Optical see-through (OST) augmented reality head-mounted displays are quickly emerging as a key asset in several application fields but their ability to profitably assist high precision activities in the peripersonal space is still sub-optimal due to the calibration procedure required to properly model the user's viewpoint through the see-through display. In this work, we demonstrate the beneficial impact, on the parallax-related AR misregistration, of the use of optical see-through displays whose optical engines collimate the computer-generated image at a depth close to the fixation point of the user in the peripersonal space. To estimate the projection parameters of the OST display for a generic viewpoint position, our strategy relies on a dedicated parameterization of the virtual rendering camera based on a calibration routine that exploits photogrammetry techniques. We model the registration error due to the viewpoint shift and we validate it on an OST display with short focal distance. The results of the tests demonstrate that with our strategy the parallax-related registration error is submillimetric provided that the scene under observation stays within a suitable view volume that falls in a ±10 cm depth range around the focal plane of the display. This finding will pave the way to the development of new multi-focal models of OST HMDs specifically conceived to aid high-precision manual tasks in the peripersonal space.