In this paper a phase recovering scheme from the optical vortex microscope is presented. Laguerre-Gaussian beam with the vortex charge equal to one passes through the phase sample and then is detected at the observation plane. The sample modifies the internal structure of the vortex beam. The way of measuring such perturbation is presented. Numerical results are confirmed by the experiment.
We present an idea to use optical vortex as a spatial light modulator (SLM) phase modulation depth marker. It can open a way to fast and efficient SLM calibration, which is required especially for SLMs that are able to change between introduced phase shift. Additionally, it may be used to control optical system aberrations and proper SLM phase shift, simultaneously. In this paper, the typical calibration method is discussed in brief. Next the new method based on vortex quality inspection is presented. The idea of the new method is preliminary verified in experiment, which is followed by a discussion of further research, that need to be done.
Optical vortex microscope is an optical system in which the beam illuminating the sample contains the optical vortex- a characteristic structure which contains a point of zero amplitude and undefined phase. Such a beam is very sensitive to the phase or amplitude defects which are introduced into it. In this paper we analyze experimentally the response of the optical vortex microscope to the small phase changes introduced into the beam.
One of the challenges for the Optical Vortex Scanning microscope is to find the effective procedures for surface
topography reconstruction. We proposed an experimental setup to support solution of this problem. The Spatial Light
Modulator (SLM) is used as a phase object. SLM allows to generate phase disturbance in the range 0-2π, which can be
easily introduced into the beam carrying optical vortex. Our system gives an opportunity to measure optical vortex
response due to phase modifications introduced by the SLM and investigate vortex sensitivity. We tested how the object
position, size affects vortex and position of the vortex point inside the beam.
In this work we consider a microscopic optical system in which the beam with an optical vortex illuminates the sample.
The sample modifies the geometry of the vortex beam wavefront and the information about it is transferred into the
detection plane. It is shown that the beam at the detection plane can be represented by two parts: non-disturbed vortex
part and sample part. We propose and test a scheme for recovering the phase changes caused by sample inserted into
the vortex beam. The numerical simulations are supported by the experimental work.
We consider a microscopic system in which the focused Gaussian beam with the embedded vortex illuminates the sample. The vortex beam is very sensitive to any imperfections introduced into it. Small defects introduced into the dark area of the vortex beam causes the change in its internal structure. We investigate theoretically and experimentally how the small rectangular groove introduced into the beam at the critical plane influence the phase structure of the beam. The analytical model of the setup is provided and following it the scheme for recovering the information about the sample is proposed.
We present the analytical model describing the Gaussian beam propagation through the off axis vortex lens and the set of axially positioned ideal lenses. The model is derived on the base of Fresnel diffraction integral. The model is extended to the case of vortex lens with any topological charge m. We have shown that the Gaussian beam propagation can be represented by function G which depends on four coefficients. When propagating from one lens to another the function holds its form but the coefficient changes.
The optical system working with focused Gaussian beam carrying a higher order optical vortex is considered. Additionally the optical vortex movement inside the beam is proposed allowing the precise scanning of the sample inserted into the beam. The analytical formula for the Fresnel diffraction integral with the shifted optical vortex has been calculated and compared with the numerical results. The experimental validation of this problem has been also presented.
We consider an optical system in which the optical vortex moves inside the focused Gaussian beam. The vortex movement is due to the vortex lens inserted in front of the focusing objective. We gradually shift the vortex lens along the x-axis which is perpendicular to the axis of laser beam propagation (z-axis). This causes that in the image plane vortex moves along a straight line but the line inclination depends on the position of the observation plane. There is a characteristic position of the observation plane, in which the vortex trajectory is perpendicular to the vortex plate shift. We call this plane a critical plane. The critical plane is sensitive to small phase variations which can be introduce by a transparent sample. We propose a way of retrieving the phase profile (at the critical plane) of such a beam. Our procedure is based on the Fourier transform phase demodulation method. We also investigate how the system reacts to the known phase variations introduced into the critical plane.
