Computational alignment of on-machine deflectometry

Accurate system calibration remains an area of active improvement in deflectometry. Since deflectometry requires the geometry information of all participating hardware to be well known, miscalibration can mar the accuracy of surface reconstruction especially in lower order shapes. To uphold reconstruction fidelity, extra measuring instruments (i.e. coordinate measuring machines, laser trackers, metering rods) or reference features (i.e. fiducial points or reference mirror) to find out the positions of a camera, a screen, and a unit under test are used. These methods provide reliable calibration but are resource-intensive. In this paper, we introduce an alignment algorithm to calibrate the geometry of a deflectometry configuration. We leverage the concept of alignment algorithm which uses a sensitivity model. With the aid of ray tracing simulation, the relationship between camera pixels and screen pixels of a deflectometer is quantitatively established. This pixel-to-pixel relationship enables us to generate computational imaging of screen and characterize the tendency of misalignments of the deflectometer. On top of that, we can calculate and make multiplexed patterns of screen which highlight the effect of misalignments. We set specific indices and corresponding screen patterns for each alignment parameters to build the sensitivity model. The initial simulation result shows that the algorithm can estimate misalignment status. We believe that this algorithm can be an alternative and efficient calibration process for the deflectometry system, especially when the usage of extra measuring devices is limited.