Patent Number: 049842595
Section: description

DESCRIPTION OF THE PREFERRED EMBODIMENTS In the first place, the principle underlying the beam scanning system according to the present invention will be elucidated by reference to FIG. 1. The X-ray beam 2 radiated from a source 1 is incident on a reflecting mirror 3 at the point P.sub.o (corresponding to the point 0 in the spatial coordinate system) with a grazing incidence angle .alpha. (the angle formed between the incident X-ray beam and a line tangential to the mirror surface at the incident point P.sub.o), whereby the X-ray beam 4 reflected by the mirror 3 reaches a point S.sub.o on an object 5. Starting from this state, the reflecting mirror 3 is rotated about a center axis 6 of rotation by a given angle so that the reflecting mirror 3 assumes a position 3' indicated by a broken line. Then, the X-ray beam 2 is incident on the reflecting mirror 3 at a point P which corresponds to a point R in the spatial coordinate system and which is spaced from the point 0 by a distance r. In this conjunction, it is to be noted that the reflecting mirror surface is contoured in the shape such that the grazing incidence angle .alpha. holds the same value, as will be made apparent later on. Consequently, the reflected X-ray beam 4' is deflected to the same direction as the light beam 4 to impinge on the object 5 at a point S which is distanced from the point S.sub.o by r.multidot.sin 2.alpha.. Thus, it will be seen that the object 5 can be scanned with the X-ray beam 2 by rotating the reflecting mirror 3 with the angle of incidence being maintained constant. Next, a procedure for determining the shape of the reflecting mirror surface capable of realizing the scanning operation described above will be explained by referring to FIG. 4, in which like items as those shown in FIG. 1 are designated by the same reference characters. It is assumed that the spatial coordinate system consists of the origin coinciding with the point 0 on the X-ray beam 2, the x-axis taken along a straight line coinciding with the beam 2 and the y-axis coinciding with a straight line intersecting the x-axis orthogonally thereto at the origin 0. Further, a mirror-associated coordinate system is so established that the origin is located at the point P.sub.o, the x'-axis coincides with the line tangential to the reflecting mirror surface at the point P.sub.o and that the y'-axis coincides with a line normal to the reflecting mirror surface at the point P.sub.o. Thus, it will be seen that rotation of the reflecting mirror 3 about the axis of rotation 6 extending perpendicularly to the plane of the drawing brings about displacement of the origin P.sub.o of the mirror coordinate system relative to the spatial coordinate system. The points 0 and P.sub.o defining the origins of both coordinate systems, respectively, coincide with each other only at a definite rotational (angular) position of the reflecting mirror. Now, let's represent two points located very closely to each other by P.sub.i-l and P.sub.i, respectively, while considering that a line segment P.sub.i-l P.sub.i constitutes a part of the reflecting mirror surface. It is assumed that when the mirror is rotated clockwise about the center axis 6 of rotation by an angle .theta..sub.i, the points P.sub.i-l and P.sub.i are moved to points Q.sub.i-l and R.sub.i, respectively, in the spatial coordinate system, wherein the coordinates of the point P.sub.i-l and P.sub.i in the mirror coordinate system are represented by (x'.sub.Pi-l, y'.sub.Pi-l) and (x'.sub.Pi, Y'.sub.Pi), respectively, while the coordinates of the points Q.sub.i-l and R.sub.i in the spatial coordinate system are represented by (x.sub.Qi-l' Y.sub.Qi-l) and (x.sub.Ri, y.sub.Ri), respectively. Then, relations given by the following expressions (1) to (4) apply valid. ##EQU1## where (x.sub.c, y.sub.c) represents the coordinates of the rotational center axis 6 of the mirror in the spatial coordinate system. The conditions for the point R.sub.i to coincide with a point (r.sub.i, O) on the x-axis and for the line segment Q.sub.i-l R.sub.i to form the angle .alpha. relative to the x-axis are given by the following expressions (5), (6) and (7): EQU x.sub.Ri =r.sub.i, . . . . . (5) EQU y.sub.Ri =0, . . . . . (6) ##EQU2## Accordingly, if the quantities .alpha., r.sub.i, (x.sub.c, y.sub.c) and (x'.sub.Pi-l, y'.sub.Pi-l ) are known and when the angle .theta..sub.i is very small, then, from the expressions (1), (2), (5), (6) and (7), the angle .theta..sub.i can be given by the following expression (8): EQU A.theta..sub.i.sup.2 +B.theta..sub.i +C=0, . . . . . (8) where coefficients A, B and C are expressed as follows: EQU A=1/2(y.sub.c cos.alpha.-x.sub.c sin.alpha.-y'.sub.Pi-l) , . . . . . (9) EQU B=x.sub.c cos.alpha.+y.sub.c sin.alpha.-x'.sub.Pi-l , . . . . . (10) EQU C=r.sub.i sin.alpha.+y'.sub.Pi-l , . . . . . (11) It will thus be seen that when .theta..sub.i is determined, the coordinates (x'.sub.Pi, y'.sub.Pi) can be determined using the expressions (3) and (4). Thus, when .theta..sub.i and (x'.sub.Pi, y'.sub.Pi) are determined as described above, the X-ray beam 2 is incident on the mirror surface with the grazing incidence angle .alpha. at the point P.sub.i which is distanced from the point O by r.sub.i. As the result of this, the reflected light beam 4' is deflected to the same direction as that of the beam 4 to impinge on the object 5 at a point S.sub.i distanced from the point S.sub.o by r.sub.i .multidot.sin 2.alpha.. Now, the shape of the whole reflecting mirror surface can be determined in the manner mentioned below. First, the incidence angle .alpha. and the center axis of rotation (x.sub.c, y.sub.c) are established appropriately. Subsequently, the coordinates (x'.sub.Pl, y'.sub.Pl) of a point on the reflecting mirror surface distanced from the origin P.sub.o (X'.sub.Po =0, Y'.sub.Po =0) by a very small length are determined