In this paper we present the Optical Vortex Scanning Microscope (OVSM) in which the new scanning method induced by vortex lens movement is introduced. This method allows to scan the sample in a simple way. The behavior of the vortex position at the sample plane and phase retrieval algorithm is discussed. The new experimental results confirming the progress in the OVSM building are presented.
In this paper we report on the progress in building the superresolution microscope using optical vortices. The outline of the general idea is presented. Some of the specific problems are discussed in more details. Specifically, the scanning
method by vortex lens movement is discussed.
In the previous paper the new scanning technique was proposed. The sample was illuminated by a focused laser beam
with an optical vortex. The vortex was introduced to the laser beam by vortex lens. When shifting the vortex lens the
optical vortex in the focused beam moves and scans the sample. In order to use this new scanning technique for
microscopic imaging a method for the focused vortex beam phase reconstruction is necessary. In this paper a fast and
accurate method for phase reconstruction of the focused vortex beam is investigated. It is shown that the propose method
is accurate enough to explore even small optical vortex shifts inside the focused beam.
Scanning vortex microscope is a system in which sample is scanned by a Gaussian beam carrying optical vortex. We
report on a new method in which the sample is scanned by moving the optical vortex inside the focused beam spot.
Figure 1 shows a scheme of the optical system. The vortex lens shift induces a precise nanometre shift of the vortex point (i.e. point where the phase is undetermined) inside the focused spot. When moving the vortex lens along a straight line vortex point goes along a straight line of much smaller size and different orientation. There is a specific distance between the focusing lens and sample plane at which optical vortex is highly sensitive on sample topography. In this special plane vortex point’s movement is perpendicular to the vortex lens’ shift. Moreover, the angle of vortex point’s trajectory changes in a very rapid way. In the paper we investigate the dynamics of the vortex shift induced by different setup parameters.
The optical vortex is introduced into the incident Gaussian beam by a vortex lens. Then the beam with the
optical vortex is focused by a lens. By changing the position of the vortex lens we can shift the optical vortex
position inside the focused beam. We discussed the relation between vortex lens shift and optical vortex
movement inside the focused beam. The influence of optical system errors on this vortex movement is also
Optical vortex interferometer (OVI) is a useful tool to generate a regular lattice of optical vortices. The lattice is
generated by the interference of the three plane waves. As was shown in earlier papers such a vortex lattice can be
practically used in metrology. Application of optical vortex interferometer in metrology depends on the precision of the
vortex points localization. In this paper we present a novel localization method, which uses the phase shifting technique
applied to the additional fourth wave. Phase shift of the fourth wave doesn't change intensity in vortex points and
increases intensity gradient in their vicinity. The applicability of this method was verified in the experiment.
We present the results of birefringent media properties measurement using two different interferometers with polarizing
elements. These setups allow to generate regular and stable lattice of optical vortices (OVs) and to record the lattice
deformations caused by introduced birefringent plate. The first setup is a polariscope arrangement with two Wollaston
compensators placed between crossed polarizers. The shape of lattice basic cell is determined by the Wollaston's
shearing angle and examined birefringent medium causes only the shift of the whole OVs lattice. The calculated
displacement vector allows determining at least two parameters of measured medium simultaneously. This setup was
used also to measure the absolute value of the phase shift introduced by examined birefringent sample by using two light
sources with slightly different wavelength. We manage to determine the phase retardance order by tracking the center of
two interferograms made with and without sample. The second setup is based on modified Mach-Zehnder interferometer
in which the Wollaston compensator is inserted into the one of interferometer's arm. The measured birefringent medium
placed in another interferometer's arm causes the mutual displacement of two OVs sublattices with different topological
signs. Calculated displacements vectors between those two sublattices allows to determine birefringent sample
The application of the optical vortex interferometer (OVI) to small-angle rotation measurements is presented. The OVI is based on a regular lattice of optical vortices. In our experimental setup a regular lattice of optical vortices is produced by the interference of three plane waves. The vortex points are stable, pointlike structures within the interference field. Distortion of one, two, or three of the interference waves results in a characteristic vortex lattice deformation. This deformation can be measured and related to the physical quantities being investigated. We show the ability of the OVI to measure the deflection angle and the orientation of the wave vector in a single measurement. Two different methods that allow comparing the geometry of the vortex lattice are used to analyze the results of the experiment. They are compared with the method based on standard two-beam interferograms. The results show that the OVI system can be successfully used to measure the deflection and orientation of the wave vector. The vortex methodology is more accurate than classical two-beam interferometry for rotation angles in the range of a few arcseconds.
