The paper concentrates on the micro-interferometric techniques that utilize a light source of the continuously tuned wavelength. The technique is called, after the light source, the variable wavelength interferometry. It can be implemented in transmitted or reflected-light modes and is useful in testing fibers, micro-structures and optical elements like retarders (wave plates). The emitted spectrum has to be continuous. When the measurement procedure advances the selected wavelength must be determined with high accuracy, which ultimately defines uncertainty of the optical path difference to be measured. The continuous character of the light source is the linking element with previously published Part I of the paper that focused on confocal sensors.
The paper focuses on two families of instruments that have been developed over several years in the Institute of applied Optics using microinterferometric and confocal approach. The continuously variable light source constitutes the binding element of these two classes of measuring devices. The light source has to emit continuous spectrum. During measurements the selected wavelength must be determined with significant accuracy, which constitutes the key and critical factor of the measurement process as a whole. The described systems are only a small part of what photonics offers but are very useful in characterizing many objects and materials in research and industrial environment.
The automotive industry has been always a driving force for all economies. Despite of its beneficial meaning to every society it brings also many issues including wide area of road safety. The latter has been enforced by the increasing number of cars and the dynamic development of the traffic as a whole. Road signs and traffic lights are crucial in context of good traffic arrangement and its fluency.
Traffic designers are used to treat horizontal road signs independently of vertical signs. However, modern light sources and growing flexibility in shaping optical systems create opportunity to design more advanced and smart solutions. In this paper we present an innovative, multidisciplinary approach that consists in tight interdependence of different traffic signals. We describe new optical systems together with their influence on the perception of the road user. The analysis includes maintenance and visibility in different weather conditions. A special attention has been focused on intersections of complex geometry.
Original matrix formulas obtained by differentiation of the system matrix in respect to movements of components are
derived. Components kinematics for the three zoom systems realized by means of interactive graphical software is presented. An optical system may be structurally designed by successive steps and its parameters determined to fulfil
requirements, such as optical conjugation, focal lengths or magnifications. Improved software developed in this work
serves both determination of optical powers and separations and movements of components. Developed methodology covers different types of fixed and zoom systems, the latter type with electronic or optical compensation. One may consider any optical system, such as the reproduction lens, objective lens or telescope system, because matrix optics distinguishes them remarkably easy. Kinematics pertaining to a full tract of the zoom system is determined at a discrete number of positions. Movements of so-called basic variable components are determined in a full cycle of work by means of iterative methods while movements of supplementary components may be inserted by means of exponential-parabolic functions also including their linear form. Any component of the zoom system may act as a variable, supplementary or fixed component, but it is mainly dependent on the structural design. Parameters of characteristics are computed as elements of a certain matrix. Designing is that to set these elements on required values by means of system parameters or movements of components. In this way, one may create complex multi-group systems with characteristics and movements which we accept. Properties of these systems are presented by numerical and graphical forms. Advantages of these systems are their more compact construction, more smooth kinematics, and better possibilities of optimization, what is particularly valuable for zoom systems with a high zooming ratio.
At present optics matrix is poorly suited to solve difficult problems of geometrical optics. The essence of the work is the
use of matrix optics for analysis and construction of optical systems in the form of original matrix equations linking
design features with working conditions of the optical system. Matrix equations are subjected to differentiation with
respect to construction parameters. Matrix analytic functions are developed further in a finite series, because of vanishing
derivatives of higher orders. In this way we obtain a methodology that is intended for analysis and construction of
elaborated optical systems. Design methodology described in this work relies on carrying out certain operations to
change the construction parameters starting with given roughly the optical system. These operations can be carried out in
the entire optical system and its parts. The program enables calculation all partial derivatives with respect of individual
and mixed construction parameters giving information if using these parameters for the correction of requirements is
possible. Tables and graphs are helpful to initial design process.
The double-sided telecentric optical zoom system can consist of only three components. Output data of the algorithm include transversal magnification in terminal positions, spaces between components in their start position and the object to image distance. Optical powers are determined from the start position but spaces - from the final position and condition on the object to image distance. In both cases it is necessary to solve the system of three non-linear equations. Afoc-al type of the entire system is taken into account in one equation. Solutions of equations depend on a free parameter val-ue which is the matrix element "b", sometimes called the modified thickness of the optical system. Powers and spaces being determined are functions of the free parameter. This parameter generates many solutions of the optical system, but the designer has to select the most useful one. Important role in the design methodology plays the use of computer graphics for the localization of the free parameter. Recommended solution is such where powers of components aren't too strong and spaces in both terminal positions enable convenient movements of components simultaneously limiting the total length of a system. When the free parameter becomes fixed it is necessary to check the components kinematics. Recommended kinematics should provide for smooth operation from start to final position while keeping the spaces as small as possible. Described methodology of calculations is illustrated by the example.
