Information Content of Photoelectric Star Images*

Abstract

The information that we can extract from a photoelectric image of a star is limited by (i) noise introduced in the signal amplification, (ii) conversion of the two-dimensional image into a temporal signal, and (iii) background radiation, optical aberrations, and photon noise. This third limitation is the primary concern in this paper; it determines the information content of the two-dimensional image. The information content of a photoelectric star image is measured by its probability of detection, and by the intrinsic error in measuring its position and intensity. The maximum achievable probability of detection is expressed in terms of the image characteristics. A detection method that maximizes the probability of detection is described; it depends on the signal-to-noise ratio. With a signal-to-noise ratio greater than 103, detection is based on image intensity. With a signal-to-noise ratio less than 103, detection is based on image shape and size, as well as intensity. The intrinsic relative errors in measuring position and intensity are inversely proportional to the square root of the number of photoelectric emissions for a fixed signal-to-noise ratio. The errors are monotonic decreasing functions of the signal-to-noise ratio. Equations are derived that express the rms error in terms of the image shape, image intensity, and signal-to-noise ratio. Several of the basic results apply to arbitrary photoelectric images. In this paper, we are interested in the intrinsic detection and measurement limits of photoelectric images, as opposed to specific techniques or devices.