Sparse modulation coding for increased capacity in volume holographic storage

In page-oriented memories, data pages commonly consist of comparable numbers of on and off pixels. Data-page sparsity is defined by reduction of the number of on pixels per page, leading to an increased diffracted power into each pixel. When page retrieval is dominated by a fixed noise floor, the number of pages in the memory is limited by the pixel diffraction efficiency. Sparsity increases the number of storable pages while reducing the amount of user information per page. A detailed analysis of sparsity in volume holographic memories shows that the total memory capacity can be increased by 15% by use of data pages that contain on average 25% on pixels. Sparsity also helps to reduce the effects of interpixel cross talk by strongly reducing the probability that worst-case pixel patterns (e.g., blocks of on pixels with a center off pixel) will occur in the data page. Enumeration block coding techniques provide construction of sparse-data pages with minimal overhead. In addition, enumeration coding offers maximum-likelihood detection with low encoding-decoding latency. We discuss the theoretical advantages of data-page sparsity. We also present experimental results that demonstrate the proposed capacity gain. The experiment verifies that it is practical to construct and use sparse-data pages that result in an overall user capacity gain of 16% subject to a page retrieval bit-error rate of 10(-4).     

Quantitative study of the gray-scale fidelity of volume holographic images

The reconstruction fidelity of gray-scale holographic images is analyzed quantitatively and assessed by use of proposed quantities, especially the correlation coefficient between the original and the retrieved images. The physical factors affecting the fidelity of photorefractive holograms are investigated experimentally, leading to results that are useful for the determination of the recording-beam ratio and the exposure dosage for high-fidelity retrieval. Investigation of the effects of noise on the fidelity of multiplexed holograms suggests that, if multiple-gray-scale data pages are multiplexed in a given volume, the total bit capacity may be competitive with that realized by means of storing binary pages.     

Irregular repeat-accumulate codes for volume holographic memory systems

We investigate the application of irregular repeat-accumulate (IRA) codes in volume holographic memory (VHM) systems. We introduce methodologies to design efficient IRA codes. We show that a judiciously designed IRA code for a typical VHM can be as good as the optimized irregular low-density-parity-check codes while having the additional advantage of lower encoding complexity. Moreover, we present a method to reduce the error-floor effect of the IRA codes in the VHM systems. This method explores the structure of the noise pattern in holographic memories. Finally, we explain why IRA codes are good candidates for the VHM systems.     

Low-density parity-check codes for volume holographic memory systems

We investigate the application of low-density parity-check (LDPC) codes in volume holographic memory (VHM) systems. We show that a carefully designed irregular LDPC code has a very good performance in VHM systems. We optimize high-rate LDPC codes for the nonuniform error pattern in holographic memories to reduce the bit error rate extensively. The prior knowledge of noise distribution is used for designing as well as decoding the LDPC codes. We show that these codes have a superior performance to that of Reed-Solomon (RS) codes and regular LDPC counterparts. Our simulation shows that we can increase the maximum storage capacity of holographic memories by more than 50 percent if we use irregular LDPC codes with soft-decision decoding instead of conventionally employed RS codes with hard-decision decoding. The performance of these LDPC codes is close to the information theoretic capacity.     

Computer simulation of reflective volume grating holographic data storage

The shift selectivity of a reflective-type spherical reference wave volume hologram is investigated using a nonparaxial numerical modeling based on a multiple-thin-layer implementation of a volume integral equation. The method can be easily parallelized on multiple computers. According to the results, the falloff of the diffraction efficiency due to the readout shift shows neither Bragg zeros nor oscillation with our parameter set. This agrees with our earlier study of smaller and transmissive holograms. Interhologram cross talk of shift-multiplexed holograms is also modeled using the same method, together with sparse modulation block coding and correlation decoding of data. Signal-to-noise ratio and raw bit error rate values are calculated.     

Application of linear minimum mean-squared-error equalization for volume holographic data storage

When target densities of volume holographic data storage systems are increased, the systems experience increased interference from adjacent pixels and noise. Here we present a method for designing and applying linear minimum mean-squared-error (LMMSE) equalization to improve the bit error rates (BER's) and hence the storage densities achievable. Numerical results with five defocused data pages indicate that a significant improvement in the BER is possible with LMMSE equalization.     

