FIELD OF THE INVENTION
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The present invention relates to the field of holographic data storage system. In particular, the present invention relates to a method and system for equalizing holographic data pages.
BACKGROUND OF THE INVENTION
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Holographic data storage systems store information or data based on the concept of a signal beam interfering with a reference beam at a holographic storage medium. The interference of the signal beam and the reference beam creates a holographic representation, i.e., a hologram, of data elements as a pattern of varying refractive index and/or absorption imprinted in a volume of a storage or recording medium such as a photopolymer or photorefractive crystal. Combining a data-encoded signal beam, referred to as an object beam, with a reference beam creates the interference pattern at the storage medium. A spatial light modulator (SLM), for example, can create the data-encoded signal beam. The interference pattern induces material alterations in the storage medium that generate the hologram. The formation of the hologram in the storage medium is a function of the relative amplitudes and polarization states of, and phase differences between, the signal beam and the reference beam. The hologram is also dependent on the wavelengths and angles at which the signal beam and the reference beam are projected into the storage medium. After a hologram is created in the storage medium, projecting the reference beam into the storage medium reconstructs the original data-encoded signal beam. The reconstructed signal beam may be detected by using a detector, such as CMOS photo-detector array or the like. The detected data may then be decoded into the original encoded data.
In a page-oriented holographic data storage device, it is advantageous to minimize the size of the holograms in order to achieve maximum storage density. One method of accomplishing this is minimizing the size of the page imaging aperture. However, minimizing the size of the aperture has the consequence of increasing blur, in terms of broadening the pixel spread function (PSF) in the page images. This blur decreases the signal-to-noise ratio (SNR) of the holographic storage device, which increases the bit error rate (BER) of the system, and which in turn limits the storage density.
Since blur in an image is a deterministic process, much of the SNR loss may be reclaimed by digitally post-processing the detected page image. Traditionally, the detected image is convolved with a small kernel matrix w, also known as a kernel, representing an inverse blurring operation (de-convolution), thereby implementing a finite impulse response (FIR) filter equalization.
The kernel of a FIR filter, for example a 3×3 or a 5×5 matrix, may be determined by several methods known in the current art. For example, if the page image pixel spread function is known, a zero-forcing equalizer may be designed by calculating the linear inverse of the PSF. An example of the zero-forcing method is described in “Channel estimation and intra-page equalization for digital volume holographic data storage,” by V. Vadde and B. Kumar in Optical Data Storage 1997, pp. 250-255, 1997. Another approach is to choose FIR filter coefficients that minimize the difference between the equalized data page image and the original data page. Such a method is described in “Application of linear minimum mean-squared-error equalization for volume holographic data storage,” by M. Keskinoz and B. Kumar in Applied Optics, vol. 38, no. 20, Jul. 10, 1999.
Performance of FIR equalization as shown in the prior art is limited in at least two aspects. First, blur in a coherent imaging system is not a linear process. Although coherent light adds linearly in electric field strength, detectors can only directly detect irradiance. This introduces a nonlinear absolute value squared transformation. Furthermore, each detector element (pixel) integrates the irradiance over an area, introducing a further nonlinearity. Prior art has disclosed ways to solve this problem either through a “magnitude model” (operating on the square root of the detected values, but lacking phase information), or through an “intensity model” (operating on the PSF and the pixel fill factors). An example of both the “magnitude model” and the “intensity model” is described in “Channel modeling and estimation for intra-page equalization in pixel-matched volume holographic data storage,” by V. Vadde and B. Kumar in Applied Optics, vol. 38, no. 20, Jul. 10, 1999.
Second, the performance of FIR equalization described by the prior art is limited because real imaging systems are not perfect shift invariant linear systems. In other words, the pixel spread function is not constant at all locations in the field of view. There are a number of factors that create variations in the width or shape of the PSF throughout the field of view. For example, variations may be caused by lens aberrations and misalignment; by distortions, shrinkage, and other non-ideal media responses; and by misalignment and wavefront errors in the reconstructing reference beam. A significant consequence of these effects in a pixel-matched system is the degradation of the pixel matching, because image distortion shifts local areas of the image with respect to the detector pixels. For example, a uniform shrinkage of the medium causes the holographic image to be magnified, producing a radial displacement such that data pixel images are no longer centered on their respective detector pixels.
Therefore, new methods and systems for addressing the issues of the prior art methods are needed. In particular, methods and systems for equalizing holographic image data are needed to improve the storage density of the holographic data storage system. Further, methods and systems for compensating nonlinearity of the holographic data storage channel are also needed to improve the storage density of the holographic data storage system.
