research papers
A new extrafocus monochromator designed for highperformance VUV beamlines
^{a}Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai Synchrotron Radiation Facility, Shanghai 201800, People's Republic of China
^{*}Correspondence email: wuyanqing@sinap.ac.cn, wangyong@sinap.ac.cn, tairenzhong@sinap.ac.cn
A new monochromator called an extrafocus constantincludedangle variedlinespacing (VLS) cylindricalgrating monochromator (extrafocus CIAVCGM) is described. This monochromator is based on the Hettrick–Underwood scheme where the plane VLS grating is replaced by a cylindrical one in order to zero the defocus at three reference photon energies in the vacuumultraviolet range. It has a simple mechanical structure and a fixed focus spot with high performance over a wide energy range. Furthermore, its mechanical compatibility with a standard VLS planegrating monochromator allows convenient extension into the softXray range.
Keywords: VUV beamline; monochromator.
1. Introduction
The design of synchrotron optics depends on many factors. Soft Xray and vacuumultraviolet (VUV) monochromators are particularly challenging as they rely on twodimensional manmade gratings as opposed to selforganized threedimensional crystal structures that can be used for hard Xrays. As a result, VUV beamlines around the world that employ these monochromators are forced to make compromises that limit their performance and/or flexibility. Special techniques, such as using a variedincludedangle planegrating monochromator (VIAPGM) (Petersen, 1982; Riemer & Torge, 1983; Pimpale et al., 1991) and extrafocus constantincludedangle variedlinespacing planegrating monochromator (extrafocus CIAVPGM) (Hettrick & Bowyer, 1983; Hettrick & Underwood, 1986; Hettrick et al., 1988) have been developed for soft Xrays to achieve high performance in terms of energy resolution, and flexibility. Nevertheless, these techniques are challenged in the VUV range.
Here we describe a new VUV monochromator approach well suited for experiments demanding high performance, such as angleresolved photoemission spectroscopy (ARPES), photoelectron emission microscopy (PEEM) etc. The ARPES method is a powerful technique that characterizes electrons' properties close to the Fermi surface in materials (Tanaka et al., 2006; Terashima et al., 2006; Damascelli & Shen, 2003). The escape length of photoelectrons emitted in solid materials exhibits the famous `Vcurve' relation with their (Somorjai, 1981). It reaches the minimum of approximately 1 nm at photon energies from 10 eV to 200 eV, which limits the ability to obtain interior information from a sample. Such surface sensitivity can be circumvented by tuning the photon energy higher (soft Xray > 1000 eV) or lower (VUV < 10 eV). Owing to its higher energy the VUV route is favoured for ARPES beamlines.
At present, many types of monochromators are utilized for ARPES beamlines. The VIAPGM type (Strocov et al., 2010; Songsiriritthigul et al., 2003; Xue et al., 2014) which can cover a wide energy range can be operated in different modes according to the experimental requirements. A normalincidence monochromator (NIM) type that can operate in the VUV range has been adopted by many beamlines (Rah et al., 1995; Janowitz et al., 2012; Petaccia et al., 2009). The fixed exit slit of the NIM can always maintain a small spot size on samples, which is required for new nanoARPES technology (Bostwick et al., 2012). Moreover, a small spot size is necessary to handle some novel samples, which are usually tiny in size. A combination of the VIAPGM type and the NIM type can cover a wider photon energy range from VUV to soft Xray (Borisenko, 2012). The dragon type is another typical choice for the VUV range and has been mounted in many beamlines (van Elp, 1997; Yu et al., 2001; Lai et al., 2001) since it is a highperformance (high energy resolution and high photon flux) monochromator. A constantlength Rowland monochromator (Reininger et al., 2007), with a moving range of 1.1 m of the premirror, was designed to obtain a fixed exit slit by setting a plane mirror before the spherical grating and varying the incidence angle on the plane mirror to fulfil the Rowland condition.
