equalizer device for a holographic memory according to claim 2, wherein the equalizer device is a holographic memory equalizer. The equalizer for a holographic memory according to any one of claims 1 to 3, wherein the piecewise linear interpolation filter is a filter represented by the following expression (A) and the following expression (B): apparatus.
  The equalizer device for a holographic memory according to claim 4, wherein the coefficient β in the above formula (B) is set to a negative value. The finite impulse response filter is a filter represented by the following formula (C) and the following formula (D) in which the number of taps is set to 3 in both the vertical and horizontal directions, and w ₁₂ in the following formula (D). , W ₂₁ , w ₂₃ , w ₃₂ are set to values of −0.26 to −0.2, and w ₁₁ , w ₁₃ , w ₃₁ , w ₃₃ are each set to −0.04. The equalizer device for a holographic memory according to claim 2, wherein the equalizer device is set to a value of +0.04 or less.
A hologram reproducing apparatus comprising the equalizer device for a holographic memory according to any one of claims 1 to 6.