Hi all,
I'm moving my first steps in DSLR photometry.
Recently I have taken 12 images of the variable U Del using a DSLR Canon 600D with 85mm lens mounted on a tripod, and set ISO 200, f/4. Each image was taken with an exposure time of 5 seconds. So 5s x 12 = 60s.
I have stacked all images with Iris and extracted green layer. I computed Green magnitude using Citizen Sky analysis spreadsheet, but I have made some small changes to this spreadsheet. Instead of using a single check star, I used all comparison stars for check. I have calculated the difference between calibrated and tabulated magnitude for all comparison stars, and then the average value of these differences. I thought I'd take this value as an error on the measure of the variable's magnitude. Is this procedure correct?
I have attached a screenshot of modified spreadsheet for better understanding.
Thanks for the attention,
Luigi
Hi Luigi,
Normally a check shall be independant from the comparison, single or ensemble, I think your process introduces a bias. Next, magnitude are not a linear representation of the light flux, that should be considered.
Personally (using my VSF technique) I use the deviation of the individual stars of the ensemble as an indicator of the "quality" of the observation. That indicator is calculated as the standard deviation of the values of the star population of the ensemble from the catalog values fitting. But this is not the error of magnitude of the target or a check, it's only a statistical indication of the quality of the observation, the probability of error, but not the error.
Clear Skies !
Roger
thanks for you
Hi Roger,
thanks for you answer.
Because of my limited experience in this field, I'm not sure I understood your answer.
However, I forgot to say that the differences between calibrated and tabulated magnitude for all comparison stars are taken in absolute value. Some differences are positive and others negative. If I consider the mean of this differences, it is zero.
Also, I have not perform any preprocess: no bias, no darks, no flats. The reason is that I have not much experience with these things yet, especially with flats. For now I think I have no problem to take account for bias and darks. But, for flats, I have serious doubts about how to get them.
Said this, do you think that the results I obtained are sufficient to be downloaded to AAVSO database? And, if so, what error I have to report in the form?
Any other advice on how to improve my work is very welcome.
Regards,
Luigi
Hi Luigi,
The flat is more important than bias and dark in fact. Most lenses have a serious vignetting at their full aperture, if your stars are not all near the image center the vignetting will create a significant reduction of the flux of that stars. As an exemple a 200 mm F4 tele-lens has a center to edge vignetting of about 40% at F4 ! Wide angle lenses are worst.
But making good flat is not that obvious, anyhow on optical view point, an usual flat is not the exact representation of the vignetting in photometry ! The flare that anyhow exists in lenses affects it. There could also be problems due to the geometric distortion of the lens. My recommendation would be to use lenses having focal of 100 mm or more, 200 mm is a good choice. It provides a large aperture diameter (more photons), have usually low geometry distortion and limited vignetting. Zoom are worst. With a 200 mm it's possible to make flat on the clear sky, at zenith when the sun is just below horizon, very simple. Take 20 images and average them (no median ! It's an usual mistake). With shorter focal the only way is to use a flat-box or an uniformely illuminated white panel, but it's not simple to ensure that illumination is uniform. 0.01 mag is just 1% !
If you use a simple dark process, bias are not useful, they are already in the dark.
Error: here I think we have a wording issue. What should be reported is the standard deviation (SD) of the measurment. The true error is, by principle, unknown. To determine the SD the best is to make five groups of pictures, either stack and measure the target in each of the five, or measure all images and average each group. Calculate the mag from the comparison as usual, then make the calculation of the SD of the five target values and divide by 2.24 to get the SD of the mean of the five groups, what you should report as the end result: mean and SD of the mean.
Each group shall cumulate at least one minute of exposure that to eliminate the dispersion due to the scintillation. Two minutes is best.
Another way to estimate the standard deviation is to use the inverse of the SNR (signal to noise ratio) but that supposes the noise of images is the only dispersion cause, that's not usually true.
