The present invention broadly relates to methods for adjusting at least one alignment control axis of a holographic data storage system or device to or towards a sufficiently optimal recovery position for recovery of the next hologram in a sequence of holograms by the holographic data storage system or device based on a derived feedback error signal and/or a derived feed-forward signal. The present invention further broadly relates to a method using a feedback error signal derived by an iterative alignment procedure for one hologram for adjusting at least one alignment control axis of a holographic data storage system or device to or towards a sufficiently optimal recovery position for recovery of the one hologram by the holographic data storage system or device.
In a holographic data storage (HDS) device or system, data-bearing holograms are recorded in a photosensitive holographic storage medium. The data in a hologram may be recovered by illuminating the holographic storage medium with a probe beam (also referred to as a recovery or reconstruction beam), which is nominally a replica of the reference beam used to record (write) the hologram. The probe beam is diffracted by the recorded hologram, thereby generating a diffracted beam, which is a replica of the original data-bearing signal beam. The diffracted beam may then be detected with a detector array, such as a camera, and the data recovered from the resulting detected holographic image.
The quality of the diffracted beam often depends on the precise alignment of the probe beam wavefront to the holographic fringes within the hologram. High storage capacity may be achieved by densely multiplexing many holograms within a medium. An HDS device or system often employs one or more multiplexing methods, each of which may require one or more control signals to select the desired hologram to be recovered. The HDS device or system may, for example, use a galvanometer in order to control the probe beam angle of incidence to effect angle multiplexing, and translation plus rotation (r, θ) actuators in order to properly position the disk-shaped medium with respect to the probe beam and recovery optics (spatial multiplexing). See Mok, “Angle-Multiplexed Storage of 5000 Holograms in Lithium Niobate,” Opt. Lett. 18:915-917 (1993). Other control signals may be used to adjust other alignment parameters not associated with multiplexing per se.
A variety of methods have been used to try to align a probe beam with respect to the hologram(s) to be recovered from the holographic storage medium. The simplest method, which may be adequate in some cases, is to simply apply an open-loop control signal. In other cases, an actuator which may contain an integrated feedback sensor, such as a linear or angular position encoder, may be used to try to position the probe beam and/or holographic storage medium properly with respect to the hologram(s) to be recovered. Servo marks may also be pre-formatted onto the holographic storage medium in order to provide positioning feedback. See U.S. Pat. No. 7,184,383 (Ayres et. al.), issed Feb. 27, 2007; Horimai et al., “Collinear Holography,” Appl. Opt. 44:2575-2579 (2005). Methods involving wavelength and temperature tuning have also been used. See U.S. Pat. Appln. No. 2007/0211321(Hoskins et al.), published Sep. 13, 2007.
According to a first broad aspect of the present invention, there is provided a method comprising the following steps:
According to a second broad aspect of the present invention, there is provided a method comprising the following steps:
According to a third broad aspect of the present invention, there is provided a method comprising the following steps:
The invention will be described in conjunction with the accompanying drawings, in which:
It is advantageous to define several terms before describing the invention. It should be appreciated that the following definitions are used throughout this application.
Where the definition of terms departs from the commonly used meaning of the term, applicant intends to utilize the definitions provided below, unless specifically indicated.
For the purposes of the present invention, directional terms such as “top”, “bottom”, “above”, “below”, “left”, “right”, “horizontal”, “vertical”, “up”, “down”, etc. are merely used for convenience in describing the various embodiments of the present invention. The embodiments of the present invention may be oriented in various ways. For example, the diagrams, graphs, axes, etc., shown in
For the purposes of the present invention, the term “coherent light beam” refers to a beam of light including waves with a particular (e.g., constant) phase relationship, such as, for example, a laser beam.
For the purposes of the present invention, the terms “data beam” and “signal beam” refer interchangeably to a beam containing a data signal. For example, a signal beam may include beams that have been modulated by a modulator such as a spatial light modulator (SLM), along with a beam generated in response to a reference beam impingent on a holographic storage medium, where the generated beam includes data. The modulation of the signal beam may be an amplitude, a phase or some combination of the amplitude and phase. The SLM may be reflective or transmissive. The signal beam may be modulated into a binary state or into a plurality of states. The signal beam may include data as well as headers that contain information about the data to be stored or where the data is stored. The signal beam may also include known bits for a servo or to detect the location of the data once it is detected by or on a detector such as, for example, a CMOS sensor array.
For the purposes of the present invention, the term “data modulated beam” refers to a signal beam that has been modulated by a modulator such as a spatial light modulator (SLM). The modulation of the signal beam may be an amplitude, a phase or some combination of the amplitude and phase. The SLM may be reflective or transmissive. The signal beam may be modulated into a binary state or into a plurality of states.
For the purposes of the present invention, the term “data modulator” refers to any device that is capable of optically representing data in a single bit or in one or two-dimensions from a signal beam.
For the purposes of the present invention, the term “holographic data” refers to data recorded, stored, written, etc., in the holographic storage medium as one or more holograms.
For the purposes of the present invention, the term “data page” or “page” refers to the conventional meaning of data page as used with respect to holography. For example, a data page may be a page of data (i.e., a two-dimensional assembly of data), one or more pictures, etc., to be written or written in a holographic storage medium. The data page may include header information and known bits for servo and channel usage, as well as bits that represent the data to be stored or processed.
For the purposes of the present invention, the term “disk” refers to a disk-shaped (i.e., generally circular-shaped) holographic storage medium.
For the purposes of the present invention, the terms “holograph” or “hologram” (collectively and interchangeably referred to hereafter as “hologram”) are used in the conventional sense of referring to an interference pattern formed when a signal beam and a reference beam interfere with each other. In cases where digital data is recorded page-wise, the signal beam may be encoded with a data modulator, e.g., a spatial light modulator, etc.
For the purposes of the present invention, the term “holographic grating” refers to a component of a hologram, e.g. an individual sinusoidal grating.
For the purposes of the present invention, the term “storage medium” refers to any component, material, etc., capable of storing information, such as, for example, a holographic storage medium.
For the purposes of the present invention, the term “holographic storage medium” refers to medium that has a least one component, material, layer, etc., that is capable of recording, storing, writing, etc., one or more holograms (e.g., bit-wise, linear array-wise or page-wise) as one or more patterns of varying refractive index imprinted into the medium. Examples of a holographic storage medium useful herein include, but are not limited to, those described in: U.S. Pat. No. 6,103,454 (Dhar et al.), issued Aug. 15, 2000; U.S. Pat. No. 6,482,551 (Dhar et al.), issued Nov. 19, 2002; U.S. Pat. No. 6,650,447 (Curtis et al.), issued Nov. 18, 2003, U.S. Pat. No. 6,743,552 (Setthachayanon et al.), issued Jun. 1, 2004; U.S. Pat. No. 6,765,061 (Dhar et al.), Jul. 20, 2004; U.S. Pat. No. 6,780,546 (Trentler et al.), issued Aug. 24, 2004; U.S. Patent Application No. 2003/0206320 (Cole et al.) published Nov. 6, 2003; and U.S. Patent Application No. 2004/0027625 (Trentler et al.), published Feb. 12, 2004, the entire disclosure and contents of which are herein incorporated by reference. The holographic storage medium may comprise photopolymers, photo-chromatic materials, photo-refractive materials, etc. The holographic storage medium may be any type, including: a transparent holographic storage medium, a holographic storage medium including a plurality of components or layers such as a reflective layer, a holographic storage medium including a reflective layer and a polarizing layer so reflection may be controlled with polarization, a holographic storage medium including variable beam transmission layer that may be pass, absorb, reflect, be transparent to, etc., light beams, grating layers for reflecting light beams, substrates, substrates with servo markings, etc. The storage medium may be highly transmissively flat (thus making multiplexing easier and better) or not flat. An example of an inexpensive flat storage medium (e.g., to better than a couple wavelengths within the area where data may be stored) may use what is referred to herein as the Zerowave™ process, which is described in U.S. Pat. No. 6,156,425 (Bouquerel et al.), issued Dec. 5, 2000, the entire disclosure and contents of which is hereby incorporated by reference. All holographic storage medium described herein may be, for example, in the shape, form, etc., of a disk, card, flexible tape media, etc.
