The men in the gray uniforms are officers in the Heer (army) of the Bundeswehr, the armed forces of what was then West Germany. Their peaked caps are a particularly distinctive feature.

The officer in the garrison cap (2nd from left) is a U.S. Army infantry colonel (O-6). He's got the silver eagle rank insignia on his shoulder straps. His branch is indicated by the crossed rifles of the branch insignia on his lapels and the sky-blue cord on his left shoulder (the same cord also worn by your grandfather). He also appears to be wearing a Combat Infantryman's Badge (CIB) on his left chest - suggesting he was a WWII and/or Korean War combat veteran. His name tag appears to read "Butler" - but it's difficult to tell. He's also appears to be carrying a swagger stick in his left hand, a rather unusual object for an American officer to carry.

As near as I can tell, other two U.S. Army officers are wearing the crossed cannon and missile insignia on their lapels, indicating they are in the newly-formed Army Air Defense Command, which had just been formed in 1957. The cannons and missile insignia wouldn't be adopted until 1958, right at the very start of the date ranges your provided! As a note, in December 1968, AADC would keep the insignia, but be renamed the Air Defense Artillery branch, the name it uses to this day.

Both of these officers have gilt oak leaves or "scrambled eggs" on their service cap brims, indicating they are ranked major (O-4) or higher. The officer with the sunglasses in the middle is probably a colonel (O-6) or brigadier general (O-7)

Some other details. The officer in the center appears to have a CIB on his left chest - again suggesting he's a WWII or Korea combat veteran. The officer at the left side has four Overseas Bars on his left sleeve - each one represents 6 months deployed outside of the United States.

Your grandfather has one chevron on his right arm, indicating he is a private first class (E-3). If you know his dates of rank, this may help you narrow down when the photo was taken.

It's hard to make out, but he appears to have a unit patch on his scarf (this was done by some units from WWII to the middle of the Cold War, when the scarf was a part of the service dress uniform). Was he in the 101st Airborne Division? That patch would be about the right shape and color to match the one in the photo. It would also explain why he's wearing the purple ribbon bar of the Presidential Unit Citation (PUC) on his right chest, since the division earned the PUC during WWII and members of the division since then have worn the decoration.

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