Boguslawa Dubik

Optical vortex generation by three plane wave interference

In this paper the generation of optical vortices by three plane waves interference is studied. The necessary conditions for such process are derived and the net structure of optical vortices generated in this way is analyzed. The results are verified experimentally.

Reconstruction of a plane wave’s tilt and orientation using an optical vortex interferometer

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.

Hybrid lens with corrected sphero-chromatic aberration

Abstract An optical imaging element is considered, which consists of a plano-convex spherical glass lens and a holographic lens recorded on the flat surface. Such a ‘hybrid lens’ enables one simultaneously to correct spherical aberration and longitudinal chromatism for two given wavelengths. The imaging quality of such an achromatic lens of focal length f = 100 mm and relative aperture 1:10 is evaluated by the ray tracing method. The results ensure that the performance of such a hybrid lens is acceptable for field angles as high as 5:100.

Aberrations of holographic lenses in image quality evaluation

The imaging quality of holographic lenses depends on parameters that include the shape of a holographic lens surface or an input pupil position. Based on the formulas for third-order aberration coefficients derived for such cases, conditions that ensure the correction of aperture and field aberrations are given. The possibility of joint correction of spherical aberration, coma, and astigmatism is discussed. The formulas presented are illustrated with a number of examples; two types of holo-lenses are taken into account: imaging and focusing. For imaging quality assessment an aberration spot calculation method based on numerical evaluation of an appropriate diffraction integral is used. The results of this method are compared with the results of imaging quality estimation using the geometrical ray tracing method.

Direct interferometric measurement of the holographic lens wave aberration

Classical interferometric methods for measurement of wave aberrations of holographic lenses have certain drawbacks. The limited diffraction efficiency of such lenses is the reason. To overcome this problem a new type of interferometer is suggested. The holographic lens under test is a basic element of the interferometer itself. The interference pattern is formed by adding the undiffracted and the diffracted waves.

Determination of the birefringent medium phase difference order in the optical vortex birefringence compensator

In this paper the two-wavelength procedure for determining of the birefringence medium phase retardance order using the optical vortex birefringence compensator (OVBC) is presented. The OVBC generates regular optical vortex lattice which moves if the measured birefringent medium is placed into the compensator setup. Due to the vortex lattice regularity, tracing the lattice shift after the measured medium is inserted, there is no possibility to determine the absolute phase retardance in the monochromatic light. This is an analogy to the well known problem in the classical fringe interferometry. Having recorded interferograms for two waves with slightly different wavelengths, one can identify the centers of the two pairs of interferogram images (with and without the examined medium in the setup) and hence in that way the absolute shift of the vortex lattice. In the paper the theoretical considerations, numerical simulations, as well as the analysis of the interferograms taken from the experiment are presented.

Reconstruction of the wave tilt and orientation of tilt axis using OVI

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.

Testing a new method for small- angle rotation measurements

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 waves the optical wedge is put into one of the interferometers 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.

Measurement of contrast sensitivity function in laser light

Visual quality depends on many factors of different nature and therefore it is not easy to define. Different measures are used to describe vision quality, such as: two point resolution, visual acuity, contrast sensitivity function (CSF) etc. We concentrate especially on CSF. There are two important factors affecting character of CSF. One of them is connected with the Optical Transfer Function (OTF) of the eye and the second one with the retinal response. Typically CSF is measured in incoherent light. Due to it is dependence on both mentioned above factors simultaneously it is impossible to extract the information on the eye optical system only. We hope that additional information offered by CSF measured in coherent light can help to solve this problem.

Measurement of wavefront aberrations of diffractive imaging elements

Diffractive optics is more and more widely used nowadays. One of its most important applications is diffractive imaging element (DIE). The DIE can be a lens (Holo-lens, diffractive lens, hybrid lens) or a part of complex imaging system (e.g. an aberration corrector). Apart of such problems occurring when dealing with DIE as its design, manufacture or copying the problem of its control is important. By this we mean the measurement of wavefront generated by DIE, i.e. the evaluation of wavefront aberrations. To this aim we propose two different experimental methods: one of them employs diffraction interferometer, the other one holographic shearing interferometer.