Martin Šarbort

Spherical media and geodesic lenses in geometrical optics

This paper presents a general approach to solving the problems of inverse scattering in three-dimensional isotropic media with a spherically symmetric refractive index distribution. It is based on equivalence of the central section of an inhomogeneous medium and corresponding geodesic lens, which is a non-Euclidean surface with constant refractive index. We use this approach for solving the Luneburg inverse problem and also for the derivation and design of absolute instruments that provide perfect imaging within the frame of geometrical optics. In addition, we solve the generalized Luneburg inverse problem, which leads to the discovery of a new class of magnifying lenses.

Detection of Interference Phase by Digital Computation of Quadrature Signals in Homodyne Laser Interferometry

We have proposed an approach to the interference phase extraction in the homodyne laser interferometry. The method employs a series of computational steps to reconstruct the signals for quadrature detection from an interference signal from a non-polarising interferometer sampled by a simple photodetector. The complexity trade-off is the use of laser beam with frequency modulation capability. It is analytically derived and its validity and performance is experimentally verified. The method has proven to be a feasible alternative for the traditional homodyne detection since it performs with comparable accuracy, especially where the optical setup complexity is principal issue and the modulation of laser beam is not a heavy burden (e.g., in multi-axis sensor or laser diode based systems).

Absolute instruments and perfect imaging in geometrical optics

We investigate imaging by spherically symmetric absolute instruments that provide perfect imaging in the sense of geometrical optics. We derive a number of properties of such devices, present a general method for designing them and use this method to propose several new absolute instruments, in particular a lens providing a stigmatic image of an optically homogeneous region and having a moderate refractive index range.

Spectral properties of molecular iodine in absorption cells filled to specified saturation pressure

We present the results of measurement and evaluation of spectral properties of iodine absorption cells filled at certain saturation pressure. A set of cells made of borosilicate glass instead of common fused silica was tested for their spectral properties in greater detail with special care for the long-term development of the absorption media purity. The results were compared with standard fused silica cells and the high quality of iodine was verified. A measurement method based on an approach relying on measurement of linewidth of the hyperfine transitions is proposed as a novel technique for iodine cell absorption media purity evaluation. A potential application in laser metrology of length is also discussed.

Comparison of Molecular Iodine Spectral Properties at 514.7 and 532 nm Wavelengths

Abstract We present results of investigation and comparison of spectral properties of molecular iodine transitions in the spectral region of 514.7 nm that are suitable for laser frequency stabilization and metrology of length. Eight Doppler-broadened transitions that were not studied in detail before were investigated with the help of frequency doubled Yb-doped fiber laser, and three of the most promising lines were studied in detail with prospect of using them in frequency stabilization of new laser standards. The spectral properties of hyperfine components (linewidths, signal-to-noise ratio) were compared with transitions that are well known and traditionally used for stabilization of frequency doubled Nd:YAG laser at the 532 nm region with the same molecular iodine absorption. The external frequency doubling arrangement with waveguide crystal and the Yb-doped fiber laser is also briefly described together with the observed effect of laser aging.

Multi-focal spherical media and geodesic lenses in geometrical optics

This paper presents a general approach to designing isotropic spherical media with complex spatial structure that provide different types of imaging for different light rays. It is based on equivalence of the spherical medium and the corresponding geodesic lens. We use this approach to design multi-focal gradient-index lenses embedded in an optically homogeneous region and multi-focal absolute instruments that provide stigmatic imaging of three-dimensional domains.

Contribution of the Refractive Index Fluctuations to the Length Noise in Displacement Interferometry

Abstract We report on investigations of how fast changes of the refractive index influence the uncertainty of interferometric displacement measurements. Measurement of position within a limited range is typical for precise positioning of coordinate measuring systems, such as nanometrology standards combined with scanning probe microscopy (SPM). The varying refractive index of air contributes significantly to the overall uncertainty; it plays a role especially in case of longer-range systems. In our experiments we have observed that its fast variations, seen as length noise, are not linearly proportional to the measuring beam path and play a significant role only over distances longer than 50 mm. Thus, we found that over longer distances the length noise rises proportionally. The measurements were performed under conditions typical for metrology SPM systems

Active Angular Alignment of Gauge Blocks in Double-Ended Interferometers

This paper presents a method implemented in a system for automatic contactless calibration of gauge blocks designed at ISI ASCR. The system combines low-coherence interferometry and laser interferometry, where the first identifies the gauge block sides position and the second one measures the gauge block length itself. A crucial part of the system is the algorithm for gauge block alignment to the measuring beam which is able to compensate the gauge block lateral and longitudinal tilt up to 0.141 mrad. The algorithm is also important for the gauge block position monitoring during its length measurement.

Automatic unit for measuring refractive index of air based on Ciddor equation and its verification using direct interferometric measurement method

In scanning probe microscopy laser interferometers are usually used for measuring the position of the probe tip with a metrological traceability. As the most of the AFM setups are designed to work under standard atmospheric conditions the changes of the refractive index of air have an influence to measured values of the length with 1.0exp(-4) relatively. In order to achieve better accuracies the refractive index of air has to be monitored continuously and its instantaneous value has to be used for compensating the lengths measured by all of the interferometric axes. In the presented work we developed a new concept of an electronic unit which is able to monitor the refractive index of air on basis of measurement of ambient atmospheric conditions: temperature, humidity, pressure of the air and the CO2 concentration. The data processing is based on Ciddor equation for calculating the refractive index of air. The important advantage of the unit is a very low power consumption of the electronics so the unit causes only negligible temperature effects to the measured environment. The accuracy of the indirect measuring method employed by the unit was verified. We tested the accuracy in comparison with a direct method of measuring refractive index of air based on an evacuatable cell placed at the measuring arm of a laser interferometer. An experimental setup used for verification is presented together with a set of measurements describing the performance. The resulting accuracy of the electronic unit falls to the 4.1 exp(-7) relatively.

Autocorrelation analysis of plasma plume light emissions in deep penetration laser welding of steel

The light emissions of the plasma plume in the deep penetration laser welding of metals typically have the character of irregular short-time pulses. Their nature indicates that the size of the plume significantly fluctuates and the plasma flows out of the keyhole in the form of short bursts rather than a continuous flow. In this paper, the authors study the plasma plume light emissions using an autocorrelation analysis. The authors show that it is an efficient tool for the detection of the plasma bursts period which is typically in the order of milliseconds. The authors compare the autocorrelation characteristics and the geometry of the welds made on a 2 kW ytterbium-doped yttrium aluminium garnet (Yb:YAG) fiber laser welding machine for the X5CrNi 18-10 stainless steel and the S235JR carbon steel. The welding parameters settings is varied over a range of laser power (1–2 kW) and welding speed (10–30 mm/s) usually used in industry. As a result, the authors identify a linear dependence between the plasma b...