WO2015168325A1 - Procédés et appareil pour canaux de données holographiques cohérents - Google Patents

Procédés et appareil pour canaux de données holographiques cohérents Download PDF

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Publication number
WO2015168325A1
WO2015168325A1 PCT/US2015/028356 US2015028356W WO2015168325A1 WO 2015168325 A1 WO2015168325 A1 WO 2015168325A1 US 2015028356 W US2015028356 W US 2015028356W WO 2015168325 A1 WO2015168325 A1 WO 2015168325A1
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Prior art keywords
spatial
local oscillator
phase
hologram
reconstructed signal
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PCT/US2015/028356
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English (en)
Inventor
Mark R. Ayres
Kenneth E. Anderson
David C. Pruett
Will A. Loechel
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Akonia Holographics, Llc
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Priority claimed from US14/484,060 external-priority patent/US20150070739A1/en
Application filed by Akonia Holographics, Llc filed Critical Akonia Holographics, Llc
Priority to EP15786499.2A priority Critical patent/EP3138098A4/fr
Priority to JP2016565251A priority patent/JP2017519323A/ja
Priority to KR1020167033508A priority patent/KR20160147987A/ko
Priority to US14/831,291 priority patent/US9703260B2/en
Publication of WO2015168325A1 publication Critical patent/WO2015168325A1/fr

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    • G—PHYSICS
    • G11—INFORMATION STORAGE
    • G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
    • G11B7/00—Recording or reproducing by optical means, e.g. recording using a thermal beam of optical radiation by modifying optical properties or the physical structure, reproducing using an optical beam at lower power by sensing optical properties; Record carriers therefor
    • G11B7/004—Recording, reproducing or erasing methods; Read, write or erase circuits therefor
    • G11B7/0065—Recording, reproducing or erasing by using optical interference patterns, e.g. holograms
    • G—PHYSICS
    • G11—INFORMATION STORAGE
    • G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
    • G11B20/00—Signal processing not specific to the method of recording or reproducing; Circuits therefor
    • G11B20/10—Digital recording or reproducing
    • G11B20/10009—Improvement or modification of read or write signals
    • G—PHYSICS
    • G11—INFORMATION STORAGE
    • G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
    • G11B20/00—Signal processing not specific to the method of recording or reproducing; Circuits therefor
    • G11B20/10—Digital recording or reproducing
    • G11B20/10009—Improvement or modification of read or write signals
    • G11B20/10268—Improvement or modification of read or write signals bit detection or demodulation methods
    • G11B20/10277—Improvement or modification of read or write signals bit detection or demodulation methods the demodulation process being specifically adapted to partial response channels, e.g. PRML decoding
    • G—PHYSICS
    • G11—INFORMATION STORAGE
    • G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
    • G11B7/00—Recording or reproducing by optical means, e.g. recording using a thermal beam of optical radiation by modifying optical properties or the physical structure, reproducing using an optical beam at lower power by sensing optical properties; Record carriers therefor
    • G11B7/12—Heads, e.g. forming of the optical beam spot or modulation of the optical beam
    • G11B7/125—Optical beam sources therefor, e.g. laser control circuitry specially adapted for optical storage devices; Modulators, e.g. means for controlling the size or intensity of optical spots or optical traces
    • G11B7/128—Modulators

Definitions

  • holographic memory systems employing holographic optical techniques
  • holographic storage systems have been suggested as alternatives to conventional memory devices.
  • Holographic memory systems may read/write data to/from a photosensitive storage medium.
  • holographic memory system When storing data, holographic memory system often record the data by storing a hologram of a 2-dimensional (2D) array, commonly referred to as a "page,” where each element of the 2D array represents a single data bit. This type of system is often referred to as a "page-wise" memory system.
  • Holographic memory systems may store the holograms as a pattern of varying refractive index and/or absorption imprinted into the storage medium.
  • the probe beam illuminates the holographic storage medium with at least one probe beam so as to generate at least one reconstructed signal beam that represents at least some information stored in the holographic storage medium.
  • the reconstructed signal beam interferes with at least one local oscillator beam to produce a first interference pattern, which a detector senses as described above and below.
  • a phase retarder increments (or decrements) a phase difference between the local oscillator beam and the reconstructed signal beam by about 2 ⁇ modulo 2 ⁇ .
  • the reconstructed signal beam interferes with the local oscillator beam so as to produce an mth interference pattern.
  • the detector senses each of these interference patterns.
  • the probe beam illuminates the holographic storage medium with at least one probe beam so as to generate at least one reconstructed signal beam that represents at least some information stored in the holographic storage medium.
  • a detector acquires at least one image of interference between the reconstructed signal beam and a local oscillator beam.
  • a processor coupled to the detector generates a representation of the information stored in the hologram based on the image, estimates misfocus in the representation, and compensates the misfocus in the representation.
  • FIG. IB illustrates the monocular holographic system 100 in record mode, wherein the system 100 is configured to record a hologram in recording medium 158.
  • the 1 st SHWP 144 is configured to transmit p-polarized light and the nascent signal/local oscillator beam 123 thus emerges p-polarized, whereupon it can be referred to as a nascent signal beam 126 because it is destined to become a signal beam 143, not a local oscillator 125. If the nascent signal/local oscillator beam 123 is destined to become the signal beam 143 and is phase adjusted by the variable phase retarder 130, it is expedient to state that the signal beam 143 has its phase adjusted by the variable phase retarder 130.
  • the holographic memory system 100 may also record data by modulating the phase and the amplitude of the incoming nascent signal beam 126 with the SLM 140.
  • each SLM pixel may impart a respective portion of the incoming nascent signal beam 126 with one of four amplitude states and one of four phase states distributed across the I-Q plane. This yields a signal beam 143 that encodes the data page as 4-bit symbols, which can be recorded and read from the holographic storage medium 158.
  • Other suitable phase and amplitude modulation techniques include partial response maximum likelihood signaling, which is explained in greater detail below.
  • the optical filter can be an angle filter, including but not limited to, a multi-layer dielectric coating.
  • the signal beam 143 emerges from the first 4F imaging assembly 150 and subsequently propagates past the knife-edge mirror 156, through objective lens 145.
  • variable phase retarder 130 can be implemented as one or more components in a transmissive geometry, as shown in FIGS. IB and 1C; as one or more components in a reflective geometry; or as a suitable combination of reflective and transmissive components. These components can be arranged in the path of the local oscillator, as shown in FIGS. IB and 1C; in the path of the probe beam; in the path of the reconstructed signal beam; or in any combination of these paths. For instance, the transmissive variable phase retarder 130 shown in FIGS.
  • IB and 1C may be implemented as a liquid crystal phase modulator (e.g., a nematic liquid crystal device), two or more cascaded binary phase retarders, or a bulk electro-optic modulator whose refractive index is varied with a voltage applied across an electro-optic crystal.
  • a reflective variable phase retarder 130 can be implemented as a mirror mounted on a piezo-electric element that moves the mirrors (and accordingly increases or decreases the optical path length) in response to an applied voltage. This voltage may be selected to provide the desired phase difference between the local oscillator 125 and the reconstructed signal beam 124.
  • the processor 182 may control the phase modulation imparted on the local oscillator beam 125 via the variable phase retarder 130 so as to achieve the desired phase difference(s) between the local oscillator beam 125 and the reconstructed signal beam 124.
  • the processor 182 can also control the orientation of the analyzer 141 so as to vary the ratio of power in the local oscillator beam 125 to the power in the reconstructed signal beam 124.
  • holographic memory system 200 may store information encoded in the holographic storage medium 202 using a coherent channel modulation technique, such as phase shift keying (PSK), which involves storing digital data as either +1 bits and -1 bits.
  • PSK phase shift keying
  • a +1 bit may be represented by a particular pixel of SLM 218 modulating the signal beam used in recording the hologram so that the signal beam at that particular pixel location has a particular phase (e.g., 0 degrees).
  • a -1 bit may be represented by a pixel of SLM 218 modulating the recording signal beam so that the signal beam is 180 degrees out of phase with the +1 pixels. In other words, there is a 180 degree phase difference between the +1 and -1 pixels.
