Abstract

A theorem is proved which relates the number of degrees of freedom in the image space of any lens to the light-gathering effectiveness of the lens. Under appropriate approximations this theorem is equivalent to Gabor’s expansion theorem. If the number of degrees of freedom is small, these approximations are not warranted and true superresolution becomes a possibility.

© 1967 Optical Society of America

On Gabor’s Expansion Theorem*

Kenro Miyamoto
J. Opt. Soc. Am. 50(9) 856-858 (1960)

Optical Transfer of the Three-Dimensional Object*†

B. Roy Frieden
J. Opt. Soc. Am. 57(1) 56-66 (1967)

Ambiguity of the Transfer Function with Partially Coherent Illumination

Richard E. Swing and James R. Clay
J. Opt. Soc. Am. 57(10) 1180-1189 (1967)

Propagation of the generalized radiance through lenses

A. Walther
J. Opt. Soc. Am. 68(11) 1606-1610 (1978)

Experiments on Superresolution Imaging of a Reduced Object Field*

A. Bachl and W. Lukosz
J. Opt. Soc. Am. 57(2) 163-169 (1967)