METHOD FOR DESIGNING MIRROR AND ASTAGITABER CONTROL MIRROR HAVING REFLECTING SURFACE WHEREIN THE DESIGN EQUATION IN THE METHOD APPLY

Abstract

To provide a method for designing a mirror that allows individual setting of a light source position and a condensation position in the vertical direction and the horizontal direction, and allows free conversion of astigmatism according to the setting.SOLUTION: In a method for designing a mirror, the intersection of a sagittal light source ray and an incident ray on an M0A point and the intersection of a meridional light source ray and the incident ray on the MA0 point are defined; the intersection of an emission ray from the MA0 point and a sagittal virtual condensed ray and the intersection of the emission ray from the MA0 point and a meridional virtual condensed ray are defined; the intersection of a sagittal virtual light source ray and an incident ray on an MB0 point and the intersection of a meridional virtual light source ray and the incident ray on the MB0 point are defined; the intersection of an emission ray from the MB0 point and a sagittal condensed ray and the intersection of the emission ray form the MB0 point and a meridional condensed ray are defined; and a mirror is designed by using a design formula of a reflection surface derived based on the fact that a light path length from a light source position to a virtual condensation position and a light path length from a virtual light source position to a condensation position are constant.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a method for designing a mirror having a first reflecting surface and a second reflecting surface that sequentially reflect light, and to an astigmatism controlled mirror equipped with reflecting surfaces for which a design equation in the design method holds true. [Background technology]

[0002] Synchrotron radiation soft X-ray beams have different characteristics in the vertical and horizontal directions. The beam size tends to be smaller in the vertical direction than in the horizontal direction. The coherent width is larger in the vertical direction than in the horizontal direction. Furthermore, in spectroscopic systems using diffraction gratings, which are widely used in soft X-ray beamlines, the divergence angle of the beam in the vertical direction increases. In addition, the spectrometers containing diffraction gratings used focus soft X-rays only in the spectral direction, resulting in "astigmatism," where the light source position is different in the spectral direction and in non-focusing directions.

[0003] One possible way to eliminate astigmatism is the toroidal mirror (Non-Patent Document 1). However, a toroidal mirror is an approximation of an existing ellipsoidal mirror, and is easily manufactured by setting a uniform radius of curvature in both the long and short directions of the reflecting surface. Even if it can eliminate astigmatism, it has the drawback that, in principle, the focused size increases.

[0004] Astigmatic off-axis mirrors (AO mirrors) have also been proposed as mirrors that can reduce the focused size compared to toroidal mirrors and can set independent light sources and focusing points vertically and horizontally (Non-Patent Document 2). This mirror is shaped to find a curved surface that smoothly connects different conic sections in the long and short directions, based on the principle that an elliptical curve is used as the ridgeline of the reflecting surface to focus a beam diverging from one point to another, a parabola is used to parallelize a beam diverging from one point, and a hyperbola is used to convert a beam focused toward one point into a beam focused toward another point.

[0005] However, this AO mirror is defined by rotating the longitudinal conic section profile around the straight line (major axis) connecting the foci of the transverse conic section to obtain a curved surface, and since the reflecting surface is approximated to an axially symmetric shape, this approximation creates a limit to the reduction of the focused size. This is not a problem for beams in the terahertz range with long wavelengths, but it cannot be used for beams in the X-ray range. In addition, the design formula is very complicated, including multiple coordinate transformations, and the parameters are also complicated, making it difficult to understand and use. [Prior art documents] [Non-patent literature]

[0006] [Non-Patent Document 1] William A. Rense, T. Violett, "Method of Increasing the Speed ​​of a Grazing-Incidence Spectrograph", JOURNAL OF THE OPTICAL SOCIETY OF AMERICA, Vol. 49, No. 2, February 1959, p139-p141 [Non-Patent Document 2] A. Wagner-Gentner, UU Graf, M. Philipp, D. Rabanus, "A simple method to design astigmatic off-axis mirrors", Infrared Physics & Technology 50, 2007, p42-p46 Summary of the Invention [Problem to be solved by the invention]

[0007] In view of the above-mentioned situation, the object of the present invention is to provide a method for designing a mirror which can fabricate a mirror that can be used suitably as an optical system for handling beams whose characteristics differ between the vertical and horizontal directions, by enabling the light source position and the focusing position to be set independently in the vertical and horizontal directions, thereby enabling free conversion of astigmatism, and by keeping the focusing size small so as to be compatible with beams in the X-ray region, with a simple design formula and a wide range of applications. [Means for solving the problem]

[0008] In view of the current situation, the inventors conducted extensive research and found that, as a method of expressing the properties of a beam having astigmatism in terms of geometrical optics, a "source ray" and a "focusing ray" were newly defined for focusing in the sagittal direction and focusing in the meridional direction, respectively, and that all incident light rays passing through the reflective surface of a mirror pass through each of the "source rays" in the vertical and horizontal directions, and all outgoing light rays emitted from the reflective surface of a mirror pass through "focusing rays" in the vertical and horizontal directions. By applying Fermat's principle, in which the "optical path length" from the light source position to the focusing position is constant, it is possible to design a reflective surface that allows for free conversion of astigmatism, and thus completed the present invention.

