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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 72, Iss. 6 — Jun. 1, 1982
  • pp: 804–808

Image-position error associated with a quadrant detector

Glenn A. Tyler and David L. Fried  »View Author Affiliations

JOSA, Vol. 72, Issue 6, pp. 804-808 (1982)

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An exact expression is obtained that evaluates the error associated with angular-position measurement of an incoherently illuminated object when a quadrant detector is used in the image plane of an optical system. The accuracy of such a measurement is inversely proportional to the signal-to-noise voltage ratio associated with the four quadrants summed to act as a single detector. In the particular case of a circular object, the rms angular measurement error is given by the expression σθ = π[(3/16)2 + (n/8)2]½(λ/D)/SNRv, where n is the angular subtense of the object divided by the diffraction angle λ/D, SNRv is the signal-to-noise voltage ratio, λ is the wavelength of the light used, and D is the diameter of the limiting aperture in the optical system under consideration.

© 1982 Optical Society of America

Glenn A. Tyler and David L. Fried, "Image-position error associated with a quadrant detector," J. Opt. Soc. Am. 72, 804-808 (1982)

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  1. G. B. Parent, Jr., and B. J. Thompson, in Physical Optics Notebook (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1969), Article 4.
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968, p. 114, Eq. (6–24).
  3. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1964), p. 486, Eq. (11.4.16).

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