Holography, speckle, and computers

Abstract

Surveys are presented on automatic and quantitative deformation measurements using CCDs and computers in holographic interferometry and speckle metrology for diffusely reflecting surfaces. For delivering relationships between object deformation and observed quantities, we discuss formations of fringes and signals observed in these methods in terms of correlation functions of spatially randomly varying complex amplitude of light. Dependencies of the observed patterns on object deformation and optical systems are discussed. Physical meanings of the derived relationships are explained in terms of the dynamic behaviors of speckles resulting from surface deformation. Automatic measurements are described in chronological orders. They include analysis of fringe patterns resulting from photographic recording of specklegrams, video recording and analysis of speckle patterns used in electronic speckle pattern interferometry as well as direct digital correlation techniques, and digital holography that uses both digital recording and reconstruction of holograms.

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.