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In addition to conventional optical methods for surface studies, various differential phase optical techniques have been developed recently which are capable of detecting variations in optical path length with very high sensitivity (up to 10 angstroms according to theoretical estimations). The differential approach is based on the measurements of phase difference between two beams reflected from two adjacent points of a sample. It results in high depth resolution, but the system response is fairly simple only for step-like structures. The authors propose a novel technique for recovering the surface optical phase relief by numerical treatment of experimentally measured differential phase scan. The image formation theory of the differential phase optical microscope (DPOM) described by Chung is developed and the differential phase scan is -- under certain assumptions -- the finite derivative of the convolution between the phase relief and the amplitude profile of the optical beam on the surface. The experimental data treatment includes the appropriate numerical method for solving the ill- conditioned integral equation to obtain the surface phase relief. This technique has been applied to studies of the refractive index profile of ion-exchanged channel glass waveguides and the surface profile of Ti:LiNbO3 channel waveguides.
Sergey I. Bozhevolnyi,E. A. Bozhevolnaya,A. V. Postnikov, andP. S. Radko
"Optical phase relief reconstruction by using differential phase optical microscope", Proc. SPIE 1723, LAMILADIS '91 Intl Workshop: Laser Microtechnology and Laser Diagnostics of Surfaces, (1 April 1992); https://doi.org/10.1117/12.58651
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Sergey I. Bozhevolnyi, E. A. Bozhevolnaya, A. V. Postnikov, P. S. Radko, "Optical phase relief reconstruction by using differential phase optical microscope," Proc. SPIE 1723, LAMILADIS '91 Intl Workshop: Laser Microtechnology and Laser Diagnostics of Surfaces, (1 April 1992); https://doi.org/10.1117/12.58651