<title>Real-time phase visualization using phase conjugating mirror</title>

Abstract

In this paper we propose a real time phase visualization technique using a phase conjugating mirror. An image of the phase derivative is formed in a coherent optical differentiation system and reflected by the phase conjugating mirror. After the passage of the reflected light through the original phase object, its phase variation is compensated and its amplitude variation remained only. This amplitude value is the derivative of the phase function and is fed to a second coherent optical integration system. An image irradiance of the output of this system is proportional to the square of the phase variation. This allows a real time quantitative visualization of actual object phase. There are no limitations to the phase objects in relation to the fine structures and large variations. Design of the setup for implementation of phase visualization is discussed. Computer simulations and experimental results are demonstrated. IntroductionIn general the human eye and square-law detectors only record the intensity of objects, while loosing the phase information. In order to record the phase variation it must be converted into an amplitude modulation. There are several well known techniques of visualizing phase objects. Phase objects are often studied by interferometric techniques. These methods are valid only for phase objects with simple structure and slow variation . They cannot directly show the shape and thickness of phase reliefs. The shlieren technique and differential shearing interference microscopy both produce image irradiance which are proportional to the derivative of phase objects 2,3 This results in a visualization of shape and size of the phase objects, but without the details of the actual magnitude of the phase. The technique of phase contrast is available for detecting a phase object whose irradiance is directly proportional to the phase variation ' . This allows a quantitative visualization of actual object phase. Howevere, the applications of this technique is limited to very small phase variations no longer than a fraction of a wavelength. An electronic scanning technique, based on phase modulation interferometry for phase visualization, was proposed . But it requires complicated electronic circuit. Phase objects were visually studied also by a pseudocolor encoding technique with incoherent processing 6 However the image irradiances are not proportional to the phase variation but sinusoidally related to phase changes. The technique of coherent differentiation and integration to obtain an image irradiance proportional to object phase for large variation phase objects was proposed by Develis and Reynolds 2and realized by Spraque and Thompson with good results . However the technique is rather elaborate and the process is not a real time operation. Furthermore, there is a restriction on the maximum slope of the object phase variation.Recently, advances in photorefractive materials have stimulated interest in the applications of phase conjugation techniques to a number of optical signal processing ...