Soft x-ray imaging with toroidal mirrors

Yoshimi Sakayanagi and Sadao Aoki

The fabrication of small toroidal mirrors in tandem for x-ray imaging is discussed. First, a male mandrel is

made by grinding and polishing a molybdenum rod. Then. a glass replica is cast and lightly polished. The

method of polishing the male mandrel is described. A photograph of a copper mesh taken with a 8.3-A x ray

is shown.

Introduction

Grazing incidence x-ray optics have been discussedtheoretically in many papers, 1 -3 but very few low pre-cision optics are reported in practical use.4' 5 Asspherical surfaces can be polished very precisely, aKirkpatrick type imaging system which uses concavespherical mirrors can be easily constructed, but thealignment of the mirrors is very troublesome. 6 -8

Moreover its numerical aperture is small, and its re-solving limit is nearly 1 ,im. In the field of astronomy,however, large paraboloid-hyperboloid mirrors aresuccessfully polished and have been used for over adecade in x-ray astronomy.9 -1 2

Small axisymmetric grazing incident mirrors, usefulfor laser-fusion diagnostic and other soft x-ray imaging,have been difficult to fabricate, because asphericalsurfaces such as paraboloidal and hyperboloidal sur-faces must be polished in a small cylindrical tube.

In the previous paper we suggested that toroidalmirrors were also useful for x-ray imaging and could bemore easily polished than quadratic surfaces.1 3 In thispaper we report on the fabrication of toroidal mirrorsby new techniques: (1) a polishing machine is devisedto polish the male mandrel; (2) reflecting surfaces areformed by replication; and (3) final light polishing isapplied to the replica.

Design of the Toroidal Mirrors

When a glancing angle to a surface is small, the x rayis totally reflected by the surface, and the critical angleof the reflection depends on the surface material andwavelength of the x ray. In designing the mirror we

The authors are with Tokyo Kyoiku University, Institute for Op-

tical Research, Hyakunintyo-3, Sinzyuku-ku, Tokyo 160, Japan.

Received 28 May 1977.0003-6935/78/0215-0601$0.50/0.C 1978 Optical Society of America.

must first decide on the glancing angle at the middlepoints of the surfaces. These angles are smaller thanthe critical angle so that the x ray falling near the edgeof the mirror can be reflected.

In our case the angles are 22 mrad. This decisioncomes from the fact that the wavelength of the x ray is8.3 A (Ka of Al), and glass reflection surfaces are to beused. If gold or other heavy metallic surfaces are used,22 mrad is far smaller than the critical angle, and theenergy loss of the x ray after two reflections would beeven smaller.

Numerical data of our toroidal mirrors in tandem areshown in Fig. 1, and these values are obtained in ac-cordance with the previous paper. The detail processof the calculations is shown in the Appendix.

It is worthwhile to keep in mind that the toroidalsurfaces must be carefully polished, but it is not nec-essary that the numerical values of Fig. 1 be strictlykept.

Method of Polishing the Toroidal Mandrel

Male toroidal surfaces are polished on a metal rod.As adjustment of the axes of two mirrors is very critical,both mirrors of the tandem pair are polished on thesame rod, and the rod is used as the master pattern ofthe replicated toroidal mirrors.

The pattern to be polished is chucked to a precisionlathe and rotates about its axis. A grinding device is seton the carriage of the lathe, and the carriage is fixed. Itconsists of a framework and a rather strong axis ofrotation. In Fig. 2 a scheme is shown where HI is theaxis of rotation fixed to the lathe, and the frameworkHILK rotates about the axis HI. A grinder axis KL andthe axis of rotation HI cross with each other at 0. Asthe framework moves to and fro about the axis HI, thegrinder attached to the axis KL moves on the sphere ofthe center at 0. The plane of the grinder, or strictlyspeaking a concave surface, is perpendicular to thegrinder axis, and the curvature of the surface is the sameas that of the sphere. Then the grinder surface is al-

15 February 1978 / Vol. 17, No. 4 / APPLIED OPTICS 601

3.0Os

B

0.004 rod

in cm

Fig. 1. Numerical data of toroidal mirrors in tandem.

Side view

R

NTop view

II

Fig. 2. A schematic drawing of the method used to polish a molyb-denum rod.

Fig. 3. A glass replica and a molybdenum mandrel.

X-ray tube t H, gas$ : °toi1 Toroidol mirrrl

Vacuum

._zzI~z:- I filmRi3 G Mylar Mylar

Magnetic Samplelens

Fig. 4. Testing arrangement of the mirrors by x ray of Al Ka, 8.3A.

ways in contact with the pattern along a line. We canchoose any radius R of the sphere by changing the anglebetween the axes HI and KL. A dental grinder set isused, and it rotates about 2000-5000 rpm. The grinderpoint is made of a molding type diamond dust wheelabout 10 mm in diameter. As the radius R is very large,the surface of the diamond wheel becomes the sameradius of curvature of the large sphere R in the courseof grinding at the cost of small wearing. Polishing isalso done by diamond paste, and an ebony plate is usedas a polishing disk. Final polishing is carried out byspecially separated fine diamond dust.

