FWHM and Bortle

[Taraobservatory]

Hello,

Probably a stupid question, but here goes.

What is the relationship between FWHM, Bortle, SQM and image scale?

I know what they are by themselves, but can we use a number from SQM and an image scale to determine FWHM? Etc etc.

The reason for the question is that a collimation software (Skywave) needs you to input FWHM to do a correct calibration, but how can you know FWHM without taking a picture to measure? If the scope is uncollimated, I assume your measurement of FWHM will be wrong.
Please correct me if I'm wrong.

Clear skies 

Roger 

[Fegato]

I'll try an answer, as you don't have any responses. But I'm no optics expert or even vaguely a physicist, so I'll probably get it wrong. Maybe someone else will then correct me!

Bortle and SQM are measuring darkness of the sky, so are directly related (Bortle is based on ranges of SQM).

However, I don't think darkness of the sky has a direct bearing on FWHM. That's impacted by seeing, which is the state of the atmosphere into which you're looking. In fact, FWHM is often used as a measure of the quality of seeing (however, it can be impacted by your optics, focus etc.)

I don't think image scale affects FWHM as such. As a star is a point source, the FWHM measure in pixels is sort of showing how much the point source has been smeared across multiple pixels by the seeing (or lack of it).

Sadly none of this answers your real question. I'm not really sure why collimation software is asking for your FWHM. I assume it wants to know about your seeing conditions as you collimate. When you know your local conditions, you can maybe estimate this, but if not, I'm not sure really. The whole seeing thing is not something I've got involved in very much. I know it's normally average at best in the UK, and we have so many clouds, I just ignore seeing and image whenever I can!

[almcl]

Wow, that's interesting. 

Had a look at the Skywave website and am totally baffled as to what it does and how one would use it, but if you need an estimate of seeing, the Meteoblue Astronomy forecast provides an estimate of the seeing for a given location.  Not sure how accurate it is, its cloud amounts frequently seem rather pessimistic, but it might be worth a try?

[Zermelo]

There was a thread here recently:

 

[vlaiv]

On 14/08/2022 at 19:24, Taraobservatory said:

What is the relationship between FWHM, Bortle, SQM and image scale?

They are terms that are of interest to astronomy enthusiasts?

SQM and Bortle scale are measures of object brightness.

SQM can measure both extended target and sky background (affected by light pollution), while Bortle scale is very crude measure often used in descriptive manner for sky brightness. Mostly used by visual astronomers.

Bortle scale ranges from 1 to 9 (best sky to worst sky).

SQM is abbreviation of "sky quality meter", but is often used as - magnitude per "square" element of sky / target (sq - square, m - magnitude) - be that arc second squared or arc minute squared - in any case, some surface. It is logarithm scale much like regular stellar magnitude - and has the same meaning - or rather, how bright patch of the sky / target would be if you took star of certain magnitude and "smeared" it over that surface (arc second squared or arc minute squared).

It is measured and besides being more precise description of the sky for visual astronomers is very handy for exposure / SNR calculations for imagers.

Here is conversion table between the two:

(not very precise, as I was able to glimpse MW at zenith from red - white border - which was about SQM18.5)

FWHM is measure of how good the seeing is at any given moment, but also - what is the resolution of long exposure image.

It stands for full width of half maximum and is measure related to Gaussian (or other similar) profile created by star in a telescope. When we talk about seeing FWHM - then definition is - FWHM of recorded star using very large aperture telescope for 2 seconds (or perfect tracking mount).

Seeing FWHM will not be equal to FWHM that you get in your image. FWHM in image is influenced in part by seeing FWHM, but mount performance and aperture size play a part. How precise is your focusing also plays a part and if telescope is diffraction limited or not (collimated well, or even optically degraded by choice - like inclusion of field flatteners / coma correctors that improve edge of the field but give away some of sharpness overall).

Image scale is simply conversion factor between angular units in the sky and linear units in focal plane - often expressed in units of pixels instead of microns - so you get arc seconds per pixel or "/px.

It depends on pixel size and focal length of telescope and formula is - image or pixel scale = pixel_size * 206.3 / focal length

(where pixel size is in micro meters and focal length in millimeters).

