Deflectometry: Analysis and Correction of Residual Errors

Summary and conclusions: In this work different error sources which have an impact onto PMD measurements have been investigated. The focus lied on systematic error sources which are affecting the global accuracy the most.

With the help of a technical solution the image elevation could be totally eliminated. This is rather practical since it is a cheap solution and it can be applied for almost all kinds of PMD systems. The problem has been solved by using a volume scattering foil which is glued directly on the projector (TFT); thereby a new light source is generated. This light source is image elevation free and has very good lambertian properties. The disadvantage os this foils is, that some luminance of the TFT and some contrast of the sinusodial pattern is lost. The contrast lost ist almost negligible since measurements with the same quality can be carried out. Apart from this, the advantages are clearly dominating. The foil totally depolarizes the light of the TFT due to the mulitple scattering processes. No polarization issues like the Brewster angle problem are aparent. Furthermore, it makes the linerization of the light source angle independent. Therebiy no expensive medical TFT screen, which have an internal linearization correction, have to be used anymore. A perfect linearization can be done with the foil even for simple TFT screens.

A mathematical algorithm which is able to solve the highly systematic error source of the circle of the confusion has been presented. This alogrithm is based on a reconstruction for the whole measurements process including the surface cuvature. For each single pixel a circle of confusion is generted and it behaviour and influence during the measurment is analyzed. This permits to compensate the introduced error of the circle of confusion.

Furthermore the TFT as a light source for PMD measurments has been reviewed. The sub-pixel design of different TFT technologies has been investigated and the influence on PMD measurements has been assessed. This analysis showed that the foil which is eliminating the image elevation also solves this problem. The contrast loss which is introduced due to the foils low pass character is averaging out these sub-pixel effects.

In addition a screen calibration of a TFT was done to see how strong the sagging effect due to the gravity is. For the big eye glass setup this has already been done because it was obvious there that the screen is sagging. For TFT this has been untended since the size is quite small. However, the results showed that even for PMD setups with small TFT's a screen calibration should be carried out since the sagging is in the mm range.

In addition the running in characteristics of different PMD setup components have been investigated. This was done to get a rule of thumb how long the required warm-up time for precise PMD measurements is.

Modulated stray light as an error source was introduced in this thesis. The rpojected pattern of the screen is back reflected by the object itself onto the screen again. Thereby the gray values of the screen are superimposed and phase errors are introduced since the back reflection is modulated light again. This effect is a fundamental problem. Therfore a recipe has been described how this error source can be reduced as much as possible.

Finally different error sources which are introduced during the data evaluation process were discussed. Moreover an improved algorithm for the evolution of patched machine integrated measurements was developed. This algorithm makes use of filgering the measured normals.

To sum up a measurment with the machin integrated setup is compared with the results where all the effects which were introdcued in this work were considered.