For the purposes of the present invention, the term “holographic recording” refers to the act of recording, storing, writing, etc., a hologram in a holographic storage medium. The holographic recording may provide bit-wise storage (i.e., recording of one bit of data), may provide storage of a 1-dimensional linear array of data (i.e., a 1×N array, where N is the number linear data bits), or may provide 2-dimensional storage of a page of data.
For the purposes of the present invention, the term “light source” refers to a source of electromagnetic radiation having a single wavelength or multiple wavelengths. The light source may be from a laser, one or more light emitting diodes (LEDs), etc.
For the purposes of the present invention, the term “processor” refers to a device capable of, for example, executing instructions, implementing logic, calculating and storing values, etc. Exemplary processors may include application specific integrated circuits (ASIC), central processing units, microprocessors, such as, for example, microprocessors commercially available from Intel and AMD, etc.
For the purposes of the present invention, the terms “recording,” “storing,” and “writing (collectively and interchangeably referred to hereafter as “recording”) refer to recording, storing or writing holograms to and/or into a holographic storage medium.
For the purposes of the present invention, the term “recording light” refers to a light source used to write holograms to a holographic storage medium.
For the purposes of the present invention, the term “reference beam” refers to a beam of light not modulated with recording data. Exemplary reference beams may include non-data bearing laser beams used while recording or writing holograms to, or reading or recovering holograms from, a holographic storage medium. In some embodiments, the reference beam may refer to the original reference beam used to write the hologram, to a reconstruction beam when used to recover holograms from the holographic storage medium, or to a phase conjugate of the original reference (reconstruction) beam. When recovering holograms, the reference beam may also be referred to interchangeably as a “probe beam.”
For the purposes of the present invention, the term “multiplexing” refers to recording (writing) a plurality of holograms in the same volume or nearly the same volume of the holographic storage medium by varying a recording (writing) parameter(s) including, but not limited to, angle, wavelength, phase code, polytopic, shift, correlation, peristrophic, fractal, etc., including combinations of parameters, e.g. angle-polytopic multiplexing. For example, angle multiplexing involves varying the angle of the plane wave or nearly plane wave of the reference beam during recording (writing) to store a plurality of holograms in the same volume. The multiplexed holograms that are recorded (written) may be recovered by using/changing the same writing parameter(s) used to record (write) the respective holograms.
For the purposes of the present invention, the term “polytopic multiplexing” refers to a multiplexing method or technique where the recording (writing) of stacks of holograms is spatially overlapped. The spacing between stacks may be at least the beam waist, which is the narrowest part of the signal beam. An aperture may be placed in the system at the beam waist. During recovery, all of the overlapped holograms at a given multiplexing angle may be recovered, but only the hologram that is centered in the aperture is passed through to the recovery optics. Examples of polytopic recording techniques that may be used in various embodiments of the present invention are described in U.S. Pat. App. No. 2004/0179251 (Anderson et al.), published Sep. 16, 2004; and U.S. Pat. App. No. 2005/0036182 (Curtis et al.), published Feb. 17, 2005, the entire disclosure and contents of which are hereby incorporated by reference.
For the purposes of the present invention, the term “fractal multiplexing” refers to multiplexing where the angle is changed in a direction which not as Bragg selective until the reconstruction is moved off the detector (e.g., camera).
For the purposes of the present invention, the term “spatial light modulator” (SLM) refers to a device that stores information on a light beam by, for example, modulating the spatial intensity and/or phase profile of the light beam.
For the purposes of the present invention, the term “spatial light intensity” refers to a light intensity distribution or pattern of varying light intensity within a given volume of space.
For the purposes of the present invention, the term “recovering holograms” refers to retrieving, recovering, reconstructing, reading, etc., holograms recorded in a holographic storage medium.
For the purpose of the present invention, the term “device” may refer to an apparatus, a mechanism, equipment, machine, controller, etc., such as, for example, a holographic data storage device.
For the purposes of the present invention, the term “SNR” refers to the signal to noise ratio.
For the purposes of the present invention, the term “reserved block” refers to a pixel pattern which is independent of the surrounding pixels and is located at known position (or positions) within a data image and which embeds known data patterns within each hologram. Reserved blocks may serve, for example, as fiducials for alignment and/or SNR measurements.
For the purposes of the present invention, the term “fiducial” (also referred to as a “fiducial marker”) refers to an object (or objects) used in the field of view of an imaging system which appears in the image produced and may be used as a point of reference or a measure for alignment.
For the purposes of the present invention, the term “quiver pattern” refers to a representation of a holographic image distortion pattern where the quiver vectors (which may be represented as “arrows”) in the pattern represent the x,y-dimensional holographic image displacement at specific sampled locations with respect to their nominal location. An example of a quiver pattern is shown in
For the purposes of the present invention, the term “quiver pattern vector” refers to a quiver pattern wherein the x,y-components of all the individual quiver vectors are arranged into a single row or column vector.
For the purposes of the present invention, the term “characteristic misalignment quiver pattern vector” refers to a quiver pattern vector that would be observed in an ideal system as the result of misalignment of a specific alignment control axis by a specific amount.
For the purposes of the present invention, the term “quiver error signal” refers to a measurement of misalignment derived from a quiver pattern.
For the purposes of the present invention, the term “centroid” refers to the conventional sense of the intersection of all hyperplanes that divide an object (e.g., a sphere) into two parts of equal moment about a hyperplane.
For the purposes of the present invention, the term “intensity centroid” refers to a two-dimensional centroid calculated from the intensity of an image. For example, the x and y intensity centroid coordinates, cx and cy, of an image are given by Equation 1:
wherein I(x,y) is the image pixel value as a function of the Cartesian coordinates x and y, or is the image intensity map as a function of the coordinates x and y.
For the purposes of the present invention, the terms “image intensity map” and “intensity map” refer interchangeably to a lower resolution version of an image. For example, a summing up of all of the 1024 pixel values within each a 32×32 pixel sub-block of an image to produce a smaller image creates an “intensity map.”
For the purposes of the present invention, the term “centroid shift” refers to the difference between the respective intensity centroid coordinates of two images.
For the purposes of the present invention, the term “centroid shift error signal” refers to a measurement of misalignment derived from a centroid shift.
For the purposes of the present invention, the term “polarization density patch” refers to a Fourier transform of the spatial electric dipole polarization complex amplitude distribution induced by a probe beam corresponding to an individual hologram.
For the purposes of the present invention, the terms “misalignment” and “misaligned” refer to a parameter, for example, a probe beam alignment control axis, a holographic storage medium alignment control axis, etc., which is out of alignment, offset, skewed, distorted, etc. Misalignment (for example, of an alignment control axis) may lead to sub-optimal recovery of holograms.
