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I want to get two images aligned first, and then I will merge them, but now I encounter a question: I don't know whether they are aligned or not? In another word, do we have any other methods to do this work? Thank you for your reply.

There are multiple ways to align/register images, which is best depends on the type and quality of the data you have. The REFERENCES task can be used to search for tasks you might use, e.g.

cl\$this->_split2($m[0]) refer align
cl\$this->_split2($m[0]) refer register

If you have a list of known pixel shifts of reference objects then you might use something like IMALIGN but beware that setting the centering box sizes can be tricky for some data. If you have a good quality WCS then something like WREGISTER can do a lot of the work for you. To merge the images (e.g. to stack) them IMCOMBINE is the task to use, note it can also use the WCS directly via the 'offset' parameter but the quality of the result depends on the how accurate the WCS is.

Thank you, fits. You said that if I have a good quality WCS then something like WREGISTER can do a lot of the work for you. I have a try, and find it did have some change. But x (or y) shift is so small, like 0.01. So I have a question: this situation can we think the two fits file are aligned alredy? Maybe the little x/y shift is caused by measurement error.

If you mean the difference is 0.01 pixels (as opposed to 0.01 degrees in the reference value of the WCS CRVAL keywords) then it is likely these images are already aligned in the WCS. The differences may be due to different seeing conditions leading to different centering values of individual objects, or just roundoff errors if positions are only printed to 2 decimal places. If you want to test it you could subtract the two images to be sure the objects subtract entirely or that the remnant little donuts left behind show the same pattern across the field (indicating just a change in PSF between the two and not a distortion where at the edge of the plates the shift is smaller/larger than elsewhere).

Thank you for your early reply. I was just doing some PSF photometry work. I think when I am familiar with PSF, I will have a test. Many thanks again.