polycapillary focusing optical lens, absorber, transmission, scatter

In this paper, we report a simple and convenient method for measuring the transmission of the polycapillary focusing optical lens in a large energy range. In the measurement, a low-power micro-focus source, a lens an absorber stacked by the aluminum absorption foils, and a detector were placed in a line. The absorber was used to reduce the dead time of the detector. Compton scattering effect in the absorption foils and the air gaps must be considered. Thus, for the returning to the original X-ray fluorescence spectrum without absorber, the attenuation coefficient of the aluminum absorber was respectively researched by calculation and simulation. The transmission efficiency of the lens can be obtained by comparing the X-ray fluorescence spectrums whether the lens was placed. The transmission efficiency to X-rays below 8 keV cannot be measured because the X-rays below 8 keV were completely absorbed by the aluminum absorption foils.

X-rays are electromagnetic waves of a wavelength of 0.01-10 nanometers. Just as the total reflection of visible-light can change the transmission direction of light, X-ray is also a kind of light wave, and total reflection occurs. The former Soviet Union scientist Markhov invented the polycapillary X-ray optical lens in the late 1980s. The polycapillary X-ray optical lens is an X-ray focusing system composed of millions of hollow glass capillary with a diameter of several microns. X-rays total reflection on the inner wall of the capillary changes the transmission direction of X-ray. According to the shape of the outgoing X-ray beam, the polycapillary X-ray optical lens can be divided into convergent lens, parallel beam lens and micro convergent lens, etc. These lenses realize the convergence of large-angle divergent X-rays or become quasi-parallel light. It greatly expands the application range of X-ray, and at the same time makes the research of X-ray optical lens a hot-spot in X-ray optics. X-rays lost part of their intensity when reflected and transmitted in a polycapillary X-ray optical lens. This is an important parameter evaluates the quality of X-ray lenses which called transmission efficiency.

Transmission efficiency can be measured by a high-rate detector and a low-power micro-focus X-rays source. However, the intensity of the X-ray after the focusing of the lens is so large that the detector cannot work in its linear detection range. Thus, transmission efficiency cannot be measured in a large energy range only by a high-rate detector and a low-power micro-focus X-rays source. Sun Tianxi et al. Measurements of polycapillary X-ray optics using the knife-edge made of polymethyl methacrylate as a scatterer. Wang Yan et al. measurement of the characteristics of monolithic polycapillary X-ray optical lenses by means of the scattering of X-rays. In these two methods, the precision of the angles among the detector, the lens and the source were strictly required. There is a need for a practical Highly-operable method for measuring the relevant properties of the polycapillary X-ray optical lens.

X-ray transmission direction can be changed by using the total reflection of X-ray on the inner wall of the capillary lens. polycapillary X-ray lenses can change the direction of X-ray transmission. For polycapillary X-ray optics lens, the collection and focusing effects come from the superposition of millions of capillary tubes, rather than from the action of a single tube. For capillary tubes, as long as the tube diameter is small enough that the angle of incidence is less than the critical angle for total reflection and grazing incidence,X-rays can be transmitted along the curved hollow tube. The formula for calculating the total reflection grazing incidence critical angle θc

Where
k is a small proportion factor,
ρ is the density of the reflective material, and
E is the energy of the X-ray.

A common capillary material is a SiO₂ glass for which the critical angle for total reflection can be used equation

A polycapillary X-ray optical lens is based on the total external reflection of X-rays, many times of total reflection will cause a certain loss of transmission namely the transmission efficiency of polycapillary X-ray optical lens. The transmission of polycapillary X-ray optical lens is the ratio of the intensity of the x-rays at the exit end of the lens to the intensity of the x-rays at the entrance end of the lens. Transmission efficiency is an important parameter to mark the quality of polycapillary X-ray optical lens. The transmission efficiency can be used equation

Where
I₁ (E) is the total intensity of the X beam of energy E emitted by the X source at the entrance end of the lens, and
I₂ (E) is the total intensity of the X beam of energy E at the exit end of the lens.

In the experiment, the counts N₂(E) of X-rays emitted from the lens and the counts N₁(E), N₂(E) and N₁(E) of the X-rays entering the lens are measured respectively with I₂(E) and I₁(E) is directly proportional, so formula in above can be rewritten as

In practice, the counts at the focal point after the X-ray is condensed by the lens are too strong. If it is directly measured, the energy spectrum will be distorted due to the limitation of the detector’s dead time, so an absorber foil is added in front of the detector. The transmission efficiency of a polycapillary X-ray optical lens is related to the energy of the X-ray.

