While doing DSLR photometry I have recently started using the ZWO ASI AIR PLUS to locate the star, auto guide and to also take data and calibration files. The unit can also create master cal files and stack with the data files in the FIT format. Have not used this for the final processed image so I do not know if it usable. So I take the files and process then with IRIS then VPHOT. Just a bit of info if others want to try using the Air Plus.
The questions are:
1. Can HFD, instead of FWHM, be used to determine an acceptable star focus to meet the minimum 8 pixel FWHM?
2. If so, what HFD value would the telescope be defocused to achieve the 8 pixel minimum?
I ask this because the Air Plus can show the HFD values on an image. Thus, this will provide a quick way to set the focus without leaving the Air app to use another program to measure the FWHM. Just take an image and see what the HFD value is. If an adjustment is needed, change the focus position and take another image. The nice thing is the Air offers different routines to capture an image to see the HFD value.
In fact, I think you will find that most focus software (e.g., Focusmax) uses HFD rather than FWHM. Apparently, this parameter is a bit more stable in practice. They do both measure the width of the star profile.
Focusmax tries to minimize the HFD to achieve best focus. Does the AirPlus device/software not do the same thing? Not sure why you would want to set a fixed default value since seeing will change from night to night? Unless you need to routinely defocus slightly to avoid undersampling/oversampling with your DSLR Bayer array?
The Air Plus can do…
The Air Plus can do manual or auto focusing using the HFD values. I have used it to manually focus to take "pretty" pictures while learning to operate the Air.
Since seeing changes from night to night will that require focus adjustment position to achieve the desired FWHM? I'm guessing it will? From what I have read, seeing also affects the HFD. I have a feeling there is a relationship between the two but could not find a paper addressing it. I'll keep looking. Hopefully that relationship could be used to determine a HFD reading which could be used to achieve a desired FWHM. Papers seem to talk more of HFD as related to astrophotography, none found on a relation to photometry. Might be a good research project.
My system needs a slight defocus to achieve the desired FWHM. Since my system is portable, the focus position needs moving inward so the OTA will fit in the case, thus losing the defocus setting. I made a gauge to return the camera at a location known to get the desired FWHM. This works fairly well but when it does not I'm looking for a better solution, hopefully using a capability of the Air Plus.
<<No, they are not the same thing, and the two values are somewhat difficult to translate between without knowing exactly the shape of the star's distribution. Here are some definition links for FWHM and HFD from the MaxIm DL online manual.
The former is easier to understand because its name tells you exactly how the value is calculated. Imagine plotting a line cut through your star's distribution from your image. Hopefully the peak is well defined, and from there find the position of the pixel where the value drops in half from the peak. The distance from one side to the other at this half peak value is therefore the "full width of the half maximum". This relies on point values. It gets problematic when the star is noisy or not well defined.
The latter is a measure of the diameter around the peak (background subtracted) where the sum of the pixel values (the "energy") inside the circle is the same as the sum of the values outside the circle, which is why it's called "half flux". This is a more robust value as it depends upon the integration or sum of many pixels rather than point values as in FWHM. It is also a bit more computationally expensive, but it handles the noise and weird distributions better.
Both can be used as indicators of the focus and tightness of stars, of course. I hope this helps and doesn't add more confusion!
P.S. If you assume a distribution, you actually can come up with a conversion between FWHM and HFD, but as I said before this is hard to do in practice when you don't really know the distribution in the first place.
Edited by BenKolt, 04 June 2018 - 12:22 PM.
#4 Alex McConahay
- Posts: 12,801
- Joined: 11 Aug 2008
Posted 04 June 2018 - 12:49 PM
Explanations can sometimes obscure.
With a well focused star and good optics, there is practically no difference between the two measurements. (and practically here means, well, in practice).
FWHM is a measurement of the width (diameter) of a star where it is half as bright as it is at its peak measurement.
HFD (diameter) or HFR (radius) is the width (diameter) or half width (radius) of a star at its statistically center of brightness.
The difference between peak measurement and statistically center of brightness is nothing with a perfectly shaped star. A perfectly shaped star has a brightness curve that extends in from infinity, gradually and evenly increases, then progressively increases more steeply to a center where it is of maximum brightness. It then reverses this, and drops off quickly, and then more gradually all the way to infinity. It is symmetrical all around.
Now, compare that to a typical star, affected by changes in seeing, screwy optics, movement, and all that. In order to find the center of energy, you have to analyze the brightness at each point within the area of the star. Say, for instance, you have a five second exposure Seeing bounces the star all around for three seconds, and then settles for two with the star on one side of the general area that the star has occupied. Plot the energy of the area affected by the star. You will see a hotspot (brighter area) on the side that the star occupied for those two seconds of stable seeing. Note that it is NOT in the middle. Statistically, the center of this stars brightness is now off center. The HFD measurement takes this into account, where the FWHM will not. (You want a graph of your stars, use the appropriate "star shape" (I think it is called) window on PhD Guiding to watch your stars as they come in. )
Want an extreme example? Get the image of a slightly out of focus star in an SCT. It will be a donut. The center of the star will be dark (in the extreme). But it will still be the center of brightness because all the way around it is an equal strength-equal spaced area of brightness.
In short, HFD is a more robust measurement, which compensates for bad seeing, poor collimation, bad optics, movement, etc, better than FWHM. Robust means it tends to give consistent measurements even though the conditions may be changing a bit.
In practice, as long as you start with fairly well focused stars, it is a moot point.>>
Start with an autofocus to best focus position and then experimentally determine how far you need to move/offset from that position to achieve the desired FWHM (8 pixels?).
Subsequently, you should be able to use that same default offset from the best focus to reach the desired FWHM. Test this a few times on different days to confirm! There may even be a place in the focus software to store this fixed offset value and apply it after each autofocus?