Abstract

The distribution of energy density is derived for the diffraction image produced by an Airy type objective of a single, uniform, opaque or transmitting particle located in a uniform, transmitting surround and illuminated by a narrow cone of axial illumination. It is shown that for a large class of particles the diffraction image can have an irregular variation in energy density in addition to a regular variation and that these variations are in accord with experiments performed with opaque particles. The irregular variation can appear as a secondary Airy disk located well within the regular Airy disk. The development of the diffraction image with increasing radii of disk-shaped particles is described. The equations which govern this development are adapted to the determination of the radius of the particle from linear or photometric measurements upon the diffraction image. The smallest measurable radii are restricted by practical limits rather than by physical limits as in the resolution of two particles. The practical limit is about 0.6 Airy unit for the linear measurements but may fall below 0.3 Airy unit with photometric measurements.

© 1950 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Diffraction Images of Disk-Shaped Particles Computed for Full Köhler Illumination

Luther W. Smith
J. Opt. Soc. Am. 50(4) 369-374 (1960)

The Measurement of Unresolved, Single Particles of Uniform Thickness by Means of Variable Phase Microscopy*

Harold Osterberg and Gilbert E. Pride
J. Opt. Soc. Am. 40(2) 64-73 (1950)

Diffraction Theory for Images of Disk-Shaped Particles with Köhler Illumination

Harold Osterberg and Luther W. Smith
J. Opt. Soc. Am. 50(4) 362-369 (1960)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (7)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Tables (3)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (50)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription