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Nice sharp well guided stars there.
Vignetting is the fall off in brightness around the edges of an image. Not normally noticable in daytime photography, but in astro imaging because we stack images and stretch the levels, the increase in contrast makes it noticable. A flat field will cancel it out, by making the image brighter in the corners by the same amount that it is dimmer in the corners. A 100% accurate flat field will give a perfectly even image.
A flat field has to be of an evenly lit area, such as a white wall, or card held in front of the end of the scope a few feet away. Professional scopes take "dome flats" that is images of the white illuminated interior of the telescope dome, or "sky flats", an image of the blue sky overhead before dark. If the camera is rotated, or focus altered, or filters changed, new flats should be taken for best results.
Scott
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