  Augmented reality (AR) has the potential to improve the immersion and
efficiency of computer-assisted orthopaedic surgery (CAOS) by allowing surgeons
to maintain focus on the operating site rather than external displays in the
operating theatre. Successful deployment of AR to CAOS requires a calibration
that can accurately calculate the spatial relationship between real and
holographic objects. Several studies attempt this calibration through manual
alignment or with additional fiducial markers in the surgical scene. We propose
a calibration system that offers a direct method for the calibration of AR
head-mounted displays (HMDs) with CAOS systems, by using infrared-reflective
marker-arrays widely used in CAOS. In our fast, user-agnostic setup, a HoloLens
2 detected the pose of marker arrays using infrared response and time-of-flight
depth obtained through sensors onboard the HMD. Registration with a
commercially available CAOS system was achieved when an IR marker-array was
visible to both devices. Study tests found relative-tracking mean errors of
2.03 mm and 1.12{\deg} when calculating the relative pose between two static
marker-arrays at short ranges. When using the calibration result to provide
in-situ holographic guidance for a simulated wire-insertion task, a
pre-clinical test reported mean errors of 2.07 mm and 1.54{\deg} when compared
to a pre-planned trajectory.
