|
Laser Visibility at Intensities Suitable forInterstellar Communications - DiscussionRadobs 08Preface: Sorry about the length of this document, but I think what I have to demonstrate here is very important. For those of you brave (or foolish) enough to print out this entire discussion document and its theoretical companion, you should be consoled by the idea that you are participating in SETI history, although you and the SETI Institute may not realize it yet. One small step for Stuart and Radobs - a giant leap for SETI! Apologies to Neil Armstrong. In this document (RADOBS.8) I prove that the laser intensities required for high-bandwidth communications, are insufficient to be visible to the naked eye, or to the "casual" astronomical observer. I aim to prove why statements to the contrary, which may be found in many SETI books and literature, are incorrect. In the process, I will demolish one of the arguments advanced for demonstrating that Optical SETI is not sensible. Possibly, although I have stated this conclusion elsewhere, you may not have believed me. Well, here now is your chance to check the accuracy of my analysis. The mathematics is very simple, and is something that could have been done on the back of an envelop, albeit a large one! It is strange that this erroneous belief has been around for so long. However, it is known that once mistaken information gets into the literature, particularly books, an air of authority is given to such thinking which belies the truth. The incorrect argument goes something like this . . . "Since a flashing laser beacon had never been observed by the naked eye or by astronomers through their telescopes, and because spectral studies have never indicated any anomalous spectral lines, there cannot be any ETI laser signals in the visible spectrum.". In the following document (RADOBS.9), I give the theory which supports the statements made herein, in the simplest mathematical form. Only the four basic operands are used; there are no differential equations or integrals. For this particular topic, the following proof does not primarily rest on any assumption about the beaming capabilities of advanced technical civilizations (ATCs), rather it just shows that the intensities required for high data-rate communications are insignificant with respect to the brightness of a typical star. First of all, let us calculate how bright the Sun would look at a distance of 10 light years. A G-type star like the Sun, which has a radius of 6.96 X 10^8 m, is emitting radiation at the rate of 3.90 X 10^26 watts per second. This is the Sun's Effective Isotropic Radiated Power (EIRP). Each square meter of the Sun's surface emits 3.90 X 10^26/[4.PI.(6.96 X 10^8)^2] watts [see Equ. (7)], i.e., 6.41 X 10^7 W/m^2. At our orbital distance of 1 A.U. (= 1.496 X 10^11 m), the solar intensity is given by 3.90 X 10^26/[4.PI.(1.496 X 10^11)^2] W/m^2, i.e., 1.39 kW/m^2. From Equ. (1) we see that the Sun has an Apparent Stellar Magnitude m = -26.8. Now 1 Light Year (L.Y.) = 63,242 Astronomical Units (A.U.), so that at a range of 10 light years, the star has an intensity (brightness) reduced by a factor (1/632,420)^2. This corresponds to a ratio of 2.5 X 10^-12. Now Equ. (1) shows that apparent stellar magnitude is proportional to [2.5 X log(brightness)], and thus at 10 light years, the stellar magnitude is reduced by +29, i.e., to a level of magnitude +2.2. For the sake of further discussion, the magnitude of a G-type star at 10 light years will be assumed to be +2. As previously shown, the Sun's output (integrated over the entire spectrum) at the Earth's distance of 1 A.U. (= 1.496 X 10^11 m) is 1.39 kW/m^2. At 10 light years, its intensity has fallen by a factor of 2.5 X 10^-12, i.e., to a level of 3.48 X 10^-9 W/m^2. From the Planckian black body radiation relationship given in Equ. (2), we show that at 1 A.U. (1.496 X 10^11 m) and a wavelength of 656 nm, Npl = 2.19 X 10^-12 W/m^2.Hz is the spectral energy density that a laser signal must compete with if it is to be detectable in the general continuum. At a distance of 10 light years we multiply these values by the 2.5 X 10^-12 factor previously calculated, to obtain Npl = 5.47 X 10^-24 W/m^2.Hz. For the detection of polarized laser radiation, the Npl level "seen" by a photodetector may be halved by the use of a polarizer, although the resulting spectral noise density will be doubled back to its original level in the output of a heterodyne receiver. Let us now assume our standard symmetrical 10 meter diameter telescope system. Equ. (3) gives the beamwidth for diffraction of a collimated