In this paper some possible applications of a new device - Optical Vortex Birefringence Compensator (OVBC) are
proposed. The arrangement consisting of two Wollaston prisms placed between the linear polarizer and analyzer allows
to generate regular and stable optical vortex lattice. Inserting the measured medium into the OVBC can result in either
the deformation or the displacement of obtained vortex lattice. Tracing the lattice shift or its geometry changes after the
inserting the measured medium one can measure its optical properties. The main applications of the presented setup seem
to be the measurements of the angular deformation of the wave front and the properties of the linearly birefringent
media. In the paper the numerical simulations as well as the analysis of the interferograms taken from experiment are
The Optical Vortex Interferometer (OVI ) uses a regular lattice of optical vortex points. Such lattice can be generated by
amplitude division obtained in the modified Mach-Zender set-up. This was reported in our previous papers ( - ).
In this work the vortex lattice obtained by wavefront division is reported. We use the opaque screen with three or more
holes. The optical vortex lattice obtained using three holes in the screen reveals some special properties as it is in three
plane waves version of OVI. We analyze the properties of such lattice as well as lattice generated by four waves and
report on possible applications of this particular simple device. The theoretical considerations are illustrated by the
In this work the application of the Optical Vortex Interferometer (OVI) to small-angle rotation measurements is
presented. OVI is based on the regular net of optical vortices. In our experimental setup a regular net of optical vortices
is produced by the interference of three plane waves. Distortion of one, two or three of the interference waves results in
a characteristic vortex net deformation. This deformation can be measured and related to the physical quantities being
investigated. In the given paper we present the ability of the OVI to measure the deflection angle of the wave vector and
its orientation in a single measurement. Two different methods which allow for comparing the geometry of the vortices
net were used to analyze the results of the experiment. They were compared with the method based on the standard two
beam interferogram analysis. The results show that the OVI system can be successfully used to measure the deflection
and orientation of the wave vector. The vortex methodology is more accurate than classical two beam interferometry in
the case of the rotation angles in the range of few arcseconds.
Optical Vortex Interferometer (OVI) is a new type of interferometer which is based on the regular net of optical vortices. Optical vortices (OV) are the point like phase singularities. The point where the phase is undetermined is called the vortex point. In OVI the net is generated by the interference of three plane waves. There might be different application of such an instrument. It can be used to small-angle wave rotation measurements and to the orientation of the tilt axis. The resolution of the instrument is on the level of well known and tested classical interferometric methods. We expand the algorithms described in our previous articles to the testing of the parallel plates.
The optical vortex interferometer (OVI) is based on the regular net of optical vortices, which is generated by the
interference of three plane waves. In this paper the use of OVI to phase determination is discussed. In classical
interferometry the phase of the wave is determined in respect to the phase of the reference wave. The quality of reference
wave must be checked by some other methods (like parallel glass plate test). It is shown that in case of OVI the phase of
the investigated wave can be reconstructed without referring to any other wave.
Optical Vortex Interferometer (OVI) is a new type of interferometer which is based on the regular net of optical vortices (OV)<sup>1,2,3</sup>. The net is generated by the interference of three plane waves. The idea of the measurement with the OVI is as follows: if one of the interfering waves is distorted then the geometry of the vortex net is changed. In our case one of the wavefronts was tilted. We can calculate the tilt of the wave by tracking the change of vortices positions. Basically it is sufficient to determine the relative change in the positions of three optical vortices (vortex triplet). If there are 200 vortices in the measurement field then we can choose about 1 million vortex triplets. The important advantage of this measurement is that two rotation angles through two perpendicular axes can be determined into one step. Also the mechanical vibrations are automatically subtracted and the system is simple.
