Relationships between FWHM, HFD and Seeing
Bob Mimiaga
Brian Valente
For me, the star profile’s values are more for diagnostic purposes than for any relationship with imaging or seeing conditions, although they are related
I use the HFD/FWHM primarily to determine if the guidescope is focused.
I use adu to determine if the guidestar is bright enough, or if I need to change exposure to ensure it won’t drop because it’s kind of dim
I also use the star profile’s graph to see if the star is oversaturated – I like for a nice pointy graph. If it has a flat top, it’s too saturated so I’ll pick another star or reduce the exposure time
Also FYI I rarely if ever manually select a guidestar – a visually attractive guidestar may not be the best guidestar from a technical perspective
Hth
Thanks
Brian
portfolio https://www.brianvalentephotography.com/
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bw_msgboard
Hi Bob. Seeing and seeing measurement is a big topic and I’m sure you know. I’ll try to answer your specific questions without drifting into a big lecture that will just put you to sleep. J
From:
open-phd...@googlegroups.com [mailto:open-phd...@googlegroups.com] On Behalf Of Bob Mimiaga
Sent: Thursday, February 21, 2019
2:38 PM
To: Open PHD Guiding
Subject: [open-phd-guiding]
Relationships between FWHM, HFD and Seeing
I've been using the Star Profile dialog for some time now as a means of focusing my OAG guide camera (ASI224MC), and for selecting a good guiding star. I've recently started studying about the the atmospheric Seeing value and it's impact on the quality of the captured images. What I really don't understand is;
1. What is the relationship between PHD2's FWHM, HFD, and the small value to the right of the HFD value in the Star Profile dialog box?
FWHM and HFD are different measures of the same basic thing, namely how “big” the star image appears on the guide camera sensor. The easiest way to picture all this is to think about drawing a graph with brightness plotted against the x/y coordinates of an area that encompasses the star. Ideally, that graph will look like a 3-D Gaussian curve like this (courtesy of Wikipedia):
For PHD2, the HFD measure is probably the most relevant, which is why it’s highlighted. That’s a measure of the circular area within the star disk that encompasses 50% of the total light. As I recall, it was brought into common use by the developers of the FocusMax auto-focusing algorithm. It’s a comparatively stable measure that makes no assumptions about star-shape. In PHD2, full-width-at-half-max is measured empirically just by determining the vertical location that matches the ½-way point on the vertical axis and measuring the x/y diameters at that point. Obviously, that’s more sensitive to star-shape. The 3rd value in the window is just the HFD in units of arc-secs based on the image scale of your guiding rig.
2. What is the relationship between FWHM/HFD and the Seeing ability on a given day?
This is where it gets more complicated. The first question is whether you are interested in the *relative* seeing just for your equipment in your location on a particular night. That’s an easier problem to solve. We think the best measure of that is going to be the RMS of the Dec displacements of your guide star corrected for whatever polar alignment error you have. That’s what the Guiding Assistant measures, for example. With the Dec motor not running and with polar alignment drift accounted for, the remaining high-frequency guide star displacements in Dec are largely caused by seeing conditions. Depending on the image scale you use for guiding, you are likely to find the other measurements, including HFD, show a lot of variation. But with experience, you may be able to factor that out and also get a sense of relative seeing with the other measures. All of this is for your own relative seeing measure because there isn’t a standard way to go from arc-sec of guiding RMS to equivalent FWHM of star images. Many people do a 2-3 minute GA run at the start of each night and look at the min-move recommendation for Dec to get an assessment of the seeing conditions. Once you’ve done this a few times, you start to know what to expect for your setup on that night.