circular beam (diffraction at a circular aperture). The beamwidth for this system is THETA = 0.014 arc seconds. Equ. (4) gives the beam diameter "D" for a collimated circular beam. In our Solar System, the beam received from a 10 light year distant source will have a diameter D = 0.051 A.U. The angular resolution is more than adequate to resolve (separate) an earth-like planet from its star at a distance of ten light years, assuming that the viewing telescope is space-based or used adaptive optics. Equ. (5) gives the gain relationship for an antenna. At this wavelength, the 10 meter diameter telescope has a huge gain of G = 153.6 dB. The tight transmitter beam, and the assumption that ATCs will not find it too difficult to "hit the bull's eye", is not essential to this particular argument (topic), only that it is a way of obtaining very strong signals, and with this, the possibility that such signals could be observed by the naked eye. Equ. (6) shows how the EIRP is related to the transmitted power. For the purposes of this analysis, we shall also assume that the ATC can launch a 1 GW diffraction limited beam, and strike the earth with an EIRP = 2.29 X 10^24 W. The beam energy density at the target is given by Equ. (7). At a distance of 10 light years, this produces a beam intensity of I = 2.04 X 10^-11 W/m^2, and a received signal Ps as predicted by Equ. (8), equal to 1.60 X 10^-9 W. The signal intensity or beam energy density should be compared to the 3.48 X 10^-9 W/m^2 for a star like the Sun at 10 light years. Comparing ratios, we see that the 1 GW transmitter is only about 0.6% of the brightness of the star, equivalent to an 8th magnitude star. (Elsewhere, I have stated a slightly different figure of 0.4%, which is caused by rounding errors associated with using exact integer values of stellar magnitude.) So even if this transmitter wasn't hidden by the light of its star, its intensity is insufficient to be seen by the naked eye, which can see to about the 6th magnitude under the best seeing conditions. If the 1 GW signal was confined to a 1 Hz bandwidth, the ratio between it and polarized Planckian radiation in the output of a heterodyne receiver, in terms of relative spectral densities, would be (2.04 X 10^-11)/(5.47 X 10^-24) = 3.7 X 10^12. This is equivalent to a ratio of 126 dB. If the aliens make use of a 20 dB Fraunhofer dark line suppression factor, the ratio could be as high as 146 dB. Note that in this analysis, no corrections have been applied to the Apparent Magnitude of the transmitter to account for the responsivity of the eye or photographic plate to its wavelength. In practice, this correction will be fairly small for wavelengths not too far removed from the center of the visible spectrum. An optical receiver can be assumed to have an equivalent effective system noise temperature, which allows its sensitivity to be compared with its microwave counterparts. Equ. (9) gives the relationship for this temperature. For the parameters under consideration in this analysis, a 656 nm optical system has a Teff = 43,900 K. This quantum noise floor is 36 dB above the noise floor of a 10 K microwave system, and implies a sensitivity penalty of 36 dB. This is one of the reasons why the SETI lore would have us believe that the optical approach is disadvantaged. However, as indicated above, the huge antenna gain G more than makes up for this penalty. Note that while a shot (quantum) noise limited optical heterodyne (coherent) receiver has a fixed quantum noise floor determined by the level of the local oscillator laser, and is essentially independent of the signal level and weak background, a photon-counting (incoherent) receiver has a variable quantum noise floor which is determined by both the level of received signal and the background. In the limit of a strong signal, the signal-to-noise ratios of either system will be approximately the same (within 3 dB). Now let us see what can be done with this signal, which is too dim to be seen with the naked eye. For a 10 meter diameter receiving telescope (A = 78.5 m^2), a beam intensity of 2.04 X 10^-11 W/m^2 produces a received optical signal Ps = 1.60 X 10^-9 W, i.e., 1.6 nW. The corresponding signal photon detection rate is approximately 2.6 billion photons per second. Equ. (10) gives the relationship predicting the shot (quantum) noise limit on the Carrier-To-Noise Ratio (CNR) in an optical heterodyne system. Substituting in the numbers for a 656 nm F.M. NTSC/PAL video link, similar to the 4/12 GHz (C/Ku-band) modulation formats used by geostationary satellites to beam TV signals around