Roadmap on digital holography [Invited].

This Roadmap article on digital holography provides an overview of a vast array of research activities in the field of digital holography. The paper consists of a series of 25 sections from the prominent experts in digital holography presenting various aspects of the field on sensing, 3D imaging and displays, virtual and augmented reality, microscopy, cell identification, tomography, label-free live cell imaging, and other applications. Each section represents the vision of its author to describe the significant progress, potential impact, important developments, and challenging issues in the field of digital holography.

A mathematical analysis of the DCT coefficient distributions for images.

Over the past two decades, there have been various studies on the distributions of the DCT coefficients for images. However, they have concentrated only on fitting the empirical data from some standard pictures with a variety of well-known statistical distributions, and then comparing their goodness of fit. The Laplacian distribution is the dominant choice balancing simplicity of the model and fidelity to the empirical data. Yet, to the best of our knowledge, there has been no mathematical justification as to what gives rise to this distribution. We offer a rigorous mathematical analysis using a doubly stochastic model of the images, which not only provides the theoretical explanations necessary, but also leads to insights about various other observations from the literature. This model also allows us to investigate how certain changes in the image statistics could affect the DCT coefficient distributions.

Discrete cosine transform domain restoration of defocused images.

In discrete-cosine-transform-based (DCT-based) compressions such as JPEG it is a common practice to use the same quantization matrix for both encoding and decoding. However, this need not be the case, and the flexibility of designing different matrices for encoding and decoding allows us to perform image restoration in the DCT domain. This is especially useful when we have severe limitations on the computational power, for instance, with in-camera image manipulation for programmable digital cameras. We provide an algorithm that compensates partially for a defocus error in image acquisition, and experimental results show that the restored image is closer to the in-focus image than is the defocused image.

Design of an optical reconfigurable shared-bus-hypercube interconnect.

We propose and evaluate the feasibility of a multiprocessor interconnect based on free-space optics for reducing network latency. The proposed interconnect supports high-throughput network links and can exploit locality of memory references through reconfiguration. Our analysis shows that the proposed interconnect can, in principle, support hundreds of nodes in the static mode and tens of nodes in dynamic mode.

Elements of a hybrid interconnection theory.

We present a textbooklike treatment of hybrid systems employing both optical and electrical interconnections. We investigate how these two different interconnection media can be used in conjunction to realize a system not possible with any alone. More specifically, we determine the optimal mix of optical and normally conducting interconnections maximizing a given figure-of-merit function. We find that optical interconnections have relatively little to offer if the optical paths are constrained to lie on a plane (such as in an integrated optics system). However, if optical paths are permitted to leave the plane, they may enable considerable increase in performance. In any event the prize in terms of performance is accompanied by a penalty in terms of system power and/or size.

Noninterferometric optical subtraction using reflection-electroabsorption modulators.

A noninterferometric technique for optical subtraction is demonstrated that employs a multiple-quantum-well reflection-electroabsorption modulator and provides lower insertion loss, larger contrast ratio, and linearity over a larger dynamic range than similar techniques previously reported.

Efficient beam-correcting holographic collimator for laser diodes.

We describe a method for recording a beam-correcting holographic collimator for laser diodes in the presence of recording-to-readout wavelength shift. An astigmatism-correcting, beam-shaping hologram recorded with this method at 488 nm displays a high-efficiency, near-diffraction-limited collimation of a diode beam at 820 nm.

Implications of interconnection theory for optical digital computing.

Heat removal, rather than finite interconnect density, is the major mechanism that limits how densely we can pack three-dimensional computing systems of increasing numbers of elements. Thus highly interconnected approaches can be employed without a further increase in system size. The use of optical interconnections for implementing the longer connections of such systems is advantageous. In fact, if the optical communication energy is sufficiently low and large-bit repetition rates are employed, conductors are useful for only the shortest connections and can be dispensed with altogether with little disadvantage. This justifies consideration of an optical digital computer.

Optical oversampled analog-to-digital conversion.