To get back to the standard deviation of the ensemble fitting we should realize that SD includes errors from the catalog and other causes (color, extinction gradient...). When in a campaign I usually readjust those values to my well established results obtained after some time. Otherwise the SD of the ensemble fitting doesn't reflect the quality of the observation. But that SD has nothing to do with the SD of the target end result, it's just an observation quality indicator. Catalogs are often not that accurate !
Clear Skies !
Roger
Luigi,
From what I am reading you are trying to decide how to calculate error? From what I see you have stacked all of your images and you are reporting the estimate from one image?
The ideal way to calculate the error in this case is esimate the value of the target star using each comp star. You will then report the magnitude of your target star as the mean of the estimate from each comp star. Ther error would then be reported as the standard deviation of the mean.
Example:
Using comp one, you estimate the variable to be 6.24, comp 2 variable est 6.30, comp 3 6.27, comp 4 6.29, and comp 5 6.27. You would report the magnitude of your variable as the mean=6.274, the std deviation would be 0.023. This would be reported as your error.
A more ideal way would be to have more than one image that you will report as a single data point (at least 3) then report the error as the standard deviation of the variable star (if there isn't a significant fluctionation in brightness over the period of your observations) or report the error as the standard deviation of the check star if there is some fluctuation in your variable.
Hope this helps.
Barbara
Hi Barbara, Roger.
Barbara,
as I said, I use the Citizen Sky project spreadsheet. In this spreadsheet the variable's magnitude is calculated with a best fit using all comparison stars. I don't know how to determine the variable's magnitude using only one comparison star.
Roger,
yes, I had to take more set of images and calculate the variable's magnitude for each set, and determine the error using the standard deviation. But in this case I have a unique set and I can't determine the standard deviation. It seems reasonable to me using the average of difference (in absolute value) between calibrated and tabulated magnitudes of the comparison stars for estimated the error on variable's magnitude. But, in effect, as you said, this is just an observation quality indicator.
However, the next time, I will take more set of images and I will stimate the error calculating the standard deviation of the each set values. But I think that this will require a lot more work. Using my 600D camera with 5s exposure, I will have to take 12 images for each group (12x5s=60s, the minimun required). With 5 groups, I will have to take 60 images. Also the subsequent phases (processing, photometry) require a work 5 times greater that I've done with a unique set. Now the question is: Is it worth?
With a unique set of 12 images, I think that I have reached an accuracy of a few hundredths of magnitude, as can be seen from the difference calibrated-tabulated magnitudes of the comparison stars. This level of accuracy seems very good compared to those of visual estimates. What do you think?
Regards and clear skies.
Luigi
Hi Luigi,
The level of accuracy / precision requested depends of the kind of program you are involved in. If you survey a Mira 0.05 mag is probably ok, but if you are studying the out of eclipse oscillation of eps AUR you need a very few milli-mag ! For a few hundredths you could probably relax the condition, this is also a question of experience and observation conditions. The scintillation varies from day to day, place to place, its effect is also depending of the diameter of the aperture: larger is better.
If you already have 12 images you could try 3 groups of 4 images and see what happen. Under good condition 20 sec could be ok. Anyhow the SD of the mean is gone to reflect the magnitude of accuracy expected from those conditions. I would recommend to make a true SD calculation that means:
SD=sqrt((d1²+d2²+...dn²)/n) where dn is the deviation from the mean for each star of the ensemble. I think such function is available in usual speadsheet. The SD_of_the_mean = SD/sqrt(n)
Next with a 85mm lens you could expose longer than 5 sec if you don't saturate. There is no problem in photometry to have somewhat elongated stars images, it's even better than defocusing in fact ! You could probably push the exposure to 15 ~20 sec.