  • the holographic memory system 200 can also use amplitude shift keying (ASK), which involves modulating the amplitude of the SLM pixels; quadrature amplitude modulation (QAM), which involves modulating the amplitude and the phase of each SLM pixel to form multi-bit symbols; and partial response maximum likelihood (PRML), which involves recording the image of the SLM at an optical resolution insufficient to resolve individual SLM pixels, so that the reconstructed pixel images are overlapped in space (i.e., blurred together) in a controlled manner.
  • ASK amplitude shift keying
  • QAM quadrature amplitude modulation
  • PRML partial response maximum likelihood
  • FIG. 2 also illustrates how to retrieve holographically stored data from the holographic storage medium 202 by performing a read (or reconstruction) of the stored data using n-rature homodyne detection.
  • the read operation may be performed by projecting a probe beam 232 onto or into the storage medium 202 at an angle, wavelength, phase, position, etc., or compensated equivalents thereof based on the angle, wavelength, phase, position, etc., or compensated equivalents thereof of the reference beam used to record the data.
  • the hologram and the reference beam interact to reconstruct the signal beam or a phase conjugate of the signal beam, depending on the interaction geometry.
  • the reconstructed signal beam 234 may comprise the reconstructed data on a phase carrier.
  • Objective lens 204 may be, for example, any type of lens, such as those
  • Lens 204 may also be located one focal length (i.e., the focal length of lens 204) from holographic storage medium 202 so that the storage medium is located at a Fourier plane of SLM 218.
  • These lenses and their locations are exemplary and in other embodiments, including the monocular system shown in FIGS. 1A-1C, the arrangement of lenses and other optical components may be different.
  • one or more of the lenses may be positioned or selected such that the storage medium 202 is located at an image plane of SLM 218, or at an intermediate location that is neither a Fourier plane nor an image plane.
  • the power of the reflected local oscillator beam 236 may be set to some power level to effect or cause the desired amount of optical gain and dynamic signal range (e.g., 100 times the nominal power of the reconstructed signal beam). This may be accomplished by splitting off a portion of the main laser beam used for generating the probe beam 232 using a fixed or variable beamsplitter as readily understood in the art.
  • FIG. 2 includes a simplified illustration of a technique for generating local oscillator beam 236 and probe beam 232 using a light source 250, an adjustable HWP 252, a PBS 254, mirror 256, and a galvonometer mirror 258.
  • Light source 250 which may be a laser such as is commonly used in holographic memory systems, generates a main laser beam 260 that propagates through HWP 252.
  • the angle of the birefringent axes of HWP 252 may be adjusted, possibly in response to commands from processor 280, to modify the polarization of main laser beam 260 such that PBS 254 splits off a portion of main beam 256 for local oscillator beam 236.
  • HWP 252 Setting the angle of the birefringent axes of HWP 252 controls the power level of local oscillator beam 236 relative to the power level of probe beam 232.
  • the remaining portion of main laser beam 260 passes through PBS 254 and may be directed by mirror 256 and galvo mirror 258 to form reference beam 234.
  • variable phase retarder 222 may be configured to switch between three or more states in which the active axis of the NLC material is electrically modulated to impart the desired phase differences (e.g., 0°-120°-240°; 0°-90 ⁇ -180 ⁇ -270°; and so on) between local oscillator beam 236 and reconstructed signal beam 234. Variable phase retarder 222 may switch between these states in response to signals from processor 280.
  • desired phase differences e.g., 0°-120°-240°; 0°-90 ⁇ -180 ⁇ -270°; and so on
  • Combined beam 238 may then enter PBS 216 which, because of the polarization of combined beam 238, directs combined beam 238 towards detector 220, which detects the received image.
  • Detector 220 may be any device capable of detecting combined beam 238, such as, for example, a complementary metal-oxide- semiconductor (CMOS) detector array or charged coupled device (CCD).
  • CMOS complementary metal-oxide- semiconductor
  • CCD charged coupled device
  • FIG. 2 shows use of NPBS 208 for combining local oscillator beam 236 with reconstructed signal beam 234, in other embodiments, other devices may be used, such as, for example, a pellicle beam splitter or a plate beam splitter.
  • the local oscillator beam 236 and the reconstructed signal beam 234 have substantially the same phase they will interfere constructively to produce a representation of the reconstructed data page at the detector 220. Where the local oscillator beam 236 and the reconstructed signal beam 234 have substantially opposite phases, then they may interfere destructively to produce an inverted representation of the reconstructed data page at the detector 220. Where the local oscillator beam 236 and the reconstructed signal beam have substantially orthogonal phases (i.e., difference near + 90°), then they may produce a washed- out (low contrast) representation of the reconstructed data page at the detector.
  • FIG. 2 illustrates one example for generating probe beam 232 and local oscillator beam 236, and that other implementations may be used, such as, for example, using two separate phase-locked lasers. In short, the geometry and components of holographic memory system 200 may be different without departing from the disclosed technology.
  • homodyne detection makes it possible to detect reconstructions of phase-modulated data pages. This in turn enables holographic data storage of information encoded using coherent channel modulation techniques, including phase-multiplexing techniques such as, but not limited to, phase quadrature holographic multiplexing (PQHM), QAM, and single-sideband holographic recording.
  • phase-multiplexing techniques such as, but not limited to, phase quadrature holographic multiplexing (PQHM), QAM, and single-sideband holographic recording.
  • PQHM phase quadrature holographic multiplexing
  • PRML partial response maximum likelihood
  • NPML noise-predictive maximum likelihood
  • Coherent channel modulation techniques offer a number of advantages over amplitude-only modulation, including but not limited to: higher storage density; higher SNR/sensitivity at a given power level using coherent detection; and lower bit-error rate (BER) for a given power level.
  • PSK modulation may reduce or eliminate the DC component in the signal beam, and may also reduce or eliminate cross-talk caused by gratings formed between pixels in the holographic recording medium (aka intra-signal modulation). Data recorded using these techniques can be reconstructed using conventional homodyne detection, quadrature homodyne detection, and the n-rature homodyne detection disclosed in greater detail above and below.
  • Phase quadrature holographic multiplexing can be considered analogous to quadrature phase shift keying (QPSK) in traditional communications theory.
  • QPSK quadrature phase shift keying
  • a second hologram can be recorded with each reference beam (e.g., two holograms at each reference beam angle for angle multiplexing), with little to no cross talk between the holograms provided they have a 90° difference in phase.
  • PQHM More generally, we refer to methods of recording holograms in both orthogonal phase dimensions as phase-multiplexing.
  • Phase-multiplexing therefore includes, but is not limited to, holograms recorded using PQHM (i.e. QPSK), higher-order PSK, and QAM holographic recording methods.
  • BPSK is not considered a phase-multiplexing method.
  • PQHM can provide a doubling of storage density, and opens the door to other advanced channel techniques. Furthermore, PQHM can be used to increase both recording and recovery speeds. [0097]
  • holographic recording is performed by illuminating a photosensitive medium with an interference pattern formed by two mutually coherent beams of light.
  • the light induces a refractive index change that is linearly proportional to the local intensity of the light, i.e.,
  • An(r ) is the induced refractive index change
  • S is the sensitivity of the recording medium
  • t is the exposure time
  • f ⁇ x, y, z ⁇ is the spatial coordinate vector
  • /(F) is the spatially- varying intensity pattern, which is in turn decomposed into a coherent summation of two underlying optical fields, E R (r ) and E S (F) , representing the complex amplitudes of the reference beam and the signal beam, respectively.
  • the unary * operator represents complex conjugation.
  • both the reference beam and the signal beams corresponding to an individual stored bit are plane waves (or substantially resemble plane waves), though other page-oriented recording techniques are also suitable for PQHM recording.
  • Eq. (2) shows that the phase of the interference term may be controlled by controlling the phase difference of the recording beams. If two holograms are recorded sequentially using the same reference and signal beams E R (f ) and E S (F) while changing ⁇ by 90°, then the holograms will have a quadrature relationship to each other. Each planar grating component in the Fourier decompositions of the interference terms of the two holograms will be identical to the corresponding component of the other hologram, excepting for a 90° phase difference.
  • binary amplitude shift keying works for this purpose because 'ones' are represented by gratings in the 0° phase in the / hologram and by gratings in the 90° phase in the Q hologram (with 'zeros' being represented by the absence of a grating in both holograms).
  • 'ones' and 'zeros' are respectively represented by 0° and 180° gratings in the / hologram, and by 90° and 270° gratings in the Q hologram.
