In case it is of use to others I've created this calculator. The example buttons on the right hand side of the calculator can be used to see the exact numbers used for the four image sensor that were compared in the previous blog post.
Examples
Reference Lux Values[3]
F/#: the F-number of the lens
Scene Reflectivity: the proportion of light reflected by an object in scene
Average Quantum Efficiency: the average proportion of light (photons) converted to signal (electrons) by the image sensor
Reference Lux Values[3]
| Illuminance (lux) | Surfaces illuminated by |
| 0.0001 | Moonless, overcast night |
| 0.05–0.36 | Full moon on a clear night |
| 20–50 | Public areas with dark surroundings |
| 100 | Very dark overcast day |
| 320–500 | Office lighting |
| 400 | Sunrise or sunset on a clear day |
| 1000 | Overcast day |
| 10,000–25,000 | Full daylight |
| 32,000–100,000 | Direct sunlight |
F/#: the F-number of the lens
Scene Reflectivity: the proportion of light reflected by an object in scene
Average Quantum Efficiency: the average proportion of light (photons) converted to signal (electrons) by the image sensor
How is the calculation performed
Estimating the read noise
Where read noise statistics are not provided by the manufacturer they can be estimated using the full well capacity and the dynamic range.The dynamic range is calculated by dividing the maximum signal, which is the full well capacity, by the read noise.[1]
`drg = 20*log_10({fwc}/{rn})`
where:
`drg` is the dynamic range `(dB)`
`fwc` is the full well capacity `(e^-)`
`rn` is the read noise `(e^-)`
If the full well capacity is not stated in the datasheet it is usually possible to calculate it by using the maximum SNR figure often provided by manufacturers. This is the maximum SNR, which occurs when the signal is equal to the full well capacity.
`SNR_{max} = 20*log_10({fwc}/{tn})`
where:
`tn` is the total noise `(e^-)`
It is usually okay to assume that the total noise is dominated by the shot noise at the maximum signal.
`SNR_{max} \approx 20*log_10({fwc}/sqrt(fwc)) \approx 20*log_10(sqrt(fwc))`
Estimating the signal
To calculate the SNR it is necessary to estimate the number of electrons generated in each pixel during the exposure. To estimate the number of electrons generated, an equation was taken from the paper “When Does Computational Imaging Improve Performance?”[2].Note: This calculation is an approximation but should be of the right order of magnitude.
`J = 10^15 (F//#)^{-2}tI_{src}R q\Delta^2`
where:
`J` is the number of generated electrons
`F//#` is the f-number of the lens
`t` is the exposure time
`I_{src}` is the incident illuminance in lux
`R` is the average reflectivity of the scene
`q` is the quantum efficiency of the sensor
`\Delta` is the size of a pixel in metres
where:
`J` is the number of generated electrons
`F//#` is the f-number of the lens
`t` is the exposure time
`I_{src}` is the incident illuminance in lux
`R` is the average reflectivity of the scene
`q` is the quantum efficiency of the sensor
`\Delta` is the size of a pixel in metres
Estimating Quantum Efficiency
For the values of the quantum efficiency (QE) it is usually necessary to estimate them from the charts put in the datasheets. For colour sensors, since each colour channel blocks approximately ⅓ of the photons, the QE can be approximated by taking the peak QE for the three colour channels and dividing by three.References
[2] When Does Computational Imaging Improve Performance?
[3] https://en.wikipedia.org/wiki/Lux
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