Microscopic shape from focus using active illumination

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Abstract
Shape from focus relies on surface texture for the computation of depth. In many real-world applications, surfaces can be smoothly shaded and lacking in detectable texture. In such cases, shape from focus generates inaccurate and sparse depth maps. This paper presents a novel extension to the original shape from focus method. A strong texture is forced on imaged surfaces by the use of active illumination. The exact pattern of the projected illumination is determined through a careful Fourier analysis of all the optical effects involved in focus analysis. When the focus operator used is a 2D Laplacian, the optimal illumination pattern is found to be a checkerboard whose pitch is the same size as the distance between adjacent elements in the discrete Laplacian kernel. This analysis also reveals the exact number of images required for accurate shape recovery. These results are experimentally verified using an optical microscope. Surfaces lacking in texture, such as, three-dimensional structures on silicon substrates and solder joints on circuit boards were used in the experiments. The results show that the derived illumination pattern is in fact optimal, facilitating accurate shape recovery of complex and pertinent industrial samples.

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