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.
Our work is focused on the problem of a theoretical analysis of imaging properties and an initial optical design of a three-element zoom optical system for laser beam expanders using lenses with a tunable focal length. Equations that enable to calculate basic paraxial properties and parameters of such optical systems are derived. Finally, the derived equations are applied on an example of calculation of parameters of the three-element zoom system for the laser beam expander.
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.
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.
The work is focused on an analysis and modeling of paraxial imaging parameters of an optical system with a variable magnification or focal length, which keeps the position of object and image planes and entrance and exit pupil planes fixed. This system does not move its elements during the change of the magnification or the focal length. Such an effect can be achieved using tunable-focus active lenses. The described double conjugate zoom lens with tunable-focus lenses satisfies the requirement that object, image and pupil planes are fixed during the change of magnification or focal length. The system must be composed of at minimum three optical elements. Formulas are derived, which enable to determine focal lengths of individual elements of the optical system in a general case, when an object is situated in a finite or infinite distance from the optical system. Such an optical system can be principally used in the design of riflescopes with a variable magnification. This design of the riflescope has the advantage of the fixed position of its optical components (tunable-focus lenses). Further, the position of the exit pupil does not change and stays fixed in a fixed distance from the eyepiece during the change of magnification.
Our work is focused on a theoretical description and mathematical modeling of the shape of a circular edge clamped pressure actuated elastic membrane, which can be used as an optical surface of an active optical element such as the membrane lens. While the theory of small deformations of elastic membranes is well developed and the calculation of a deflection of the membrane can be done with a relatively good accuracy, modeling of large membrane deflections is more complicated. Classical approaches given in literature adopt certain approximations that affect the accuracy of the calculated shape of a membrane. In our work a generalized nonlinear differential equation describing a given problem is derived and the method for solving this equation is proposed. The numerical solution is based on the expansion of the solution into series and transformation of the problem into the constraint optimization problem. It is shown on examples that the deviation of the shape calculated using the proposed generalized equation and the classical solution is not negligible in terms of the requirements on the optical surface accuracy. The influence of the membrane shape on the optical quality of membrane fluidic lenses is also investigated.
This work is focused on a description and an analysis of an optimization method for the evaluation of small deviations of
optical surface shape in interferometric testing. The proposed method does not require a detailed analysis of the
interference field as it is necessary with classical evaluation methods of interference patterns and it uses the optimization
techniques for the determination of the deviation of the tested surface from its nominal shape. This method compares
interferograms, which correspond to the nominal shape of optical surfaces, and interferograms of the tested optical
surfaces using the suitable merit function based on variance of two interference patterns. It can be used for the
comparison of two surface shapes.
This work presents a scanning deflectometric approach to solving a 3D surface reconstruction problem, which is based
on measurements of a surface gradient of optically smooth surfaces. It is shown that a description of this problem leads
to a nonlinear partial differential equation (PDE) of the first order, from which the surface shape can be reconstructed
numerically. The method for effective finding of the solution of this differential equation is proposed, which is based on
the transform of the problem of PDE solving to the optimization problem. We describe different types of surface
description for the shape reconstruction and a numerical simulation of the presented method is performed. The
reconstruction process is analyzed by computer simulations and presented on examples. The performed analysis
confirms a robustness of the reconstruction method and a good possibility for measurements and reconstruction of the 3D shape of specular surfaces.
We present an approach to an analysis of the third order monochromatic and chromatic aberrations of thin refractive
fluid lenses with a variable focal length. A detailed theoretical analysis is performed for a simple variable-focus lens and
formulas are derived for an optical design of such lenses. Aberration coefficients of the third order of the variable-focus
lens can be completely characterized by three parameters which depend only on refractive indices of fluids forming the
variable-focus lens. The calculations are provided for Varioptic lens Arctic-416. Potential applications for a primary
optical design of modern liquid lens-based optical systems are emphasized.
The aim of this work is to design an interferometric system that will adapt the shape of the reference wavefront to the
shape of the measured optical surface. The designed adaptive two-beam interferometer uses the electromagnetic
deformable mirror MiraoTM52 from ImagineEyes for a generation of the reference wavefront and it can be applied for
measurements of flat and spherical surfaces and even for measurements of free-form surfaces. We perform a detailed
analysis of this technique and several possible measurement setups and principles of measurement and calibration of the
designed adaptive interferometer are described. The principle of measurement is shown on an example of the
experimental set-up of the adaptive interferometer in our laboratory.