For the purposes of the present invention, the terms “Bragg-matched” and “Bragg-matching” refer to the illumination of a holographic grating by a probe beam in a manner which satisfies an optimal Bragg diffraction condition. For example, the part or portion of a polarization density patch which lies on a k-sphere is considered Bragg-matched. See description below with reference to
For the purposes of the present invention, the terms “Bragg-mismatching” and “Bragg-mismatched” refer to the illumination of a holographic grating by a probe beam in a manner which does not satisfy the optimal Bragg diffraction condition. For example, the part or portion part of a polarization density patch which does not lie on a k-sphere is considered Bragg-mismatched. See also description below with reference to
For the purposes of the present invention, the term “probe beam angle” refers to an angle of the probe beam incident on the holographic storage medium in the plane containing the reference and signal beam optical axes.
For the purposes of the present invention, the term “probe beam pitch” refers to the probe beam angle in a direction perpendicular to the plane containing the reference and signal beam optical axes.
For the purposes of the present invention, the term “probe beam wavelength” refers to a wavelength of the probe beam during recovery of holograms.
For the purposes of the present invention, the term “cross-talk” refers to any signal unintentionally affecting another signal.
For the purposes of the present invention, the term “alignment control axis” refers to an axis which may be adjusted to align a parameter in a holographic storage device or system to achieve a more optimal position for recovery of a recorded hologram. Alignment control axes may include probe beam alignment control axes, holographic storage medium alignment control axes, hologram shift position, hologram exposure timing, wavelength tuning, etc.
For the purposes of the present invention, the term “probe beam alignment control axis” refers to an alignment control axis which may be adjusted to align the probe beam in a holographic storage device or system to or towards a more optimal recovery position for recovery of a recorded hologram. Probe beam alignment control axes may include the probe beam angle (also referred to as the “φ axis”), the probe beam wavelength (also referred to as the “λ axis”), and the probe beam pitch (also referred to as the “ρ axis”), as well as any combination of these axes.
For the purposes of the present invention, the term “holographic storage medium alignment control axis” refers to an alignment control axis which may be adjusted to align the holographic storage medium in a holographic storage device or system to or towards a more optimal recover position for recovery of a recorded hologram. For a disk-shaped holographic storage medium, the holographic storage medium alignment control axes may include the radial translational axis (also referred to as the “r axis”), and the rotational axis (also referred to as the “κ axis”).
For the purposes of the present invention, the terms “feedback error signal” and “feedback alignment error signal” refer interchangeably to a feedback signal derived from alignment-indicating data from a recovered hologram(s), which identifies, detects, measures, quantifies, etc., a misalignment in one or more alignment control axes (e.g. a probe beam alignment control axis or axes) of a recovered hologram(s), and which may be used to adjust the at least one alignment control axis to or towards a sufficiently optimal recovery position for recovery of a hologram(s).
For the purposes of the present invention, the term “wobble” refers to imparting an offset to one or more alignment control axes during the sampling of recovered holograms. For example, an embodiment of a probe beam angle wobble may involve imparting an alternating positive (+) or negative (−) angular offset to even numbered and odd numbered holograms. While wobbles may be imparted in an alternating manner (e.g., a positive (+) wobble, then a negative (−) wobble, and so forth), wobbles may also be imparted in a non-alternating manner (e.g., two consecutive positive (+) wobbles, then followed by two consecutive negative (−) wobbles, and so forth). Wobble(s) may also be imparted to the alignment control axis to be aligned or adjusted, or may be imparted to a different alignment control axis to generate data for aligning an alignment control axis to which the wobble is not imparted. For some embodiments of the present invention, the wobble offset imparted may be relatively small, for example, ˜±0.002° in the case of an alternating probe beam angle wobble.
For the purposes of the present invention, the term “wobble error signal” refers to a detected misalignment based on sampled holograms while one or more alignment control axes are being subjected to wobble. For example, where an alternating angular offset is imparted during sampling of even numbered and odd numbered holograms, as measured by the respective SNRs, an angle wobble error signal may be indicated by a difference in the SNRs of the even numbered and odd numbered holograms (e.g., by not being centered about the respective SNR peaks); a pitch wobble error signal may be indicated by a shift in the x-component of the intensity centroids of the even numbered and the odd numbered holograms (see description below with reference to
For the purposes of the present invention, the term “alignment-indicating data” refers to data from one or more recovered holograms which may be used to indicate, measure, detect, determine, quantify, etc., the magnitude and/or direction of misalignment (alignment error) from the nominal for a hologram. Such alignment-indicating data may include quality metrics, such as SNR values, diffracted beam intensity, total image intensities, distortions of the holographic image(s) (e.g., from quiver patterns), changes (shifts) in the position of the intensity centroid of the detected image, changes in the intensity patterns (e.g., intensity map) of the detected images, etc.
For the purposes of the present invention, the term “optimal recovery position” refers to a recovery position where the recovered hologram has the highest quality, e.g., the highest SNR, no or minimal errors, distortions, degradations, etc., affecting the quality of, properties of, condition of, images, data or information provided by, etc., the recovered hologram, etc.
For the purposes of the present invention, the term “displacement from the optimal recovery position” refers to the difference (in direction and magnitude) between the optimal recovery position (i.e., the position where the recovered hologram has the highest quality), and the actual position from which the hologram is recovered.
For the purposes of the present invention, the term “feed-forward signal” refers to a signal derived from recording and recovery operating condition data for a hologram(s), and which may be used to adjust the at least one alignment control axis to or towards a sufficiently optimal recovery position for recovery of a hologram(s).
For the purposes of the present invention, the term “recording and recovery operating condition data” refers to data relating to one or more operating condition parameters which may differ in some measurable, predictable, calculatable, etc., way or aspect between the recording and recovery of a given hologram, and which may be used to derive a feed-forward signal. These operating condition parameters may include temperature, humidity, pressure, exposure history for recording and recovering holograms, compositional parameters of the holographic storage medium affected by operating conditions (e.g., medium parameters relating shrinkage, coefficient of thermal expansion, etc.), etc., as well as combinations of any of these operating condition parameters.
For the purposes of the present invention, the term “recovery position” refers to the n-tuple of positional values of all, or a subset, of the alignment control axes (e.g. [r, θ, λ, φ, ρ] axes, hologram shift position, hologram exposure timing, wavelength tuning, etc.) which may be used to define the position of the hologram during recovery from the holographic storage medium.
For the purposes of the present invention, the term “sufficiently optimal recovery position” refers to a recovery position for a hologram which is the optimal recovery position for the recovered hologram or which is sufficiently close to, approaches, etc., the optimal recovery position such that the quality of the recovered hologram has a sufficiently high SNR, no or minimal errors, distortions, degradations, etc., affecting the quality of, properties of, condition of, images, data or information provided by, etc., the recovered hologram, etc.
For the purposes of the present invention, the term “optimum recovery position” refers to a recovery position for a hologram where the recovered hologram has the highest quality, e.g. no or minimal errors, distortions, degradations, etc., affecting the quality of, properties of, condition of, images, data or information provided by, etc., the recovered hologram.
For the purposes of the present invention, the term “starting position” refers to the initial position for the alignment control axis or axes at the beginning of an iterative alignment procedure.
For the purposes of the present invention, the term “offset” refers to a difference between a baseline value (for example, a nominal alignment control axis position), and a displacement from that baseline value. These offsets may be alternating and opposite offsets, for example, positive (+) or negative (−) offsets such as, for example, a wobble imparted to a nominal position of an alignment control axis, may be non-alternating offsets, for example, imparting two or more consecutive positive (+) or negative (−) offsets, etc.