[0009] That is, the present invention includes the following inventions. (1) A method for designing a mirror having a first reflecting surface and a second reflecting surface from which light is sequentially reflected, the optical axis of a beam incident on the first reflecting surface is defined as the z1 axis, a cross section perpendicular to the z1 axis is defined as the x1y1 plane, the optical axis of a beam emitted from the first reflecting surface which becomes a beam incident on the second reflecting surface is defined as the z2 axis, a cross section perpendicular to the z2y2 plane, the optical axis of a beam emitted from the second reflecting surface is defined as the z3 axis, a cross section perpendicular to the z3y3 plane, the x1 axis, x2 axis, and x3 axis are parallel to the sagittal directions of the first reflecting surface and the second reflecting surface, and the beam incident on the first reflecting surface is defined as an intersection point M0 of the z1 axis and the z2 axis on the first reflecting surface. A From the z1 axis along L 1s A At the displaced position, a light source for sagittal focusing is provided, and the intersection point M0 on the z1 axis is provided.A From the z1 axis along L 1m A At the displaced position, a light source for focusing in the meridional direction is provided, and the beam emitted from the second reflecting surface is focused at the intersection M0 of the z2 axis and the z3 axis on the z3 axis for focusing in the sagittal direction. B From the z3 axis along L 2s B The light is focused at a displaced position, and the intersection point M0 on the z3 axis for focusing in the meridional direction is B From the z3 axis along L 2m B When it is assumed that the light is focused at a displaced position, and all the incident light rays passing through the first reflecting surface pass through a sagittal light source line that passes through the position of the light source in the sagittal direction focusing and extends in a direction perpendicular to both the x1 axis and the z1 axis, and a meridional light source line that passes through the position of the light source in the meridional direction focusing and extends in a direction perpendicular to both the y1 axis and the z1 axis, and all the outgoing light rays emitted from the second reflecting surface pass through a sagittal converging line that passes through the focusing position in the sagittal direction focusing and extends in a direction perpendicular to both the x3 axis and the z3 axis, and a meridional converging line that passes through the focusing position in the meridional direction focusing and extends in a direction perpendicular to both the y3 axis and the z3 axis, and further, the outgoing beam from the first reflecting surface travels straight without being reflected by the second reflecting surface, the intersection point M0 on the z2 axis for the sagittal direction focusing is A From the z2 axis along L 2s A The light is focused at a displaced position, and the intersection point M0 on the z2 axis for focusing in the meridional direction is A From the z2 axis along L 2m AThe light is focused at a displaced position, and the outgoing light beam from the first reflecting surface passes through a sagittal virtual focusing line that passes through the focusing position in the sagittal direction and extends in a direction perpendicular to both the x2 axis and the z2 axis, and a meridional virtual focusing line that passes through the focusing position in the meridional direction and extends in a direction perpendicular to both the y2 axis and the z2 axis. All incident light beams passing through the second reflecting surface intersect with both light source lines on their extension lines, with the sagittal virtual focusing line in the sagittal direction focusing for the first reflecting surface being a sagittal virtual light source line, and the meridional virtual focusing line in the meridional direction focusing for the first reflecting surface being a meridional virtual light source line. An arbitrary point on the first reflecting surface is defined as M A As the sagittal light source line and M A Intersection of the incident ray at the point, and the meridional light ray and M A The coordinates of the intersection points of the incident ray to the point are 1s A , L 1m A and the M A The intersection of the outgoing ray from the point and the sagittal virtual focusing ray, and M A The coordinates of the intersections of the outgoing ray from the point and the meridional virtual condensed ray are 2s A , L 2m A and any point on the second reflecting surface is expressed as M B As the sagittal virtual source line and M B Intersection of the incident ray to the point, and the meridional virtual light source line and M B The coordinates of the intersection points of the incident ray to the point are 2s A , L 2m A , and M0 A M0 B The distance between the two points is expressed as L, and M B The intersection of the outgoing ray from the point and the sagittal focusing ray, and M B The coordinates of the intersections of the outgoing ray from the point and the meridional condensed ray are 2s B , L 2m Band designing the mirror using a design equation for the reflecting surface which is derived based on these coordinates, that the optical path length from the light source position to the virtual focusing position is constant for any point on the reflecting surface for focusing in the sagittal direction and focusing in the meridional direction on the first reflecting surface, and that the optical path length from the virtual light source position to the focusing position is constant for any point on the reflecting surface for focusing in the sagittal direction and focusing in the meridional direction on the second reflecting surface.

[0010] (2) The sagittal light source line and the meridional light source line are respectively aligned along a straight line S extending in the y1-axis direction. s , a straight line S extending in the x1-axis direction m The sagittal virtual focusing line and the meridional virtual focusing line are respectively defined as a straight line F extending in the y2-axis direction. s A , a straight line F extending in the x2-axis direction m A The sagittal virtual light source line and the meridional virtual light source line are respectively defined as the straight line F s A The line S that matches s B , the straight line F m A The line S that matches m B The sagittal and meridional focusing lines are respectively defined as straight lines F extending in the y3-axis direction. s , a straight line F extending in the x3-axis direction m and calculating the optical path length for focusing light in the meridional direction or the sagittal direction on the first reflecting surface or the second reflecting surface by the following (i) to (iv):

[0011] (i) Calculation of the optical path length of the sagittal direction focusing light on the first reflecting surface: A The length of incidence to the point is the meridional light source ray S m and z1 axis intersection point P m0 The sagittal light source line S sand z1 axis intersection point P s0 The circular arc passing through and extending perpendicular to the x1 axis is called the sagittal light source line S s The rotational arc surface rotated around the axis is called equiphase surface A. 1s The incident light and the equiphase surface A 1s The meridional light ray S is one of the two intersection points with m From the intersection closest to A The distance to the point, M A The exit length from the point to the virtual focusing position is the meridional virtual focusing line F m A and the z2 axis intersection point Q m0 A A virtual sagittal focusing line F s A and the z2 axis intersection point Q s0 A The circular arc that passes through and extends in a direction perpendicular to the x2 axis is called the sagittal virtual focusing line F s A The rotational arc surface rotated around the axis is called equiphase surface A. 2s A The outgoing light ray and the equiphase surface A 2s A Among the two intersections with the meridional virtual focusing ray F m A From the intersection closest to A From this, the optical path length for the light focused in the sagittal direction on the first reflecting surface is calculated.

