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.
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.
Photon Transfer Curve
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
- \(\sigma_{\text{DN}}^2\): Variance in digital numbers
- \(K\): System gain ($e^-/\text{DN}$)
The slope in the shot-noise region gives conversion gain K in e-/DN.
- \(\sigma_{\text{read}}\): Readout noise
Dark-frame variance near zero signal estimates read noise.
- \(PRNU\): 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.