In this work the paraxial optical imaging is generally described by means of three square matrices: one unitary system matrix and two operation matrices with determinants equal the Lagrange-Helmholtz invariant. Elements of system matrix are functions of design parameters while elements of the operation matrix depend on input and output coordinates of characteristic rays. Each matrix has only three independent elements. Internal system parameters are determined from equations created of system matrix elements, which values are dependent on the operation matrix. Matrix approach enables the solution of only three non-linear equations with respect to system parameters. Matrix approach has also another advantage. It enables the determination of number of degrees of freedom. We have a superiority of parameters over the number of equations when the number of components is bigger than 2. The more complex is model the higher degree of freedom it has. There are special ways of reducing the number of degree of freedom: by selection of spaces between component, introduction of additional requirements and criteria of distribution of optical powers. Significant help is in defining all the spaces between components, what means full control of the components position and their di-mensions. In such a case the only thing left is the determination of optical powers, while the number of degree of freedom is equal k-1 (k is the number of components). In this work the computer program realizing described algorithms has been developed. This program was tested with specially selected examples. Results of calculation for two interesting applica-tions are also given.
The initial optical design concerns the determination of the thin-component parameters based on the knowledge of ray coordinates, requirements and restrictions. The ground of the approach is heuristics that relies on an analysis of aims and means. The method may be used twice either as development of some new algorithms or the numerical computation of the optical thin-component model. In the first case, from the beginning we may select relations, and next establish the proper mathematical forms. In the second case we have been changing the introductory state influencing on results in this way. The methodological table plays an important role in this method. Different types of parameters are found in lines of this table while successive components are in columns. In this table we show in the initial state, methodology for applying relations in the right order and check for its correctness.
Computation for the riflescope illustrating possibilities, and advantages of the improved version is given in this paper.
The algebraic method for correction of aberrations was exploited in this work both for solving the problem of optical glass selection and for determining the radii of curvatures of cemented doublet. Exact aperture aberrations in the meridional plane are taken into consideration and the only limitation is the usage of the spherical surfaces. Optical properties of the hypothetical optical glass were determined with the use of only two parameters. Method consists in the solution of the system of 13 nonlinear equations, where unknowns are the angles of incidence at each surface of 4 specific rays and one parameter connected with the optical glass properties. Finite lens thicknesses selected for given aperture are fixed similarly to some glass parameters. Two approaches are recommended to solve the problem of the selection of the first optical glass. The algebraic analysis of the selection of hypothetical optical glass in the cemented doublet with the leading crown for the most interesting range of variation of the refractive indices of the crown and flint glass was performed. An example of full calculations of cemented doublet f10013 was given together with the algebraic choice of catalog glasses and determination of radii of curvatures.
Coloring of the spot center given by the microscope objective is proposed as a measure to aid the lens designer in the image quality evaluation. Results of computation for the different types of microscope objectives are presented. Distribution of Strehl number and optimal defocusing in the visual spectrum range strongly influence the coloring of the spot center.
Essence of this work is formulation of nonlinear dependencies, which allow to determine parameters of an optical system. Previous methods of the aberration correction have commonly used algebraic methods in a simple form for primary aberrations and thin lenses. Efficiency of those methods should be appreciated critically because they usually need a further aberration correction. Nowadays, progress in development professional mathematical software commercially available encourages to taking out works concerning algebraic correction methods. In this work aberration dependencies are investigated in their full complexity without simplification and approximation. Dependencies containing angles and ratios of dimensions have form of very complex trigonometric expressions. An optical system may be corrected by controlling these dependencies in the entire optical systems. Solution of the problem require the selection of number of unknowns, and expression of all residual relations as a function of these unknowns. Problem of the algebraic correction relies on solving of a non- linear equation system with separately described auxiliary functions which are nested up to certain depth. Radii of curvatures and eventual distances between surfaces are determined in the second final stage after solving the nonlinear equation system and taking account of the scale. Two simple numerical examples are presented.
