Holography, speckle, and computers
Introduction
Holographic interferometry and speckle techniques made it possible to measure surface shape and/or deformation of diffusely reflecting surfaces with interferometric sensitivity. Advantages of these techniques are well known and it is now desired to establish quantitative and automatic measurement using CCD cameras and computers in these methods. This effort started from electronic speckle pattern interferometry (ESPI) that produces fringe patterns by superposition of video speckle images. Automatic analysis of the resulting fringe patterns as well as those obtained from photographic recording of holograms and speckle patterns were also developed. Although digital fringe analysis has been successful for the fringe patterns observed from mirror surfaces [1], some problems arose in those obtained from diffusely reflecting surfaces leading to speckle noise. However, speckles also constitute the fringe patterns which are observed in holographic and speckle interferometry and whose contrast is governed by dynamic behaviors of speckle caused by surface deformation [2]. These dynamic behaviors consisting of displacement and decorrelation can be described in terms of cross-correlation function of intensity distribution [3]. Speckle displacement was first used in speckle photography where Young's fringes arising from optical Fourier transformation of doubly exposed negatives are observed. The fringes, always straight and periodic, are very suited for automatic analysis [4]. Advances in microcomputers and linear image sensors enabled direct calculation of cross-correlation function that could be used for real-time measurement of translation, rotation, and strain [3]. More recently, speckle patterns were recorded with a matrix CCD followed by a computer which calculates 2-D cross-correlation of subimages to deliver distribution of speckle displacement [3], [5]. Recent advances of computers and CCDs finally realized digital recording of holograms and computer reconstruction called as digital holography [6]. It also strengthens the performance of conventional imaging systems. In this paper, we discuss fringe formation in the above methods to show how CCD cameras and computers have been introduced in holography and speckle metrology.
Section snippets
Correlation properties of scattered light
All the quantities observed in holographic interferometry and speckle metrology that are applied to diffusely reflecting surfaces are expressed in terms of correlation functions of their complex amplitude or intensity [2], [3], [7]. Here, we describe the functions for linear transmission system that includes both free-space geometry and imaging system. We assume first the linear system shown in Fig. 1. The complex amplitude at the observation point can be represented by a linear
Holographic interferometry
In usual holographic interferometry, the complex amplitudes before and after object deformation are superposed in the image field of the object as shown in Fig. 3. The fringe intensity averaged over speckles is given bywhere U1 and U2 are the complex amplitudes before and after object deformation. The averaging is carried out mathematically over a statistical ensemble of the microscopic structure of the object and physically
Speckle interferometry
Speckle size in the image field can be adapted to resolution of recording media by adjusting the aperture diameter. In ESPI, speckle patterns formed by interferometric setups are recorded by a CCD camera, subtracted from the initial pattern, and squared by video circuits or a computer to display contour lines of object displacement. An arrangement used for measurement of out-of-plane displacement is shown in Fig. 4. The displayed brightness is proportional to
Speckle photography
Principles of speckle photography are illustrated in Fig. 7. It consists of recording of a double exposure specklegram and analysis of Young's fringes arising from optical Fourier transformation of the specklegram illuminated by a narrow laser beam. The transmission function of the specklegram is represented bywhere we assumed that the specklegram is recorded at the image plane of the object with Z=0. The intensity distribution of Young's fringes that appear in the
Electronic speckle correlation
Advances in CCD cameras and computers made it possible to analyze directly the cross-correlation of video speckles. It was first demonstrated by using a linear CCD whose output signals were analyzed by a microcomputer [9]. The computation could be accelerated to real-time by binary correlation algorithm that makes use of high contrast of speckles. If we record speckle patterns at image plane by a matrix CCD, we can derive a distribution of speckle displacement by calculating two-dimensional
Digital holography
Recent remarkable advances in CCD devices and computers have made it practical to record holograms by a CCD camera and to reconstruct three-dimensional images by computers. This technique, called digital holography, saves a trouble of photographic processing and delivers the distributions of both intensity and phase directly. In reconstruction focusing is adjusted numerically from a single recording. Since the distributions of not only intensity but also phase can be calculated, object
Conclusions
In this paper we have surveyed fringe formation in holographic interferometry and speckle metrology in terms of correlation properties of complex amplitude and intensity in observation fields. In holographic interferometry and speckle interferometry contour lines of phase change of the scattered light due to object deformation are observed as fringe patterns. In speckle photography orientation and spacing of Young fringes are related to orientation and magnitude of speckle displacement. In
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