Freejet experiments were conducted in the hypersonic flight-duplicated shock tunnel (JF-12) to understand the detonation combustion mode in the combustor of a standing oblique detonation ramjet (Sodramjet) engine prototype. Besides the traditional schlieren imaging to capture the oblique shock positions in the combustor, we implemented laser absorption spectroscopy of hydroxyl (OH) radical with three laser beams around the shock front. The Sodramjet engine combustor provides an ideal condition to measure OH because its molar fraction within the detonation front is estimated to exceed 0.03, which is much higher than other combustors. However, the harsh environment of freejet shock tunnel test poses a great challenge to the reliability of measurement systems. In this work, near-infrared tunable laser diode sensors centered at 1528 nm were chosen to measure the line-of-sight average of OH partial pressure. Continuous absorption measurements were conducted near the shock front, indicating a thin OH region after shock compression that could only be achieved by detonation combustion. The time-varied OH partial pressure was well predicted by the computational fluid dynamics (CFD) prediction. Our measurement results verified the detonation combustion of Sodramjet engine prototype and showed that in situ, real-time detonation diagnostics based on laser absorption spectroscopy is possible in freejet experiments of shock tunnel.