Realization and accuracy of a phase-shifting speckle interferometer for full 3D shape measurement

In a two-wavelength phase-shifting speckle interferometer for object contouring one usually obtains only the height coordinate of the object surface, which is parallel to the direction of observation. In order to measure the lateral surface coordinates x and y by the same technique the light source is shifted in two directions perpendicular to the optical axis. Two additional phase maps of parallel fringes are generated, which are then used to assign the lateral coordinates x and y to the corresponding pixels of the camera. Nevertheless, the intensity distribution of speckle fields seems unfavourable in terms of precision metrology, as interferometers have to rely on a photodetector, exhibiting saturation, and an analog-to-digital converter with finite resolution. We calculate the optimum beam ratio, modulation of the camera and lens aperture for a speckle interferometer with maximum phase-measurement accuracy. To obtain the minimum error of 10.6 mrad, it is found that the mean speckle intensity ought to be adjusted to be 1/11 times the saturation intensity of the camera, the beam ratio is to be 4 and that the space-bandwidth product must be chosen 0,31. The latter is of particular practical interest, because stopping down the lens increases the need for a high-power laser. The results are valid for all kinds of speckle interferometers and are not restricted to the above-mentioned arrangement. They are confirmed by computer simulation of a two-wavelength speckle interferometer.