Spatially Constrained 3-D Reconstruction from Limited-Angle Projections in Optical Microscope Tomography

In earlier work, we invented a principle of optical microscope tomography and developed a prototype system to achieve tomographic microscope imaging of three-dimensional specimens [1,2]. In this paper we describe the principle of optical microscope tomography and the algorithm to reconstruct the 3-D distribution of the sample from the obtained images. Since the system is angularly band-limited, we have to constrain the inverse equation of the system by some a priori information to lead to a unique solution. We use the information of the knowledge of the spatial outer boundary of the object to truncate the projection system function. The outer boundary of the object is easily measured. Since this constraining preserves the linearity of the system, reconstruction can be simply performed by a linear-system solving method.