the globe, we find that the CNR = 19 dB. Because of the 36 dB quantum noise sensitivity penalty of the optical system, a microwave system would be able to achieve the same CNR if the received power was only 0.40 pW. Since, only a 7 to 8 dB CNR is required to reach F.M. threshold, this would produce an excellent Signal-To-Noise Ratio (SNR) and broadcast-quality pictures. Of course, to obtain this SNR we must be able to achieve very narrow optical detection bandwidths, something we can easily do with heterodyne detection, and also be able to suppress Planckian radiation from the alien star. The latter can be assisted by the aliens choosing to operate within a dark Fraunhofer line, such as the H-alpha line at 656 nm. We can get about an extra 20 dB, or an extra factor of 100 in optical detection bandwidth by this means. Also, by using space-based receiving telescopes or ground-based adaptive telescopes, nearby (less than a few hundred L.Y.) stars and their alien transmitters, can be separated in the focal plane, and thus will prevent SNR reduction by Planckian radiation entirely. Of course, if pulses were used instead of the continuous wave (C.W.) signals assumed for the purposes of this analysis, the ETI signal would stand out even better above Planckian starlight and/or daylight. The performance of this symmetrical 10 meter diameter telescope system has been previously expressed in the form of a CNR = 34 dB with respect to a 1 Hz bandwidth and a 1 kW transmitter. See the Spectral Level Graph shown in the earlier uploaded document (RADOBS.3) on "Detecting a laser in a dark Fraunhofer line". In that graph, the relative noise levels are plotted on a received noise power basis, and are larger than the intensity spectral levels quoted below by a factor of 78.5, which corresponds to the area of a 10 meter diameter mirror. Since the CNR = 19 dB re 30 MHz re 1 GW, if it was normalized to a bandwidth of 1 Hz, it would rise to a level of 94 dB. Thus, the quantum shot noise floor spectral density is -94 dB with respect to 2.04 X 10^-11 W/m^2, i.e., 8.1 X 10^-21 W/m^2.Hz. We have already shown that Npl = 5.47 X 10^-24 W/m^2.Hz. Thus, the Planckian noise continuum is about 32 dB below the quantum noise (see RADOBS.3). Thus, the optical bandwidth would have to be increased to over 1.5 kHz before the Planckian background noise exceeds the quantum noise due to the signal; to over 150 kHz if we make use of the 20 dB Fraunhofer suppression, and above the required 30 MHz I.F. bandwidth if we can actually separate the transmitter from its star. Whilst I do not mean to imply that either aliens are sending us "real-time" TV signals or using "crude" F.M. analog modulation techniques, the fact is that if they could efficiently harness the entire power-output of a terrestrial-type power station and turn its energy into laser light, and also target this planet with a diffraction limited beam, then it would be possible to send wideband signals over tens of light years - such is the "power" and "relative efficiency" of the optical approach. By bringing to bear the prowess of ATC technology, ETIs can minimize the wastage of power in empty space. The philosophy of this approach is very different to the conventional SETI rationale, which says in effect, that communications over interstellar distances are so difficult, that all ETIs could hope to achieve would be to communicate with Hz-type bandwidths! Some SETI scientists appear to have a pathetic estimation of the abilities of ATCs. One could argue that ATCs have "all the time in the universe" in which to send their data, so that even at very low date-rates, over a period of time, substantial amounts of data could be transferred. But why do so if one is not constrained by the laws of the universe or one's own technology? Material sent to me this week by Bob Dixon, would seem to indicate that we do not even have to worry about interstellar dispersion effects causing significant spectral broadening of optical carriers. Note that if sophisticated encoding schemes were used, much like what now is being applied to compress HDTV signals into small bandwidths, "real-time" TV at these ranges could be achieved with significantly less transmitter power. One would suspect that relatively high definition "real-time" TV signals would be a very effective means of rapidly bridging the cultural and language barriers between island civilizations and radically different intelligent life-forms. What this analysis shows, is that even if an optical ETI signal in the visible spectrum can be strong enough to transmit very wideband signals, it