Optimization of a Calibration Strategy to Reduce the Retrace Error in Structured Illumination Macroscopy (SIMA)

In the main part of this work the systematic errors that existed in the first model-free calibrationimplementation by Yang is investigated. These systematic error sources are classifiedinto three main parts and optimized accordingly.

The first category of error sources are those errors which are introduced during measuring the retrace error over the full field and full angular dynamics. These include errors due to the photogrammetric accuracy, the instability of the calibration hardware and the intrinsic error in the SIMA measured height due to bat-wing effect at the boundary of the markers. The photogrammetric accuracy is estimated and the instability is optimized by careful design of the calibration marker plate and the calibration hardware. Furthermore, to improve the effect of bat-wing in the SIM measured height, vertical and horizontal sinusoidal fringe are projected in a single measurement and the height of the marker is evaluated from the mean contrast fromvertical and horizontal fringes. By doing so it has been managed to improve the bat-wing effectas well as reduce the magnitude of the retrace error in general.

The second categories of error sources are those errors which are introduced during approximating the underlying 5D calibration function (LUT). From simulation as well as measurements it is known that the retrace error has sharp dip in the angular domain at around zero degree. However, polynomial approximation usually fails to represent such sharp deeps. In order to solve this problem, different kind of freeform approximation algorithms like RBF and NURBS are investigated and implemented. This investigation has shown that NURBS and RBF can represent the freeform surface with accuracy in the order of the noise level.

The third error source that is optimized is the systematic error in the slope measured by PMD. This error source was not taken into account in the first implementation of the model-free calibration. However, it was one of the biggest error sources. For example, on a measured slope of ball bearing of diameter 10mm using PMD in +/-17°  angular dynamics there was systematic error up to 6°. Using a model-free calibration approach this systematic error is reduced by more than half on the calculated slope Sx and Sy compere to the previous modal-based approach. However, due to the discontinuity on the marker plate, there are still remaining systematic error of 2.5°  for example on the slope Sy. This could be further improved by using an appropriate calibration object such as a half-sphere.

 

After these optimization procedures it is managed to reduce the systematic error of SIMA by a factor of six compared to not corrected data . Compared with the first implementation by Yangthe systematic error has been reduced by nearly a factor of three on ball bearing of diameter 10mm measured by SIMA in +/-17°  angular dynamics. In addition to the systematic error, it is also managed to increase the angular dynamics of SIMA from +/-12°  in the first implementation to +/- 17° .

In the final part of this work the optimization of precision by integrating SIMA with μPMD is presented. This has been done by extracting the good features from SIMA and μPMD and integrating them together. By combining the global shape from SIM and the local detail in formation from μPMD we managed to optimized local precision down to few nanometers.

The improvement in the systematic error is significant as discussed above. However, there is still some room for improvement. For instance, the slope measurement sensor is still one of the biggest error source and instability of the marker due to thermal expansion could cause a bigsystematic error. The bat-wing effect is managed to tackle only for marker position of Φ close to π/4 and 3π/4 . However, for marker plate position of ‑ close to π/4 and 3π/4 we still have bat-wing effects in our measurement. This remaining error could be up to 20μm at the edge of the FOV of a marker plate tilted by Θ = 18  for Φ close to π/4 and 3π/4 . This can be improved further by projecting additional fringes other than the vertical and horizontal fringes or using a sphere as a calibration object.