ELIMINATING GRADIENTS FROM IMAGE BACKGROUNDS.
Image reduction involving flat fielding does not necessarily lead to gradient free backgrounds.
Hot spots, field flooding, and the pitfalls of imaging from light polluted sites can produce less than satisfactory results.
Let's look at a particularly bad example.

The image shows clear variations in the background.
There is a procedure in Photoshop which can remove the gradients. The process involves creating an artificial background and merging this background into the original image while preserving the original object data.
The procedure is as follows:
(A) Using the eyedropper tool select an area in the original image which is free of noise and slightly darker than the background level. In this case it is the point "X" in the image.
(B) Go to File -> New image in the menu. Set the width and height to the same pixel values as the original image.

(C) Using the bucket tool click on the new image. The background is changed to the selected point in the original image.

(D) Now comes the important step. The background must be made lighter to ensure that the merged image does not retain the gradients of the original image. If however the background is made too light, faint details in the merged image will be clipped.

In this case the background has been brightened by using Image adjustments-> Brightness/contrast. The brightness level has been increased by a value of 10. Save the new image.
(D) Click on the original image go to Image -> Apply image and set up the parameters as shown.

The source is the new image "Background2.jpg". Set the blending mode to lighten. If gradients are still present in the merged image go back to the new image and lighten further. If the gradients are eliminated but faint details are clipped the new image needs to be made darker. Experiment until you are satisfied with the final result. Remember to save the image after each adjustment.
Here is a comparison of the original and blended images.

The background variation in the right hand image has been eliminated without loss of detail.
The resultant background of the merged image is completely noise free. While this is a desirable feature, the background may appear unnaturally "too flat". This can be adjusted by adding noise to the new image. Go to Filter-> Noise-> Add noise. A 2% level of uniform noise is sufficient. The added noise is only confined to the background and will not affect the object data of the merged image.
The procedure can also be used to eliminate the effects of vignetting.