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Converting surface brightness in stellar magnitudes to photon flux?

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#51 Shiraz

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Posted 25 May 2016 - 06:49 AM

Got to agree Frank - measurement is clearly the best way, especially under heavy pollution.

 

However, if you don't have any measurements, for whatever reason, an extrapolation from the best available sky data will still be useful for "what if" type questions when designing a system. 

 

Ray


Edited by Shiraz, 25 May 2016 - 06:51 AM.


#52 ecorm

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Posted 23 March 2019 - 04:28 PM

I was wondering the same thing as the OP, and stumbled upon this thread when I searched. From the book jhayes_tucson suggested, they give the formula for the photon rate at a focal plane from a star of magnitude m (which I post here under the doctrine of Fair Use for the purpose of commentary and research):

 

(1)    S = NTπ/4(1-ε2)D2 Δλ10-0.4m

 

where:

  • S is the photon flux in photons/second
  • N is the irradiance of a magnitude-zero reference star
  • T, ε, D, and Δλ are parameters related to the telescope, atmospheric transmittance, and bandpass
  • m is the magnitude

Instead of guessing/researching a bunch of parameters to use the above equation, one could use their own telescope/camera to establish a simple relationship between magnitude and electron flux.

The photon flux can be expressed as the electron flux, I, divided by the quantum efficiency η, so:

(2)    I / η = NTπ/4(1-ε2)D2 Δλ10-0.4m
 

where I is in electrons/second. Rearranging to isolate I:

 

(3)    I = ηNTπ/4(1-ε2)D2 Δλ10-0.4m

 

If we lump the quantum efficiency, reference star irradiance, transmittance, telescope, and bandpass parameters into a single constant K, we get a simple relationship between magnitude and electron flux:

(4)    I = K 10-0.4m

 

If one uses their own telescope/camera to measure the electron flux of an object with known magnitude, mtest, they can calculate the constant K for their specific optical/imaging train for a certain degree of atmospheric extinction. For example, I could point my telescope near the zenith away from extended objects, and measure the sky fog with a Sky Quality Meter. The electron flux of the sky could be calculated by using the mean value of a test exposure, adjusted for bias and dark current.

So, for the test measurement, we have:

 

(5)    Itest = K 10-0.4mtest

 

rearranging gives:

 

(6)    KItest / 10-0.4mtest

Once we've calculated K, we can thereafter use equation (4) to estimate the electron flux for a different object at the same atmospheric extinction with known magnitude m.

To adjust for atmospheric extinction, you can reduce m by 0.2 magnitudes per airmass, or use whatever other extinction model you see fit to adjust m.

Atmospheric transparency varies from night-to-night, so I assume the electron flux estimate from equation (4) would only be a rough estimate if K was calculated on a different night. I suppose one could calculate K for nights of different transparency, and use the one that most closely matches the night when one wants to estimate the electron flux for an object of known magnitude.

 

The formula given by the book is for the entire focal plane, but I'm pretty sure the relationship that I derived at equation (4) applies at the per-pixel level.

 

Disclaimer: I'm still fairly new at AP, so it's quite possible I made a mistake in my reasoning above. I'd be happy to hear critiques or corrections.


Edited by ecorm, 23 March 2019 - 04:33 PM.

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#53 freestar8n

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Posted 23 March 2019 - 06:07 PM

I think you are essentially deriving what I show in post #47 - except that I include pixel size and f/ratio as parameters.

 

And I point out that you can find a constant for each filter if you want to break it down across the spectrum.

 

I don't think I ever did a calibration but it would be interesting to compare numbers people get.

 

If you explicitly include pixel size and f/ratio then the constants would be more directly comparable among different systems.

 

Frank



#54 ecorm

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Posted 23 March 2019 - 06:38 PM

I think you are essentially deriving what I show in post #47 - except that I include pixel size and f/ratio as parameters.

 

And I point out that you can find a constant for each filter if you want to break it down across the spectrum.

 

I don't think I ever did a calibration but it would be interesting to compare numbers people get.

 

If you explicitly include pixel size and f/ratio then the constants would be more directly comparable among different systems.

 

Frank

 

Oops! I admit I was skimming this thread once I had reached page 2, so I somehow missed that post.

 

It appears your model assumes the transmittance and obstruction parameters are the same (or close enough) with other systems having different focal ratios.