[0012] (ii) Calculation of the optical path length of the light focused in the meridional direction on the first reflecting surface: A The length of incidence to the point is the sagittal source line S s and z1 axis intersection point P s0 The meridional light source line S m and z1 axis intersection point P m0 The circular arc that passes through and extends in a direction perpendicular to the y1 axis is called the meridional light source ray S m The rotational arc surface rotated around the axis is called equiphase surface A. 1m The incident light and the equiphase surface A1m Of the two intersections with the sagittal light source line S s From the intersection closest to A The distance to the point is calculated as M A The exit length from the point to the virtual focusing position is the sagittal virtual focusing line F s A and the z2 axis intersection point Q s0 A A meridional virtual focusing line F m A and the z2 axis intersection point Q m0 A The arc that passes through and extends perpendicular to the y2 axis is called the meridional virtual focusing line F m A The rotational arc surface rotated around the axis is called equiphase surface A. 2m A The outgoing light ray and the equiphase surface A 2m A Of the two intersections with the sagittal virtual focusing line F s A From the intersection closest to A Calculate the distance to the point, In this way, the optical path length for the light collected in the meridional direction on the first reflecting surface is calculated.

[0013] (iii) Calculation of the optical path length of the sagittal direction focusing light on the second reflecting surface: B The incident length to the point is the meridional virtual light source ray S m B and z2 axis intersection point P m0 B A virtual light source line S with a center at the sagittal position s B and z2 axis intersection point P s0 B The circular arc that passes through and extends in a direction perpendicular to the x2 axis is called the sagittal virtual light source ray S s B The rotational arc surface rotated around the axis is called equiphase surface A. 1s B The incident light and the equiphase surface A 1sB Among the two intersections with the meridional virtual light source ray S m B From the intersection closest to B The distance to the point, M B The exit length from the point to the focusing position is the meridional focusing line F m and the z3 axis intersection point Q m0 The sagittal focusing ray F s and the z3 axis intersection point Q s0 The circular arc passing through and extending perpendicular to the x3 axis is called the sagittal focusing ray F s The rotational arc surface rotated around the axis is called equiphase surface A. 2s The outgoing light ray and the equiphase surface A 2s Of the two intersections with the meridional condensing ray F m From the intersection closest to B From this, the optical path length for the light focused in the sagittal direction on the second reflecting surface is calculated.

[0014] (iv) Calculation of the optical path length of the light focused in the meridional direction on the second reflecting surface: Calculation of the optical path length of the light focused in the meridional direction on the second reflecting surface from the virtual light source position M B The incident length to the point is the sagittal virtual source line S s B and z2 axis intersection point P s0 B A virtual light source ray S centered on and meridional to m B and z2 axis intersection point P m0 B The arc that passes through and extends perpendicular to the y2 axis is called the meridional virtual light source ray S m B The rotational arc surface rotated around the axis is called equiphase surface A. 1m B The incident light and the equiphase surface A 1m B Of the two intersections with the sagittal virtual light source line S s B From the intersection closest to BThe distance to the point is calculated as M B The exit length from the point to the focusing position is the sagittal focusing line F s and the z3 axis intersection point Q s0 The meridional focusing ray F m and the z3 axis intersection point Q m0 The circular arc that passes through and extends perpendicular to the y3 axis is called the meridional focusing ray F m The rotational arc surface rotated around the axis is called equiphase surface A. 2m The outgoing light ray and the equiphase surface A 2m Of the two intersections with the sagittal focusing ray F s From the intersection closest to B The optical path length for the light collected in the meridional direction on the second reflecting surface is calculated based on the distance to the point.

[0015] (3) In calculating the optical path length of the above (i) (sagittal direction focusing of the first reflecting surface), the incident light beam and the equiphase surface A on the first reflecting surface are 1s The meridional light ray S is one of the two intersection points with m From the intersection closest to A The distance to the point is the distance between the incident ray and the sagittal source ray S s Intersection point P s From the above M A The distance to the point is calculated, and the distance is multiplied by the intersection point P s From the equiphase surface A 1s and calculating the distance to the arc that defines the output light beam on the first reflecting surface and the equiphase surface A 2s A Among the two intersections with the meridional virtual focusing ray F m A From the intersection closest to A The distance to the point is the distance between the exit ray and the sagittal virtual focusing ray F s A Intersection point Q s A From the above M A The distance to the point is calculated, and the distance is multiplied by the intersection point Q s A From the equiphase surface A2s A The distance to the arc that defines the distance is added or subtracted.

[0016] In addition, in the calculation of the optical path length of the above (ii) (light focusing in the meridional direction on the first reflecting surface), the incident light on the first reflecting surface and the equiphase surface A 1m Of the two intersections with the sagittal light source line S s From the intersection closest to A The distance to the point is the distance between the incident ray and the meridional light source ray S m Intersection point P m From the above M A The distance to the point is calculated, and the distance is multiplied by the intersection point P m From the equiphase surface A 1m and calculating the distance between the emitted light beam and the equiphase surface A on the first reflecting surface by adding or subtracting the distance to the arc that defines the 2m A Of the two intersections with the sagittal virtual focusing line F s A From the intersection closest to A The distance to the point is the distance between the exit ray and the meridional virtual focusing ray F m A Intersection point Q m A From the above M A The distance to the point is calculated, and the distance is multiplied by the intersection point Q m A From the equiphase surface A 2m A The distance to the arc that defines the distance is added or subtracted.