An extrafocus CIAVPGM monochromator type (Hettrick–Underwood scheme) has already been employed by many beamlines (Kiyokura et al., 1998; Ono et al., 2001; Yan et al., 1998; Underwood & Gullikson, 1998). It is a highperformance monochromator with a variety of advantages, such as high energy high throughput, a simple scanning mechanism and a fixed exit slit. However, in the VUV range the focus drifts more dramatically because of larger defocus aberration (which will be discussed below). In this study, a modified Hettrick–Underwood scheme based monochromator with a simple mechanical structure is designed. The plane variedlinespacing (VLS) grating in an extrafocus CIAVPGM type is suggested to be replaced by a cylindrical one. With this change, the advantages of the extrafocus CIAVPGM can be retained in the VUV range. The newtype monochromator (extrafocus CIAVCGM) will have a fixed focus by suppressing the defocus aberration by an order of magnitude while retaining high energy and high It has the potential to meet the harsh requirements of a highperformance VUV beamline.
2. CIAVCGM monochromator
For a VLS grating, the line spacing d is a function of the position w in the dispersive direction. The function can be expanded as a power series of w, namely
where d_{0} is the line spacing at the centre of the grating, and b_{2}, b_{3} and b_{4} are the spacevariation parameters. The defocus term (F_{20}) and the coma term (F_{30}) in an optical path function can be eliminated by choosing an appropriate linear coefficient term b_{2} and quadratic term b_{3}, respectively, according to
where m is the diffraction order, α is the incidence angle, β is the diffraction angle, r_{1} is the objective distance, r_{2} is the imaging distance and R is the grating radius (for a plane grating, R → ∞).
In an extrafocus CIAVPGM type monochromator [R → ∞ in equation (2)] the focusing mirror produces a converging beam and a virtual source to the grating, and the grating produces a real image on the exit slit with an imaging distance that is almost identical to the virtual source distance. To correct the defocus aberration, certain optimization methods can be applied. The defocus term can be eliminated directly (F_{20} = 0) at one reference energy or be approximated equal to zero using b_{2} ≃ 2/r (Sinn et al., 2012). Better focusing performance over a wide spectral range (Yan & Yagishita, 1995a; Hettrick & Underwood, 1988) eliminates defocus aberration at two specific photon energies. Nevertheless, owing to drastic changes in the focus condition over the VUV energy range it is difficult to effectively suppress the defocus term and this type of monochromator is generally favoured for the soft Xray or extreme ultraviolet range (Kiyokura et al., 1998; Ono et al., 2001; Yan et al., 1998; Underwood & Gullikson, 1998) but not the VUV range. To extend the photon energy into this range, we replace the plane grating in an extrafocus CIAVPGM type monochromator with a cylindrical grating (Fig. 1). With this change, a new optimized method can be used to eliminate defocus aberration at three reference energies. The defocus curve of the cylindrical surface can compensate for the defocus behaviour of the VLS grating in the VUV range. In this way the focusing performance can be improved. In the following we will refer to this new type of monochromator as an extrafocus constantincludedangle variedlinespacing cylindricalgrating monochromator (extrafocus CIAVCGM).
The optical schematic of an extrafocus CIAVCGM is shown Fig. 1. As in an extrafocus CIAVPGM, the focusing mirror produces a converging beam and a virtual source behind the grating and the grating produces a real image on the exit slit. Yet a major difference is prominent: the imaging distance is not equal to the virtual source distance. In order to illustrate the improved performance of an extrafocus CIAVCGM, we take a 4 mlong undulator as a realistic optical source and typical distance values between optical elements for a model CIAVPGM and a model CIAVCGM as an example comparison. The beam sizes and divergences are calculated from the vector sum of the electron beam RMS values (σ_{x}, , σ_{y}, ) on the orbit and the single electron radiation values (σ_{r}, ). The single electron radiation values are calculated using the approximations = and = , where λ is the wavelength of the radiation and L is the length of the insertion device. For both models, the object distance of the focusing mirror is 20 m and the imaging distance of the grating is 29 m. Two optical elements are separated by 0.5 m. The calculated RMS values of the total photon beam size (Σ_{yA}) and total photon divergence () are shown in Figs. 2(a) and 2(b). The corresponding full width at halfmaximum (FWHM) of the beam spot in the dispersion direction at the exit slit for the model CIAVCGM is also shown in Fig. 2(c). Detailed parameters for the models are listed in Table 1.