Selectivity and tolerance calculations with half-cone-shaped reference beam in volume holographic storage

When developing a compact holographic storage system it is beneficial to use a reflection-type arrangement, where the entire optical system is on the same side of the storage material. For reflection type holographic discs, it is important to use half-cone-shaped spherical reference beams to avoid the ghost images caused by phase conjugate readout. The goal of this paper is to look for appropriate engineering tools to model diffraction efficiency of finite volume holograms created by half-cone-shaped reference beams. Two numerical methods – volume integral and beam propagation – were applied to calculate the shift selectivity curves. Simulation results show significant discrepancies between the shift selectivity curves corresponding to the approximated analytical equation and the numerically calculated shift selectivity curves; there are no Bragg zeros and there are no selective and nonselective directions. Beside the shift selectivity curves, track, focus, tilt and wavelength tolerance values are shown for finite volume holograms.     

Improvements in the capacity of computer-generated holographic storage using the Lee method with sparse multivalued reconstructions

The use of sparse multivalued data encodings for the purpose of increasing the capacity of parallel-access optical memories based on Fourier-transform computer-generated holography is discussed. Results based on the Lee method indicate that a sparse encoding of nonbinary data words can be used to increase the storage-area utilization efficiency from 35% to > 70%. It is also found that for signal-to-noise ratios greater than 200, five-level data encoding can be used to achieve bit error rates less than 10(-12) reliably with 60% area efficiency.     

Improvement to human-face recognition in a volume holographic correlator by use of speckle modulation

We show that a speckle-modulation technique can improve the parallelism and the recognition accuracy of volume holographic correlators. The object patterns are modulated by a speckle pattern generated by a diffuser. These modulated patterns are stored as Fourier holograms by use of angular-fractal multiplexing. With the speckle modulation the sidelobes are completely suppressed, the cross talk is negligible, and the correlation peak becomes a bright sharp spot. Thus higher recognition accuracy is achieved. The angular separation between adjacent patterns in the multiplexing could be much smaller, resulting in larger capacity and higher parallelism of the correlator. Also, this technique can be combined with other methods such as wavelet filtering to achieve a large invariant tolerance range. Theoretical analysis, numerical evaluation, and experimental results are presented to confirm that sidelobes and cross talk are sharply suppressed by the speckle modulation.     

Channel modeling and estimation for intrapage equalization in pixel-matched volume holographic data storage

We present two different channel models (the magnitude model and the intensity model) for a pixel-matched volume holographic data storage system that employs the 4-focal-length architecture. First, a framework to describe the channel models is developed. We evaluate the linearity of the channel models by comparing data values obtained from diffraction-limited interference with data values predicted by the channel models. The models are evaluated for linearity and equalization gain under different storage and read-back conditions, such as fill factors, apertures, and contrast ratios. Bit error rate results obtained by use of linear equalization methods in conjunction with the channel models developed are also presented. Our results suggest that the magnitude model leads to better performance when the fill factors are small, whereas the intensity model appears to be more appropriate for the high-fill-factor cases. The magnitude model, when suitable, appears to provide a storage density improvement of as great as 65%, whereas the intensity model seems capable of providing as much as 15% density gain through deconvolution. The optimum aperture for storage seems to be close to the Nyquist aperture.     

Discrete magnitude-squared channel modeling, equalization, and detection for volume holographic storage channels

As storage density increases, the performance of volume holographic storage channels is degraded, because intersymbol interference and noise also increase. Equalization and detection methods must be employed to mitigate the effects of intersignal interference and noise. However, the output detector array in a holographic storage system detects the intensity of the incident light's wave front, leading to loss of sign information. This sign loss precludes the applicability of conventional equalization and detection schemes. We first address channel modeling under quadratic nonlinearity and develop an efficient model named the discrete magnitude-squared channel model. We next introduce an advanced equalization method called the iterative magnitude-squared decision feedback equalization (IMSDFE), which takes the channel nonlinearity into account. The performance of IMSDFE is quantified for optical-noise-dominated channels as well as for electronic-noise-dominated channels. Results indicate that IMSDFE is a good candidate for a high-density, high-intersignal-interference volume holographic storage channel.     

Deformation of the modulation profile in phase holographic gratings

Among all the parameters that characterize a phase grating, the most difficult to control is the modulation profile of the refractive index. In fact, it covers many scalar parameters that are the Fourier coefficients of the profile. To study the influence of processing baths on the modulation profile, in phase holographic gratings made of dichromated gelatin, we have observed that the shape of the profiles obtained sometimes presents a slight concavity or a convexity in the middle, leading to an increase or a decrease in the diffraction efficiency. We present the experimental results and a numerical study in the form of a theoretical prediction, which confirms the experimental observations.     

