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.
This work presents detailed theoretical analysis of the effect of finite dimensions of an amplitude diffraction grating to the edge response function of the Talbot imaging. A diffraction of a plane wave is studied as well as a diffraction of a spherical one. The derived formulas can be used to refine the description of field propagation behind the amplitude diffraction grating; therefore, an analysis and an improvement of current applications, where the Talbot effect is used, can be realised.
A focal length is a basic optical characteristic of an optical system. Thus, it is important to be able to measure this value for a given optical system very accurately in practice. At present there exist various physical principles of the focal length measurement which can achieve a different measurement accuracy. In our work we analyse several methods of measurement of the focal length with respect to factors, which are important for a measurement accuracy. The analysis is performed on examples.
The paper presents a theoretical analysis of paraxial properties of the three-element zoom systems for the transformation of circular Gaussian beams. It is required from the optical system that the distance between a beam waist of the incoming Gaussian beam (object waist) and beam waist of the output Gaussian beam (image waist) does not change during the change of the magnification of the system. Relations enabling the computation of the paraxial parameters of a three-element zoom optical system are derived and applied on an example of a zoom optical system with a continuously adjustable magnification. It is shown that the kinematics of the optical system for the transformation of a Gaussian beam differs from the kinematics of the optical system for the transformation of a classical beam and the direct application of the theory of classical zoom systems for the transformation of laser beams is thus not possible. With lasers generating Gaussian beams with different parameters, it would be necessary to design a special zoom system for each type of laser. However, practically it is possible to design a zoom system for Gaussian beams with specific parameters and the adjustment to another Gaussian beam is achieved by a suitable optical system. Using the derived equations it is further possible to solve a number of other issues of transforming the Gaussian beam such as beam expansion etc.
The paper presents formulas for a ray tracing in the optical system of one-mirror and two-mirror optical scanners with a variable focus lens. The procedures for modelling of one-mirror and two-mirror systems, which are used frequently in practice, are described. The result of the analysis describes a general calculation of the position of the beam spot in the detection plane with respect to deflection angles of scanner mirrors. Furthermore, equations for the calculation of the focal length which ensure focusing of a beam at the desired point in a detection plane are derived. The chosen vector approach is general. Thus, the application of the formulas in various configurations of the optical systems is possible. An uncertainty analysis of the position of the beam spot in the detection plane is performed. Using derived formulas one can calculate deflection angles of scanner mirrors and required focal length of the variable focus lens provided that the position of the focused beam in space is given with a required tolerance. Computer simulations are performed on examples of one-mirror and two mirror optical scanners with a variable focus lens.
This work presents a method of determination of internal parameters of an optical system of a classical cemented doublet. The method is noninvasive and parameters are calculated from noncontact measurements without any damage or dismantling of the doublet.
This work presents a primary analysis of an adaptive laser scanner based on two-mirror beam-steering device and focustunable components (lenses with tunable focal length). It is proposed an optical scheme of an adaptive laser scanner, which can focus the laser beam in a continuous way to a required spatial position using the lens with tunable focal length. This work focuses on a detailed analysis of the active optical or opto-mechanical components (e.g. focus-tunable lenses) mounted in the optical systems of laser scanners. The algebraic formulas are derived for ray tracing through different configurations of the scanning optical system and one can calculate angles of scanner mirrors and required focal length of the tunable-focus component provided that the position of the focused beam in 3D space is given with a required tolerance. Computer simulations of the proposed system are performed using MATLAB.
The paper presents an analysis of deflection of a reference plate and a tested plane parallel plate due to gravity during measurement with the Fizeau interferometer. Detailed expressions for the calculation of a deflection assuming different supports are presented. Furthermore, the relations for the calculation of a minimum thickness of a reference plate of the interferometer ensuring the required accuracy of measurement are given as well.