The second term at the righthand side of equation (2) vanishes with an infinite radius R (a plane grating). However, this term comes into play in the cylindrical grating case because R is no longer infinite. Thus, r_{2} (or r_{1}, one of them should be fixed), b_{2} and R can be determined by imposing the condition that F_{20} vanishes at three reference energies, i.e. the defocus aberration is simultaneously suppressed at these three reference energies. The criterion for optimizing the model CIAVCGM is to ensure that the defocus term of the cylindrical surface can effectively compensate that of the variedlinespacing plane grating (VLSPG) (Fig. 3) in the VUV range by testing various sets of reference energies. The defocus term of a concave VLS grating in the model CIAVCGM contains two parts: the defocus of a VLSPG (Fig. 3, squares), (cos^{2}α/r_{1} + cos^{2}β/r_{2}) − b_{2}mλ/d_{0}, and the contribution of the cylindrical surface (Fig. 3, circles), (cosα + cosβ)/R. Both parts counteract each other in the VUV range. Therefore, the contribution of the cylindrical surface can effectively compensate for that of the VLSPG to keep F_{20} very low over the entire VUV range.
The reference energies for the two model monochromators are chosen to make the defocus as small as possible. After optimizing, the defocus vanishes at 7 eV, 8.5 eV and 25 eV and the coma vanishes at 7 eV for the model CIAVCGM. For the model CIAVPGM, the defocus aberration is optimized under several different energy sets and the coma vanishes at 7 eV too. The grating line density is assumed to be the same (1000 lines mm^{−1}) in the model. A few parameters can be derived under these conditions and are listed in Table 2.

The energy F_{30}) are small and negligible. Figs. 4(a) and 4(b) show the calculated RP with various grating line densities of the model monochromator, with the RP defined as the inverse of the relative spectrum width (RSW). Their contributions to the RSW, Δλ/λ_{total}, are as follows:
(RP) calculated in this study is mainly determined by seven factors: source size, exit slit size, meridian slope error of the grating and focusing mirror, the aberrations from the defocus and coma, and the grating diffraction limit. Highorder aberrations (smaller thanVirtual source size:
Exit slit size:
Meridian slopes errors of grating:
Meridian slopes errors of mirror:
Aberration from defocus:
Aberration from coma:
Diffraction limit:
where β is the diffraction angle, α is the incidence angle, m is the diffraction order, R is the grating radius, s is the exit slit size, d is the grating spacing, r_{1}, r_{2} are the virtual object distance and imaging distance of the grating, Σ_{yV} is the RMS value of the virtual source size (Σ_{yV} = MΣ_{yA}, M is the magnification of the focusing mirror); σ_{gr}, σ_{fo} are the meridian RMS slope errors of the grating and the focusing mirror; W is the half of the illuminated length of the grating and N is the number of coherently illuminated grating grooves.
In each case the RP without the defocus term is shown as a benchmark. Grating line densities higher than 1200 lines mm^{−1} are not considered because the grating incidence angle for them would be larger than 90° at 7 eV according to the grating equation. For the model CIAVCGM, the RP does not suffer much from the defocus for all gratings. This is easily understood because the defocus aberration is well suppressed in the model CIAVCGM and the RSW from the defocus aberration does not dominate as shown in Fig. 5. However, for the comparable CIAVPGM, it is difficult to find a suitable energy set to suppress defocus over a wide VUV energy range. The RP degradation caused by the defocus aberration is shown in Fig. 4(b). It can be found that the RP degradation caused by the defocus aberration could be ignored for the model CIVVCGM.
