Phase Retrieval by Optical Phase Differentiation.

The problem of retrieving the phase of coherent optical wave functions from irradiance measurements is considered. Following a literature review, five new methods of phase retrieval are presented. In four of the new methods phase derivatives are measured by a technique referred to as phase differentiation by coherent processing; one of these four methods allows phase to be retrieved in real time and is therefore a form of wave-front sensing. The fifth new method is based on a form of interferometry. In the technique of phase differentiation by coherent processing a coherent processing system is used to form the optical Fourier transform of an object wave function. This Fourier-transform wave function passes through a filter, referred to as a differentiation filter, which has a constant amplitude-transmittance gradient within the transform-plane aperture. The resulting image-plane irradiance is a quadratic function of (1) a partial derivative of the phase of the object wave function, (2) the magnitude of the object wave function, and (3) a partial derivative of the magnitude of the object wave function. Three of the new phase-retrieval methods require a number of image-plane irradiance distributions measured with different differentiation filters in the Fourier-transform plane. Experimental results and noise analysis are given for these three methods. The new wave -front sensor uses a special rotating differentiation filter to form a time varying image-plane irradiance from which the object-plane phase may be inferred. In the new interferometric method of phase retrieval two interference patterns are formed using different amounts of reference-beam phase shift, and the irradiance distribution of each pattern is measured. Measurement of the irradiance distribution of the object beam, the (constant) irradiance of the reference beam, and the approximate difference between the two reference-beam phase shifts then allows phase to be determined. All five new methods of phase retrieval rely on a well known least-squares technique for estimating phase from phase-gradient data. This technique is discussed in detail in an appendix to the thesis.