Poor quality export (Banding)

I have a photo, taken with a flash, of a very sharp subject and a very dark background. The photo, including the background looks great when viewed in Lightroom. However, the export (jpeg or tiff) has a poor quality background. To be specific, instead of a smooth gradient from light to dark (or dark to less dark), there are consentric rings of monotonal areas. It kind of looks like a topographical map. It's also very pixelated. I'm only seeing this poor quality in the dark background and not the well-lit subject. Also, the poor quality is not seen in the preview image in lightroom. Any help would be appreciated.