A novel calibration technique of 3D coordinate measuring machines using noncontact interferometric technique is
described and a design of a new construction of length standards (ball bar, ball plate) for calibration of 3D coordinate
measuring machines is proposed. The proposed optical technique uses as a sensor a small spherointerferometer for the
determination of the coordinates of the center of the ball bar. Formulas are derived, which make possible to calculate an
accuracy of the centre position of the spherical surface that is used for the length standard. An analysis of the proposed
method is performed based on the third order aberration theory. The proposed technique can be used as a practical tool
for a simple, rapid check of a positioning performance of 3D measuring machines.
We present an approach to an analysis of the third order monochromatic and chromatic aberrations of refractive fluid
lenses with a variable focal length. A detailed theoretical analysis is performed for a simple variable-focus lens and
formulas are derived for an optical design of such lenses. The advantage of these active lenses is their capability to
change continuously the focal length within a certain range. These lenses give a possibility to design non-conventional
optical systems which change their parameters (focal length, magnification, etc.) in a continuous way without a need for
mechanical movements of lenses. Such lenses with a variable focal length make possible to design optical systems with
functions that are difficult or even impossible to combine using conventional approaches. We perform an analysis of
optical design of such lenses. The experimental analysis and calculations are provided for Varioptic lens Arctic-416.
Potential applications of variable-focus liquid lenses in optical microscopy are analyzed and simulated. We also
investigate a possibility of increasing the depth of focus using such lenses and the influence of a variable-focus lens on
the image quality.
Classical optical systems with variable optical characteristics are composed of several optical elements that can be
moved with respect to each other. The mechanical change of position of individual elements (or group of elements) then
enables to achieve desired optical properties of these optical systems e.g. the range of focal length or magnification. The
disadvantage of such systems is that individual elements of these optical systems have to move very precisely along
calculated trajectories, which results in high requirements on mechanical construction of such systems. Therefore it
would be advantageous to be able to build optical systems without moving parts that would have the same (or similar)
properties as above mentioned classical zoom systems. Nowadays, there exist several types of tunable lenses with a
variable focal length based on different principles. This fact makes possible to perform the analysis of zoom optical
systems based on variable power lenses. Our work deals with the analysis of possible designs of zoom optical systems
using such lenses.
A shape of a wave-front that is transformed by an optical element (or system) is changed depending on physical and
geometric properties of such a system. This fact can be used in many areas of science and technology. For example,
various applications can be found in adaptive optics where active optical elements are used for wave-front correction.
Our work presents a detailed analysis of aberration properties of a simple deformable planar mirror from both the aspect
of modeling the shape of reflecting surface of the mirror and the mechanisms that enable to reach this desired shape for
correction of spherical aberration. Finally, a simple experimental device for practical realization of the optical system for
partial wave-front correction is proposed.
The work deals with the problem of non-contact measurement of the surface topography using chromatic (confocal) sensor. A detailed analysis of the influence of the refractive index of the plan-parallel plate material on the accuracy of measurement using chromatic sensor is performed. Relations which describe this phenomenon and enable to calculate an error due to material dispersion are derived. It can be seen from the performed analysis that the dispersion of plan parallel plate material causes measurement error that cannot by neglected for precise measurements.
The imaging quality of an optical system depends on the magnitude of residual aberrations of the optical system.
Aberrations of optical systems can be analytically expressed as a sum of aberrations of different orders. The most
important for practice are the third-order aberrations (Seidel aberrations) and the fifth-order aberrations. Our work shows
one of possible methods for determination of third-order aberration coefficients that is based on measurement of
spherical aberration of the investigated optical system. The advantage of this method for determination of the third-order
aberration coefficients is the fact that the measurement of spherical aberration can be experimentally relatively easily
performed with a sufficient accuracy. This work presents a detailed theoretical analysis of the proposed method and
relations for calculation of the third-order aberration coefficients.
Ultrashort light pulses are distorted in optical systems due to a different magnitude of the phase and group velocity of
the wave. Our work is focused on the analysis of the problem. The presented work provides a theoretical analysis of the
influence of the imaging optical systems on the transformation of the light pulse that propagates through such systems.
