Etendue & Radiometry Calculator

Calculate collection geometry solid angles, model optical etendue limits, and construct detailed noise budgets to estimate detector Signal-to-Noise Ratio (SNR).

Parameters

Wavelength (λ, nm)

Optical Power (P)

Transmission (τ, %)

Quantum Efficiency (QE, %)

Integration Time (t_int)

Precision Mode

Outputs Readout

Photon Rate2.6782e+15 photons/s

Electron Rate2.1425e+15 e⁻/s

Photoluminescent Current0.00034327 A

Total Photons (t_int)2.6782e+15

Total Electrons (t_int)2.1425e+15

Etendue & Noise Equations Theory

Etendue Throughput

G = n^2 A \Omega

Calculates the physical light-gathering capability. In any lossless optical system, etendue cannot be increased.

Solid Angle Fraction

\Omega = 2\pi(1 - \cos\alpha)

Calculates solid angle exactly. Small angle approximation ( $\Omega \approx \pi D^2 / 4z^2$ ) exhibits errors at low distance-to-aperture ratios.

Signal-to-Noise Ratio (SNR)

\mathrm{SNR} = \frac{N_e t_{\mathrm{int}}}{\sqrt{N_e t_{\mathrm{int}} + N_b t_{\mathrm{int}} + I_{\mathrm{dark}} N_{\mathrm{pix}} t_{\mathrm{int}} + \sigma_{\mathrm{read}}^2 N_{\mathrm{pix}} N_{\mathrm{frames}}}}

Computes the noise budget of CCD/CMOS detectors, including shot noise, background, dark current, and read noise contributions.