Time-resolved Diffraction
Which optic is the best suited for my experiment
You may ask yourself: which kind of optics is the best for my application? There are single crystals, multilayers, capillaries, … A recent experimental study by Bargheer et al. [Appl. Phys. B 80 (2005), 715 - 719] may answer your question. Bargheer et al. made an experimental comparison of four different focusing x-ray optics: (1) a doubly curved Ge (111) single crystal where the (444) reflection was used, (2) a Montel multilayer optic, (3) an ellipsoidal monocapillary, and (4) a polycapillary. The authors used a laser-excited point source with a Cu target and a focal spot of about 10 µm diameter. The spectrum was composed of characteristic Cu line emission and Bremsstrahlung, similar to a conventional laboratory x-ray source. The table below shows a compilation of the data. The most important values are highlighted.
|
| GE (444)
| multilayer
| monocap
| polycap
|
| magnification |
1 |
2 |
7 |
0.7 |
| solid angle (sr) |
2.30*10-03 |
8.80*10-04 |
4.00*10-04 |
1.10*10-02 |
| transmission |
0.03 |
0.2 |
0.8 |
0.09 |
| flux (a.u.) |
6.90*10-05 |
1.76*10-04 |
3.20*10-04 |
9.90*10-04 |
| 1D convergence (deg) |
1.5 |
0.45 |
0.2 |
3.5 |
| flux/convergence |
4.60*10-05 |
3.91*10-04 |
1.60*10-03 |
2.83*10-04 |
| focal size (µm) |
23 |
32 |
155 |
105 |
| flux density (a.u.) |
1.30*10-07 |
1.72*10-07 |
1.33*10-08 |
8.98*10-08 |
| brightness (a.u.) |
5.80*10-08 |
8.49*10-07 |
3.33*10-07 |
7.33*10-09 |
| brightness in % |
6.8% |
100.0% |
39.2% |
0.9% |
| spectral purity |
good |
very good |
poor |
poor |
| temporal broadening (fs) |
90 |
6 |
10 |
1000 |
The polycapillary optics provides the highest flux, due to the large capturing solid angle. Therefore, in applications where the integral flux is the only important factor, the polycapillary optics is the best choice. The smallest foci and therefore the largest flux densities are produced by the multilayer optic followed by the Ge crystal. However, the different flux densities are the result of the different magnifications, and it is relatively easy to design the optics with other magnifications. In other words, a high flux density is not a good quality criterion. On the other hand, the brightness, defined as the flux density divided by the 2D convergence, is a very good quality criterion. High brightness means that one can obtain a very concentrated beam of high intensity (= flux density) with moderate divergence. Therefore, brightness is the most important feature in many applications such as single-crystal diffraction or small-angle scattering. Obviously, the multilayer optics is superior in terms of brightness. The spectral purities of both capillaries are expectedly far poorer than the ones of the two Bragg optics. Finally, as is of interest for femtosecond x-ray diffraction, the time smearing is lowest for the multilayer optics, but unacceptably high for the polycapillary optics.
In summary, the multilayer optics shows the best performance in most applications. We note that the transmission of the multilayer optics measured by Bargheer et al. was only 20 %, possibly because their optics was a prototype model with non-optimum performance. With a typical multilayer reflectivity of 70 %, we expect a transmission of about 50 % for a double bounce Montel multilayer optic of production quality.