It is derived the theoretical formula for calculation of the change of wave aberration of the optical system in dependence
on the frequency of light passing through the optical system. New relations are described that enable to calculate the
complex amplitude of the wave field transformed by the optical system with aberration. These relations are valid even
for the systems with a large numerical aperture and are not restricted to the paraxial or the third order aberration space.
Our work describes a method for testing a shape of optical surfaces (i.e. flat, spherical or aspherical surfaces) using
correlation analysis of interference patterns and optimization techniques. The aim of this work is to propose a diverse
evaluation method for industrial control of optical surfaces that makes possible to speed up the testing process of optical
surfaces in special cases. The proposed method does not require an implementation of a detail analysis of the detected
interference field as it is necessary with existing interferometric methods. The deviation of the tested optical surface
from its nominal shape can be characterized by the correlation coefficient between the tested wave field and reference
wave field that corresponds to the nominal shape of surface. The shape of the tested optical surface and the deviation
from its nominal shape can be calculated by optimization of the correlation coefficient.
The problems of topography of surfaces are very important in various parts of science and engineering. Several
approaches exist for measurement of surface figure and roughness. Measurement methods can be divided into two
distinct categories, contact and non-contact techniques. Our work describes a relatively simple method for topography
measurements that uses special optical systems (hyperchromats) with a linear dependence of longitudinal chromatic
aberration on the wavelength of light. The aim of this work is to show a possible application of hyperchromatic optical
systems for topography of surfaces. The work describes the theory for calculation of design parameters of
hyperchromats, i.e. optical systems with large longitudinal chromatic aberration that is in our case linearly dependent on
the wavelength of light. On the basis of the performed analysis, such optical systems (chromatic sensors) can be
designed that permit to perform measurements of topography of surfaces, i.e. determine a figure or roughness of
surfaces. The described theory makes possible to design the chromatic sensor with the required measurement accuracy
and dynamic range. The sensor uses polychromatic light and relatively simple experimental arrangement. The proposed
measurement technique seems to be quite simple and cost effective with respect to other measurement methods.
Ultrashort light pulses are distorted in optical systems due to a different magnitude of the phase and group velocity of the wave. Our work is focused on the analysis of the problem. The presented work provides a theoretical analysis of the influence of the imaging optical systems on the transformation of the light pulse that propagates through such systems. It is derived the theoretical formula for calculation of the change of wave aberration of the optical system in dependence on the frequency of light passing through the optical system. New relations are described that enable to calculate the complex wave field transformed by the optical system with aberration. These relations are valid even for the systems with a large numerical aperture and are not restricted to the paraxial or the third order aberration space.
Our work deals with a method of measurement of the wavefront shape using the lenslet array objective based on the
Shack-Hartmann method. An analysis and computer simulation was carried out for the designed wavefront sensor,
devoted to optical testing applications. The obtained accuracy is comparable to common interferometric techniques in
optical industry, and it is sufficient for testing of optical elements and systems. Our work focuses on an application of
the sensor for image quality testing of optical systems and measurement of centricity of optical systems. Several
experiments were made for testing optical systems in UV and visible spectrum using the wavefront sensor, which
verified the reliability and accuracy of the sensor for the case of optical system testing in optical industry.
Our work deals with the influence of the wavelength of light on values of wave aberration coefficients. It is proposed a technique for calculation of the dependence of aberration coefficients on the wavelength, their interpretation and the connection to chromatic aberrations. It is also shown the calculation of the Strehl definition using chromatic aberration coefficients and the tolerance limits are given. The proposed method for calculation of chromatic aberration coefficients is shown for the case of the imaging of axial point by the rotationally symmetrical optical system. Relations that enable calculation of chromatic aberration coefficients up to fifth order are carried out. These relations are accurate enough for most optical systems in practice.
The work analyses an influence of the change of object position on the accuracy of optical and optoelectronic
measurement systems using both geometrical and diffraction theory. It is shown that in case of the change of position of
the measured object the imaging properties of the used optical measurement instrument are changed. This position
change affects the image quality. If some optical measurement system is aberration free for a specified position of the
measured object, then for other object positions the optical system has aberrations. The consequence of this effect is the
change of the measurement accuracy for the specific optical system. The described effect is not removable on principle
and it is necessary to take account to it in high accuracy measurements.
