photon noise
Photon Noise
Photon noise is a type of shot noise that results from the inherent statistical variation in the arrival rate of photons in a CCD. The time interval between photons arriving at the Detector follows a Poisson distribution, so the photon noise is equal to the square root of the number of incident photons. When the photon signal is small, the photon noise is large compared to the photon signal, resulting in a decrease in the signal-to-noise ratio of the system. Due to their different growth rates, however, the photon noise becomes less important relative to the photon signal when the number of photon signals becomes large. Although the amount of photon noise increases as more light hits the Detector, the photon signal increases at a greater rate, resulting in an increased signal-to-noise ratio. It is important to note that at small signal levels dark noise is the dominant noise source, but at large signal levels photon noise dominates. In general, the term "shot noise" is often used instead of photon noise.
shot noise
Shot Noise
Shot noise is a statistically generated variation that exists in any discrete random system. Types of shot noise associated with spectrometers are photon noise and dark noise.
SNR
Signal to Noise Ratio
The signal-to-noise ratio (SNR) is defined as the ratio of signal strength to noise strength at a specific signal level—so it will vary from measurement to measurement. Due to photon noise, the noise usually grows as a function of the signal, and the SNR function is actually a plot of individual SNR values versus that signal for which they are acquired. Spectrometer SNR values reported in Ocean Optics data sheets are the maximum possible SNR values (obtained at Detector saturation). It is assumed that the SNR response curve of each pixel is the same.
The specific measurement is as follows: When the light source is selected so that the spectral peak is saturated at the lowest integration time or integration time well below the thermal noise limit (the spectrum still needs to have a region below 0 counts (count value) or thereabouts ); To calculate the signal-to-noise ratio, you need to take 100 scans without light incident, calculate the average baseline value of each pixel, and then take 100 scans with light incident, calculate the average output value of each pixel value and standard deviation; then the signal-to-noise ratio is given by:
SNRρ = (S – D)/σρ
here
SNR=signal-to-noise ratio
S = the average spectral response intensity of the sample (with light incident)
D = mean value of the dark spectrum (no light incident)
σ = standard deviation of the sample (with incident light)
ρ = number of pixels
To get a complete SNR vs. signal plot, plot the calculated SNRρ values (noise) and Sρ – Dρ values (signal). This would cover a wide range of peaks (from the spectral dark state to near saturation). Since all cells have the same response curve, the data for SNR and signal maps can come from different cells. Since photon noise is the main source of noise at large values of the signal, a satisfactory spectrogram should resemble the graph of y = √x.
Note that applying different types of signal averaging methods can improve the signal-to-noise ratio. With time-based signal averaging, the signal-to-noise ratio increases with the square root of the number of spectral scans. For example, if the signal-to-noise ratio is 300:1, if 100 scans are averaged, the signal-to-noise ratio will become 3000:1. In spatially based signal averaging, the signal-to-noise ratio increases by the square root of the number of cells averaged.
While these methods are useful for obtaining precise data, it can confound comparisons of different spectrometers. Ocean Optics gives SNR values for all spectrometers without signal averaging. Some of our competitors use signal averaging to artificially increase the signal-to-noise ratio of some poor quality spectrometers.
