Shape reconstruction from gradient data in an arbitrarily-shaped aperture by iterative discrete cosine transforms in Southwell configuration

The shape reconstruction from gradient data is a common problem in many slope-based metrology applications. In practice, the gradient data may not be ideally available for the whole field of view as expected, due to the aperture or the unmeasurable part of sample. An iterative method by using discrete cosine transforms is addressed in this work to deal with the integration problem with incomplete gradient dataset in Southwell configuration. Simulation indicates that the discrete cosine transform provides better initial values than discrete Fourier transform does, and it converges to a more accurate level by updating with spectrum-based slopes comparing to the slope updates from finite difference in classical method. Experimental results show the feasibility of the proposed approach in a practical measurement.