For the purposes of the present invention, the term “alignment value” refers to the degree of displacement in terms of magnitude and/or direction from an optimal position for an alignment control axis, as determined a-priori or from a measurement procedure, e.g. based on alignment-indicating data. An “optimal alignment value” refers to an alignment value wherein the alignment control axis is at an optimal or sufficiently optimal recovery position.
For the purposes of the present invention, the term “threshold alignment error criteria” refers to a criteria used to determine when the magnitude of an alignment error (e.g. as shown by the alignment value) is minimal or small enough such that an alignment control axis is considered to be at a sufficiently optimal recovery position for the holograms, and thus requires no further adjustment of the alignment control axis.
For the purposes of the present invention, the term “in a manner that reduces alignment error” refers to an adjustment of an alignment control axis which tends to reduce the magnitude of the alignment error of that axis.
For the purposes of the present invention, the term “sampling,” in the context of taking holographic image exposures, refers to the recovery of selected holograms for the purpose of detecting, determining, quantifying, etc., the alignment or misalignment of one or more alignment control axes. Accordingly, as used in this context, “sampling” may refer to obtaining, detecting, and analyzing the resulting diffracted beam from the selected holograms recovered.
For the purposes of the present invention, the term “exposure,” in the context of recovery of holograms, refers to the illumination of a holographic storage medium with a probe beam and the detection of the resulting diffracted beam. In the context of recording holograms, “exposure” refers to the illumination of a holographic medium with a signal beam and a reference beam in order to record the resulting interference pattern.
For the purposes of the present invention, the term “controller” refers to a system, device, machine, mechanism, computer, processor, microprocessor, integrated circuit, etc., which creates, produces, provides, generates, etc., data, results, outputs, signals, instructions, commands, etc., from inputs to, for example, a control system compensation algorithm and/or uses the data, results, outputs, signals, instructions, commands, etc., for example, from the control system compensation algorithm to adjust one or more alignment control axes. Controllers may include, for example, control loop feedback mechanisms, such as proportional-integral-derivative (PID) controllers, microcontrollers, programmable logic (PLC) controllers, etc.
For the purposes of the present invention, the term “servo” refers to a method, technique, algorithm, procedure, routine, etc., for minimizing a system or device error by feedback.
For the purposes of the present invention, the term “servomechanism” refers to a device, mechanism, etc., which uses a feedback error signal(s) to correct the performance of a device, machine, apparatus, mechanism, system, etc., where the feedback error signal help controls the mechanical position or other parameters of the mechanism system, etc.
Description
In many instances, optimal data recovery of holograms from a holographic storage medium may not be achieved without feeding back the quality of the diffracted data from the recovered holograms. In angular multiplexing, for example, hundreds of holograms may be multiplexed within a few dozen degrees of probe beam angular range. In some instances, the accuracy required to recover a single hologram may be as small as about ±0.005°, yet mechanical variation may require the actual angular uncertainty to be as much as about ±0.5° under different hologram recovery conditions. In such a case, it may be necessary, for example, to manually align a galvanometer to recover the hologram(s), or to have an electronic controller perform a fine scan of all possible galvanometer positions in order to ascertain the optimal recovery position for the hologram(s). Alternatively, a coarser scan may be performed and an interpolation or peak-fitting calculation may be employed to estimate the optimal position for recovery of the hologram(s).
Because servo signals may be unavailable, the electronic controller may need to rely on hologram recovery data based on a quality metric such as diffracted beam intensity or signal-to-noise-ratio (SNR). But such quality metrics may provide no direct information as to direction and/or magnitude of the misalignment. Consequently, these alignment operations may require more than one, and often may require many read exposures per hologram recovered, thus greatly reducing the maximum hologram recovery rate from the holographic storage medium. Often, the goal may be to recover a number of multiplexed holograms in sequence at the highest practical speed. In order to approach the maximum speed of about one read exposure per hologram, a method for predicting or estimating the optimal location of the next hologram to be recovered in the sequence from information obtained during recovery of the previous holograms may be required.
To provide optimal recovery of holograms from a holographic storage medium, the holograms may be precisely aligned with the probe beam with respect to one or more of three controllable or adjustable alignment control axes of the probe beam. These probe beam alignment control axes are the probe beam angle (the “φ axis”), the probe beam wavelength (the “λ axis”), and the probe beam angle in a direction perpendicular to the plane containing the reference and signal beam optical axes, also referred to as the “probe beam pitch” (the “ρ axis”). Optimal recovery of the holograms may also depend somewhat on the holograms being at least coarsely aligned in the translational (r) and rotational (θ) spatial dimensions or axes of the holographic storage medium (e.g., for disk-shaped holographic storage media). But optimal data recovery of the holograms from the holographic storage medium often depends primarily on the holograms being optimally aligned, or as optimally aligned as possible, with respect to the φ axis, the λ axis, and/or the φ axis of the probe beam.
Unfortunately, upon playback (recovery) of the holograms, misalignment(s), medium shrinkage (or expansion), thermal effects, and/or other distorting perturbations may cause displacement of the optimal recovery position of the holograms with respect to one or more of these probe beam alignment control axes. One such situation is illustrated in
Curve 104 in
While some embodiments of the present invention are illustrated in the context of finding optimal probe beam angles in an angle-multiplexed system, other embodiments of the present invention may also be used to align one or more of the other probe beam alignment control axes (i.e., the probe beam wavelength or “λ axis”, and/or the probe beam pitch or “ρ axis”), as well as other non-probe beam alignment control axes (e.g., hologram position shifting, hologram exposure timing, wavelength tuning, etc.) to optimize hologram recovery. For example, some embodiments of the present invention may be used to find optimal recovery positions in a shift-multiplexed system (see Psaltis et al., “Holographic Storage Using Shift Multiplexing,” Opt. Lett. 20:782-784 (1995), the entire contents and disclosures of which are hereby incorporated by reference), wherein the alignment control axis may be the r and/or θ spatial dimension positions (e.g., for a disk-shaped holographic storage media), or the x- and/or y-spatial dimension positions (e.g. for a rectangular- or square-shaped holographic storage media), or optimal recovery wavelengths in a wavelength-multiplexed system (see Curtis et al., “Cross Talk for Angle- and Wavelength-Multiplexed Image Plane Holograms,” Opt. Lett. 19:1774-1776 (1994) and Horimai et al., “Collinear Holography,” Appl. Opt. 44:2575-2579 (2005), the entire contents and disclosures of which are hereby incorporated by reference), wherein the alignment control axis may be wavelength tuning. Some embodiments of the present invention may also adjust multiple alignment control axes simultaneously. For example, an embodiment of multi-axis alignment involving a sequential recovery of holograms is described below in section 1c. See also section 4 below for description of an embodiment of a method for simultaneously aligning the probe beam angle (“φ axis”), the probe beam pitch (“ρ axis”), and wavelength (“λ axis”) in the recovery of angle-multiplexed holograms in an iterative procedure.
