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Journal of the Optical Society of America

Information in Noisy Photon Beams

Ellen Hisdal

Published Jul 1, 1968• 4 citations
Publisher

Abstract

The fluctuations in a thermal beam due to the superposition of two similar thermal beams are computed. The information loss due to superimposing a quasi-monochromatic thermal-noise beam on a similar signal beam is investigated for two types of noise beams, sample noise, and path noise. In the Wien and Rayleigh–Jeans limits, the information loss j23 per macrocell is found to depend only on the signal-to-noise ratio. The relative loss in maximum obtainable information, I3,max/I2,max, for given signal and noise beams is given as well as some numerical examples.

DOI
10.1364/josa.58.000977

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The fluctuations in a thermal beam due to the superposition of two similar thermal beams are computed. The information loss due to superimposing a quasi-monochromatic thermal-noise beam on a similar signal beam is investigated for two types of noise beams, sample noise, and path noise. In the Wien and Rayleigh–Jeans limits, the information loss j23 per macrocell is found to depend only on the signal-to-noise ratio. The relative loss in maximum obtainable information, I3,max/I2,max, for given signal and noise beams is given as well as some numerical examples.
The information content in a thermal photon beam and in a single-mode maser beam is computed, taking account of the limited quantum efficiency of the detector, and extending the results to polychromatic radiation in the thermal case. Formulas for fluctuations of the measured quantity in a polychromatic thermal beam are found, both for a photoelectric and for a thermal type of detector. Numerical examples of the information content are given for three common thermal light sources, using the eye as detector. For all three sources the information is found to be of the order of 104–105 bits/sec for a sample of 1 cm2 at 1 m distance from the the eye.
A quasimonochromatic photon beam is constructed by the superposition of quasimonochromatic plane waves with certain mutual coherence properties. The information which the photon beam can carry about the reflectivity of a specular sample is investigated, taking radiation fluctuations into account. In Sec. 4 an expression is found for the information content of the beam as a function of the resolution of the detector system. In Sec. 5 it is found that there exists a maximum information which a given thermal photon beam can carry. This is obtained with a detector system of a specified resolution. The information contained in an idealized maser beam is computed in Sec. 6 and compared with the information in a beam from a low-pressure mercury emission line. It is found that the information in the maser beam can be several orders of magnitude higher. It is limited mainly by the highest obtainable scanning rate.
The information rates achievable by using electromagnetic radiation affected by thermal noise and signal decoherence are studied. The standard coherent Gaussian model is compared with an alternative photon gas model which represents lack of a shared phase reference between transmitter and receiver. At any frequency, information rates over the photon gas model essentially coincide with those over the Gaussian model when the signal-to-noise ratio is below a threshold. Only above the threshold does decoherence cause a loss in information rates; the loss can amount to half of the capacity. The threshold exceeds 40 dB for radio frequencies and vanishes at optical frequencies.
The information rates achievable by using electromagnetic radiation affected by thermal noise and signal decoherence are studied. The classical coherent-state Gaussian model is compared with an alternative photon gas model which represents lack of a shared phase reference between transmitter and receiver. At any frequency, the information rates in the presence of decoherence essentially coincide with those over a Gaussian model when the signal-to-noise ratio is below a threshold. Only above the threshold does decoherence cause a significant loss in information rates; the loss can amount to half of the capacity. The threshold exceeds 40 dB for radio frequencies and vanishes at optical frequencies.