Effects of system apertures and defocus on the measured phase shift in interferometric displacement measurements

The difference between the phase shift occurring at the objectsurface owing to displacement and the phase shift occurring at theobservation plane of the imaging system of the interferometer isstudied. Analytical expressions for the phase shift for a number ofsurface displacements are found. From these expressions it is foundthat the difference between the phase shifts at the object and theobservation planes depends on the number of speckle-correlation modesin the observation plane and the product between the relative apertureand the relative defocus of the imaging system. For generaldisplacement the results indicate that the accuracy of a phase-shiftmeasurement with a small-aperture interferometer is limited only by thenumber of speckle-correlation modes at the observation plane for thecase of a focused system. For a large-aperture interferometer thephase shift at the observation plane becomes sensitive to defocusing ofthe imaging system. Agreement between theory and experiments is observed.