FWHM of the image and pixel scale are related like this - there is match between where pixels match what can be recorded in terms of sharpness. This is called optimum sampling.

If you sample with less pixels per sky angle - this is called under sampling and is in itself not a bad thing. In general, there are artifacts associated with under sampling - but those artifacts never happen in astrophotography (due to nature of blur that is imparted on image by atmosphere, mount and telescope). If you read that "stars are square" due to under sampling - well that is simply not true (they can be square if one uses improper interpolation algorithm - but that is whole another story).

If you sample with more pixels per sky angle than you need - you are over sampling. Over sampling is bad.

It produces poor results when image is viewed at 100% zoom - being soft with bloated stars, but there is much more important aspect of over sampling and why it is bad. We always want to take "faster" images of the night sky and produce smoother better looking images with less noise in given amount of time.

Over sampling prevents us from doing this - over sampled images have much lower SNR then they need to. This is because light is spread over more pixels (than it needs to be) - and signal per exposure is lower and hence signal to noise ratio is lower. This is very similar to using very high magnification visually - object just gets dimmer and you don't get to see additional detail.

Proper sampling is when you properly match FWHM and pixel scale and it lets you capture most detail with having best SNR for given time.

[Taraobservatory]

25 minutes ago, vlaiv said:

They are terms that are of interest to astronomy enthusiasts?

SQM and Bortle scale are measures of object brightness.

SQM can measure both extended target and sky background (affected by light pollution), while Bortle scale is very crude measure often used in descriptive manner for sky brightness. Mostly used by visual astronomers.

Bortle scale ranges from 1 to 9 (best sky to worst sky).

SQM is abbreviation of "sky quality meter", but is often used as - magnitude per "square" element of sky / target (sq - square, m - magnitude) - be that arc second squared or arc minute squared - in any case, some surface. It is logarithm scale much like regular stellar magnitude - and has the same meaning - or rather, how bright patch of the sky / target would be if you took star of certain magnitude and "smeared" it over that surface (arc second squared or arc minute squared).

It is measured and besides being more precise description of the sky for visual astronomers is very handy for exposure / SNR calculations for imagers.

Here is conversion table between the two:

(not very precise, as I was able to glimpse MW at zenith from red - white border - which was about SQM18.5)

FWHM is measure of how good the seeing is at any given moment, but also - what is the resolution of long exposure image.

It stands for full width of half maximum and is measure related to Gaussian (or other similar) profile created by star in a telescope. When we talk about seeing FWHM - then definition is - FWHM of recorded star using very large aperture telescope for 2 seconds (or perfect tracking mount).

Seeing FWHM will not be equal to FWHM that you get in your image. FWHM in image is influenced in part by seeing FWHM, but mount performance and aperture size play a part. How precise is your focusing also plays a part and if telescope is diffraction limited or not (collimated well, or even optically degraded by choice - like inclusion of field flatteners / coma correctors that improve edge of the field but give away some of sharpness overall).

Image scale is simply conversion factor between angular units in the sky and linear units in focal plane - often expressed in units of pixels instead of microns - so you get arc seconds per pixel or "/px.

It depends on pixel size and focal length of telescope and formula is - image or pixel scale = pixel_size * 206.3 / focal length

(where pixel size is in micro meters and focal length in millimeters).

FWHM of the image and pixel scale are related like this - there is match between where pixels match what can be recorded in terms of sharpness. This is called optimum sampling.

If you sample with less pixels per sky angle - this is called under sampling and is in itself not a bad thing. In general, there are artifacts associated with under sampling - but those artifacts never happen in astrophotography (due to nature of blur that is imparted on image by atmosphere, mount and telescope). If you read that "stars are square" due to under sampling - well that is simply not true (they can be square if one uses improper interpolation algorithm - but that is whole another story).

If you sample with more pixels per sky angle than you need - you are over sampling. Over sampling is bad.

It produces poor results when image is viewed at 100% zoom - being soft with bloated stars, but there is much more important aspect of over sampling and why it is bad. We always want to take "faster" images of the night sky and produce smoother better looking images with less noise in given amount of time.

