1. 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

2. 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

3. Sky, Atmosphere For Details: Atmospheric Extinction: Sky Background:
Atmospheric Extinction:
F(Earth) = F(above atmos) * k(λ)
mag extinction: k(Z, λ) = X k(Z=0, λ)
airmass: X = 1/cos(Z) = / (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

4. 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

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

6. 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