Microscopic shape from focus using a projected illumination pattern

Since its invention, the optical microscope has been used primarily as a device to view and image biological and industrial samples. This paper presents a technique for recovering the three-dimensional shapes of microscopic samples by focus analysis. Shape from focus relies on surface texture for the computation of depth. In many real-world applications, surfaces can be smooth and lacking in detectable texture. In such cases, shape from focus generates inaccurate and sparse depth maps. This paper presents a novel extension to previous shape from focus approaches. A strong texture is forced on imaged surfaces by the use of active illumination. The pattern of the active illumination is determined through a careful Fourier analysis of all the optical and computational elements 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 equals the distance between adjacent weights in the discrete Laplacian kernel. This analysis also reveals the minimum number of images required for accurate shape recovery. These results are experimentally verified using a fully automated microscopic shape from focus system. The shapes of samples lacking in texture, such as three-dimensional structures on silicon substrates and solder joints on circuit boards were recovered with high precision using the developed system. The results demonstrate that the derived illumination pattern is in fact optimal, and facilitates accurate shape recovery of complex and pertinent industrial samples.