In case of total reflection at a boundary surface between two different optical media, the ray reflected at the boundary is
spatially shifted with respect to a point, where an incident ray intersects the boundary. The light penetrates into the
second medium and the evanescent electromagnetic wave propagates along the boundary. The described problem is
called the Goos-Hanchen effect. Our work describes an influence of the Goos-Hanchen effect on the imaging properties
of optical systems and it is derived a differential equation of a wave-front meridian that corresponds to a reflected bundle
of rays. It is shown that the wavefront can be described by d'Alambert differential equation. This equation make possible
to determine the coordinates of individual points on the wave-front meridian. Moreover, the paper also investigates the
influence of total reflection on the value of the Strehl definition of the reflected ray bundle.
Optical lens systems have always chromatic aberration. Optical systems that are used for imaging in optical
instruments, e.g. in binoculars, microscopes, cameras and projectors, have chromatic aberration corrected
very well in order not to reduce imaging quality. In many cases, it is necessary to use optical systems with
relatively large chromatic aberration. The optical systems that are characterized by a chromatic aberration of a
predefined form are called hyperchromats. Our work describes a theory of hyperchromats with a linear
dependence of longitudinal chromatic aberration on wavelength. The equations are derived for calculation of
basic design parameters of these optical systems and several examples of calculations are shown. Mentioned
optical systems can be used especially in 3D imaging systems and confocal microscopy.
It is well-known from the theory of optical imaging that optical systems generally show a presence of a chromatic
aberration, which originates from a variation of the refraction index of glass on the wavelength of light. The chromatic
aberration must be well corrected in order to obtain a good quality of optical image. In practice, it is used a proper
combination of optical elements manufactured from different types of optical glass with a different dispersion in order
to suppress the chromatic aberration. Our work shows a way how to correct spherochromatic aberration using a system
of thin aspherical layers. The equations are derived for determination of parameters of thin layers with respect to a
required spherochromatic aberration.
Our work describes a method for wave-front shape evaluation in microwave range. The evaluation is carried out by
measurement and analysis of the interference field that originates from interference of the reference microwave field
with the investigated (object) wave field. The phase of investigated microwave field is then determined from values of
squared amplitude of the electric field intensity using the phase-shifting technique. The advantage of the proposed
method is the fact that the method is based only on scalar measurements of microwave field. The proposed evaluation
method is an analogy to phase-shifting interferometry in optical testing, but it uses microwaves instead of optical
wavelengths. Due to physical properties of microwaves, the method can be used for various applications in
nondestructive testing.
Our work presents a method for evaluation of very small phase variations that uses the interference of polychromatic light using the principle of polarization interferometry. The phase change affects the color of the interference pattern, and color of the interference pattern corresponds to a specific phase change that can be evaluated using colorimetric techniques. We describe and analyse the colorimetric method for phase evaluation in our work. The proposed method offers accurate results and it is suitable for practical utilization in optical testing techniques.
The design process of optical systems requires to obtain residual aberrations of designed optical systems as small as possible. By analysis of the dependence of aberrations on the numerical aperture and field of view, it is possible to find such values of numerical aperture and field of view, where the residual aberration is zero. Such values of numerical aperture and field of view are called correction zones. The work theoretically analyses the described problem and equations are derived for expression of wave aberration coefficients using correction zones for aberrations of the third and fifth order. Finally, there was done an analysis of optimal values of correction zones and optimal position of the centre of reference sphere using derived equations. This analysis was performed for the case when it is required the maximal value of wave aberration to be minimized.
The work deals with the influence of the wavelength of light on the values of wave aberration coefficients. It is proposed a methodics for calculation of the dependence of aberration coefficients on the wavelength, their interpretation and the connection to chromatic aberrations of the optical system. The relations for the calculation of chromatic aberration coefficients up to the fifth order are derived for the case of the imaging of axial point by the rotationally symmetric optical system.
Optical systems with variable optical characteristics (zoom lenses) find broader applications in practice nowadays and methods for their design are constantly developed and improved. Our work describes a methodics of the design of zoom lenses using the third order aberration theory. The proposed method makes possible to determine, which elements of the optical system can be only simple lenses and which elements must have more complicated design, e.g. doublets or triplets. It is also shown the method for optical system design that permits to calculate the radii of curvature and optical glass types for individual lenses.
