A new formulation of the lateral imaging process of point-scanning optical coherence tomography (OCT) and a new differential contrast method designed by using this formulation are presented. The formulation is based on a mathematical sample model called the dispersed scatterer model (DSM), in which the sample is represented as a material with a spatially slowly varying refractive index and randomly distributed scatterers embedded in the material. It is shown that the formulation represents a meaningful OCT image and speckle as two independent mathematical quantities. The new differential contrast method is based on complex signal processing of OCT images, and the physical and numerical imaging processes of this method are jointly formulated using the same theoretical strategy as in the case of OCT. The formula shows that the method provides a spatially differential image of the sample structure. This differential imaging method is validated by measuring in vivo and in vitro samples.
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