[0017] In addition, in calculating the optical path length of the above (iii) (sagittal direction focusing of the second reflecting surface), the incident light on the second reflecting surface and the equiphase surface A 1s B Among the two intersections with the meridional virtual light source ray S m B From the intersection closest to B The distance to the point is the distance between the incident ray and the sagittal virtual source ray S s B Intersection point P sB From the above M B The distance to the point is calculated, and the distance is multiplied by the intersection point P s B From the equiphase surface A 1s B and the distance to the arc that defines the second reflecting surface is added or subtracted to obtain the distance between the emitted light beam and the equiphase surface A 2s Of the two intersections with the meridional condensing ray F m From the intersection closest to B The distance to the point is the distance between the exit ray and the sagittal focusing ray F s Intersection point Q s From the above M B The distance to the point is calculated, and the distance is multiplied by the intersection point Q s From the equiphase surface A 2s The distance to the arc that defines the distance is added or subtracted.

[0018] In addition, in the calculation of the optical path length of the above (iv) (light focusing in the meridional direction on the second reflecting surface), 1m B Of the two intersections with the sagittal virtual light source line S s B From the intersection closest to B The distance to the point is the distance between the incident ray and the meridional virtual light source ray S m B Intersection point P m B From the above M B The distance to the point is calculated, and the distance is multiplied by the intersection point P m B From the equiphase surface A 1m B and the distance to the arc that defines the second reflecting surface is added or subtracted to obtain the distance between the emitted light beam and the equiphase surface A 2m Of the two intersections with the sagittal focusing ray F s From the intersection closest to B The distance to the point is the distance between the emitted ray and the meridional convergent ray F m Intersection point Q m From the above M BThe distance to the point is calculated, and the distance is multiplied by the intersection point Q m From the equiphase surface A 2m The method for designing a mirror according to (2), further comprising the steps of: adding or subtracting the distance to the arc defining said arc;

[0019] (4) A method for designing a mirror according to any one of (1) to (3), further comprising: defining a Cartesian coordinate system UVW having an origin at the intersection of the z1 axis and the z3 axis, a direction parallel to the z2 axis as the u axis, a direction parallel to the x1 axis, the x2 axis, and the x3 axis as the v axis, and a direction perpendicular to both the u axis and the v axis as the w axis; and transforming the UVW coordinates into an x1y1z1 coordinate system based on the optical axis of the beam incident on the first reflecting surface, an x2y2z2 coordinate system based on the optical axis of the beam emerging from the first reflecting surface which becomes the beam incident on the second reflecting surface, and an x3y3z3 coordinate system based on the optical axis of the beam emerging from the second reflecting surface, respectively; and expressing the design equation in the UVW coordinate system.

[0020] (5) Intersection point M0 of the z1 and z2 axes on the first reflecting surface A The surface in contact with the reflecting surface is defined as u A v A Let the plane be u A v A Plane M0 A The direction of the normal passing through w A axis, v A The direction perpendicular to both the z1 and z2 axes, u A Axis v A axis and w A The direction is perpendicular to both axes, and the intersection point M0 A is the origin, u A v A The oblique incidence angle between the plane and the optical axis z1 is θ0 A The Cartesian coordinate system u with the first reflecting surface as the reference A v A w A Define Intersection point M0 of the z2 axis and the z3 axis on the second reflecting surface B The surface in contact with the reflecting surface is defined as u B v B Let the plane be u B v B Plane M0 BThe direction of the normal passing through w B axis, v B The direction perpendicular to both the z2 and z3 axes, u B Axis v B axis and w B The direction is perpendicular to both axes, and the intersection point M0 B is the origin, u B v B The oblique incidence angle between the plane and the optical axis z2 is θ0 B The Cartesian coordinate system u with the second reflecting surface as the reference B v B w B Define u A v A w A Coordinate system and u B v B w B The coordinate systems are respectively transformed into an x1y1z1 coordinate system based on the optical axis of the incident beam on the first reflecting surface, an x2y2z2 coordinate system based on the optical axis of the outgoing beam from the first reflecting surface, which is the incident beam on the second reflecting surface, and an x3y3z3 coordinate system based on the optical axis of the outgoing beam from the second reflecting surface, and the design formula is transformed into the u A v A w A Coordinate system and u B v B w B The mirror design method according to (4), further comprising expressing the axial direction of the mirror in a uvw coordinate system.

[0021] (6) The design formula is a first formula f derived from the fact that the optical path length from the light source point to the virtual focusing point is constant for the focusing in the sagittal direction on the first reflecting surface. s A (u A ,v A ,w A )=0, and the optical path length from the light source point to the virtual focusing point is constant for the focusing of the light in the meridional direction on the first reflecting surface, so that the second formula f m A (u A ,v A ,w A)=0, and the third formula f s B (u B ,v B ,w B )=0, and the optical path length from the virtual light source point to the light collection point in the meridional direction on the second reflecting surface is constant, so that the fourth formula f m B (u B ,v B ,w B 6. The method for designing a mirror according to claim 5, comprising the following formula (2) in which:

[0022]

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[0023] (7) The light source line S is calculated by the following formula: s From the focused ray F s Any sagittal focusing magnification M up to s and the source line S m From the focused ray F m Any magnification M for meridional focusing up to m Using L 2m A , L 2s A The method for designing a mirror according to any one of (1) to (6), further comprising setting

[0024]

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[0025] (8) A mirror having a reflecting surface for which the design formula according to any one of (1) to (6) is satisfied, 1s A and L 1m A The values ​​of L are different. 2s B and L 2mB An astigmatism control mirror, which has the same value of and can obtain a focused output beam from an input beam with astigmatism.

