Measuring Thermal Signal

The THERMAL calibration frame is trickier than collecting a BIAS frame. Due to the thermal signal being a time-integrated term, we cannot simply take a $0s$ exposure as we did with the BIAS–there would be no thermal signal in such a frame!

Consider removing all possible source signal:

$$L_{ij}(\lambda) = \Bigl[\epsilon_{ij}(\lambda)I_{ij}(\lambda) + T_{ij}(\lambda)\Bigr]t + B_{ij}(\lambda) ~~|~~ I_{ij}(\lambda)=0 ~ \forall ~ i,j$$

$$L_{ij}(\lambda) = T_{ij}(\lambda)t + B_{ij}(\lambda)$$

We are now left with the Dark Signal as defined on our Data Reduction page. $$L_{ij}(\lambda) = T_{ij}(\lambda)t + B_{ij}(\lambda) = D_{ij}(\lambda)$$

This brings up an important point in reduction pipelines. A point that is often lost on those new to the idea of data reduction. YOU.MUST.ALWAYS.ACCOUNT.FOR.BIAS. Some forums and guides suggest otherwise, saying that you don't need to take bias frames for calibration.

What the authors of those posts neglect to say is, “ DARK frames contain THERMAL signal and BIAS signal”. That is, if you take a THERMAL frame, it'll have the BIAS frame built-in. This is evident in the quick maths above. What is also evident is that the THERMAL frame must be of the same integration time as the LIGHT frame.

If you are unlucky in your calibration frame collection and neglect to take DARK or THERMAL frames of the same integration time as your LIGHT frames, you can cheat. Please note that this cheating is not perfect, and it'll almost always be better to take DARK frames of the appropriate integration time.

Such frames that account for both are called DARKS. They have both thermal and bias signals in them and are of the same integration time as the light frames.

Say you have LIGHT frames integrated over 10s, but DARK frames integrated only over 5s. If you have also collected BIAS frames, you can remove the BIAS signal from the DARK frames, which should isolate the 5s-integrated THERMAL signal. You can then scale each pixel in the resulting THERMAL frame by $2\times(=\frac{10s}{5s}\times)$. The resulting scaled THERMAL frame should be roughly equivalent to a full 10s-integrated THERMAL frame. In the reduction pipeline, you'll need to then subtract the scaled THERMAL frame from the LIGHT frame as well as subtract the BIAS frame.

Never scale a DARK frame. Doing so inappropriately scales the BIAS signal as well, introducing unwanted signal to your attempt at a science frame.