Digital color halftoning with generalized error diffusion and multichannel green-noise masks.

In this paper, we introduce two novel techniques for digital color halftoning with green-noise--stochastic dither patterns generated by homogeneously distributing minority pixel clusters. The first technique employs error diffusion with output-dependent feedback where, unlike monochrome image halftoning, an interference term is added such that the overlapping of pixels of different colors can be regulated for increased color control. The second technique uses a green-noise mask, a dither array designed to create green-noise halftone patterns, which has been constructed to also regulate the overlapping of different colored pixels. As is the case with monochrome image halftoning, both techniques are tunable, allowing for large clusters in printers with high dot-gain characteristics, and small clusters in printers with low dot-gain characteristics.

Limits of scalar diffraction theory for conducting gratings.

Scalar diffraction theory and electromagnetic vector theory are compared by analyzing plane-wave scattering by a perfectly conducting, rectangular-grooved grating. General field solutions for arbitrary angles of incidence are derived by using scalar and vector theories. Diffraction efficiencies for the scalar and the vector cases as functions of wavelength, grating period, and angles of incidence are determined numerically and plotted. When the wavelength of the incident field is much shorter than the grating period, the diffraction efficiencies match. But when the wavelength is of the order of the grating period, large differences between the scalar and the vector solutions emerge. One general conclusion is that, depending on polarization, scalar theory should not be used when the grating period becomes smaller than ten wavelengths.

Efficient storage, computation, and exposure of computer-generated holograms by electron-beam lithography.

An efficient storage format was developed for computer-generated holograms for use in electron-beam lithography. This method employs run-length encoding and Lempel-Ziv-Welch compression and succeeds in exposing holograms that were previously infeasible owing to the hologram's tremendous pattern-data file size. These holograms also require significant computation; thus the algorithm was implemented on a parallel computer, which improved performance by 2 orders of magnitude. The decompression algorithm was integrated into the Cambridge electron-beam machine's front-end processor.Although this provides much-needed ability, some hardware enhancements will be required in the future to overcome inadequacies in the current front-end processor that result in a lengthy exposure time.

Efficient electron beam pattern data format for the production of binary computer generated holograms.

Current pattern data formats for electron beam lithography are specifically designed to meet the needs of the VLSI industry. As a result, pattern data file size is often the limiting factor in the production of a binary computer generated hologram and not the spatial bandwidth product. This paper explores one alternate pattern data format that facilitates the full utilization of the e-beam machine's spatial bandwidth product without introducing prohibitive amounts of pattern data. The pattern data format uses two well-established data compression techniques specifically tailored to remove the redundancies present in holographic fringe patterns.

Relative phases of electromagnetic waves diffracted by a perfectly conducting rectangular-grooved grating.

A complete solution of plane-wave scattering from a groove-corrugated surface of infinite extent for arbitrary incidence is presented. The electromagnetic wave is decomposed into fast and slow modal representation, and the solution is accomplished through the use of the mode-matching method. We solved for the zero-order diffraction efficiency and the phase of each polarization component for arbitrary incident angles. Our results have verified special cases previously published by others and have illustrated the phase shift between polarizations associated with the diffraction process as a function of the incident angles.

Synthetic approach to designing optical alignment systems.

The objective of this study is twofold: to design reticle patterns with desirable alignment properties; to build an automatic alignment system using these patterns. We design such reticle patterns via a synthetic approach; the resultant patterns, so-called pseudonoise arrays, are binary and their autocorrelation functions are bilevel. Both properties are desirable in optical alignment. Besides, these arrays have attractive signal-to-noise ratio performance when employed in alignment. We implement the pseudonoise array as a 2-D cross-grating structure of which the grating period is much less than the wavelength of impinging light used for alignment. The short grating period feature, together with the use of polarized light, enables us to perform essentially 2-D optical alignment in one dimension. This alignment separability allows us to build a system that performs alignment automatically according to a simple 1-D algorithm.

Reducing quantization error in Hsueh-Sawchuk holograms.

Expressions for the quantization error in Hsueh-Sawchuk holograms are presented. These expressions suggest that the Hsueh-Sawchuk algorithm may be improved using a technique called prequantization. We demonstrate that the addition of prequantization reduces the quantization error in Hsueh-Sawchuk holograms by ~25%.

Nondetour phase digital holograms: an analysis.

An expression for the required special bandwidth of a computer generated hologram is desired using results from the theory of frequency modulation. The expression is the same as a rule of thumb first presented by Lee. A simple quantization error model is presented for one type of nondetour phase class. It is shown that this hologram may be used to achieve a near optimum simulation of the quantization problem for random phase images.

Nondetour phase digital holograms: an analysis: errata.

An expression for the required special bandwidth of a computer generated hologram is desired using result from the theory of frequency modulation. The expression is the same as a rule of thumb first presented by Lee. A simple quantization error model is presented for one type of nondetour phase class. It is shown that this hologram may be used to achieve a near optimum simulation of the quantization problem for random phase images.

Comprehensive error models and a comparative study of some detour-phase holograms.

A general fidelity criterion and a procedure are developed to evaluate the performance of different detourphase-type computer-generated holograms. Three types of detour-phase hologram are evaluated and compared using both the aforementioned procedure and experimental data.

Optimum quantization in digital holography.

Finite plotter resolution introduces quantization into the representation of digital holograms. By utilizing the statistical properties of the Fourier transform of random phase images, optimum quantization schemes are derived and tabulated for the representation of these transforms. These schemes are applied to Lohmann and Lee type holograms where it is found that measured quantization errors agree with theoretical predictions. Methods for predicting optimum quantization schemes and associated mean squared errors are simplified to table-lookup procedures.

Binary phase digital reflection holograms: fabrication and potential applications.

A novel technique for the fabrication of binary-phase computer-generated reflection holograms is described. By use of integrated circuit technology, the holographic pattern is etched into a silicon wafer and then aluminum coated to make a reflection hologram. Because these holograms reflect virtually all the incident radiation, they may find application in machining with high-power lasers. A number of possible modifications of the hologram fabrication procedure are discussed.

Real-time optical signal processors employing optical feedback: amplitude and phase control.

The development of real-time coherent optical signal processors has increased the appeal of optical computing techniques in signal processing applications. A major limitation of these real-time systems is the. fact that the optical processing material is generally of a phase-only type. The result is that the spatial filters synthesized with these systems must be either phase-only filters or amplitude-only filters. The main concern of this paper is the application of optical feedback techniques to obtain simultaneous and independent amplitude and phase control of the light passing through the system. It is shown that optical feedback techniques may be employed with phase-only spatial filters to obtain this amplitude and phase control. The feedback system with phase-only filters is compared with other feedback systems that employ combinations of phase-only and amplitude-only filters; it is found that the phase-only system is substantially more flexible than the other two systems investigated.

Aliasing error in digital holography.

The use of the discrete Fourier transform in digital holography introduces aliasing error in the reconstructed image. Spectrum shaping to reduce dynamic range may also result in a serious increase in aliasing error. The effect of aliasing in digital holography is analyzed. It is proposed that the bandwidth be constrained when shaping the image spectrum. Experimental results show the approach to be quite effective.

Method for Computing Kinoforms that Reduces Image Reconstruction Error.

An analysis of kinoform image reconstruction error is presented. This analysis considers the effects of the error introduced by the kinoform approximation and the quantization effects of plotting. The error measure developed is applied to a proposed method for computing kinoforms. Numerical results indicate that images produced by this method offer considerable reduction in the error when compared with images produced from kinoforms made with the random phase method.