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

We first provide an overview of 3-D shape measurement us- ing various optical methods. Then we focus on structured light tech- niques where various optical configurations, image acquisition tech- niques, data postprocessing and analysis methods and advantages and limitations are presented. Several industrial application examples are presented. Important areas requiring further R&D are discussed. Finally, a comprehensive bibliography on 3-D shape measurement is included, although it is not intended to be exhaustive. © 2000 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(00)00101-X)

Overview of three-dimensional shape measurement using optical methods

Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

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

Thermophysical Properties Research Literature Retrieval Guide Edited by Y. S. Touloukian, J. K. Gerritsen and N. Y. Moore Second edition, revised and expanded. Book 1: Pp. xxi + 819. Book 2: Pp.621. Book 3: Pp. ix + 1315. (New York: Plenum Press, 1967.) n.p.

/pdf/heat-and-mass-transfer-1yaijfx8vp.pdf

Heat and Mass Transfer

We present a system for 3-D shape measurement in large volumes based on combined digital-fringe-Gray-code projection. With the help of a new calibration procedure, the system provides accurate results despite its crossed-axis configuration and unknown aberrations of the digital light projector and CCD camera. Also, the separate clouds of points captured from different directions are automatically merged into the main cloud. The system delivers results in the form of (x,y,z) coordinates of the object points with additional (R,G,B) color information about their texture. Applicability of the system is proven by presenting sample results of measurements performed on complex objects. The uncertainty of the system was estimated at 10 4 of the measurement volume.

Digital fringe projection system for large-volume 360-deg shape measurement

A successful application of self-interference digital holographic microscopy in combination with a sample-rotation-based tomography module for three-dimensional (3-D) label-free quantitative live cell imaging with subcellular resolution is demonstrated. By means of implementation of a hollow optical fiber as the sample cuvette, the observation of living cells in different 3-D matrices is enabled. The fiber delivers a stable and accurate rotation of a cell or cell cluster, providing quantitative phase data for tomographic reconstruction of the 3-D refractive index distribution with an isotropic spatial resolution. We demonstrate that it is possible to clearly distinguish and quantitatively analyze several cells grouped in a “3-D cluster” as well as subcellular organelles like the nucleoli and local internal refractive index changes.

https://www.spiedigitallibrary.org/journals/journal-of-biomedical-optics/volume-19/issue-4/046009/Tomographic-phase-microscopy-of-living-three-dimensional-cell-cultures/10.1117/1.JBO.19.4.046009.pdf

Tomographic phase microscopy of living three-dimensional cell cultures.

High accuracy Fourier transform fringe pattern analysis

The spatial-carrier phase shifting (SCPS) technique that is related to both Fourier transform and phase-shifting methods of calculating the phase is analyzed. In this technique, a large amount of tilt is introduced into an interferogram, so that the phase difference between successive pixels equals (pi) /2. Three successive pixels are used to recover the phase using the adequate standard phase shifting formula. The detailed error analysis is presented. Examples of application of this method in conventional and moire interferometry, as well as in optical triangulation, are shown. As the SCPS technique requires a single frame only for phase calculation, it is capable of making high-speed measurements or performing testing in adverse environments.

Spatial-carrier phase-shifting technique of fringe pattern analysis

This paper presents an extended viewing angle holographic display for reconstruction of real world objects in which the capture and display systems are decoupled. This is achieved by employing multiple tilted spatial light modulators (SLMs) arranged in a circular configuration. In order to prove the proper reconstruction and visual perception of holographic images the Wigner distribution function is employed. We describe both the capture system using a single static camera with a rotating object and a holographic display utilizing six tilted SLMs. The experimental results based on the reconstruction of computer generated and real world scenes are presented. The coherent noise removal procedure is described and implemented. The experiments prove the possibility to view images reconstructed in the display binocularly and with good quality.

/pdf/extended-viewing-angle-holographic-display-system-with-whjs6j3jno.pdf

Malgorzata Kujawinska

Papers

Digital fringe projection system for large-volume 360-deg shape measurement

Tomographic phase microscopy of living three-dimensional cell cultures.

High accuracy Fourier transform fringe pattern analysis

Spatial-carrier phase-shifting technique of fringe pattern analysis

Extended viewing angle holographic display system with tilted SLMs in a circular configuration.