[0026] (9) A mirror having a reflecting surface for which the design formula according to any one of (1) to (6) is satisfied, 1s A and L 1m A The values ​​of L 2s B and L 2m B An astigmatism controlled mirror has different values ​​of , resulting in an astigmatism-bearing output beam from an input beam diverging from a single point.

[0027] (10) A mirror having a reflecting surface for which the design formula according to any one of (1) to (6) is satisfied, 1s A and L 1m A The values ​​of L match 2s A and L 2m A The values ​​of L are different. 2s B and L 2m B The first reflecting surface of the astigmatism-control mirror has the same value as the second reflecting surface of the astigmatism-control mirror, and the second reflecting surface of the astigmatism-control mirror eliminates the astigmatism and provides different reduction ratios in the vertical and horizontal directions.

[0028] (11) A mirror having a reflecting surface for which the design formula according to any one of (1) to (6) is satisfied, the magnification of a beam from a light source line to a focusing line is a sagittal magnification M defined by the following formula (3): s , and the meridional magnification M m Using equation (4), L 2m A , L 2s AThis astigmatism control mirror is designed to set the beam diverging from a single point in both the vertical and horizontal directions so that it converges to a single point again after two reflections, and the beam becomes circular at the convergence point or at the divergence point further downstream.

[0029]

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[0030]

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[0031] (12) A mirror having a reflecting surface for which the design formula according to any one of (1) to (6) is satisfied, 1m A and L 2m A and L 2m B The value of L is positive or negative infinity, and 1s A and L 2s A and L 2s B is a given value (where L 1s A +L 2s A ≠0 and (LL 2s A )+L 2s B ≠0) and has light-gathering performance only in the sagittal direction.

[0032] (13) A mirror having a reflecting surface for which the design formula according to any one of (1) to (6) is satisfied, wherein, for sagittal direction focusing, s and z1 axis intersection point P s0、 Virtual focusing ray F s A and the intersection point Q of the z2 axis s0 A , focusing ray F s and the intersection point Q of the z3 axis s0 The three points are on the same line, and the light source line Sm and z1 axis intersection point P m0 , virtual focusing line F m A and the intersection point Q of the z2 axis m0 A , focusing ray F m and the intersection point Q of the z3 axis m0 So that the three points of are on the same line, L 2s A and L 2m A By setting the astigmatism control mirror, the installation angle tolerance range is expanded. Effect of the Invention

[0033] According to the mirror design method of the present invention, the light source position and the focusing position can be set independently in the vertical and horizontal directions, and thus a mirror capable of freely changing astigmatism can be fabricated. In addition, the focusing size can be made smaller to accommodate beams in the X-ray region. Furthermore, the design formula is simple and the range of applications is wide, making it suitable for use as an optical system that handles beams with different characteristics in the vertical and horizontal directions.

[0034] Furthermore, according to the design method of the present invention, focusing performance can be obtained by reflecting the light two or more times between the first and second reflecting surfaces for both vertical and horizontal focusing. This makes it possible to suppress off-axis aberrations and improve imaging performance compared to the case where focusing performance is obtained with a single reflection, and it is possible to provide a mirror that allows for free conversion of astigmatism as described above while at the same time being resistant to installation angle errors.

[0035] In addition, in the present invention, if the first reflecting surface on the upstream side is designed to impart astigmatism while the second reflecting surface on the downstream side is designed to eliminate this, it is possible to provide a mirror that focuses a beam from one point to another while providing different reduction ratios in the vertical and horizontal directions. Furthermore, it is possible to provide a mirror that circularizes the focused size of a beam whose source size differs greatly between the vertical and horizontal directions. It is also possible to provide a mirror that circularizes the shape of the beam incident on the second reflecting surface on the downstream side, thereby forming a beam with a circular intensity profile at the divergence position. [Brief description of the drawings]