would still be so dim as not to be visible to the naked eye. By my estimates, nearby aliens would have to be pulsing mean powers of over 300 GW, perhaps something approaching one trillion watts into their transmitting telescopes (holy smokes!), for there to be even a small chance that mankind would see a noticeable brightening of a star with the naked eye. If the reader feels that I have been "extravagant" with the EIRPs suggested, then the probability of detecting visible laser signals with conventional optical telescopes, even the largest in the world, is virtually zero. We have shown what utter nonsense it is to suggest that because such signals have never been seen by Earth observers, they don't exist! If we consider communications out to distances of 1,000 L.Y., then Planckian intensities and alien signals strength will fall by a factor of 10,000, equivalent to a stellar magnitude decrease of 10. A G-type star would be a 12th magnitude body, while the 1 GW transmitter would appear as an 18th magnitude body [see Equ. (1)]. Aliens at those and greater distances, will have to reduce their transmission bandwidths or turn up the juice if they wish to communicate. This is good reason for ETIs throughout the Milky Way Galaxy to cooperate and relay each other's signals. It would be ironic if optical communications, perhaps the oldest form of terrestrial communications, which first saw light (sorry about the pun) in the form of bonfires, smoke signals, heliographs and semaphores, and more lately as free-space atmospheric and guided-wave systems, should in the end be the ultimate form of electromagnetic communications in the universe! It is foolish to assume that laser signals, if they exist, would have been detected by now. We need only consider the fact that for 30 years, SETI enthusiasts have been systematically searching the microwave signals for ETI signals, all to no avail. The chances of accidently discovering optical SETI signals is remote indeed. What is needed is an optical version of the Microwave Observing Project (MOP) with optical telescopes equipped with heterodyning receiver arrays. Optical SETI does presently have one decided advantage over Microwave SETI, and that is, the low level of artificial terrestrial pollution, and the unlikely detection (interference) of a terrestrial source of laser radiation! Even this advantage is likely to disappear in a few decades, as NASA and communications satellite organizations begin to use this technology for more down to earth needs. I liken the problem of not correctly identifying the preferred ETI frequencies, to that of a remote terrestrial civilization, e.g., indians in the Amazon jungle, who has just "discovered" radio. Unknown to them, microwave signals from small artificial satellites in geostationary orbit are bombarding them daily. These signals form part of the Terrestrial Communications Network, to which this remote emerging terrestrial civilization is entirely oblivious. We speak about the "Global Village" because Arthur C. Clarke's "Extraterrestrial Relays" have united mankind in a manner which is unprecedented in Earth's history. To the indians in deepest Amazona, radio is the ultimate form of long-distance electromagnetic communications technology, which can bring them the sounds of distant places. Could they imagine that pictures of even more distant places, images of exotic places on the other side of the globe of which they were hardly aware, were raining down upon them, day and night? So too could it be with mankind as a whole, and the Galactic Communications Network. The "Cosmic Village" awaits us; only we may have been too blind to see. History may show that for a few distracting years (on the cosmic time- scale), mankind (and womankind) got side-tracked by the lure of radio- frequency communications, only then to realize that it could not give them what they sought; the answer to the ultimate question "are we alone?". They had, in effect, been too clever by half in trying to outguess ETIs, and the technologies they would use. December 23, 1990 RADOBS.08 BBOARD No. 276 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Dr. Stuart A. Kingsley Copyright (c), 1990 * * AMIEE, SMIEEE * * Consultant "Where No Photon Has Gone Before" * * __________ * * FIBERDYNE OPTOELECTRONICS / \ * * 545 Northview Drive --- hf >> kT --- * * Columbus, Ohio 43209 \__________/ * * United States .. .. .. .. .. * * Tel. (614) 258-7402 . . . . . . . . . . . * * skingsle@magnus.ircc.ohio-state.edu .. .. .. .. .. * * CompuServe: 72376,3545 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
|