Exposure time calculator
Estimate the exposure time, signal-to-noise ratio or limiting magnitude for the TDT array, for any number and size of unit telescopes and spectral resolution.
Solve for
Telescope, Observation Parameters & Results
Telescope Configuration
Observation
Spectrograph
Exposure Time
—
Total Collecting Area
—
m²
Equivalent Diameter
—
m
Fibre Diameter
—
arcsec
Diffraction Limit
—
arcsec
Source Photon Rate
—
photons/s per telescope
Parameter Space Explorer
Assumptions & Equations
Fixed Parameters
Central wavelength (λ)
550 nm
Fibre diameter
1.5 × diffraction limit
Detectors
User-defined read noise
Pixels per res. element
2.5 (N_PIX)
Noise regime
Mixed (Background + Read Noise)
System throughput (η)
15%
Sky brightness (μsky)
22.0 mag/arcsec²
AB zero-point flux (φ₀)
1004.7 γ/s/cm²/Å
Equations Used
Signal-to-Noise
SNR = S · √(N) · t / √(t(S + Ssky) + Npix · RN²)
— per resolution element
Source photon rate
S = φ₀ · 10−0.4m · Atel · Δλ · η
— photons/s per telescope
Sky photon rate
Ssky = φ₀ · 10−0.4μ · Ωfibre · Atel · Δλ · η
— μ = sky brightness per arcsec²
Diffraction limit
θDL = 1.22 · λ / D
— in radians, converted to arcsec
Fibre angular size
θfibre = 1.5 · θDL , Ωfibre = π (θfibre/2)²
— solid angle on sky
Collecting area
Atel = π (D/2)²
— per unit telescope, in cm²
Bandwidth
Δλ = λ / R
— Ångström per resolution element
Exposure time
t solves: S²·N·t² - SNR²·(S+Ssky)·t - SNR²·Npix·RN² = 0
— quadratic solution for t