The problems of topography of surfaces are very important in various parts of science and engineering. Several approaches exist for surface figure and roughness measurement. The measurement methods can be divided into two distinct categories, contact and non-contact techniques. Our work describes a relatively simple method for topography measurements that uses special optical systems (hyperchromats) with a linear dependence of longitudinal chromatic aberration on the wavelength of light. The aim of this work is to show a possible application of hyperchromatic optical systems for topography of surfaces. The work describes a basic analysis of parameters of hyperchromats, i.e. optical systems with large longitudinal chromatic aberration that is in our case linearly dependent on the wavelength of light. On the basis of the performed analysis, it can be designed such optical systems (optical sensors) that permit to perform measurements of topography of surfaces, i.e. determine a figure or roughness of surfaces. The sensor uses polychromatic light and relatively simple experimental arrangement. The proposed measurement technique seems to be quite simple and cost effective with respect to other measurement methods.
Measurements of very small phase changes in optical measurement techniques are usually performed by interferometric methods that are based on evaluation of interference patterns, which correspond to a phase change of the investigated wave field. If values of the phase change are small, it is difficult to determine accurately the phase values, and one needs very expensive measurement systems. Our work presents a simple method for evaluation of small phase variations that uses the interference of polychromatic light. The phase change affects the color of the interference pattern, and color of the interference pattern corresponds to a specific phase change that can be evaluated using colorimetric analysis. We describe and analyse the colorimetric phase evaluation method in our work. The proposed method offers accurate results and it is suitable for practical utilization in optical industry.
An experimental technique for testing the image quality of microscope objective lenses and optical systems is described. Our work deals with a theoretical analysis of properties of a small and compact shearing interferometer, which was designed, manufactured and tested on several microscope objectives. The designed shearing interferometer can be used for testing the quality of optical systems, e.g. microscope objective lenses and camera lenses. The proposed shearing interferometer enables to determine the residual wave aberration of the tested optical system (e.g. microscope objective lens). The wave-front deformation can be analysed using colorimetric methods or standard phase evaluation techniques for interferometry. The device is characterized by very small dimensions, which provide its easy portability. The described compact shearing interferometer is practically insensitive to vibrations and the mechanical design is also very simple. The proposed evaluation method offers very accurate results and it is suitable for practical utilization in optical industry. The interferometer is suitable for testing laboratories and service engineers in the field of optical microscopy. The asame inferometer can also be used not only for wave abberation measurement, but also for measurement of the modulation transfer (MTF) of tested optical systems.
The theory and method for design of the optical systems for realization of the Fourier transform in systems for optical data processing is described. There are given relations for initial design of these optical systems using the third order theory of aberrations. As an example, the parameters of the four element optical system are given, which enables to obtain a suitable image quality required in systems for optical image processing.
A theory of deformation of the thin flat mirror, which vibrates harmonically in the direction of the normal to its surface, is shortly introduced in our work. Vibrating thin flat mirrors are used in various areas of science and engineering, e.g. in optical measurement systems. These mirrors can be generally deformed with respect to environmental conditions during measurements. The mirror deformation is closely related to the dynamic wave aberration of the wave-front, reflected from the mirror. The consequence of the wave aberration is a spatially inhomogeneous frequency shift of the light reflected from the vibrating mirror. The influence of the wave aberration on the frequency shift is studied theoretically and examples are given.
The work deals with an influence of aberrations of optical systems that are used in optical information processing systems. A detailed analysis of the influence of aberrations on the image formed using the optical system is carried out. Furthermore, the effect of aberrations of the wave field, which illuminates the object, is also studied. A theoretical analysis is carried out using the third order aberration theory, and several examples are shown for an object of a circular shape.
It is shown that a specific position of an axial object point can be found for every optical element, where the spherical aberration is either zero or minimal. If we image this point with an optical element, then its point spread function will be almost identical to the point spread function of the diffraction limited optical system. It can be used for testing of centricity of very precise very precise optical elements, because we can simply detect unsymmetry of the point spread function, which is caused by the decentricity of the tested optical element. Furthermore, one can also use this method for testing optical elements in connection with a cementing process. It is also derived a simple equation for calculation of the coefficient of third order coma, which is caused by a decentricity of the optical surface due to a tilt of the surface with respect to the optical axis.
