Measurement Techniques

, Volume 55, Issue 8, pp 894–899

Methods of calibrating standard plasma radiators using an electron synchrotron with an intense magnetic field

Authors

    • All-Russia Research Institute of Optophysical Measurements (VNIIOFI)
  • Yu. M. Zolotarevsky
    • All-Russia Research Institute of Optophysical Measurements (VNIIOFI)
  • V. S. Ivanov
    • All-Russia Research Institute of Optophysical Measurements (VNIIOFI)
  • V. N. Krutikov
    • All-Russia Research Institute of Optophysical Measurements (VNIIOFI)
  • O. A. Minaeva
    • All-Russia Research Institute of Optophysical Measurements (VNIIOFI)
  • R. V. Minaev
    • All-Russia Research Institute of Optophysical Measurements (VNIIOFI)
  • D. N. Lashkov
    • All-Russia Research Institute of Optophysical Measurements (VNIIOFI)
  • D. S. Senin
    • All-Russia Research Institute of Optophysical Measurements (VNIIOFI)
Optophysical Measurements

DOI: 10.1007/s11018-012-0056-2

Cite this article as:
Anevsky, S.I., Zolotarevsky, Y.M., Ivanov, V.S. et al. Meas Tech (2012) 55: 894. doi:10.1007/s11018-012-0056-2
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Methods of calibrating secondary standard plasma radiators, based on the use of a synchrotron with an intense magnetic field, are developed, which enable problems of both vacuum coupling of the acceleration chamber and the plasma radiator to be solved, and also enable the degree of polarization of the synchronous radiation to be taken into account. It is shown that a comparison of the characteristics of the synchrotron radiation of the storage ring and of the electron synchrotron in the visible region using a telescope and cooled CCD matrix ensures that the relative synchrotron spectrum is absolute.

Keywords

plasma radiatorselectron synchrotron with an intense magnetic fieldelectron storage ringCCD matrixradiometers-dosimetersspectroradiometers

Standard plasma radiators have found wide application in solving problems of spectroradiometry in such rapidly developing areas of science and technology as nanolitography of the extreme ultraviolet, photochemistry and fluorescence analysis, supermolecular chemistry, structural analysis, space monitoring systems, thermonuclear synthesis, the technology of the construction of multilayer nanostructures, etc. [1, 2]. These radiators serve to reproduce the energy units of spectroradiometry when measuring the spectral characteristics of plasma radiation, while determining its composition, concentration and temperature, for investigating plasma dynamics in plasmotrons, stellarators, and power equipment. Despite considerable experience in producing a primary standard source based on a high-temperature hydrogen arc, plasma radiators are used at present exclusively as secondary standard sources, since spectroradiometry of ultraviolet radiators is based on the use, by national metrological institutes, of primary standard sources of synchrotron radiation – electron storage rings and synchrotrons, the spectral energy characteristics of which are calculated with much higher accuracy over a wide spectral range [36].

In the long-wave ultraviolet region of the spectrum, deuterium, hydrogen, xenon and krypton gas discharge lamps with a window of magnesium fluoride and sapphire are used as secondary standard plasma radiators. In the short-wave ultraviolet region, where there are no transparent materials, sources based on a capillary discharge, a plasma focus and electron-cyclotron resonance are employed in addition to open flow helium lamps. The need to develop highly accurate methods of calibrating secondary standard plasma radiators is due to new problems in investigating the characteristics of the optical components of projection systems for experiments on nanophotolitography, calibrated portable integrated radiometer-dosimeters and spectroradiometers with a wide spectral range, by investigating the characteristics of multilayer nanostructures.

At the All-Russia Research Institute of Optophysical Measurements (VNIIOFI) and in other national metrological institutes, work is being carried out to calibrate secondary standard plasma radiators using synchrotron radiation – one of the main areas of investigation of optical spectroradiometry [7]. The main problems for comparing the spectral density of the radiation intensity of a plasma and of the synchrotron radiation of an electron storage ring are relevant to the need for vacuum coupling of the very high vacuum chamber of the accelerator and of the chamber of the radiator, which are subjected to the action of the erosive plasma that accompanies the radiation. The use of a differential pump-out system is not a simple solution, since it reduces the synchrotron radiation flux and makes it difficult to detect. Another difficulty in comparing the characteristics of the plasma radiation and the synchrotron radiation of electron storage rings is the need to take into account the degree of polarization of the synchrotron radiation. It is preferable here to use the relative spectrum of the synchrotron with an intense magnetic field under electron bunching conditions with large axial dimensions, which is distinguished by a wide angular uniformity of the intensity of the polarization components of the synchrotron radiation [8]. The use of a synchrotron then makes it necessary for the relative spectrum in the long-wave region to be made absolute using an electron storage ring.