  • the optical path length can be increased or decreased by moving one or more mirrors in the beam path(s) using a piezo, galvonometer, or micro-electro-mechanical system (MEMS).
  • MEMS micro-electro-mechanical system
  • One or both of the beams may also be phase-modulated with a suitable SLM, such as a switchable liquid crystal SLM.
  • the / and Q holograms can be modulated and recorded over a sequence of exposures with a binary SLM or in parallel during a single exposure with a gray-scale SLM with at least four modulation levels.
  • the grayscale SLM modulates each pixel into one of the four quadrature phase states of 0°, 90°, 180°, and 270°.
  • the binary state of each pixel in the I and Q images together may be encoded into a single state of the gray-scale phase SLM in a manner that produces quadrature-multiplexed gratings indistinguishable from those produced by sequential writing.
  • a gray-scale SLM can be implemented by cascading two or more binary SLMs in series, or by cascading non-binary SLMs in series to produce the four or more phase/amplitude states.
  • the four states might not correspond to the four quadratic states of 0°, 90°, 180°, and 270°.
  • parallel phase-quadrature recording of two binary ASK-modulated holograms might be accomplished with an SLM (or cascaded series of SLMs) that produces two bright states at phase 0° and 90° with 1/V2 amplitude, a bright state at phase 45° with unity amplitude, and a dark state.
  • SLM or cascaded series of SLMs
  • FIG. 3 illustrates a process for recording PQHM data pages with the system 100 shown in FIGS. 1A-1C.
  • this process can be combined with other compatible multiplexing techniques, including angle multiplexing, polytopic multiplexing, dynamic aperture multiplexing, and spatial multiplexing, to increase the areal storage density of holographic storage medium 158. It can also be implemented using holographic data storage systems using other architectures.
  • the basic technique for modulating the phase difference between a reference beam and a signal beam can be applied to other coherent channel modulation techniques, including but not limited to quadrature amplitude modulation (QAM).
  • QAM quadrature amplitude modulation
  • the first operation 302 in PQHM recording process includes recording a first interference pattern as a first hologram in a holographic recording medium 158.
  • the 1 st SHWP 144 is configured to transmit p-polarized light
  • the 2 nd SHWP 146 is configured to transmit s-polarized light.
  • the first interference pattern is created by interference of a first signal beam with a first reference beam.
  • Data is encoded in the first signal beam in the form of a first data page.
  • the first data page typically includes pixels of varied intensity created using a data encoding element 140 illustrated in FIG. IB (ASK mode).
  • the data encoding element 140 which in this case is a reflective SLM, encodes the first data page in the first signal beam.
  • the pixels of varied intensity have one or the other of two intensity states, the two intensity states typically being referred to as light and dark (binary ASK mode).
  • the first data page includes pixels that have varied phase states (PSK mode).
  • the varied phase states are limited to one or the other of two phase states that have a phase difference from each other of 180° (binary PSK mode).
  • the reflective SLM 140 can be used for ASK mode, and in combination with a half wave plate 138 for PSK mode, as described above.
  • Some embodiments embed data in signal beams by use of other data encoding elements, including but not limited to transmissive SLMs, grayscale SLMs, gray-scale phase SLMs, and data masks.
  • the first reference beam is a plane wave reference beam
  • the recording medium 158 typically, but not necessarily, comprises a combination of photoactive polymerizable material and a support matrix, with the combination typically residing on a substrate or sandwiched between two substrates.
  • Other storage media familiar to persons skilled in the art can also be used, including but not limited to LiNb03 crystals and film containing dispersed silver halide particles.
  • Other methods of optical data recording can use reference beams other than plane wave reference beams, including but not limited to spherical beams and in-plane cylindrical waves.
  • variable phase retarder 130 in FIG. IB is set at a first phase position, and the first hologram is recorded with the first signal beam being in a first phase state relative to the first reference beam. Recording the first hologram is typically performed by opening and closing a shutter (not shown).
  • the first hologram can be referred to as an in-phase (I) hologram.
  • the recording medium 158 records a second interference pattern, called a quadrature (Q) hologram, created by interference of a second reference beam with a second signal beam.
  • the variable retarder 130 is set at a second phase position for the second operation 304, and the second hologram is recorded in the recording medium with the second signal beam being in a second phase state.
  • the second phase state differs from the first phase state by 90°.
  • the first signal beam has a phase difference of 90° from the second signal beam.
  • Recording the second hologram is typically performed by opening and closing the shutter (not shown).
  • the second operation 304 is typically performed with the system 100 configured as shown in FIG. IB, wherein the 1 st SHWP 144 is configured to transmit p-polarized light and the 2 nd SHWP 146 is configured to transmit s-polarized light.
  • the second reference beam is typically substantially identical to the first reference beam.
  • the second signal beam includes a second data page encoded therein by use of the SLM.
  • the second data page typically, but not necessarily, differs from the first data page.
  • both the first and second data pages include reserved blocks comprising known pixel patterns.
  • the term "reserved block" refers to a region of known pixel pattern(s) that is encoded in a page stored in the holographic storage medium.
  • a reserved block residing at a specific location in the first data page is typically matched by a complementary reserved block residing at an identical specific location in the second data page, wherein the reserved blocks have complementary pixel patterns.
  • the reserved blocks and processing using the reserved blocks are discussed in greater detail below.
  • the second hologram is recorded in a substantially identical location in the photosensitive recording medium 158 as the first hologram, such that the first and second holograms overlap completely to share a common space.
  • the first and second holograms have a phase difference from each other of 90°.
  • refractive index gratings of each and every Fourier component of the first and second holograms have a phase difference from each other of + 90°.
  • the first and second holograms are thus said to be phase quadrature multiplexed, and form a phase quadrature hologram pair, sometimes referred to as a phase quadrature pair or a PQHM pair.
  • Each hologram of a phase quadrature hologram pair is a species of phase-multiplexed hologram.
  • first and second holograms are recorded using first and second signal beams that do not have a phase difference, which is to say the first and second signal beams have a phase difference from each other of 0°.
  • a phase difference between the first and second holograms of a phase quadrature pair can be achieved using first and second reference beams that have a phase difference from each other of 90°.
  • a phase difference between two reference beams can be achieved by placing a phase retarder in a path of the first and second reference beams.
  • the phase difference can also be manipulated by adjusting the phases of both the signal beams and the reference beams so as to have a relative phase difference that switches between 0° and 90°.
  • a processor or other suitable component in or operably coupled to the holographic data storage system 100 determines whether or there are any more data pages to be recorded in operation 306. If so, then the holographic data storage system 100 shifts to a new angle, position, dynamic aperture setting, and/or other multiplexing setting in operation 308, then repeats operations 302, 304, and 306 to record the desired number of multiplexed data pages. Once the multiplexed data pages have been recorded, recording ends in operation 310.
  • the holographic memory systems disclosed herein may be used to record and recover data modulated with higher-order PSK constellations.
  • PSK encoding may be extended generally to incorporate any number of phase states - for example, 8-PSK.
  • 8-PSK recording is performed by recording a data page composed using a gray-scale phase SLM with each pixel taking one of eight phase states, e.g., 0°, 45°, 90°, 135°, 180°, 225°, 270°, or 315°.
  • Higher-order PSK holograms may be detected using a modified quadrature homodyne detection or n-rature homodyne detection algorithm. Any number and distribution of phase states may be thus accommodated.
  • PSK holograms can also be recorded sequentially using a binary phase SLM (0° and 180°), and a separate phase retarder in a manner analogous to the sequential PQHM recording method disclosed immediately above. Note, however, that for PSK orders higher than four, the sequentially -recorded images may not constitute independent binary data pages. 8-PSK, for example, involves the sequential exposure of four SLM images but may yield only three bits per pixel of data (not four) since the number of data bits may be equal to the log base 2 of the number of phase states.
  • the holographic memory systems disclosed herein may also be used to record and recover data modulated in both amplitude and phase.
  • 16-QAM for example, is a well-known method for encoding 4 bits per symbol using a constellation of typically 4 x 4 states distributed uniformly in the I-Q plane.
  • any digital QAM constellation may be recorded holographically using a phase and amplitude-modulating SLM capable of providing an appropriate number of phase and amplitude states, or with a sequence of exposures of varying amplitude and phase using a binary phase SLM. Any number and distribution of states may be thus accommodated.
