His papers are filed under the name A. K. Middelton, Assistant Surgeon, [cross referenced from M331 filed under the name A. F. Middelton] recorded as in the field with the 10th Battalion State troops, October 1863, appears on a Return of the Medical Officers of the Regular Army, Volunteer Corps and Militia, including Physicians employed under contract, serving in the District of Texas, New Mexico and Arizonia, November 1863, present January 1864 at Galveston, 2nd State Troops, Infantry (Six Months, 1863-64).
I believe the rate of pay for an Assistant Surgeon was $110/month, which is equivalent to the rank of Lieutenant.
George Martin