In the case of a large bunch, the synchrotron radiation possesses the property of angular uniformity of the ratio of the intensity of the polarization components, which is particularly important for metrology. The spectral and angular distributions of the synchrotron radiation intensity of an individual electron is represented in Fig. 1, where λ is the wavelength, and ψ is the angle of deflection from the plane of the equilibrium orbit.
https://static-content.springer.com/image/art%3A10.1007%2Fs11018-012-0056-2/MediaObjects/11018_2012_56_Fig1_HTML.gif
Fig. 1

Spectral (a) and angular (b) distributions of the intensity of synchrotron radiation of an individual electron; ψ is the angle of deflection from the plane of the orbit; σ and π are the polarization components.

The broadening of the angular distribution of the synchrotron radiation flux and the fact that there is no reduction in the intensity of the polarization π-component in the median plane are explained as follows. For a finite axial dimension of the electron bunch, the angular distribution of the intensity of the synchrotron radiation components is described by the convolution of the angular dependence of the relative spectral density of the energy irradiance of an individual electron of the bunch and the distribution of the electrons of a bunch over the angles of deflection of the direction of the velocity vector from the plane of the equilibrium orbit. Large bunch operation occurs when the distribution of its electrons over the angles of deflection of the velocity from the plane of the orbit is wider than the angular dependence of the relative spectral density of the energy irradiance of the synchrotron radiation of an individual electron.

It is particularly important to obtain uniformity of the angular distribution of the ratio of the intensity of the polarization components of the synchrotron radiation for highly accurate transfer of the units of spectroradiometric quantities by secondary standard radiators of unpolarized plasma radiation. For this purpose, a spectral comparator is used, which contains an optical focusing system, a monochromator, a radiation receiver and an additional system of mirrors for introducing the radiation of the secondary standard sources and of the synchrotron into the optical channel.

The equations describing the signals of the spectral comparator as a function of the intensity of the components of the ultraviolet radiation, polarized in planes of the equilibrium orbit and in perpendicular planes, can be represented in the form
$$ {U_{\mathrm{s}}}=\int\limits_{{{\psi_0}}} {I_{\mathrm{s}}^{\parallel }} \left( {\psi, \lambda } \right){\tau^{\parallel }}\left( {\psi, \lambda } \right){S^{\parallel }}\left( \lambda \right)\varDelta \lambda \varDelta \varphi d\psi +\int\limits_{{{\psi_0}}} {I_{\mathrm{s}}^{\bot}\left( {\psi, \lambda } \right){\tau^{\bot }}\left( {\psi, \lambda } \right){S^{\bot }}\left( \lambda \right)\varDelta \lambda \varDelta \varphi d\psi; } $$
(1)
$$ {U_{\mathrm{p}}}=0.5I_{\mathrm{p}}^{\parallel}\left( \lambda \right)\int\limits_{{{\psi_0}}} {{\tau^{\parallel }}} \left( {\psi, \lambda } \right){S^{\parallel }}\left( \lambda \right)\varDelta \lambda \varDelta \varphi d\psi +0.5I_{\mathrm{p}}^{\parallel}\left( \lambda \right)\int\limits_{{{\psi_0}}} {{\tau^{\bot }}} \left( {\psi, \lambda } \right){S^{\bot }}\left( \lambda \right)\varDelta \lambda \varDelta \varphi d\psi . $$
(2)

Here Us and Up are the signals of the spectral comparator, proportional to the amplitude value of the spectral density of the synchrotron radiation power and of the spectral density of the radiation power of the secondary standard plasma radiator, respectively; ψ0 is the aperture angle of the optical system of the spectral comparator in a plane perpendicular to the plane of the equilibrium orbit; Is|| (ψ, λ), Is(ψ, λ) are the amplitude values of the spectral density of the synchrotron radiation power, polarized in the planes of the orbit and perpendicular to it, respectively; Ip||(λ), Ip(λ) are the spectral densities of the radiation powers of the secondary standard source, polarized in the planes of the orbit and perpendicular to it respectively; τ||(ψ, λ), τ(ψ, λ), S||, S are the transmission coefficients of the spectral instrument and the spectral sensitivities of the photorecording system of the comparator for radiation polarized in the planes of the orbit and perpendicular to it; Δλ is the spectral resolution of the comparator; and Δφ is the aperture angle of the optical system of the comparator in the plane of the equilibrium orbit.

