Calibration of an optical see-through head-mounted display with variable zoom and focus for applications in computer-assisted interventions

Abstract

During the last few years head mounted displays (HMD) became more important in Computer assisted surgery (CAS). Rapid head movements of the surgeon enforce to change the focal plane and the zoom value without loosing the calibration. Starting from previous work in developing an optical see through head mounted display we adapted our HMD to measure the focal and zoom values. This made it possible to extend the calibration to different zoom and focus values. The case of the HMD was opened to gain access to the zoom lenses, which was necessary to measure the different zoom values. Focusing in our HMD is realized by changing the angle between the two tubes. Therefore we marked two points at the tubes to measure the focal adjustment. We made a series of planar calibrations with seven different fixed zoom and focus values using Tsai´s algorithm for camera calibration. Then we used the Polaris optical tracking system (Northern Digital, Ontario, Can) to measure the transformation from the planar calibration grid to a tracker probe rigidly mounted to the HMD. The calibration parameters transformed to this tracker probe are independent of the actual position of the calibration grid andare the parameters we want to approximate. Then least square approximating polynomial surfaces were derived for the seven calibration parameters. The coefficients of the polynomial surfaces were used as starting values for a nonlinear optimization procedure minimizing an overall error. Minimizing the object space error (which is the minimal distance of the line through the center of projection and the image point to the real world point) in the last step of the procedure described above we had a mean object space error 0.85 ±0.5 mm. Calibration of the HMD is not lost during minor changes in zoom and focus. This is likely to be the first optical see through HMD developed for CAS with variable zoom and focus, which are typically facilities of operating microscopes. Employing an automated calibration in common with more zoom and focus steps and more accurate measurement of the position of the zoom lenses and the focal plane should reduce the error significantly, enabling the accuracy needed for CAS.