The CIAVCGM with 1000 lines mm^{−1} or 1200 lines mm^{−1} gratings could achieve 0.4 meV energy resolution at 10 eV (Fig. 4). This should lay a solid foundation for a highperformance ARPES beamline, because such an energy resolution from a beamline is five times smaller than the energy resolution of a stateofart electron analyzer (energy resolution of about 2 meV).
The total RSW and its various components of a 1000 lines mm^{−1} cylindrical grating (Fig. 4a) are shown in Fig. 5. It is shown that the defocus aberration is negligible and the extrafocus CIAVCGM is almost an aberrationfree system in this energy range. The largest two contributions to the total energy are from the source size and the exit slit size. As mentioned above, the exit slit size here is a variable value, which is chosen according to the beamline demagnification, with which the FWHM value of the spot is allowed to pass through the exit slit. The third largest contribution to the RSW is from the diffraction limit 1/N, where N is the number of coherently illuminated grooves. At an undulator beamline, the included angle for an extrafocus CIAVCGM is much larger than that for a NIM, which allows the beam incoming with a grazing incidence on the grating. Therefore, the illuminated area on the grating will be much larger than that in the NIM and the contribution from the grating diffraction limit of the CIAVCGM is much lower than that of the NIM. Yet the benefit of enlarging the illuminated area has to be weighed against the disadvantage caused by increased aberrations. Technically speaking, the slope errors of the cylindrical optics are generally a few times worse compared with the plane optics; nevertheless, the resulting degradation of the RP is marginal. As an example, the RP will be degraded from 5.8 × 10^{4} to 5.2 × 10^{4} at 7 eV with the slope error varying from 0.3 µrad to 1 µrad for the 1000 lines mm^{−1} cylindrical grating. It turns out that the partition contribution to the total RSW from the slope errors in the VUV range is much smaller than that from the source because of the long wavelength.
We would like to stress that the small contribution from the coma shown in Fig. 5 is due to a careful choice of optimization energy. As shown in Fig. 6, the RSW could be much worse for the CIAVCGM by choosing other energies, because the coma aberration is most severe at 7 eV, whereby the spot size on the grating is at its maximum value.
3. Defocus aberration with different optical lengths
For the CIAVCGM, it can be seen from Fig. 5 that the largest contribution to the RSW is from the source size and the exit slit size. It is tempting to increase the object distance of the focusing mirror in order to minimize both sizes. However, one should bear in mind that the illuminated length on the grating will be simultaneously enlarged with increased object distance. This has two consequences: (i) the component RSW by grating diffraction limit will decrease; (ii) the component by the defocus and the coma will increase: the defocus is proportional to the width of the illuminated length on the grating and the coma is proportional to its square. Fig. 7 shows the dependence of component (exit slit size, source size, diffraction limit, defocus and coma aberration) RSWs and total RSWs on the object distance of the focusing mirror at 14 eV and 40 eV. As seen, even though the defocus and the coma aberrations increase with the distance, they hardly impact the total RSW when the object distance of the focusing mirror is cautiously contained within 30 m.
4. Stability and efficiency analysis in a CIAVCGM
4.1. Stability
In practice, the focusing mirror radius R_{F}, the grating radius R_{G} and the grating b_{2} coefficient have machining errors, and this will cause instability in the monochromator design. Fig. 8 shows that the focus aberration increases considerably with introducing moderate errors (squares): 3% on R_{F}, 2% on R_{G} and 3% on the b_{2} coefficient. Nevertheless, such effects can be corrected (upward triangles) by properly adjusting the object distance (5.3%) and the imaging distance (2.4%). After correction, the final RP is almost the same as for the original design. The effects of residual measurement errors can be recorrected online by adjusting the grating incident angle slightly.
