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zero point, AIP4WIN

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I am currently trying to get to grips with the tutorials for both AIP4WIN and IRIS in terms of analyzing DSLR images.In the AIP4WIN package, relating to the eps Aur sample images, what is a suitable zero point? All the best,Chris Allen / Swedenwww.variablestarsweden.se

Zero point not needed for differential photoetry AIP4WIN

Hi Chris, To see the zeropoint Zp drop out - Write the photometric equations for V1 the variable and V2 the comparison: V1 = v1 + Tc*(B-V)1 - k'*X1 + Zp V2 = v2 + Tc*(B-V)2 - k'*X2 + Zp Subtract the two i.e. we perform differential photometry: V1-V2 = v1-v2 + Tc*[(B-V)1 - (B-V)2] - k'*(X1-X2) Add V2 to both sides of the equation: V1 = V2 + v1-v2 + Tc*[(B-V)1 - (B-V)2] - k'*(X1-X2) Solve for variable star V1 which is epsilon using say lambda as a comparison star V2. Note: AIP4WIN calles the first star to be measured Var and the second measured star C1. V2 = cat value of lambda = 4.705Vmag v1-v2 is measured by AIP4WIN seeMeasure, Photometry, Single Image window. Click first on epsilon Var, then on lambda C1, then click get magnitude and plug the differential magnitude reported by AIP4WIN into v1-v2 above. Besure to average enough frames so that sintillation errors of short exposures are the equivalent of one long exposure of about 1 minute. Tc is the color transformation coefficient determined elsewhere. My NikonD100 with a skylightfilter is -0.1204. I thinksomeCannonDSLR have about +0.15.Negative values means myNikon's greenfilter is too blue of Johnson V filter. The CannonI believe are positive meaning they are too yellow ofthe Johnson V filter. (B-V)1 is epsilon pre-eclipse cat value = +0.54mag. Caution, eclipse may alter the color index. Check with those who can measure UBV for changes. (B-V)2 is lambda cat value = +0.624mag k' is a positive number usually between 0.2 and 0.5 that must be measured from various field star pairs each night while high air mass conditions exist. Pick field pair stars far apart in altitude such a Lambda and Eta so as to measure a greater airmass as possible. Later, say end of September, with epsilon much higher from the horizion, you may choose to take a short cut and totally ignore differential extintion. For now try k'=+0.25 and see how close you get to other reports. You can use the above differential equation to solve for k' each night using using two or more pairs of stars having know cat values, say lambda for V1 and eta for V2. X1-X2 is the difference in air mass between epsilon and lambda in that order. Use AAVSO or other airmass calculator. I like www.mirametrics.com/airmass_planner.htm There you have itAND NOZERO POINT! Read the earlier disscussion in this interest area for tips on how to import your raw camera images into AIP4WIN and how to debayer it properly. Dark frame subtraction is about the only pre calibration I would recommend. Nikon D100 does dark frame subtraction inside the camera. Most skip flats as it is hard to obtain a wide field illumination source. Watch out for saturation! AIP4WIN analysis can help detect over exposure. Defocus to AIPWIN default of about 6 pixel radii. etc. Tc, the color tranformation coefficient can be determined from others that have the same camera model (i.e. sensor). Or measure several non variable close star pairs having greatly different color index and use the equation: Tc = [(V1-V2)cat - (v1-v2)AIP4WIN] divided by [(B-V)1 - (B-V)2]cat.Average at least half a dozen different pairs. You should be able to derive this equation from the differential photometry equation above. When eps is near zenith this fall/winter you can use Brian Skiff's list of stars see http://www.hposoft.com/Campaign09.html news letter #6 else use AAVSO's map generator and data base for something near zenith right now. Good luck, Charlie Hofferber

Zp not needed for one star, but what if...

Charlie, You are correct that the zero point is not needed if you calibrate against one star (it drops out exactly like you stated above). We elected to calibrate against several stars in our tutorials to remove the chance that the varability in the comparision stars (all stars are variables to some extent) would affect the resulting number. Plus by fitting multiple stars using a least-squares method we can also determine errors in both the transformation coefficient and zero point offset. We also include several stars in our reduction to determine the extinction coefficient for that exposure, hopefully yielding a more accurate estimate for the target star(s) brightness. I've worked up the spreadsheet for doing these calculations and we're testing it now. I'd be more than happy to have your input as well (see this thread). Cheers, Brian

Zp not needed for one star, but what if ...

