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

If the best phase measurements are to be achieved, phase-stepping methods need algorithms that are 112 insensitive to the harmonic content of the sampled waveform and 122 insensitive to phase-shift miscalibration. A method is proposed that permits the derivation of algorithms that satisfy both requirements, up to any arbitrary order. It is based on a one-to-one correspondence between an algorithm and a polynomial. Simple rules are given to permit the generation of the polynomial that corresponds to the algorithm having the prescribed properties. These rules deal with the location and multiplicity of the roots of the polynomial. As a consequence, it can be calculated from the expansion of the products of monomials involving the roots. Novel algorithms are proposed, e.g., a six-sample one to eliminate the effects of the second harmonic and a 10-sample one to eliminate the effects of harmonics up to the fourth order. Finally, the general form of a self-calibrating algorithm that is insensitive to harmonics up to an arbitrary order is given.

Design of algorithms for phase measurements by the use of phase stepping

(1979). Linear Systems, Fourier Transforms and Optics. Optica Acta: International Journal of Optics: Vol. 26, No. 7, pp. 836-836.

Linear Systems, Fourier Transforms and Optics

Interference microscopy plays a central role in noncontact strategies for process development and quality control, providing full 3D measurement of surface characteristics that influence the functional behavior of manufactured parts. Here I briefly review the history and principles of this important technique, then concentrate on the details of hardware, software, and applications of interference microscopy using phase-shifting and coherence scanning measurement principles. Recent advances considered here include performance improvements, vibration robustness, full color imaging, accommodation of highly sloped surfaces, correlation to contact methods, transparent film analysis, and international standardization of calibration and specification.

Principles of interference microscopy for the measurement of surface topography

High-resolution, real-time 3-D shape measurement

The theory and practice of phase-measuring interferometry (PMI) are reviewed. The phase measurement algorithms are discussed and phase modulation and wavefront reconstruction are examined as part of the implementation of PMI. The performance limitations of PMI are addressed.

Review of phase-measuring interferometry

Several techniques for testing aspheric surfaces are presented, with the emphasis on interferometry. Techniques for setting up configurations to produce easily understandable null interferograms are described. Attention is also given to techniques that improve the readability of the more complicated interferograms produced when an asphere is tested at its center of curvature.

Aspheric surface testing techniques

The Ronchi test is performed by placing a periodic grating at or near the focus of an optical system. Like most geometric tests, the Ronchi test measures wavefront slope instead of the contour of the wavefront like conventional interferometry. A two-channel Ronchi test with a horizontal and a vertical grating can be used to reconstruct a non-symmetric test surface. This paper investigates the errors introduced by different rotational and translation misalignments of the gratings in the two-channel Ronchi test relative to one another. The Ronchigrams are analyzed with a modal technique based on Zernike polynomials. The severity of each misalignment is dependent upon the frequency of the gratings used and on the f/# of the system.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Sensitivity of two-channel Ronchi test to grating misalignment

The design and system performance of an infrared phase-stepping interferometer is reviewed. This instrument is capable of measuring rms surface roughness with a repeatability of 0.02 waves. The instrument uses a 4-bucket unwrapping algorithm. Calibration of the interferometer and removal of inherent system aberrations are discussed along with the system performance, including repeatability and accuracy. The interferometer is an all-reflective optics design to permit use at any wavelength, accommodating both far- (10.6 micron) and near- (5 micron) infrared sources. Testing applications include infrared windows and surface testing.

Design review of an infrared phase-shifting interferometer

A non-contact (i.e., optical) technique is required to measure the deformation of a free oil surface under the influence of a localized thermal load. This deformation is caused by surface tension driven thermal convective flow inside the fluid, and can be as large as 250 micrometers . Therefore, conventional interferometry is not possible. Instead, a Ronchi technique is proposed for contour mapping the oil surface. This paper presents a design concept for a two channel Ronchi instrument and some preliminary results from a feasibility study using a single channel Ronchi instrument.

H. Philip Stahl

Papers

Review of phase-measuring interferometry

Aspheric surface testing techniques

Sensitivity of two-channel Ronchi test to grating misalignment

Design review of an infrared phase-shifting interferometer

Contouring of a free oil surface