
Laser Visibility at Intensities Suitable forInterstellar Communications TheoryRadobs 09Preface: This document (RADOBS.9) is in support of the discussion document (RADOBS.8). Handy conversions: 1 Astronomical Unit (A.U.) = 1.496 X 10^11 m 1 Light Year (L.Y.) = 9.461 X 10^15 m 1 Light Year (L.Y.) = 63,242 A.U. 1 Parsec (psc) = 3.26 L.Y. The relationship between Apparent Stellar Magnitude (m) and the brightness or intensity of a star may be expressed in the form: m = [19 + (2.5).log(I)] (1) where I = received intensity (W/m^2). The threshold for nakedeye visibility is m = +6. The Sun's total output (EIRP) = 3.90 X 10^26 watts. Here are several intensities and corresponding magnitudes as a function of range R: At R = 1 A.U. (1.496 X 10^11 m): I = 1.39 kW/m^2 m = 26.8 At R = 10 L.Y. (9.461 X 10^16 m): I = 3.48 X 10^9 W/m^2 m = +2.2 At R = 100 L.Y. (9.461 X 10^17 m): I = 3.48 X 10^11 W/m^2 m = +7.2* At R = 1000 L.Y. (9.461 X 10^18 m): I = 3.48 X 10^13 W/m^2 m = +12.2* * Not visible to the naked eye.  With no allowance for the Fraunhofer dark line absorption, the Planckian (black body) starlight continuum level (spectral energy density) is given by: 2.PI.h.f^3r^2 Npl =  W/m^2.Hz (2) c^2[e^(h.f/k.T)  1]R^2 where h = Planck's constant (6.63 X 10^34 J.s), c = velocity of light (3 X 10^8 m/s), Wl = wavelength (656 nm), f = frequency (c/Wl = 4.57 X 10^14 Hz), k = Boltzmann's constant (1.38 X 10^23 J/K), T = temperature (5778 K), r = radius of star (6.96 X 10^8 m), R = distance of receiver (10 L.Y. = 9.461 X 10^16 m). At R = 1 A.U.: Npl = 2.19 X 10^12 W/m^2.Hz At R = 10 L.Y.: Npl = 5.47 X 10^24 W/m^2.Hz  For the purposes of this analysis we shall assume a fully (uniformly) illuminated aperture and not a beam with a Gaussian intensity profile, as might be obtained from a TEMoo singlemode laser. The diffraction limited halfpower (3 dB) beamwidth is given by: (57.3).Wl THETA =  degrees (3) d where d = diameter of telescope (10 m). THETA = 0.0135 arc seconds  The halfpower (3 dB) beam diameter is given by: (1.22).Wl.R D =  meters (4) d At R = 1 A.U.: D = 12 km At R = 10 L.Y.: D = 7.57 X 10^9 m = 0.0506 A.U.  The gain of an antenna is given by: 4.PI.At G =  (5) Wl^2 where At = area of transmitting telescope mirror (78.5 m^2). G = 153.6 dB  For a mean transmitted power Pt, the Effective Isotropic Radiated Power (EIRP) is given by: EIRP = G.Pt Watts (6) For Pt = 1 GW: EIRP = 2.29 X 10^24 W  The intensity of the beam at the receiver is given by: EIRP I =  W/m^2 (7) 4.PI.R^2 At R = 1 A.U.: I = 8.1 W/m^2 At R = 10 L.Y.: I = 2.04 X 10^11 W/m^2  The signal power received by a telescope is given by: Ps = I.Ar Watts (8) where Ar = area of receiving telescope mirror (78.5 m^2). At R = 1 A.U. Ps = 0.64 kW Phew!! At R = 10 L.Y.: Ps = 1.60 X 10^9 W  The effective system noise temperature of an optical receiver may be expressed in the form: h.f Teff =  K (9) eta.k where eta = photodetector quantum efficiency (0.5). Teff = 43,900 K  The CarrierToNoise Ratio in a perfect shot (quantum) noise limited optical heterodyne system is given by: eta.Ps CNR =  (10) hfB where Ps = received optical power (1.6 nW), B = Intermediate Frequency bandwidth (30 MHz). At R = 10 L.Y.: CNR = 19 dB There was no need to do a calculation for R = 1 A.U. since the optical receiver went up in smoke! Hence, CNR effectively equal to zero! December 23, 1990 RADOBS.09 BBOARD No. 277 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 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) 2587402 . . . . . . . . . . . * * skingsle@magnus.ircc.ohiostate.edu .. .. .. .. .. * * CompuServe: 72376,3545 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