by placing i=1 and r.sub.l =.DELTA.r. More specifically, with i=1, the coefficients A, B and C are first determined in accordance with the expressions (9), (10) and (11), since the grazing incidence angle .alpha. and the coordinates x.sub.c and y.sub.c have already been determined to assume the respective predetermined values. Thus, .theta..sub.1 can be determined in accordance with the expression (8). With .theta..sub.1 having been determined, the coordinate x'.sub.Pl and y'.sub.Pl can be determined from the expressions (3) and (4), respectively. Next, with reference to the coordinates ('.sub.P1, y'.sub.P1) of the point P.sub.1 thus determined, the coordinates (x'.sub.P2, y'.sub.P2) of a point P.sub.2 distanced from the point P.sub.1 by a very small length are determined through the same procedure as that for determining the point P.sub.l described above on the conditions that i=2 and r.sub.2= 2.multidot..DELTA.r. In this manner, the angles .theta..sub.i and the coordinates (x'.sub.Pi, Y'.sub.Pi) can be sequentially determined for r.sub.i =i.multidot..DELTA.r where i=3,4 . . . , n. Finally, the points P.sub.0, P.sub.1, . . . , P.sub.n as determined are interconnected to define a smooth curve which represents the contour of the reflecting mirror surface. By giving the shape determined in this manner to the reflecting surface of the mirror 3, the grazing incidence angle .alpha. constantly assumes the same value so far as the rotation angle .theta. of the reflecting mirror is in the range of 0.ltoreq..theta..ltoreq..theta..sub.n. Although the foregoing description has been made on the presumption that x'&gt;0, a similar beam scanning can of course be performed in the region in which x'&lt;0. In this case, on the conditions that r.sub.i =-i.multidot..DELTA.r (where i=1, 2, 3, . . . , n), the coordinates for the envisaged mirror surface can be determined through the similar procedure as described above. In practical application of the present invention, the reflecting mirror surface may also be configured in a concave form as viewed in FIG. 2B in a plane orthogonal to the x'y'-plane and parallel to the y'-axis. With the mirror imparted with the reflecting surface shaped in this manner, it is possible to collimate the beam radiated from the synchrotron source in a plane orthogonal to the xy-plane (i.e. the orbital plane of electrons in) for thereby obtaining the beam of a desired width on the object. Now, an exemplary embodiment of the present invention will be described by referring to FIG. 5 in which like reference characters as those used in FIG. 1 designate the same items. In the case of the instant embodiment, the grazing incidence angle .alpha. at the mirror 3 is set to 25 mrad. When gold is used for the reflecting surface material, there can be obtained a reflectance above 70% in the soft X-ray region. The center 6 of rotation is set on the x-axis (optical axis) at a position distanced from the point O by 1000 m toward the light source 1. In that case, the rotation of the mirror 3 within an angular range of .+-.10 mrad brings about movement of the reflection point R on the x-axis by 823 mm. As the consequence, the reflected X-ray beam scans the object 5 over a width of about 40 mm. The mirror surface is coucave, as will be seen in FIG. 5. For allowing the beam to scan the object over the range mentioned above, the length of the mirror in the x'-direction must be of the order of 800 mm (.+-.400 mm). This size can readily be realized in practice. In the foregoing description, the beam width of the SR in the vertical plane is regarded to be infinitesimal. However, the X-ray beam which is used for exposure are radiated within the angular range of about 1 mrad in the vertical plane. By collimating this diverging beam vertically and scanning with the direction of the reflected beam being maintained constant, there can be attained a high throughput and an enhanced printing accuracy. In general, in order to collimate the light beam radiated from a point light source, an off-axis paraboloidal mirror having the focal point coinciding with the point light source is used. In the beam scanning system according to the present invention, the reflecting mirror can be made to approximate very closely the collimating off-axis paraboloidal mirror by setting the center of rotation of the reflecting mirror at the optimal position. Referring to FIG. 5, the distance between the source 1 and the point O is set to 5 m with the grazing incidence angle .alpha. being 25 mrad, by way of example. In that case, the center 6 of rotation is located at the position on the x-axis (optical axis) distanced from the point O by 10 m toward the source 1. Then, the reflecting surface is of such a shape as illustrated in FIG. 7. When the reflecting mirror 3 is rotated within the angular range of .+-.1 mrad, the reflection point R moves by about 800 mm on the x-axis, resulting in that the reflected beam 4 scans the object 5 over the width of about 40 mm. At that time, the diverging beam from the light source is well collimated to impinge onto the object regardless of the position of the reflection point R. FIG. 8 shows a mechanical structure for rotating the reflecting mirror according to an embodiment of the invention. Referring to the figure, a pair of linear motion mechanisms constituted, respectively, by motors 37 and 37' and lead screws 36 and 36' are installed in the atmosphere. Female screw members 35 and 35' engaging threadwise the lead screws 36 and 36' have connecting rods 34 and 34' fastened thereto, respectively, which in turn support a reflecting mirror 31 through flexure hinges 38 and 38', respectively. The reflecting mirror and the connecting rods are placed in a vacuum chamber 32, wherein vacuum-tightness is ensured by bellows 33 and 33'. By controlling the movements of the lead screws coordinatively, desired rotation of the reflecting mirror can be accomplished.