  • Partial response maximum likelihood (PRML) signaling can also be used to increase the density with which phase- and amplitude-modulated data is stored in a holographic medium.
  • PRML signaling is used in communications and magnetic storage applications where, for instance, the bits on a data track are packed so closely that four or six individual magnetic flux reversal response pulses may overlap each other. This allows the channel to operate at four or six times the data density it would achieve if the pulses were completely separated. The cost for this improved performance is increased complexity in the form of a decoder that can recover the original data from the convolved signal.
  • a Viterbi or Bahl, Cocke, Jelinek, and Raviv (BCJR) decoder is used to select the optimal data pattern consistent with the observed signal.
  • the detector is optimal in the maximum likelihood sense, hence the term partial response, maximum likelihood.
  • a partial response resampling filter creates an output which resembles the convolution of the binary data pattern with some specific channel impulse response, h.
  • this resampling filter can be employed in two spatial dimensions rather than in one temporal dimension for time- varying images.
  • the optical response of neighboring SLM pixel images overlap with each other (blur) when the spatial resolution grows coarser.
  • the superposition of overlapping pixel fields resembles a linear convolution that is amenable to PRML processing. Because homodyne detection permits the detection of optical amplitude, it enables PRML signaling by linearizing the channel response.
  • PRML signaling for holographic data storage can be implemented by detecting the optical amplitudes of the overlapping pixel fields using a homodyne detection technique (e.g., n-rature homodyne detection), then applying PRML processing techniques on the detected optical amplitudes.
  • a homodyne detection technique e.g., n-rature homodyne detection
  • Partial response signaling may reduce the signaling bandwidth, increase the signaling capacity for a given bandwidth, or both. Partial response signaling may also allow the designer to select a target channel response that is closer to the native, physical response of the channel, thus reducing noise amplification due to aggressive equalization.
  • FIG. 4A illustrates a process for recording and retrieving data holographically using PRML signaling.
  • an SLM e.g., SLM 140 in FIGS. IB and 1C
  • a suitable modulation technique e.g., PSK, ASK, QAM, etc.
  • the spatially modulated signal beam propagates through an optical filter (e.g., an appropriately apodized aperture) in the Fourier plane of the SLM (e.g., in the position of the polytopic aperture 155 shown in FIGS. IB and 1C).
  • an optical filter e.g., an appropriately apodized aperture
  • the shape and size of the aperture is chosen such that it does not resolve individual pixels in the signal beam; that is, propagation of the signal beam through the aperture blurs the image shown on the SLM.
  • the blurring can be in one or two spatial dimensions (e.g., x, y, or x and _y) and be implemented, e.g., using a static aperture, a shutter, a grayscale SLM, etc.
  • the transmission function of the aperture may produce the shape of a double-sinc response as described below with respect to FIG. 4E.
  • the blurred signal beam interferes with a reference beam in the holographic storage medium to produce a hologram representing the blurred SLM image in operation 406.
  • the hologram can be read out using n-rature homodyne detection, quadrature homodyne detection, or any other technique that yields the complex amplitude of the reconstructed signal beam.
  • the signal beam is reconstructed in operation 408 by illuminating the hologram with a probe beam, e.g., as described with respect to FIGS. 1C and 2.
  • the reconstructed signal beam propagates through an aperture, typically of the same shape and size as the aperture used to blur the original signal beam in operation 410 (e.g., a 2D cosine-rect aperture, disposed at the position of polytopic aperture 155 in FIG. 1C, that gives a double-sinc point spread function).
  • the reconstructed signal beam interferes with a local oscillator on a detector, which senses the resulting interference pattern in operation 412. And in operation 414, the detected interference pattern is decoded, e.g., as explained with respect to FIG. 4C, to yield a PRML estimate of the information stored in the hologram.
  • the interference pattern may be deconvolved using the channel impulse response, h, and an appropriate deconvolution technique, such as the iterative multistrip algorithm.
  • partial response class 1 PR1
  • duobinary modulation PR1
  • the discrete channel response may be represented by polynomial multiplication of the data sequence by ⁇ +D, where D is the sample delay operator.
  • FIG. 4B illustrates an embodiment of a 2D target response, dubbed PR1-2D. It is simply the two dimensional generalization of the PR1 response illustrated in FIG. 4B.
  • a pixel-matched system implementing this response can be implemented by aligning the detector pixels to the corners of SLM pixels, where the four fields overlap, rather than their centers (shown in FIG. 4C).
  • corner alignment can be performed in postprocessing using a modified version of the resampling method disclosed below.
  • the full response oversampling process disclosed below uses the 4x4 detector pixel window closest to each SLM pixel image and applies coefficients optimized (selected) to determine the state of that SLM pixel alone; conversely, the partial response resampling method selects the 4x4 detector pixel window closest to the corner of four SLM pixel images and applies coefficients optimized (selected) to determine the sum of the four SLM pixel responses.
  • Coefficients can be determined by simulation using a modified version of the computer code used to derive the full response resampling coefficients as described below with respect to FIGS. 6A-6D.
  • Imaging through a square polytopic aperture in the Fourier plane produces a sinc- shaped point spread function (impulse response) in the image plane.
  • a reduced (minimal) bandwidth channel comprising two displaced sine functions as shown in FIG. 4E can be used.
  • This PR1-2D point-spread function may be physically realized in a holographic data storage system by apodizing the transmittance function of the polytopic aperture.
  • V A V A .
  • the data may be decoded using a two-dimensional version of the Viterbi algorithm, the BCJR algorithm, the Iterative Multi-Strip algorithm, or any other suitable algorithm.
  • Single sideband holographic recording involves removing redundant spectral components of the holographic signal in order to increase storage density.
  • the redundant spectral components can be removed by occluding half of the polytopic aperture. Since the polytopic aperture is placed in a Fourier plane of the signal beam, the complex amplitude distribution in the plane is conjugate-symmetric about the origin, so long as the signal beam is real- valued (as it is typically for binary modulation schemes, such as PSK and ASK).
  • single sideband holographic recording can be implemented with a phase carrier that is resolved by coherent detection (e.g. , n-rature homodyne detection).
  • coherent detection e.g. , n-rature homodyne detection
  • the resolution depends on the reserved block spacing (discussed below).
  • up to half of the Fourier plane may be blocked without removing signaling information, so long as at least one sideband of each frequency component is passed.
  • the half of the Fourier plane corresponding to negative frequencies in x or y e.g., the bottom or left half of the polytopic aperture
  • the size of the polytopic aperture determines the size of the holograms, so halving the aperture area doubles the recording density.
  • Single-sideband multiplexing introduces an imaginary component in the detected signal that is normally not present due to cancellation of the imaginary parts in the conjugate sidebands of a double-sideband recording.
  • the imaginary part of the signal (as expressed in the recorded phase basis) is discarded or suppressed, e.g., by recovering only the real part of the signal.
  • the real part of the signal can be retrieved without the imaginary part by reading a single-sideband hologram using n-rature homodyne detection, quadrature homodyne detection, or any other suitable digital or optical reconstruction technique.
  • n-rature homodyne detection is a coherent channel detection process for reconstructing holographic ally stored data, including data encoded using the coherent channel modulation techniques disclosed herein.
  • one or more detectors sense n images (e.g., IA, , Ic, etc.) of a particular data page. Each of these images is produced by sensing the interference pattern between a local oscillator beam and a reconstructed signal beam diffracted by the holographic storage medium.
  • n the phase difference between the local oscillator beam and the reconstructed signal beam is I mln, where n > 3 is the total number of images.
  • phase difference can be implemented using a liquid crystal-based phase modulator, an electro-optic phase modulator, a movable mirror, or any other suitable phase modulator in the path of the local oscillator beam, the probe beam, or the reconstructed data (signal) beam.
  • the phase differences of successive images do not have to be arranged in any particular sequence or order; rather, the phase difference can be varied as desired such that the resulting n images can be ordered in phase difference increments or decrements of 2 ⁇ .
  • n-rature homodyne detection involves more holographic exposures than conventional homodyne detection or quadrature homodyne detection, it enjoys other benefits, including the rejection of common intensity noise. Eliminating common intensity noise using n-rature homodyne detection increases the SNR of the detected signal.
