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Laser Visibility at Intensities Suitable for

Interstellar Communications - Discussion

Radobs 08

 
Preface:  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                                                           *
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