Replication Techniques and Final PolishingA glass replica is made from the polished rod as fol-

lows. The rod is put into a glass tube. The glass tubeis so formed that the clearance between the glass walland the rod is less than 1 mm. The glass tube is evac-uated and set in an electric furnace. The tube is slowlyheated to the softening point of the glass, then atmo-spheric pressure collapses the glass wall, and the glasscontacts the rod. When all polished surface contactsthe glass, heating is stopped, and the glass is left in thefurnace to cool naturally. Pyrex glass is used, and amolybdenum rod is recommended, because the expan-sion coefficients of the Pyrex glass and that of molyb-denum near the softening temperature of the glass arenearly equal, but the expansion coefficient of the Pyrexglass at room temperature is smaller than that of mo-lybdenum. Therefore, even if there are partial tem-perature differences on the rod surface, the preciseshape is transformed. Below 3000C the rod peels offthe glass due to the expansion difference of the twomaterials. The appropriate portion is then cut off fromthe tube. Replication in this manner copies even veryfine scratches, and they protrude from the surface. Asthe glancing angle is very small, these protrudingscratches become severe obstacles to x-ray imaging andproduce considerable scattering of the x ray. To reducethis wide angle scattering we applied a final light pol-ishing to the replica surfaces. (See Fig. 3)

Testing the Mirrors with X RaysAs an x-ray source a microfocus x-ray tube is used to

increase the brightness of the source. The testing ar-rangement is shown in Fig. 4. An electron beam is fo-cused by a magnetic lens on an A foil of 10-gm thick-ness which is also a window of the x-ray tube. Since8.3-A x rays are absorbed by a long air path, the toroidalmirrors are set in a tube, and the two ends of the tubeare Mylar windows of 12-gm thickness. Hydrogen gasis flowed through the tube. On the other hand ab-sorption of the x rays by a several-mm air path is small,and samples are set between the aluminum window andthe Mylar window, and photographic films are placedbehind the Mylar window at the other end of thetube.

In Fig. 5 a photograph of a copper mesh is shown.The mesh is # 1000, that is, the pitch is 25 gm, and thewidth of the wire is about 7 gim. Scattering is rather

602 APPLIED OPTICS / Vol. 17, No. 4 / 15 February 1978

_r,=120

Fig. 5. Photograph of mesh #1000 or 25-,m pitch and 7-um wire

width. Original magnification is about 20, and photographic en-largement is about 8.

strong, and this comes from the roughness of the re-flection surfaces. Before light polishing of the glasssurface is applied, scattering is strong, and the resolu-tion of the mesh is worse. On the other hand there isno stray light in the visible light images. Even if we usethe unpolished replicas we get clear images. Theoriginal replica surfaces are smooth enough to visiblelight but not smooth to soft x rays. Therefore, we ap-plied the final light polishing, but the technique is notyet perfected, and there still remains some scattering.

Throughout the photograph no distortion of the meshcan be seen. The illumination of the image correspondsto the shape of the x-ray source, or the electron beam,and we set the optical axis of the system as near aspossible to the center of the x-ray source. However, thex-ray source changes its position, and in some cases theilluminated portion of the object is not on the opticalaxis. Nevertheless, the pictures recorded in these caseslook similar to Fig. 5.

Discussion

The key point of an imaging system is to polish pre-cise surfaces. Theoretically good surfaces are not al-ways good surfaces from the point of view of polishing,and practical polishable surfaces are preferable. Ourpolishing device can polish very good toroidal surfaces,and our replication process also makes it possible toobtain small toroidal mirrors.

In x-ray optics the smoothness of a surface is anotherkey point of imaging, and the development of our finallight polishing technique is now in progress. At presentthe resolving power of our toroidal surfaces is far belowthe theoretical resolving power, but our mirrors are near

to Kirkpatrick type microscopes in resolution. More-over, the former are brighter and more easily adjustablethan the latter. They should have a wide field of ap-plication. If our polishing techniques, shaping andsmoothing the surface, are perfected in the future, wecould approach the theoretical limit of X/N.A. = 8.3/0.084 = 1oo A.

Appendix

As glancing angles to the surfaces are given we havezA + IC = 4 X 0.022 rad. Then the magnification of themirror should be settled as 21. (This number is givenfrom the easiness of calculation.) As the magnificationm is given by 1A/C = m = 21, we have zA = 0.084 rad,ZC = 0.004 rad, and all angles of apex A,0 1 ,0 2,C areknown. Next the real scale should be given. For ex-ample we put r, = 120 cm and 0102 = 3 cm, then wehave rb' = 0 2B = 12 cm, rb = 12 - 3 = 9 cm, and ra =4.29 cm.

The radius of curvature at 01 is given by the formulain the previous paper, 1 3

R = - , 6 =-, a=--0.022.cosa 6-1 ra 2

Then we have R1 = 745 cm, and the radius of curvatureat 02 is given by the equations

r, 2 rc 7rR2 = 2 6 =C - Or 0 = 0022.

coso6 + 1 rb, 2

Then we have R 2 = 990 cm.

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