Study Of Image Processing And Analysis And Correction Of Wavefront Reconstruction Errors In Digital Phase-shifting Interferometry

As the hybrid of phase-shifting interferometry (PSI) and digital holography, phase-shifting digital holography can eliminate the effect of twin-image so that only the object field on the recorded plane is retrieved by calculating several interferograms obtained in the phase-shifting interferometer and the tested complex wave field on the original plane can be further reconstructed by inverse Fresnel tranformation. Combining the advantages of digital holography and phase-shifting interferometry, phase-shifting digital holography is also easily and flexibly realized and the measurement results can be analyzed qualitatively and quantitatively. At the same time, it can perform the whole-field testing with high precision. Therefore it has been widely studied and applied in various fields of science, engineering and biomedicine.The aims of my dissertation are to give a systematic and comprehensive analysis on this technique theoretically and experimentally and further propose some new algorithms and new methods to improve it. The concrete works are as follows:As a theoretical guide for practice work, some review on the basic principles related to PSI including the recording and retrieving theory of digital holography, various means of reconstructing hologram with computer, principles and experimental configurations of phase-shifting interferometry, the ways of realizing phase-shift and some typical algorithms as well as the designing approaches for these algorithms are introduced in Chapters 2 and 4.The objects to be processed in phase-shifting digital holography are the interferograms captured by CCD, so the qualities of these interferograms have important effects on the calculation results. In Chapter 3, we give a brief discussion about previous image processing techniques and then put forward a novel method which can perform the contrast-enhancement and skeleton-extraction for an interference pattern with low contrast and considerable luminance variation at the same time, yielding a uniform brightness and high contrast over the whole image area.The key of phase-shifting interferometry is the reconstruction formula. Up to now, lotsof phase-shifting retrieval algorithms have been proposed and all these existent methods can be divided into three catalogs: standard algorithm, equal-step algorithm and general PSI with arbitrary phase steps, and the third one seems to be the trend in this research field. In Chapter 5, we first make some analysis of previous works in this area, and then present two methods to determine the unknown actual phase-step values directly from the intereferograms based on the statistic property of the phase distribution of the diffraction field in recorded plane. The object wave field can then be calculated by using the generalized PSI wave reconstruction formulae of 3- or 4-steps with arbitrary phase shifts derived by us. The effectiveness and correctness of thes algorithms are verified by a series of computer simulations.The shortcoming of phase-shifting interferometry is the sensitivity to a variety of error sources. So investigation of the effects caused by those errors on measurement and derivation new error-compensating methods have been the research hot in this field in the last two or three decades. We found all the previous work were concentrated on the study of the phase error in the recorded plane. However, in many applications of phase-shifting digital holography, the actually recorded object wave is the diffraction field of an object surface. In this case, not only the phase error but also the amplitude error in the retrieval process has effects on the object wave reconstruction in its original plane. In Chapter 6, for the first time we know, the amplitude errors in wave reconstruction in phase-shifting interferometry are discussed systematically. Some general relations between the amplitude errors and the phase errors are revealed, and a series of new results of these two errors for different algorithms are quantitatively obtained. These results can be used for evaluating the complete wave in PSI and developing new methods for their correction.In Chapter 7, we propose correction methods to revise the wavefront errors caused by arbitrary phase shifts errors and the detector nonlinearity of the second order. Firstly, we derived the expressions of amplitude error and phase error in the standard four-step algorithm and correct them at the same time using our new method. Then the application of this approach is extended to the generalized phase-shifting interferometry with arbitrary phase-step design and arbitrary unknown phase shift errors. This method can depress both the amplitude error and the phase error by two magnitude orders without the need of phasestep calculation. Both the simulations and optical experiments are carried out to verify the usefulness of this error-correction approach. At last, another novel and simple algorithm of digital data processing for correcting the wave-front reconstruction errors caused by detector nonlinearity of the second order in PSI is also introduced and satisfactorily verified by computer simulations.In Chapter 8, we introduce two useful attempts in phase-shifting digital holography. One is the novel application of digital holography: a simple and flexible method of carrying out sensitivity adjustable contouring by a virtual reference wavefront simulated in computer. Another is the new method of phase-shifting interferometry with a binary grating displayed on a high-resolution electrically addressed amplitude-only liquid-crystal spatial light modulator as a phase shifter, which can achieve accurate phase shifts just by moving this grating digitally.