  • quadrature homodyne detection the detector acquires two images, IA and , of the interference between the reconstructed signal beam and the local oscillator beam. The phase difference between the reconstructed signal beam and the local oscillator beam is shifted by 90° for one of the images.
  • the irradiance of the detected images can be expressed as:
  • Is is the signal (reconstructed data) beam irradiance
  • ho is the local oscillator irradiance
  • ⁇ is the phase difference between the signal beam and the local oscillator.
  • are the magnitudes of the optical fields, i.e.,
  • the signal magnitude ⁇ E S ⁇ may be estimated by:
  • Eq. (6) represents common intensity noise and is an additive noise source in the estimate of
  • Common intensity noise is so denoted because it includes components of the detected images proportional to the direct intensity terms, TLO and , in addition to the desired interference term. Although increasing the local oscillator intensity may increase the SNR of the detected signal, it will not necessarily eliminate the common intensity noise in quadrature homodyne detection.
  • n-rature homodyne detection suppresses or eliminates common intensity noise and can increase the SNR of the detected signal.
  • n 3.
  • the detector images may be written as:
  • cancelation forcing may be employed.
  • the coefficients for combining the images in Eq. (8), cos ⁇ ⁇ ) , cos ⁇ ⁇ ) , and cos ⁇ (p c ) can be determined by correlation operations on the detected images. Perfect common intensity noise cancelation occurs when these coefficients sum to zero, but this may not be the case in practice due to measurement noise or phase errors in the constituent images.
  • cancelation forcing may be practiced by adjusting the coefficients to sum to zero, for example by subtracting ⁇ ln of the mean from each coefficient.
  • FIG. 5A illustrates a process for reading holographically stored data using n-rature homodyne detection. Although this process is described with respect to the holographic data storage system 100 shown in FIGS. 1A-1C, it can be performed with any suitable holographic data storage system, including the system 200 shown in FIG. 2. The operations shown in FIG. 5A are based with respect to retrieving data from an in-phase (I) hologram and a quadrature (Q) hologram recorded using a PQHM process, e.g., as shown in FIG. 3.
  • I in-phase
  • Q quadrature
  • the I hologram can be retrieved with the 1 st SHWP 144 configured to transmit s-polarized light and the 2 nd SHWP 146 configured to transmit p-polarized light as shown in FIG. 1C.
  • the quadrature (Q) hologram of the PQHM pair is retrieved simultaneously with the in-phase hologram, and the in-phase and quadrature holograms can be distinguished from each other by use of n-rature homodyne detection.
  • n-rature homodyne detection begins with operation 502, which includes acquiring a background image of the local oscillator beam without any reconstructed signal beam.
  • the holographic data storage system 100 generates a probe beam for use in generating reconstructed signal beams from the first and second holograms.
  • the probe beam of operation 504 is a plane wave beam having a substantially identical wavelength to the first and second reference beams.
  • the probe beam is a phase conjugate of the first and second reference beams. Variations include probe beams that are not phase conjugates of their respective reference beams.
  • Other embodiments of methods include probe beams that are not necessarily plane wave beams.
  • variations of probe beams include, but are not limited to, spherical probe beams and in-plane cylindrical waves.
  • the probe beam diffracts off the in-phase hologram and the quadrature hologram to generate a reconstructed signal beam, which interferes with the local oscillator as discussed above.
  • a detector senses this interference pattern, and a memory stores a representation of the detected interference pattern as one of the n n-rature homodyne images.
  • a processor coupled to the memory may subtract the background image acquired in operation 504 from the interference pattern detected in operation 504 in order to remove direct terms (e.g., non-signal components, such as ho and Is) from the representation of the interference pattern. Examples of operation 505, also called detector image modification, are described in greater detail below.
  • the phase difference between the local oscillator and the reconstructed signal beam is shifted by 3607 « using the variable phase retarder 130 in operation 508.
  • the mth local oscillator in the set of n local oscillators has a relative phase of (360° x m)ln.
  • each of the three local oscillators is shifted by a phase difference of 120° (360 3) with respect to the other local oscillators.
  • the system repeats operations 504 and 506 in an iterative fashion at incremented phase differences of 3607 « until all n images have been captured.
  • n images undergo postprocessing in operations 509 and 512.
  • a processor combines the n images captured by the detector into a pair of images suitable for further processing as explained below.
  • This combination operation 509 can be applied to images reproduced from holograms recorded using ASK, PSK, QAM, and single- sideband recording techniques.
  • the resulting image pair referred to as a quadrature image pair, undergoes spatial wavefront demodulation in operation 512. (Spatial wavefront modulation is explained in greater detail with respect to FIG. 5B).
  • operations 509 and 512 can be implemented in a single processing operation by the processor.
  • Each of the n reconstructed signal beams may contain portions of a reconstruction of both the in-phase and quadrature signal beams used in the PQHM recording process. Each of the n reconstructed signal beams thus typically contains portions of a reconstruction of both the first and second data pages.
  • the n reconstructed signal beams are generated by projecting the probe beam to the phase quadrature hologram pair (comprising the first hologram and the second hologram) in the recording medium 158, in a manner familiar to person skilled in the art.
  • FIG. 5A do not necessarily have to occur in the sequence provided here, and indeed the operations may be temporally intermingled to some extent.
  • the background image in operation 502 can be acquired before, after, or between acquisitions of the interference patterns in operations 504 and 506.
  • operations 505, 509, and 512 can be performed at least partially during or after operations 504 and 506.
  • FIG. 1C illustrates how each local oscillator 125 can be combined collinearly with a respective reconstructed signal beam 124 to form a combined beam 131 that produces an interference pattern on the detector 142 in operation 504 of FIG. 6A.
  • the system 100 illuminates the in-phase and quadrature holograms with a probe beam 133 so as to produce a reconstructed signal beam 124.
  • the probe beam 133 is a phase conjugate of the first (in-phase) reference beam and the second (quadrature) reference beam
  • each of the n reconstructed signal beams 124 is s-polarized and propagates part way through the holographic system 100 in a direction opposite that of an incident signal beam 143.
  • the 2 nd SHWP 146 is configured to transmit p-polarized light when the holographic system 100 is in read mode. Accordingly, each of the n s-polarized reconstructed signal beams has its polarization rotated 90° by the 2 nd SHWP 146 to emerge p-polarized and thus propagates through the PBS 139 towards the detector 142.
  • the first SWHP 144 is oriented to transmit an s-polarized local oscillator 125, which reflects off PBS 139 towards detector 142 to combine with the corresponding reconstructed signal beam 124. If the local oscillator 125 and the reconstructed signal beam 124 are aligned with each other, they propagate substantially collinearly towards the detector 142, thereby forming combined beam 131.
  • An analyzer 141 (e.g., a linear polarizer) between the PBS 139 and the detector 142 transmits projections of the s-polarized local oscillator 125 and the p-polarized reconstructed signal beam 124 into a particular polarization state (e.g., a linear diagonal polarization state).
  • a particular polarization state e.g., a linear diagonal polarization state.
  • Changing the polarization state transmitted by the analyzer e.g., by rotating the analyzer 141 about the optical axis of the combined beam 131
  • the detector 142 senses the interference pattern generated by the local oscillator and the reconstructed signal beam and produces an electronic signal (e.g., a current or voltage) whose amplitude is proportional to
  • the local oscillators 125 may be generated at a substantially identical, fixed wavelength, which is substantially identical to the wavelength of probe beam 133.
  • the fixed wavelength should remain constant over time, within the capability of a holographic system 100 to maintain a constant wavelength.
  • Persons skilled in the art recognize that small, unintentional variations in wavelength are typically unavoidable. For example, laser mode hops, current variation, and temperature variation can limit wavelength stability for light beams in any holographic system.
  • phase difference between the local oscillator 125 and the reconstructed signal beam 124 can be incremented in operation 508 with the variable phase retarder 130 shown in FIG. 1C.
  • n 3
  • a second local oscillator phase is retarded by 120° compared to a first local oscillator phase
  • a third local oscillator phase is retarded by 120° compared to the second local oscillator phase.
  • the phase differences described above are thus achieved, where each of the 3 local oscillators has a phase difference of 120° from both others of the 3 local oscillators.
