292
J. Eur. Opt. Society-Rapid Publ. 21, 27( 2025)
that these multiplicative disturbances are eliminated by normalization with the sum signal [ 33 ]. Here, this mechanism does not work, as two independently fluctuating laserdiodes are used for the calculation of the differential curve. This results in the aperiodic fluctuations that limit the axial resolution to 3 nm.
A possibility to improve this could be the integration of Faraday isolators to the beam path. Since the fiber-coupled laserdiodes’ own facet turns is causing the fluctuations, a shift to a free-space system with additional fiber-coupling would be necessary. An approach that aims for the use of fiber components might be the observation of the individual fluctuation. It could be included in the calculation of the FES. This would require additional observer photodiodes for each laserdiode that must be properly scaled for the integration with the signals detected from the specimen. This integration will be possible, as a growing number of laserdiodes include the photodiode on the same chip for optical power control application. Another approach could be the rewiring of the optical fibers, so that the opposite laserdiode’ s detector can directly acquire the additional fluctuation. Proper signal scaling becomes more demanding in such an optical setup.
Additionally, the keen reader might have noticed, that the results for the chromatic differential confocal were only covered by D and not the FES, although the latter would be necessary for the elimination of the fluctuations. As it turned out, the sum signal R of the two confocal peaks is unfavorable for the normalization as illustrated by Figure 23. The resulting FES shows a reduced linearity and sensitivity for its lower part of the non-ambiguous range compared to the corresponding difference D. Even severe, the prominent minimum and maximum on the FES vanished. This results from the asymmetric shapes of the confocal response signals as seen in Figure 13. They cause a big widening of the signal D, especially for the values below the half maximum of R. Subsequently, the drop of the FES outside the non-ambiguous range is not reaching zero as ideally assumed, but lifted to a long tail for positive z-values. It may even be amplified at far away defocused positions as seen for negative z-values in Figure 23.
Although the non-ambiguous range has reduced sensitivity and higher non-linearity, it would still be usable for surface profilometry. It was tested, but was found to be too instable for surface scans on the shown specimen. Due to the axially separated focal planes the two measurement lasers are focused onto, the diffraction they are subjected to becomes different, too. As the working point is in between the two response peaks( comp. Fig. 13), the two unequal sides of the asymmetric depth responses are evaluated. This amplifies the different diffraction that is caused by the different focal planes on the specimen. In a third step, the calculation of the FES via equation( 2) would lead to another amplification of the effect on the resulting differential curve via a distorted R in the denominator. This additional sensitivity by the denominator is implied by the higher non-linearity of the FES shown in Figure 23. The here observed effects thereby confirm the observations in [ 67 ] for a single source and wavelength.
Figure 23. FES calculation from D and R corresponding to Figure 14.
Given this instability, the difference signal D solely was employed for surface profilometry in this article. This requires to perform characterizations on every specimen to account for their respective reflectivity and may lead to erroneous measurements when scanning over heterogeneous specimen. In order to incorporate this robustness in future chromatic differential confocal probes, the initially requested optimum axial separation of u D = 5.61mustbe questioned. While this value may apply for detection paths, applying it to the illumination causes the described loss in robustness. This effect also leads to the significantly amplified diffraction effects in profile measurements as seen in Figure 17. If the two focal planes as well as the wavelength of the measurement beams are closer, their perceived diffraction becomes more similar. This would make the application of the FES possible again. The limiting case of this would be the use of the spectrum of a single laserdiode, which might also show more similar power fluctuation pattern for both signals.
6 Conclusion
This article introduced a new approach on the development of an integrated optical tool head for direct laser writing on curved substrates with the NPMM-5D. By incorporating axial and angular measurement, feedback signals are provided that allow the tool to be focused onto an unknown curved substrate, perpendicular to its local slope. The axial measurement thereby is realized as a chromatic differential confocal microscope. A new design methodology for the paraxial chromatic design was developed to find suitable initial systems that can combine exposure and measurement beams adequately. Here, the required achromatism between the exposure and the median measurement wavelength, but with a high axial chromatic separation for the two measurement wavelength, formed a special optical design goal. For this given use-case, this design methodology has proven useful for a three-lens design. It reduced the necessary experience from the designer and may speed