Get up to speed with digital holography with this concise and straightforward introduction to modern techniques and conventions. Building up from the basic principles of optics, this book describes key techniques in digital holography, such as phase-shifting holography, low-coherence holography, diffraction tomographic holography and optical scanning holography, discussing their practical applications, and accompanied by all the theory necessary to understand the underlying principles at work. A further chapter covers advanced techniques for producing computer-generated holograms. Extensive Matlab code is integrated with the text throughout and available for download online, illustrating both theoretical results and practical considerations such as aliasing, zero padding and sampling. Accompanied by end-of-chapter problems and an online solutions manual for instructors, this is an indispensable resource for students, researchers and engineers in the fields of optical image processing and digital holography.

Introduction to Modern Digital Holography: With Matlab

We derive theoretical expressions for the eigenvalues and the eigenvectors for a twisted-nematic liquid-crystal display (LCD) as a function of the twist angle and the birefringence by use of the Jones-matrix formalism. These polarization eigenvectors are of particular interest for phase-only transmission because they propagate unchanged through the display. We find that the eigenvectors are elliptically polarized and that the ellipticity changes as a function of the birefringence of the LCD (which is proportional to the external voltage applied to the display). We can define an average eigenvector over a desired range for the applied voltage. We show, using Jones matrices, how this average eigenvector can be generated using a quarter-wave plate and a linear polarizer having appropriate orientation angles. Using this average eigenvector, we show that superior phase-only operation can be obtained over a given operating range for the LCD compared with other approaches.

Polarization eigenstates for twisted-nematic liquid-crystal displays.

A method to perform a predictive search for a given amplitude and phase modulation response in twisted nematic liquid crystal displays is presented. The algorithm is based on a simple physical model that we recently proposed and that considers the effect of liquid-crystal layers located in the vicinity of the edges, which are not able to tilt. This model was demonstrated to explain accurately the experimental transmittance modulation curves. Here the model is applied to perform a predictive search for an optimized modulation by changing the input and output polarization configurations. A generalized configuration to generate and detect elliptically polarized light is proposed. The method is applied for seeking two different configurations useful for optical image processors: phase-only modulation and amplitude-only modulation. The excellent agreement with the experimental measurements validates the potential of the proposed method.

Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model

We propose a novel optical method to display a complex Fresnel hologram using a single spatial light modulator (SLM). The method consists of a standard coherent image processing system with a sinusoidal grating at the Fourier plane. Two or three position-shifted amplitude holograms displayed at the input plane of the processing system can be coupled via the grating and will be precisely overlapped at the system's output plane. As a result, we can synthesize a complex hologram that is free of the twin image and the zero-order light using a single SLM. Because the twin image is not removed via filtering, the full bandwidth of the SLM can be utilized for displaying on-axis holograms. In addition, the degree of freedom of the synthesized complex hologram display can be extended by involving more than three amplitude holograms.

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Complex Fresnel hologram display using a single SLM

We present a model to more accurately describe the optical properties of a twisted nematic liquid crystal display (LCD). In particular, we study the optical properties of molecules near either edge of the LCD that are unable to twist and tilt under the application of an external elec- tric field. The properties of these layers can be deduced from the inten- sity transmittances measured using different configurations of the exter- nal linear polarizers. The agreement between the theoretical and the experimental transmittances is excellent, thus enabling the prediction of the actual modulation for any configuration of the polarizers. © 2000 So- ciety of Photo-Optical Instrumentation Engineers. (S0091-3286(00)01412-4)

Characterization of edge effects in twisted nematic liquid crystal displays

The properties of a liquid crystal television to be used as a spatial modulator of the polarization of a laser beam are studied. It is found that the model most commonly used for the display description does not adequately reproduce the transmission through crossed polarizers. A new model is proposed that takes into account additional birefringence effects resulting from border effects near the television windows. With this correction, the anomalous behavior of the television is explained and the throughput for different configurations is properly predicted.

Matias Zaldarriaga

Papers

Characterization of a liquid crystal television as a programmable spatial light modulator