  • each of the 4 local oscillators has a phase difference of 90° (360 4) from two of the 4 local oscillators, and each of the 4 local oscillators has a phase difference of at least 90° from the 3 other local oscillators.
  • E Q COS(A ⁇ - 90°) 7 a + COS(A ⁇ - 90° - 120°)7 s + COS(A ⁇ - 90° - 240°)7, (15) cos C - 210°
  • n may be accommodated analogously.
  • PA, PB, ⁇ correspond to the upsampled reserved block correlations for the / image reserved block patterns.
  • One skilled in the art would also recognize that it is possible to modify the expressions in Eqs. (14) and (15) to instead employ correlations for the Q image reserved block patterns, or to incorporate both.
  • Detector Image Modification In operation 510 of the n-rature detection process shown in FIG. 5 A, a background image representing the local oscillator alone is optionally subtracted from the detected images. This background subtraction reduces or removes the contribution of non-signal terms (the local oscillator) from the in-phase and quadrature images before subsequent processing, and may improve upon common intensity noise cancelation alone, which also serves to reduce the contribution of the local oscillator. This process of removing the non-signal contributions is called detector image modification. It can be applied to n-rature homodyne detection, quadrature homodyne detection, and other coherent channel detection techniques that involve the detection and subsequent processing of images containing a superposition of a local oscillator with the signal of interest.
  • an aberration function corresponding to the design-nominal or as-built performance of the optical system is used as a predetermined wavefront.
  • This predetermined wavefront may also be modified according to current conditions to account for changes in environmental conditions (e.g., temperature, vibration), wavelength, etc.
  • One or more predetermined wavefronts can also be used to remove the known phase aberrations imparted by a phase mask. Phase masks are commonly used to mitigate the effects of the "DC hot spot" and inter-pixel noise in ASK-modulated data. The use of a phase mask along with a predetermined wavefront estimate allows the application of spatial wavefront demodulation to ASK modulation and other modulation schemes that use phase masks.
  • FIG. 6A illustrates a process for cross-correlating an upsampled reserved block target pattern.
  • a processor or controller identifies one or more windows of interest 604 in a detected image 602.
  • FIG. 6C illustrates a process for generating a cross-correlation peak strength map from n images (e.g., image A, image B, ...) detected using n-rature homodyne detection.
  • Cross-correlation peak strengths measure the projection of the detected signal onto the reserved block pixel pattern, and thus provide contrast information about the pixels in the region encompassing the reserved block.
  • a processor or controller identifies and locates one or more windows of interest 654 and 674 in the respective detected images A and B (not shown). Each window of interest 654 and 674 is then cross-correlated with a corresponding upsampled reserved block target pattern 656 and 676 to produce corresponding sampled correlation matrices 658 and 678.
  • the processor or controller combines correlation matrices 658 and 678 (XA, XB, ⁇ ) (e.g., by computing a root- mean-square (RMS) sum, XRMS, of the peak matrices) in order to produce combined sampled correlation matrix 662.
  • correlation matrices 658 and 678 e.g., by computing a root- mean-square (RMS) sum, XRMS, of the peak matrices
  • Pixels diagonal to the peak would then be included if they have three neighbors included in the peak neighborhood according to the previous rules, yielding the 2x2, 2x3, 3x2 or 3x3 peak neighborhood.
  • the processor locates the corresponding neighborhoods in sampled correlation matrices 658 and 678, and sums the values of the pixels in those neighborhoods to yield peak strengths PA, PB, . . .
  • the peak strengths of all reserved blocks are combined to form peak strength maps that can be used to estimate the spatial modulation as explained below.
  • a higher-quality estimate ⁇ of the spatial wavefront modulation may be generated by performing blind de-aliasing on an aliased estimate of the spatial wavefront modulation. For example, suppose an aliased estimate is produced by interpolating reserved block samples in an ordinary data page recovered with a large tilt component. In such a case, the estimate ⁇ will exhibit a Fourier peak at a spatial frequency which is an aliased version of the true frequency. The set of true frequencies that will alias to the observed frequency is discrete, so it is possible to blindly replace the observed frequency with candidates from this set and retry the page decoding operation.
  • CRC cyclic redundancy check
  • a phase factor corresponding to ⁇ may be demodulated (removed) from detected holographic images using a suitable processor, e.g., as in operations 558 and 564 of the spatial wavefront demodulation process shown in FIG. 5B.
  • Local oscillator spatial wavefront demodulation can remove high-frequency components of the local oscillator fringe pattern that would otherwise cause aliasing when sampled by data page reserved blocks, leading to degraded performance.
  • Local oscillator spatial wavefront demodulation can thus be used to increase tolerance to medium positioning errors, or to undesired components of ⁇ introduced for any other reason, e.g., thermal distortion of the hologram, manufacturing imperfections, Bragg mismatches during hologram recovery, etc.
  • Local oscillator spatial wavefront demodulation may be performed at different stages of acquiring and processing the detected holographic images. For instance, demodulation can be performed at any stage while the images are still at the detector resolution (as opposed to the SLM resolution), e.g., before coarse alignment determination (if any); after coarse alignment but before reserved block correlation operations; and/or after reserved block correlation operations. In practice, it is advantageous to perform detector domain local oscillator fringe demodulation before any coarse alignment or reserved block correlation operations, as those operations can benefit from fringe demodulation.
  • I c ' I A cos (- 240° - ⁇ )+ I B cos (- 120° - ⁇ )+ I c cos (-
  • the number of images may also be changed in the demodulation process.
  • An example of this principle is in the combination of three or more n-rature detection images into two images constituting a quadrature image pair, which may subsequently be processed using quadrature homodyne detection techniques instead of n-rature homodyne detection techniques.
  • (23) and (24) may be generalized to demodulate 0 from any starting number of images n into any finishing number of images m:
  • the quadratic phase error associated with error(s) in the position of the detector with respect to the focal plane of the hologram can be estimated and/or compensated using a suitable beam propagation algorithm. It is well known that the digitally-sampled complex optical field distribution at one transverse plane can be algorithmically transformed to that of another transverse plane by means of a beam propagation algorithm. Thus, in cases where a focus error exists, the out-of-focus detected image can be converted to an in-focus image if the focus error is known. In the case where the focus error is not known, the controller may iteratively try beam propagation refocusing using different propagation distances, selecting that distance that optimizes a given figure of merit, such as the SNR of the detected signal.
  • FIGS. 7A-7D are plots of SNR versus beam propagation refocusing distance for different alignments of the detector with respect to the focal plane of the reconstructed hologram.
  • Refocusing was performed on a hologram recovered in 4-rature homodyne detection and converted to a quadrature image pair during the removal of a calibrated spatial wavefront.
  • E was then transformed according to a beam propagation algorithm. The values of i A ' and i B ' were then replaced by the real and imaginary parts of the transformed E, and processing continues.
  • FIGS. 7C and 7D show SNR versus refocusing distance for the same hologram with the detector in the focal plane (FIG. 7C) and the detector positioned 0.5 mm from the focal plane (FIG. 7D).
  • the upper curves indicate SNR calculated using reserved blocks and the lower curves indicate SNR calculated using BER.
  • the peak SNR is roughly the same in all cases shown in FIGS. 7A to 7D and reflects little to no loss in SNR loss from beam propagation. Refocusing by beam propagation thus represents a method to restore SNR lost because of a detector focal plane error caused by any reason, be it factory alignment error, change in focus due to environmental or operating condition perturbations, or change in focal plane due to interchange.
  • the resolution of the detector may exceed the resolution of the data page.
  • the detector 142 has more elements than the SLM 130.
  • an image detected using n- rature homodyne detection may have more pixels than the underlying data page. Fortunately, this resolution mismatch can be compensated by resampling (downsampling) the detected image from the detector resolution to the data page resolution.
  • FIGS. 8 A and 8B illustrate processes for resampling in-phase and quadrature images recovered from a PQHM holographic storage medium using n-rature homodyne detection or another suitable detection process.
  • Each block in FIGS. 8A and 8B represents a 2D array containing data associated with the process step, along with the size/resolution of the particular array.
  • Arrays marked with size/resolution "[det]" indicate that the data therein correspond to detector pixels, and the array would typically have size equal to that of the detector array, e.g., 1710 rows by 1696 columns of pixels in an exemplary embodiment.
