Digital fringe projection in 3D shape measurement - an error analysis

Optical 3D measurement systems are used in a lot of applications, for instance for quality control and reverse engineering. Active optical 3D measurement systems are very often based on the fringe projection technique. The key element of such a shape measurement system is the projection unit, where nowadays digital projection units based on LCD /1/, LCoS /2/, or DMD /3, 4, 5/ technology are used. Despite of a lot of opportunities these displays reveal some disadvantages for the use in fringe projection, which can reduce the phase measurement accuracy. In contrast to slide-like structures, these displays are separated in small picture elements - so called active pixels - with dimensions of about 8x8mum(2) up to 20x20mum(2). For this reason the cos(2) function which has to be projected is spatially quantized. Therefore this function is not continuous. Another problem is the reproduction of the correct intensities given by the cos(2) function in the projection. Usually, every projection engine shows some kind of gamma correction function or nonlinearity. This is either caused by the micro display itself or (in the case of video beamers) it is implemented into the beamer's electronic to project proper visual images. All these effects will distort the intensity to be projected. All the mentioned effects cause phase measurement errors of different strength. Here we discuss different approaches to determine and compensate these influences of the projection engine to the 3D measurement. If the compensation is well accomplished, the accuracy of the measurement results may increase by up to one magnitude.