Our first results show<sup>5</sup> that using about 1000 triplets we can measure the small angle with an error of 1.2arcsec (on the base of standard deviation). Performing the analysis we observed however that the real sensitivity of the OVI is higher than resolution resulting from the basic analysis methods. We observe the change of the histogram of the calculated angle if the tilt by the angle of 0.05arcsec is introduced. In the paper we analyze this effect. If the rotation angle is small then optical vortices change their positions by the small part of the distance between the measurement points. Due to detector quantization some of vortices can be still localized as lying in the same measurement point while the others are localized as shifted. This effect causes the histogram shift. The method of recomputing such histogram shift into the value of rotation angle is presented. In result we can achieve 6-10 times better resolution of the OVI.
We present one of the applications of the Optical Vortex Interferometer (OVI). OVI is based on the regular net of optical
vortices which are generated by the interference of three plane waves. Disturbing one of the interfering waves causes a
change in the position of the vortex points in the vortex net. The measurement is based on tracking the vortex position
change. This method can be used to determine small-angle rotation. OVI distinguishes two axis of rotation and the
corresponding two rotation angles can be measured with sub-second resolution. The linear vibrations of the measured
element are automatically subtracted. The single measurement provides hundreds of measurements points, so the
statistical methods for data analysis and corrections can be effectively applied. In the paper we present the experimental
testing of the method. To get the precise rotation of one of the interfering wave's the optical wedge is put into one of the
interferometer's arm. The analysis shows that the amplitude`s decrease does not influence the measurement accuracy.
From the vortex net shifting the rotation angle of one of the interfering waves is calculated and this rotation is also used
to calculate the refracting angle of the applied optical wedge.
Different methods of vortex localization in the vortices aided interferometry (VAI) presented in our previous work are presented and compared. The methods are tested first on the computer generated and then on the experimental interferograms. On the numerical generated interferograms vortex points can be localized with the accuracy of 1 pixel. On the experimental inteferograms different methods give the difference up to 4 pixels. Simple measuring scheme is applied to test this kind of the interferometer.
The cornea does not play any significant role in accommodation and is not expected to alter in curvature during the process. Nevertheless, some residual shape change may occur. In this paper we present preliminary results of a study in which we looked at the shape of the cornea for two separate accommodative states. Corneal power was measured with a Javal keratometer in tow states of the eye on one eye each from 12 emmetropic subjects aged between 20 and 28 years. These results suggest that there may be slight changes in central corneal curvature with accommodation.
In this paper we studied the chromatic properties of the bovine eye. Dispersion of the ocular liquids was measured in the Pulfrich refractometer. The measurements was done for five different wavelengths. From this data the dispersion curves and Abbe number of the eye substances was derived. To measure the distribution of the refractive index within the crystalline lens we modified the Pulfrich refractometer. Gradient of the refractive index of the crystalline lens was measured for three wavelengths. Distribution of the refractive index within the crystalline lens was be approximated by the parabolic function. Additionally, we measured the spherical aberration of the bovine crystalline lens for four different wavelengths. The experiment showed, that crystalline lens is corrected for the spherical aberration.
The numerical model of refractive properties of the eye lens is given. Crystalline lens is presented in a form of hundreds ellipsoidal shells with rotational symmetry, having the constant refractive index inside every shell. The refractive index between the surfaces increases from the cortical shell to the inner one, according to the exponential dependency. To complete the model of the optical system of the eye, the cornea approximated by two ellipsoidal surfaces is added in front of the crystalline lens. Ray tracing procedure is applied to study the refraction of rays through such a system. By changing the refractive index profile, optical properties of given model are analyzed. Results of calculations are compared with experimental data.