  • Arrays marked with size/resolution "[rb]" indicate that the data therein correspond to reserved blocks, which are known data patterns embedded within the holographic data page format. These arrays may have, e.g., 18 rows by 19 columns of entries corresponding to the 18x19 reserved block distribution of an exemplary data page.
  • FIG. 8A can be implemented with a processor or controller to combine Image A 802a and Image B 802b (collectively, images 802), which are at the detector resolution [det], to form a resampled image 816 at the SLM resolution.
  • Cross- correlating the reserved blocks in the images 802 yields arrays of cross-correlation peaks, or quiver peaks 804a and 804b (collectively, quiver peaks 804), at the reserved block resolution [rb].
  • the arrays of quiver peaks 804 are upsampled to the detector resolution [det] to form upsampled peak arrays 806a and 806b (collectively, upsampled peak arrays 802), which are used to form a quadrature combined image 814 at the detector resolution [det].
  • the cross- correlation also produces yields a quiver alignment array 810 at the reserved block resolution [rb].
  • the quiver alignment array 810 is upsampled to the data page resolution [SLM] and used to resample the quadrature combined image 814 at the data page resolution [SLM].
  • the detected images are combined at the detector resolution, which is typically finer than the data page (SLM) resolution. Because the detected images are combined at the detector resolution, the reserved block cross-correlation peaks do not necessarily land on a rectilinear pixel grid. As a result, up-sampling the cross-correlation peak locations to the detector resolution [det] may involve relatively complicated interpolation.
  • SLM data page
  • FIG. 8B illustrates an example of another resampling process, called enhanced resampling, that involves finding the upsampled quiver peaks at the data page resolution [SLM], not the detector resolution [det]. More specifically, the A and B Quiver Peaks 804 are upsampled to produce upsampled quiver peaks 856a and 856b (collectively, upsampled quiver peaks 856) at the SLM resolution [SLM]. Enhanced resampling does not yield a quadrature combined image; instead, a resampled image 866 is created at the SLM resolution from the images 806, the upsampled alignment 812, and the upsampled quiver peaks 856
  • Upsampling from the reserved block resolution [rb] to the detector page/SLM resolution [SLM] is computationally simpler than upsampling to detector resolution [det] because the reserved blocks may be positioned on a rectilinear grid within the SLM image. Upsampling may thus be performed by relatively simple processes, such as inserting an integral number of values in each dimension, e.g., using a bi-linear interpolation algorithm. Upsampling from the reserved block to the detector resolution, by contrast, involves upsampling reserved block information that does not necessarily lie on a rectilinear grid due to real-world image distortions. In addition, the upsampling ratio may be a non-integer that varies throughout the image. Thus the process of upsampling from the reserved block resolution [rb] to the SLM resolution [SLM] may be both simpler and more accurate than upsampling from the reserved block resolution [rb] to detector resolution.
  • the enhanced resampling process shown in FIG. 8B can exhibit other advantages over the resampling process shown in FIG. 8A.
  • the memory size to store SLM resolution arrays is typically smaller than that to store detector resolution arrays.
  • the enhanced resampling process of FIG. 8B may require less memory than the resampling process of FIG. 8A.
  • reserved block ([rb]) to SLM ([SLM]) upsampling yields the upsampled alignment 812 from the quiver alignment 810.
  • the upsampling and perhaps the hardware itself may be shared for both purposes.
  • FIGS. 8A and 8B may be applied to all n images captured during the n-rature homodyne detection. That is, the number of detector images used may be increased from two to three or more, e.g., using detector images IA, IB, IC, . . .
  • the detector pixel values I in the Quadrature Combined Image may be replaced by the corresponding pixel values in the IA and detector images.
  • the detector pixel values I in the Quadrature Combined Image may be replaced by the corresponding pixel values in the IA and detector images.
  • the detected pixel values in these images may be modified, such as by subtracting a global image mean, etc., as described above.
  • CA, CB, ⁇ represent the combination coefficients for the respective detector pixel value sets.
  • these combination coefficients may be determined by the cosine projection of the data page upon the local oscillator used to detect it as measured by the reserved block correlation peak strengths, e.g.,
  • the combination coefficients may be determined from the cosine projections of the reserved blocks from a different data page, e.g., when performing phase quadrature holographic multiplexing as disclosed above.
  • the data value of the corresponding SLM pixel in the I (in phase) data page could be estimated by applying equations (28) and (29) as presented, and then the data value of the corresponding SLM pixel image in the Q (quadrature) image could be estimated by using different combination coefficients, e.g.,
  • 0 Q is the known phase difference between the / and Q images, e.g., preferably 90°. In this manner separate correlation and upsampling operations do not need to be performed for the reserved block patterns in the Q image; instead the entire image combination and resampling process may be accomplished using the reserved block patterns of the / image.
  • 220 holograms were recorded in each "book" (spatial location) using angle multiplexing.
  • a grid of 6x9 books at a pitch of 304 ⁇ was so recorded using polytopic multiplexing, yielding a raw areal bit density of 2.004 Tbit/in 2 .
  • Dynamic aperture multiplexing was also employed.
  • the holograms were recorded in a 1.5 mm thick layer of photopolymer media with a total M/# (dynamic range) of 173.
  • Each of the 220 holograms was recorded using sequential PQHM recording, and thus contains two separate data pages (an in-phase page and a quadrature page) separated in phase by 90°.
  • the 220 holograms were four ⁇ calibration holograms, also recorded using PWHM.
  • FIGS. 9A-9C, 10A, 10B, and 11 illustrate the sequence of operations used to decode the hologram at the second multiplexing angle (angle 2) using the calibration hologram at the tenth multiplexing angle (angle 10).
  • a detector image of the local oscillator alone is taken using the same exposure time used for acquiring the data and demodulation images.
  • the reference beam is aligned to the calibration hologram at angle 10, and four n-rature demodulation detector images of the calibration hologram are exposed.
  • the local oscillator image is subtracted (pixel-wise) from each of the four demodulation detector images.
  • the predetermined fringe demodulation pattern, ⁇ ⁇ shown in FIG. 9A is demodulated from the four demodulation detector images.
  • the demodulation is performed using n-rature to quadrature fringe demodulation to yield two demodulation images.
  • the demodulation pattern ⁇ ⁇ was formulated empirically to remove fringe components common in typical recoveries by the holographic data storage device.
  • Equation (22) the best- fit quadratic wavefront shown in FIG. 7B was then demodulated from the two demodulation images using Equation (22), yielding two further demodulated images.
  • location and peak strengths all of the reserved blocks in the ⁇ calibration holograms were found using cross-correlations.
  • the peak strengths were upsampled and processed per Eq. Error! Reference source not found, to produce a reserved block-based estimate of the remaining phase difference, ⁇ .
  • the final demodulation wavefront is determined by the sum of these three components:
  • FIG. 9C shows the final demodulation wavefront. Note the hemispherical outline with a vertical gap in the middle. This represents the shape of the data page, and hence the region of support for ⁇ .
  • the final demodulation wavefront A ⁇ , emod may then be used to demodulate fringes from the n-rature recoveries of data pages.
  • this demodulation wavefront derived from the calibration hologram at angle 10 was used to demodulate the data holograms at angles 0 through 54, excluding the demodulation hologram at angle 10 itself.
  • the reference beam is aligned to the data hologram at angle 10, and four n-rature data detector images of the data hologram are exposed.
  • the local oscillator image is subtracted (pixel- wise) from each of the four data detector images.
  • the measured fringe demodulation pattern, ⁇ , 6 ⁇ () is demodulated from the four data detector images.
  • the demodulation is performed using n-rature to quadrature fringe demodulation to yield two data images constituting a quadrature image pair.
  • E r and E Q images were then resampled to produce E r and E Q images, containing estimates of the optical field for each recorded pixel in the I and Q data pages, respectively, using resampled quadrature homodyne detection in combination with PQHM recovery.
  • the I and Q reserved blocks were jointly detected in the two data images and used to produce a wavefront A dat representing the fringe pattern still present in the data hologram after removal of the demodulation pattern, A ⁇ , emod .
  • This fringe pattern A dat is shown in FIG. 10. Note that A dat exhibits considerably lower fringe spatial frequencies than A ⁇ , emod , allowing it to be accurately estimated using the reserved blocks in the data pages, which in this case are considerably sparser than the reserved blocks in the demodulation pages.