Embodiments of the present invention provide an estimate of the optimal recovery position for the next hologram in the sequence using available information (data). In one embodiment, the available information (data) may comprise a quality metric, such as the SNR, the diffracted beam intensity, etc., from or for the previously recovered holograms in the sequence. This estimation process may be generally described as comprising three basic steps: (1) deriving a feedback error signal which is an estimate of the direction and magnitude of the misalignment for previously recovered holograms; (2) deriving a feed-forward signal which estimates the optimal alignment value for at least one alignment control axis for one or more holograms in the sequence based on prior knowledge of the recording and recovery operating condition data for the one or more holograms in the sequence; and (3) applying (using) one or both of the feedback error and/or feed-forward signals, for example, as inputs to a control system compensation algorithm (e.g., involving a control processor, such as a controller, using, implementing, applying, executing, etc., such an algorithm) which then generates (e.g., through the control processor, such as a controller) one or more control axis commands to adjust one or more of the alignment control axes of a holographic data storage system or device to provide a sufficiently optimal recovery position for recovery of the next hologram in the sequence to be recovered by the holographic data storage system or device, i.e., used for the recovery of subsequent holograms in the sequence. In other words, the embodiments of the present invention may resemble a servo control system, and thus many of the techniques of analysis and implementation for servo control systems may be used in embodiments of the present invention. See R. C. Dorf, Modern Control Systems, (Third Edition, Addison-Wesley Publishing (1983), the entire contents and disclosure of which is hereby incorporated by reference. In some embodiments, adjustment of the alignment control axes to or towards a sufficiently optimal recovery position for a single hologram may be obtained based on a feedback error signal which is derived by an iterative alignment procedure involving only data recovery, for example, from a single hologram.
According to some embodiments of the present invention, either one or both of the feedback error and feed-forward signals may be used to adjust the alignment control axes of the holographic data storage system or device to or towards a sufficiently optimal recovery position. In some embodiments, both feedback error and feed-forward signals are used. The feedback error signal, the feed-forward signal, the control system compensation algorithm to which these signals may be inputted, and iterative alignment procedure aspects, respectively, of such embodiments are described in further detail below:
1. Derivation of Feedback Error Signals
a. Wobble Error Signals
In one embodiment, a quality metric such as SNR may be used as the basis for deriving a feedback displacement error signal. The SNR may be calculated, for example, by embedding known data patterns within each hologram (“reserved blocks”), and measuring the fidelity of the detected pattern according to a formula, for example, according to Equation 2:
wherein μ1 and μ0 are the measured means of the detected ones and zeros, and σ1 and σ0 are the respective standard deviations, from the reserved block(s). For further details on how to carry out such SNR measurements, see U.S. Pat. Appln. No. 2005/0286388 (Ayres et. al.), published Dec. 29, 2005; Ayres et al., “Image Oversampling for Page-Oriented Optical Data Storage,” Applied Optics, 45(11):2459-2464 (Apr. 10, 2006); and Ayres, “Signal Modulation for Holographic Memories,” ISBN-9780549315193 (2007), the entire contents and disclosures of which are hereby incorporated by reference.
The SNR for a given hologram as a function of probe beam angle generally has the form of a sharp peak, with the SNR reaching a maximum value at an optimal angle and falling off sharply on either side or slope of the peak as the angle deviates from the optimal, and may be approximated by Equation 3:
SNR(φ)=SNR0−C(φ−φ0)2 (3)
wherein φ is the probe beam angle with respect to the medium normal in degrees, φ0 is the optimal probe beam angle, and C≅8.5×103 dB/degree2 is a constant (which may be empirically derived for the particular system) defining the quadratic peak shape. SNR0, the peak SNR of the hologram, may not be known in advance and indeed may vary somewhat from hologram to hologram. An alignment error indicating both the sign (direction) and magnitude of the probe beam angle error, err=φ−φ0, cannot be determined from a single SNR sample. However, from this SNR peak model, the derivative of SNR(φ) is proportional to probe beam angle error, err. The probe beam angle error, err, may thus be determined from two SNR samples offset in φ according to Equation 4:
wherein Δφ is a constant probe beam angle offset.
In order to estimate Δφ while recovering a sequence of holograms with only one exposure which is near the peak SNR for each hologram, it may be necessary that: (1) Δφ be relatively small; and (2) each probe beam angle error, err, sample be calculated from the difference in SNR between two different holograms within the sequence, i.e., according to Equation 5:
wherein the subscript h denotes the hologram number in the sequence. The nominal probe beam angles φh and φh−1 should be separated by the true spacing between holograms h and h−1 in order to produce the most accurate estimate. In one embodiment, φh and φh−1 may be the estimated positions for the hth and h−1th holograms determined by the control system compensation algorithm, as described below in section 3. Inaccuracy in these positions may translate into inaccuracy (noise) in the error signal. Additionally, differences in the peak SNRs, SNR0,h and SNR0,h−1, may produce error signal noise, as may departures in the actual peak shape compared to the ideal.
The probe beam angle offsets may also be applied, with the opposite sign, according to Equation 6:
In one embodiment, the probe beam angle offset Δφ may be applied with an alternating polarity, e.g. holograms are recovered at φh−Δφ when h is even (i.e., an even numbered hologram), and φh+Δφ when h is odd (i.e., an odd numbered hologram). Equation 5 above may then be used for even numbered holograms, h, while Equation 6 above may be used for odd numbered holograms, h, so that an errh sample is generated for every hologram recovery. This approach may be considered analogous to “wobble tracking” for conventional optical disk drives, wherein following of the data track is accomplished by imparting a low frequency, alternating offsets (“wobble”) to the playback head back and forth across the data track, and deriving a tracking error signal proportional to the difference between the signal strength at the opposite wobble offsets. See Marchant, Optical Recording: A Technical Overview, (Addison-Wesley Publishing, 1990), pp. 180-181.
One disadvantage of wobble tracking is that there may be a diminution of signal quality since the average positioning error is not zero. This effect may be mitigated if the wobble displacement, Δφ, is made as small as possible. For example, if Δφ=±0.002°, then the SNR loss due to the wobble itself is only 0.034 dB given the peak model of Equation 3 above.
In alternative embodiments, the wobble technique may be used with alignment control axes other than the probe beam angle. For example, in a shift multiplexing system (see Psaltis et al., “Holographic Storage Using Shift Multiplexing,” Opt. Lett. 20:782-784 (1995) and Horimai et al., “Collinear Holography,” Appl. Opt. 44:2575-2579 (2005), the entire contents and disclosures of which are hereby incorporated by reference), a x-dimensional spatial position wobble offset of ±Δx (wherein the x-dimensional spatial position may correspond to, for example, the r, θ, x-, and/or y-spatial positions) may be applied to the recovery positions of the holograms in order to produce a feedback error signal for correcting hologram shift positions. Alternatively and equivalently, a timing wobble offset of ±Δt may be imparted to the recovery exposure sampling interval while the holographic storage medium is shifting at a velocity (e.g., constant velocity) to correct for hologram exposure timing for shift multiplexing. This may be considered to be equivalent to wobbling the “θ-axis” and possibly the “r-axis” spatial position of a rotating holographic storage disk medium wherein the spatial sampling position of the medium is wobbled a very small amount. In another example, a probe beam wavelength wobble offset of ±Δλ may be imparted to the wavelength of the probe beam to produce a feedback error signal for correcting wavelength tuning (and may be useful for any system, whether or not it employs wavelength multiplexing). Generally, embodiments of the present invention allow for the perturbation of any alignment control axis signal in order to detect the local gradient of signal quality, and then to seek a local maximum.
