J. Eur. Opt. Society-Rapid Publ. 21, 16( 2025) 167
Fig. 1. Schematic representation of microcylinder-assisted conventional, interference( a) and confocal microscopes( b) showing the imaging( red) and illumination( blue) beam path. The area marked by the green rectangle corresponds to the reference arm, which is apparent in case of an interference microscope and replaced by an absorber for conventional microscopy. Note that in the measurements a microsphere is used, in the simulation this is represented by a microcylinder( BSC: beam splitter cube).
provided by an integrated pinhole disc. The measurement capabilities are described by an extensive characterization in [ 30 ].
Besides the optical limitations, the system is also limited by the pixel pitch of 7.4 lm leading to a lateral sampling interval on the specimen of Dx = 163.4 nm. Using Nyquist’ s sampling theorem this leads to a limited resolvable period length of K Ny = 326.8nm. Asitisshownin [ 30 ], in practice the lateral resolution of the confocal microscope corresponds to K min = 0.565k / NA leading to K min 300 nm. This results from the principle of Rayleigh’ s resolution criterion applied to the narrowed Point Spread Functions( PSF). The pinhole disc provides filtering in the imaging and illumination beam paths, which directly influences the image formation [ 31 ] and therefore the PSF. Following this, the significance of the results regarding high-resolution measurements should be addressed, as only a few data points per period are available. In [ 32 ] the capabilities of this system are compared with simulations taking into account the limited sampling rate. Although the results should therefore be evaluated with caution, the optical resolution capabilities of the system can be estimated.
Figure 1 shows the schematic setup including a microcylinder placed in the near-field of the specimen, a linewidth / pitch standard manufactured by supracon, which is analyzed elsewhere [ 33 ]. Taking advantage of the microsphere-induced additional magnification, the overall resolution of the optical system can be enhanced, which is shown in Section 4.
3 Model
Since all of the required modeling aspects are documented in detail, but spread over several previous publications, we compile the relevant literature and just give a short introduction. Figure 1 sketches the considered measurement setups, where conventional and interference microscopes differ in the reference arm marked by the green rectangle in Figure 1a. It should be noted that we focus on microcylinders due to significantly less computational requirements compared to microspheres.
The interaction between light and the sample with microcylinder placed on is simulated using an FEM model generally described in [ 34 ], where no microcylinder is considered. The extension to a scattering geometry including microcylinder is shown elsewhere [ 17 ]. In [ 27 ] we explain how to model all of the three considered microscope setups using the same theory approximating the light surface interaction by Kirchhoff’ s diffraction theory. Here, we use exactly the same instrument modeling, simply exchanging the scattered field computation by FEM.
In summary, the model can be described by the following steps:
Rigorous 2D FEM simulations of the near field. The simulation is repeated for plane waves of different angles of the incidence, forming a conical illumination. In this way, the illumination portion of the simulation, which is the same for CSI and conventional microscopy, is represented. This method of including all possible angles of incidence within the NA of the system is chosen to represent Köhler illumination. For confocal microscopy, the illumination through the pinhole disc is represented by a delta function which is laterally shifted to various positions x 0, y 0.
In a second step, the calculated fields are used for a far-field expansion. Fourier optics modeling is used for the mapping from object to image plane, which is calculated for each plane wave simulation separately. For confocal microscopy, the introduction of the pinhole disc as a delta-function leads to a phase shift in the Fourier plane eliminating the phase term in the Fourier series for E s completely [ 27 ], assuming detection at the same pinhole as illumination.
Depending on the setup, this is followed up by