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_θ = π[(3/16)² + (n/8)²]^1/2(λ/D)/SNR_v, where n is the angular subtense of the object divided by the diffraction angle λ/D, SNR_v 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

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