There is a paper by Reach et al. (2005) in which you can find useful information to estimate the photometric errors. But, you should be carefully in the way to calculate the background emission.  An example of how to use it can be see in my paper. I hope this can help.

Article A deep look at the nuclear region of UGC 5101 through high a...

Thank you, Mariela. I think I have found a proper algorithm to compute an optimum artificial comparison star and determine its error. This is just some techniques to data reduction, but still thanks for your answer.

Photometric errors are mostly based on counting statistics - you don't need an artifical comparison star, you just use a real one with a highly determined flux at each of the pass bands.   If you can figure out the actual number of photons being registered on your detector (need to convert electron gain to photons) you can then determine your errors.

So if my measured flux in say the B-band is determine by 1 million incoming photons then my parasitical error is small  (square root of million/million) = .001

Thank you for your answer, Bothun. The real one comparison star may have intrinsic variable luminosity, and you ignore the errors introduced by the different extinction behaviors of comparison star of unknown spectral type, just as what I said in the question. What I am doing now is want to achieve high-precison differential photometry, so it is useful to use all available field stars.

As always, knowing the accuracy (closeness to the correct answer) is exceeddingly difficult - if you know the correct answer, there's no point in making the measurement.  Precision, how repeatable the answer is, is relatively simple, make multiple measures, average them, and find the standard deviation (of the mean).  IRAF etc estimates for one measure based on photon, readnoise, etc characteristics.  Your accuracy can't be better than your precision, except by random chance.

Hello Dongchun. You are right to be skeptical of canned uncertainties popping out of image processing software. Forgive the detail I am about to give you, but I find that when things are broken down, the answer comes more easily, even though you probably already know all or most of the following.

First, you need to distinguish between image processing and data reduction. The former involves bias and bias-structure and dark subtraction as well as flatfield normalization. I will omit discussion of these processes, especially the flatfielding, because there have always been different philosophies for their optimum treatment, but the accuracy of your result will depend critically on these steps being done correctly.

For the data reduction, the best procedure is to compute the air mass difference between your comparison star and target star; this is a well-known function of the hour angles and declinations, and the sidereal time. The extinction depends on the air mass as well as the extinction coefficient and the determination of the latter can be done by plotting the raw magnitude of the comparison star against air mass or by solution of a linear least squares equation with the extinction coefficient as the slope and the outside-atmosphere magnitude  as the zero point. The product of the differential air mass and the determined extinction coefficient will give you the difference in extinction correction for the differential photometry, Finally, even though you have now obtained outside-atmosphere differential magnitudes, you may want to transform these to the magnitudes of a standard system, such as Johnson's, Stromgren's, or whatever other passband is close to what your filter and your detector's sensitivity best match.  Now the precision of these differential values can be obtained by examining the differences between the time-successive comparison star magnitudes, and, for only small variations of the target star, the differences in the successive differential magnitudes.  The accuracy of your differential results is a bit trickier to establish because of systematics, but you can certainly make a good effort at doing this. You can see the various algorithms and equations to accomplish these steps in a number of sources. One available place that may be useful is the volume "Astronomical Photometry: Past, Present, and Future," by Milone & Sterken, eds., Springer, 2011. There are several papers in here that you will find useful, and many references to even more comprehensive and detailed sources.  Good luck!

Short answer

A long time ago in the single channel world and chopping secondary mirror this kind of differential precise photometry was relatively easy to do .   With digital detectors it is significant more difficult to perform single-band precision photometry with any kind of long exposures. (long being more than 1 second).  If you can sample your field, the sky, and the reference star very fast - you can do better - but this is hard with digital detectors as you have to read them out. 

You also have not stated what level of precision your after.  If your trying to do 1% photometry, that can be done.  If your trying to do 0.1% photometry that is extremely hard.

Thanks, Odell, Milone and Bothun. I am sorry for some unclear and misunderstanding concepts. We know that high precision differential photometry is important, one application is planetary transits. My work involves image processing and data reduction, both of them will produce poisson error and some other random or systematic or unknown error.

In general, the errors mostly depend on the data reduction. I heard that the best precision of differential photometry is 0.5% on ground, and 0.1% in space. Just as Bothun says, to do high precison photometry is indeed difficult, it requires a careful technique and reduction process. Summarize all my work, there is one error I still do not understand-flat filed correction error. Until now, I still have not found one optimum method and its error calculation formula. If anyone has good flat field reduction techniques, please tell me, I will appreciate your help.

Dongchun, my response gave you a means to compute the empirical error, not one based on Poisson statistics, which is but one contributing factor. This will enable you to obtain an accurate value for the precision. The overall accuracy is quite another matter. The only way to handle that problem is to look at a field of well-calibrated standards, such as one of Landolt's E-regions (if your field of view is wide enough), and you are working in the Johnson-Cousins system, applying all the image processing and extinction treatment discussed above that you apply to your target fields. This should work whether you use dome or sky flats although there may be an issue if the color index of your targets are quite different from the standard stars (although Landolt observed a wide spectral range of standards). Perhaps this is helpful?

Hello, Milone. Your answer is helpful to me, actually there is someone told me to take some standards to do photometry, fitting the result with calibrated magnitude after changing instrumental magnitude to standard magnitude. I think I will have a try if I have time later. Thanks again.

It is well known that the photometric errors calculated by IRAF routines and SExtractor are not accurate. Probably the most complete model for differential photometry errors was done by Howell et al. 1986. I have also made some empirical contributions that you may find interesting (see de Diego 2010, 2014 and de Diego et al. 2015).

References: 

Howell SB, Warnock A, III, Mitchell KJ. 1988. Statistical error analysis in CCD time-resolved photometry with applications to variable stars and quasars. AJ 95: 247-56

de Diego JA. 2010. Testing Tests on Active Galactic Nuclei Microvariability. AJ 139: 1269-82

de Diego JA. 2014. On the reliability of microvariability tests in quasars. AJ 148: 93

de Diego JA, Polednikova J, Bongiovanni A, Pérez García AM, De Leo MA, et al. 2015. Testing Microvariability in Quasar Differential Light Curves Using Several Field Stars. AJ 150: 44

See Broeg et al for computing an optimum artificial comparison star:

CH. BROEG, M. FERNANDEZ, and R. NEUHAUSER. "A new algorithm for differential photometry: computing an optimum artificial comparison star". Astron. Nachr. / AN 326, No. 2, 134–142 (2005) / DOI 10.1002/asna.200410350