A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Chaos-based image encryption using a hybrid genetic algorithm and a DNA sequence

A novel chaotic image encryption algorithm using block scrambling and dynamic index based diffusion

Image encryption

Double image encryption based on discrete multiple-parameter fractional Fourier transform and chaotic maps

Double image encryption using double pixel scrambling and random phase encoding

A parallel two-step spatial carrier phase-shifting common-path interferometer with a Ronchi grating placed outside the Fourier plane is proposed in this paper for quantitative phase imaging. Two phase-shifted interferograms with spatial carrier can be captured simultaneously using the proposed interferometer. The dc term can be eliminated by subtracting the two phase-shifted interferograms, and the phase of a specimen can be reconstructed through Fourier transform. The validity and stability of the interferometer proposed are experimentally demonstrated via the measurement of a phase plate.

Parallel two-step spatial carrier phase-shifting common-path interferometer with a Ronchi grating outside the Fourier plane

Fractional Fourier-domain random encoding and pixel scrambling technique for double image encryption

A common-path interferometer is proposed with a tri-window. It is built using a 4f optical system with Ronchi ruling as a spatial filter. The input rectangular aperture is formed by three windows; the central window supports a phase object, and the other two are used for reference beams. Using an appropriate grating period relative to input aperture size, an interferogram containing three patterns can be obtained in the output plane. The object phase can then be reconstructed from the three patterns using just one interferogram. The experiments are carried out to demonstrate the feasibility and reliability of the proposed scheme.

Hao Bengong

Papers

Double image encryption based on discrete multiple-parameter fractional Fourier transform and chaotic maps

Double image encryption using double pixel scrambling and random phase encoding

Parallel two-step spatial carrier phase-shifting common-path interferometer with a Ronchi grating outside the Fourier plane

Fractional Fourier-domain random encoding and pixel scrambling technique for double image encryption

Common-path interferometer with a tri-window.