This work describes and analyzes a method for an evaluation of interferometric testing of optical surfaces, which is based on evaluation of similarity between the interferogram of the tested surface and the virtual interferogram of the nominal surface. The evaluation process is described as an optimization problem and the correlation coefficient between both interferograms is used as a merit function. The performance of the method is presented on examples of testing optical surfaces.
In the interferometry, the Fourier Transform Method (FTM) is one of the efficient ways for an interferogram evaluation and it can be used in many practical applications. Fourier transform used in the process of phase reconstruction gives an opportunity to eliminate some unwanted phenomena which are carried in the interferogram due to the process of measuring – for example a random noise of the sensor or a variation in the background intensity. Moreover, reconstructed phase can be obtained only from one registered interferogram, thus this method can be simply implemented in a real measurement process. During the FTM interferometry, an interferogram is reconstructed in several steps. Viewed from a mathematical part and a software implementation, the most complicated is a step called unwrapping; discontinuous image – as a result of atan function – is processed and the continuous phase is retrieved. This work presents a modified solution of an interferogram phase reconstruction without using the unwrapping process – the phase is obtained from its gradient using the piecewise quadratic function.
This work presents an algebraic analysis and computer simulations of imaging properties of a refractive tunable-focus fluidic lens with two continuously variable radii of curvature. Such lenses make possible to change aberration properties. It is shown that such a tunable-focus lens makes possible to correct simultaneously its spherical aberration and coma, which is not possible with the conventional fix-focus lens. Formulas are derived for the calculation of paraxial parameters and Seidel aberration coefficients of the lens. Imaging properties are demonstrated on several examples.
Metal thin film functional properties depend strongly on its nanostructure, which can be manipulated by varying nucleation and growth conditions. Hence, in order to control the nanostructure of aluminum thin films fabricated by RF magnetron sputtering, we made use of in-situ monitoring of electrical and optical properties of the growing layer as well as plasma characterization by mass and optical emission spectroscopy. The electrical conductivity and I-V characteristics were measured. The optical constants were obtained from optical monitoring based on spectral ellipsometry. The relevant models (based on one or two Lorentz oscillators and B-spline functions) were suggested to evaluate the data obtained from the monitoring techniques. The results of the in-situ monitoring were correlated with scanning electron microscope analyses. We demonstrated the monitoring was able to distinguish the growth mode in real-time. We could estimate the percolation threshold of the growing layer and control layer nanostructure. The nanostructure was effectively manipulated by RF power variation. Optical functions exhibiting plasmonic behavior in the UV range and a strong nonlinear character of I-V curves were obtained for an ultrathin Al film deposited at a lower growth rate.
Ultrathin nanostructured metal films exhibit unusual properties and performances. Film functional properties depend
strongly on the nanostructure that can be manipulated by varying nucleation and growth conditions.
Hence, in order to control the nanostructure of aluminium thin film fabricated by RF magnetron sputtering, we focus on
in-situ monitoring of electrical and optical properties of the growing layer as well as plasma characterization by mass and
optical emission spectroscopy. The electrical conductivity and I-V characteristics were measured. The optical constants
were obtained from optical monitoring based on a spectral ellipsometry. The relevant models (based on one or two
Lorentz oscillators and B-spline function) are suggested to evaluate the data obtained from the monitoring techniques.
The results of the in-situ monitoring are correlated with SEM analyses.
We demonstrate the monitoring can distinguish the growth mode in the real-time. We can estimate the percolation
threshold of the growing layer and control layer nanostructure. We show that the nanostructure can be manipulated by
RF power variation. Optical functions exhibiting plasmonic behaviour in the UV range and a strong nonlinear course of
I-V curves were obtained for ultrathin Al film deposited at lower growth rate.
In this work, determination of the refractive index profile and the optical gap E02 of PbZr1-XTiO3 thin films is described. Measurements were performed with the J. A Woollam spectral ellipsometer working on rotate analyzer mode. The temperature dependence of optical constants was obtained with a specially designed heating device.
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