Then in astronomy it's usual to process many images, the time we are involving in image processing is large, often much larger than the observation time itself ! What has been proposed under Citizen Sky is just for initiation. For serious photometry work you will need an automated software. It's possible to make series photometry with IRIS but it's not perfect from my experience. There are number of software able to do it but I don't know them well as I use my own software under Dyalog APL (no Windows or Linux...). You could have a look at the AAVSO DSLR Manual, if I remember well there are a couple of cases in it.
Clear Skies !
Roger
thanks for your
Hi Roger,
thanks for your help, I will try to follow your advice for my next attempts.
Now, with my 12 images, I have create 3 groups of 4 image, like you said. I have calculate average value and standard deviation for the variable and comparison stars (look attachment in this post).
What do you think?
Regards,
Luigi
Hi Luigi,
your table shows excellent results given the exposure condition. The SDs look coherent to me, it's normal to have such SD deviations from star to star given the few images and groups involved. For mag 6 and your exposure condition you should get about 15000 electrons in the two green channels and an SNR of 120. By the way the SD is expected about 0.008 for the photon noise itself, that's coherent with what you got overall.
Clear Skies !
Roger
Thanks very much, Roger!
Luigi
Hi Roger,
sorry, but I still need your help. Clearly, also the help of others is welcome.
I have just noticed that the AAVSO Photometric Table indicates the uncertainty about the value of the magnitude (shown in brackets, near the value of the magnitude). Only now I have noticed this! Since the magnitude was shown to three decimal places, I thought the error was on the third decimal place!
Now, 4 of the 6 comparison stars that I have used in my analysis have an uncertainty of 0.1 mag.
At this point I wonder: what sense does it indicate 0.017 as error on the estimate of the variable, if the comparison stars have an uncertainty of 0.1?
I think that maybe I should choose comparison stars with an error on the second decimal place. Is it right?
Regards,
Luigi
Hi Luigi,
No problem, but here I think you touch something critical (and probably controversial !).
In fact as I said earlier the trueness (in ISO sense) need is very depending of the type of observation. There are observations where 0.1 is ok and others that need 0.002 or so. But often in the second case the true mag, or its conformity to standard band-pass, is not important. One example is the observation of transit of exoplanet or binaries. Observing the oscillations of stars like Eps AUR is another case. Here what is critical is the precision / coherence of observations within a series or a long term curve of a given observer. What is more difficult is to make coherent the observation of multiple observers and this is the purpose of VSP. But it's a difficult task !
Anyhow I am not happy with the wording being used (uncertainty, MAGERR...), I think we should only speak of "scatter" of our own results, like it's done in some good catalogs. That scatter could be defined by its standard deviation but i think it's not enough. If the single image exposure of the series is short it is affected by the scintillation (at least). Then that scatter is meaning less and doesn't reflect the overall precision of the observation. We need to know how the images have been combined, in what number / series. But this is not possible to report it in the Aavso format. Today the best is to report the standard deviation of the mean. This is what I do using the results of five series, each long enough to eliminate the scintillation. I do not care about the catalog uncertainties.
Such causes of error, essentially systematic, are difficult, maybe impossible, to determine. One is what you point: the accuracy of catalogs (possibly through VSP). For us their deviations are just systematic errors, they don't change from image to image. I try to use only the best cases, not always VSP. Tycho 2 is a very good source, the only well coherent. In it, number of stars have a clear definition of the scatter. But ok, there are stars with high uncertainty in VSP that are not so bad ! If we compare the individual deviations of our ensemble they do not deviate that much. What I do to prepare a campaign is first to determine a large ensemble, make several observations in several nights, check the individual deviations from the ensemble. Stars that are to much a problem and not in best color and position are just eliminated. If the discrepant star looks anyhow interesting (color, mag, position) I check for possible blending of nearby small star and calculate the correction to apply. The purpose of an ensemble, beside a best reference, is to reduce the part of scatter due to the comparison and also to provide a tool to analyze the quality of the observation (sky...). At a certain point it's perfectly right to re-calibrate its stars from standard ones.
Clear Skies !
