In the researches of astrophysics, plasmas, high energy density physics, and inertial confinement fusion (ICF), information of the x-ray sources is usually concerned. To diagnose the radiative sources, the wave lengths of the x-ray lights should be properly chosen at first. This is usually done by using the monochromatic method, the bandpass method, or the method of whole spectral planar response [1
1. J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, Phys. Plasmas 11, 339 (2004). [CrossRef]
3. A. Rindby, Nucl. Instrum. Methods Phys. Res. A 249, 536 (1986). [CrossRef]
]. When we adopt the monochromatic techniques, such as the gratings, crystals, or bandpass, the radiative strengths and spectral characteristics of the sources are generally needed to be considered. Planar response spectrum is usually used in the general diagnostics of the radiative strengths or the radiative flux as the spectrum is known. The bandpass method is widely used in practical works since it is usually composed of planar mirrors and filters. It is in fact a compromise of the whole spectrum of planar response and the monochromatic method, and can be used for the absolute strength measurement. For example, in the research of ICF, it can be applied in the soft x-ray power instrument and used for the measurements of the x-ray flux, the radiative temperature, the x-ray reflection ratio, and the transfer efficiency [2
2. K. M. Campbell, F. A. Weber, E. L. Dewald, S. H. Glenzer, O. L. Landen, R. E. Turner, and P. A. Waide, Rev. Sci. Instrum. 75, 3768 (2004). [CrossRef]
The x-ray bandpass method, which is composed of planar mirrors and filters, has a structure of grazing incidence reflection. Though the merit of such a structure is its simplicity, it is not accurate enough in experimental measurements. For example, in the diagnostics of radiative flux, the multichannel soft x-ray power spectral instrument is composed of multichannel grazing incidence reflection planar mirrors. Because the structures and the assembly of the mirrors may lead to some uncertainties, the calibrations and applications need very high accuracy due to the angular sensitivity of the mirrors. Furthermore, for dynamic radiative sources, because the view angle of the spectral instrument is nearly 8°, it is almost impossible to correct the differences caused by the angular factor of the channels. Another example is in the research of plasma dynamics using the bandpass method. Where the mirrors and pinhole are combined to image the plasma source, the system focusing and the intrinsic angle of the image would lead to difficulties in system designs and practical applications [4
4. F. Ze, R. L. Kauffman, J. D. Kilkenny, J. Wiedwald, P. M. Bell, R. Hanks, J. Stewart, D. Dean, J. Bower, and R. Wallace, Rev. Sci. Instrum. 63, 5124 (1992). [CrossRef]
5. F. Ze, S. H. Langer, R. L. Kauffman, J. D. Kilkenny, O. landen, D. Ress, M. D. Rosen, L. J. Suter, R. J. Wallace, and J. D. Wiedwald, Phys. Plasmas 4, 778(1997). [CrossRef]
]. For overcoming these difficulties, a transmission bandpass method has thus been developed which can greatly reduce the view angle difference in the multichannel method and then can resolve the structural problems in bandpass imaging.
In the present Letter, we introduce a soft x-ray planar transmission bandpass filter based on the microchannel plate (MCP) x-ray optics [6
6. D. Mosher and S. J. Stephanakis, Appl. Phys. Lett. 29, 105 (1976). [CrossRef]
8. M. Watanabe, I. H. Suzuki, T. Hidaka, M. Nishi, and Y. Mitsuhashi, Appl. Opt. 24, 4206 (1985). [CrossRef]
]. This instrument has been calibrated on the Beijing Synchrotron Radiation Facility, which shows excellent experimental results.
shows the principles of a square-pore MCP. When parallel lights are incident from the direction of a certain angle, the total number of reflections will be different as the incidence position is different at the gate. The deeper the position, the lesser the number of the reflections will be. Obviously, the number of reflections is determined by the length and the width of the channel as well as the incidence angle and the position at the gate. If we neglect the x-ray transmissions through the channel walls, the transport efficiency of the microchannel could be written as
is the wavelength of the x-ray,
the open area fraction of the MCP,
is the number of reflections, and
refers to the reflectivity of single reflection at incidence angle
. According to the geometry of the microchannel shown in Fig. 1(b)
, we obtain
is not an integer, the number of the reflections of partial lights will be
, and the remains will be
. In the transmitted light beam, the
times reflected lights have a fraction of
of the total, where
. The fraction of the
times reflected lights is then to be
. Thus, the reflectivity of the transmission lights could be written as
Fig. 1. Reflection geometry of a square-pore MCP.
Using the 4B7B soft x-ray calibration beam (an upgrade of 3W1B) of the Beijing Synchrotron Radiation Facility, we performed accurate experiments on calibrating the MCP x-ray transmissions. The energy of the 4B7B soft x-ray beam ranges from 50 to 1500 eV and has a resolution power of 200. The energy of the secondary harmonic is less than 5% of the total. The photon flux is beyond
(250 mA, 2.5 GeV). The setup of the calibration experiment is shown in Fig. 2
. When a light beam passes through the monochromatic system, it becomes a monochromatic light. Then we obtain the transmission spectrum by the ratio of the transmission light and the incidence monochromatic light. In order to reduce the experimental uncertainties caused by the light diffusion, the distance between the MCP sample and the detector is arranged to be less than 1 mm. The intensity of the light source is measured by using a silicon photodiode standard detector, and the output signals are recorded by a weak current amperemeter. Repeatable transmission measurements performed with such a system is found to be within 1% uncertainty. The roughness of the MCP mirror is less than 2 nm.
