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

A new type of wave front shearing interferometer is described in which two images of the wave front under test which are of different sizes are made to interfere. When the centres of the two images coincide, this results effectively in shear along the radial direction. It is shown that the interpretation of the resulting interferogram is comparatively easy. In addition, the instrument is extremely convenient to handle, since all the adjustments can be made with a white light source.

Radial shearing interferometer

Enhanced high dynamic range 3D shape measurement based on generalized phase-shifting algorithm

The imaging quality of quantitative phase imaging (QPI) based on the transport of intensity equation (TIE) can be improved using a higher-order approximation for defocused intensity distributions. However, this requires mechanically scanning an image sensor or object along the optical axis, which in turn requires a precisely aligned optical setup. To overcome this problem, a computer-generated hologram (CGH) technique is introduced to TIE-based QPI. A CGH generating defocused point spread function is inserted in the Fourier plane of an object. The CGH acts as a lens and grating with various focal lengths and orientations, allowing multiple defocused intensity distributions to be simultaneously detected on an image sensor plane. The results of a numerical simulation and optical experiment demonstrated the feasibility of the proposed method.

Single-shot higher-order transport-of-intensity quantitative phase imaging based on computer-generated holography

Real-time phase step measurement using the volume enclosed by a surface algorithm in self-calibrating phase-shifting interferometry

In this research a novel interferometric system is reported, which allows the generation of four simultaneous interferograms with phase shifts of π/2 The system consists of three coupled interferometers: a rectangular Sagnac interferometer which generates a primary pattern with crossed circular polarizations, coupled to two Michelson interferometers which operate as a multiplexing system, and generating replicas of the primary pattern The two coupled Michelson interferometers generate four patterns retaining their polarization properties, which allow independent phase shifts by placing a linear polarizer over each pattern, thereby, four interferograms with relative phase shifts of π/2 are obtained The optical phase is calculated using the well-known four-step algorithm With knowledge of the optical phase, different properties of the samples can be calculated or analyzed; in this case, by knowing the mean refractive index, we can calculate the mean thickness of test objects The results obtained for static transparent samples are presented The capability of the system to analyze dynamic events is shown when results for the calculation of a temperature field of a heat flow are presented

Measurement of mean thickness of transparent samples using simultaneous phase shifting interferometry with four interferograms.

Diffraction theory of binary amplitude and phase gratings with applications for Ronchi test

Simultaneous measure of refractive index and thickness of dielectric plane parallel plates by fringe counting: a case for generalized regression

In this research we implemented a two-step phase shifting system based on two cyclic-path coupled interferometers for slope measurements of transparent samples. The optical system generates two π-shifted interferograms, and the phase shift between interferograms is obtained by rotating a linear polarizer, generating four interferograms with relative π/2-phase shifts; this simplifies the number of phase steps necessary to retrieve the optical phase, since is only necessary perform a shift operating a linear polarizer. The optical phase was processed by a four-step algorithm. In order to present the capabilities of the system, results obtained for slope for transparent structures are presented.

Phase Shifting Interferometry Using a Coupled Cyclic Path Interferometers

possible by a post-recording process. General one-dimension motion is considered here. Two cases are discussed: constant velocity motion and constant acceleration motion. Image simulations representing those degradation mechanisms are shown, as well as the corresponding restored images after using the method which is described in this work. This method is based on Dirac delta function propreties. We also show real digital images affected by those motions. It can be experimentally obtained by using an air-rail. The blurred images are processed digitally by spatial filters given by the proposed method. Numerical and experimental results are shown.

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G. Rodríguez Zurita

Papers

Measurement of mean thickness of transparent samples using simultaneous phase shifting interferometry with four interferograms.

Diffraction theory of binary amplitude and phase gratings with applications for Ronchi test

Simultaneous measure of refractive index and thickness of dielectric plane parallel plates by fringe counting: a case for generalized regression

Phase Shifting Interferometry Using a Coupled Cyclic Path Interferometers

Image restoration of blurring due to rectilinear motion: constant velocity and constant acceleration