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International Year of Astronomy | American Association of Variable Star Observers (AAVSO)
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International Year of Astronomy | American Association of Variable Star Observers (AAVSO)
Hi Richard,
Thanks for your interest in this problem. You suggested that finding a solution requires one to, "…multiply an extinction coefficient suitable for your observing site times the computed airmass to produce extinction-corrected instrumental magnitudes for each star." This is true, but determining the extinction coefficient is a real challenge. Knowing the airmass solves the geometric portion of the problem, but the much more difficult part is meteorological. Atmospheric variabilityhas a major influence on extinction. Determining the coefficient for a given light path requires an integration of humidity values along the line-of-site through a constantly changing atmosphere. That atmospheric data can only be obtained from an upper air sounding taken in close proximity to the astronomical observation – not a very likely prospect for most of us. But, do we need an absolute value for extinction? Since we are doing differential photometry,isn'tdetermining a differential extinction between stars sufficient?
Concerning the use of sky brightness, you said, "…sky brightness is not a proxy for airmass. Sky brightness depends on your local light pollution, scattering properties of the air, etc. Extinction depends on the length of the air path and amount of light absorbed." I agree that sky brightness is not a proxy for airmass, but it may be a proxy for determining differential extinction. Variations in the magnitude of light pollution should not affect differential measures of extinction. Whether light pollution is high or low, differences in sky brightness along various lines-of-sight will indicate differences in extinction. I propose that in a given image, stars in regions of equal sky brightness have light paths of equal extinction; higher brightness means more extinction and lower brightness, less extinction.
This analysis approach has the added advantage of combining the effects of both airmass and meteorological conditions in a single measure. Right now, I’m using the method qualitatively to select comparison stars that display similar values of extinction. Hopefully, if this method proves to have promise, someone in our group will develop a quantitative method of analysis. Best regards, Tom
Richard, Just done the tests on just one set of old data for 22 May 2010 where I took 10s images and 15 s images, a stack of each. I was doing some tests to check the value of mirror lock. I have taken the 10sec and stacked (ml on) and came out with 3.442 mag corrected. I took 5 of the original 15sec green channels and did them individually and by chance came out with 3.441 when average calculated. So it did not seem to make any difference. Maybe this is just chance. Might try to do the photometry on the 10 sec images but very hard to see lambda. Why is this? Well stacking is probably a better averaging tool than calculating the average for each set of calculations. Also I feel that the spreadsheet will need to be expanded so that you can do a conversion for each frame with all the check stars before calculating the corrected mag. I think the colour gradient of the atmosphere changes quite rapidly with time ( I think I could see the difference between frame 1 and frame 10.) Too much complicated stuff!! I should probably start the process again and document carefully on a sunday morning. It is also interesting to see the level of scatter of visual obs in the light curve. I am not sure we need more accurate but maybe a greater number might be the way to go. While being a science type person I love accuracy and predictable process sometimes pragmatic approach might be volume assessment. Best regards, John Mallett
Richard, If you have experience of single frame photometry being significantly better in terms of accuracy, have you taken the following into account: 1. At the moment we (I) follow the "beginners guide" published on this site.This will need to be changed. 2. I have reduced theexposure time to a minimum assuming a stack of 10 with darks etc. I would need to increase exposure time to undertake photometry at the same accuracy. The overall accuracy may be degraded by this process. 3.the time to process would increase by a factor ofup to 30.As somepeople do 2 or 3 sets of 10 images in order to assess accuracy. This may in fact reduce the number of observations unless the photometry could be automated in some way. 4. The mosteffort is put into the actual selection of flats, collecting darks at the same time as exposure and then the photometry. If photometric examination had tobe done on 30 images for say 5 variables, I think this would mean that toprocess data would take about a week for me, for one night observing. I have automated the collection(DSLR mounted on the Meade), preprocessing (according to the beginners guide) and storeage of the basic information like centre frame time and folder generation. I use AA4 for capture and file managementand AIP4WIN for preprocessing. I cannot howerver find a reliable stacking and photometry automated process. Maybe there is some further investigation needed or alternate methods not so heavy on the time consuming stacking and photometry tasks. I really do not see that it is possible to reduce the time spent on eachimage(stack currently) as ensuring the frame is goo and rings are the correct size etc is key togood results. Best regards, John Mallett
Interesting. I was going to write some software to do all the calculations in Perl so that it will work out the exposure based on all the usual factors (mag of star, alt, camera, temp, F, G to V correction ) then put in the ADUs for each ref and target. Then it can fill in the spread sheet or just generate a report. Try to cut down the time processing images and spend more time in the dome! Never have liked too much paperwork ;-(
