A Twyman-Green interferometer is used to measure the phase induced by a liquid-crystal spatial light modulator (LC-SLM) via spatial-carrier phase measurement methods in order to characterize the phase response as a function of applied voltage. With the phase response characterized, the LC-SLM can be operated in a closed-loop adaptive optics system. Four separate phase unwrapping algorithms are ...

This chapter describes the progress in using optical technology to construct high-speed artificial higher order neural network systems. The chapter reviews how optical technology can speed up searches within large databases in order to identify relationships and dependencies between individual data records, such as financial or business time-series, as well as trends and relationships within th...

The 2-D Fourier transform has been generalized into the 2-D separable fractional Fourier transform (replaces 1-D Fourier transform by 1-D fractional Fourier transform for each variable) and the 2-D separable canonical transform (further replaces the fractional Fourier transform by canonical transform) in [3]. It also has been generalized into the 2-D unseparable fractional Fourier transform wit...

Suppose we have a function s(t) that measures the sound level at time t of an analog audio signal. We assume that s(t) is piecewise-continuous and of finite duration: s(t) = 0 when t is outside some interval a ≤ t ≤ b. Make a change of variable x = (t− a)/(b− a) and set f(x) = s(t). Then 0 ≤ x ≤ 1 when a ≤ t ≤ b, and f(x) is a piecewise continuous function of x. We convert f(x) into a digital s...

A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT's in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from -1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT...

This chapter covers the fundamental principles and current applications of Fourier transform (FT) infrared and Fourier transform Raman spectroscopies as utilized in the analysis of polymeric materials. The primary emphasis of the first part is on the principles and advantages of these interferometric methods, whereas the remaining sections illustrate numerous applications focusing on the struct...

We are developing a new type of miniature Fourier transform (FT) Raman spectrometer; the spatial heterodyne Raman spectrometer (SHRS), which provides high spectral resolution in a very small system with high light throughput. The resolution of the SHRS is not dependent on a slit, so miniature systems, <1 cm footprint, can be made with high spectral resolution. The ability to miniaturize the SHR...

We consider a general formulation of the problem signal reconstruction from incomplete priori information about it and measurements intensity its Fourier transform. Some special cases are studied when is even or odd part signal, as well real imaginary signal. Exact solutions in quadratures constructed. An algorithm for solving proposed only image intensities known.

This paper proposes new image compression technique that uses Real Fourier Transform. Discrete Fourier Transform (DFT) contains complex exponentials. It contains both cosine and sine functions. It gives complex values in the output of Fourier Transform. To avoid these complex values in the output, complex terms in Fourier Transform are eliminated. This can be done by using coefficients of Discr...

Using a phase-only spatial light modulator (SLM) in a Fourier transform setup together with fast diffractive optics design algorithms provides a way to automatically generate complex and rapidly changing laser illumination patterns in the far-field. We propose a hierarchical software structure for the adaptive, on-line design of far-field illumination patterns. Using the on-line design system t...