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Hi if you are applying a gaussian blur then this effect will be shown trying to save this as a jpeg and check it shows or not otherwise it depends your resolution of file try on 300...regards
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As you saw, blurring makes it look worse. A common way of dealing with this is to add a small amount of noise to the area with banding, just enough to obscure the banding, but not so much to make it look "noisy" (less than 1%). If the problem area were a Smart Object, you could make changes to the amount of noise, while keeping your original intact.
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Work in 16bit.
Did you apply the Filters as Smart Filters?
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First off, this may not be in the data, it may be simply part of the display path. You first must always view this at 100% zoom or greater. Zooming OUT subsamples the preview and isn't an accurate way to view the data.
Even in 16-bit, if your display path isn't fully high bit (more than 8-bits per color), meaning the video card and display itself, you can still see banding. Again, this isn't in your data, it's a result of the bit depth of the video path.
So there may be an issue here or maybe, it's how you're viewing the data. We need more info to know.
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As long as you work in 16 bit color depth, any banding you see is in your display system.
Even if the file is 16 bit, your display pipeline is 8 bit (unless you have an expensive 10-bit capable monitor). That's where the banding happens.
It's not in the underlying data. If it bothers you, a little noise will break it up, as Semaphoric describes.