5. Influence of beamline setups
The above discussion of an extrafocus CIAVCGM is based on a simple model monochromator. In reality, the setup of a beamline is far more complicated besides optic principles. For example, the focusing mirror can be placed horizontally or vertically, corresponding to meridional and sagittal focusing mode, for different purposes such as reducing the influence of aberrations in a bending beamline or heat load in an undulator beamline, etc. as shown in Figs. 9(a) and 9(b). Another plane mirror may be needed to deflect the beam to facilitate a required beamline layout. We have carried out raytracing simulations on the two beamline setups with meridional or sagittal focusing mode, respectively, under three energies, 7 eV, 14 eV and 40 eV, whereby 7 eV is the chosen optimization energy, and 14 eV and 40 eV are the energies at which the defocus is the most severe. The parameters in the meridional focusing mode are the same as the basic aforementioned model CIAVCGM, but they are relisted in Table 3 against some different and important parameters in the sagittal focusing mode.

The shadow raytracing results are shown in Fig. 9. As demonstrated, both modes can achieve energy resolving powers of 58000 at 7 eV, 16000 at 14 eV and 7000 at 40 eV, matching well with the calculated results (Fig. 4b) of the basic model CIAVCGM (Fig. 1). This is proof of robust behaviour in the energy of the CIAVCGM against the adjustment in the beamline setup.
It is a common practice to focus the beam at the exit slits in the nondispersion direction. To do this, a toroidal mirror could be employed as the focusing mirror in the meridional focusing mode or a sagittal cylindrical mirror takes the place of the planar deflecting mirror in the sagittal focusing mode. Additional slope errors for good optical surface will not significantly affect the RP, as has been discussed for the component RSWs in Fig. 5.
6. Probability of extending the energy range from VUV to soft Xray
The foregoing discussion is focused on the application of the CIAVCGM in the VUV range. In fact, because of its strong focusing capability, this monochromator is capable of achieving high performance over an ultrawide energy range from VUV to soft Xray using a multiCIA setup.
As we noticed, the energy et al., 2012). It should be noted that the grating used in the soft Xray range will have an optimized grating radius R sufficiently large to be equivalent to a plane grating. That is to say, the CIAVCGM for the VUV range can be combined with a CIAVPGM for the soft Xray range. The two monochromators could be easily combined, as their mechanical structures are the same. In addition, it can be found that the beamline setup is compatible with VIAVPGM as in Fig. 9(b). Therefore, an ultrawide photon energy range could be achieved with the above two schemes.
for a single CIAVCGM is degraded at the high energy end because the included angle is not suitable for higher energy. Therefore, in order to keep the high performance over the whole range, we suggest introducing a multiCIA setup with different included angles to cover the wider energy range. The different focusing mirrors correspond to different included angles. A few VLS gratings might be mounted in this system. The optical layout of the monochromator is similar to that described in the TDR report of the European XFEL (Sinn7. Conclusion
In this report, the design for a new monochromator type (an extrafocus CIAVCGM) is described for the VUV range. The defocus aberration is well suppressed in the VUV range and a fixed focus spot can be obtained. Therefore, a highperformance (high energy
and high photon flux) monochromator with a fixed exit slit can be realised with few technical difficulties in the VUV range (especially 7–40 eV). Furthermore, this new type of monochromator has the potential to be combined with the current extrafocus CIAVPGM or VIAVPGM type to extend its energy range from VUV to soft Xray.Acknowledgements
This work was supported by the National Natural Science Foundation of China (Nos. 11275255, 11205236 and 11005146) and the Open Research Project of Large Scientific Facility from Chinese Academy of Sciences: Study on SelfAssembly Technology and Nanometer Array with UltraHigh Density. The authors thank Professor Y. L. Yan (Institute of High Energy Physics) for his helpful discussions. The authors are also grateful to the Xray Interference Lithography beamline (BL08U1B) staff for their help.
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