Astronomy 920 Commissioning of the Prime Focus Imaging Spectrograph Meeting 5 Signal/ Noise Model; Planning Tool Ken Nordsieck Oct 7, 2005 Ast 920 Meeting 5

Signal/ Noise Signal: Noise units: detected photons Star = Flux * Atmos * Effective Area * Throughput * Bandpass * Exposure Ssky = Brtness * Atmos * Solid Angle of Res El * Effective Area * Throughput * Bandpass * Exposure Flux = (erg/s-cm2-Ang) / hν Brtness = (erg/s-cm2-arcsec2-Ang) / hν (also use for diffuse target) units: detected photons Noise N = sqrt (Star + Ssky + RON2) Oct 7, 2005 Ast 920 Meeting 5

Sky, Atmosphere For Details: Atmospheric Extinction: Sky Background: http://www.sal.wisc.edu/PFIS/docs/archive/protected/pfis/3170/3172AS0005-spec-sim-1.1.pdf Atmospheric Extinction: F(Earth) = F(above atmos) * 10-0.4 k(λ) mag extinction: k(Z, λ) = X k(Z=0, λ) airmass: X = 1/cos(Z) = 1.25 +/- 0.1 (Z = 37 +/-6) UV: Ozone; Blue: Rayleigh ; Red: aerosols Sky Background: Airglow: atomic, molecular, lines + pseudocontinuum (Na, O, O3, OH, etc). varies by 2x over solar cycle Zodiacal Light: ~ solar spectrum, lowest at ecliptic poles Moonlight: ~ solar spectrum. intensity varies with phase; color & intensity varies with Lunar angular elongation Seeing: Sutherland: 10%, 50%, 90% at zenith: 0.6, 0.9, 1.5” FWHM ~ FWHM (Zenith) * X0.8 Telescope imaging: 0.6”  10%, 50%, 90% image size: 0.9, 1.2, 1.8” Oct 7, 2005 Ast 920 Meeting 5

Effective Area, Telescope Throughput Effective Area: defined as area of illuminated primary Pupil: projection of exit stop (in payload) back on primary mirror: 11m diameter circle Central Obscuration: about 3 m circle: 83% Obscuration due to pupil falling off primary: mean over track ~85%: 67 m2 Telescope throughput Cmir - Primary: Al; Spherical Aberration Corrector: 4x “LLNL” multilayer: ~ 80% Oct 7, 2005 Ast 920 Meeting 5

Spectrograph Throughput slit * mirror * lenses * dispersor eff * CCD eff if assume gaussian seeing I = I0 e-(r/r0)^2, linear slit of width 2rs: throughput = erfc(rs / r0) 1 fold mirror: LLNL coating ~96% 16 air-glass interfaces: 3 different anti-reflection coatings ~83% grating efficiency: 50-90%; etalon 70% Oct 7, 2005 Ast 920 Meeting 5

Bandpass By Mode: Imaging: effective width of filter Grating Spectroscopy: Δλ correspond to slit Fabry-Perot: Δλ of etalon For sky, use arcsec2 corresponding to resolution element Imaging, Fabry-Perot: ΔΩ = area of seeing disk Grating Spectroscopy: ΔΩ = (2 rs) * (2 r0) To calculate readout noise, need number of bins corresponding to resolution element n = ΔΩ/(bx*by / (7.8 pix/arcsec)2) RON = RON/bin * sqrt(n * #readouts) Done! Oct 7, 2005 Ast 920 Meeting 5