Roger
Thanks Roger for your comprehensive explanation.
But, in VSP, the ensamble must be chosen from a unique catalog (for example Tycho-2) or can I choose it from different catalogs? Sometimes, as in my recent observation of khi Cyg, the brightest stars are taken from BSC catalog that have a scatter of 0.1 mag.
Regards,
Luigi
Hi Luigi,
I am also observing Khi Cyg and I can say the "coherence" between the bright stars noted in VSP is in most cases well below 0.01 . But there are problems of blending with dimmer stars and that correction shall be applied. For such bright star I use a 200 mm focal length F4, with your 50 mm lens you could have even more blending issues.
My standard deviation for those stars is below 0.005, they are well stable (sometime we get weak variable !). I have no idea why they got this 0.1 SD (normally it's not the overall scatter but the SD, it could simply means: unknown). As an example "50" is known with a very high accuracy from several catalogs: Hipparcos SD is 0.0006 (ok difficult to transform, but the star is very stable), Tycho-2 SD is 0.009, HIC has it at 5.000 V (0.031). UCAC4 shows "99" that usually means the SD is unknown, in fact here V and B are the Tycho BT and VT and the SD is well known, anyhow not transformed ! (and an old version, apparently not Tycho-2). Confusing...
You can explore many catalogs using the CDS Vizier (search for catalog) or Simbad (such for object) :
http://vizier.u-strasbg.fr/viz-bin/VizieR
Tycho-2 is the I/259 catalog:
http://vizier.u-strasbg.fr/viz-bin/VizieR-3?-source=I/259/tyc2
One option is to work with Tycho-2 from Vizier (most stars from the chart are known), it needs no DSLR transformation for VT (only the extinction gradient if at low elevation, and some atmosphere color correction if at very low elevation).
Then the end result (target and check) should be transformed from VT to VJ... (there are standard rules for).
Have fun exploring the CDS !
Roger
P.S. looks like "64" is an eclipsing binary, after Simbad....
Hi Roger,
I use a 85mm lens (not 50mm) but, you are right, often I have blending issues in the fields of Milky Way. For this reason I have opened, on this forum, the thread "Aperture photometry: different radius for each star".
Your approach is very interesting, but I am a beginner and , for the moment, I would not use data other than those provided in the VSP.
However, just for curiosity, if I understood well, the Tycho2 catalog needs no DSLR transformation. Then, if we indicate with VTc the cataloged Tycho magnitude of a comparison star, the Tycho magnitude VTt of target will be:
VTt = VTc - 2.5*log(It/Ic)
where It and Ic are the measured intensity of target and comparison star.
If so, when I have calculated the VT magnitude for the target star, how can I transform it in Johnson's VJ ?
Online, I have find this formula:
VJ = VT -0.090*(BT-VT)
Is it correct?
Further, the target magnitude is calculated with only one comparison star, or doing the mean from an ensamble?
Regards,
Luigi
P.S.
I have searched your recent observations of khi Cyg. I have seen that you submitted 5-6 observation separated by a time distance of a few minutes. Why?
Luigi, that formula is approximate but useful, you could find more details on such transformation in the Hipparcos ESA report:
http://www.rssd.esa.int/SA/HIPPARCOS/docs/vol1_all.pdf
The photometry discussion is in the chapter 1.3 .
You could also have a look at the ASCC 2.5 catalog from Kharchenko, in Vizier (I/280B), this is a compilation essentially based on Tycho 2, it provides a conversion toward Johnson.
Clear Skies !
Roger
Sorry Roger, but the link don't work.
Regards,
Luigi
Now it should work, it seems there is something strange in this forum software, hidden caracters ?
Roger
Hi,
A friend of mine calculates the error in this way.
Suppose that we have a set of five images. He measures the target in each of the five, then calculates the average M and the standard deviation STD. Further he measures the SNR of the target (Maxim DL provides this value).
