J. Eur. Opt. Society-Rapid Publ. 21, 16( 2025) 171
Fig. 7. Difference of reconstructed surface profiles for a) K 1 = 260 nm and b) K 2 = 300 nm with microcylinder-assistance. The difference is taken from each simulation with the reconstructed surfaces h rec( x) and h rec, inv( x).
Fig
. 6. Intensity distributions for simulated confocal study cases. The first column shows the I( x, z) for the sinusoidal grating for K 1 = 260 nm( a, c) and K 2 = 300 nm( e, g). The second column depicts DI( x, z), respectively. In c), d) and g), h) the results with microcylinder-assistance are shown.( The intensity distributions for I inv( x, z) are not plotted).
surface h rec( x). Since the cylinder introduces aberrations mainly towards the edges of the field of view, the difference for both structures( phase shift 0 ° and 180 °) is again calculated, which leads to Dh rec( x) = h rec( x) � h rec, inv( x). In Figure 7 this is shown for a) K 1 = 260 nm and b) K 2 = 300 nm.
Overall, the reconstruction results show something like a sinusoidal surface overlaid by strong aberrations. In Figure 7b some outliers can be recognized, which are probably due to the sensitivity of the signal processing algorithm to irregularities. These simulation results underline the experimental results shown in Figure 4.
6. Conclusion
Confocal microscopy is a powerful tool that enhances depth sectioning and the lateral resolution capabilities of a conventional microscope. When coupled with microsphereassistance, this technique achieves even higher resolution.
Like it is discussed in [ 24 ], the confocal effect on microscopic imaging plays a pivotal role in the capability of the system to resolve structures below the diffraction limit. Furthermore, for commercially available systems the pixel resolution can be improved due to the additional magnification by the microspheres. Additionally, a method is introduced to simulate measurement results obtained by microcylinder-assisted conventional, interference, and confocal microscopy as the most common optical profiling techniques. With a simulation study on the difference an added microcylinder makes for confocal imaging, conclusions can be drawn on the resolution capabilities of the system. The resolution enhancement observed in the simulation validates the experimental results.
Future investigations considering rigorous simulations should meticulously analyze the transfer behavior of a confocal microscope considering microspheres, enabling a comprehensive comparison with MAM and interference microscopy. Simulations will be performed for these instruments to study resolution enhancement capabilities using e. g. approaches presented in literature [ 17, 38, 39 ] in order to elucidate the potential of MAM.
Funding
The partial support of this work by the Deutsche Forschungsgemeinschaft( DFG, LE992 / 15-3) is gratefully acknowledged.
Conflicts of interest The authors have no conflicts of interest to declare.
Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.
Author contribution statement
According to the Contributor Role Taxonomy( CRediT) the authors’ contributions are:
L. Hüser: Conceptualization, investigation, formal analysis, data curation, visualization, writing.
T. Pahl: Methodology, investigation, formal analysis, data curation, visualization, writing.
S. Hagemeier: Investigation.