How to correct uneven illumination when center of image appears brighter (or darker) than edges with microscope images generally at lower magnifications (2X, 4X, 10X). This is called vignetting. Note that more recent versions have a Vignette correction tool:
Filter > Lens Correction: In Lens Correction box Custom choose Vignette amount and low value Midpoint (~10).
How to Correct for Vignetting in GIMP
Follow same steps as in video except:
• Create sampling points by holding down Control/Command key and dragging “guidelines” from ruler area. Check values in Sample Points palette (Windows > Dockable Dialogues > Sample Points)
• After duplicating layer, choose Edit > Fill with FG color or BG color, whichever is black.
• For the Filter, under Filter > Light and Shadow, choose Lighting Effects. In Lighting Effects box, click on small blue dot, and move to the center of the box. Increase distance to create a vignette pattern similar to your sample.
• After inverting (Color > Invert) and choosing Screen for the Layer mode, adjust Opacity slider until sample points are within 5 – 10 points of each other.
How to Vignette Correct in Image J
You may try the Subtract Background tool: Process > Subtract Background. Be sure to check Sliding Paraboloid. Set the Radius iteratively until you get a visually acceptable result.