Fig. 2. Schematic diagram of the experimental configuration.
shows the transmission spectra measured in the calibration experiments. The structures near the photon energy 300 and 540 eV are due to the carbon and oxygen absorption edges in the MCP glass. The spectra in Fig. 3(a)
are measured using an MCP of
, and the open area fraction 68%. The incidence angles are 0, 17, 34, and 51 mrad, respectively. It shows that, with the increase of the incidence angle, the energy cutoff point will appear as soon as the direct pass-through light is terminated. For this MCP, the critical angle is 27.9 mrad. In Fig. 3
, one can see that the high energies are cut off rapidly when the incidence angle becomes larger than the critical angle. The energy cutoff point will shift lower when the angle becomes larger. The cutoff point is 1500 eV at 34 mrad while shift to 540 eV at 51 mrad.
Fig. 3. Calibration experiments using square-pore MCPs: (a) shows the transmission spectra of the MCP of the geometry , while (b) shows the results of the geometry , .
The spectra in Fig. 3(b)
were measured using an MCP of
, and the open area fraction 68%, which corresponds to the measured results at the incidence angles of from 0 to 61 mrad. In this case, the critical angle is 14 mrad. Similar to the results in Fig. 3(a)
, it shows that high energies are also cut off rapidly when the incidence angle is larger than the critical angle. The cutoff points are 1400, 600, and 540 eV at the angles of 27, 44, 61 mrad, respectively. Comparing the Figs. 3(a)
, we can see that with the increase of the ratio
the cutoff effects of high energies become better, and the critical angle gets smaller.
We note that both the spectra at the incidence angle of 0 mrad in Fig. 3
still have slight C and O absorption edges. The reason is that the light source of the synchrotron radiation has a small diffuse angle of about 1.5 mrad so that a few reflected lights mix into the direct pass-through lights and lead to the slight C and O absorption edges in the both cases.
According to Eqs. (1
) and (2
) as well as the MCP geometry profile, we have deduced the reflectivity of single reflection from the spectra in Fig. 3(b)
at three grazing incidence angles of 27, 44, and 61 mrad, respectively. The results are shown in Fig. 4
. From this figure, one can see that the reflectivity decreases with the increase of the photon energy. This is the reason why the x rays of high energies are cut off rapidly after multireflections in the channels of the MCP.
Fig. 4. Calculated reflectivity of single reflection at three grazing incidence angles of 27, 44, and 61 mrad, respectively.
Combined with different filters, we can make the MCP a narrow bandpass. Several measured transmission spectra are shown in Fig. 5
. It shows that in the case of
, the MCP has a narrow energy bandpass of the width 48 eV around 280 eV when it is combined with a 3 μm thick C filter. For
, the MCP combined with a 6 μm thick Ti filter achieves an energy bandpass of the width 80 eV around 450 eV. For
, the MCP combined with a 9 μm thick Fe filter achieved an energy bandpass of the width 75 eV around 705 eV. For
, the MCP combined with a 15 μm thick Cu filter achieves an energy bandpass of the width 97 eV around 930 eV.
Fig. 5. The bandpass spectra of MCP combined with different filters.
In contrast to the multiple band selector consisting of planar mirrors, the present transmission MCP bandpass method can change the energy range and the bandwidth by simply changing the incidence angle of the light and the length–width ratio of the pore. In practical research, this method has obvious advantages of simplicity, high efficiency, and reliability. For example, if the width of a light beam is 10 mm, then at the grazing incidence angle of 34 mrad, the length of a planar mirror is required to be at least 300 mm and therefore the mirror area to be . However, for a square-pore MCP with the channel width 7 μm, the length can be greatly reduced to 0.205 mm if only single reflection is considered. By internal multireflections, the MCP can cut off the high energies much faster than planar mirror does. Furthermore, the mirror usually becomes much longer when the incidence angle decreases to very small value, which is difficult to fabricate. The MCP method, however, can be easily used at smaller grazing incidence angles, and by plating high-Z materials on the internal sides, the energy bandpass of the MCP can be extended to the range of 2–10 keV. This will be the next focus of our work in the future.
In summary, we have introduced a soft x-ray planar transmission bandpass filter based on the MCP x-ray optics. The experiments show that the MCP bandpass has the advantages of high efficiency, simplicity, and broad energy band selections. This novel method could be expected to be applied to many research fields, such as radiative flux diagnostics and narrow band soft x-ray imaging. For example, by placing the square-pore MCP in front of a CCD camera, one can measure high spatially resolved x-ray images directly.