SQM (sky background) measurement using an image and the ASTAP program

[mgutierrez]

Han, I have another question. I don't know how astap really makes the calculation. I thought it was based at least partially on the background level. But it seems there are more factors. In any case, I don't fully understand why (apparently) the focal ratio of the tube does not play a role. At the same exposure time, normally a lower F would have a higher background level than a slower one

[vlaiv]

8 minutes ago, mgutierrez said:

Han, I have another question. I don't know how astap really makes the calculation. I thought it was based at least partially on the background level. But it seems there are more factors. In any case, I don't fully understand why (apparently) the focal ratio of the tube does not play a role. At the same exposure time, normally a lower F would have a higher background level than a slower one

Image is plate solved and thus plate scale (arc seconds per pixel) is known.

That is all you need to calculate magnitude per arc second squared (that and comparison value - like star flux in the image compared to star magnitude)

 

[mgutierrez]

thanks for the reply @vlaiv. Sorry, I don't fully get it. Could you please elaborate further?

The focal ratio is an example. The same doubt applies by using filters; eventually, the problem I imagine is the lack of light compared to other setups. So, does it mean that is enough if the image can be plate solved?

[vlaiv]

18 minutes ago, mgutierrez said:

So, does it mean that is enough if the image can be plate solved?

It is enough to plate solve properly calibrated image.

In order to establish SQM reading you need to do the following:

1. Count number of photons per unit area of the sky (arc second squared)

2. Compare that with known quantity that represents 0 on magnitude scale

When you have plate solved image - you know how many pixels there is in one arc second squared - because you for example have 1.5"/px. That is linear measure not area - in order to have area you need to calculate area of a pixel (which is one - one side x one side)

1.5" / px * 1.5" /px => 2.25 "²  per pixel²

From that you can say - let's measure ADUs per pixel in the background and say you have 29ADU per pixel

Now you can get ADU per arc second squared - because you know that you have 2.25 arc second squared per one pixel - so ADU per arc second squared will be 29ADU / 2.25 = 12.888...

You might think it is a problem that you don't have actual photons - but it really isn't a problem because magnitude is log of a ratio between two quantities. It does not matter if quantities are expressed in pounds or kilograms - object A will be x4 as heavy as object B regardless of the unit of measure you use (but you must use the same units on both objects).

So in order to get magnitude you do the following - you select a star in your plate solved image. Since image is plate solved - you have coordinates of that star and you can look it up in star catalog and get its magnitude. You can then also get star's flux by measuring it from the image (just make sure you don't use clipped star) - this flux will again be in ADUs - which is handy since you can now compare those two quantities.

You calculate the ratio between star ADUs and background ADUs and convert that in magnitudes and you add that magnitude to magnitude of the star to get magnitude of the background sky.

It does not matter if you've used some sort of filter to do this because your reference in catalog of stars will be V magnitude (that is what we'll use) - and ratio of intensity for one filter will be roughly the same as ratio of intensity for different filter (they won't be the same, but if spectral characteristics of both sources are fairly similar - difference will be small).

In any case - to avoid bias - you can use average of many stars in the image - thus side stepping any spectral bias that might arise from using overly cold / red or overly hot / blue star.

[mgutierrez]

thanks again @vlaiv. Definitely, my problem is the lack of knowledge of some astro-topics.

I've been reading around but honestly I'm still a bit confused with some terms. So, if I've understood properly, the calculations and data involved are sky background, measured star flux and reported star magnitude from a catalog, right?

Quote

You calculate the ratio between star ADUs and background ADUs and convert that in magnitudes and you add that magnitude to magnitude of the star to get magnitude of the background sky.

I can't grasp the details of that explanation. How can that calculation lead to the magnitude of the background sky?

Quote

It does not matter if you've used some sort of filter to do this because your reference in catalog of stars will be V magnitude

so, as I've read, V filter bandwidth is about 80nm centered on ~500. Does that mean that doing this measure with a Ha filter would fail? Just only for my understanding.

 

Thanks for your patience, Vlaiv

[vlaiv]

1 minute ago, mgutierrez said:

I can't grasp the details of that explanation. How can that calculation lead to the magnitude of the background sky?

Ok, so let's do this step by step.

This is definition of magnitude:

So, say we have a star that is x100 times dimmer than our reference star - its magnitude will be

-2.5 * log_base_10 ( 1/100) = -2.5 * -2 = 5

So magnitude 5 star is x100 less bright than magnitude 0 star.

Now, from properties of logarithm

If star A is x10 less bright than star B and star B is x20 less bright than reference star - star A will be x10 * x20 = x200 times less bright than reference star - brightness multiplies - but magnitudes add / subtract

so magA = magRefB + magBA (or magnitude between reference to star A is magnitude from reference to B and magnitude from B to A)

It is just simple rule of logs and products.

Now back to discussion of sky background brightness.

What is SQM?

SQM is defined like this - if you had star of some magnitude and you spread it's light on 1 arc second x 1 arc second - and do this with every arc second squared of the sky - that is your brightness.

Amount of photons (or flux) coming from patch of the sky must be the same as if coming from a single star of certain magnitude - then we say that sky has brightness of given magnitude per arc second squared.

Given above - it is easy to calculate magnitude of patch of the sky if you can find ratio of flux between it and some star in the image.

Say you have 20ADU per arc second squared (again - you average per pixel and use plate scale to get per arc second squared value) and you've identified mag9 star in the image which you measured to have 40000ADU.

Hypothetical star that corresponds to 1x1" patch of the sky would be 40000/20 = 2000 dimmer than our mag9 star.

If we calculate magnitude of that ratio it will be mag = -2.5 * log_base_10(1/2000) = ~ 8.25mag

Now we have mag9 star and difference of additional 8.25 magnitude, this means that our sky is 9 + 8.25 = mag17.25 or SQM 17.25

It is as simple as that.

