45th International Astronautical Congress

This extract is from the theory section of the paper presented at the 45th International Astronautical Congress. It indicates how extremely high EIRPs are possible if diffraction-limited performance is assumed for the aperture equivalent of a 10 meter telescope operating in the visible regime and if a transmitter laser beam of 1 GW mean power is converted into attention-getting beacon pulses of 1 ns duration that repeat once every second.

Kingsley, S.A., "Design for an Optical SETI Observatory", 45th International Astronautical Conference, 23rd Review Meeting of the Search for Extraterrestrial Intelligence (SETI), SETI: Science and Technology, Jerusalem, Israel, 9-14 October 1994.

Abstract 4

Peak Power:

The relationship between peak power P_pk and average power for a pulsed laser is given by:

        P_av
P_pk = -----  W                                                                             (1)
       Tau.r 

where  Tau  = pulse width (1 ns),
       r    = pulse repetition rate (1 Hz),
       P_av = average power (1 GW).


Substituting the values in parentheses for a pulsed ETI laser beacon system with a 1 Hz
repetition rate, we find that:

P_pk = 10^18 W.


Diffraction-Limited Telescope Gain:

The gain of a diffraction-limited dish or telescope is given by:

     pi.D
G = [----]^2                                                                                (2)
      Wl

where  D  = diameter of transmitter aperture (10 m),
       Wl = wavelength (550 nm).


Substituting the values in parentheses for an ETI uplink transmitting at the center of the
human photopic response, we find that:

G = 155.1 dB.


Effective Isotropic Radiated Power:

The Effective Isotropic Radiated Power is the power that the transmitter appears to have if
it radiated isotropically.  It is given by:

EIRP = P.G  W                                                                               (3)



Substituting the values for P and G given above, we find that:

EIRP_laser = 3.2 X 10^33 W.


For a star like the sun:

EIRP_star = 3.9 X 10^26 W.


Note that EIRP_laser is the peak EIRP of the laser, while EIRP_star is the mean EIRP of
the star.


Received Intensity:

The intensity of the received signal and stellar background noise is given by:

      EIRP 
I = --------  W/m^2                                                                         (4)
    4.pi.R^2

where R = range (9.461 X 10^16 m).


Substituting the values in parenthesis for a range of 10 light years, we find that just
outside the atmosphere:

I_laser = 2.8 X 10^-2 W/m^2.

I_star = 3.5 X 10^-9 W/m^2.


Detected Power:

The optical power appearing at the photodetector is given by:

                       Pi.d^2  
S = T_atm.A_eff.F_eff.[------].I  W                                                         (5)
                         4  

where  T_atm = atmospheric transmission (0.25),
       A_eff = telescope aperture efficiency (0.5),
       F_eff = optical filter efficiency (0.5),
       d     = diameter of receiver aperture (0.254 m).


For the ETI laser:  S_laser = 8.9 X 10^-5 W.

For a solar-type star:  S_star = 1.1 X 10^-11 W.


Magnitude:

For a solar-type star and a laser centered on the human visual response, the apparent
magnitude may be expressed in terms of its intensity I:

m = -[19 + 2.5log(I)]                                                                       (6)

where  I_laser = 2.8 X 10^-2 W/m^2,

       I_star  = 3.5 X 10^-9 W/m^2.


Substituting the above values for a range of 10 light years, we find that:

m_laser = -15.

m_star = 2.


During each brief pulse, the laser is brighter than the ETIs' star by a factor of
nearly 10 million!


Photon Detection Rate:

The photon detection rate is given by:

    Eta.S 
N = -----                                                                                   (7)
     h.f

where  Eta = photodetector quantum efficiency (0.17),
       h   = Planck's constant (6.63 X 10^-34 J.s),
       f   = optical frequency (5.45 X 10^14 Hz).

Substituting the values in parentheses for a center wavelength of 550 nm, we find
that the "signal" photon detection rate N_laser:

Signal = 44,000 counts per pulse.

For a solar-type star, we find that the stellar background "noise" photon detection
rate N_star:

Noise = 6,000,000 counts per second.


Conclusions:

The "signal" is buried in the noise and the ratio between the "signal" and "noise"
photons is pproximately -20 dB.  However, during each one nanosecond laser pulse,
the SNR is positive and nearly 70 dB!  This is the very important benefit of searching
for very short pulses in adjacent time slots corresponding to the expected pulse
duration, even if the "signal" consists of only one or two detected photons per pulse.
Another important benefit is that knowledge of the "magic frequency" is not required.

Note that the National Ignition Facility upgrade to the NOVA laser at the Lawrence
Livermore Laboratories will increase the peak power output from 10^14 W to
10^15 W, albeit at only one pulse per day.  By the year 2002, we humans, over a
period of 40 years, will have increased peak laser output powers on this planet from
3 kW to 10^15 W.  How long will it take to increase the peak output power from
10^15 W at one pulse per day to 10^18 W at one pulse per second?  The answer,
of course, is no time at all on the cosmic time scale.