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J. Eur. Opt. Society-Rapid Publ. 21, 19( 2025)
Figure
5. Results of Zernike fit to the height difference values of position sweeps of simulated data for different specimens.( a) Zernike coefficients for an asphere moved along the optical axis.( b) Defocus-coefficient( Z 4) for four different specimens over axial position.( c) Zernike coefficients for an apshere moved laterally.( d) Primary x-Coma for different specimens over lateral position.
by a threshold operation, dividing it into the bright region of the evened-out interference patch and the dark background. Afterwards, a contour finding operation [ 28, 29 ] is performed to find the perimeter of the interference patch. The center-of-gravity of the interference patch can then be calculated by dividing the first moment of the contour pixels by the zeroth moment along each lateral direction [ 30 ]. To align the specimen’ s apex with the optical axis of the interferometer, the center-of-gravity of the rectangular patch has to be aligned with the interference patch position that corresponds with the optical axis. This position is estimated by the simulations described in Section 2.2. The difference vector between target position and the current center is calculated. Then the on-screen vector is translated to the movement of the specimen perpendicular to the optical axis using the previous simulation for estimating the translation factor. Afterwards, the center-of-gravity of the interference patch is estimated again and the calculation of the difference vector and the subsequent movement is repeated to refine the positioning and account for measurement inaccuracies and possible mismatch between simulation and real positioning. Usually now, the patch center matches the desired position within one or two pixels difference. With the simulations from Section 2.2 pixel shift of ± 2 in patch center-of-gravity correspond to ± 34 lm of specimen translation in lateral direction.
After this coarse lateral alignment of the specimen with the optical axis, the specimen is coarsely brought into the proximity of the Cat’ s Eye reference position, which corresponds to the region of an enlarged circular interference patch as seen in Figure 3a and b. In this region, the Defocus and the primary x- and y-Coma are linear over the respective axial and lateral displacements( compare Fig. 5b and d). Since the area of the interference patch depends on the axial position, it can be used for determining the rough distance to the Cat’ s Eye position and for bringing the specimen into the proximity. For this, the camera image is blurred and thresholded as before and the contour is calculated. Then, a floodfill operation inside the contour is performed and the number of pixels inside the contour is counted. With the data from the simulation shown in Figure 4b, the distance to the Cat’ s Eye position can be estimated and the axial position of the specimen can be changed accordingly. Here, it is only important to get into the linear regime of the Defocus- and Coma-coefficients.
To deduce the Cat’ s Eye reference position from the Defocus-coefficient of height values of the interferogram, the height values have to be calculated from the measurement data first. For this, the phase of the interferogram is retrieved by using 5 phase shifted interferograms. The reference arm of the TWI contains a phase-shifting element that is used to shift the angle of the reference phase in