A new approach to optical analog-to-digital (A/D) conversion based on oversampling and interpolative coding techniques is described, and both interferometric and noninterferometric architectures based on this method are presented. This new approach combines the high resolution of classical oversampled A/D conversion with the high speed of optical processing technology to extend the resolution and conversion rates beyond that currently possible with other electronic or optical converters. The proposed optical converters are simple, consisting of multiple quantum well self-electro-optic effect devices, photodetectors, and common optical components that are capable of operating at sampling rates of up to 15 Gbits/s and that can provide scalable resolutions of 16 and 8 bits at a conversion rate of 117 and 938 MHz, respectively.

Oblique-incidence liquid-crystal-tunable étalon.

The experimental properties and a detailed model of a nematic liquid-crystal-tunable Fabry-Perot étalon with obliquely incident light are reported. As a single-wavelength switch, the étalon has an extinction ratio of 20.3 dB, an insertion loss of -1.7 dB, and a millisecond switching speed. As a filter, the étalon has a finesse of 15.1, a free spectral range of 20.4 nm, and a continuous tuning range of over 40 nm with less than 5 V.

Design of Fourier-transform holographic lenses in the presence of a recording-readout wavelength shift.

A method for recording Fourier-transform holographic lenses, in the presence of a recording-readout wavelength shift, is presented. The method is illustrated with a holographic lens recorded at 488 nm and reconstructed at 633 nm, with high diffraction efficiencies and low aberrations over a wide field of view of +/-10 degrees .

Refractive index modulation mechanism in bleached silver halide holograms.

We present a simple technique for observing and studying the onset of microstructure in silver halide gratings, which can also be used to improve processing chemistry.

Design of substrate-mode holographic interconnects with different recording and readout wavelengths.

A method for recording a substrate-mode holographic interconnect system, composed of two identical holographic optical elements (HOEs) which were recorded on the same plate, has been developed. Since the possible recording wavelengths for efficient holograms are usually different from the readout wavelengths, the holographic elements must be recorded with predistorted wavefronts to assure high diffraction efficiencies and low aberrations. The predistorted wavefronts are derived from simple spherical holograms whose readout geometries differ from those used during recording. The method is illustrated with HOEs recorded at 488 nm and read out at 633 nm. Nearly diffraction-limited imaging and high efficiencies were achieved.

Analytic design of an achromatic double grating coupler.

A method for designing a double grating for coupling a polychromatic wave out of a waveguide with negligible angular dispersion is presented. It is based on calculating analytically two different grating functions, such that the chromatic dispersion of the first grating function is compensated by the second grating function. It is shown that the usable wavelength range can be increased by more than 2 orders of magnitude relative to conventional grating couplers for typical angular tolerance.

Use of synthetic discriminant functions for handwritten-signature verification.

Handwritten-signature verification is treated as a two-class synthetic discriminant function (SDF) problem. Images of valid and casually forged signatures are collected and binarized, using an electronic digitizing camera. Performance of this approach with a small number of valid signatures in the training set is examined, and substantial improvement is demonstrated when forgeries are included in the set. In particular, the equal-error rate for the SDF classifier with forgeries included is shown to average approximately 4% across nine different subjects. The effects of image preprocessing on false acceptance and true rejection rates are examined. The use of alternatives to forged signatures in the training matrix is explored. Finally, SDF performance is shown to deteriorate when the tested forgeries are produced with some a priori knowledge of the target signature.

Recursive design of a holographic focusing grating coupler.

A method for designing and recording a holographic optical element that is used as a waveguide focusing grating coupler is presented. It is based on recording the holographic coupler with two predistorted wave fronts, derived from interim holograms, whose readout and recording geometries are different. The corrected holographic coupler has almost aberration-free performance even for couplers with very small f/numbers or with large wavelength shift between recording and readout.

Liquid crystal 1 x N optical switch.

The design, experimental results, and analysis of a 1 x N ferroelectric liquid-crystal optical switch based on polarization rotation are reported. The switch is broadband and tolerant to errors in the ferroelectric liquid-crystal tilt angle and cell thickness. Moreover, the cross talk in the switch is noncumulative and independent of the switch size N. The results of an experimental 1 x 4 switch are presented. The switch has a signal-to-cross-talk ratio ranging from 21.6 to 37.1 dB, a switching time of 50 microsec, and a worst-case insertion loss of 3.5 dB.