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

There are two kinds of tutorial articles: those that provide a primer on an established topic and those that let us in on the ground floor of something of emerging importance. The first type of tutorial can have a noted expert who has been gracious (and brave) enough to write a field guide about a particular topic. The other sort of tutorial typically involves researchers who have each been laboring on a topic for some years. Both sorts of tutorial articles are very much desired. But we, as an editorial board for both Systems and Transactions, know that there has been no logical place for them in the AESS until this series was started several years ago. With these tutorials, we hope to continue to give them a home, a welcome, and provide a service to our membership. We do not intend to publish tutorials on a regular basis, but we hope to deliver them once or twice per year. We need and welcome good, useful tutorial articles (both kinds) in relevant AESS areas. If you, the reader, can offer a topic of interest and an author to write about it, please contact us. Self-nominations are welcome, and even more ideal is a suggestion of an article that the editor(s) can solicit. All articles will be reviewed in detail. Criteria on which they will be judged include their clarity of presentation, relevance, and likely audience, and, of course, their correctness and scientific merit. As to the mathematical level, the articles in this issue are a good guide: in each case the author has striven to explain complicated topics in simple-well, tutorial-terms. There should be no (or very little) novel material: the home for archival science is the Transactions Magazine, and submissions that need to be properly peer reviewed would be rerouted there. Likewise, articles that are interesting and descriptive, but lack significant tutorial content, ought more properly be submitted to the Systems Magazine.

What is a tutorial

Phase shifting algorithms for fringe projection profilometry: A review

https://febs.onlinelibrary.wiley.com/doi/pdf/10.1002/1873-3468.13948

The promise and the challenges of cryo-electron tomography.

In traditional phase measuring profilometry (PMP) setup, the connecting line between the exit pupil center of projector and entrance pupil center of CCD camera must parallel to the reference plane and the optical axes of projector and CCD camera must intersect at the same point on the reference plane. At this condition, the coefficients of phase-to-height mapping are constants because they are proved to be only dependent on the structural parameters. But lots of experimental results show that some of coefficients are not constants. Further analyzing this phenomenon, it is found that the above two restricted conditions can hardly to be guaranteed due to the invisible of the exit pupil, the entrance pupil and the optical axes. The more popular situation is that the above connecting line may not parallel to the reference plane and the above optical axes do not intersect on the reference plane. So a new universal mapping algorithm is derived at this situation. It reveals some of coefficients of the mapping really remain constants which are dependent on only the structural parameters, while some of coefficients are really not constants which are dependent on not only the structural parameters but also the phase distribution of the reference plane. It also reveals that the traditional mapping algorithm is just a special case of the derived mapping algorithm. Furthermore, it reveals that the accuracy of PMP can be improved distinctly by calibrating the phase of the reference plane. Experimental results have shown the feasibility and validity of the derived phase-to-height mapping algorithm.

Intrinsic feature revelation of phase-to-height mapping in phase measuring profilometry

Recently, a computer-generated moire profilometry was proposed by our research group. It can effectively avoid the influence of the transient caused by moire fringes’ direct acquisition and generally owns a higher accuracy. But when the spatial spectrum of the captured deformed pattern is severely aliased caused by the measured object, the accuracy of this method may be affected to some extent due to the impure background light component extraction. So, a high precision computer-generated moire profilometry based on background light component’s accurate elimination is proposed. By adding an additional special phase-shifting sinusoidal grating to accurately extract valid information in the spatial domain and improve the sinusoidal feature of the pattern, the measurement precision can be improved effectively. Though the single-shot feature is broken, the real-time measuring feature is still maintained successfully. Experimental results show the feasibility and validity of the proposed method.

/pdf/high-precision-computer-generated-moire-profilometry-3ll7qjktb2.pdf

High precision computer-generated moiré profilometry

A new 3D measuring method based on computer-generated moire fringes is proposed. The two AC components of the 0-degree and 90-degree phase-shifted fringe patterns on reference plane are prepared in advance. While the AC component of the single-shot deformed pattern is multiplied by the two prepared AC components, respectively, two computer-generated moire fringes can be retrieved. The ratio of the two computer-generated moire fringes is just the tangent of the phase modulated by the object. It is of great potential in real-time or even dynamical 3D measurement due to its single-shot deformed pattern feature, and it avoids the influences of the object's reflectivity simultaneously. Compared to the Fourier transform profilometry, its error is smaller due to its higher first-order spectrum. Experimental results show the feasibility and validity of the proposed method.

Computer-generated Moiré profilometry.

Object motion can introduce unknown phase shift and thus measurement error in multi-image phase-shifting methods of fringe projection profilometry. This paper presents a new method to estimate the unknown phase shifts and reduce the motion-induced error by using three phase maps computed over a multiple measurement sequence and calculating the difference between phase maps. The pixel-wise estimation of the motion-induced phase shifts permits phase-error compensation for non-homogeneous surface motion. Experiments demonstrated the ability of the method to reduce motion-induced error in real-time, for shape measurement of surfaces with high depth variation, and moving and deforming surfaces.

Real-time motion-induced-error compensation in 3D surface-shape measurement.

The time-dependent phase error induced by the instability of projection light source (IPLS) is systematically studied for phase-shifting profilometry (PSP) The IPLS of the projection device is investigated by a specially designed experimental setup Based on the results of the investigation, a new mathematical model to analyze the time-dependent phase error induced by IPLS is established and verified Two real-time phase error correction methods using a new designed three-dimensional shape measurement system are proposed for the effect of IPLS Experimental results demonstrate the two methods can effectively eliminate the induced time-dependent phase error with a good robustness and high accuracy The two real-time correction methods for PSP will be promising for high-accuracy measurements

Yingying Wan

Papers

Intrinsic feature revelation of phase-to-height mapping in phase measuring profilometry

High precision computer-generated moiré profilometry

Computer-generated Moiré profilometry.

Real-time motion-induced-error compensation in 3D surface-shape measurement.

Instability of projection light source and real-time phase error correction method for phase-shifting profilometry.