Dear all, I am also looking at this subject and I amwritting an addition to my automated photometrycode under APL to take care of the low height extinction. But I have also searched for literature on the subject and I find only good data from an old french book "Rayonnements Optiques" from F.Desvignes. From that reading I conclude the air-mass is one inputto that problem but the true issue is to know the resulting extinction that depends on the conditions of air layers being involved (humidity... ) From the tables of that book the extinction factor for a given air-mass could vary with a very large factor (several times !) How are you gone to take care of this ? On my side I am planning to make a measurment of the differential extinction by taking several series of shots separated by 10~20 minutes (time to scan a couple of degrees of height) make an interpolation curve, apply it to the stars intensity depending their height... I am now waittingfor clear sky to test it ! Another issue is the stronger blue extinction of the extra blue being captured by the green filters of the DSLR. The usual "transform" technique doesn'ttake care of it ! I alreadyapplie another technique instead that is to use the blue channel intensity from the DSLR to correct the green intensity. I use it for a year now with very good results. Yours truly, Roger
Roger, I think we could make this over complex. If I can arrive at a simple calculation (already have an idea of this) that is just used based on alt of star and say an observer altitude and say winter and summer this will be close enough. There are more than enough local effects to have a bigger impact but if we can elliminate all the relatively straitforward ones that will help. looks to me that at sea level: Summer at 45 deg this would be a 0.13( at 0.5Km up it is 0.11) Summer at 30 deg 0.54 Winter at 45 deg this would be about 0.10( at 0.5Km up it is 0.09) Winter at 30 deg 0.47 It may be ok to ignore altitude of observasion unless you are very high. I would also say that you can probably ignore winter and summer variations as you are doing comparison photometry. However, the angle of observation does seem to be quite significant as you get closer to the horizon, so it may be worth a correction. I need to work out the worst case error onany set of comparisons assuming you never go below say 15 deg. Could be as much as say 0.03 per degree. However, how often are comparison stars that far apart? Sorry if I haverambled through this thinking process...
In reply to Roger's questions:
I too did a search for air mass correction literature. I pulled up a couple books and a few papers. I converted all of the methods over to using the true zenith angle (remember, the zenith angle can get projected below the horizon for angles close to 90). Ihave a Python module that does all of these calculations which I hope to eventually make public, but as you mention above, the problem becomes quite complicated. Given that over 10 minutes air mass does not change considerably, I was going to have our participants look up the air mass (using the AAVSOcalculator) for every star in the middle frames in their data and use those values. After we have the air mass, we *should* be able to extract all of the information (airmass correction, transformation coefficient, and zero point offset) from a single frame provided that we have at least three stars. I think this can be solved using linear algebra, but Ihaven't had time to do the work (big deadline this Friday/Saturday). I've created a list below of references and corrections for extinction. The polynomical approximations were done on data in a different filter set, and therefore may not be "quite right" for use on present data, although they should be close. In all cases, the equations ignore the effect of altitude. I've just placed the references below, Ithink they are mostly journal articles (but one is an obscure book). I think ADS will list all of the bibliographic information, so that's a good place to start. For now, this information should suffice:
Method 1: The simple approximation
This one is really simple, it's just the secant (i.e. 1/cos(alpha)) of the true zenith angle.
Method 2: Young's Simple Approximation
You can read about this in "Observational technique and data reduction" in Astrophysics V. 12 1974 pg. 152. This formula is good to 0.001 up to four air-masses.
Method 3: Young's "Complex"approximation:
This can be found in Young's "Air mass and refraction" 1994. This method is good to 0.001 air mass up to six air masses and takes into consideration atmospheric refraction to produce a maximum error of 0.0037 air masses at the horizon.
Method: The Hardie Approximation
Hardie, 1962 published in "Astronomical techniques." Hiltner, William Albert editor, Chicago, University Press (1962) pg. 180. This technique is a polynomial approximation to the data presented by Bempoard and is considered accurate to 0.1% to air masses of ~6.8 and 1% to air masses of ~10.
Hi! After some distractions ( like business travels and an incredible long period of bad weather where I live) I come back to Eps Aur observing...and of course by now it's a real challenge because it's so low in the sky. What I plan to do whenever there is a chance (weather-wise) is to get out on a clear day and try to get a series of frames of Eps Aur and comp stars starting in twilight over a longer time and then see how this fits with theoretical extinction models. I see two options: 1) still do photometry on a single frame , and try to correct for extincion differences of V and comp stars or , a more outside-the box-concept: 2) do photometry using multiple frames, one frame per star, where the timing is chosen so that the extinction value of the stars will be the same. Option 2) has many obvious drawbacks : at different points in time, several conditions will not be the same: sensor temperature, sky background brightness, other atmospheric conditions (thin, invisible cloud covers...) and I do not really expect this to work, but I'd like to try nevertheless, just for fun. I also wonder whether telescopes might help to catch eps Aur while it is still higher in the sky, I can remember that Brian made some tests on daylight photometry of eps Aur with some professional telescope (on Mt. Wilson also, right?) CS Heinz
Hello Heinz, I have been reading with interest the range of ideas concerning how best to compensate for variations in air mass. Sadly, my math skills are not up to the rigors required to comment on the various methods suggested so far. I thought, however, you might be interested in a "qualitative" analysis method I have been experimenting with.