Hi Brian, I also calibrate or average aginst up to 5 or 6 stars. I wrote the differential form of the photometric equations to show how Zero point drops out for determining Tc and k' as well epsilon itself. So far I see no need to determine the Zero point. I understand Zero point and the traditional least - squares methode slope and intercept, but have neverused it. Using up to 5 pairs of non variable field stars, I measure differentially to get 5 values of k' thentake a simple average of k'. I then measureepsilon differentially aginst 5 different comparison stars, apply green filter color correction, extintion correction, then average the 5 epsilon Vmags and finnally compute the SD of the average. This methode only works well for very high air mass because epsilon and k' are all measured from the same set of 10 exposure. Also any error in theX air massmodel is absorbed in k' measurement. Also it is easy to find pairs of stars in the wide field that have significant differential air mass. As epsilon climbs higher, i.e. X become smaller, this method will fail because field star pairs do not have enough differential extinction to calculate k' accurately. I think this will happen at about X = 2.0. I will then likely assume a seasonal average k' or if I have time, follow a star(s) 30 minutes either side of my main exposue sequence. In the winter it is 20 deg below in Minnesota, but eps will be near the zenith and I will take 10 quick expsoures and ignore extinction all together! I am aware of a couple spread sheets out there, but have nottried them. They would probably save time and reduce accounting errors. Charlie Hofferber

AIP4WIN magnitudes

Hi Charlie, Once again, many thanks for taking the time to help me with this- it really is much appreciated! I think I am now more on the right lines as I have clicked on the 'Get magnitude'. The file I am using to practise with is the sample file from the citizen sky site and not one of my own files. These are the values I now derive for the 6 comp stars: C1- minus 1.037 plus/minus 0.018 C2- minus 0.469 plus/minus 0.016 C3- plus 0.023 plus/minus 0.013 C4- plus 0.337 plus/minus 0.012 C5- plus 0.539 plus/minus 0.012 C6- plus 0.869 plus/minus 0.010 Looking at C1, I derive an instrumental magnitude of 4.705 minus 1.037= 3.668 for eps which is roughly what might be expected (not sure when the images where taken). If you could just 'walk' me through the equations with these values I would be most grateful. Am I correct in saying that it is not necessary to stack lots of images for a bright variable like Eps and that you could do an average for a number (say 10-20) of separate images? I have taken some pictures of my own of beta Lyr and will see how far I get with this as eps is currently so low, even from Sweden where I live. All the best, Chris

