I have two images. One image is a brown rectangle with a radial gradient. The second image is a round circle/disk colored green. I want to do a diff of the images so that I end up with a circle/disk that that is the brown dithered color. I have tried to get the brown dithered circle but am not able to. Instead I just end up with a hole punched through the rectangle. See attached image.

Note that the circle lies on top of the circle when I do the image difference. 
I have also tried lowering the selected circle so that it lies beneath the rectangle, and then doing a diff, but when I do that then both images disappear?

So how can I get the dithered brown circle I want using the image difference technique?
 

I'd fill the circle object with the gradient and not use the rectangle at all.

http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Attributes-Fill-Stroke.html#Attributes-Gradients

You could use Path Intersection or try clip instead

Thanks All for the great ideas. dwhall, thanks so much, that intersection works.