SNR Calculator
Compute the signal-to-noise ratio for a CMOS image sensor pixel under various operating conditions. Understand the interplay between quantum efficiency, pixel size, noise sources, and scene illumination.
SNR & Photon Transfer Curve Calculator
Calculate signal-to-noise ratio and related metrics for a CMOS pixel given sensor parameters.
Photon Transfer Curve (PTC)
SNR vs Illuminance
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.
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Pixel Signal-to-Noise Model
Imagine trying to hear someone whisper in a noisy room — what matters is the whisper compared to the background noise, not the whisper alone. In a pixel, the signal is the electrons created by light, while the background noise comes from random photon arrivals, thermal dark current, and the readout circuit. SNR tells you how clearly the image rises above the noise floor.
SNR follows from the signal charge divided by the root-sum-square of shot, dark, read, and fixed-pattern noise terms.
Assumptions
- Signal and noise are expressed in electrons before ADC conversion unless a conversion gain is explicitly applied.
- Shot noise, dark-current noise, read noise, and PRNU are combined as independent variance terms.
- Spatial image processing, temporal denoise, demosaic, and tone mapping are outside the scalar SNR model.
Outputs
- SNR, dynamic range proxy, noise-regime breakdown, and full-well or read-noise bottleneck indicators.
- A quick comparison of how QE, pixel area, exposure, dark current, read noise, and full well move image-quality limits.
Validation Example
- With read noise and dark current set near zero, the curve should approach the photon limit $SNR\approx\sqrt{S}$.
- At very low signal, increasing read noise should move the SNR floor almost directly.
Core Equations
- \(S\): Collected signal (electrons)
- \(\Phi_{\text{ph}}\): Incident photon flux (photons/area/time)
- \(A_{\text{px}}\): Pixel area
- \(t_{\text{exp}}\): Integration time
Signal scales with photon flux, pixel area, exposure time, and quantum efficiency.
- \(\sigma^2\): Total noise variance (electrons squared)
- \(D\): Dark current (electrons/s)
- \(\sigma_{\text{read}}\): RMS read noise (electrons)
- \(PRNU\): Photo-response non-uniformity factor
Shot and dark noise are Poisson terms; read and PRNU terms are added in variance.
- \(\sigma\): Total noise (RMS electrons)
The dB form is useful for comparing operating points across illumination levels.
Model Interpretation
- At low signal, read noise dominates; at high signal, photon shot noise dominates.
- Full well capacity clips signal before the formula can continue to improve.
- PRNU is signal-proportional, so it matters most in bright regions.
Regime Map
- Read-noise limited: when $S \ll \sigma_{\text{read}}^2$, increasing exposure or QE gives nearly linear SNR improvement.
- Shot-noise limited: when $S$ dominates the variance, $SNR\approx\sqrt{S}$, so doubling signal improves SNR only by $\sqrt{2}$.
- PRNU limited: at bright levels, $(PRNU\cdot S)^2$ can cap SNR even when read noise is excellent.
Calibration Inputs
- Estimate conversion gain and read noise from photon-transfer data before comparing electron-domain SNR.
- Use dark frames at temperature to calibrate $D$; dark current can change exponentially with temperature.
- Measure PRNU from flat fields after removing DSNU and illumination shading.
Known Missing Physics
- The formula assumes independent noise terms; row noise, column noise, flicker noise, and ADC nonlinearity may violate this.
- Spatial processing, demosaic, denoise, and tone mapping can change perceived image SNR after sensor readout.
- Full-well, saturation, blooming, and dual-conversion-gain switching need a piecewise model beyond this compact equation.