It is possible to calibrate a pyroelectric detector (which will give a voltage proportional to the incident power) using the Stefan-Boltzmann law, along with the inverse square law, and using a commercially available blackbody source (they can be somewhat expensive), and measure the temperature of other sources with it, with the assumption that the source being measured has emissivity ## \epsilon=1.0 ##. ## \\ ## For small sources of known geometry, the inverse square law will apply. The equation of interest is the power incident on the detector, (using the inverse square law), ## P= \frac{L \, A_s \, A_d}{s^2} ##, where ## L=\frac{\sigma \, T^4}{\pi} ##. The ## \pi ## is kind of an odd factor, but arises because the intensity ## I(\theta)=I_o \cos(\theta) ## for a Lambertian source, and the radiated power is ## P=\iint I(\theta, \phi) \, d \Omega=\int\limits_{0}^{2 \pi} \int\limits_{0}^{\frac{\pi}{2}} I(\theta) \, \sin(\theta) \, d \theta \, d \phi =I_o \, \pi=\sigma \, T^4 \, A_s ## over a hemisphere. Thereby the on-axis intensity ## I_o=L \, A_s=\frac{\sigma \, T^4}{\pi} \, A_s ##
