Yes. This kind of microscope vignetting is usually handled either optically or with flat-field correction.

Practical options mentioned were:

• Flat-field correction in software: capture or derive a correction image from a uniformly illuminated field, then use it to compensate for edge falloff. This is often the simplest solution for stitching because it can make frame brightness much more consistent.
• Optical correction at the light source: a Fresnel lens can help distribute illumination more evenly across the field. Some microscopes already include similar optics.
• Optical correction near the sensor: a plano-convex lens may help, though it can also change magnification, focus, and sharpness.
• Physical mask correction: one answer describes making a compensating mask that is darker in the bright center and clearer toward the edges, then placing it in the illumination path to even out the field.

Since your eyepiece view looks uniform but the camera capture does not, the most practical starting point is usually flat-field correction, then consider illumination-path optics if needed.