Influence of aberrations and roughness on the chromatic confocal signal based on experiments and wave-optical modeling

Abstract

This paper addresses the effect and influence of wave optical aberrations and surface roughness on the chromatic confocal signal and resulting measurement errors. Two possible approaches exist for implementing chromatic confocal imaging based on either refraction or diffraction. Both concepts are compared and an expression for the expected chromatic longitudinal aberrations when using a diffractive optical element is derived. Since most chromatic confocal sensors are point sensors, the discussion on wave-optical aberrations is focused on spherical aberrations. Against common belief, the effect of spherical aberrations cannot be eliminated in the calibration process using for instance a piezo mounted mirror. It will be shown in the following that even a diffraction limited system with peak to valley spherical aberration smaller than 0.25 wavelength suffers from measurement errors. Experimental results will be shown to highlight this important issue. In order to develop a deeper understanding of the underlying physics, a wave-optical simulation environment has been realized. This wave-optical model furthermore enables the investigation of the influence of roughness. Herethereto the correct choice of numerical aperture when investigating a rough surface is based on a heuristic approach. Using the wave-optical simulations an explanation for the increased noise when employing a low numerical aperture to examine rough surfaces will be derived. Furthermore, a formula is presented to support the selection of the correct numerical aperture with regards to the roughness parameters of the surface under investigation.

A novel cubic‐exp evaluation algorithm considering non‐symmetrical axial response signals of confocal microscopes

“…The field of application of the cubic algorithm is not limited to depth response signals obtained by confocal microscopes. Asymmetrical signals or spectra to be evaluated also occur if other sensor principles such as coherence scanning interferometry (Lehmann & Xie, 2015;Serbes et al, 2021), optical coherence tomography (Fercher et al, 2002(Fercher et al, , 2003, chromatic confocal microscopy (Chen et al, 2019;Claus & Nizami, 2020) and focus variation microscopy (Cui et al, 2018;Xu et al, 2022)…”

“…The field of application of the cubic algorithm is not limited to depth response signals obtained by confocal microscopes. Asymmetrical signals or spectra to be evaluated also occur if other sensor principles such as coherence scanning interferometry (Lehmann & Xie, 2015; Serbes et al, 2021), optical coherence tomography (Fercher et al, 2002, 2003), chromatic confocal microscopy (Chen et al, 2019; Claus & Nizami, 2020) and focus variation microscopy (Cui et al, 2018; Xu et al, 2022) are being used. The cubic signal processing algorithm can be applied to increase the accuracy of the detection of the maximum position of a signal or spectrum compared to common approaches based on symmetrical approximations.…”

A novel cubic-exp evaluation algorithm considering non-symmetrical axial response signals of confocal microscopes

“…The field of application of the cubic algorithm is not limited to depth response signals obtained by confocal microscopes. Asymmetrical signals or spectra to be evaluated also occur if other sensor principles such as coherence scanning interferometry (Lehmann and Xie, 2015;Serbes et al, 2021), optical coherence tomography (Fercher et al, 2002(Fercher et al, , 2003, chromatic confocal microscopy (Chen et al, 2019;Claus and Nizami, 2020) and focus variation microscopy (Cui et al, 2018;Xu et al, 2022) are being used. The cubic signal processing algorithm can be applied to increase the accuracy of the detection of the maximum position of a signal or spectrum compared to common approaches based on symmetrical approximations.…”

Online Correction of Laser Head Nozzle Position for Laser Metal Deposition Using a Chromatic Confocal Displacement System

“…By using the system’s calibration curve, defined as the dependence of the amplitude argument (wavelength) as a function of the material surface displacement, it is possible to determine relative distances with micrometric accuracy [ 23 ]. However, in the case of engineering material surfaces with significant roughness, the accuracy of such a system decreases [ 24 ].…”