Motivation: The FICNH EYE takes hyperspectral images of the ground. At an altitude of 500km, it is supposed to resolve plots of land measuring 100m by 100m. One can appreciate that very little light intensity reaches the satellite from that plot of land, especially since this light is then spread into a spectrum.

e.g., solar constant on earth = 1000W/m^2, reflectance = 0.3 , Area = 100m * 100m

→ reflected light on one ground sample is P = 3MW.

But this is spread over 2pi steradians (one hemisphere) and at a distance of R=500km,

P_received = P/(2 pi R^2) = 2 uW (microWatts!) of “white light”

And this is without applying atmospheric losses on the way up, and without applying dispersion (i.e., this number is the sum of energies for all wavelengths, the energy in the range 900nm-1700nm will be much lower. Possibly in the nano-Watts)

There are detectors that are able to measure nano-Watts, but they have to be carefully designed to mitigate noise. A detector, typically made from semiconducting materials, works by absorbing photons and generating “photoelectrons”. Photons with energies that are equal to (or slightly greater than) the band gap of the photosensitive material can promote an electron from the valence band to the conduction band. Electrons in the conduction band can be then transferred to a capacitor for storage; the voltage on the capacitor can be digitized to yield a measurement of brightness. However, thermal vibrations can impart sufficient energy to electrons to hop-up to the conduction band. Thermally generated electrons are generated randomly and do not correlate with the signal we seek to measure and are therefore considered as “noise”. This is why photodetectors are typically cooled during operation - for every 5-9 degree Celsius of cooling, the noise goes down by a factor of two or so.

So, they key question is: will the signal reaching our camera be larger than the noise?

Our team worked on an SNR calculation previously, but it has several flaws and is out of date: FIN-Signal-to-NoiseRatioAnalysis-240822-1854-336.pdf - Google Drive They took notes on their calculations here: Signal to Noise Ratio Analysis - Working Research Document - Google Docs

There are several papers on the subject: CCD Noise Sources and Signal-to-Noise Ratio

• slow but quality explanation of noise. a bit too verbose. (don’t read completely)

Comparison of SNR image quality metrics for remote sensing systems

• derivation of Signal to Noise ratio formula, consideration of nose sources. Section 1 & 2 useful

Optical Design of a Miniaturized Airborne Push-Broom Spectrometer

• Section 3 discusses SNR. Read also section 2.

Signal-to-Noise Ration Evaluation of Luojia 1-01 Satellite Nighttime Light Remote Sensing Camera Based on Time Sequence Images

• haven’t read this, looks useful

See also: Chapter 1 in Pedrotti