Abstract
Considering a coherent microscopy setup, influences of the substrate below the sample in the imaging performances are studied, with a focus on high refractive index substrate such as silicon. Analytical expression of 3D full-wave vectorial point spread function, i.e. the dyadic Green's function is derived for the optical setup together with the substrate. Numerical analysis are performed in order to understand and compare magnification, depth of field, and resolution when using silicon substrate versus the conventional glass substrate or usually modelled condition of no substrate. Novel insights are generated about the scope of resolution improvement due to near field effect of the silicon substrate. Importantly, we show that the expected resolution varies greatly with the position of the sources and the substrate interface relative to the focal plane. Both better and worse resolution as compared to glass substrate may be expected with small changes in their positions. Therefore, our studies show that deriving a single indicative number of expected resolution is neither possible nor judicious for the case of silicon substrate.
Highlights
Fluorescence imaging [16] suffers from photobleaching and blinking, and the imaging duration is limited by the photochemically toxic environment
A full electromagnetic wave approach, rather than ray optics, increases the applicability of the computational models of microscope to high NA systems. This was for example demonstrated before in the case of solid immersion lens [11; 5; 6], where computational modeling used for identification of the suitable pinhole dimension that allows better resolution by balancing the collection of light from longitudinal and lateral dipoles induced in the sample region
The angular semiaperture of the objective lens is θombajx. Both the objective lens and the tube lens are represented by Gaussian reference spheres (GRS) [14]
Summary
Fluorescence imaging [16] suffers from photobleaching and blinking, and the imaging duration is limited by the photochemically toxic environment. A full electromagnetic wave approach, rather than ray optics (geometric optics), increases the applicability of the computational models of microscope to high NA systems. This was for example demonstrated before in the case of solid immersion lens [11; 5; 6], where computational modeling used for identification of the suitable pinhole dimension that allows better resolution by balancing the collection of light from longitudinal and lateral dipoles induced in the sample region. A more general version, without assuming solid immersion lens is available in [14] While general, it lacks one inevitable aspect of microscopy, especially when used for biological imaging. This aspect is the presence of an interface due to the resting surface of sample, for example petri dish in Fig. 1(a) and the silicon substrate in Fig. 1(b) in modern
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