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A method for equalizing a holographic image page includes receiving the holographic image page and dividing the holographic image page into a plurality of local image regions. The method further includes generating a local alignment error vector for each local image region, computing a local finite impulse response kernel for each local image region according to the corresponding local alignment error vector, and adjusting misaligned pixels of each local image region using the corresponding local finite impulse response kernel.
In another embodiment, a method for compensating nonlinearity of a holographic data storage channel includes selecting a metric for measuring data accuracy of a holographic image page and computing a set of values of the metric over a predetermined set of linearization exponents. The method further includes selecting a desired linearization exponent for generating a desired value of the metric that corresponds to a desired data accuracy of the holographic image page, and adjusting the nonlinearity of the holographic data storage channel in accordance with the desired linearization exponent.
In yet another embodiment, a method for equalizing a holographic image page includes receiving the holographic image page and dividing the holographic image page into a plurality of image regions, and deriving an expected blur and an actual blur for each image region. The method further includes computing a pixel-signal-error-ratio between the actual blur and the expected blur for each image region, computing a local finite impulse response kernel in accordance with the pixel-signal-error-ratio and a predetermined global final impulse response, and adjusting misaligned pixels of each local image region using the corresponding local finite impulse response kernel.
BRIEF DESCRIPTION OF THE DRAWINGS
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The aforementioned features and advantages of the invention as well as additional features and advantages thereof will be more clearly understood hereinafter as a result of a detailed description of embodiments of the invention when taken in conjunction with the following drawings.
FIG. 1 illustrates a holographic data storage system according to an embodiment of the present invention.
FIG. 2A illustrates an exemplary 21 pixel×21 pixel image data generated by the spatial light modulator.
FIG. 2B illustrates the 21 pixel×21 pixel image data of FIG. 2A detected at the output of the holographic data storage system without being processed by the inventive techniques.
FIG. 2C illustrates the 21 pixel×21 pixel image data of FIG. 2A after being processed according to an embodiment of the present invention.
FIG. 3A is a histogram of the unprocessed pixel image data according to an embodiment of the present invention.
FIG. 3B is a histogram of the processed pixel image data after being processed according to an embodiment of the present invention.
FIG. 4A illustrates a portion of a 3 pixel×3 pixel of an exemplary data image.
FIG. 4B illustrates an intensity profile resulting from adding and squaring the electric field strengths of pixels in the first row of FIG. 4A according to an embodiment of the present invention.
FIG. 5 illustrates a method for selecting a linearization exponent according to an embodiment of the present invention.
FIG. 6 compares the signal-to-noise ratio versus imaging aperture according to the various equalization schemes discussed.
Like numbers are used throughout the figures.
DESCRIPTION OF EMBODIMENTS
Methods and systems are provided for equalizing holographic image pages and for compensating nonlinearity of a holographic data storage system. The following description is presented to enable any person skilled in the art to make and use the invention. Descriptions of specific techniques and applications are provided only as examples. Various modifications to the examples described herein will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other examples and applications without departing from the spirit and scope of the invention. Thus, the present invention is not intended to be limited to the examples described and shown, but is to be accorded the widest scope consistent with the principles and features disclosed herein.
In a holographic data storage system, the detector (camera) is typically aligned with the holographic image during a read operation such that each pixel in the image is centered on a single pixel on the detector. This alignment process is generally referred to as “pixel matching.” The objective of “pixel matching” is to sample the holographic images of data-containing holograms on the detector in a manner that preserves the information content so that the detected image that have a low bit error rate (BER). Pixel misalignment may occur because one or more components of the holographic data system may be translated or rotated causing translational, tilted, rotational, magnification, or defocusing errors in the detected image. Misalignment, unless otherwise indicated, may refer to one or more of translational, tilt, rotational, magnification, or defocusing errors of the detected image.
Equalizing a Holographic Image Page
FIG. 1 illustrates a holographic data storage system according to an embodiment of the present invention. The holographic data storage system includes a light source 110, a first lens 112, a beam splitter 114, a SLM 116, a first microcontroller 117. The holographic data storage system further includes a first mirror 118, a second lens 120, a storage medium 124, a third lens 126, a detector 128, a second microcontroller 129, a second mirror 130, a microprocessor 136 and a memory 138. The memory 138 comprises an operating system 140, an application layer 141, an equalization module 142 and a linearization module 143.
