Keywords: pdbi-amp-cal

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## Low opacity approximation

To outline the relative importance of all parameters, I will now derive an approximate formula for the calibration factor in the limiting (but frequent) case where the opacities are weak and equal in the image and signal bands.

| (25)

where is the physical temperature of the absorbing layers. Thus

| (26)

| (27)

| (28)

Eliminating gives

| (29)

Although is a weighted average of the physical temperature of the cabin and the outside temperature, it is not very different from . Hence we can simplify :

| (30)

It is important to note that in this formula, is dependent mostly on the outside temperature and pressure (and site altitude of course), and weakly on because is the (physical) temperature of the absorbing layers. is the effective temperature seen by the antenna, and hence small compared to . The parameters are , and . Setting reasonable numbers :
, , , and ,
yield

| (31)

Next: SKYDIP effects Up: Critical parameters, biases and Previous: Critical parameters, biases and Contents