Determination of electric field distribution for the combined optical system of cylindrical lens and spherical lens: a complete theoretical model for light sheet fluorescence microscopy

The physical characteristics of obtainable diffraction-limited light sheets (thickness ∼µ<i>m</i>) are keys to the determination of achievable imaging performance of light sheet fluorescence microscopy (LSFM) imaging modality. The beam shape and its characteristics are solely defined by the optical characteristics of the illumination arm, i.e., by the optical characteristics of the optical components in the illumination arm and the beam profile of the incident optical beam. Typically, the illumination arm in LSFM is constituted by a cylindrical lens and a diffraction-limited spherical (converging) lens. The existing theoretical or analytical models are limited only to (i) an optical illumination arm with a single cylindrical lens (without a spherical lens) and (ii) a planar incident optical beam instead of the practically more relevant beam, for example, Gaussian. We report a complete and unique angular-spectrum-based theoretical formulation of beam-shaping, i.e., combining cylindrical and spherical lenses, for LSFM that holds true for Gaussian as well as planar beams. Validation studies, both experiments and numerical simulation, were conducted. Results demonstrate that our model enables us to estimate the performance indices with better accuracy [spatial (axial) resolution (∼2.18<i>%</i>), imaging depth or admissible sample size/thickness (∼1.30<i>%</i>), field of views (FOVs) (∼39.15<i>%</i>), signal contrast ratio (CR) (∼8.65<i>%</i>), and SNR (∼2.47<i>%</i>)]. This report will be of significant impact on imaging (in general) and LSFM (specifically) and its technological advances.