#55 freestar8n

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Posted 23 March 2019 - 06:48 PM

Oops! I admit I was skimming this thread once I had reached page 2, so I somehow missed that post.

 

It appears your model assumes the transmittance and obstruction parameters are the same (or close enough) with other systems having different focal ratios.

You can go ahead and include obstruction, system transmission, and QE to make it more complete.  The last two depend on wavelength - and transmission can be hard to know very well.

 

But I can see if I can get values from some of my exposures.

 

For the specific example of trying to map an SQM value to the flux with an Ha filter - it is fundamentally hard because the SQM doesn't distinguish red glow from blue.  But once you calibrate it for the filter, it should apply across different systems as long as the sky spectrum doesn't change much.

 

Frank


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#56 ecorm

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Posted 23 March 2019 - 07:22 PM

Is AperturePhotometry the correct way one estimates the flux of stars in PixInsight? According to the documentation, the table it spits out contains the magnitude and flux of the stars detected in the image. One could use that table to calculate their system's "constant" using several stars averaged out.



#57 freestar8n

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Posted 23 March 2019 - 07:55 PM

Hi-

 

I don't know exactly how it works in PI, but what you describe is fairly standard.  You get the integrated flux from the star as measured in electrons above the background across the central aperture.

 

For several stars you would get an idea of how magnitude maps to flux with the system.

 

For more accurate results you would do it with two different filters and factor in the role of color and atmospheric extinction - to correct for reddening that would make blue stars dimmer than expected due to the airmass.

 

Photometry gets fairly involved if you want to get accurate results.  But just using visual magnitude and a single filter should be in the ballpark.

 

Frank


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#58 ecorm

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Posted 23 March 2019 - 08:43 PM

For more accurate results you would do it with two different filters and factor in the role of color and atmospheric extinction - to correct for reddening that would make blue stars dimmer than expected due to the airmass.

 

Photometry gets fairly involved if you want to get accurate results.  But just using visual magnitude and a single filter should be in the ballpark.

 

For the AperturePhotometry, I would choose a starfield near the zenith to simplify the atmospheric extinction aspect. I think I would perform the test for only my luminance filter, since luminance is where I care the most about achieving high SNR. I guess it's about time I list my gear in my signature so that others on this forum can better help me.

 

A ballpark figure is all I need. My goal is similar to Jon's, where I'd like to be able to estimate in advance the total integration time I need to reach a certain SNR goal.

 

I don't know yet what constitutes a "good" SNR for the purpose of pretty pictures, but I hope I'll get a feeling for that as I gain experience. I suppose I can play around with stacking increasing numbers of light frames until I no longer see aesthetic improvements. I understand that SNR only makes sense in terms of a specific part of the image: the background sky, a galaxy arm, a wisp of nebulosity, etc.

When it comes to narrowband imaging, I'm a bit lost when it comes to figuring out the relationship between photon flux and the published magnitudes of emission nebulae. I'll read over this thread more carefully, and will do some more studying.

 

I truly appreciate you helping me understand stuff here and in other threads.


Edited by ecorm, 23 March 2019 - 08:45 PM.


#59 freestar8n

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Posted 24 March 2019 - 01:29 AM

For the AperturePhotometry, I would choose a starfield near the zenith to simplify the atmospheric extinction aspect. I think I would perform the test for only my luminance filter, since luminance is where I care the most about achieving high SNR. I guess it's about time I list my gear in my signature so that others on this forum can better help me.

 

A ballpark figure is all I need. My goal is similar to Jon's, where I'd like to be able to estimate in advance the total integration time I need to reach a certain SNR goal.

 

I don't know yet what constitutes a "good" SNR for the purpose of pretty pictures, but I hope I'll get a feeling for that as I gain experience. I suppose I can play around with stacking increasing numbers of light frames until I no longer see aesthetic improvements. I understand that SNR only makes sense in terms of a specific part of the image: the background sky, a galaxy arm, a wisp of nebulosity, etc.

When it comes to narrowband imaging, I'm a bit lost when it comes to figuring out the relationship between photon flux and the published magnitudes of emission nebulae. I'll read over this thread more carefully, and will do some more studying.

 

I truly appreciate you helping me understand stuff here and in other threads.

Sounds great!  I will aim to see if I can get numbers from my system.

