Mathematical correction model for image aberrations in 3D multispectral image data acquisition

Abstract

This work presents a correction model for a multispectral method for 2.5D shape measurement, based on the Shape from Focus principle. Using a monocular imaging system of a filter wheel camera, depth information is derived from the respective focus position. Both lateral (2D) and axial (z-axis) measurement accuracy must be ensured, which are limited by the occurrence of optical aberrations. These errors arise when capturing a stack of images with a multispectral camera using a moving image sensor, where the axial movement of the sensor leads to geometric distortions and other imaging errors. The method is performed with standard lenses (wide-angle lenses with endocentric design, constant numerical aperture, fixed focal length and aperture), with the aim of capturing a large field of view, which increases flexibility and practical applicability but introduces uncertainty regarding measurement accuracy. The aim is to demonstrate the efficiency of the presented correction model, based on affine transformations, with such standard lenses, to determine the optimal degree of approximation, and to identify the number of physical reference points required to correct 3D distortion at each Z-position of the image sensor, thus enabling precise 3D measurements. A key feature of this approach is that the image sensor is moved for both focusing and 3D scanning. The central challenge, therefore, lies in compensating for optical aberrations – the magnification varying across the working range, the object-distance-dependent distortion in 2D, and the focus-dependent z-distortion – to achieve reliable and accurate measurement results.