This work describes a method for an experimental determination of a paraxial back focus position and a paraxial focal length of optical systems. It is analyzed an influence of spherical aberration on the value of the measured effective focal length of an optical system and the method is proposed for an elimination of this influence and the determination of the paraxial back focus position and the paraxial focal length of a lens from its effective focal length and the Strehl definition measurements.
This paper proposes a procedure for automatized fine-focusing of particles’ image in digital microscopy. First, analytical formulas for a calculation of axial defocus are derived using the complex amplitude propagation. Afterwards, the formulas are used for a design of an iterative algorithm for the fine-focusing. Uncertainty analysis and error simulations are then presented. In the final part of the paper, the method is verified by a simple experimental setup. The proposed strategy can find utilisation in many practical applications of automatized processes, not only in digital microscopy.
This contribution deals with the problem of determination of basic parameters of unknown lenses, namely their radii of curvature, thicknesses and refractive indices of materials (e.g. optical glasses) from which these lenses are made. The aim of this work is to present and analyze a method for the determination of internal parameters of unknown lenses, namely index of refraction and Abbe number. The method is proposed to obtain these parameters and mathematical relationships are derived that allow us to determine the refractive index and Abbe number of lens material based on the measured radius values, the thickness and the position of the focal point or the focal length. It is also performed an uncertainty analysis of the proposed method.
The aim of this contribution is to derive third-order aberration (Seidel) coefficients for a thick lens in air with arbitrary focal length. The explicit analytic dependence of individual aberration coefficients on a lens thickness will be presented. Such formulas make possible to analyze an influence of the lens thickness on lens aberration properties and the replacement of a thick lens optical system by a thin lens model. Equations are described for the re-calculation of aberration coefficients for a different value of focal length and a different value of entrance pupil position. The presented formulas have a fundamental importance for the optical design of optical systems consisting several thick lenses, because these formulas show the influence of the thickness of individual lenses on aberrations of the whole optical system. Furthermore, the thickness of individual lenses can be analytically calculated in order the lens had a required value of specific aberration. The designed optical system then may serve as an initial system for further optimization using optical design software.
This paper is focused on a theoretical general description of membrane deformation in membrane liquid lenses, which is
based on the theory of large deformations of thin plates under uniform hydrostatic loading. The general formulas are
derived, leading to a system of differential equations that describe the shape of a deformed membrane. Since an
analytical solution cannot be found, numerical methods are applied and the membrane shape is calculated for given
practical examples. Further, the dependency of maximal deflection of the membrane on the applied hydrostatic pressure
is analysed. For a better understanding and possibility of modelling the membrane shape in an optical design software,
the shape is depicted as aspherical. Finally, the theoretical simulations are compared with experimental results for a
given membrane and applied loadings. It is clearly seen that the shape of the membrane does not correspond to a sphere
even under low applied pressures. Therefore, the presented analysis could have a significant impact in optical design.
Using the results of the paper and numerical examples, one can easily model many cases of membrane liquid lenses and
exploit the results of the simulation for precise description of optical systems with active components.
This contribution describes how to model the influence of spherical aberration coefficients on the depth of focus of
optical systems. Analytical formulas for the calculation of beam's caustics are presented. The conditions for aberration
coefficients are derived for two cases when we require that either the Strehl definition or the gyration radius should be
the identical in two symmetrically placed planes with respect to the paraxial image plane. One can calculate the
maximum depth of focus and the minimum diameter of the circle of confusion of the optical system corresponding to
chosen conditions. This contribution helps to understand how spherical aberration may affect the depth of focus and how
to design such an optical system with the required depth of focus. One can perform computer modelling and design of
the optical system and its spherical aberration in order to achieve the required depth of focus.
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