Over sampling prevents us from doing this - over sampled images have much lower SNR then they need to. This is because light is spread over more pixels (than it needs to be) - and signal per exposure is lower and hence signal to noise ratio is lower. This is very similar to using very high magnification visually - object just gets dimmer and you don't get to see additional detail.

Proper sampling is when you properly match FWHM and pixel scale and it lets you capture most detail with having best SNR for given time.

Hello Vlaiv, 

 

 

I was hoping to get an answer from you. I learn allot thank you! 

So in light of this information, what Skywave asks for is you lopcal seeing in FWHM. And I can get a rought idea from that though SQM reading or Meteoblue, right? an SQM reading of 21.78 would come to 1.3 somethig ? 

Here is a link if anyone is interested. Software looks pretty interesing. 

 

Kind regards

Clear Skies 

 

[vlaiv]

43 minutes ago, Taraobservatory said:

So in light of this information, what Skywave asks for is you lopcal seeing in FWHM. And I can get a rought idea from that though SQM reading or Meteoblue, right? an SQM reading of 21.78 would come to 1.3 somethig ? 

SQM reading has nothing to do with local seeing.

You can use Meteoblue for seeing forecast and they are usually right about high altitude seeing, but very important part is local seeing - that one you can't predict.

It has to do with how well your scope is cooled down, what part of sky you are observing in (how close to horizon) - what thermal object you have around you like large concrete buildings or maybe large bodies of water. What sort of wind is blowing and what sort of terrain you are in.

If you have rolling hills and you are on top of the small hill and there is nice smooth breeze blowing - local seeing is going to be good, but if you are observing over roof tops in winter time, or perhaps over lake in hot summer evening or there is mountain near by and wind blowing from that direction  - you are probably going to have rather poor seeing.

For what the software is asking - Meteoblue forecast rounded to nearest half FWHM (like if forecast is 1.89" set it to 2" and if it is 1.56" set it to 1.5") should be good enough since this is very arbitrary analysis given that it is using long exposure image of a real star.

If you want to be precise about it and you want good analysis - take a telescope and look thru it at actual star and use Pickering scale to determine FWHM.

see here for details:

https://www.handprint.com/ASTRO/seeing2.html

and here

https://www.damianpeach.com/pickering.htm

Do analysis on the night when star is mostly stationary with diffraction rings being visible and not broken (Pickering 6 and above)

[Taraobservatory]

Thank you Vlaiv, 

 

again, thank you for the information. I think these will come in handy for this purpose. 

The Wavefront guys got in touch with me and told me bascically what you just did. Its not required to be very acurate, just within a resonable range as the the software dont actually measure FWHM but only concerns itself with difraction. 

Clear skies

[dan_adi]

42 minutes ago, Taraobservatory said:

Thank you Vlaiv, 

 

again, thank you for the information. I think these will come in handy for this purpose. 

The Wavefront guys got in touch with me and told me bascically what you just did. Its not required to be very acurate, just within a resonable range as the the software dont actually measure FWHM but only concerns itself with difraction. 

Clear skies

I've added a FWHM estimate in the exposure time app. I will update it hopefully by the end of the week. See the pics on the last page

 

 

[Baudat]

On 14/08/2022 at 13:24, Taraobservatory said:

Hello,

Probably a stupid question, but here goes.

What is the relationship between FWHM, Bortle, SQM and image scale?

I know what they are by themselves, but can we use a number from SQM and an image scale to determine FWHM? Etc etc.

The reason for the question is that a collimation software (Skywave) needs you to input FWHM to do a correct calibration, but how can you know FWHM without taking a picture to measure? If the scope is uncollimated, I assume your measurement of FWHM will be wrong.
Please correct me if I'm wrong.

Clear skies 

Roger 

Dear Roger,

 

SKW uses the FWHM (seeing) for two reasons.
One is as an input for the  SKW mathematical model (an artificial neural network trained for your scope under seeing limited conditions) which outputs the aberrations and related wavefront used for the calculation of the collimation score and collimation screw adjustment directions, SKW engine is an actual wavefront sensing, metrology, tool.
A rough estimate of the FWHM  is enough for providing good wavefront measurement and related aberrations to be used for the telescope collimation.

