The magnetic field potentially regulates the process of star formation and the evolution of molecular clouds. The Zeeman splitting measurement is the only method to estimate the magnetic field strength along the line of sight directly. The correlation between magnetic field strength and hydrogen column density provides a unique insight into discerning whether and where magnetic fields possess the strength to support gravitational contraction within clouds. Recent observations of OH absorption toward pulsars raise the possibility that the magnetic field strength estimates derived from Zeeman splitting in OH absorptions may be influenced by the angular sizes of background sources. We propose the continued monitoring of four pulsars exhibiting OH absorptions and observe two new pulsars located behind the molecular cloud regions where Zeeman detections of OH absorptions have been identified to constrain the magnetic field strength in quiescent molecular clouds with a characteristic spatial scale of several AUs for the first time, thus shedding light on the physics of star formation and the interstellar medium.
