J. Eur. Opt. Society-Rapid Publ. 21, 27( 2025) 281
Figure 2. Axial confocal response I z and its sensitivity S z, alias the differential confocal signal.
Most common is the approach to use two defocused pointdetectors. These are symmetrically axially defocused from the focal plane of the detection tube lens [ 32 ]. The two acquired signals are then taken into difference D and are normalized by their sum R to create the so called focus error signal( FES) [ 33 ]:
FES ¼ I 1 � I 2 I 1 þ I 2
¼ R: ð2Þ
Early works already managed to achieve nanometer sensitivity [ 34 ]. Many works then improved this method regarding robustness [ 33 – 36 ], axial resolution [ 32, 33 ], lateral resolution [ 37, 38 ], the extension of its non-ambiguous range for direct measurement [ 39, 40 ], and parallelization for faster measurements [ 41 ]. Further methods to create a DCM developed. The divided aperture method could simplify the detection path by using a single camera that observes light from a partially illuminated objective pupil [ 42 ]. While the discussed methods involve static defocus, recently dynamically defocusing to create a differential curve re-emerged [ 43, 44 ]. Thereby, the focal plane of the objective has been axially modulated, or the detection plane of the tube lens. This allowed to achieve nanometer axial sensitivity by using a simple confocal beam-path.
However, these methods employing static defocused point detectors or addtitional optical elements require space and different beam-paths of illumination and detection. Therefore, we suggest the rarely employed approach to exploit axial chromatic aberration to create the defocus between two confocal signals [ 45 ]. This enables the creation of a differential curve from two wavelengths focused into different focal planes in front of the objective, while using a common fiber for illumination and detection. This target beam-path is sketched in Figure 3. Two confocal peaks will appear at different distance from the objective. This allows for the application of equation( 2). Opposite to FD-OCT and CCM, the spectrometer is reduced to two wavelength-specific photodetectors, which enables fast signal processing. A key challenge is to create this axial chromatic aberration for the two long measurement wavelengths, while being achromatic towards the exposure wavelength of the structuring beam.
Figure 3. Target schematic of the optical tool, integrated with a chromatic differential confocal probe and its required axial chromatic separation of focal planes. Additionally, angular measurements are realized through a camera chip.
Here we present our approach to design such an optical probe. Section 2 proposes a design procedure for the axial chromatic design. Section 3 briefly integrates an angular measurement beam-path and a possibility for wide-field observation. Furthermore, it introduces the complete realized tool head. Section 4 shows results that characterize the realized measurement systems and demonstrates measurements on a grating and a sphere. Afterwards, Section 5 discusses these measurements and draws connections to the design approach. Finally, the article is concluded in Section 6.
2 Chromatic optical design
As required by the chromatic differential confocal principle [ 45 ], the measurement is performed by two wavelengths, k C1 and k C2. Henceforth, their median wavelength may be defined as their effective wavelength k C. The optical design procedure now has to join the exposure tool beam with the wavelength k F and the effective measurement beam as illustrated by Figure 3. All three wavelength are emitted from a common fiber facet. That common fiber shall pose as receiver after reflection on the substrate’ s surface, too. The first primary design goal is the achromatism between the focal lengths of the exposure f F and the effective measurement wavelength f C:
ðIÞ f F ¼ f C: ð3Þ
The second primary design goal stems from the chromatic differential confocal principle. The axial defocus z D1 / 2 between the focal planes f C1 / 2 of the two measurement beams decides for the axial sensitivity, range and signal to noise ratio( SNR) of the resulting differential curve. In normalized axial optical distances this is given as u D, opt = 5.61 as shown in other works [ 32, 46 ]. According to equation( 1), the relationship between the normalized u D and a real z D is scaled by the employed wavelength and the acting NA. For simplification of the design process, it is suggested, to maximize the z D as the second primary design goal:
ðIIÞ maxðz D1 � z D2 Þ ¼ max ðf C1 � f C2 Þ: ð4Þ