15 minutes ago, mgutierrez said:

so, as I've read, V filter bandwidth is about 80nm centered on ~500. Does that mean that doing this measure with a Ha filter would fail? Just only for my understanding.

Not necessarily - it would depend on spectra of reference star and that of sky background.

Say we have two stars with the same spectrum:

One is just x10 brighter than the other.

Sensor + filter will simply integrate over above spectrum (with added sensor sensitivity as well).

If stars have same spectrum - only one is x10 brighter - then that means that in every wavelength this holds true. It does not matter if you integrate in 400-500 range or 500-600 range or some other range like 656 +/- 3nm, once you perform integral and find ratio of those two - you will get same number: it will be x10

Problem arises when you have two sources with different spectral characteristics and you try to compare sections of those spectra - like this:

here we have comparison of common spectra for different stellar classes.

Here you can see that for example B5V has higher B filter values than K0V star and ratio of integration of these regions won't be the same as ratio of integration performed in V region as most values are simply higher.

This is by the way how we define stellar color (in astronomical sense) - as difference in magnitudes between two filters compared to reference star.

So there are cases where you have to be careful of how you "transition" from one filter to other in terms of magnitudes and apply correction, but for simple SQM - you can simply use green filter (or green component of color image). That will be very good approximation for V filter in most cases.

 

 

 

[han59]

23 hours ago, mgutierrez said:

Han, I have another question. I don't know how astap really makes the calculation. I thought it was based at least partially on the background level. But it seems there are more factors. In any case, I don't fully understand why (apparently) the focal ratio of the tube does not play a role. At the same exposure time, normally a lower F would have a higher background level than a slower one

Vlaiv thanks for the explanation.

The reason that the telescope focal ratio, exposure, camera quantum efficiency and light losses do not play a role because  the stars are used as reference. Sky glow and star light are both going through the same instrument, your telescope and camera. So if your instrument is less sensitive both the sky glow and star light will reduce  the same.  The star measurement provides a calibration factor,  magnitude ==> flux. The star flux is the sum of pixel adu values illuminated by the star.  A defocus will not play a role either. The star flux stays the same. The sum of the star adu values stays the same. Solving is required to identify the stars an their magnitudes from the database.

The sky glow is increasing the background value of the image. This is also a flux.  The background flux in one square arc second can be converted to magnitude resulting in the SQM value. To calculate how many pixels there are in one arc second you need to solve the image. Probably less then one pixel but mathematical it doesn't make a difference.

The only thing which could  influence the calibration is a difference in colour  and altitude.  The colour difference is ignored. The altitude is compensated. So at lower altitudes the program assumes the star light is reduced equal to the amount of air mass.  The sky glow is assumed constant. While writing this maybe this last assumption is maybe not 100% fully valid. But an SQM measurement you would not do at very low altitudes of 30 degrees or lower.

Han

Edited August 7, 2023 by han59

[mgutierrez]

thanks a lot @han59 and @vlaiv for your replies.

I need some time to digest the info and fully understand it. But, basically, the key point is to measure the difference in magnitudes between the sky background and the chosen star, and then compare (actually add) it to the reported star magnitude, if I understood well.

I will re-re-re-re-read it one more time

thanks again!

[han59]

19 minutes ago, mgutierrez said:

I need some time to digest the info and fully understand it. But, basically, the key point is to measure the difference in magnitudes between the sky background and the chosen star, and then compare (actually add) it to the reported star magnitude, if I understood well.

 

Yes that is it. 

In practise a few hundred stars are used and some statistics are applied to get a common magnitude to flux ratio.

For photometry you compare the variable star with a reference/check star. For SQM measurement you compare a star or stars with the increased background value.

 

[Vulisha]

Hi, 

 

I just found this! Although I do use astap on my astroberry that version does not have this awesome feature. Bit as it would have it, something does not work on my end. I am trying to solve and get data using Dwarf2 smart telescope, but D50 base does not seem to be able to solve it, despite being a quite wide field.  Here is fits. 

I did try those tips and tricks 

 

0000.fits

Edited September 1, 2023 by Vulisha

[MalcolmP]

11 hours ago, Vulisha said:

, but D50 base does not seem to be able to solve it, despite being a quite wide field.  Here is fits. 

It solves ok for me using the G05 data in about 11sec blind  on an old slow windows7
00 43 51.5 +41 24 24

I have been using that G05 for my widefield DSLR+135mm lens
I think it solvs ok in 14sec with D20 but I am not sure if it is remembering some of the settings from the G05 use  ( I am new to ASTAP ! Great software thanks Han   ) 

 

Edited September 2, 2023 by MalcolmP

[Vulisha]

Can you please send me screenshot of your settings, mine is simply not solving... Got 8 core 16 thread ryzen processor 

[MalcolmP]

The only difference I noticed were the two " Ignore stars . . " figs 1_left & 2_right  ( I need a bigger monitor ! )
So I changed them to your settings and it still solved, fig 3 in which after solving the "Field of view .." has changed from auto to 1.79

 

 

 

 

 

 

 

Edited September 3, 2023 by MalcolmP

[Vulisha]

@MalcolmP thank you so much I was playing for days with this, itnwas nerve racking, and then by S. Holmes logic, if we have exactly the same settings here, issue must be on another place, so I have searched and searched and remembered that I clicked Auto debayer option. 

As soon I have disabled that solver did its job in 1.5s.

 

Thank you so much on your help I would have palyed with this settings for months I think haha. 

 

Now, I got 18.98 SQM. I have also made home made arduino SQM and I am eger to test it and compare! 

Edited September 5, 2023 by Vulisha