Abstract

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 σ<sub>θ</sub> = π[(3/16)<sup>2</sup> + (n/8)<sup>2</sup>]<sup>½</sup>(λ/<i>D</i>)/SNR<sub>v</sub>, where n is the angular subtense of the object divided by the diffraction angle λ/<i>D</i>, SNR<sub>v</sub> is the signal-to-noise voltage ratio, λ is the wavelength of the light used, and <i>D</i> is the diameter of the limiting aperture in the optical system under consideration.

© 1982 Optical Society of America

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References

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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).

Abramowitz, M.

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).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968, p. 114, Eq. (6–24).

Parent, Jr., G. B.

G. B. Parent, Jr., and B. J. Thompson, in Physical Optics Notebook (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1969), Article 4.

Stegun, I. A.

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).

Thompson, B. J.

G. B. Parent, Jr., and B. J. Thompson, in Physical Optics Notebook (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1969), Article 4.

Other (3)

G. B. Parent, Jr., and B. J. Thompson, in Physical Optics Notebook (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1969), Article 4.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968, p. 114, Eq. (6–24).

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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