In other alternative embodiments, a quality metric other than the SNR may be maximized. For example, the diffracted beam intensity may be employed, or a detected bit error rate (e.g., the number of bit errors in the reserved blocks; or the number of cyclic redundancy check (CRC) errors) may be determined over a section of known data. The choice of quality metric is independent of the choice of control axis (or axes), and all combinations thereof may considered in embodiments of the present invention. For example, a ±Δφ wobble may be used with a quality metric maximizing diffracted beam intensity in an angle multiplexing system, or an ±Δx wobble may be used with a quality metric minimizing detected bit errors in a shift multiplexing system.
b. Quiver Error Signals
In an alternate embodiment of the invention, the probe beam misalignment, erri, for example, may be measured by detecting a slight distortion of the holographic image which occurs when the probe beam angle used for hologram reconstruction (recovery) differs from the optimal Bragg angle. For example, when a Bragg-mismatched plane wave probe beam with wave vector {right arrow over (k)}P illuminates an ideal plane wave grating, the angle of the diffracted beam may deviate from the nominal Bragg-matched diffraction angle according to Equation 7:
ΔθD sin θS=ΔθP sin θR (7)
wherein θR and θS are the internal propagation angles, respectively, of the reference and signal beams with respect to the medium normal, {circumflex over (n)}, (and which are nominally the Bragg-matched probe and diffraction angles); and ΔθP and ΔθD are, respectively, the deviations of the internal probe and diffracted beams from the Bragg-matched condition.
The non-linear dependence of the diffracted beam deviation on the Bragg-matched angles may cause distortion in the holographic image, as illustrated by
The Bragg-mismatch created by the angular deviation ΔθP of the probe beam may also cause image distortion out of the plane of
In a small internal probe beam angle deviation ΔθP regime, the quiver pattern will resemble what is shown as pattern 300 in
Quiver pattern 300 shown in
Given the availability of the quiver pattern, all that remains is to extract the component corresponding to the characteristic misalignment pattern shown in
wherein errB is the misalignment of the characteristic misalignment quiver vector, {right arrow over (Q)}B, and ∥{right arrow over (Q)}B∥ is its 2-norm, {right arrow over (Q)}h is the measured quiver pattern vector, and the binary operator is the dot product of vectors {right arrow over (Q)}B and {right arrow over (Q)}h. The quiver pattern vectors {right arrow over (Q)}B and {right arrow over (Q)}h are formed simply by taking the scalar x- and y-components of the individual quiver vectors in the corresponding quiver patterns and arranging them into a single 640-element column vector. The normalized misalignment vector
may be pre-computed so that the only operation required in real time is the 640-element dot product.
In an alternative embodiment, the characteristic misalignment quiver vector may be pre-processed in order to enhance measurement accuracy. For example, the magnification component of {right arrow over (Q)}B may be removed so that operating conditions which produce magnification or demagnification in the {right arrow over (Q)}h quiver pattern (for example, a wavelength change, or expansion of the holographic storage medium) do not introduce a spurious component in the error signal. The rotation component, as well as the x- and y-translation components, of the holographic image may be similarly removed.
More generally, misalignment in other alignment control axes and/or other changes in operating conditions may cause their own characteristic quiver patterns. When several different perturbations are simultaneously present, the combined quiver pattern may contain elements of all these characteristic distortions. This may permit simultaneously determining the misalignment of several alignment control axes from a single quiver pattern. However, since the set of characteristic quiver patterns may not be mutually orthogonal, the misalignments determined by the preceding method may contain considerable cross-talk among alignment control axes. Furthermore, the composite quiver pattern of a real hologram may not be guaranteed to be a linear superposition of characteristic quiver patterns, although this assumption may be accurate in a small perturbation regime.
For these reasons, it may be desirable to use a pre-processing operation that removes or reduces the mutual cross-talk contributions from the entire set of characteristic quiver patterns. In one embodiment, this may be accomplished using a least squares error (LSE) optimization criterion. For example, it is assumed that N different normalized characteristic quiver patterns vectors, {right arrow over (Q)}n, 1≦n≦N, have been determined, each corresponding to a different misalignment (wavelength tuning error, rotation or translation of the medium, etc.) or operating condition parameter (temperature, etc.). Some characteristic quiver patterns may correspond to alignment control axes, but others may correspond to distortions caused by misalignment or imperfections that are not adjustable by the controller. In this case, the probe beam angle error described above might be one among the N. Then, a simultaneous estimation of all N axes from a measured quiver pattern vector {right arrow over (Q)}h in matrix form may be made according to Equation 9:
wherein {right arrow over (ê)}h is an N element vector of estimated misalignment values, and Q is the quiver pattern observation matrix according to Equation 10:
This version of {right arrow over (ê)}h, however, may still contain cross-talk caused by the non-orthogonal components among the {right arrow over (Q)}n. Defining the actual misalignment vector as {right arrow over (e)}h, a modified version of Q, referred to as Q′, which minimizes the estimation error may be determined according to Equation 11:
A solution to this set of equations may be made according to the LSE estimator matrix Equation 12:
Q′=(QTQ)−1QT (12)
wherein QT denotes a matrix transpose, and (QT Q)−1 denotes a matrix inverse. Since the characteristic quiver pattern matrix Q is known before-hand, the LSE estimator matrix Q′ may also be pre-computed. Furthermore, the entire set of N values need not be computed simultaneously. If only one axis misalignment is required, the corresponding row of the Q′ matrix may be used to compute it with a simple dot product.
c. Centroid Shift Error Signals
In addition to the SNR-maximizing derived wobble error signal described above in section 1a, a wobble imparted to the probe beam recovery positions may be used to determine other misalignments in an angle-multiplexed HDS system. This is possible because the presence of these misalignments cause the wobble offset to produce a shift in the best Bragg-matched region(s) of the holographic image. This shift may be detected, for example, as a change in position of the intensity centroid of the detected holographic image, or by an offset in the position of the highest intensity peak in a cross-correlation between two images. In this section, the intensity centroid method of detecting this shift is described.
The principle for this measurement of a centroid shift error signal is conceptually illustrated in
When holographic exposures are taken at the two angular probe beam offsets indicated by probe wave vectors {right arrow over (k)}P1 and {right arrow over (k)}P2 in
This shifting of the best Bragg-matched part (i.e., “lighter” shaded portions 628 or 728) of the polarization density patch 504 in the y-(horizontal) direction (i.e., as indicated by dimension vector {right arrow over (k)}y) conceptually illustrated in
The centroid shift(s) conceptually illustrated in
The change in location of “brighter” vertical stripe 928 of
In yet another embodiment, centroid shifts in the vertical, or x-direction (as opposed to the horizontal, or y-direction as described with reference to
Similar to intensity maps 800 and 900 of
In a similar manner to the centroid shifts in the y-(horizontal) direction (as illustrated by
Like the SNR-based feedback wobble error signals of section 1a above, the two holographic images (or intensity maps of those images) used to determine the intensity centroid shift may actually be two separate holograms. In one embodiment, an alternating probe beam angle wobble of Δφ=±0.002° may be used as the holograms in a stack are recovered in sequence, and independent control loops based on the SNR-based probe beam angle wobble error signal of section 1a and the centroid shift-based probe beam pitch error signal of this section are operated simultaneously to minimize the alignment error of both of these probe beam alignment control axes.
d. Cross-Correlation Derived Error Signals
In section 1c above, the probe beam pitch and probe beam wavelength misalignments may be determined by the differences in intensity centroid positions of the holographic images detected at two (alternating) probe beam angle offsets. In an alternative embodiment to detecting this difference between the two holographic images by this intensity centroid operation, a cross-correlation operation or a modified cross-correlation operation, may be performed. This cross-correlation (or modified cross-correlation) operation may be particularly useful in deriving a feedback error signal for a single hologram, as described below in the iterative alignment procedure of section 4.
