Holographic method for topography measurement of highly tilted and high numerical aperture micro structures
This paper presents an analysis of the topography characterization of a tilted sample by interferometric measurement systems in transmission and reflection configurations. The developed analytical expressions permit the direct reconstruction of the three-dimensional shape of a tilted sample. The first method presented in this paper, the so-called Thin Tilted Element Approximation (TTEA) method, is an extension of the well-known Thin Element Approximation for tilted geometry, which can be applied to the case of large sample tilts, but it requires the numerical aperture (local shape gradients) of the sample to be low. The second method presented here, the so-called Tilted Local Ray Approximation (TLRA) algorithm, is based on the analysis of local ray transition through a measured object. The method can be applied for the accurate shape characterization of tilted samples with high shape gradient. The developed algorithms require focused images, while in the inclined sample configuration the image plane is tilted relatively to the detection plane. To overcome this problem we propose the application of an efficient algorithm for the numerical propagation between tilted planes. The accuracy of TTEA and TLRA algorithms is successfully proven with simulations and experimental measurements for the case of low and high NA microlenses.