The radiation of the plasma source is not polarized, and hence in (2) the radiation intensity is divided equally between the polarization components. To transmit the units of spectroradiometric quantities by secondary standard radiation sources, it is necessary to solve system of equations (1), (2) and to determine the spectral density of the radiation power Ip(λ) of the secondary plasma radiation. The aperture angle of the optical system of the spectral comparator ψ0 = 10 mrad, which enables one to obtain uniformity of the angular distribution of the intensity of the polarization components when transmitting the unit of spectral radiation power density for the synchrotron and plasma radiator.

An aperture stop is placed on a spherical mirror, which produces an image of the radiating region of the orbit of the synchrotron and of the secondary standard source of ultraviolet radiation in the plane of the entrance slit, common to both spectral instruments in the ultraviolet and visible spectral bands. An overall view of the spectral comparator is shown in Fig. 2.
https://static-content.springer.com/image/art%3A10.1007%2Fs11018-012-0056-2/MediaObjects/11018_2012_56_Fig2_HTML.jpg
Fig. 2

Overall view of the spectral comparator.

The equation describing the calibration of the spectral density of the radiant intensity of secondary standard plasma radiators for the spectral comparator of the accelerator with an intense magnetic field, taking into account the angular uniformity of the synchrotron radiation flux within the limits of the aperture stop and the equality of the spectral sensitivities of the radiation receiver of the spectral comparator for the polarization components S||(λ) = S(λ), has the form
$$ {I_{\mathrm{p}}}\left( \lambda \right)=\frac{{2{U_{\mathrm{p}}}}}{{{U_{\mathrm{s}}}}}\frac{{I_{\mathrm{s}}^{\bot}\left( \lambda \right)\left[ {\nu \left( \lambda \right)T\left( \lambda \right)+1} \right]}}{{\left[ {T\left( \lambda \right)+1} \right]}}, $$
(3)
where τ||(λ)/τ(λ) = T(λ); I||(λ)/I(λ) = ν(λ); I0)/I||(λ) = ν(λ, λ0).
The optical arrangement of the comparator enables one to measure signals proportional to the spectral density of the radiant intensity of the synchrotron and of the secondary standard plasma radiators, simultaneously in two regions of the spectrum: the ultraviolet region at a wavelength of λ and the visible region at a wavelength of λ0. Hence, Eqs. (1)–(3) can be written for λ0, and (3) takes the form
$$ {I_{\mathrm{p}}}\left( \lambda \right)={I_{\mathrm{p}}}\left( {{\lambda_0}} \right)=\frac{{{U_{\mathrm{p}}}\left( \lambda \right){U_{\mathrm{s}}}\left( {{\lambda_0}} \right)}}{{{U_{\mathrm{p}}}\left( {{\lambda_0}} \right){U_{\mathrm{s}}}\left( \lambda \right)}}\frac{{\left[ {1+T\left( {{\lambda_0}} \right)} \right]}}{{\left[ {1+T\left( \lambda \right)} \right]}}\frac{{\left[ {1+\nu \left( \lambda \right)T\left( \lambda \right)} \right]}}{{\left[ {1+\nu \left( {{\lambda_0}} \right)T\left( {{\lambda_0}} \right)} \right]}}{\nu^{\bot }}\left( {\lambda, {\lambda_0}} \right), $$
(4)
where Ip0) is the spectral density of the radiant intensity of the secondary standard deuterium radiator or of a solid-state radiator at a wavelength of λ0 in the visible region.

Hence, to determine the spectral density of the radiant intensity of secondary standard plasma radiators, the results of a calculation of the spectral energy polarization characteristics of the radiation of a synchrotron are used together with a measurement of the relative transmission coefficient of the comparator for the polarization σ- and π-components. To obtain absolute values of the relative spectral density of the radiant intensity using the synchrotron radiation of an electron storage ring in the visible part of the spectrum, i.e., to determine I0), one can use a filter radiometer based on a telescope with a cooled CCD matrix.

