CCD Photon Transfer Curve Lab (2D): Gain, Read Noise, Dark Current and Full Well

Presets

Live readouts

Graphs

Photon transfer curve: variance against mean signal (log-log)

Pixel signal to noise against exposure time

Linearity: mean signal against exposure time

Numerical checks

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How to use

The flat-field frame, the bias frame and the histogram show one simulated exposure; they refresh with new photon noise every half second.
The first graph is the photon transfer curve: orange dots are measured flat pairs at 22 exposure levels, the blue line is theory. The slope of the straight part is 1 / gain; the left plateau is the read noise.
Raise the temperature to see dark current build up; raise the read noise to lift the left of the curve; lower the full well to see saturation.
Compare the true gain and read noise with the values the lab recovers from the PTC and from a bias pair.
Keys: Space pauses the noise refresh, R resets.

The science

A CCD turns light into electrons, stores them in potential wells (pixels) and moves the charge packets row by row to an output amplifier, where it becomes a voltage and then a number from the analog-to-digital converter. The photon transfer curve (PTC, Janesick 1970s) measures how noisy a pixel is as a function of its signal, and from that gives the gain, the read noise and the full well without any special equipment, using flat-field exposures.

Var_ADU = S_ADU / g + (σ_r / g)² + 1/12 + (p S_ADU)²

Here S is the mean signal in ADU, g the gain in electrons per ADU, σ_r the read noise in electrons, 1/12 the ADC quantisation term and p the pixel response non-uniformity. Photon arrival is Poisson (variance equals mean charge), so on a log-log plot the shot-noise region has slope 1/2 in noise and slope 1 in variance, and the line is Var = S/g: its slope gives 1/g. The flat part at low signal is the read noise, and where the curve breaks down is the full well. The p S term (slope 2 in variance) is a fixed pattern: subtracting two flats removes it, so the page uses the flat-pair method, Var = Var(F1 - F2) / 2.

SNR = S / √( S + D + σ_r² ), D = D₂₀ · 2^{(T - 20)/6} t

Dark current D doubles roughly every 6 degrees C of heating, which is why science cameras are cooled. Dynamic range is full well divided by read noise. Above the linear knee the collected charge is modelled as rolling off exponentially to the full well, which is why the measured PTC bends over.

Honest simplifications. Each pixel is independent (no charge-transfer inefficiency, blooming, cosmic rays, hot pixels, amplifier glow, 1/f noise or bias gradients). Read noise is Gaussian and independent of the signal. Dark current is uniform and doubles every 6 C by a rule of thumb (real chips differ). The gain is a single number for the whole chip and the ADC has ideal bins. The PTC is measured on a 64 by 64 patch of simulated pixels (an error of about 2-3 percent in each variance), so the fitted gain scatters by a few percent just like a real measurement. Quantities are not tied to a specific detector.