Background fluctuation limit

The background limit for a photon detector depends upon the spectral distribution of the target, the spectral distribution of the background, the spectral response of the detector, the temperature of the detector, the mode of 

Here Tb is the temperature of the background and M(v, Tg) is the Planck distribution function in terms of Tg instead of T.  

The modulation frequency dependence of the mean square fluctuations in the rate of generation of current carriers due to the arrival of detectable photons 

The rate of generation of carriers excited by photons from a monochromatic source of power g incident on the detector is given by 

The rms fluctuations in the bandwidth B are given by the square root of the quantity 2B times the frequency dependence of the mean square fluctuations. Thus, for signal equal to noise. 

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The analysis of the signal and background limits which follows, while detailed, is not exhaustive. Since thermal detectors respond to radiant power rather than photon arrival rate, the signal and background fluctuation limits derived below do not apply to them. Rather, it is necessary to repeat the derivations in terms of power rather than photon rate. An analysis of the background fluctuation limit for thermal detectors is found elsewhere [2.159]. 

Composite Signal Fluctuation and Background Fluctuation Limits... 

The intersections of three pairs of curves for which the bandwidths of the signal and background fluctuation limits are equal are emphasized in Fig. 2.19. Note that all lie between 1.0 pm and 1.5 pm. To illustrate the composite, that for an area of Icm (applicable to the background fluctuation limit) and a... 

Fig. 2.19. Minimum detectable monochromatic power as a function of wavelength for composite of signal fluctuation limit (SFL) and background fluctuation limit (BFL) for two detector areas and electrical bandwidths. Background temperature is 290 K and field ofview is 2x steradians. Detector long wavelength limit is assumed equal to source wavelength...

Figure 2.20 illustrates the minimum detectable power from a 500 K black body as a function of wavelength, illustrating the composite of the signal fluctuation and background fluctuation limits. The same values of the param-... 

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