A survey of the available photographic holdings in the Library of congress reveals the following images relevant to the 3rd Michigan Infantry.
First up is a photo taken by W. H. Tipton, a Gettysburg photographer and is a stereoview of the 3rd Michigan Monument in the Peach Orchard. Note the orchard in the background.
This was most likely taken c. 1889. Note that in his catalogue of Gettysburg battlefield monument images this image is not listed.
Next up are two images of Annie Etheridge (see her biographical sketch).
Next is Israel Canton Smith. He began as captain of Company E and ended the war as a brevet brigadier general. This photo is from 1862, possibly after he was transferred to command Company F.