The Flawed Analysis of Project Cyclops
On page 50 of the 1972 report on Project Cyclops there is a table (Table 5-3) summarizing a comparative analysis between the optical and microwave approaches to SETI. That optical analysis is seriously flawed by a complete failure of imagination of what is possible with optical telescopes. In particular, the assumed sizes of telescope mirrors causes substantial degradation in system performance, as will shortly be illustrated. The Cyclops study only considered ground-based telescopes, whereas this study assumes space-based telescopes at each end of the system, or ground-based adaptive telescopes with deformable mirrors or phase conjugation. The Cyclops study assumed that optical telescope sizes were limited by atmospheric coherence cell size. For the near infrared wavelength of 1.06 µm used for one of the models, the single telescope mirror size at the transmitter was restricted to a diameter of 22.5 cm, and four hundred 5-meter diameter mirrors were specified at the incoherent detection (photon- counting) receiver.
Let us see the SNR penalty caused by down-sizing mirrors of a single telescope coherent heterodyne system from 10 meters to 0.225 meters diameter. Since the beamwidth is inversely proportional to mirror diameter, the energy density at the receiver is proportional to the square of the mirror diameter, viz
Transmitter Beamwidth Penalty = 10.Log(10/0.225)2 = 10.Log(1975)
= 33 dB
By a strange coincidence, "1975" was the number of receiver mirror elements for the incoherent CO2 System A modeled in the Cyclops study.
Similarly, at the receiver, the light collection efficiency is proportional to the square of the mirror diameter, viz
Receiver Light Collection Penalty = 10.Log(10/0.225)2
= 33 dB
Thus, it would appear that the total system performance penalty is 66 dB. The system performance in 10 meter diameter systems at 1 W of transmitter power, could only be produced by 4 MW in a symmetrical near infrared optical heterodyne system based on 22.5 cm diameter mirrors.
But wait, if we further assume that the maximum transmitter power is not limited by laser technology, but by the energy density in the telescope, i.e., mirror heating, and this is a safe assumption for small telescopes, then the maximum transmitted power is approximately proportional to the area of the mirror.
Maximum Transmitted Power Penalty = 10.Log(10/0.225)2
= 33 dB
Total SNR Penalty 100 dB!
Because the coherence cell size and thus mirror size would be even smaller in the visible, the total SNR (power-limited) penalty at 656 nm would climb to about 120 dB! With the inability of small telescopes to separate the Planckian starlight from the transmitters in nearby star-systems, for moderate bandwidths, e.g. 1 MHz, the actual SNR penalty may be over 20 dB worse.
Incredibly, the SNR penalty in the visible imposed by the Cyclops analysis technique could be higher than 140 dB! In the Cyclops study a 2.25 meter mirror was assumed for the CO2 system. The total SNR penalty in that case (including transmitter power limitations) would be a more modest 39 dB; almost a factor of 10,000.
By effectively objecting to beamwidths < 1 arcsecond because nearby star systems are too close, so that the beam would most likely miss all the planets in a star system, many people who oppose the optical approach would rather cripple the optical system at the outset by specifying tiny mirrors at both the transmitter and receiver. If there is a problem in aiming a very narrow beam into a nearby star system, then rather degrading the system performance, simply construct the largest telescope that your technology can produce at a cost that is bearable, and defocus the beam for nearby star systems.
This author believes that advanced technical civilizations have the capability of imaging the planetary bodies of nearby star systems and to determine their orbital periods. They will thus have the means to aim a tight beam to strike a target planet, over what is equivalent to the round-trip light time between the transmitter and prospective receiver.
Possibly, these same alien civilizations have at some time visited our star system or sent out interstellar probes, and thus would have considerable knowledge about our planetary system. At distances of several hundred light years, the beam becomes so large, that with proper advanced aiming, the entire target planetary system would be illuminated simultaneously.
It should be noted that in the Cyclops Optical System B operating at 1.06 µm, the transmitting mirror size was 22.5 cm and the peak power specified was a 105 W pulse lasting for 1 second. This implies an energy density at the mirror during the pulse of 251.5 W/cm2.
In Viewgraph 9010-024 we indicate that in a symmetrical 10-meter diameter visible system at a range of 10 light years, a CNR of 19 dB could be obtained in a 30 MHz bandwidth if transmitter powers of 1 GW were used. The energy density in that case would be 1.27 kW/cm2. If the Cyclops report had modeled a visible system with a 10 cm coherence cell size and a corresponding 10 cm diameter mirror, the energy density for a transmitted power of 100 kW would have been the same.
Thus, we see that by a poor assumption about mirror sizes and beamwidths, the viability of the Optical SETI approach is substantially skewed if not destroyed. It is unfortunate that the optical assumptions in Project Cyclops have been largely unchallenged for nearly two decades, for it has reinforced the SETI lore that Optical SETI is useless. Possibly, alien civilizations have been trying for years to catch our attention - if only those dumb Earthlings would tune to the correct frequency!
Even though it is now almost 20 years on and there have been substantial improvements in optoelectronics and optical telescope technology, it is very difficult to understand how the optical part of the Cyclops study could have been so compromised. Surely, no one expected aliens to employ transmitting telescopes that are smaller than what many terrestrial amateur astronomers use?