That is a lithograph based directly on an early war wet-plate by Brady. Berdan actually posed twice in the session; one with his cap on, the other with his cap off. The badge appears different in the litho because it actually looks something like that in the original image due to the contours and design of the badge itself and the angle at which the photo was taken. It's just the US/rifles/SS seen in early war photos of officers.
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Brian WhiteWambaugh, White, & Companyhttp://www.wwandcompany.com----------------------------------
Randolph Mess, U.S. Sharpshooters