If the nonlinearity of the motion of a piezoelectric transducer (PZT) can be described as a quadratic function, the integrated intensity of one frame in phase shift interferometry can be calculated using the Fresnel integral. For a PZT with smaller nonlinearity, the rms phase error is almost linearly proportional to the quadratic coefficient The effects of PZT nonlinearity on the three- and the four-bucket algorithms are compared.

We describe a modified three-flat method. In a Cartesian coordinate system, a flat can be expressed as the sum of even-odd, odd-even, even-even, and odd-odd functions. The even-odd and the odd-even functions of each flat are obtained first, and then the even-even function is calculated. All three functions are exact. The odd-odd function is difficult to obtain. In theory, this function can be solved by rotating the flat 90°, 45°, 22.5°, etc. The components of the Fourier series of this odd-odd function are derived and extracted from each rotation of the flat. A flat is approximated by the sum of the first three functions and the known components of the odd-odd function. In the experiments, the flats are oriented in six configurations by rotating the flats 180°, 90°, and 45° with respect to one another, and six measurements are performed. The exact profiles along every 45° diameter are obtained, and the profile in the area between two adjacent diameters of these diameters is also obtained with some approximation. The theoretical derivation, experiment results, and error analysis are presented.

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The phase errors caused by spurious reflection in Twyman-Green and Fizeau interferometers are studied. A practical algorithm effectively eliminating the error is presented. Two other algorithms are reviewed, and the results obtained using the three algorithms are compared.