Analysis of 320X240 uncooled microbolometer focal plane array ...

8where the proportionality constant K is the thermal conductance G between the detectormaterial and the surrounding.From Equation 2.1, the rate of heat flow can also be described asd (As) c d (AT)dt dt •(2.3)Assuming the detector material is at higher temperature than the surrounding temperature,the heat flow is from the material to the surrounding. Since the temperature of thematerial is higher than the surrounding, the rate of heat flow d(Ae) is negative. WithdtEquations 2.2 and 2.3 equated, the heat transfer equation becomesd (AT)C — GAT .dt(2.4)The change in the detector material temperature with the presence of radiation isd (AT) + G(AT) = 77P ,dt(2.5)P= Po exp(j cot) ;where P is a modulated source power with frequency co, and ri is the detector IRabsorption. The value of i depends upon the detector material, the thickness and spacingof the layers, and the pixel fill-factor (the fraction of detecting area to the total area).The solution to Equation 2.5 is equal toAT = ZS.To exp( —G— t) +77.130 exp( cot)G + j coC(2.6)