In our work there is shown one of possible approaches to education of various parts of optics with a mathematical system MATLAB. The work is focused mainly on education of interference and diffraction of light and the diffraction theory of optical imaging. In our laboratories students can simply perform a computer simulation of various problems, which they can meet in practice, e.g. two-beam interferometry, imaging in coherent, partially coherent or incoherent
light, diffraction from gratings of different types, etc. The system Matlab can be also used for simulating problems in holography and holographic interferometry of static and dynamic events. Students can further simulate transforming of optical beams through a simple lens or a system of lenses by means of ray tracing. For every described part of optics we have the software programmed in the Matlab system. Matlab seems to be a very good tool for numerical modelling of
properties of various optical systems and for teaching optics.
The most frequently appearing criteria of the quality of optical surfaces and elements are analysed in detail in this article. There are described both geometrical-optics criteria and diffraction criteria. The connection between different criteria is also escribed. Some terms lacking classical analogy in optics are described, e.g. the focal length of the plane parallel plate, prism etc.
The proposed method is based on the law of reflection and can be used for large reflective continuous surfaces, which behave approximately as a deformable mirror of a general type. For successful application of the ray method for deformation measurement is crucial the reflectivity of the surface. If the measured surface is optically rough, then the light is diffusely scattered in different directions relating to the microstructure of the surface, and the described method cannot be used. To limit the influence of the surface roughness the plastic reflective foil can be affixed on the test surface. The research was focused on several theoretical and experimental aspects of evaluation of the deformations with the ray method, especially on problems of measuring extended objects in engineering practice and automatic process for evaluation of deformations.
Interferometric measurement methods are based on the principle of interference of two coherent wave fields (object and reference) and consequent evaluation of the interference pattern. The measured quantity, e.g. deformation, is related to the optical path difference between both wave fields, which depends on the phase of the object wave field. The phase can be obtained from the values of the intensity of the interference field with phase measuring techniques. In the work there was proposed an optical method for measuring of static deformations based on the interference of coherent wave fields and phase shifting procedure. Detailed analysis of the measurement and evaluation process with respect to most important factors is performed.
Our work analyzes an influence of the change of imaging conditions on the accuracy of optical and optoelectronic measurement systems, which are used in various industrial branches, e.g. in mechanical engineering, optical industry, building industry, etc. It is shown that in case of the change of position of the measured object the imaging properties of the used optical measurement instrument are changed. This position change affects the image quality. If some optical measurement system is aberration free for a specified position of the measured object, then for other object positions the optical system has aberrations. The consequence of this effect is the change of the measurement accuracy for the specific optical system. The described effect is not removable on principle and it is necessary to take account to it in high accuracy measurements.
Our work analyzes several multiframe phase-shifting algorithms with unknown values of phase shifts. The presented paper offers new algorithms for evaluation of phase values in interferometric measurements. Nonlinear multi-frame phase-shifting algorithms, which use five, six and seven intensity frames to determine phase values in interferometric measurements, are described theoretically. The proposed algorithms compensate for linear phase-shift errors, i.e. miscalibration of phase-shift, which are very common in practice of interferometric measurements. The phase-shift value is assumed unknown but constant in these algorithms, so that at least four phase shifted intensity frames have to be recorded. An advantage of the described algorithms is a possibility of pointwise phase-shift calculation. An analysis of proposed algorithms with respect to possible influences on the process of interferometric measurements is also carried out. Several important potential error sources were chosen and the sensitivity and accuracy of phase evaluation algorithms was compared. The algorithms derived in this work can be used in any phase-shifting measurement technique and they offer the advantage of insensitivity to the linear phase-shift errors.
Flat mirrors are often used for designing many optical measurement systems. These mirrors can be generally deformed with respect to environmental conditions during measurements. The detailed theory of deformation of the thin flat mirror, which vibrates in the direction of the normal to its surface, is introduced in our work. It is also derived the relation for the dynamic wave aberration. On the basis of this relation, it is carried out the calculation of the Strehl definition of the deformed mirror. Obtained results can be used for analysis of the influence of mechanical vibrations on the accuracy of optical measurement systems in various practical applications.
An optical method for measurement of static deformations is presented. This non-contact technique is based on interference of the light and the principle of phase shifting. The theory of phase shifting interferometry is shortly described and there are given four possible multistep algorithms for evaluation of the phase difference of the interference field induced by a static deformation. It is shown a new way how to evaluate the phase difference of the interference wave field, which is closely related to deformations of tested objects. The main part of this paper deals with an analysis of proposed algorithms. The experimental system, which is applied in static deformation measurement and which can be easy modified for industrial applications, is described and the method is demonstrated on an example.
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