If you’re interested in a more standardized measure of seeing, something you can share with other imagers or compare to other locations, the problem becomes harder. Let’s start by how this is normally measured. One approach is to use a seeing monitor, which does high-frequency sampling of a star near the celestial pole (e.g. Polaris) and measures the tiny movements of that star. The measurements are treated statistically and adjusted to show the expected value at the zenith and out pops a FWHM number. That’s a good approach but the devices are expensive and most people don’t have them. A second approach is somewhat better IMO because it measures what you really care about – the size of the stars in your main camera images. If you take a sequence of 10-second exposures, you can analyze them with an imaging app of some kind that will compute the FWHM values of all the stars in the field and produce an average. A 10-second exposure will effectively average out the high-frequency seeing fluctuations and incorporate that into the average FWHM measure. This corresponds to what we see in our images. On nights of good seeing, the stars are small and sharp while bad seeing produces larger “blobby” star images. The stars will be round in either case, it’s just a matter of how far the light from the star’s diffraction pattern (the Airy disk) is spread across the pixels on the sensor. If you have a long focal length setup – actually a setup that has a fine image scale – this will be a good measure of seeing subject to certain assumptions. The first assumption is that the optics of the scope are diffraction limited and are producing star images that look like the Gaussian plot above. Poor collimation, optical aberrations, and poor focus can degrade these results. A second assumption is that the mount can track well enough in 10 seconds to not significantly blur the star images relative to the seeing effects. The last assumption is possibly the most important – the image scale has to be fine enough that you can adequately sample the star images. That typically means the image scale in arc-sec/px must be about 1/3 the size of the FWHM caused by seeing. So if you want to measure 2 arc-sec seeing, you would need an image scale of around 0.7 arc-sec/px. If you’re imaging with a short focal length scope, maybe a refractor that produces an image scale of 2 arc-sec/px, you won’t be able to get an accurate measure of seeing – or at least not a measure that is in any way standardized. I can give you a couple of quick examples from my setup. When I’m imaging at a scale of 0.6 arc-sec/px, I typically see FWHM values that fall between 2.0 and 2.5 arc-sec at my site. It can get much worse of course, I’ve seen them get above 4.0. When that happens, I just go inside and find something else to do. On the few occasions that I’ve used a 350mm refractor for imaging, the image scale is something like 4 arc-sec/px and the FWHM values are huge. The seeing conditions are the same but the image scale is much too coarse to get an accurate measure of the brightness distribution in the star images. That’s not bad news, it really means this setup is pretty much bullet-proof against bad seeing. Once you’ve done these measurements a few times, you can probably see a correlation between the Dec guiding RMS values and the FWHM measurements you did. At that point, there’s no need to re-measure the star sizes directly as the session progresses, you can just watch the guiding statistics and have a pretty good idea of what’s going on.
So in the unlikely event you’re still awake at this point, I hope this helps. <lol> And, of course, it’s just my interpretation of things.
Bruce
Thanks in advance for any help you can give,
Bob
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Bob Mimiaga
bw_msgboard
Thanks for the kind words Bob. If you want to discuss this further, you can contact me off-forum: bw underscore msg01 at earthlink dot net. I’m not an expert in this stuff, I’ve just spent a lot of time looking into it. I can probably point you to other useful references if it’s something you want to pursue.
Cheers,
Bruce
From: open-phd...@googlegroups.com [mailto:open-phd...@googlegroups.com] On Behalf Of Bob Mimiaga
Sent: Friday, February 22, 2019
7:38 AM
To: Open PHD Guiding
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Brian Valente
bw_msgboard
Hi Brian. No, HFD is just a statistic that’s computed as part of the code that computes the centroid – it’s a derived value. The centroid calculation is essentially a center-of-mass calculation, where the “mass” at each point is the brightness value.
https://en.wikipedia.org/wiki/Centroid
Of course, it’s not quite that simple because we have to reject hot pixels, reject background sky brightness, determine the boundaries of the star region, etc. But this approach is why PHD2 is indifferent to the star shape so long as the shape isn’t changing wildly. HFD and FWHM are computed during the process as a way to record estimates of the star size, mostly for support purposes. The “mass” of the star is used to compute the centoid, it’s basically the numerator in the equation.
Hope this helps,
Bruce
Brian Valente
Tom Kennedy
bw_msgboard
Hi Tom, see below.
From:
open-phd...@googlegroups.com [mailto:open-phd...@googlegroups.com] On Behalf Of Tom Kennedy
Sent: Friday, February 22, 2019
2:40 PM
To: Open PHD Guiding
Subject: Re: [open-phd-guiding]
Relationships between FWHM, HFD and Seeing
Thanks for that excellent explanation on seeing Bruce - I learned a great deal from that and will use that going forward.
After reading it it would seem to me that another way to evaluate this is through the autofocus routine in SGP. I do 8 second exposures and as it goes through the process it finds the lowest HFR. I have noticed that my HFR is sometimes higher and sometimes lower, and if I extrapolate your explanation to what I see with autofocus, that could be due to seeing.
Does that make sense? If so, I could use the output of my autofocus routine as a guage of relative seeing.
I would say yes subject to my lack of experience with SGP. I don’t know how SGP picks the star or how much averaging it’s doing at each trial focus position. You’d want to be sure the target star wasn’t saturated, for example. I do something much like you suggest. I use the PlaneWave auto-focus routine which uses all the available stars in my frame, and I use 10-second exposures. As you thought, the optimum focus position gives me what I was talking about before, an average HFD using the 10-sec exposures. It’s a nice way to kill two birds with one stone. J The only other difference for me is that I also measure a few frames with a tool that fits a Gaussian curve to the stars in the frame to produce FWHM measurements. But that’s kind of extra credit, it doesn’t tell me anything new about the relative seeing conditions. By the way, this is also an easy way to keep an eye on collimation – if the collimation gets out of whack, the star sizes start to grow systematically.
Bruce
Tom Kennedy
bw_msgboard
Thanks Tom. I think this should serve you pretty well as a quick estimator of relative seeing conditions.
Bruce