The large bunch mode, which gives a constant ratio of the polarization components of synchronous radiation within the aperture angle, is obtained by increasing the amplitude of the axial oscillations of the electrons and by optimizing the drop of the guiding magnetic field of the synchrotron. The ratio of the polarization components of the synchrotron radiation within the aperture stop, occurring in (4), can then be calculated with high accuracy as [9]:
$$ \nu \left( \lambda \right)={{{\int\limits_{{-{\pi \left/ {2} \right.}}}^{{{\pi \left/ {2} \right.}}} {I_{\mathrm{s}}^{\parallel }} \left( {\psi, \lambda } \right)d\psi }} \left/ {{\int\limits_{{-{\pi \left/ {2} \right.}}}^{{{\pi \left/ {2} \right.}}} {I_{\mathrm{s}}^{\bot }} \left( {\psi, \lambda } \right)d\psi; }} \right.} $$
(5)
$$ \nu \left( {{\lambda_0}} \right)={{{\int\limits_{{-{\pi \left/ {2} \right.}}}^{{{\pi \left/ {2} \right.}}} {I_{\mathrm{s}}^{\parallel }} \left( {\psi, {\lambda_0}} \right)d\psi }} \left/ {{\int\limits_{{-{\pi \left/ {2} \right.}}}^{{{\pi \left/ {2} \right.}}} {I_{\mathrm{s}}^{\bot }} \left( {\psi, {\lambda_0}} \right)d\psi; }} \right.} $$
(6)
$$ {\nu^{\bot }}\left( {\lambda, {\lambda_0}} \right)={{{\int\limits_{{-{\pi \left/ {2} \right.}}}^{{{\pi \left/ {2} \right.}}} {I_{\mathrm{s}}^{\parallel }} \left( {\psi, \lambda } \right)d\psi }} \left/ {{\int\limits_{{-{\pi \left/ {2} \right.}}}^{{{\pi \left/ {2} \right.}}} {I_{\mathrm{s}}^{\bot }} \left( {\psi, {\lambda_0}} \right)d\psi .}} \right.} $$
(7)
The spectral density of the intensity of the synchrotron radiation of the polarization components in expressions (5)–(7) can be calculated from Schwinger’s theory:
$$ {I_{\mathrm{s}}}\left( {\lambda, \psi } \right)=\left[ {{27N \left/ {{\left( {32{\pi^3}} \right)}} \right.}} \right]\left[ {{{{{e^2}c}} \left/ {{{R^3}}} \right.}} \right]{{\left( {{{{{\lambda_{\mathrm{s}}}}} \left/ {\lambda } \right.}} \right)}^4}{\gamma^8}{{\left[ {1+{{{\left( {\gamma \psi } \right)}}^2}} \right]}^2}\left\{ {{{{K_{{{2 \left/ {3} \right.}}}^2\left( \xi \right)+K_{{{1 \left/ {3} \right.}}}^2\left( \xi \right){{{\left( {\gamma \psi } \right)}}^2}}} \left/ {{\left[ {1+{{{\left( {\gamma \psi } \right)}}^2}} \right]}} \right.}} \right\}, $$
where Is(ψ, λ) = Is||(ψ, λ) + I(ψ, λ); N and e are the number and charge of the electrons; c is the velocity of light; R is the radius of the synchrotron orbit; γ is the relativistic factor; γ = E/E0, where E and E0 are the energy of the motion and the potential energy of the electron; λs is the critical wavelength, λs = (4/3)πRγ–3; K1/3 and K2/3 are special MacDonald funcsstions; and ξ = [λs/(2λ)][1 + (γψ)2]3/2.

To measure T(λ) and T0) from (4), high-Q six-mirror polarimeters are employed, and to reduce the uncertainties of the calibration, the spectral comparator includes vacuum monochromators, using normal or glancing incidence which serve to select the polarization σ- and π-components. The filter-radiometer-comparator includes an aperture stop, a telescope, a system of narrow-band optical filters and a cooled CCD matrix, and is designed for comparing the spectral density of the synchrotron radiation flux and of the electron storage ring [10].

The signals of the filter radiometer-comparator Ce.s and Cp are proportional to the power exposure of the synchrotron radiation of the storage ring and of the radiation of the secondary deuterium plasma radiator at a wavelength of λ0, respectively:
$$ \begin{array}{*{20}{c}} {{C_{\mathrm{e}.\mathrm{s}}}=\varDelta \varphi {\psi_0}\varDelta {t_{\mathrm{e}.\mathrm{s}}}\int\limits_{\varepsilon } {{I_{\mathrm{e}.\mathrm{s}}}\left( {{\lambda_0}-\varepsilon } \right)\tau \left( {{\lambda_0}-\varepsilon } \right){S_{\mathrm{CCD}}}\left( {{\lambda_0}-\varepsilon } \right)d\varepsilon; } } \\ {{C_{\mathrm{p}}}=\varDelta \varphi {\psi_0}\varDelta {t_{\mathrm{p}}}\int\limits_{\varepsilon } {{I_{\mathrm{p}}}\left( {{\lambda_0}-\varepsilon } \right)\tau \left( {{\lambda_0}-\varepsilon } \right){S_{\mathrm{CCD}}}\left( {{\lambda_0}-\varepsilon } \right)d\varepsilon .} } \\ \end{array} $$

Here ε is the deviation of the wavelength from the maximum of the spectral transmission coefficient of the radiometer-comparator filter, Ie.s0– ε) is the spectral density of the radiant intensity of the electron synchrotron, τ(λ0– ε) is the spectral transmission coefficient of the radiometer-comparator filter, SCCD0– ε) is the spectral sensitivity of the CCD matrix, and Δte.s and Δtp are the exposure times of the CCD matrix when measuring the signals from the synchrotron radiation and from the deuterium plasma radiator.

