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Improvement in the resolution of three‐dimensional data sets collected using optical serial sectioning
Author(s) -
Garza F. Macias,
Diller K. R.,
Bovik A. C.,
Aggarwal S. J.,
Aggarwal J. K.
Publication year - 1989
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.1989.tb00561.x
Subject(s) - distortion (music) , optics , optical sectioning , microscope , focus (optics) , optical transfer function , resolution (logic) , plane (geometry) , cardinal point , planar , optical axis , image plane , aperture (computer memory) , microscopy , image quality , physics , materials science , computer vision , computer science , artificial intelligence , image (mathematics) , mathematics , geometry , acoustics , lens (geology) , computer graphics (images) , optoelectronics , amplifier , cmos
SUMMARY In this paper an approach for improving the quality of 3‐D microscopic images obtained through optical serial sectioning is described and implemented. A serially sectioned image is composed of a sequence of 2‐D images obtained by incrementing the focusing plane of the microscope through the specimen of interest; ideally, the image obtained at each focusing plane should be in focus, and should contain information lying only within that plane. In practice, however, the images obtained contain redundant information from neighbouring focusing planes and are blurred by a three‐dimensional low‐pass distortion. These degradations are a consequence of the limited aperture of any optical system; using principles of geometric optics and allowing for the passage of light through the specimen, we are able to demonstrate that the microscope distortion can be described as a linear system, if the absorption of the specimen is assumed to be linear and non‐diffractive. The transfer function of the microscope is found to zero a biconic region of 3‐D spatial frequencies orientated along the optical axis; a closed‐form expression is derived for the low‐pass transfer function of the microscope outside the region of missing frequencies. The planar resolution of the serial sections can be greatly improved by convolving the image obtained with the inverse of the low‐pass distortion function, although the missing cone of frequencies is not recoverable. The reconstruction technique is demonstrated using both simulated images, to demonstrate more clearly the effects of the distortion and the accuracy of the subsequent reconstruction, and actual experiments with a pollen grain and a stained preparation of human cerebellum tissue.