Suppose a beam of parallel X-rays with energy E is in a direction, the intensity perpendicular to the uniform absorber is I₀, and when the beam passes through the material of t, the intensity of beam becomes I because of the absorption of matter. The intensity attenuation caused by scattering and absorption depend on the type, thickness and quality of the absorbing material. The formula can be expressed as

where
I₀ (E) is the intensity of the X-ray energy before the incidence of E,
I(E) is the intensity of the X-ray energy after the attenuation of E,
μ is the attenuation coefficient of the material, and
t is the thickness of the material.

For polychromatic energy spectrum, the intensity of X-rays as they pass through the material is

Where
I_0i is the X-ray intensity with energy Ei before entering the material, and
μ(E_i) is the attenuation coefficient with energy E_i.

When X-rays pass through a substance, different parts of the energy spectrum are attenuated differently. The same material has different attenuation coefficients for X-rays of different energy. The higher the X-ray energy, the smaller the attenuation coefficient, so low-energy X-rays are first absorbed, Causing the X-ray beam to harden.

DS067, from OXFORD INSTRUMENTS, with the maximum anode voltage of 50kV and the maximum power of 12W, was used as a micro-focus source. AMPTEK X-123 is an X-ray silicon drift detector(SDD) with an FWHM of 145eV at 5.9 keV (Fe), and its sensitive area is 6mm2 or 25mm². About the polycapillary focusing optical lens, The entrance focal length, the exit focal length and the geometric length of the lens are 48mm, 16.4 mm and 40 mm respectively In order to build up and commission the experimental setup conveniently, a copper sleeve with a length of 50.2mm and an outer diameter of 16.08mm was set outside the polycapillary focusing X-ray optical lens. At the same time, the copper sleeve can be used as a collimator of the X-rays and a protective shell of the lens.

The anode voltage of the X-ray source was set to 20kV; Tungsten target was used; The anode current was set to 1uA, and the power was 0.02W.The measurement result of SlDD X-123 is incredible when the death time is over 60%.

Fig. 1 Experimental table with the Aluminum absorption foils and detector

Firstly, to prevent the detector from being counting-overloaded, an aluminum absorber was set in front of the detector. Aluminum absorption foils of 0.5 mm and 0.2 mm thickness were respectively used. The measurement time of the SDD X-123 were recorded. A schematic diagram of the experimental apparatus is shown in figure 1. The X-ray fluorescence spectrum detected under such experimental conditions is shown in figures 2.

Fig. 2 X-ray fluorescence spectrum of different layers of (a) 0.2mm and (b) 0.5mm thick aluminum absorber foils

Keeping the same experimental conditions, under the condition with aluminum absorbing foils and without aluminum absorbing foil, we added the polycapillary focusing X-ray optical lens, and used the SDD X-123 measuring the X-ray fluorescence spectrum. The experimental tables were shown in Figure 3.

Fig. 3 Experimental table (a) the polycapillary focusing X-ray optical lens and detector (b) the polycapillary focusing X-ray optical lens, aluminum absorber and detector

The detected X-ray fluorescence spectrums were shown in Figure 4 and Figure 5.

Fig. 4 X-ray fluorescence spectrum with the polycapillary focusing X-ray optical lens

Fig. 5 X-ray fluorescence spectrums with aluminum absorption foil thickness of (a)1 mm, (b) 2 mm and (c)3 mm

In order to research the scatter effect in the aluminum absorbers, and X-ray fluorescence spectrums with different thickness (0.5mm and 0.2mm) and combination of absorbers were compared. The thickness of these two absorption foils were superposition of lmm,2mm and 3mm. The energy spectrums measured by SDD x-123. And the Monte Carlo code was used to simulate the effect of the scattering produced by the superposition of aluminum foils of different thickness on the return to X-ray fluorescence spectrum. In the simulation, aluminum absorption foils of 0.5 mm and 0.2 mm thickness were used. Then, the foils were used to superimpose into the absorbers of 1 mm,2 mm and 3 mm thickness, and the intermediate spaces were filled with the air. The simulation results are shown in Figure 6. When the thickness of the superimposed aluminum foil is lmm and 2 mm, the count rate of 0.5 mm thickness aluminum foil has a slightly higher than 0.2 mm, and the X-ray fluorescence’s shape is almost coincident. When the thickness of the superposed aluminum foils is 3 mm thicknesses, the count rate of the 0.5 mm aluminum foil is slightly higher than the count rate of 0.2mm.

