How can I reduce the background gradient in phase contrast microscopy?
If you're not already doing so, make sure you set up Kohler illumination every time you use the microscope -- see this tutorial by Steven Ruzin.

The lamp or the phase ring may be misaligned. There are usually small hexagonal set screws on the lamp housing and the condenser, respectively, to adjust these.

Imaging near the edge of a dish or well can lead to uneven illumination as the light is bent by the walls of the culture vessel. If this might be the cause, try re-doing the Kohler illumination before you take each image.

If you can't find the cause of the problem, there are several ways to correct for uneven background described here. Maybe one of them will work with your analysis.