CCD Quantum Efficiency Calculator Formula

Understand the math behind the ccd quantum efficiency calculator. Each variable explained with a worked example.

Use the CCD Quantum Efficiency Calculator

Formulas Used

Photoelectrons per Pixel

electrons = photon_flux * pixel_area * quantum_efficiency * exposure

Shot Noise

shot_noise = sqrt(photon_flux * pixel_area * quantum_efficiency * exposure)

Variables

VariableDescriptionDefault
photon_fluxPhoton Flux(photons/m2/s)10000000000
pixel_areaPixel Area(m2)1.406e-11
quantum_efficiencyQuantum Efficiency0.8
exposureExposure Time(s)60

How It Works

CCD Quantum Efficiency and Electron Count

Quantum efficiency (QE) is the fraction of incoming photons that produce a detectable photoelectron in the sensor.

Formula

N_e = F * A * QE * t

  • *F* = photon flux (photons per m2 per second)
  • *A* = pixel area
  • *QE* = quantum efficiency (0 to 1)
  • *t* = exposure time

    • Shot noise follows a Poisson distribution: sigma = sqrt(N_e).

    Worked Example

    3.75 um pixels (A = 1.406e-11 m2), QE = 0.80, flux = 1e10 ph/m2/s, 60 s exposure.

    photon_flux = 10000000000pixel_area = 1.406e-11quantum_efficiency = 0.8exposure = 60
    1. 01N_e = F * A * QE * t
    2. 02N_e = 1e10 * 1.406e-11 * 0.8 * 60
    3. 03N_e = 0.1406 * 0.8 * 60
    4. 04N_e = 6.749 electrons
    5. 05Shot noise = sqrt(6.749) = 2.60 e-

    Frequently Asked Questions

    What is a good quantum efficiency?

    Modern scientific CCDs reach 90% or higher at peak wavelength. Consumer CMOS sensors typically achieve 50-80%.

    Does QE vary with wavelength?

    Yes, significantly. QE peaks in the visible or near-infrared and drops in the blue and UV. Spectral QE curves are important for filter selection.

    What limits detection of faint objects?

    Read noise at short exposures and sky background shot noise at long exposures. Higher QE helps in all regimes.

    Ready to run the numbers?

    Open CCD Quantum Efficiency Calculator