where ε = emissivity, f = fractional blackbody integral, σ = Stefan-Boltzmann constant, T = temperature (deg K), A_{detector} is detector area and (Ω_{object}/π) is projected solid angle of an object with respect to the detector. It can be shown that power received by each object is numerically equal to its projected solid angle [1]. Therefore, to determine TSE, one can perform a reverse raytrace in FRED. After the raytrace is complete, incident power on each object can be obtained. This value may be substituted for (Ω/π) in equation the equation above. TSE contribution from each object can be calculated, given values of T and ε (Figure 6).

**Figure 6**. *Calculating thermal self-emission from a Cassegrain telescope using a spreadsheet such as Excel. The column “Incident Power” is actually projected solid angle of the object. The column “Contribution” implements eq. 5.*

Using advanced raytracing capabilities in FRED, along with techniques derived from radiometry, it is possible to perform thermal imaging, narcissus, stray light, thermal illumination uniformity, and thermal self-emission calculations in a small fraction of the time it would take to trace the requisite number of rays in a brute force manner. FRED can also track each path traced through the system. The Raytrace Paths Report provides the contribution of each path to power reaching the detector. With these tools, one can quantify the effect of spurious signals in the detector and add features to the system to reduce these effects.

[1] R. Pfisterer, “Clever Tricks in Optical Engineering” (invited paper), Proceedings SPIE, Vol. 5524, October 2004.