Optimal mass transportation problem in the design of freeform optical elements generating far-field irradiance distributions for plane incident beam

2019 ◽  
Vol 58 (33) ◽  
pp. 9131 ◽  
Author(s):  
Dmitry A. Bykov ◽  
Leonid L. Doskolovich ◽  
Albert A. Mingazov ◽  
Evgeni A. Bezus
Keyword(s):  
Transportation Problem ◽  
Incident Beam ◽  
Far Field ◽  
Mass Transportation ◽  
Optical Elements

Characterization of X-ray gas attenuator plasmas by optical emission and tunable laser absorption spectroscopies

2017 ◽  
Vol 24 (6) ◽  
pp. 1195-1208 ◽  
Author(s):  
Álvaro Martín Ortega ◽  
Ana Lacoste ◽  
Stéphane Béchu ◽  
Alexandre Bès ◽  
Nader Sadeghi
Keyword(s):  
Incident Beam ◽  
Tunable Laser ◽  
Optical Emission ◽  
High Energy ◽  
Beam Power ◽  
Beam Path ◽  
Optical Elements ◽  
X Ray ◽  
Laser Absorption ◽  
X Ray Absorption

X-ray gas attenuators are used in high-energy synchrotron beamlines as high-pass filters to reduce the incident power on downstream optical elements. The absorption of the X-ray beam ionizes and heats up the gas, creating plasma around the beam path and hence temperature and density gradients between the center and the walls of the attenuator vessel. The objective of this work is to demonstrate experimentally the generation of plasma by the X-ray beam and to investigate its spatial distribution by measuring some of its parameters, simultaneously with the X-ray power absorption. The gases used in this study were argon and krypton between 13 and 530 mbar. The distribution of the 2pexcited states of both gases was measured using optical emission spectroscopy, and the density of argon metastable atoms in the 1s5state was deduced using tunable laser absorption spectroscopy. The amount of power absorbed was measured using calorimetry and X-ray transmission. The results showed a plasma confined around the X-ray beam path, its size determined mainly by the spatial dimensions of the X-ray beam and not by the absorbed power or the gas pressure. In addition, the X-ray absorption showed a hot central region at a temperature varying between 400 and 1100 K, depending on the incident beam power and on the gas used. The results show that the plasma generated by the X-ray beam plays an essential role in the X-ray absorption. Therefore, plasma processes must be taken into account in the design and modeling of gas attenuators.

scholarly journals Design and fabrication of a freeform mirror generating a uniform illuminance distribution in a rectangular region

2020 ◽  
Vol 44 (4) ◽  
pp. 540-546
Author(s):  
E.S. Andreev ◽  
E.V. Byzov ◽  
D.A. Bykov ◽  
М.А. Moiseev ◽  
L.L. Doskolovich
Keyword(s):  
Numerical Simulations ◽  
Assignment Problem ◽  
Transportation Problem ◽  
Design Method ◽  
Experimental Measurements ◽  
Mass Transportation ◽  
Rectangular Region ◽  
Linear Assignment Problem ◽  
Linear Assignment ◽  
Good Agreement

The design of a freeform mirror generating a uniform illuminance distribution in a rectangular region with angular dimensions of 30°x15° is presented. The design method is based on the formulation of the problem of calculating the "ray-mapping" as a Monge-Kantorovich mass transportation problem and its subsequent reducing to a linear assignment problem. We describe a mirror fabrication process with the use of milling technology and present results of experimental measurements of the light distribution generated by the mirror. The experimental results are in good agreement with the results of numerical simulations and thus confirm the manufacturability of mirrors designed by the method proposed.

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