1. N A S A G O D D A R D S P A C E F L I G H T C E N T E R I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y APS Formation Sensor ELECTRO-OPTICAL Eric Young 15 March 2002

2. Electro-Optic I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Eric Youngp215 March 2002APS Formation Sensor SNR Calculation (Laser Beacon) Wavelength632.8 nm Laser Power (W)0.003 Beam Diver (rad)0.003 Target Distance(m)50000 Telesc Diam(m)0.1 Telesc Area(m 2 )7.854E-03 Beam Area(m 2 )1.767E+04 Optics Thru8.858E-01 Filter-Bandpass5.000E-01 Filter(ND=0.5)3.162E-01 Pixels Lit1.963E+01 QE8.000E-01 1/hc5.028E+24 Lambda(m)6.328E-07 Sig Rate(phot/s)2.421E+07 Int Time(s)1.000E-03 Signal(photons)2.421E+04 SNR 1.556E+02

3. Electro-Optic I n s t r u m e n t S y n t h e s i s a n d A n a l y s i s L a b o r a t o r y Eric Youngp315 March 2002APS Formation Sensor Signal to Noise SIGNAL TO NOISE RATIO (per pixel) CALCULATION OVERVIEW For the Laser Beacon we first calculate the diameter of the Laser Beam at the tracker, which is just the beam divergence in radians times the distance. We then calculate the area of the beam at the tracker. The ratio of this area and the telescope area is multiplied by the Laser Power to yield the received power. This received power is then propagated thru the system by multiplying by the next three factors: 6 element imager(0.98 each), bandpass filter, and neutral density filter. The fourth factor to be multiplied is the quantum efficiency of the detector QE. The number of pixels lit is the circle circumscribed by a 5X5 pixel array. The net power is divided by this factor to yield the per pixel power received. The power is just converted to photons per second by the next two factors. Lambda is the HeNe wavelength of 632.8nm. With a millisecond integration time, the received photon number S is computed; and the signal to noise ratio SNR is computed as the square root of S in this photon noise limited case.