On page 17 of the Guide in the section on Sampling there is a nice diagram illustrating FWHM. The accompanying description says that FWHM "... is defined as the number of pixels that are filled to one-half the dynamic range between the background and the brightest (fullest) pixel in the star's image."
IMO that is not correct. A better definition would be something like:
"The FWHM is the width of the point spread function of the image of the star at one half of its maximum value."
Apart from its application to photometry on digital images, FWHM is a parameter applied generally to certain mathematical functions. Considered in this context (where no pixels can be filled or half filled) it is clear that the parameter represents the width or extent of the function at a certain point, namely, half its maximum value.
Roy
Hi Roy,
Thank you for the suggested correction to the FWHM definition. We will include it in the next update.
Of course, we will also have to define "point spread function" if we use it in that sentence. Suggestions on how best to define that in a clear simple way are welcome.
Many thanks,
Sara
In the last paragraph of page 17 the Guide had just defined "seeing disk". I'd suggest using Roy's definition but substituting "seeing disk" for "point spread function". Also, to keep this definition focused on the topic under discussion, sampling, I think we should keep "pixels" in the definition. So....
"The FWHM is the number of pixels across the width of the seeing disk at one half of its maximum value."
Phil
I agree with Phil.
Ed
This is a case where a careful pictoral description is definitely needed, perhaps a bell curve marked with a FWHM span, displayed next to an example signal from an image also marked with a FWHM span. The different views about wording is a strong clue that words alone won't be enough.
Eric,
There actually is a figure, just as you describe, inset into the paragraph which discusses FWHM (bottom of page 17). To me the figure seems quite clear, but a couple of beginning students in the CCD1 class still had trouble with the concept. I now think they may have been confused by the definition in the text.
Phil
I agree with Phil that it would be ideal if a simple, short description of FWHM could be used.
His suggestion "The FWHM is the number of pixels across the width of the seeing disk at one half of its maximum value" has that quality. I'm just concerned at the possibility of confusing measurements across an image or part of it, with measurments across a mathematical function describing the profile of that image.
I agree with Eric that a diagram and a description of it may be the way to go, and the existing diagram is IMO good. How about something like:
"The diagram illustrates a profile of the counts (ADUs) across a well-focussed image of a star, and represents the point spread funtion of those counts. The FWHM, shown in the diagram, is defined as the number of pixels across the width of the point spread funtion at half its maximum value."
ADUs have already been described in a previous section of the Guide.
Roy
Sorry, should have been In PSF not PSR in title of previous post.
Roy
"I'm just concerned at the possibility of confusing measurements across an image or part of it, with measurments across a mathematical function describing the profile of that image."
Roy,
Suppose we use Ed's term, "the FWHM of the seeing disk" instead of just the naked "FWHM". Would that ease your concern?
Phil
Phil,
It's succinct but IMO is not scientifically correct. The seeing disk is the image of the star, not the profile of the ADUs from the image. Therefore I don't believe the seeing disk itself can have a FWHM.
Roy
Perhaps we should just leave it the way it stands.
Phil,
I didn't mean to give you a heart attack, but I stand by my last comment, and can defend it if necessary.
However, it is more productive to draft an alternative definition. Here is a modification of what I suggested:
"The diagram represents the profile of a well-focussed image of a star. The FWHM, shown in the diagram, is defined as the number of pixels across the width of the profile at half its maximum value."
Roy
Thank you, Roy. I like that, and I'd recommend it for the next revision of the CCD Guide.
Phil