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Beginner reduction spreadsheet valid at all air masses?

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Roy's picture
Roy
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I've had an email exchange with Brian off the forum on this topic. I thought it might be of interest for others to see what I've been doing.

In the documentation on DSLR photometry, it is stated that the beginner reduction spreadsheet should be used only at relatively low air mass.

I've done some tests on a star field in Grus, with only slightly more than 1 degree separation between the comp, check and target stars (DSLR images taken through a 600mm focal length refractor).

The results suggest that the spreadsheet can be used at any air mass with no or minimum loss of precision. Remember, this spreadsheet does not specifically include calculations to correct for air mass.

I'd be curious to hear if anyone else has tried this. If you haven't, you might find it interesting to give it a go.

Roy

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Roger Pieri
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Hi Roy,

This is not very surprising, images made at long focal length, narrow FOV, are not very sensitive to the extinction gradient. That gradient is typically 20 mmag per degree at 30 degrees height. At low height, 10 degrees, it typically reaches 200 mmag/deg. With a separation of only one degree at h=30 deg, the difference would be 0.02 mag only and probably less depending the gradient direction related to the stars.
Don't forget most CS people use a 50~70 mm focal length and stars at large separation. By the way their images are 10 times more sensitive to the extinction gradient than yours !

Anyhow with your refractor  you could achieve a precision much better than possible with a short focus lens, a couple of mmag is possible. To reache that precision you will have to take in account the extinction gradient !

There is also a very large variability of that gradient depending the atmosphere condition. The extinction is not only a question of air-mass, it also depends from the extinction coefficient. At low altitude, urban area, my records show an "epsilon" at 0.2 , best days, up to 0.6 at worst ! Overall, between zenith and three air-masses this could result in a 1 to 9 range depending the day !

Another factor more or less linked to the extinction is the reddening of the atmosphere. It also shows a strong variability. Its filtering effect is not depending of the star separation but their color. This factor is not negligible at all in case of stars of significant B-V difference, long focus or not...

Clear Skies !

Roger

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Hi Roger,
 

I'm not quite sure that we are saying the same thing. I agree entirely, of course, that the extinction gradient across a field 1 degree in width is quite small for most of the sky.
 

That's important for what I was saying, but it wasn't the main message.
 

What I was trying to say is that, provided the field of view is small, the beginner spreadsheet can be used to determine magnitude in that field, at various altitudes, and that extinction can be ignored for most of the sky.
 

The reason for this is that the spreadsheet utilizes a form of ensemble photometry, with several comp stars, the measurments of which are plugged into the transformation coefficient formula (V-v) = e(B-V) + z to calculate V for the target and check stars. Critically, it seems to me, that formula is valid for whatever air mass or extinction exists in the field that has been imaged.
 

To me, this is a new realization, and is entirely different from traditional differential photometry, where there is one target star, one comp star, and one check star. In this traditional circumstance, extinction and transformation coefficients are typically required for accurate photometry, unless the target and comp stars are of similar colour.
 

Cheers.
 

Roy

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Hi Roy,

Not sure the CCD/DSLR "ensemble" photometry with color transform (and more) is so new...  We are some using it, have a look at the reports... the publications...

Using the typical figures it's easy for anyone to calculate the possible extinction impact against the needed accuracy for a given project. In addition at low height the law is often very non-linear and not predictable.

To me, suggesting the "beginner speadsheet" is right at  "all air-masses", in "most of the sky" is too much in any case.

Clear Skies !

Roger

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Roy
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Hi Roger,

You wrote:

"Not sure the CCD/DSLR "ensemble" photometry with color transform (and more) is so new...  We are some using it, have a look at the reports... the publications..."

Apart from the Citizen Sky documentaion, I've not had any luck finding reports and publications on this type of technique. I would be grateful if you could give me some references.

Clear skies,

Roy


Hi Roy and Roger,

I'll second this comment.  We know extinction happens and it has been characterized by several different methods (see Wikipedia's page) so we should attempt to correct for it.  The intermedia spreasheet implements corrections for experimentally observed extinction (Young's 1994 formula if I recall correctly) which is robust over most airmass ranges where we would observe.

