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

Increasing technological capabilities to produce active microelements (incl. microbeams, micromembranes and micromirrors) and their expanding areas of application introduce unprecedented requirements concerning their design and testing. Conventional two beam interferometry is one of the most popular testing method of microelements that have reflecting surface. Sometimes elements under test have complicated shape or shape gradients which restricts their testing by means of interferometer with flat reference mirror. In this paper we propose to use Liquid Crystal On Silicon (LCOS) spatial light modulator which serves as an adaptive reference mirror and phase shifter in Twyman-Green interferometer applied for microelements measurement. Initial tests have been performed and results confirming applicability of LCOS in active interferometer system are presented.

Active microinterferometer with liquid crystal on silicon (LCOS) for extended range static and dynamic micromembrane measurement

In this paper a new, hardware-based solution for extending the depth of field in holographic tomography is presented. The solution is based on a 4f system and an electric, focus-tunable lens, which provides fast, motion-free defocusing of the plane conjugate with the camera, which acquires holograms. The optimum parameters for the required axial scanning are provided for a specific model of a commercially available tunable lens. Then, the quality of the system equipped with the designed module is analyzed and the reconstruction of a standard object (microsphere) scanned by the 4f-based defocusing system is presented. Finally, the result of the increased depth of field in the measurement domain is demonstrated with a reconstruction of a mouse fibroblast cell.

Focus-tunable lens in limited-angle holographic tomography

Current design, analysis and control engineering applications require effective experimental methodologies and tools for determination of displacement and strain fields as well as material characterization. The quality of experimental data obtained at industrial environment has to be sufficient to introduce them into further numerical analysis by FEM (CAE) or use immediately for product quality assessment process. In the paper we present two novel types of full-field laser extensometers based on four-beam, grating (moire) interferometry method. The first type of extensometers is designed for medium size field of view (6 x 4.5 mm ). It is integrated and works directly on a standard loading machine with the possibility to control the load on the base of local on-line strain measurements. It enables the measurements during static, monotonic and cyclic loads and full-field analysis of arbitrary sequence of images, The second type, based on the concept of waveguide interferometer, is designed for small size field of view (min. 0.18 x 0. 12 mm2). It is integrated with a standard optical microscope and it seems to be an excellent tool for local material studies and strain analysis of microcomponents. The waveguide extensometer presented includes miniature Twyman- Green interferometer, which allows to measure out-of-plane displacements. Both extensometers give high contrast and good quality interferograms, are insensitive to vibrations and work with simple, low cost laser diode. The capabilities of the extensometers are presented on the example of low cyclic fatigue testing of a steel specimen and local displacement and strain investigations performed at the ferritic-austenic steel sample and silicon microbeam.

New generation of optical extensometers based on grating (moire) interferometry

In science revolutions do not happen often, however they influence our life significantly. We had definitely experienced the revolution connected with introduction of lasers, powerful desktop computers and matrix detectors. However several problems should still be solved. At the moment the evolution of the active optoelectronic and MEMS based devices as well as phase analysis and processing methods bring us to the higher level of fulfilling the requirement formulated by the users of the measurement systems. Several efficient solutions have been demonstrated. The presented concepts of the micromeasurement systems demonstrate that sophisticated photonic and micromechanical devices, and their associated electronic control, can be made small, low power, and inexpensive, even permitting the device to be disposable.

Malgorzata Kujawinska

Papers

Active microinterferometer with liquid crystal on silicon (LCOS) for extended range static and dynamic micromembrane measurement

Focus-tunable lens in limited-angle holographic tomography

New generation of optical extensometers based on grating (moire) interferometry

New Challenges for Optical Metrology: Evolution or Revolution

Optical design of a DOE-based laser interferometer for inspection of MEMS/MOEMS