 

SKW also uses the FWHM value for its collimation score (in the collimation tool view-port) as well as for the simulated seeing limited PSF (the predicated star profile), see the "display option" radio buttons (on the top right of the SKW GUI) under "seeing limited PSF".

For most scopes and sites one is seeing limited, excepted perhaps for apertures below few inches in diameter, found essentially in some refractors.

Therefore SKW collimator tool score (from 0 to 10) is based on the user provided FWHM value (that you can change freely regardless of the mathematical model in use) such your telescope collimation is optimal for the conditions at which the scope is operated.

You want to hit a score of at least 8, or greater, for DSI work (exposure time > 1 minute or so), hence seeing limited conditions.

 

You can certainly change the FWHM used by SKW to a lower value for increasing the SKW score sensitivity but there is a point of diminishing return, see example below, at which you will not see any difference/improvement at your operating seeing, even if the actual scope Strehl ratio (SR) is below 0.8 indeed. The seeing is the fundamental limitation here.

The SKW collimator qualitative feedback (its score) is designed with that in mind (again you can change the FWHM value to target any operational seeing level you may like, even 0").

 

For planetary work, especially when using lucky imaging (LI implies video rates, hence short exposure times) you are operating your scope at its optical limits since the seeing as been mostly removed by keeping only the DL frames (few % of them for the visible band with LI).
In this context the goal is to collimate the scope at its DL, one should set the FWHM value to 0 or close.

The figure below shows the in-focus PSFs, wavefronts, and associated MTFs without any seeing (upper part) and also the predicated star profiles with their FWHM values and SKW scores under seeing limited conditions (lower part) for 3 situations:

-1- Perfect optics and fully collimated scope (SR=1), labeled DL in this figure

 

-2- With collimation induced coma (3rd order) aberration, yet still a DL optics with a SR  = 0.82 (82%)

 

-3- With collimation induced spherical (3rd order) aberration, SR = 0.5 (50%)

 

       

 

Without any seeing (say when using LI in our case) the in-focus perfect PSF -1- and the one with the spherical aberration -3- (SR=0.5) seems essentially the same at first glance.

However looking at -3- more carefully reveals a bit larger and brighter first diffraction ring (and maybe for sharp/trained eyes one can spot the second diffraction ring too).

Here (in -3-) some of the  central peak energy has been transferred to the periphery of the PSF, yet the PSF's shape remains nice and symmetric.

It is interesting to notice that at a SR as low as 50% the actual impact on the PSF profile (no seeing), in-focus, remains quite minimum. On the other hand the impact on the MTF (image contrast without any seeing) is quite dramatic, there is a drop around 50% of contrast for pretty much all the spacial frequencies (red curve), a bad situation for planetary imaging.

The wavefront shows a clear spherical aberration pattern and even with a FWHM seeing of 1.5" the SKW score is only 7.0, with a FWHM=0" SKW would have reported a score near 5.
Finally the comatic PSF -2- exhibits a classical "comet" like asymmetric shape, but here the telescope is still DL with a SR=0.82 (DL means SR>=0.8). As a result the MTF drops less than 20% in average (no seeing). The related wavefront is typical of coma.

 

When seeing limited (say for DSI and therefore long exposure time > 1 minute, to pick a number), see bottom part of the figure, the FWHM values of the star profiles (the PSFs blurred by the seeing) for case -1- (DL) and case -2- (with coma) are essentially identical, with respectively a FWHM of 1.5" for a perfect scope (the seeing value) and 1.51" with the coma aberration added. SKW collimator scores (for a user FWHM set at 1.5") are 10 (-1-) and 9.6 (-2), they reflect that, both star profiles are nearly the same indeed (here the scope aperture is 20", opened at f/6.8, calculations @650nm).
The case -3- (spherical aberration) with a SR=0.5 leads, without any surprise, to the worst outcome with a FWHM of 1.69" now, about 12% more than the DL situation (-1- and -2-). The reported SKW collimator score is 7.0 (for a user seeing set at 1.5"), below the suggested minimum target of 8.0.

Edited August 27, 2022 by Baudat