Create a duplicate layer, use the threshold button to highlight the lightest area of the black background, then click the 'color sampler' tool on that lightest area, this will leave a little target, then dump the threshold.

Go to levels, pick the black eyedropper, click it on the little target left by the color sampler, and then hey presto you'll have a perfect black background and the plate and it's contents will remain the same. Hit clear to get rid of the target and flatten the layers, if it effects the food just use the eraser to bring back the original layer before flattening.

Hope I've explained that easily I'm not that good at teaching, but that's what you need to do, don't bother with burning,paint bucket or anything else, you just need to tell the image where the darkest part of the image is.

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Richard