Then he calculates the error (er) on the measured magnitude with this formula:
er = 2.5*Log(1+M/SNR)
Finally, he calculates the final error (that he reports to AAVSO)
Error= sqrt(STD^2 + er^2)
In this way we take into account the standard deviation of the measures and, in addition, the error from SNR.
In fact, I have noticed that the stardard deviation is almost the same for all stars, regardless of their magnitude. Instead, the SNR depends from the target's magnitude.
For example, if I have a STD=0.001, but the target has SNR=100, I don't think that the only STD is a meaningful estimate of the error.
What do you think?
Hi Luigi,
That idea of your colleague is just wrong ! From the physics of the photometry operation the standard deviation of the end result is the quadratic addition of all perturbations, mostly the scintillation, the shot noise and the instrumental noise. If you make an extra addition of 1/SNR you just count the noises two times !
By the way the SD is in any case stronger than 1/SNR. From many analysis of photometry results I have never seen the opposite, by far ! If you found a case like you mention there is certainly an error somewhere. Note that the end SNR shall be such of the series not such of a single image.
Clear Skies !
Roger
Hi, Roger
you are right. I have verified and actually the STD is larger than SNR. I don't know where my friend took the formula:
1) er = 2.5*Log(1+M/SNR)
The next time I'll ask him.
Actually, this formula calculate the error in a more complicated way than 1/SNR.
If I calculate the error with this formula, I find an error larger than STD.
For example, in my recent observation of RW Cep I have:
M=6.430
STD=0.014
SNR=125 (I averaged SNR from five set of images)
With the formula 1) I have er=0.054, that is larger than STD.
Regards,
Luigi
Luigi, the SNR is just = Signal / SDnoise. If your SNR is 125 the relative SD of that perturbation is 0.8%, that's also 0.008 mag ! Not 0.054
But ok, the SNR of one set is not the average of the images SNR but the quadratic addition of them.
Roger
Yes, Roger, I understand.
1/SNR=0.008, but the value 0.054 is what you get from the formula 1). I don't know where my friend took the formula.
Regards,
Luigi
Luigi, that "M" is just wrong in the formula, it shall be "1". Anyhow that noise is included in the SD, no way to add it a second time !
Clear Skies !
Roger
Ok, Rogers, thanks for your clarification.
Regards,
Luigi
Hi Roger,
I have attached an article of Koppelman in which the error is calculated in a slightly different way (look at formula 11).
In this formula, sigma(K-C) is the standard deviation of a series of (Check - Comparison) measurements.
Then, the error is calculated adding in quadrature sigma(K-C) and (1/SNR), i.e. taking into account the uncertainty for the overall time series of the K-C measurements and the uncertainty from the SNR calculation.
What do you think?
Luigi
Hi Luigi,
This is a special technique that is valid only if the star(s) used for determining the sky SD is significantly brighter than the target star, enough bright to make its 1/SNR negligible against the sky deviations. But if the mags of that star and the target are similar you count two times the 1/SNR through the formula 11: Just wrong !... And even very wrong as the shot noise is far the major contributor for the overall standard deviation of both.
I would be very surprised if someone of us use that technique, I have never seen any example. It implies the target is significant dimmer than the comp star and this is a serious drawback. Anyhow such technique is only approximate.
The simple way generally used by the current software is to measure and calculate the SNR of the target (it can't be 100% measured, it needs the estimate of the shot noise through sqrt(N_electron) ). That 1/SNR of the target doesn't includes the sky deviations and by the way somewhat underestimate its true SD but it's usually enough, we don't need to know it with high accuracy. One question mark here is how the software makes the calculation in electrons ? (mandatory !). How is the astronomers said "G" calibration coefficient known from the software ? ( e-/ADU, not the electronics gain that "G" !... I am an electronics guy...)
The other common technique is to calculate directly the SD of the target from several images, preferably 5 or more. That SD is all ! no way to quadratically add 1/SNR .
Clear Skies !
