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Spectrometer Sensitivity


Here now is a calculation to determine the expected photon flux that we can detect in each pixel of a spectrometer.  See viewgraphs 9006-019, 9006-020, 9006-021 and 9006-022 for background information on how the values in the table were obtained.  The assumed ETI transmitter's EIRP is that which would be produced by a mean laser power of 1 GW transmitted through an array with a diffraction-limited performance equivalent to that of a 10 meter aperture telescope.


Parameter Value
Wavelength, nm 656
Frequency, Hz 4.57 x 1014
Effective Diameter, m 10
Antenna Gain, dB 153.6
Power, W 1 x 109
EIRP, W 2.29 x 1024
Range, L.Y. 100
Beam Diameter at Target, A.U. 0.43
Intensity, W/m2 2.04 x 10-13
Diameter, m 0.254
Antenna Gain, dB 121.7 dB
Signal, W 1.03 x 10-14
Signal Magnitude +13
Stellar Magnitude +7
Planckian Background, W/m2.Hz 5.48 x 10-26
Planckian Background, W/m2.nm 1.38 x 10-14
Spectrometer Resolution, nm 1.5
Planckian Background, W 1.05 x 10-15
Signal-To-Planck Ratio, dB 9.9
Telescope/Quantum Efficiency 0.20
Signal Photon Detection Rate, s-1 6800
Planckian Background Photon Detection Rate, s-1 693
Spectrometer Sensitivity, photons/count 86
Integration Time, s 10
Signal-To-Noise Ratio, dB 14.9


This table shows that under the assumption of a mean ETI EIRP of  2.3 x 1024 W, a small SCT will yield detectable signals with 1 second integration times.  Since SNR is proportional to the square root of the signal integration time, a 10 second integration time would yield a respectable SNR = 15 dB.  For a 2048 pixel linear CCD array, it would take 5.7 hours to scan between 350 nm and 900 nm.  Note that no account is taken of increased contrast ratio, typically about 10 dB, that may be found in deep Fraunhofer lines.

This suggests that it is indeed sensible to make the case that AMOSETI enthusiasts can place a commercial fiber optic-coupled CCD spectrometer in the focal plane of their telescopes with a reasonable hope that a strong laser beacon of mean EIRP of the order of two trillion trillion watts, would indeed be detectable.  This laser beacon could be a continuous wave signal or a pulsed signal of stated mean EIRP.  If the beacon consisted of 1 ns pulses repeated every second, the peak EIRP would be 2.3 x 1033 watts.  This is about seven orders of magnitude brighter than the sun.



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