AIP4WIN Magnitudes Walk Thru

Hi Chris, I can see you are on the right track with measuring raw differential mags in AIP4WIN. I would caution beginners to not click on more than one comparison star. C2, C3, C4 C5 etc. form a super composite comparison star that is hard to use and will not tell you epsilon differential mag directly. Always Click CLEAR before you make another measurement of a pair of stars. The first star you click is my v1 which AIP4WIN labels yellow V. Inthis case it looks like you selected epsilon. The second star is my v2 which AIP4WIN labels green C1. Then as you have done, click GET MAGNITUDE and record the differential mag as -1.037 which is my (v1 - v2). After clicking CLEAR, I suggest you also measure the pairs epsilon - eta, and epsilon- 62 Aur. If photometry isdone right, the three comparsion stars should yeild appoximately the samemagnitude for epsilon. You can then average the three estimates for epsilon and determine a Standard Deviation. Let me now walkyou thru the differentialform of the photometric equation for Vmag. Assume the online image was takenDec 20, 2009 at about 11pm localatan observatory about +47 deg north lat (just happens to be my location). I pulled up The SKY planetarium and see that epsilon isonly 5 deg fromzeneth.The sky reports Epsilon Air Mass X1 = 1.00 and Lambda Air Mass X2= 1.01 The differentialphotometric equation: V1 = V2 + (v1 - v2) + Tc * [(B-V)1 - (B-V)2] - k' * (X1 -X2) Assume the test online image was taken with a Cannon DSLR camer having Tc = +0.15 V is epsilonhaving V=variable, (B-V) assumed cat value of +0.54(yes the B-V of eps couldbe variable also, but most assume this eclipse isgray thus does not change much). C1 is lambda comparison star cat values of V=4.705, (B-V) = +0.624 AIP4WIN measured -1.037 for the epsilon - lambda pair Thenightly k' was measuredor assumed to be a typical +0.24 value. V1 = 4.705 + (-1.037) + 0.15 * [(+.54) - (+.624)] - 0.24 * (1.00 - 1.01) V1 = 3.668 + (-0.0126) - (-0.0024) = 3.657 reported mag for 20 Dec 2009! Thus V1 = 3.657 = epsilon reported Vmagtransformed to Johnson V filter and corrected for extinction. See V band composite light curve at http://www.hposoft.com/Campaign09.html for other observer reports on orabout 20 Dec 2009. As you see the color correction of -0.0126mag is sizeable due to the camera green filter not being the same as Johnson's standard Vband filter. As expected, the extinction correction of just -0.002mag is so low it can be ignored in differential photometry if the star to be measured is only a few degrees from the comparison catalog star and both are say 30 degrees or less from the zenith. Finnaly, you need to stack about 10 exposures or measure 10 frames separtely and average them with a calculator due to sintillation, i.e. star twinkle. The rull of thum is the number of short exposures should add up to about 1 minute or more total. There is some sintillation estimators on the web. The last time I checked for my 50mm f.l. lens at about f2.8 and 8 sec exposure, the error was about +/-0.02 mag. So by averaging 10exposures the sintillation error is reduce to about0.002 mag. I am kinda embarrassed here in that I have not taken the time to get AIP4WIN stacking of images to work, soI waste a lot of time with the calculator averaging. One final note youdo not need to use the +/- error reported by AIP4WIN. It is based upon some S/N statistics. You should report a standard deviation of epsilon measuredby three or more different comparison stars. Others, measure epsilon only aginst lambda. To report standard deviationthen you need 3 sets of 10 exposures. Average the three estimates and report a SD. There are SD and Air Mass estimator tools on the web, do a google search. All the best Charlie

k' and Tc

Hi again Charlie, I have just a couple of last questions before trying to put this all into practice on Beta Lyr (as Eps is still so low). Firstly I wondered if you could again walk me through the calculation of Tc using the AIP4WIN data for Eps Aur. Seeing how the values plug into the equation really is a very big help! Secondly, how do you determine k'? Is 0.25 a typical value? Hopefully I will soon stop pestering you and start reporting data! I have been interested in variable stars for many years (I am a member of the AAVSO and BAA VSS) but this measurement of digital images is new to me. All the best from a rainy Swedish island Chris

k' and Tc

Hi Chris, You are almost ready, but need to determine your camera/lense system Tc, and maybe k' if you can not observe within 60 degrees of the zenith. I think all the differential form of the equaions I use have been presented by now in the thread that was startedto show zero point is not needed.Rather than extend the length of this thread to show how Tc and k' are extracted from real images, let me work with you by direct email. If your email found on your web site is current I will contact you there. I amexamining somepreadsheets that others have developed in this form. The beginner/tutorialversion should determine your Tc and Zero point as well as the Variable mag to report. It lacks extinction correction. An intermediate spreedsheet is under development to includeextinction. Spreadsheets help automate the process.It is still important to understandthe basis and to be able to hand check your resultsusing the photometric equations. Clear Skies, Charlie Hofferber

spreadsheets and instrumental magnitudes

Hi Charlie, Thanks for your reply. I am aware of the need to get spreadsheets to work in order to make this process manageable- I have a question about the spreadsheet found on the Citizen Sky website which I wonder if you could help me with. In AIP4WIN, firstly I click on the variable, eps, which comes up yellow and then on the six comp stars in turn, which are then labelled C1- c6 respectively. The tutorial talks about check stars / calibration stars. Am I correct in thinking that the first comp star I click on, C1 or lambda will be the check star. The differential magnitudes which AIP4WIN reports when I click 'get magnitude' will then be differential with respect to lambda. Thus if I get a value for C2 (rho) as -0.469, the instrumental magnitude I report in the yellow space in the spreadsheet for rho will then be 4.705-0.469 = 5.174? I then repeat this for the remaining comp stars which the spreadsheet will then compare with the catalogue values for the computation of Tc. Is this a correct understanding? If you have an old spreadsheet with your own values in, this would be useful to see. If you give me your email address I'll correspond with you directly. My email address is chris.allen@telia.com All the best, Chris