Performance analysis of content-addressable search and bit-error rate characteristics of a defocused volume holographic data storage system

One of the methods for smoothing the high intensity dc peak in the Fourier spectrum for reducing the reconstruction error in a Fourier transform volume holographic data storage system is to record holograms some distance away from or in front of the Fourier plane. We present the results of our investigation on the performance of such a defocused holographic data storage system in terms of bit-error rate and content search capability. We have evaluated the relevant recording geometry through numerical simulation, by obtaining the intensity distribution at the output detector plane. This has been done by studying the bit-error rate and the content search capability as a function of the aperture size and position of the recording material away from the Fourier plane.     

Experimental study of the effects of a six-level phase mask on a digital holographic storage system

We measure the M/# and the bit-error rate of a digital holographic storage system with a 4f optical arrangement for three configurations: recording at the Fourier plane with and without a phase mask and recording outside the Fourier plane without a phase mask. Unexpectedly, no significant change in the dynamic range was observed when a phase mask was used to record in thick crystals. However, we show that a phase mask is a key component in a 4f digital holographic storage system if high-fidelity holograms with optimum volumetric density are to be stored.     

Improvement of photopolymer materials for holographic data storage

Photopolymer materials are practical materials for use as holographic recording media due to the fact that they are inexpensive, self-processing materials with the ability to record low loss, highly diffraction efficient volume holographic gratings. In general these materials absorb light of an appropriate wavelength, causing photo-polymerization of the local monomer, inducing a change in the material’s refractive index. These small changes in refractive index enable the storage of large quantities of data using holographic techniques. In an attempt to further develop the data storage capacity and quality of the information stored, i.e., resolution, in such materials, a deeper understanding of the photochemical mechanisms present during the formation of holographic gratings has become ever more crucial. From this understanding the response of an acrylamide/polyvinylalcohol based photopolymer to high spatial frequency information is improved through the addition of a chain transfer agent, i.e., sodium formate, HCOONa.     

Beam-width-dependent filtering properties of strong volume holographic gratings

The finite dimension of the incident beam used to read out volume holographic gratings has interesting effects on their filtering properties. As the readout beam gets narrower, there is more deviation from the ideal response predicted for monochromatic plane waves. In this paper we experimentally explore beam-width-dependent phenomena such as wavelength selectivities, angular selectivities, and diffracted beam profiles. Volume gratings in both reflection and transmission geometries are investigated near 1550 nm. Numerical simulations utilizing the technique of Fourier decomposition provide a satisfactory explanation and confirm that the spread of spatial harmonics is the main contributing factor.     

Polarization holographic high-density optical data storage in bacteriorhodopsin film

Optical films containing the genetic variant bacteriorhodopsin BR-D96N were experimentally studied in view of their properties as media for holographic storage. Different polarization recording schemes were tested and compared. The influence of the polarization states of the recording and readout waves on the retrieved diffractive image's intensity and its signal-to-noise ratio were analyzed. The experimental results showed that, compared with the other tested polarization relations during holographic recording, the discrimination between the polarization states of diffracted and scattered light is optimized with orthogonal circular polarization of the recording beams, and thus a high signal-to-noise ratio and a high diffraction efficiency are obtained. Using a He-Ne laser (633 nm, 3 mW) for recording and readout, a spatial light modulator as a data input element, and a 2D-CCD sensor for data capture in a Fourier transform holographic setup, a storage density of 2 x 10(8) bits/cm2 was obtained on a 60 x 42 microm2 area in the BR-D96N film. The readout of encoded binary data was possible with a zero-error rate at the tested storage density.     

Interleaving and error correction in volume holographic memory systems

We study the use of error-correction coding (ECC) and two-dimensional interleaving for volume holographic memory (VHM) systems suffering from both random and systematic errors. The bit-error rate (BER) is used as the data-fidelity measure and as a design metric for optical 4f systems. The correlated error patterns arising from both lens aberrations and misalignment errors are analyzed, and we discuss the information theoretic storage capacity of VHM in the presence of such correlated error patterns. The performance of interleaving and ECC is analyzed from both BER and storage-capacity perspectives. Magnification, rotation, tilt, and defocus errors are also studied, and an experimental demonstration that combines ECC with two-dimensional interleaving is included.