The radiometer-comparator includes a narrow-band filter, symmetrical about λ0, so that the spectral density of the flux and of the synchrotron radiation of the storage ring, and the radiation of the secondary deuterium plasma radiator, are linear within the filter passband, and depend linearly on the wavelength. To eliminate the nonlinearity of the CCD-matrix characteristic, the exposure time is chosen so that the ratio of the signals Cp/Ce.s = 1. Then (4) takes the form
$$ {I_{\mathrm{p}}}\left( \lambda \right)={I_{\mathrm{e}.\mathrm{s}}}\left( {{\lambda_0}} \right)\frac{{\varDelta {t_{\mathrm{e}.\mathrm{s}}}{U_{\mathrm{p}}}\left( \lambda \right){U_{\mathrm{s}}}\left( {{\lambda_0}} \right)}}{{\varDelta {t_{\mathrm{p}}}{U_{\mathrm{s}}}\left( \lambda \right){U_{\mathrm{p}}}\left( {{\lambda_0}} \right)}}\frac{{\left[ {1+T\left( {{\lambda_0}} \right)} \right]}}{{\left[ {1+T\left( \lambda \right)} \right]}}\frac{{\left[ {1+\nu \left( \lambda \right)T\left( \lambda \right)} \right]}}{{\left[ {1+\nu \left( {{\lambda_0}} \right)T\left( {{\lambda_0}} \right)} \right]}}{\nu^{\bot }}\left( {\lambda, {\lambda_0}} \right). $$
(8)
According to (8), the main sources of the total uncertainty, which occurs when calibrating the secondary standard plasma radiators using synchrotron radiation, are the following uncertainties:
  • the calculation of Ie.s0) at the wavelength λ0, which occurs when measuring the energy and number of electrons of the electron storage ring;

  • the transfer of the unit of spectral density of the radiant intensity at the wavelength λ0 to the secondary standard deuterium radiator when measuring the exposure time of the CCD matrix;

  • the measurement of the pulsed signal of the spectral comparator taking into account the scattered radiation and higher diffraction orders;

  • the calculation of the spectral energy polarization characteristics of the synchrotron radiation with the intense magnetic field;

  • the measurement of the relative transmission coefficient of the spectral comparator for the polarization σ- and π-components;

  • consideration of the effect of the finite axial, radial and phase dimensions of the electron bunch of the synchrotron with the intense magnetic field on the characteristics of the synchrotron radiation;

  • the determination of the equilibrium radius of the electron orbit of the synchrotron;

  • the wavelength calibration of the spectral comparator in the vacuum ultraviolet region.

The relative expanded uncertainty (for a coverage factor k = 2) of the calibration of the secondary standard plasma radiators in the 400–1 nm spectral range is 0.8–3.0%.

Hence, the methods of calibrating secondary standard plasma radiators, based on the use of a synchrotron with an intense magnetic field, which have been developed, enable one to solve the problem of the vacuum coupling of the accelerator and plasma radiator chambers, and also enable one to take into account the degree of polarization of the synchrotron radiation. A comparison of the characteristics of the synchrotron radiation of the storage ring and of the electron synchrotron in the visible range using a telescope and a cooled CCD matrix enables the problem of making a relative spectrum of the synchrotron absolute to be solved. An analysis of the methods of calibrating secondary standard plasma radiators based on synchrotron radiation shows that the estimate of the level of scattered radiation in the spectral comparator has the greatest influence on the accuracy of the result of the calibration. To increase the calibration accuracy, it is suggested that one should use both the possibility of changing the energy of the electrons during the process of calibrating the standard plasma radiators, and to design special filters based on multilayer nanostructures.

This research was supported financially by the Ministry of Education and Science of the Russian Federation within the framework of the Federal Targeted Program on Investigations and Developments on the Priority Directions of the Development of the Scientific-Technological Complex of Russia in 2007–2013, as part of research under package (Code 20111.8-518-012) “Conducting scientific research using unique benches and equipment, and also unique objects of scientific infrastructure (including observatories, botanical gardens, scientific museums, etc.) according to the basic ways of realizing the Program” (State Contract No. 16.518.11.7103).

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© Springer Science+Business Media New York 2012