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.
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 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.
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.
We consider the physical limitations imposed on the information content of an image by the wave and quantum nature of light, when the image is obtained by illuminating a reflecting or transmitting planar object by natural---i.e., fully thermalized---light, or by observation of an object emitting incoherent (thermal) radiation. The discreteness of the degrees of freedom and the statistical properties of thermal radiation are taken into account. We derive the maximum amount of information that can be retrieved from the object. This amount is always finite and is proportional to the area of the object, the solid angle under which the entrance pupil of the receiver is seen from the object, and the time of observation. An explicit expression for the information in the case where the information recorded by the receiver obeys Planck's spectral distribution is obtained. The amount of information per photon of recorded radiation is a universal numerical constant, independent of the parameters of observation.
We consider the physical limitations imposed on the information content of an image by the wave and quantum nature of light, when the image is obtained by illuminating a reflecting or transmitting planar object by natural (i.e., fully thermalized) light, or by observation of an object emitting incoherent (thermal) radiation. The discreteness of the degrees of freedom and the statistical properties of thermal radiation are taken into account. We derive the maximum amount of information that can be retrieved from the object. This amount is always finite and is proportional to the area of the object, the solid angle under which the entrance pupil of the receiver is seen from the object, and the time of observation. An explicit expression for the information in the case where the information recorded by the receiver obeys Planck’s spectral distribution is obtained. The amount of information per photon of recorded radiation is a universal numerical constant, independent of the parameters of observation.
Expressions for the information rate and capacity of amplitude-modulated photon beams are available in literature. Recent interest in position-modulated laser pulses has motivated the investigation of the following model: A random variable D, which can take on values in the interval (−T, T), is transmitted by centering a narrow, coherent, single-mode light pulse of duration 2D and constant irradiance at t=D. It is assumed that no other than quantum fluctuations, of the otherwise stable source, disturb the transmission. The information that the received photon packet carries about D is registered as the instants {tk} of emission of photoelectrons at the detector. If H denotes the D and Q, the expected number of photoelectrons is 2D, and D≪T, then the mutual information between the D− and {tk} ensembles is, for large Q, approximately H−ln(2D/ρQ). Here, ρ = exp(γ − 1) and γ is Euler’s constant. Under the peak-excursion constraint |D|≤T, this is maximized by H = ln2T, for uniformly distributed D, so that for large Q the capacity C = ln(ρQT/D). The accurate expression, valid for all Q, involves the exponential integral E1(Q). The value of C is used to derive a lower bound on the mean-square error of any estimator of D, by the rate-distortion method. The bound, which decreases as Q2, is compared with the variance of maximum-a-posteriori-probability estimators of delay which, in the case of differentiable pulses, decreases only as Q.
The amount of information transmitted via a photon beam that is modulated in s equal, discrete steps from a given maximum expected number of pulses kmax and down to a given kmin is computed. The numbers of pulses refer to the counts of a photoemissive detector. The information i reaches a maximum im for a certain number s = sm for which the difference δk of the expected number of detected pulses from successive levels is about 2.7 times the rms fluctuation of the kmax level. The reliability (ratio of the information obtained in the presence of noise to the information that would be obtained without noise) of this maximum information im is about 0.8. im is very nearly a function of the single parameter c=(kmax−kmin)/kmin12. These results hold, provided that the rms fluctuation of the kmax level is not too different from that of the kmin level. For kmin = 0, maximum information is obtained with a somewhat smaller spacing δk, and its reliability is about 0.61 for kmax ≥ 20.