J. Eur. Opt. Society-Rapid Publ. 21, 16( 2025) 169
Fig. 4. Confocal microsphere-assisted topography measurements of grating structures on the linewidth / pitch standard. Reconstructed surface data is shown for a period length of a) K 1 = 260 nm and b) K 2 = 300 nm. The limited field of view induced by the microspheres( SiO 2, diameter d = 5lm) is visible as a circular cut-out of the measurement area. The additional magnification introduced by the microsphere leads to enlarged period lengths in the measurement results.
a small field of view, Atomic Force Microscope( AFM) measurements of the structures used are included to provide a better overview on the specimen. The results are shown in Figure 2. In particular, the structures with K 1 = 260nm( height: 55 nm) and K 2 = 300 nm( height: 85 nm) are important for the following experiments, as they are close to the optical resolution limit of the confocal microscope. The microspheres are made of SiO 2 and have a diameter of 5 lm( fabricated by micromod Partikeltechnologie GmbH).
An image stack is recorded with a confocal microscope. Depth scanning in the z-direction provides the signals required for further signal processing. In the focal plane, the result is compared with an image of the same field of view taken with conventional microscopy. When comparing the confocal microsphere-assisted result with the MAM image of the same field of view in Figure 3, it becomes clear that the confocal technique affects the imaging process. The image of the conventional microscope provides significantly lower contrast in the region of interest, as it is shown in Figure 3b. It does not sufficiently resolve the K 2 = 300nm structure, whereas in Figure 3a, the contrast is improved due to the confocal effect which is beneficial for microsphere-assisted imaging. As introduced in Figure 2, the square surrounding of the grating structure also becomes visible.
After acquiring the image stack, topography data are reconstructed by appropriate signal analysis algorithms. 3D representations of measured surfaces for different grating periods( K 1 = 260 nm and K 2 = 300 nm) are shown in Figure 4. Neither structure is resolvable with conventional or confocal microscopy without microsphereassistance due to the large pixel pitch of the camera. Additionally, the period length of 260 nm is below the optical resolution limit of the system. The additional magnification induced by the microspheres is M 1.3. The limited camera resolution of the commercially available confocal microscope becomes relevant when measuring small structures. Nevertheless, the resolution of the system is improved overall by the use of microspheres, as the topographic measurement of K 1 = 260 nm shows. In order to clarify about the optical resolution enhancement by the microsphere, a comparison with the simulated data is shown in the subsequent chapter.
5 Simulation
For comparison, simulations are carried out with the previously presented model. A microcylinder with radius r = 2.5lm and refractive index n = 1.4621 [ 36 ] isplaced on a structure similar to the linewidth / pitch standard used in the measurements. It contains a SiO 2 substrate with a silicon structure( n Si = 4.2620 + 0.045187i, [ 37 ]) on top forming gratings of period lengths K 1 = 260 nm( step height h 0, 1 = 55 nm) and K 2 = 300 nm( step height h 0, 2 = 85nm). The arrangement of microcylinder and grating is assumed to have periodic boundary conditions with a period length of 13.2 lm. A microcylinder instead of a microsphere is used in order to achieve reasonable computation times. The illuminating light of wavelength k = 505 nm is considered to be monochromatic and TM polarized and the numerical aperture( NA) of the microscope objective lens is 0.95. Figure 5 shows cross-sections of image stacks obtained for conventional( Figs. 5a and 5b), interference( Figs. 5c and 5d), and confocal( Figs. 5e and 5f) microscopy for both period lengths. Note that more information on definition of the polarization are provided in a previous publication [ 34 ]. In agreement with previous observations [ 12, 38 ], the influence of the grating appears more pronounced for TM polarization in the area of the cylinder and therefore only the results for TM polarization are shown. Especially for interference and confocal microscopy, the grating can be recognized in the phase( interference) and contrast( confocal) of the image stacks( the areas of interest are marked in green). It should be noted that the grating considered as a measurement object more or less corresponds to a phase grating and hence only a weak influence on conventional microscope images is to be expected. For results of amplitude gratings we refer to [ 38 ]. Furthermore, the simulated image stacks shown in Figure 5 underline the observation that in the imaging process with microsphereassistance the role of non-linearity should not be neglected when analyzing the data. Changing the period length