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Lenses and mirrors with freeform surfaces are the latest step in the evolution of optical components. However, the measurement of these components still challenges metrology. We have developed a gradient-based measurement technique that is able to measure freeform specular surfaces either if their form is known or not. The measurement of freeform surfaces is a challenge for every measurement system. Especially if the form of the surface is not known in advance. Our measurement system can measure continuous freeform surfaces with up to 10° deviation from a plane surface even if the surface model is not known in advance. Therefore, a ray, represented by a narrow laser beam, is targeted on the surface under test (SUT) under a certain angle. Affected by its slope, the surface reflects the ray in a new direction. This direction is measured by using a variation of Experimental Ray Tracing (ERT). This includes the measurement of the position of the reflected ray in two parallel planes. Calculating the difference of the position on these planes, the direction of the ray in relation to them can be calculated. Having the direction of the reflected ray, as well as the direction of the incident ray, one can determine the surface normal at the point of reflection. By moving the SUT, the incident ray targets on a different point on the SUT. Therewith, various points are investigated. Using appropriate integration methods, the surface can be reconstructed. Although, with the introduction of the incident ray under a certain angle comes the issue, that the point of reflection changes with the sag of the SUT. This leads to an unequal distant measurement grid of points of reflection even if the SUT has been moved to equal distant sample points. This shift has to be considered for the reconstruction of the surface. This issue is solved in different ways for known or unknown surfaces. For an unknown surface, the investigated sample points are transferred into a coordinate system where they are equal distant. This is the coordinate system of the incident beam. Performing the integration here and transferring the reconstructed surface back into the coordinate system of the SUT leads to the expected shift of the sample points. For a known surface, the expected surface form is taken into account to determine the sample point shift. Therewith, the difference between the measured surface normals and the expected normals can be calculated and the integration can be performed only on the normal residuals. By adding the residuals to the model, the surface can be reconstructed. The measurement technique described above has been implemented in an experimental setup. To show the abilities of this technique, we will show the process of the measurement of a known and an unknown surface using the same sample. The results will be evaluated and compared.
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