In one embodiment, the light source 110 is a laser for providing a coherent beam of light. The beam splitter 114 is positioned to split the laser beam into an object beam and a reference beam. The object beam is directed to the SLM 116 where it is encoded, for example, by an encoding unit within the first microcontroller 117. The object beam is encoded with data associated with a data page that creates a two-dimensional image signal. The signal beam, modulated with the data page image, is then directed to the recording storage medium 124 via the first mirror 118.
The first microcontroller 117 may include software and/or hardware capable of encoding data sequences into pixel values by appropriately addressing the array of addressable elements of the SLM 116. The first microcontroller 117 may also encode various registration marks or known pixel patterns for determining misalignments, i.e., rotation, translation, and the like of the SLM 116, storage medium 124, or detector 128. For example, the first microcontroller 117 may include an encoder and/or a decoder, or the like, and may address the SLM 116 and detector 128 through firmware commands or the like.
The microprocessor 136 communicates (as indicated by the double arrow) with the first microcontroller 117 as well as the memory 138 and other components of the system.
The memory 138 may include high-speed random access memory and may include non-volatile memory, such as a flash RAM. The memory 138 may also include mass storage that is remotely located from the microprocessor 136. The memory 138 preferably stores:
an operating system 140 that includes procedures for handling various basic system services and for performing hardware dependent tasks; and
an application layer 141 for interfacing between the operating system and other applications of the holographic data storage system.
The microprocessor 136 further communicates with an equalization module 142 and a linearization module 143 of the holographic data storage system, where
the equalization module 142 reduces the variations of signal intensity for both the ON and OFF pixels; and
the linearization module 143 compensates the channel nonlinearity of the holographic data storage system.
The equalization module 142 and the linearization module 143 may include executable procedures, sub-modules, tables and other data structures. In other embodiments, additional or different modules and data structures may be used, and some of the modules and/or data structures listed above may not be used. The equalization module 142 and the linearization module 143 may be implemented in software and/or in hardware. When implementing in hardware, the equalization module 142 and the linearization module 143 may be implemented in application specific integrated circuits (ASICs) or in field programmable gate arrays (FPGAs).
The holographic data storage system of FIG. 1 may also include micro-actuators (not shown) configured to move at least one of the SLM 116, detector 128, and recording medium 124. According to one example, micro-actuators may be controlled, for example, by the first microcontroller 117 or the second microcontroller 129 through microprocessor 136. Microprocessor 136 may receive signals from detector 128 and use a servo feedback loop or the like to move at least one of the SLM 116, detector 128, or recording medium 124 to increase the performance of the holographic storage device. For example, an error signal associated with a misalignment may be sent to the first microcontroller 117 or the second microcontroller 129 (or a micro-controller controlling the position of storage medium 124) to activate one or more micro-actuators.
Generally, alignment of holographic components is set at the time of manufacturing. Over time, however, the components may become misaligned due to vibrations, shocks, temperature changes, medium shrinkage, and the like. The spatial extent over which stored holograms have useable signal-to-noise ratio (SNR) may be approximately only a few microns or less. Therefore, even slight movement of the hologram based on movements of the SLM, detector, or storage medium due to mechanical error, vibration, temperature change, medium shrinkage, and the like often degrades the performance of the holographic system.
In the United. States patent application Ser. No. 10/305,769, entitled “Micro-Positioning Movement of Holographic Data Storage System Components”, filed on Nov. 27, 2002 and commonly owned by InPhase Technologies, Inc., a method is disclosed for measuring page misalignment at local regions of the image by performing a cross-correlation between a part of the image and a known portion of the data page. The entire content of the 10/305,769 application is incorporated herein by reference. The 10/305,769 application further discloses how the method for measuring page misalignment may be applied at a plurality of sample positions within an image in order to generate a map of pixel misalignment over the whole image. The misalignment at each sample position is a vector with two alignment error components, e=(Δx, Δy), representing the x and y misalignment, respectively, measured in pixels. Given this measured misalignment information about an image, the disclosed method utilizes the alignment error vector in improving the performance of FIR equalization.
In one embodiment, an image page is divided into n local image regions, each of which is characterized by a local alignment error vector ei (i=1 . . . n). Then, each local image region is equalized with a local FIR kernel, wi, which is a modified version of the global FIR kernel, w. In other words, the method determines the magnitude and direction of the local pixel alignment error for each local image region, and then compensates the local FIR kernel wi accordingly in order to remove the local pixel alignment error. In particular, wi is formed by shifting w in the opposite direction of ei so as to reverse the effects of the local pixel alignment error. For example, in the case where w is a 3-by-3 matrix, w is of the form