 

The main thing complicating magnitude calculations is that ccd's record photons and don't care if they are blue or red.  But magnitudes of stars are always described in terms of some assumed passband.  That makes it hard to convert an SQM visual magnitude to whatever photon count you might get in a given filter.

 

One thing to remember is that any time you have two different fluxes in e/s, you can take the ratio and express it as a magnitude difference.  Even if you don't know what the magnitudes mean on some absolute scale - it can be handy to know the difference in terms of a delta magnitude.

 

If your sky background is 1 e/s at one site - and 100 e/s at another with the same setup - you know it is 5 magnitudes brighter - without needing to know a lot of other details.

 

Frank



#60 ecorm

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Posted 24 March 2019 - 02:20 AM

The main thing complicating magnitude calculations is that ccd's record photons and don't care if they are blue or red.  But magnitudes of stars are always described in terms of some assumed passband.  That makes it hard to convert an SQM visual magnitude to whatever photon count you might get in a given filter.

Yeah, I've just been reading-up on the UBVRI photometric system, as well as B-V color indices. I've seen someone (perhaps you) in another thread mention that SQM has its own passband standard. I now understand that star magnitudes in catalogues are specified for the V band, and have a certain B-V color index. The way I understand it, to convert from V magnitude to some luminance filter passband, one would need to figure out a conversion factor for their specific luminance filter, based on the blackbody spectral curve for that particular star. This conversion factor would be different for stars having a different spectral curves!

At least with the SQM, the conversion factor to a luminance filter should be consistent if one assumes the sky color remains the same.

This is getting a lot more complicated than I thought. I might as well just estimate the electron flux directly for my object of interest using a test exposure. During my imaging sessions, I should try to reserve some time to grab a few test exposures for my "next" target. This way, I have test data that I can use to plan for the next imaging run. If the telescope ends up being different on the next imaging run, I could use the formulas in this thread to convert the measured electron flux accordingly (the filters would remain the same).

My brain hurts from trying to give myself a crash course in basic photometry, so I hope what I wrote above is somewhat coherent.  lol.gif 
 

If your sky background is 1 e/s at one site - and 100 e/s at another with the same setup - you know it is 5 magnitudes brighter - without needing to know a lot of other details.

 

My imaging rig would effectively become an oversized/overpriced SQM after it's been "calibrated" for the sky in my backyard!


Edited by ecorm, 24 March 2019 - 02:26 AM.


#61 Jon Rista

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Posted 24 March 2019 - 03:57 AM

This is getting a lot more complicated than I thought. I might as well just estimate the electron flux directly for my object of interest using a test exposure. During my imaging sessions, I should try to reserve some time to grab a few test exposures for my "next" target. This way, I have test data that I can use to plan for the next imaging run. If the telescope ends up being different on the next imaging run, I could use the formulas in this thread to convert the measured electron flux accordingly (the filters would remain the same).

My brain hurts from trying to give myself a crash course in basic photometry, so I hope what I wrote above is somewhat coherent.  lol.gif

 

Welcome to the club. :p You are now where I ended up a couple years ago when I asked this question. It is pretty complicated...more complicated than I cared to deal with once I really got into it. 

 

I have such variable skies that photometry never really became a thing for me. Too many variables. 

 

In the end, it doesn't take much experimentation with a few test exposures to figure out what you need to do to create pretty pictures, if that is your goal...and you don't really need to deal with all the math at all (unless you want to.)



#62 Mert

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Posted 24 March 2019 - 05:33 AM

Maybe I'm totally off, but there is an option in meteoblue.com if you select

meteorological maps just before special options, you get another screen and

on the right side and select Air quality, there is an option of Aerosol

Optical Depth which more or less gives you the transparency of the

atmosfere.

 

Here is the descriptin of what they define:

Aerosol optical depth
The optical depth is a measure of how well electromagnetic waves can pass through a medium. Therefore, the aerosol optical depth is the measure for the reduction of light transmission caused by atmospheric aerosols. It describes the total light extinction in the vertical atmospheric column, which depends on the light's wavelength and the amount of atmospheric aerosols. The greater the value of optical depth, the greater the aerosol concentration. Sources of aerosol can be diverse: wild fire, desert dust or anthropogenic air pollution. The aerosol optical depth is dimensionless.

Maybe it helps a little?

 

Regards,

Mert




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