As Auriga has migrated westward with the changing seasons, I noticed that the correlation results for my Transformation Coefficient calculations were steadily deteriorating. I’ve attached two Spreadsheets, one from January and the other from April, which illustrate the problem. I was sure that air mass was the culprit but did not know what to do about it. Then, I noticed that the background of my Spring images (taken at an elevation away from the zenith) displayed a steady transition from black to light grey across the field. It was clear that this grey shade change was caused by air mass variations. I’ve attached an image from April illustrating this change in the background.
Next, I decided to see what would happen if I chose comparison stars from a similar grey shade area, i.e., similar air mass. I selected lambda, rho and mu Aurigae (C1, C2, and C3). The results are shown in the third spread sheet. As you can see the correlation is much better.
Roger Pieri brought up the point that weather also affects extinction. This qualitative method has the advantage of integrating the effects of geometry (air mass) and meteorology (humidity) into one result.
One last point, AIP4WIN, provides quantitative values for background brightness in the "Star Image Tool". There may be a way to use these figures to compute a correction factor that could be applied to all the comparison stars in the field. Best wishes, Tom
Tom, Just as a matter of interest, why are you not using zeta and eta? They are close to the same grey level. Another question: What was the origin of your spreadsheet. It seems slightlydifferent to the one I use. It has extra comments on it. I notice that you list individual images on your spreadsheet. I stack 10images(with dark and flat)then do the photometry on the stack. This was the process that was in the beginners guide. Do you see an advantage in doing the individual images? I have submitted a couple of estimates recently and it looks like eps is on the increase. Best regards, John
Hi John, I don't use zeta because I believeit's a variable. Concerning eta, I started months withit as my primary comparison star but found lambda worked better. I have not usedeta sinceas comparison star, but I will go back and check it.Thanks for bringing it to my attention. The spreadsheet is one I developed whenwe first started discussions about methods for computing a TC. Iputin all the commentsto, hopefully, make the sheet self explanatory. I'm still using it more for consistency than anything else. I stack 30 imageswith 10 darks and 10flats. The image numbers are the first and last in a series. I redo the calculations (using three sets often images) to compute a standard deviation. From what others have said,thirty images may bemore than necessary but, again, I continue to do it for consistency. That's interestingabouteps brightening.Do you think it's the beginning of mid-eclipse brightening? What a shame that we'relosing Auriga behind the sun at this critical time - ugh! Warm regards, Tom
Tom, I think I only have a few more days, maybe early June. So we might miss all the interesting inner part of the rings. Regards, John
John, Yes, it's very sad. Plus, to make matters worse, the weather has been uncooperative here. I did check your suggestion about using eta. On the April 16 image eta and eps are in a very similarregion of "greyness". However,the sky brightness for eta is different from thatofthe stars I was usingin the TC calculation. The Star Image Tool in AIP4WIN gavethe following values for sky background: Eta-108, lambda-102, sigma-101 and rho-99. It's my theory that equal values of sky brightness means equal values of Air Mass. By selecting stars with nearly equal Air Mass, I avoid the need for compensating calculations. Tom
Hi! >It's my theory that equal values of sky brightness means equal values of Air Mass. interesting theory, one could actually check that with some online air mass calculator. But I think that for the sake of eps aur measurements, the main inflence on sky brightness will be position of the sun below the horizon. later in the night, the glow from human made light polution near the horizon should be dominant, right? Meanwhile, I'm eager to try some twilight photometry thru a small telescope, but no luck: lots of clouds. I have a feeling tho that this would work well. CS Heinz
Hello Heinz, You are quite right, twilight willcontaminate the resultsas eps aur approaches the sun. I live in the middle of a large urban area so I am surrounded by sky glow. It's a real pain for every other astronomical applicationexceptthis one, so I'm hoping it works. Tom
Airmass can be a tricky thing to work with. I was thinking we could use the AAVSO airmass calculator, otherwise we'll have to write macros which not everyone permits to run in Excel (and they may not port correctly to OpenOffice asI've found out several times. Given that an observing session is ~10-minutes, the differential air mass for zenith angles less than 60 degrees should be minimal (I'll need to prove this formally to double-check it's validity). So we would only need to calculate air mass once for the whole set of data. Brian