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

Mathematica--A System for Doing Mathematics by Computer.

Active, optical range imaging systems collect three-dimensional coordinate data from object surfaces. These systems can be useful in a wide variety of automation applications, including shape acquisition, bin picking, assembly, inspection, gauging, robot navigation, medical diagnosis, cartography, and military tasks. The range-imaging sensors in such systems are unique imaging devices in that the image data points explicitly represent scene surface geometry in a sampled form. At least six different optical principles have been used to actively obtain range images: (1) radar, (2) triangulation, (3) moire, (4) holographic interferometry, (5) lens focusing, and (6) diffraction. The relative capabilities of different sensors and sensing methods are evaluated using a figure of merit based on range accuracy, depth of field, and image acquisition time.

Active optical range imaging sensors

Dynamic 3-D shape measurement method: A review

This paper describes the use of an Electro-Optic Holography system for measuring vibration patterns on diffusely reflecting objects. The system provides a high-quality display of fringes for identifying modal frequencies and setting vibration levels after which image brightness data can be transferred to a host computer. A bias vibration is introduced into the illumination beam to shift the 0 fringes so that fringe shift algorithms can be used to determine vibration amplitude. Using this approach, high spatial density displacement fields for vibrating objects were obtained directly form the time-average interferograms recorded by the Electro-Optic Holography system. These results show good correlation with the reconstructions from the holograms and with the vibration characteristics predicted by the Finite Element Methods.

Measurement Of Vibration Patterns Using Electro-Optic Holography

Characterization of surface shape and deformation is of pri- mary importance in a number of testing and metrology applications re- lated to the functionality, performance, and integrity of components. In this paper, a unique, compact, and versatile state-of-the-art fiber-optic- based optoelectronic holography (OEH) methodology is described. This description addresses apparatus and analysis algorithms, especially de- veloped to perform measurements of both absolute surface shape and deformation. The OEH can be arranged in multiple configurations, which include the three-camera, three-illumination, and in-plane speckle corre- lation setups. With the OEH apparatus and analysis algorithms, absolute shape measurements can be made, using present setup, with a spatial resolution and accuracy of better than 30 and 10 mm, respectively, for volumes characterized by a 300-mm length. Optimizing the experimental setup and incorporating equipment, as it becomes available, having su- perior capabilities to the ones utilized in the present investigations can further increase resolution and accuracy in the measurements. The par- ticular feature of this methodology is its capability to export the measure- ments data directly into CAD environments for subsequent processing, analysis, and definition of CAD/CAE models. © 2000 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(00)02601-5)

http://users.wpi.edu/~cfurlong/Docs/oeJan00.pdf

Absolute shape measurements using high-resolution optoelectronic holography methods

An optical microscope, utilizing the principles of time- averaged hologram interferometry, is described for microelectrome- chanical systems (MEMS) applications. MEMS are devices fabricated via techniques such as microphotolithography to create miniature actua- tors and sensors. Many of these sensors are currently deployed in auto- motive applications which rely on, or depend on, the dynamic behavior of the sensor, e.g., airbag sensors, ride monitoring suspensions sensors, etc. Typical dimensions of current MEMS devices are measured in mi- crometers, a small fraction of the diameter of a human hair, and the current trend is to further decrease the size of MEMS devices to submi- crometer dimensions. However, the smaller MEMS become, the more challenging it is to measure with accuracy the dynamic characteristics of these devices. An electro-optic holographic microscope (EOHM) for the purpose of studying the dynamic behavior of MEMS type devices is de- scribed. Additionally, by performing phase measurements within an EOHM image, object displacements are determined as illustrated by rep- resentative examples. With the EOHM, devices with surface sizes rang- ing from approximately 353400 to 5318 mm are studied while undergo- ing resonant vibrations at frequencies as high as 2 MHz. © 1998 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(98)00505-4)

Holographic microscope for measuring displacements of vibrating microbeams using time-averaged, electro-optic holography

This paper deals with the quantitative interpretation of time-average holograms of vibrating objects. It is shown that the images obtained during reconstruction of such holograms are modulated by a system of fringes described by the square of the zero-order Bessel function of the first kind. A procedure for quantitative interpretation of these fringes is described and illustrated with examples. The experimental results, obtained directly from the time-average holograms, show good agreement with the exact solution of the differential equation of motion based on the beam theory and with the mode shapes determined by the finite element modeling of the vibrating beam.

Time Average Holography in Vibration Analysis

Increased demands on the performance and efficiency of me- chanical components impose challenges on their engineering design and optimization, especially when new and more demanding applica- tions must be developed in relatively short periods of time while satisfy- ing design objectives, as well as cost and manufacturability. In addition, reliability and durability must be taken into consideration. As a conse- quence, effective quantitative methodologies, computational and experi- mental, should be applied in the study and optimization of mechanical components. Computational investigations enable parametric studies and the determination of critical engineering design conditions, while ex- perimental investigations, especially those using optical techniques, pro- vide qualitative and quantitative information on the actual response of the structure of interest to the applied load and boundary conditions. We discuss a hybrid experimental and computational approach for investiga- tion and optimization of mechanical components. The approach is based on analytical, computational, and experimental solutions (ACES) meth- odologies in the form of computational, noninvasive optical techniques, and fringe prediction (FP) analysis tools. Practical application of the hy- brid approach is illustrated with representative examples that demon- strate the viability of the approach as an effective engineering tool for analysis and optimization. © 1998 Society of Photo-Optical Instrumentation Engi- neers. (S0091-3286(98)00405-X)

https://users.wpi.edu/~cfurlong/Docs/oeMay98.pdf

Ryszard J. Pryputniewicz

Papers

Measurement Of Vibration Patterns Using Electro-Optic Holography

Absolute shape measurements using high-resolution optoelectronic holography methods

Holographic microscope for measuring displacements of vibrating microbeams using time-averaged, electro-optic holography

Time Average Holography in Vibration Analysis

Hybrid computational and experimental approach for the study and optimization of mechanical components