Roger
Hi Roger,
thanks for your answer, and excuse me if I try in every way to raise the error in my estimates. ;)
I'd like see the question from another point of view.
Sometimes I obtain a SD of target of few millimag (0.005 or so). I could not explain why, but I am not sure that the error of my estimate is so small. For example, one of my doubts is that this value takes into account only the variation of the target between images without take into account, for example, the quality of best fit for the determination of color transformation. In the spreadsheet of Citizen Sky, the quality of best fit depends from the choice of comparison stars, from the error of their tabulated magnitudes and color index. Further, if one or more comparison have near companion that you include in your aperture, you obtain a different coefficient of the color transformation. In many cases it is not always possible to choose perfect comparison stars (with small catalog error), or choose isolated star without near faint companion.
For example, just for try, I have take my photometry spreadsheet of W Cyg. In this spreadsheet I have for W Cyg a standard deviation of 0.008. Then I have tried to subtract a value to the instrumental magnitude for one or more comparison (for simulate near companion), or/and change the tabulated magnitude and color index for some comparison stars. Clearly, with those changes, the best fit becomes completely unrelated, with R^2 near zero, but the standard deviation of target is always the same.
Don't you think that somehow we must also take into account the quality of best fit for the error's determination?
Luigi
Luigi, it's normal, there is no relationship between that color correction and the SD calculation. A color mismatch generates a systematic kind of error, it has nothing to do with the variability of the target flux. The SD is just a measurement of the various kind of scatters that affect the result, not an analysis of possible systematic errors that don't generate scatter but a constant deviation (usually unknown). The error is to speak about error ! We should only say "standard deviation" or scatter instead MAGERR or so... but there are such traditions in astronomy like that gain "G" which has nothing to do with a true gain !
The R² shows you there is a possible source of systematic error : most of the time a non-even extinction, clouds... if the ensemble is usually ok. Otherwise it could be due to other problems like catalog errors, poor color correction... But it doesn't say you what the systematic error on end result could be, it could be either high or zero. It just says you there is something that needs more analysis, sometimes a second order extinction correction, any...
The SD of the target end result reports all scatter contributions: sky, instrumental noise, shot noise (that is usually dominant) from the combined target and ensemble, but no systematic error estimate.
Clear Skies !
Roger
Roger, I understand what you say but at this point I think that the SD not always is a good indicator of the estimate's accuracy. If I see that the systematic errors are relevant (R^2 <<1) then I must somehow take into account this fact. I can't to report an error of 0.008 if I have, for example, R^2=0.5 or so, because surely in this case the error will be much greater.
Cheers,
Luigi
Hi Luigi,
If you have that R² ~0.5 your data looks ok, you can certainly report ! The tutorial says R² (residual of the ensemble fitting) BELOW 0.7 is ok.
A systematic error has nothing to do with the AAVSO's MAGERR parameter. Systematic errors exist but are usually unknown and by the way doesn't imply any reporting. If a systematic error is identified the only thing to do is to apply the corresponding correction before reporting.
The CS's R² only shows the fitting coherence of the ensemble. If it's bad ( >0.7 following the tutorial ) you could just decide to not report considering your observation is non-valid, nothing else. Better would be to try to understand the origin of that poor fitting. It's often just the poor coherence of the catalog data, it could also be a second order extinction (to see the tutorial), any... For example: if one star of the ensemble has a catalog systematic error of +0.1 and a second one -0.1 you will certainly get a very bad R². But the related systematic error of the target will be just zero !
Clear Skies !
Roger
Hi Roger,
I referred to CS's beginner spreadsheet. Here R2 must be near to 1 for having good fit. Is it right?
Luigi
Luigi,
You are right, I just checked both spreadsheets and R² is not the same in beginner and intermediate ! In intermediate this is a residual well documented, in beginner this is a stat R² ! But there is no mention of that R² in the beginner documentation, it only appear in the graph.
Roger