[0036] [Figure 1] FIG. 2 is a conceptual diagram of a mirror designed by the design method according to the present invention. [Diagram 2] (a)~(c) are conceptual diagrams showing the x1y1z1 coordinate system, the x2y2z2 coordinate system, and the x3y3z3 coordinate system, respectively. [Diagram 3] FIG. 2 is a conceptual diagram illustrating a "light source ray" and a "collected ray" on the first reflecting surface. [Figure 4] 1 is a conceptual diagram illustrating the "light source ray" and "collected ray" on the second reflecting surface. [Diagram 5] 1A is an explanatory diagram showing the points at which the incident beam and outgoing beam intersect with the virtual light source line and the virtual focusing line on the first reflecting surface, and FIG. 1B is an explanatory diagram showing the points at which the incident beam and outgoing beam intersect with the virtual light source line and the virtual focusing line on the second reflecting surface. [Figure 6] A conceptual diagram showing the uAvAwA coordinate system and the uBvBwB coordinate system. [Figure 7] 1 is a conceptual diagram showing an equiphase surface A1s in the vicinity of an intersection point Ps on a sagittal light source line Ss. [Figure 8] A conceptual diagram showing an equiphase surface A1m near the intersection point Pm on the meridional light source line Sm. [Figure 9] A conceptual diagram showing the uvw coordinate system. [Figure 10] Cross-section of the source and collection rays in the uw plane of the mirror. [Figure 11] Conceptual diagram showing examples of mirrors that can be designed. [Figure 12]1 is a conceptual diagram showing other examples of mirrors that can be designed. [Figure 13] 1 is an explanatory diagram showing the positional shift between the meridional focusing point Fm and the sagittal focusing point Fs when the glancing angle is increased in focusing of light on an ellipsoidal mirror. FIG. [Figure 14] A schematic diagram showing the reaction of a two-reflection mirror (integral type) when a glancing angle error is input. [Figure 15] 11 is a graph showing the optimization results of the exit length L2A of the first reflecting surface. [Figure 16] Graph showing optimized L2 A and response to glancing angle error. [Figure 17] FIG. 2 is an explanatory diagram showing an optical system arrangement of mirrors according to the first embodiment. [Figure 18] 1A is a diagram showing the two-dimensional distribution of the height of the mirror in Example 1, and FIG. 1B is a diagram showing the longitudinal cross-sectional profile. [Figure 19] FIG. 4 is an explanatory diagram showing an installation angle error to be input. [Figure 20] Graphs showing responses to pitch angle error: (a) meridional focus size response, (b) sagittal focus size response, (c) meridional focus misalignment response, and (d) sagittal focus misalignment response. [Figure 21] Graphs showing responses to yaw angle error: (a) meridional focus size response, (b) sagittal focus size response, (c) meridional focus misalignment response, and (d) sagittal focus misalignment response. [Figure 22] Graphs showing response to roll angle error: (a) meridional focus size response, (b) sagittal focus size response, (c) meridional focus misalignment response, and (d) sagittal focus misalignment response. [Diagram 23] 13A and 13B are diagrams showing the mirror shape (height distribution) of Example 3, in which (a) shows the two-dimensional distribution of height, and (b) shows the longitudinal cross-sectional profile. [Figure 24] FIG. 11 is a diagram showing the results of outputting the distribution of light rays at a focal point by ray tracing calculation for the mirror of Example 3. [Diagram 25] 13A and 13B are diagrams showing the mirror shape (height distribution) of Example 4, in which (a) shows the two-dimensional distribution of height, and (b) shows the longitudinal cross-sectional profile. [Figure 26] FIG. 13A is a diagram showing the output result of the distribution of light rays at the focal point by ray tracing calculation for the mirror of Example 4, and FIG. 13B is a diagram showing the output result of the distribution of light rays at a position 10 m downstream from the focal point. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0037] The mirror design method of the present invention relates to a method for designing a mirror having a first reflecting surface and a second reflecting surface that sequentially reflect light. Hereinafter, the mirror design method of the present invention will be described with reference to typical embodiments.

[0038] The present invention aims to freely convert astigmatism, and designs mirrors with higher accuracy based on Fermat's principle, which states that "light follows the path with the shortest optical distance." When limited to converging (or diffusing) mirrors, Fermat's principle can be translated into the expression that "for any point on the mirror surface (reflecting surface), the sum of the distance from the light source point and the distance to the converging point is constant." When the incident beam or outgoing beam has astigmatism, the law of constant optical path length cannot be immediately applied. This is because, as the name suggests, an astigmatized beam does not have a single light source point or converging point. In this invention, the idea of ​​newly defining "light source line" and "converging line" has been conceived, and a design method has been realized by making it possible to express the properties of an astigmatized beam in terms of geometrical optics.

[0039] (Definition of "light source ray" and "focused ray") Fig. 1 is a conceptual diagram of a mirror designed by the design method according to the present invention. Symbol A indicates a first reflecting surface (also called mirror A), and symbol B indicates a second reflecting surface (also called mirror B). As shown in Figs. 2(a), (b), and (c), the optical axis of the incident beam on the first reflecting surface is the z1 axis, the cross section perpendicular to this is the x1y1 plane, the optical axis of the outgoing beam from the first reflecting surface, which becomes the incident beam on the second reflecting surface, is the z2 axis, the cross section perpendicular to this is the x2y2 plane, the optical axis of the outgoing beam from the second reflecting surface is the z3 axis, the cross section perpendicular to this is the x3y3 plane, and the x1 axis, x2 axis, and x3 axis are parallel to the sagittal directions of the first reflecting surface and the second reflecting surface.

[0040] First, the "source ray" and "collected ray" for the first reflecting surface will be described. As shown in FIG. 3, for the sagittal direction collection on the first reflecting surface, the incident beam is incident on the z1 axis at the intersection M0 of the z1 axis and the z2 axis on the first reflecting surface. A From the z1 axis along L 1s A If we assume that the light source is located at a displaced position and that the emitted beam travels straight without being reflected by the second reflecting surface, the intersection point M0 on the z2 axis is A From the z2 axis along L 2s A Assume that the light is focused at a displaced position.

[0041] For focusing in the meridional direction, the intersection point M0 on the z1 axis A From the z1 axis along L 1m A If we assume that the light source is located at a displaced position and that the emitted beam travels straight without being reflected by the second reflecting surface, the intersection point M0 on the z2 axis is A From the z2 axis along L 2m A Assume that the light is focused at a displaced position.

[0042] All the incident light rays passing through the first reflecting surface are oriented in a sagittal light source line (S s), and a meridional light source line (S m ) is considered to pass through the sagittal light source ray (S s ), meridional light ray (S m )

[0043] In addition, all of the outgoing light rays emitted from the first reflecting surface are oriented along a sagittal virtual focusing line (F s A ), and a meridional virtual focusing line (F m A ) is considered to pass through the sagittal virtual focusing ray (F s A ), meridional virtual focusing ray (F m A )

[0044] Next, the "light source ray" and "light collecting ray" will be described for the second reflecting surface. As shown in FIG. 4, all incident light rays passing through the second reflecting surface are extended along the sagittal virtual collecting ray (F s A ) is the sagittal virtual source line (S s B ), and the meridional virtual focusing ray (F m A ) is the meridional virtual light ray (S m B ) can be defined as L 1s B =LL 2s A , L 1m B =LL 2m A It is defined as:

[0045] In addition, for the sagittal focusing of the second reflecting surface, the exit beam is focused on the intersection point M0 of the z2 axis and the z3 axis on the second reflecting surface. B From the z3 axis along L 2s B In addition, for focusing in the meridional direction of the second reflecting surface, the emitted beam is focused at the intersection point M0 on the z3 axis. B From the z3 axis along L 2m B Assume that the light is focused at a displaced position.