Greetings Chris, I'll field

Greetings Chris, I'll field this one for Charlie if he hasn't replied to you directly. We tried to make the spreadsheets as simple as possible and, in an effort to minimize errors, made it so you need not compute anything by hand. So you'll just plug in the imags from your photometry software directly, i.e. the -0.469 you mentioned above. After you insert the calibrator's V-magnitude, and B-V value (from the calibration standards page or from the 2MASS catalog we link to there), you'll see that the D Cat value (your 5.174) is automatically computed (the value will actually be -5.174 due to the algebra involved in rearranging the equation, I think we explained that in the tutorial... please let me know if we didn't). At a minimum, you'll need to measure the imags for at least three stars: your target and two calibrators. I'd suggest using six calibration stars: lam Aur, rho Aur, mu Aur, ome Aur, sig Aur, and 58 Per. You can use one of these stars or some other field star as a check star. You'll use this star to verify that you are getting reasonable values out of the equations. The spreadsheet will automatically compute the transformation coefficient and zero point based upon the best fit to the comp star data you provide. The transformation coefficient is the slope of the graph and the zero point is the intercept. Ideally all of your points should fit very closely to the line and the R-squared term should be close to 1. If you notice that one star is far from the line, it is likely that something was mis-measured or incorrectly entered into the sheet. Lastly you'll put in the check star imags and target star imags into the cells in the bottom table and the equations in the sheet will automatically compute the calibrated magnitudes. If the check star is within a few 10s of milli-mags of the catalog value, you'll likely have a valid value for the target object. As Charlie mentioned above, the beginner spreadsheet doesn't account for air mass. The intermediate spreadsheet has been through the ropes and is ready to be used in general. I'm in the process of writing the documentation for this spreadsheet and Ihope to have it up over the weekend. Please let us know if you think anything needs to be clarified on the tutorials! Dark Skies, Brian

Greetings Chris, I'll field

Hi Chris and Brian, Sorry to take so long getting back to you,I am busy and wanted to try out Brian's Intermediate form of the spreedsheet since the beginner version does not correct for extinction. For observation of epsilon on 2010/07/25, RJD 5402.8666, 08:47:53 UTC I obtained: Calculator method: V3.644,SD.012,X=2.213, Tc=-.1204, k'=+0.2309 Brian's Spread Sheet: V3.657, ______, X=2.213, Tc=-.1140, k'=-0.2910 The difference in the two results is only 0.013Vmag or about 1% The Tc differed about 5% k' differed by 20%, but Irejectederrant measures before averagingonly 3 star pairs to determine k'. The spreed sheet performs a least squares fits of all 6 stars even if some appear morescattered. NOTE, do not be concerned with the sign of k'.The sign of k' isdetermined differently but consistant within each methode. Classically, I think k' is a positive number. The "Calculator" method is based on the differential phometric equations I presented in this thread. I used 5 comparison stars's average measure of epsilon having the SD noted above. I think Brian's advanced version will have statistical estimate of error and other features perhaps k". Chris, for beta lyra, you can try the beginner version if imaging is done 60 degrees or less of overhead. For epsilon Aur, theextinction corrections requires you to use theintermediate version at present X=2 or so. Brian, as an aside, epsilon aur seem to have a dome shaped brightning curve heading for a peak of>= 3.6Vmag in 20 days. I know we are not suppose to extrapolate, but it is fun to speculate on the "donute hole". Good luck with your visit to CHARA. Clear Skies, Charlie Hofferber

Many thanks

Many thanks, Charlie This is now beginning to make some sense. I might have to pester you with a few more questions though! All the best, Chris

calculations

Hi Charlie, Many thanks for taking the time to answer my questions. I have a few more questions about the calculations:

Tc = [(V1-V2)cat - (v1-v2)AIP4WIN] divided by [(B-V)1 - (B-V)2]cat Towork out Tc, you need to know the catalogue value of V1 but surely this is the value of the variable you are trying to measure? From AIP4WIN, I derive v1-v2 as -(minus) 5.7000plusminus 0.017. Am I correct: Tc= (V1-4.705) - (-5.700) / (0.54-+.624). What answer do you get? As I struggle with maths, I wondered whether you could help me by plugging values into the equation below and again giving me the answer V1 = V2 + v1-v2 + Tc*[(B-V)1 - (B-V)2] - k'*(X1-X2) Many thanks for helping me, Chris Allen / Sweden