In this alternative operation, a cross-correlation between the two holographic images (or between reduced-size, smaller intensity maps of the two images) is performed, followed by determining the location of the peak in the cross-correlation grid or matrix which indicates the offset position where the two images best match each other. For example, if the position of the “brighter” vertical stripe in the intensity map shifts to from the right (e.g., from the position where “brighter” vertical strip 828 is in intensity map 800 of
A modified version of this cross-correlation operation may be used in order to enhance accuracy and minimize computation. Like a standard cross-correlation operation, in this modified cross-correlation operation, the image intensity maps may be provided to the controller in the form of, for example, two 36×37 sample grids, wherein each element or value of each “pixel” of the grid corresponds to the summed intensity of the resampled 32×32 pixel tile within the detected image. The cross-correlation, xci,j, may then be computed by calculating the dot products of the D.C.-free versions of the two image intensity maps to provide, for example, a 3×3 cross-correlation grid or matrix.
But unlike the standard cross-correlation operation, the dot products of the modified cross-correlation are calculated at only the +1,0,−1 offset pixel locations (i.e., excluding the location 0,0) of the cross-correlation grid or matrix, i.e., by using the following Equation 13:
wherein {tilde over (M)}r,c and Ñr,c are the D.C.-free versions of the image intensity maps, Mr,c and Nr,c (i.e.,
etc for Ñr,c . . . ). The result of Equation 13 provides a 3×3 modified cross-correlation grid or matrix with (at most) 8 non-zero or “computed” values, corresponding to the outer 8 matrix elements of the 3×3 matrix. In this modified 3×3 cross-correlation matrix, the value of the center matrix element is not computed or calculated because it carries no information about the shift of the image. The “peak” of the resulting 3×3 matrix may then be located with a centroid calculation according to Equation 1 above. However, since this matrix may contain negative values, it may be advantageous to subtract the minimum value from each of the matrix elements in order to produce a matrix that is positive (or zero) before computing the centroid. In addition, cross-correlation grids or matrices larger than 3×3 may be obtained, for example, 4×4 grids/matrices, 5×5 grids/matrices, etc., up to 2n−1 by 2m−1, wherein n×m is the image intensity map size (here a 36×37 sample grid).
This modified version of the cross-correlation operation is further illustrated by reference to
Similarly,
In poorly aligned initial conditions for the alignment control axes, the modified cross-correlation operation may perform better than the intensity centroid operation described in section 1c above because multiple hologram vertical stripes (or horizontal bands) may appear in a single image. As a result, the intensity centroid may actually move opposite the direction of the “true” hologram motion if one vertical stripe (e.g. 628) or hologram disappears off one edge (e.g., at 514), while a different vertical stripe (e.g., 728) or hologram enters or appears on the other or opposite edge (e.g., at 516).
2. Derivation of Feed-Forward Signals
Changes in recording and/or recovery operating conditions may also cause deterministic changes in optimal alignment for hologram recovery. In this case, detection of these recording and/or recovery operating conditions and an estimation of the required alignment adjustments may aid in the recovery of holograms. Such a feed-forward signal may be used alone, or, in one embodiment, in combination with one or more of the feedback error signal operations described above in section 1.
But often there are significant enough temperature differences between the recording and recovery of the holograms such that the holographic storage medium expands or contracts. As a result of this expansion (or contraction), the angular hologram recovery locations in the holographic storage medium are shifted or displaced relative to the angular hologram recording locations. In fact, thermal expansion (or contraction) of the holographic storage medium may cause a larger shift or displacement in the angular hologram recovery locations of the holograms recorded at higher reference beam angles versus at lower reference beam angles. This is conceptually illustrated in
Often, the displacement or shift of the angular hologram recovery locations is approximately linear with respect to the temperature change between recording and recovering holograms, so that this shift may be represented by Equation 14:
Δφff(φ,ΔT)≈ΔT(a φ2+bφ+c) (14)
wherein Δφff(φ, ΔT) is the feed-forward angular recovery displacement as a function of the probe beam angle φ, ΔT=TR−TW is the difference in temperature between the read (recovery) and write (record) operations, and a, b, and c are regression constants established either experimentally or by opto-mechanical modeling.
Thus, if the temperature change can be established by the use of a thermometer or other temperature sensor, the feed-forward angular displacement for each hologram recovery location may be predicted in advance and incorporated into the control system compensation algorithm as a feed-forward signal. The temperature change may be established by measuring and recording the write (record) temperature (TW), and then subtracting the write temperature from the read (recovery) temperature (TR). Alternatively, the temperature measured at writing (recording) time may be used to pre-compensate the reference beam angles and writing (recording) wavelength to make the hologram stack appear as though it had been written (recorded) at some standard temperature, wavelength, hologram spacing, etc., thus providing a predetermined pre-compensation recording temperature for each recorded hologram. Then, the effective ΔT may be established by simply measuring the temperatures during the read (recovery) operation and subtracting the predetermined pre-compensation recording temperature for each recovered hologram.
The difference in wavelength, Δλ, between the probe beam and the writing (recording) beam has a similar, predictable effect on the angular displacement for each hologram recovery location. By including Δλ, along with ΔT and φ, this angular recovery displacement for each hologram recovery location may be represented by a quadratic equation according to Equation 15:
Δφff(φ,ΔT,Δλ)=(AΔT+BΔλ)φ2+(CΔT+DΔλ)φ+EΔT+FΔλ (15)
wherein the angular recovery displacement Δφff(φ, ΔT, Δλ) is now a function of Δλ as well as φ and ΔT. In an exemplary configuration, the fitting constants may, for example, have values A=−8.843658×10−6; B=6.071955×10−5; C=2.786626×10−4; D=−2.642586×10−3; E=−4.583689×10−3; and F=1.020074×10−1, wherein φ is measured in degrees from the medium normal, ΔT is in ° C., and Δλ is in nanometers (nm).
3. Control System Compensation Algorithm
The embodiments of the present operations or methods for generating feedback error and feed-forward signals may be used with, for example, conventional control system techniques in order to achieve a method for adaptively adjusting one or more alignment control axes while reading (recovering) holograms in a sequence of holograms. For example, probe beam angle feedback alignment may resemble a phase locked loop, wherein a servo control system may be used to align an oscillator to a (quasi) cyclical signal. In this case, the probe beam recovery angles may be aligned to the actual angular recovery positions of the holograms.
Various applicable techniques for the design and analysis of control systems may be used in embodiments of the present invention. See R. C. Dorf, Modern Control Systems, (Third Edition, Addison-Wesley Publishing (1983), the entire contents and disclosure of which is hereby incorporated by reference. In one such example, a proportional-integral-derivative (PID) controller may be adapted for use, e.g., according to Equation 16:
wherein the {circumflex over (φ)}h are the estimated hologram angles (i.e., without any wobble), h is the hologram number, KP, KI, and KD are the proportional, integral, and differential control constants, respectively; D is the nominal spacing between the holograms, and errh are the observed error samples. Different linear control forms may also be used, as might approaches based on fuzzy logic or other non-linear methods.