  • the E ⁇ and E Q images could subsequently be used to generate soft decision estimates of the state of each pixel, which are fed into a soft-decision decoder to reduce the bit error rate of the recorded user data to an acceptably low level, e.g.,
  • the pixels in the E r and E Q images may, however, also be used to generate a hard decision about the binary state of each pixel by simple threshold detection. Comparing this decision to the true value produces a raw bit error rate which is diagnostic of the quality of the recording channel, and may be used to determine the amount of forward error correction required for the soft-decision decoder. Additionally, bit error maps may be produced showing the location of erroneously detected pixels within the data pages. Bit error rates may be converted into equivalent signal-to-noise ratios, e.g., denoted BSNR and defined as the SNR in decibels of an additive white Gaussian noise (AWGN) channel achieving the same bit error rate.
  • BSNR equivalent signal-to-noise ratios
  • FIGS. 11 A and 1 IB show the bit error maps for the I and Q data pages, respectively, in the example recovery (white pixels were detected in error), raw bit error rates are 9.8xl0 ⁇ 2 and 7.8xl0 "2 for the I and Q data pages, respectively.
  • the SNRs, as determined from the embedded reserved blocks, are 2.56 dB and 3.66 dB, respectively. In both cases the pages are of sufficient quality to decode error- free using the proposed soft-decision decoder.
  • FIGS. 12A and 12B show the results of an experiment comparing the performance of direct detection, quadrature homodyne detection, and n-rature homodyne detection.
  • an SLM was illuminated with 405 nm laser light, and imaged on to a detector array with a pixel pitch of about 0.75 that of the SLM (i.e., 4/3 oversampling).
  • the SLM was configured for binary ASK modulation (i.e., bright and dark pixels).
  • the SLM was configured for binary PSK modulation ( ⁇ 180° phase pixels), and a collimated local oscillator beam with about 30 times the intensity of the signal was mixed with the signal.
  • a mirror in the local oscillator path was mounted to a piezoelectric actuator in order to effect the phase differences required by the quadrature homodyne detection and n-rature homodyne detection algorithms.
  • FIG. 12A is a plot of the simulated SNR of the recovered data page versus the ratio of signal power to noise power for different combinations of ASK and PSK recording, direct detection, and quadrature homodyne detection. It shows that, for ASK recording, using quadrature homodyne detection instead of direct detection increases the page SNR for a given ratio of signal power to noise power. It also shows that PSK recording instead of ASK recording further increases the page SNR for a given ratio of signal power to noise power.
  • the leftward shift of the n-rature curve compared to the direct detection curve represents the amount of optical SNR degradation sustainable with n-rature homodyne detection for the same performance achieved by direct detection.
  • the 9 dB improvement shown over direct detection matches the theoretical prediction remarkably well.
  • the experimental results for quadrature homodyne detection also match the predicted improvements (e.g., about 5 dB) in the simulation shown in FIG. 12A.
  • references in the specification to "one embodiment”, “an embodiment”, “another embodiment, “a preferred embodiment”, “an alternative embodiment”, “one variation”, “a variation” and similar phrases mean that a particular feature, structure, or characteristic described in connection with the embodiment or variation, is included in at least an embodiment or variation of the invention.
  • the phrase “in one embodiment”, “in one variation” or similar phrases, as used in various places in the specification, are not necessarily meant to refer to the same embodiment or the same variation, components, or objects, in which no other element, component, or object resides between those identified as being directly coupled.
  • inventive embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, inventive embodiments may be practiced otherwise than as specifically described and claimed.
  • inventive embodiments of the present disclosure are directed to each individual feature, system, article, material, kit, and/or method described herein.
  • a computer may be embodied in any of a number of forms, such as a rack-mounted computer, a desktop computer, a laptop computer, or a tablet computer. Additionally, a computer may be embedded in a device not generally regarded as a computer but with suitable processing capabilities, including a Personal Digital Assistant (PDA), a smart phone or any other suitable portable or fixed electronic device.
  • PDA Personal Digital Assistant
  • a computer may have one or more input and output devices. These devices can be used, among other things, to present a user interface. Examples of output devices that can be used to provide a user interface include printers or display screens for visual presentation of output and speakers or other sound generating devices for audible presentation of output. Examples of input devices that can be used for a user interface include keyboards, and pointing devices, such as mice, touch pads, and digitizing tablets. As another example, a computer may receive input information through speech recognition or in other audible format.
  • Such computers may be interconnected by one or more networks in any suitable form, including a local area network or a wide area network, such as an enterprise network, and intelligent network (IN) or the Internet.
  • networks may be based on any suitable technology and may operate according to any suitable protocol and may include wireless networks, wired networks or fiber optic networks.
  • the various methods or processes may be coded as software that is executable on one or more processors that employ any one of a variety of operating systems or platforms. Additionally, such software may be written using any of a number of suitable programming languages and/or programming or scripting tools, and also may be compiled as executable machine language code or intermediate code that is executed on a framework or virtual machine.
  • inventive concepts may be embodied as a computer readable storage medium (or multiple computer readable storage media) (e.g., a computer memory, one or more floppy discs, compact discs, optical discs, magnetic tapes, flash memories, circuit configurations in Field Programmable Gate Arrays or other semiconductor devices, or other non-transitory medium or tangible computer storage medium) encoded with one or more programs that, when executed on one or more computers or other processors, perform methods that implement the various embodiments of the invention discussed above.
  • the computer readable medium or media can be transportable, such that the program or programs stored thereon can be loaded onto one or more different computers or other processors to implement various aspects of the present invention as discussed above.
  • program or “software” are used herein in a generic sense to refer to any type of computer code or set of computer-executable instructions that can be employed to program a computer or other processor to implement various aspects of embodiments as discussed above. Additionally, it should be appreciated that according to one aspect, one or more computer programs that when executed perform methods of the present invention need not reside on a single computer or processor, but may be distributed in a modular fashion amongst a number of different computers or processors to implement various aspects of the present invention.
  • Computer-executable instructions may be in many forms, such as program modules, executed by one or more computers or other devices.
  • program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types.
  • functionality of the program modules may be combined or distributed as desired in various embodiments.
  • data structures may be stored in computer-readable media in any suitable form.
  • data structures may be shown to have fields that are related through location in the data structure. Such relationships may likewise be achieved by assigning storage for the fields with locations in a computer-readable medium that convey relationship between the fields.
  • any suitable mechanism may be used to establish a relationship between information in fields of a data structure, including through the use of pointers, tags or other mechanisms that establish relationship between data elements.
  • inventive concepts may be embodied as one or more methods, of which an example has been provided.
  • the acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments.
  • a reference to "A and/or B", when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.
  • the phrase "at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements.
  • This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase "at least one" refers, whether related or unrelated to those elements specifically identified.
  • At least one of A and B can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.

Abstract

L'invention porte sur des procédés et des dispositifs pour des techniques de canaux de données holographiques cohérentes. Des techniques cohérentes pour une détection de données comprennent de manière générale des détections homodyne et hétérodyne. Des techniques de détection homodyne en quadrature, de détection homodyne en quadrature à ré-échantillonnage, de détection homodyne en n-rature, et de démodulation de front d'onde spatial sont présentées. Des techniques de détection cohérentes permettent à leur tour des techniques de modulation de canaux cohérentes de telle sorte qu'une modulation de phase (comprenant une modulation par déplacement de phase binaire, ou BPSK; un multiplexage holographique en quadrature de phase, ou de QPSK; et une modulation d'amplitude en quadrature, ou QAM). Une détection cohérente peut également permettre ou améliorer les performances d'autres techniques de canaux telles que la probabilité maximale de réponse partielle (PRML), les diverses classes de PRML étendue, et de détection à probabilité maximale de prédiction de bruit (NPML).
PCT/US2015/028356 2013-09-11 2015-04-29 Procédés et appareil pour canaux de données holographiques cohérents WO2015168325A1 (fr)

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JP2016565251A JP2017519323A (ja) 2014-04-29 2015-04-29 コヒーレントなホログラフィックデータチャネルのための方法および装置
KR1020167033508A KR20160147987A (ko) 2014-04-29 2015-04-29 코히어런트 홀로그래픽 데이터 채널을 위한 방법 및 장치
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