Range formulation for a staring electro-optical and imaging system incorporating the effects of atmospheric transmission, focal plane 1/f noise and fixed pattern noise

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To increase the detection range in staring FPAs, commonly the integration time Ti is increased, as the range is assumed to increase as one-fourth power of Ti, (T1/(4)i). It is shown here that the range dependence on Ti is weaker thanT1/(4)i , because of the effect of atmosphere. Since the atmospheric transmission coefficient decreases with increasing range, the effect of increasing Ti on the range is considerably reduced. It is also shown that when detector 1/f noise dominates over other noise sources, the dependence of range on Ti is much weaker thanT1/(4)i , having a logarithmic dependence. Calculations have been done by integrating equations involving spectral functions-photon flux, atmospheric transmission coefficient, optics transmission coefficient and responsivity-over wavelength, in the spectral range from 8 μm to 12 μm. LOWTRAN2 has been used for spectral atmospheric transmission coefficients, for different conditions of ambient temperature (-30°C to 55°C) and relative humidity (50-85%). The range formulation also distinguishes between distant targets (point sources) and nearby targets (extended sources). The analysis is applicable for terrestrial imaging, where the temperature difference of the target and the background is small. The effect of fixed pattern noise (FPN) in mercury cadmium telluride (MCT) FPAs has also been considered by modeling FPN in terms of a composition variation in the MCT. It is seen that range, both in the point source and the extended source cases, is not a sensitive function of FPN.

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