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I used my phone with long-exposure mode to capture the night sky. The focus was set to far point. Why do concentric circles appear in long-exposure photograph of the sky?

image1

After levels adjustment to make the circles more visible.

image2

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The circles themselves are likely caused by vignetting of the camera lens.

As for the discrete colours that you're getting: Did you save your image as jpg or raw? If it's jpg then it's highly likely that the levels are due to digitising noise. Grey level in each channel are only represented by 256 values, so in the dark sky, the pixels would only have low values like 1,2,3,4. When you adjust the curves/contrast in your image these discrete levels gets stretched out to an extend that you eye can distinguish them. Compression of jpg files may also have a role to play in this posterisation effect but are not the dominant cause in your case.

https://fstoppers.com/education/can-you-see-difference-between-10-bit-and-8-bit-images-and-video-footage-166977

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