PRECISE AND ROBUST PHASE MEASUREMENT ALGORITHMS

摘要

Explicit analytical expressions for families of 3-point, 4-point, 5-point, and 6-point (m-point) phase-measurement formulas are presented, which are exactly valid for 1, 2, 3, 4, (m-2) different values of the phase-steps, applied in the sequence of intensity-measurements. These values are the "design phase-steps", which can be chosen in accordance with the actual necessity. These formulas are equally suited for the temporal as well as for the spatial case. In the spatial case, the formulas can be used as components to design very compact two dimensional convolution kernels, which lead to high spatial resolution and minimized sensitivity to higher-order miscalibration errors. We also present formulas with m points, which have (m-2) design phase-steps located symmetrical with respect to π/2. These formulas give the lowest errors over the largest range. Finally we present formulas which are insensitive to linear phase-shifter calibration errors and at the same time to nonlinearity of the intensity measurements or non-cosine fringe profiles. The basic theory to derive these formulas and to design two dimensional convolution kernels was established by the author in 1986 and applied during the production of the ESO-NTT primary from 1986 to 1987 within the Carl Zeiss company. It was patented by Carl Zeiss, was called the "Direct Measuring Interferometry" (DMI) method, and implemented in the Laser-Interferometer DIRECT 100, which has realtime wavefront measuring and evaluating capability on a set of 480 X 480 measurement points. The features of this method have been presented in different papers, the theory behind some of the formulas is given in greater detail in [7].