168
J. Eur. Opt. Society-Rapid Publ. 21, 16( 2025)
Fig
. 2. Tactile AFM measurements of the a) 260 nm and b) 300 nm grating structure on the linewidth / pitch standard( fabricated by supracon [ 35 ]) for reference.
– CSI: Incoherent summation of the resulting intensity distributions, considering the reference plane field distribution. The electromagnetic field distribution considering the scattered field E s and the reference field E ref is given by
Eðx; z; h in; u in Þ ¼ E s ðx; z; h in; u in Þ
þ E ref ðx; h in; u in Þ; ð1Þ
from which the intensity for each near-field computation is calculated. Therefore, the resulting intensity distribution for the complete depth scan can be described by
Iðx; zÞ ¼
Z 2p
0
Z hin; max du in dh in P 2 ðh in ÞI hin; u in ðx; zÞ
0 sinðh in Þ cosðh in Þ; ð2Þ
with u in as the incident angle and h in, max = arcsin( NA) as the maximum opening angle of the microscope objective, P( h in) representing the pupil function and I hin; u in as the intensity distribution for each incident angle. – Confocal microscope: In contrast to CSI, the superposition for each incident angle is done coherently with the electromagnetic field distribution. The intensity of the resulting field is then calculated, resulting in the desired output for the depth scan.
– Conventional microscope: The electromagnetic field described in equation( 1) is given by E = E s neglecting the reference field, which is not considered for conventional microscopy. With this, the intensity distribution can be calculated likewise it is shown in equation( 2).
Fig. 3. Slice of an image stack acquired with confocal microscopy( a) compared to a conventional microscopic image( b) of the same field of view. The area used for the surface reconstruction shown in Figure 4 is marked in red. The complete image section shows one of the squarely arranged structures on the measurement object( supracon linewidth / pitch standard, K 2 = 300 nm) with the microspheres placed on it. The focal plane is selected so that the focus is visible through the microspheres.( Note that in( b) the colorbar of the image is heavily adapted to make the red-marked area sufficiently visible).
Summarizing, the different setups are all described under the same conditions and the resulting intensity distributions can be used for further analysis and comparison.
4 Measurement results
The results of the experimental investigations are presented below, with the focus on the comparison between conventional and confocal microscopy. The linewidth / pitch standard produced by supracon AG [ 35 ] is used as a sample. It offers a selection of grating structures with period lengths from 160 nm to 4 lm. Since the presented results only show