Arrays of photon-counting detectors and associated digital signal processors have been proposed for receivers in optical communication systems in which the optical signals propagate through the atmosphere and are relatively weak upon reception. The digital signal processor would execute algorithms that adapt the overall responses of the receivers to the temporally varying photon counts of the individual detectors in such a manner as to reduce the deleterious effect of atmospheric turbulence.

In a system to which this proposal applies, the receiver would include a diffraction-limited telescope with an aperture diameter on the order of 1 to 10 m and a focal length on the order of twice the aperture diameter, and would be used to detect a signal at a wavelength around 1 µm. In the absence of atmospheric turbulence, most of the received signal power could be focused onto a single focal-plane detector no larger than the diffraction-limited spot size, and background radiation from directions other than that of the signal source would be effectively spatially filtered out.

An Array of Photon-Counting Detectors would capture atmospheric-turbulence-induced random excursions of a received signal from a central, diffraction-limited focal spot. The digital signal processor would execute an algorithm that would weight the contributions of detectors in such a way as to reduce the relative contribution of background radiation.

In the presence of atmospheric turbulence, the phase of the optical signal arriving at a telescope becomes uncorrelated over distances greater than a coherence length that ranges from approximately 20 cm at night to as little as 2 to 4 cm during the day. The result is that the signal power is spread over a spot much wider than the diffraction-limited spot in the focal-plane, and the portion of signal power received at a given point in this wider spot tends to fluctuate on a time scale of about 10 to 100 ms. Hence, in order to capture most of the received signal power, it would be necessary to use a correspondingly larger-diameter detector, which, because of its greater field-of-view, would also capture more of the undesired background radiation.

In a system according to the proposal, a single large detector would be replaced by an array of smaller detectors, the photon-counting outputs of which would be fed to a digital signal processor (see figure). In the processor, the temporally varying photon counts from the detectors would be effectively weighted and combined by algorithms that assign greater weights to detectors receiving greater signal powers; thus, the contribution of undesired background radiation from detectors receiving less signal power would be reduced, the net effect being that the overall signal-to-noise ratio of the received signal is increased.

The detection algorithms have been formulated specifically for a communication system that uses M-ary pulse-position modulation in which the receiver attempts to determine which of M possible symbols has been received by observing the photon counts accumulated during each of the Mtime slots of a symbol period. It is assumed that the receiver is synchronized and, hence, "knows" the beginning and ending times of each symbol period as well as the time of arrival of each detected photon, and that these times and the associated photon counts can be stored for the limited amount of time needed for processing. It is also assumed that the photon-count outputs of the detectors are Poisson-distributed in time.

One of the algorithms utilizes continuous weighting of the counts from the individual detectors to implement an optimum array-detector receiver. However, this algorithm is not practical because the computational burden quickly becomes excessive as the number of detectors increases.

In the alternative simplified algorithm, continuous weighting is replaced by hard decisions on the selection of detectors from which the counts are to be considered at a given instant. This algorithm would implement a computationally simpler, suboptimum array-detector receiver. Computational simulations for representative cases have shown that the performance of the simpler suboptimum algorithm is almost equal to that of the more complex optimum algorithm, and that the improvement in performance over a single detector of diffraction-limited size would be equivalent to an increase in signal strength of about 5 dB under realistic operating conditions.

This work was done by Victor Vilnrotter and Meera Srinivasan of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at under the Electronic Components & Systems category.

In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to

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Refer to NPO-21041, volume and number of this NASA Tech Briefs issue, and the page number.

This Brief includes a Technical Support Package (TSP).
Adaptive Focal-Plane Detector Arrays for Optical Communications

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