In transmission microscopy, many objects are three dimensional, that is, they are thicker than the depth of focus of the imaging system. The three-dimensional (3-D) image-intensity distribution consists of a series of two-dimensional images (optical slices) with different parts of the object in focus. First, we deal with the fundamental limitations of 3-D imaging with classical optical systems. Second, a transfer theory of 3-D image formation is derived that relates the 3-D object (complex index of refraction) to the 3-D image intensity distribution in first-order Born approximation. This theory applies to weak objects that do not scatter much light. Since, in a microscope, the illumination is neither coherent nor completely incoherent, a theory for partially coherent light is needed, but in this case the object phase distribution and the absorptive parts of the object play different roles. Finally, some experimental results are presented.
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