Calculations

Hi Chris, Hang in there, it took me a while to figure some of this photometry out. I am worried if AIP4WIN is giving you -5.700 for (v1-v2) measurement. With lambda as the comparison star V2and Ignoring color correction and extinction, corrections we have for V1 epsilon: V1 = V2 + (v1 - v2) where (v1- v2) is the differential magnitude reported by AIP4WIN epsilon Vmag = 4.705 + (-5.7000) = -0.995 Vmag for epsilon! This would make epsilon the brightest star in the sky even under eclipse conditions! Right now (mid July 2010) most observers are reporting Epsilon Vmag = 3.7 or a little brighter. In AIP4WIN, after reseting or clearing previous measurments, besure you click first on epsilon and it will label the star V, then click on say lambda and it will be labeled C1. Then click GET MAGNITUDE to find the differential magnitude (v1 - v2). You should get something close to 3.7 - 4.705 = -1.005. Some things to check: Do not overexpose or you will saturate one ormore stars. I use 8sec at f2.8 to f4.0 at ASA 400 for a 50mmfocal length lens. The raw DSLR image loadsinto AIP4WINso dark you can not see any stars until you click AUTO to scale the image for monitor display. Under Preferences, DSLR, I only click DeBayer, White balance using camera settings, and BILIN (Bi-Linear Interpolation). On my camera I use white balance sun or daylight. Check on this blog page about 6 months ago, for Richard Berry, the author of AIP4WIN,slightly different recommendations. I assume you split the color DSLR image by clicking color, split, RGB. Click X-off the other separatedcolors so you only use the "Green" debayered image. Agin check with the discussion about 6 month ago with Richard Berry for recommendations if you stack images. I have not got the stacking to work, so I measure 10 images and average using a calculator. You need about 10 images to reduce sintillation error of short exposures. Let me know when you can get AIP4WIN diff mag of about -1.0 for the eps - lambda pair and I can walk you through the rest of the equations. SHORT CUT: If you measure epsilon using the comparison star 62 Aur (05h 07m, +43deg 10') you can come within about 0.03mag of epsilon's true mag without ever correcting for color or extinction. This only works for 62 Aur because it is very close to eps and has almost the same color index (B-V). 62 Aur = 6.218Vmag, B-V = +0.451 and is about 1 degree away from eps. I found your web site but not sure what DSLR and lens you are using. Please get back to me with exposure info so I can try to understand your data. Also you may have been resetting the AIP4WIN zero point, try to reset AIP4WIN to its defaults to be sure you do not have clipping going on. Good Luck, Charlie Hofferber

Calculations

Hi Chris, Forgot to answer you question about determining Tc. We do not use epsilon or any other variable star for V1 or v1. Here V1 and v1are the 1st star which AIP4WIN always calls V. V2 and v2 are the second star which AIP4WIN calls C1. We pick stars having well known catalog values. I use capital letters usually for cataloge values, while small letters represent measured i.e. AIP4WIN values. It is important to keep the 1st star 2nd star order to avoid sign errors. Never click on lambda the comparison star 1st then on eps the variable second or a sign error will result. We wait untill epsilon's field of starsare near the zenith so we do not have to worry about extinction. Then we find pairs of stars close to each other aginto minimize extinction corrections. The pairs of stars should have widely different color indexes (B-V) i.e. a blue star nearby a yellow star. Avoid the realy red stars. Right now, the stars near epsilon will not be near the zenith till fall so we would have to use another field. Fourtunately, we only have to measure Tc once provided we do not change camera, lens, or telescope. Jeff Hopkins's Epsilon Aurigae news letter #6 has a list of suitable star near by eps. I can give you an example later if you wish to evaluate the Tc. For now let work on getting AIP4WIN to report the correct differential magnitudes. Charlie Hofferber

These might be them...

