Detecting a Laser in a Dark Fraunhofer Line

Radobs 03

This document not only demonstrates why it is probably "impossible" for
optical astronomers to have "accidently" discovered an Extraterrestrial
Intelligence (ETI) signal, but also why daylight Optical SETI should be
possible.

This graph shows the estimated signal and noise levels per pixel in a focal
plane array for a symmetrical diffraction limited 10 meter diameter optical
telescope link operating over a range of 10 light years at the Halpha
wavelength of 656 nm.  Each pixel corresponds to the diffraction-limited
spot size.

You should note that in appreciating the implications of the relative
spectrum levels, it is not necessary to believe the ETIs have the capability
to employ beamwidths as small as 0.014 arcseconds, and still hit the target.
Rather, the signal level just represents an Effective Isotropic Radiated
Power (EIRP) of 2.3 X 10^18 W.

All the power in the 1 kW signal, which is sitting within the Halpha line,
is assumed confined to a 1 Hz bandwidth, and the optical detection bandwidth
is normalized to 1 Hz.  For every factor of 10 that the optical bandwidth is
increased, the noise levels rise by 10 dB.  Note that the Quantum Noise
level is unaffected by optical bandwidth - it only depends on the electrical
output bandwidth of the receiver.  The 1 kW transmitter looks like a 23rd
magnitude star, and has a detected power level of 1.6 X 10^-15 W (-148 dBW).

If the signal power is increased by a million times to 1 GW, the Carrier-To-
Noise Ratio (CNR) increases from 34 dB re 1 Hz to 94 dB re 1 Hz.  This
corresponds to a detected power at the receiver of 1.6 nW (-58 dBm).  This
is a reasonable amount of power, somewhat typical of powers at the end of a
long low-bandwidth fiber-optic link.  Assuming no signal-to-noise ratio
degradation due to planckian radiation or daylight, if the optical bandwidth
is increased to 30 MHz, the CNR will fall by 10.log(3 X 10^7), i.e., by
75 dB, producing a CNR = 19 dB.  Since a 10 dB CNR is required for
broadcast-quality NTSC/PAL F.M. video, this system is capable of sending
"real-time" TV signals over 10 light years!  The 1 GW transmitter looks like
an 8th magnitude star, just 2 magnitudes below naked-eye visibility.  A
solar-type star looks like a 2nd magnitude object at 10 light years, so a
1 GW transmitter is only 0.4% of the intensity of the star.

The high resolution spectrograph in the Hubble Space Telescope (HST) has a
resolution of 1 in 100,000, equivalent to a 0.0066 nm or 4.6 GHz bandwidth
at a wavelength of 656 nm.  The CNR of the 1 GW signal would fall to -3 dB
in this bandwidth, and would thus not be detectable in a 30 MHz post-
detection bandwidth.  Since all the noise sources may be treated as random
"white-noise", the monochromatic power in the signal could only be detected
by post-detection integration, where the SNR increases at rate proportional
to the square-root of the signal integration time.




                              SPECTRAL LEVEL GRAPH

Relative Levels Per Pixel
    |
    |
        |
  34 dB |___1 kW Signal               ***        1.6 X 10^-15 W______
        |                             *S*
        |                             *I*
        |                             *G*
   0 dB |___Quantum Noise_____________*N*________6.3 X 10^-19 W/Hz___
        |                             *A*
        |                             *L*
        |                             * *
 -32 dB |___Planckian Continuum_      * *      __4.0 X 10^-22 W/Hz___
        |                       \     * *     /
        |                        \    * *    /
 -52 dB |___Fraunhofer Dark Line  \___*_*___/    4.0 X 10^-24 W/Hz___
        |                        <----------->
        |       Halpha (656 nm) Bandwidth = 0.402 nm = 280 GHz
 -72 dB |___Daylight_____________________________4.0 X 10^-26 W/Hz___
        |
        |
        |
        |
        |
        |
        |
-154 dB |___Night________________________________2.5 X 10^-34 W/Hz___
        |
        |____________________________Halpha__________________________
                            Wavelength or Frequency


For you astronomers out there, you will know that Edwin Hirsch sells Halpha
"DayStar" filters with bandwidths of about 0.6 A (= 0.06 nm).  This is about
ten times the bandwidth of the HST spectrograph, so the CNR with Halpha
filters will be about ten times worse, i.e., about -13 dB.  Now in ground-
based astronomy, we don't have the situation that we can separate the
Planckian radiation from the aliens' star and transmitter.  So, what governs
the CNR or SNR is the Planckian radiation background not quantum noise.

