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

High-speed 3D shape measurement with structured light methods: A review

Transport of intensity equation: a tutorial

Schlieren and shadowgraph techniques are used around the world for imaging and measuring phenomena in transparent media. These optical methods originated long ago in parallel with telescopes and microscopes, and although it might seem that little new could be expected of them on the timescale of 15 years, in fact several important things have happened that are reviewed here. The digital revolution has had a transformative effect, replacing clumsy photographic film methods with excellent—though expensive—high-speed video cameras, making digital correlation and processing of shadow and schlieren images routine, and providing an entirely-new synthetic schlieren technique that has attracted a lot of attention: background-oriented schlieren or BOS. Several aspects of modern schlieren and shadowgraphy depend upon laptop-scale computer processing of images using an imagecapable language such as MATLABTM. BOS, shock-wave tracking, schlieren velocimetry, synthetic streak-schlieren, and straightforward quantitative density measurements in 2D flows are all recent developments empowered by this digital and computational capability.

https://iopscience.iop.org/article/10.1088/1361-6501/aa5748/pdf

A review of recent developments in schlieren and shadowgraph techniques

We describe a simple method for visualization of phase objects The phase object is placed between a printed two-dimensional periodic pattern and a CCD camera The ray deflection that is due to the phase object distorts the image of the pattern This image is subtracted from a reference image and then, by squaring and low-pass filtering, a measurement of the two-dimensional refractive-index changes is obtained Because the optical system does not require special alignment or illumination, the method presented has potential application for detection of gas leaks in industrial environments

Visualization of two-dimensional phase gradients by subtraction of a reference periodic pattern.

Three-dimensional shape measurements by sinusoidal fringe projection using phase-shifting interferometry algorithms are distorted by the nonlinear response in intensity of commercial video projectors and digital cameras. To solve the problem, we present a method that consists in projecting and acquiring a temporal sequence of strictly binary patterns, whose (adequately weighted) average leads to a sinusoidal fringe pattern with the required number of bits. Since binary patterns consist of “ones” and “zeros”—and no half-tones are involved—the nonlinear response of the projector and the camera will not play a role, and a nearly unit contrast gray-level sinusoidal fringe pattern is obtained. Validation experiments are presented.

Three-dimensional profiling with binary fringes using phase-shifting interferometry algorithms

A synchronous polarimeter was set up for the measurement of
small rotation angles of the polarization plane of light. The
polarimeter is based on a polarizer–Faraday modulator–analyzer
structure with a synchronous detection scheme, which produces a linear
system response. The theoretical background is studied, and the
system performance is investigated experimentally. We achieved an
accuracy of the order of 10-4 deg, or 5 mg/dl of glucose
in a 1-cm light path.

Precision synchronous polarimeter with linear response for the measurement of small rotation angles.

We demonstrate that one can cancel the bending-induced linear birefringence in single-mode fibers by inducing a controlled anisotropy in a direction orthogonal to the bending plane. In particular, the controlled anisotropy can be generated by application of a lateral compressive stress on the fiber. This effect can be applied for the construction of birefringence-free fiber coils in Faraday sensor heads (e.g., in current sensors) to improve their sensitivity.

César D. Perciante

Papers

Visualization of two-dimensional phase gradients by subtraction of a reference periodic pattern.

Three-dimensional profiling with binary fringes using phase-shifting interferometry algorithms

Precision synchronous polarimeter with linear response for the measurement of small rotation angles.

Cancellation of bending-induced birefringence in single-mode fibers: application to Faraday sensors

A new scheme for phase-shifting ESPI using polarized light