Greeting Chris, I think they were about 0.10 for the slope (transformation coefficient) and 2.17 for the intercept (zero point). Don't be worried if the zero point offsets between the two software packages don't agree as they probably don't use the exact same method for determing insturmental magnitudes. They should, however, yield the same or similar calibrated magnitudes given the same input data. Cheers, Brian

zero point

Thanks, Brian. I think you are referring to the graph generated by the Excel data (see tutorial) but in order to determine the coefficient, surely I need to derive a realistic instrumental magnitude from the stacked image first. I enclose a screen shot from AIP4WIN- would be grateful to know what values to feed in to generate a realistic instrumental magnitude. From the sample image files, I have so far derived instrumental magnitudes of about 5.2 to 6.1 for the comp stars. Is this realistic? Grateful for any help you can provide. Best wishes, Chris Allen

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Just need i-mags with a constant (arbitrary) zero-point

Greetings Chris, One of the tricky parts about how we've implemented our spreadsheet is that the instrumental magnitudes you get don't necessarily need to match what other people are getting. Although you are using the sample data, most photometric packages let you apply a constant offset term to the data that, in turn, changes the zero-point offset which, in turn, modifies the instrumental magnitudes. That's one of the reasons why we didn't include any goal-numbers in our tutorials! In the document you attached, you can safely set the zero point to anything you wish. I'd suggest using zero, but it's completely arbitrary. The math behind the situation is thus: (V - v) = e * (B-V) - z The import term is the z on the end which is the zero point offset (see the beginner calibration page for a complete explanation of the other terms). If you add a constant value of say 3.5 to every star (which is your current zero-point offset in your settings tab), we have the following equations: Star 1: (V - v) = e * (B-V) - (z + 3.5) Star 2: (V - v) = e * (B-V) - (z + 3.5) ... Star 3: (V - v) = e * (B-V) - (z + 3.5) Then, when we do a least-squares fit to solve for the transformation coefficient, 'e' and the zero-point offset, 'z' we find that z = something - 3.5 where the "something" is the true zero-point offset from your camera and the 3.5 mag is subtracted to remove the boost of 3.5 given in the above equations. So, in that respect, the zero point values you obtained are completely reasonable. I am, however, interested in what you obtained for a calibrated magnitudes for the stars in the data set. You should obtain a more-or-less constant comp-star reading (I had changes in the third decimal place for lam aur) and get a calibrated magnitude for eps Aur around mag 3.7xx(ranging between 3.713 - 3.730) What I'm really trying to stress above is that the zero-point offset is (for our purposes) a completely arbitrary number that is removed during the calibration process. Because of this, comparing your i-mags with other people's i-mags shouldn't be done. Also, because of atmospheric changes and camera drift, comparing i-mags over different nights shouldn't be done unless you really, really understand what is happening with your instrument night to night. Hope that helps, Brian

Use of zeropoint

I calibrate all my images by setting an offset in my photometry program so that I get Vi=4.705 for lambda. As pointed out what you set really don't matter, but I think it is nice to get roughly the same values for Vi as for V. In my spreadsheet then I calculate Tc, k' and Zp. The zeropoint now become the valuewhere the sum of (V calculated - V catalog) for all compairsion stars is zero. This is about the same as: -Tc * (B-V)lambda - k' * AMlambda. It is exactly this value if it happens that V=Vi=4.705 for lambda. But in general Vi for lambda, as the other compairsion stars, suffer of random error of about +/-0.02 magnitudes, that can make the zeropoint to differ by that amount to get the best fit value.

significance of zero points (if any)

Hi Chris Zero points are highly overrated :-) Now seriously, if you are doing differential photometry, you just don't care about the zero-point. Let me explain: By selecting a certain zero-point for the instrumental magnitude calclulation, you effectively add a constant offset value to your instrumental magnitude values. So let's say you make two arbitrary choices for the zero point, one being 10.0 higher than the other. You might get these results for the instrumental mags: 1st choice: Var star: 4.3 Comparison star: 3.7 2nd choice: Var star: 14.3 Comaprison star: 13.7 Quite dramatic, but then again, we are doing differential photometry. So we know that (say) the comparison star has catalog magnitude 3.2 In both cases the result from your measurement is that the var star is 0.6 mag darker than the comp star (4.3 - 3.7 ) = (14.3 - 13.7) , so we add this to the catalog mag of the comp star and get 3.8 for the variable star, no matter what zero point we selected. That's the beauty of differential photometry: sometimes it's so much easier to measure the difference of two values than their absolute values. Zero point would be interestinrg if you tried to make a measurement without a comparison star, but that requires so much more calibration precision that it's not a good idea unless you are somehow forced to do that (e.g. absolutely no suitable comparison star in the field). Hope that helps, HB

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