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The strong requirements in particular the fast data acquisition and stability that are imposed on optical in-line inspection systems, have resulted in a rather limited choice of possible optical techniques. Chromatic confocal point sensors fulfill many of the requirement and are therefore often applied. However, when investigating technical surface scattering samples with a small NA a highly disturbed signal is obtained. Moreover, aberrations can lead to a misinterpretation of the confocal signal. It is therefore utmost important to have some guidance in selecting the correct optics and to eliminate for the aberration induced measurment errors. This can be achieved via realistic modelling of the chromatic confocal signal, for which multiple parameters have to be considered such as NA, measurement of off or an-axis object point, wave-aberrations, size of pinhole, spectral bandwidth of light source employed, spectral intensity distribution of light source, chromatic axial spread, spatially coherent or incoherent light, and roughness properties of the object. Summarizing the impact of all these parameters in a single equation is per se an impossible task. Moreover, some artifacts cannot be modelled using a ray tracing approach, such as speckles. We, therefore, developed a chromatic confocal model, which is based on scalar wave-propagation theory. This enables the application of each individual wavelength and in case of a spatially incoherent system multiple source points and their respective coordinates, finally resulting in a realistic signal. With respect to surface roughness, the NA of the wave-optical model can be adjusted until an undisturbed signal is obtained. Moreover, the influence of wave-aberrations on the signal can be simulated, which results in a changed shape and spectral peak position of the chromatic confocal signal, resulting in a false estimate of the z-position. Simulated results and their experimental validation with various parameters, such as numerical aperture, object roughness, object inclination, spatially coherent and spatially incoherent light will be presented.
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