Error-compensating phase measuring algorithms in a Fizeau interferometer

In phase-shifting Fizeau interferometers, nonlinear motion of the phase shi fter and multiple-beam interference are the most common sources of systemat ic errors affecting high-precision phase measurement. A new class of algori thms with extended compensating capability for these errors is proposed. Me asurement errors for the new algorithms and two groups of conventional algo rithms: discrete Fourier algorithms and the Schwider-Larkin-Hibino algorith ms are estimated as a function of the number of sampled images when these s ystematic error sources are equally dominant. It is shown that the conventi onal phase-measuring algorithms produce significant errors when the reflect ivity of the testing surface exceeds ten percent. Also, these algorithms ha ve an optimum number of samples at around seven with which the residual err ors become minimum. The new class of algorithms shows a substantial reducti on of the residual errors when the number of samples exceeds ten. There is no optimum number of samples for the new algorithms. For fewer than six sam ples, discrete Fourier algorithms which have no error-compensating capabili ty for the nonlinearity of phase modulation give a minimum error.