# Contrast Enhancement for Topographic Imaging in Confocal Laser Scanning Microscopy
## 4 Simulation  
To demonstrate the principle of contrast enhancement and investigate the influence of aberrations, simulations based on modeling electromagnetic field propagation have been performed. For that purpose, the simulation software VirtualLab (Version 6.2.1.15) from LightTrans is used. A Gaussian wave with a monochromatic wavelength of 405 nm is sent into a confocal system with two lenses (L1, f1 = 2.78 mm and L2, f2 = 18.5 mm), an aperture and a power detector. We compare the detected intensity of the top of the target structure with the reflection from the bottom, while moving the aperture in axial direction. For this purpose, purely the height difference of the structures is considered. The height of the structures is 40 nm. The contrast from both intensity recordings can be calculated according to  
\[C=\frac{\Delta I}{\overline{I}} \tag{2}\]  
with \(\Delta I\) range of signal and \(\overline{I}\) average signal [6]. We show the effects of the contrast enhancement for two cases, a confocal system with ideal lenses and with a real lens. For showing the fundamental principle of contrast enhancement, ideal thin lenses without aberrations are simulated in the confocal system. To analyze how aberrations could influence the experimental data, we replace the ideal lens L1 in the simulations with a real lens as it is also used in the experiment. The real lens is simulated according to the characteristics given by the manufacturer to investigate the influence of aberrations. In Figure 3 both intensity distribution and contrast calculation are shown for ideal lenses and the real lens.  
In order to run the simulations for ideal lenses and a real lens under comparable conditions, the minimal spot size is measured in the pinhole plane for each case. The minimal spot size in focus is 1.6 \(\upmu\)m for the ideal lenses and 5 \(\upmu\)m for the real lens which are thus equivalent to 1 AU. The simulations are done with a 10 AU pinhole which corresponds to a size of about 16 \(\upmu\)m in the ideal and 50 \(\upmu\)m in the real case. The contrast originates from intensity differences from top to bottom of the structures which can be seen in Figure 3. The intensity distribution for the ideal lenses is symmetric for both  
Figure 3: Simulations with an aperture size of 10 AU. (**a**) Simulation with ideal lenses. (**b**) Simulation with a real lens and a magnification of the intensity difference from the top and bottom of the structures.  
directions of displacement. Aberrations are probably causing the asymmetry in the intensity graph of the real lens. Nevertheless, the contrast enhancement for the real lens is higher than for the ideal lenses. Especially at the slopes of the intensity curve the contrast shows its maximum. Due to the asymmetric intensity distribution in the real case, the contrast shows a similar behavior.  
A simulation of depth scans at the focus, _PDM far_ and _PDM close_ positions in z-direction can be seen in Figure 4.  
The in-focus depth scan intensity distribution is acquired at the perfect in-focus pinhole position, while the pinhole in the other two curves is shifted closer or further away from the upper lens. Therefore, the focal point of the upper lens is not at the maximum of both PDM depth scans but at the slope, in the picture at z = 0 AU.