The missing cone problem and low-pass distortion in optical serial sectioning microscopy

In optical serial sectioning, the 3-D structure of a microscopic specimen is observed by incrementing the focusing plane of a light microscope through the specimen. If the depth of field of the microscope is infinitesimal, the image obtained from each focusing plane is an in-focus slice of the optical density of the specimen. The authors show that the finite aperture of any practical microscope inevitably results in the loss of a biconic region of frequencies in the 3-D Fourier spectrum of the optical density, oriented in the direction of the optical axis. Thus, the resolution along this axis is severely reduced. Outside the missing cone of frequencies, the spectrum is distorted by a strong low-pass effect. A closed form expression is obtained for the overall distortion function using principles of geometric optics, and by assuming that the absorption of the specimen is linear and nondiffractive. Methods for restoring the 3-D images obtained through optical serial sectioning are considered, and several examples are provided