Phase Retrieval by Optical Phase Differentiation.
Abstract
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 wavefront 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 Fouriertransform wave function passes through a filter, referred to as a differentiation filter, which has a constant amplitudetransmittance gradient within the transformplane aperture. The resulting imageplane 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 phaseretrieval methods require a number of imageplane irradiance distributions measured with different differentiation filters in the Fouriertransform 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 imageplane irradiance from which the objectplane phase may be inferred. In the new interferometric method of phase retrieval two interference patterns are formed using different amounts of referencebeam 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 referencebeam phase shifts then allows phase to be determined. All five new methods of phase retrieval rely on a well known leastsquares technique for estimating phase from phasegradient data. This technique is discussed in detail in an appendix to the thesis.
 Publication:

Ph.D. Thesis
 Pub Date:
 1984
 Bibcode:
 1984PhDT........87B
 Keywords:

 Physics: Optics