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Photon Transfer Curve (PTC)

Visualize the fundamental noise-vs-signal relationship to extract read noise, conversion gain, full well capacity, and PRNU from a single log-log plot.

Photon Transfer Curve (PTC)

Visualize the relationship between signal and noise to extract read noise, conversion gain, FWC, and PRNU in a single log-log plot.

Read Noise Floor
5.0 e−
SNRmax
40.0 dB
Shot/Read Crossover
25 e−
PRNU/Shot Crossover
10000 e−
1310301003001k3k10k1310301003001000FWCTotalReadShotPRNUSignal (e-)σ (e−)

Model scope

Use this browser tool for intuition, relative trends, and design-space exploration. Its local simplified model is not a substitute for RCWA/FDTD sign-off, silicon calibration, or vendor process data.

Physics Notes

Photon Transfer Curve

Plain-English Intuition

If you measure how noisy a pixel is at many different brightness levels and plot it on log-log axes, three distinct regions appear: a flat read-noise floor (in the dark), a 1/2-slope photon shot-noise region (mid tones), and an upturning PRNU region (bright). This shape is so consistent across silicon pixels that engineers use it as a fingerprint to reverse-engineer the sensor gain, read noise, and full-well from real measurements.

PTC uses the relationship between mean signal and variance to estimate conversion gain, read noise, full well, and PRNU.

Assumptions

  • The PTC uses standard mean-variance relationships with shot noise, read noise, PRNU, and saturation regimes.
  • Gain is treated as a scalar conversion between electrons and digital numbers.
  • Column effects, ADC quantization details, black-level instability, and temporal processing are not explicitly solved.

Outputs

  • Mean-variance curve, read-noise floor, conversion gain, shot-noise slope, PRNU region, and saturation region.
  • A regime map that separates read-noise limited, shot-noise limited, fixed-pattern limited, and saturated operation.

Validation Example

  • In the shot-noise region, variance should grow approximately linearly with mean signal.
  • At low signal, raising read noise should lift the variance floor without changing the high-signal shot slope much.

Core Equations

Shot-noise region
$$\sigma_{\text{DN}}^2 \approx \frac{\mu_{\text{DN}}}{K}$$
  • \(\sigma_{\text{DN}}^2\): Variance in digital numbers
  • \(K\): System gain ($e^-/\text{DN}$)

The slope in the shot-noise region gives conversion gain K in e-/DN.

Read noise
$$\sigma_{\text{read}, e^-} = K \cdot \sigma_{\text{read}, \text{DN}}$$
  • \(\sigma_{\text{read}}\): Readout noise

Dark-frame variance near zero signal estimates read noise.

PRNU region
$$\sigma_{\text{total}}^2 \approx \sigma_{\text{shot}}^2 + (PRNU \cdot S)^2$$
  • \(PRNU\): PRNU coefficient

At high signal, multiplicative non-uniformity bends the curve upward.

Model Interpretation

  • The log-log PTC separates read-noise, shot-noise, and saturation regions.
  • Linearity and flat-field quality affect gain extraction.
  • PTC is a measurement method; the simulator shows idealized trends.

Curve Regions

  • At low signal, variance flattens near the read-noise floor.
  • In the shot-noise region, variance grows linearly with mean signal, enabling conversion-gain extraction.
  • Near saturation, clipping and nonlinearity break the simple variance relationship.

Acquisition Checklist

  • Use pairs of flat frames at each exposure so temporal noise can be separated from spatial non-uniformity.
  • Subtract black level and verify linear exposure spacing before fitting gain.
  • Avoid saturated and strongly non-linear points when estimating the shot-noise slope.

Known Missing Physics

  • The idealized PTC does not include ADC quantization structure, row/column noise, or temporal drift.
  • PRNU and DSNU extraction depends on flat-field uniformity and dark-frame stability.
  • Dual conversion gain or HDR sensors require segmented PTC interpretation.