In this paper the problem of athermalization is considered. We assume that the both mechanical and optical parts of the device has its actual structure divided into separate housings. Two variants of passive and active athermalization is taking into account. We present also our results with computer-aided athermalization program.
Methods to solve paraxial pupil problems in zoom systems are not sufficiently developed up till now. A method intended to solve any paraxial pupil problems in different types of zoom systems is presented here. Among pupil problems such as the correction, stabilization, and required pupil location, stabilization is the most important. In the first stage of the method a zoom system is treated as a black box. Outside imaging parameters of this black box are determined by means of two-conjugate ray parameters. In the second stage of the method a zoom system is treated as a white box with the given number of thin components. Construction parameters of this white box, i.e. optical powers and spacings, are determined as those fulfilling the outside imaging parameters. In the third stage of the method components' kinematics is determined to keep both conjugations. The third moving component is called a pupil stabilizator, however, all moving components collaborate with each other to maintain the stabilization. To solve the non-linear system of equations the available standard mathematical software is used.
To determine paraxial properties of the general four-component zoom system with mechanical compensation we must have the methods to obtain the optical power distribution and test and evaluate kinematics. There are two important approaches to general conception of a four- component zoom system. The first refers to the expansion of the method for three types of zoom systems. According to the location of an object and image in relation to a zoom system, we distinguish the following zoom systems: variable focal lenses, projection or reproduction systems, and afocal attachments. The second refers to the expansion of kinematic possibilities of all zoom components and even an object plane. Research led to the conclusion that knowing the marginal positions and extreme values of the main useful parameters connected with them is quite sufficient to obtain the optical power distribution of the individual components. Changing the input data we may minimize the longitudinal dimension of the zoom system. Sort of a zoom system is determined by paraxial aperture coordinates at the edges of a zoom system. The first optical power is calculated from the equation being four degrees of polynomial. We have four solutions of this equation and have four propositions of the optical power distributions in a four-component zoom system. All remaining optical powers in the four-component zoom system are expressed by the first optical power. Calculation of optical powers in this way means that the zoom system is good only in both marginal positions. Research led to the statement that, optical conjugate and fixed image location are determined from a quadratic equation. To verify kinematics of the zoom system it is necessary to determine the variation of the main useful parameter and, if required, variation of movements of the first and fourth component. After kinematic calculations we should first test whether the travel from start to the final position is smooth. Later we evaluate kinematics and, if possible, correct it by mentioned changes or even by modification of marginal positions.
Secondary spectrum aberrations are especially destructive in high performance refractive optical systems having large apertures and long focal lengths. It is derived that secondary spectrum level of such systems is dependent on a certain structural sum and a deviation of the optical materials used in the system. The structural sum is the main reason of the secondary spectrum aberrations in the achromatic refractive optical systems built with ordinary materials. Reduction of secondary spectrum aberrations is based on the minimization of the structural sum and use of optical material deviation. Essence of the matter is both sign and magnitude of the deviation for the given spectrum direction. A coefficient of secondary spectrum reduction has been introduced. This coefficient receives values in interval from 0 to 1, where value 1 respects the theoretical correction. Medium contributions of this coefficient indicate, whether applied extraordinary optical materials are effective for the secondary spectrum reduction.
Photoelastic sensor with fringe image transfer by an image-guide to a computer for stress analysis was constructed for those applications where the place of measurements is hard to reach and electrical instruments are not permissible. Two types of sensors are presented: one, disc-like, for uniaxial stress observations and the second one, called a hollow glass cylinder, with axially bored stress concentrator for biaxial stress measurements. Sensor is a central cylinder glass cemented in a cubical concrete block. The sensor is connected to autocollimating polariscope, which allows the sensor to be lit and transport an isochrome image to digital image processor card. The numerical analysis of the fringes images is done in many ways. The original programs for the analysis are presented.
Two identical gratings crossed by a small angle Φ create moiré fringes. Knowledge of the distance d between the fringes allows one to state a value of angle Φ between the gratings. The angle Φ can be used a measure of either angular or linear movement. The above is utilized for the construction of sensors having a linear relation between angular and linear displacements. Two solutions for measuring the distance d in a real time situation are presented: one with an "optical path" and the other with an "electronic path". In both the CCD elements are used.
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