In another embodiment, a compensator based on a state estimation method, such as a Kalman filter, may be used. In one embodiment, the state estimation may be based on a recursive least squares (RLS) filter. In this approach, the state of the system may be parameterized into some mathematical form, and the RLS algorithm may be used to derive the coefficients for the state parameters that minimize the sum of squared errors between the parameterized model and the observations. In one embodiment, the parameterized model may be a simple straight line wherein the x-axis represents the hologram number, and the y-axis represents the optimal recovery angle for each hologram. Thus, the RLS algorithm may be used iteratively to determine the slope a and intercept b of the line best fitting the observed hologram positions according to Equation 17:
{circumflex over (φ)}h=a h+b where Σ[{circumflex over (φ)}h−(φh+errh)]2 is minimized (17)
wherein the {circumflex over (φ)}h are the RLS estimated hologram angles, h is the hologram number, and (φk+errh) are the observed hologram angles. The RLS algorithm may efficiently update the values of a and b every time a new error observation, errh, is made so that the least-squares (LS) relationship may be maintained over the entire set of observations. In an embodiment of the present method, the RLS algorithm may be implemented with a “forgetting factor,” φλ, (which is different from the symbol for wavelength above) which causes the most recent observations to be weighted more heavily, and the influence of past observations to be diminished by λ at every iteration (i.e.,
is minimized). This may aid in the accuracy of the predicted or estimated values in the case where the actual hologram positions deviate from the parameterized model over longer sequences of holograms.
In addition to improved accuracy and immunity to noise in the error signal, this form of the RLS compensator may have the advantage of decoupling the estimation process from the observation process. Thus, the state variables a and b may be updated whenever a new observation is available, and the estimation of future hologram positions may be made whenever required. Thus, in a “pipe-lined architecture” (i.e., where different stages of the image processing electronics are working on different images at the same time) wherein the SNR of a given hologram is not available until several subsequent hologram exposures have been performed, the positions for the subsequent holograms may be determined using the available values of a and b without waiting for the SNR of the given hologram. The latency between estimation and observation need not even be constant, the only consequence being that the quality of the estimates may degrade slowly as the latency increases.
Feed-forward information such as the temperature/wavelength displacement curve of Equation 15 above may also be incorporated to improve the accuracy of the position estimates. Feed-forward signals may be generally accommodated using various established techniques of control systems, just as with feedback signals. In one embodiment, the feed-forward component(s) may be removed before application of the feedback loop, and then restored afterwards, e.g., such as according to Equation 18:
φ′h=φh−Δφff(φh,ΔT,Δλ),
φ′h+1=ah+b,
φh+1=φ′h+1+Δφff(φh+1,ΔT,Δλ). (18)
In this manner, the known quadratic components introduced by the Δφff(φ, ΔT, Δλ) displacement of Equation 14 may be removed from the RLS algorithm, which fits the remaining components to its linear model within the φ′ coordinate system. The quadratic components may then be restored after the fact in the true φ coordinate system. This may be implemented by analytical solution of Equation 15 above, either dynamically or by using a pre-computed look-up table.
4. Iterative Alignment Procedure for Single Hologram
The embodiments of the present operations or methods may also use feedback error signal(s) to adjust the alignment control axes to or towards a sufficiently optimal recovery position for a single hologram. In these embodiments, the feedback error signal(s) may be derived from one or more iterations of an iterative alignment error value procedure using the single hologram in order to achieve a sufficiently precise alignment (relative to, for example, a threshold alignment error criteria) for use in recovery of the single hologram at a sufficiently optimal recovery position of the specific hologram. In other words, these embodiments use what is referred to herein as an iterative alignment procedure with reference to the single hologram to derive the feedback error signal(s).
One embodiment of this iterative alignment procedure is described as follows. The three probe beam alignment control axes—probe beam angle (φ), probe beam pitch (ρ), and probe beam wavelength (λ)—may be initialized to starting positions referred to, for example, as φ0, ρ0, and λ0, which represent, for example, the best guess as to the optimal recovery position of the particular hologram. A “positive” offset of +Δφ is then applied or imparted to angle φ and a first holographic image exposure is then taken or sampled; similarly a “negative” offset of −Δφ is applied or imparted to angle φ and a second holographic image exposure is then taken or sampled. The alignment error value in angle φ (“errφ”) is then determined by Equation 19:
errφ=kφ(SNR2−SNR1) (19)
wherein kφ is a scaling constant (empirically derived or by modeling for the particular system), and SNR1 and SNR2 are the signal-to-noise ratios measured from first and second holographic image exposures, respectively. The alignment error value in pitch ρ (“errρ”) may determined by Equation 20:
errρ=kρ(CY2−CY1) (20)
wherein kρ is a scaling constant (empirically derived or by modeling for the particular system), and CY1 and CY2 are the intensity centroids for first and second holographic image exposures in the y (horizontal) direction, vector {right arrow over (k)}y, (i.e., transverse to the direction of Bragg selectivity) determined from the first and seconds holographic image exposures, respectively. The alignment error value in wavelength λ(“errλ”) is determined by Equation 21:
errλ=kλ(CX2−CX1) (21)
wherein kλ is a scaling constant (empirically derived or by modeling for the particular system), and CX1 and CX2 are the intensity centroids in the x (vertical) direction, vector {right arrow over (k)}x, (i.e., longitudinal to the direction of Bragg selectivity) determined from the first and seconds holographic image exposures, respectively. Then, all three axes positions may be adjusted in a manner which reduces the alignment error, e.g., φ1=φ0−errφ, ρ1=ρ0−errρ, and λ1=λ0−errλ.
The iterative alignment procedure may be repeated by using the new probe beam alignment control axes positions as the “new” starting positions. At the completion of each iteration, the alignment error values may be checked. If a settling or “threshold” criteria is met or satisfied (e.g., the magnitude each error sample is equal to or less than a predetermined threshold alignment error criteria), then alignment may be deemed to be achieved and the iterative alignment procedure may then be terminated. Optionally, the iterative alignment procedure may be repeated for a fixed or predetermined number of times (cycles) before terminating the iterative procedure. Also optionally, a final aligned holographic image exposure (without a ±Δφ offset) may be taken to evaluate the alignment, or to actually recover the data.
Many variations on the above iterative alignment procedure may be used. In one variation, image intensities may be used instead of SNRs in the calculation of errφ. This may be desirable if SNRs for the hologram(s) are not available, as may often be the case with a relatively poor starting alignment. In another variation, alignment values from repeated measurements may be averaged within each iteration of the respective alignment control axis. In yet another variation, a modified cross-correlation operation (as described in section Id above) may be used instead of a centroid shift operation (as described in section 1c above) in order to determine errρ and/or errλ.
All documents, patents, journal articles and other materials cited in the present application are hereby incorporated by reference.
Although the present invention has been fully described in conjunction with several embodiments thereof with reference to the accompanying drawings, it is to be understood that various changes and modifications may be apparent to those skilled in the art. Such changes and modifications are to be understood as included within the scope of the present invention as defined by the appended claims, unless they depart therefrom.
This application claims the priority of U.S. Provisional patent Application No. 61/028,628 entitled “SERVO FOR HOLOGRAPHIC DATA STORAGE” filed Feb. 14, 2008, the entire disclosure and contents of which is hereby incorporated by reference. This application also makes reference to the following U.S. patent application Ser. No. 12/266,637 entitled “REPLACEMENT AND ALIGNMENT OF LASER” filed Nov. 7, 2008, which is a division of U.S. patent application Ser. No. 11/440,368, filed May 25, 2006; U.S. Provisional Patent Application No. 61/098,445 entitled “METHOD FOR FINDING AND TRACKING SINGLE MODE OPERATION POINT OF AN EXTERNAL CAVITY DIODE LASER” filed Sep. 19, 2008; U.S. Provisional Patent Application No. 60/980,604 entitled “LAYOUT METHOD FOR MULTIPLEXED HOLOGRAMS” filed Oct. 17, 2007; U.S. patent application Ser. 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