Lang and I spent the morning on the early pages of our paper on how to detect a source in multi-epoch imaging. As I have mentioned before, this turns out to be a non-trivial question if you take it very seriously. In order to clarify our answer to the question, we decided to be very specific about our model of an image, starting at the intensity field impinging on the telescope. This is clarifying, to the point that we understood the problem better at the end of our discussions.
I am still a bit confused about the different questions you can be asking: Do you want to know if there is a source in the image, or do you want to know the flux of the source given a proposed position, or do you want to know the position of the source given a proposed flux (or flux limit)? These are all different questions with different answers. Really in most cases that people are detecting sources they want to know Is there a source near this position that I ought to include in my catalog?
This question has never been properly answered, to my knowledge, in part because it is ill-posed: If you think that flux and position information is always probabilistic (as I do), then there is no fact of the matter about whether any particular source meets catalog requirements (and I am leaving aside whatever is meant by the word ought
).
In some cases you will have a position (and associated uncertainty) from another wavelength and will want to know the flux at that position.
ReplyDeleteBut, sticking to point sources, in general I want the probability that a given flux enhancement is not spurious, and a probability distribution for its flux and position. And I promise to be clear about what probability cuts I do downstream of that to construct a catalog.