Have a good evening,
Brian

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Hi Brian,

I can see I am not getting anywhere with my suggestion that the beginner reducation spreadsheet has wider potential for images with narrow fields of view.

For anyone who is reading this, I just ask that you consider carefully the formula in that spreadsheet, and the science behind it, and consider its implications when the field of the image is very small (say, 1 degree). The formula represents a transformation coefficient calculated for several comparison stars, for the particular conditions that apply to that field.  The slope and intercept in the formula are determined by the responses of your system (lens or telscope and camera), and the air mass and extinction through which the image was taken.

I can say no more. I'll put my results together and try to publish them.

Roy


Hi Roy and others,

I completely agree with your suggestion that the beginner reduction spreadsheet is applicable elsewhere, especially where the FOVs are small.  But I wish for DSLR photometry to be competitive with traditional ground-based photometric methods.  DSLR photometry is clearly disadvantaged in that it only can get one, perhaps two, colors.  But the very wide FOV > 1 degree affords the simultanious measurement of hundreds of stars over a wide range of magnitudes and colors.  Clearly DSLR photometry can beat out many traditional methods that focus on one star at a time by measuring so many stars en masse.  Also, to get decent photometry on these stars only ten or so exposures are often required, meaning an automated DSLR photometry system could get hundreds of photometric points on thousands of stars each night!  It is really quite amazing.  The only issue is that of precision.  The best photometric surveys I've seen have fully calibrated (internal AND external) errors of 0.005 magnitudes.  I've seen internal standard errors from several observers at the 0.001-0.002 level, so with proper catalogs we can easily compete with this.

Let us, for a moment, assume we use the beginner spreadsheet and ignore contributions from airmass.  Let us also assume we wish to acheive 0.005 mag internal precision.  How much differential airmass (i.e. between two stars) can be tolerated?  Going back to the calibration equation:

(V - v)i = -k' Xi - e * (B-V)i - Z

and taking the derivative with respect to air mass:

dVi = -k' dXi

Which shows the error from not doing air mass correction is directly proportional to the extinction coefficient times the differential airmass across the FOV.  Using Thomas's Karlsson's earlier results we'll assume k' ~ 0.2 mag/airmass.  So if we wish to acheive 0.005 mag uncertainties at worst, we just plug in numbers and do the algebra: 0.005 = 0.2 dX => dX = 0.025 atmospheres.  If we had chosen 0.1 mag / airmass, dX = 0.05.  In either case, 0.02 - 0.05 airmasses is fairly small.  Depending on which airmass law you use, this can be anywhere between ~3 degrees at the zenith to much less than 1 degree at 30 degrees above the horizon.

So, in summary, I completely agree with you that the beginner spreadsheet is very applicable, but if you wish to acheive the maximum possible precision your camera can do, you will have to correct for airmass unless you are using very narrow fields of view.  Unfortunatly when you use narrow FOVs you increase the likelihood that you lose calibration stars that bracket your target object BOTH in color AND in airmass.  When this happens you are extraplating the behavior of your camera instead of interpolating the behavior between measured data points, which is itself a dicey procedure.  

As long as you are aware of these potential pitfalls and carefully inspect your results I think what you suggest is perfectly fine, but for the first-time photometrist who doesn't quite understand these issues or the uber-user who wishes to calibrate every star in the FOV, it is easier to simply apply air mass correction and look for outliers.

Cheers,
Brian


Replying to my own post:

I should also add that when I worked out the math for the beginner spreadsheet to find the tipping point of precision as it were.  I found with a 10 degree FOV (a little big for a DSLR) you can go up to z ~ 35 degrees away from the zenith before the error due to differential airmass exceeds 0.01 magnitudes.  I don't remember the other conditions (like the extinction coefficient).

Brian

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Hi Brian,

Many thanks for the excellent discussion on air mass and extinction. I agreee that, at high air mass, the price to pay is a small field of view and therefore fewer stars, making some fields untenable for accurate photometry. However, the method could be used not only with DSLR cameras, but also with more sensitive CCD cameras. With the latter, target stars can be fainter, and therefore more comp stars of appropriate colour may be in a small field. Even so, some CCD fields may not be tenable for accurate determinations if the range of colour indices is small.

Roy

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