LCD screen calibration for deflectometric systems considering a single layer refraction model

Techniques based on deflectometry provide absolute shape measurements on specular surfaces by displaying a series of patterns on an LCD screen and using a camera to observe their reflection on the surface. These techniques can provide accurate measurements, but are prone to calibration errors. The extrinsic calibration of the screen, a key element in the calibration process, is often based on a flat surface model, which does not account for the refraction that occurs in the transparent layers of the LCD screen. Several authors have shown that a single glass layer model can reduce measurement errors, but two parameters that are not always available are needed: the index of refraction and the thickness of the refractive layer of the LCD screen. The method presented in this work allows the experimental computation of both parameters, taking into account the non-flat shape of the screen. A series of markers are placed on the front surface of the LCD and a coordinate measuring machine is employed to obtain its shape. Additional virtual markers are displayed on the screen and observed with a calibrated camera from different positions and orientations. The captured images show view-dependent displacements of the displayed features due to the refraction. Photogrammetric techniques are applied to relate the displacements observed in the images and the measured front surface, and a mathematical minimization algorithm is employed to estimate the LCD screen parameters. Several simulation experiments are performed to evaluate the approach, including the influence of measurement errors. The results indicate feasibility of the method.