Fig. 6 X-ray fluorescence spectrums with (a) 1mm, (b) 2 mm and (c) 3mm of aluminum absorber foils by Monte Carlo simulation

The aluminum absorber was used to reduce the dead time of the detector. For returning to the original X-ray fluorescence spectrum without absorber, the attenuation coefficients μ(E) need to be known. As shown in Figure 7, the attenuation coefficients were calculated by equation (4) and simulated by MCNP. X-rays with energy below 8 keV was almost completely absorbed by the aluminum absorption foils. Monte Carlo code is used to simulate the absorption effect of aluminum foils on X-rays, and the attenuation coefficient of aluminum is calculated according to exponential decay law.

Simulation and experimental calculation results are in good fit.

Fig. 7 Attenuation coefficient of aluminum absorber (a) by calculation (b) by simulation

After calculating the attenuation coefficient of the aluminum absorption, the X-ray fluorescence spectrum is attempted to be reduced according to the exponential decay law. The energy spectrum of the reduction was shown in Figures 8.

Fig. 8 the return of the X-ray fluorescence spectrum, (a) 0.2mm, (b) 0.5mm

It can be seen from figure 8 that the returned to the spectrum of X-ray fluorescence is similar in spectral shape, but there has difference in intensity. On the account of the aluminum absorption foils used in this experiment is superimposed by different thicknesses, and the superposition of aluminum foils has the presence of the air, and the influence of scattering effect on the reduction X-ray fluorescence’s spectrum needs to be considered.

Through the comparison of the three sets of data in the figure 6, we can see the effect of scattering of X-ray between aluminum foils. The Monte Carlo code was used to simulate the effect of the aluminum absorber scattering effect on the X-ray fluorescence spectrum. As a result, the simulated scattering effect gradually increases as the number of aluminum foils increases. The results of the simulation are the same as the results of the experiment. As the energy increasing, the scattering effect and the hardening effect becomes more pronounced. When returning of X-ray fluorescence spectrometry, the exponential decay of the absorption foils cannot be simply considered, and the influence of the Compton scattering effect should be involved.

In all, as the thickness of the absorption foils increases, the hardening effect on X-rays becomes more and more obvious. As the number of absorption foils increases, the effect of scattering becomes more and more significant.

The absorption foils method was used to measure the transmission efficiency of an overall X-ray converging lens. By comparing the peak of the continuum spectrum of using the polycapillary focusing X-ray optical lens with the peak of the continuum of using the aluminum absorption foils, the peak of the continuum of the polycapillary focusing X-ray optical lens is about 5 keV(in the figure 4), and the peak of the continuum of the aluminum absorption foils is behind 15 keV. According to formula(3), the change of transmission efficiency of the polycapillary focusing X-ray optical lens with energy were calculated as shown in Figure 9. Since the attenuation of X-rays in the air was small, and the length of the polycapillary focusing X-ray optical lens used in this experiment is only 40 mm, the attenuation of X-ray transmission in the air was ignored.

Fig. 9 The transmission efficiency of the lens varies with the X-ray energy

It can be seen from the calculation that the maximum transmission efficiency of the polycapillary focusing X-ray optical lens used in this experiment is 8.5%, and the transmission efficiency of the lens is continuously decreasing from the increase in energy from 8 to 20 keV. This is the diameter of the polycapillary tube is relatively large, and as the energy increases, the critical angle of total reflection decreases, and the tube diameter is limited, and the transmission efficiency is continuously reduced.

There are generally three factors that affect the transmission efficiency of the overall X-ray lens:

1. The critical angle for total reflection decreases from the increase in X-ray energy, which reduces the transmission efficiency of X-rays in the polycapillary focusing X-ray optical lens;
2. The effect of roughness, the higher the energy of X-ray, the greatest of roughness;
3. The absorption of capillary walls and air, it has a more pronounced effect on the transmission of low energy X-rays.

Studying by using combination of the absorption foils, the detector and a low-power micro-focus source was used to measure the transmission efficiency of the polycapillary focusing optical lens in a large energy range. Comparing with the method of measuring the transmission efficiency of the polycapillary focusing optical lens in the past experiment, the design of the experimental is not used the pinhole and scattering materials, and the calculation is simpler, and the design of the experimental is also closer to reality. the precision of the angles among the detector, the lens and the source were strictly required measure the transmission efficiency. However, only the micro-focus source, the absorption foils and the detector are placed on a line, it is Highly-operable. In the subsequent research, a suitable absorption material can be selected for the high-energy X-rays. The absorption of the high-energy X-rays is stronger than the low or combination of pinholes and the other high energy absorber to measure the polycapillary focusing optical lens transmission efficiency.