For a 1 kW signal, the Signal-To-Planck Ratio (SPR) at 656 nm, considering
the 20 dB reduction in the continuum level, is 86 dB re 1 Hz.  For a 4.6 GHz
HST spectrograph bandwidth, the SPR = -11 dB.  Thus, with this bandwidth
there is no way that the 1 kW signal could make a spectral line appear on a
photographic plate with any sort of contrast.  For the Halpha filter, with
ten times the bandwidth, the SPR = -21 dB.  Obviously, if a 1 GW signal was
transmitted, the signal would produce a spectral line that would be clearly
visible above the Fraunhofer dark-line continuum.  However, there is a
complication that may prevent detectability or make it more difficult.  This
is the problem caused by Doppler shifts and chirps.

Any Doppler shift and chirp (drift) due to our relative motion with respect
to the alien star and planet would be common to both the Fraunhofer line and
the signal.  Thus, even though the line and signal would be displaced, the
signal would remain in the Fraunhofer line.  The same applies, of course, to
any Doppler shifts or chirps produced by our own local velocities or
accelerations along the line-of-sight.  However, if the aliens did not
compensate for their local Doppler shifts and chirp produced in our line-of-
sight with respect to their star, it is possible for the signal to move
outside the 20 dB trough formed by narrow Fraunhofer lines.  Typical Doppler
shifts of a transmitter in orbit about a star would be about +/-45 GHz,
while chirps would be at the insignificant level of about +/-9 kHz/s.  Since
the Halpha line is about 280 GHz wide, this would seem sufficiently wide to
keep the signal always within the trough.  A transmitter in synchronous
orbit about its alien planet might have a smaller Doppler shift of only
+/-4.7 GHz, but its Doppler chirp would be at the higher level of about
+/-340 kHz/s.  Of course with would like to assume that ETIs would help us
out by removing their Doppler chirps, and perhaps their Doppler shifts. 
From a communication prospective, it is much more important to remove local
Doppler chirp than Doppler shift, so the latter may not be removed.  For the
656 nm Fraunhofer line, it doesn't appear that either Doppler shifts or
chirps would significantly affect out ability to detect ETI signals with
relatively wideband incoherent filters.

Because I do not presently have knowledge of any fine-line structure within
dark Fraunhofer lines, it is not possible to say that such structure might
not interfere with the detection of ETI signals if we had much higher
spectral resolution, as could be provided by Fabry-Perot Interferometers, or
heterodyne techniques.

The conclusion is, that unless the ETI optical transmitters at nearby star
systems are extremely powerful, we would never detect these laser lines with
conventional optical telescopes, even within dark Fraunhofer lines.  So we
shouldn't expect to find such artificial lines in old spectrograph plates.
If we did, they would imply very tightly-beamed megawatt to gigawatt
transmitters.

As it is, it is not yet presently clear as to what are the "magic
wavelengths" in the visible region of the spectrum.  Unfortunately, there
don't appear to be efficient laser transitions at deep, and wide-band
Fraunhofer lines.  Thus, it may not be possible for ETIs to place their
signals at such wavelengths.  I will be conducting further investigations to
see what laser transitions in the visible spectrum might be useful for ETI
transmitters.  Stay tuned, without Doppler shift or chirp!


December 15, 1990
RADOBS.03
BBOARD No. 267


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* Dr. Stuart A. Kingsley                       Copyright (c), 1990        *
* AMIEE, SMIEEE                                                           *
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