[0046] All of the outgoing light rays emitted from the second reflecting surface are focused in a sagittal focusing line (F s ), and a meridional focusing line (F m ) is considered to pass through the sagittal focusing ray (F s ), meridional condensation ray (F m )

[0047] In this example, the sagittal light source line (S s ), meridional light ray (S m ), sagittal virtual focusing ray (F s A ), meridional virtual focusing ray (F m A ), sagittal virtual source line (S s B ), meridional virtual light source (S m B ), sagittal focusing ray (F s ), meridional condensation ray (F m ) are straight lines, but they may be curved lines.

[0048] Also, in Figure 3, L 1s A >L 1m A >0 and L 2s A>L 2m A Although the case shown is >0, these constants can also be negative. 1s A or L 1m A If L is negative, the beam incident on the first reflecting surface is reflected by the reflecting surface on its way downstream. 2s A or L 2m A When takes a negative value, the beam emitted from the first reflecting surface has a wavefront that appears to diverge from a position upstream of the reflecting surface.

[0049] Similarly, in Figure 4, L 1s B <L 1m B <0 and L 2s B >L 2m B >0. 1s B or L 1m B If L is negative, the beam incident on the second reflecting surface is reflected by the reflecting surface on its way downstream. 2s B or L 2m B When takes a negative value, the beam emitted from the second reflecting surface has a wavefront that appears to diverge from a position upstream of the reflecting surface.

[0050] (Derivation of design formula) By defining the "light source ray" and the "light collecting ray" as above, it is possible to define the incident ray and the outgoing ray that pass through any point on the reflecting surface of the mirror. That is, as shown in FIG. 5(a), if any point on the first reflecting surface is M A As the sagittal light source line (S s ) and M A Intersection point with the incident ray to the point (P s ), and meridional light rays (S m ) and M A Intersection point with the incident ray to the point (P m ) are the coordinates of the L 1sA , L 1m A Similarly, M A Rays emerging from a point and sagittal virtual focusing rays (F s A ) and the intersection point (Q s A ), and M A Rays from a point and meridional virtual focusing rays (F s A ) and the intersection point (Q m A ) are the coordinates of the L 2s A , L 2m A It can be expressed as:

[0051] Also, as shown in FIG. 5(b), an arbitrary point on the second reflecting surface is M B As the sagittal virtual source line (S s B ) and M B Intersection point with the incident ray to the point (P s B ), and meridional virtual light rays (S m B ) and M B Intersection point with the incident ray to the point (P m B ) are the coordinates of the L 2s A , L 2m A , and M0 A M0 B Similarly, the distance L between the B Emanating rays from a point and sagittal focusing rays (F s ) and the intersection point (Q s ), and M B Emitted rays from a point and meridional convergent rays (F m ) and the intersection point (Q m ) are the coordinates of the L 2s B , L 2m B It can be expressed as:

[0052] And these P s , P m, Q s A , Q m A , P s B , P m B , Q s , Q m Based on the fact that the optical path length from the virtual light source position to the focusing position is constant for any point on the reflecting surface for the sagittal focusing and meridional focusing on the first reflecting surface, and the optical path length from the virtual light source position to the focusing position is constant for any point on the reflecting surface for the sagittal focusing and meridional focusing on the second reflecting surface, design equations for the first reflecting surface and the second reflecting surface can be derived.

[0053] Any point M on the first and second reflecting surfaces A , M B is the u A v A w A Cartesian coordinate system, u B v B w B Define the Cartesian coordinate system and A (u A ,v A ,w A ), M B (u B ,v B ,w B ) can be expressed as

[0054] That is, as shown in Figure 6, the Cartesian coordinate system u A v A w A is the intersection point M0 of the z1 and z2 axes on the first reflecting surface. A The surface in contact with the reflecting surface is defined as u A v A Let the plane be u A v A Plane M0 A The direction of the normal passing through w A axis, v A The direction perpendicular to both the z1 and z2 axes, u A Axis vA axis and w A The direction is perpendicular to both axes, and the intersection point M0 A is the origin, u A v A The oblique incidence angle between the plane and the optical axis z1 is θ0 A It was decided.

[0055] Cartesian coordinate system u B v B w B is the intersection point M0 of the z2 axis and the z3 axis on the second reflecting surface. B The surface in contact with the reflecting surface is defined as u B v B Let the plane be u B v B Plane M0 B The direction of the normal passing through w B axis, v B The direction perpendicular to both the z2 and z3 axes, u B Axis v B axis and w B The direction is perpendicular to both axes, and the intersection point M0 B is the origin, u B v B The oblique incidence angle between the plane and the optical axis z2 is θ0 B It was decided.

[0056] However, in FIG. 6, the sagittal light source line (S s ) and meridional light rays (S m ) is u A Note that the sagittal virtual focusing ray (F s A ) and meridional virtual focusing line (F m A ) is perpendicular to the output beam optical axis z2. A v A w AAlthough it is possible to directly calculate the optical path length from the light source line and the virtual focusing line that are set at an angle to the coordinate system, this is complicated. Therefore, in this embodiment, the optical path length is calculated after converting into a coordinate system based on each of the incident beam optical axis and the outgoing beam optical axis, and then substituted into the design formula for the astigmatism control mirror. The same applies to the focusing of the second reflecting surface.

