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**Direct optical link at 10.6 μ**

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For coherent reception of a signal arriving at a zenith angle of 70 deg, a receiver aperture of only a half meter (50 percent aperture illumination efficiency) would be expected to suffer a 3-dB loss in aperture gain with typical atmosphere distortions of the signal wavefront. Careful selection of the site and perhaps tower-mounting of the receiver should permit doubling of the aperture diameter for the same over-all aperture efficiency, giving a 60-dB enhancement.

A further 3 dB can be gained by increasing the aperture diameter at the expense of a 50 percent loss in efficiency. For greater diameters, overall aperture efficiency drops rapidly and there is little advantage to further increases. A single-element receiver aperture is therefore limited to about a 2-meter diameter corresponding to a nominal gain of 112 dB but with a 6-dB loss (included among the fixed losses in Table 2) due to atmospheric turbulence.

The gain of the transmitter aperture is limited by the accuracy with which the transmitter can be pointed at the earth station. For an effective pointing accuracy of five μrad, or a minimum allowable beamwidth of ten μrad, the gain is limited to 112 dB, corresponding again to a 2-meter aperture diameter (50 percent efficient).

A transmitter power of 500 W is assumed corresponding at the lower laser efficiency to the same raw power requirement set for the microwave case. On this basis, over-all performance in terms of the information-rate parameter for a single-element ground-based receiver amounts to 85 dB. An additional 5 dB is required to meet the 90-dB goal.

The deficit could be made up in principle by improving spacecraft pointing accuracy from five to three μrad, allowing an appropriate increase in transmitting aperture gain; but in practice, this would require a corresponding increase of aperture diameter to just over 3 meters. More practically, a three-element ground-receiver aperture could be used. Individual aperture elements would be phase-locked to the incoming signal to compensate for the atmospheric phase distortion and the signals would be correlated at the IF frequency. This alternative is given in Table 2.

**Satellite relay link at 10.6 μ**

Aperture diameter of a satellite receiver is limited by achievable pointing accuracies. However, the pointing problem reduces to a simple closed-loop angle-tracking problem internal to the receiver. Considerably smaller pointing errors can be anticipated for the receiver than for the transmitter, where the detected error angle must be translated to a predicted pointing angle for the transmitter to overcome such problems as bore-sight misalignment and lead angle.

If an achievable rms error of 1.5 μrad is assumed for the receiver tracking angle, a gain of 122 dB should be allowable for the receiver aperture. This corresponds, however, to a diameter of about six meters and requires optical-quality fabrication tolerance of σ/D = 10^{-7}. The fact that such an aperture exceeds the dimensions of the Mt. Palomar telescope should not be used to discount entirely the possibility since, for a monochromatic radiation, focusing techniques such as the use of Fresnel-zone plates might be developed to permit light-weight, space-deployable apertures.

A more predictable solution to the problem, however, would be a receiver aperture of two meters, equal to the spacecraft transmitter aperture, and having a gain of 112 dB.

A transmitted power of 500 W, similar to that for the direct spacecraft-to-earth link, is then required to meet the desired performance goal of 90 dB.

The choice between a satellite-relay and a direct optical communication link reduces essentially to an evaluation of the costs of a satellite receiver (one or at most two required) as opposed to multiple ground-based receivers in widely dispersed locations.