Coherence scanning interferometry CSI with a broadband light source (short known as white light interferometry) is,
beside the confocal technique, one of the most popular optical principles to measure surface topography. Compared to
coherent interferometry, the broadband light source leads, theoretically, to an unambiguous phase information.
The paper describes the properties of the correlogram in the spatial and in the frequency domain. All deviations from the
ideal correlogram are expressed by an addition phase term. The uncertainty of height information is discussed for both,
the frequency domain analyse (FDA) proposed by de Groot and the Hilbert transform. For the frequency domain
analyse, the uncertainty is quantified by the Cramér-Rao bound.
The second part of the paper deals with the phase evaluation of the correlogram, which is necessary to achieve a high
vertical resolution. Because the envelope function is often distorted, phase jumps lead to ambiguous height informations.
In particular, this effect can be observed measuring rough surfaces.
The mathematical fundamentals of some black box calibration procedures for fringe projection system are introduced. These calibration procedures are based upon a direct mathematical transformation between the measuring volume and the image data obtained with a camera. Aided by a mathematical model of a fringe projection system various calibration procedures are compared to each other in numerical simulations. The numerical simulations facilitate statements about the attainable measuring error depending on the calibration procedure and system parameters.