[0057] That is, u A v A w A Coordinate system and u B v B w B The coordinate systems are respectively transformed into an x1y1z1 coordinate system based on the optical axis of the incident beam on the first reflecting surface, an x2y2z2 coordinate system based on the optical axis of the outgoing beam from the first reflecting surface, which is the incident beam on the second reflecting surface, and an x3y3z3 coordinate system based on the optical axis of the outgoing beam from the second reflecting surface, and the design formula is expressed as u A v A w A Coordinate system and u B v B w B Expressed in a coordinate system.

[0058] The transformation to the coordinate system based on the incident beam axis is as follows: Point M on the mirror A The coordinates (x1, y1, z1) are given by equation (5).

[0059]

number

[0060] point M A The incident ray and the sagittal source ray S s Intersection point P s , and also the incident ray and meridional light ray S m Intersection point P m The coordinates of the displacement L are expressed in the x1y1z1 coordinate system. 1s A , L 1m A can be expressed as (6) and (7) below.

[0061]

number

[0062] Similarly, the transformation into a coordinate system based on the optical axis of the output beam at the first reflecting surface is as follows: A (x2 A ,y2 A ,z2 A ) are given by equation (8).

[0063]

number

[0064] Point M on the first reflecting surface A The exit ray passing through and the sagittal virtual focusing ray F s A Intersection point Q s A The coordinates of the exit ray and the meridional virtual focusing ray F m A Intersection point Q m A The coordinates of the displacement L are expressed in the x2y2z2 coordinate system. 2s A , L 2m A Using these, it can be expressed by the following equations (9) and (10).

[0065]

number

[0066] Point M on the mirror B (x2 B ,y2 B ,z2 B ) are given by equation (11).

[0067]

number

[0068] point M B The incident ray and the sagittal virtual source ray S s B Intersection point P s B , and the incident ray and meridional virtual light ray S m B Intersection point P m B The coordinates of the displacement L are expressed in the x2y2z2 coordinate system. 1s B , L 1m B Using these, it can be expressed by the following equations (12) and (13).

[0069]

number

[0070] Similarly, the transformation to a coordinate system based on the optical axis of the output beam at the second reflecting surface is as follows: B The coordinates (x3, y3, z3) are given by equation (14).

[0071]

number

[0072] Point M on the second reflecting surface B The exit ray and the sagittal focusing ray F s Intersection point Q s The coordinates of the exit ray and the meridional focusing ray F m Intersection point Q m The coordinates of the displacement L are expressed in the x3y3z3 coordinate system. 2s B , L 2m B can be expressed as follows (15) and (16).

[0073]

number

[0074] And, as mentioned above, these P s , P m , Q s A , Q m A , P s B , P m B , Q s , Q m A design formula for the reflecting surface is derived based on the fact that the optical path length from the light source position to the virtual focusing position is constant for any point on the reflecting surface for the sagittal focusing and meridional focusing on the first reflecting surface, and the optical path length from the virtual light source position to the focusing position is constant for any point on the reflecting surface for the sagittal focusing and meridional focusing on the second reflecting surface.

[0075] In this embodiment, the intersection points P s , P m , Q s A , Q m A , P s B , P m B , Q s , Q m and any point M on the first / second reflecting surface A , M B The distance between the light source line and the light collecting line is not directly used as the incident length or the exit length, but the following optical path length compensation is performed to obtain a more accurate design formula by using the coordinates of the intersection of the light source line and the collecting line defined by straight lines.

[0076] (Optical path length compensation) Consider Fermat's principle when a normal light source point and a focal point can be defined. The equiphase surface near the light source point is a sphere centered on the light source point, and the equiphase surface near the focal point is a sphere centered on the focal point. Keeping in mind that light rays are always perpendicular to the equiphase surface, the law of constant optical path length can be rephrased as the optical path of a light ray connecting an arbitrary point on a specific equiphase surface near the light source point and a corresponding point on a specific equiphase surface near the focal point is constant. Even when the incident beam contains astigmatism as in the present invention, a more accurate design formula can be derived by performing compensation taking into account the equiphase surface.

[0077] (Compensation of the optical path length on the incident side of the first reflecting surface) First, on the incident side of the first reflecting surface, the sagittal light source line S s The intersection point P mentioned above s Consider the equiphase surface in the vicinity of the sagittal source line S s Now, the meridional light source ray S m Under this assumption, a wavefront converging toward the sagittal source line S s Although it is not possible to define the phase above precisely, we use S m The intersection point with the z1 axis is P m0 Tooki, S s Above is P. m0 There is a phase distribution according to the distance from the mirror. In other words, the beam before entering the mirror (reflecting surface) is a meridional light source line S in the y1-axis direction. m Based on this idea, as shown in Figure 7, the meridional light source line S m and z1 axis intersection point P m0 The sagittal light source line S s and z1 axis intersection point P s0 Circular arc B passing through and extending perpendicular to the x1 axis 1s , the sagittal light source line S s The rotational arc surface formed by rotating around the axis is called the equiphase surface A. 1s The distance from the light source position for sagittal focusing is M A The length of incidence to the point is the incident ray and the equiphase surface A 1s The meridional light ray S is one of the two intersection points withm From the intersection closest to A It is more accurate to calculate it as the distance to a point.

[0078] Here, the incident light and the equiphase surface A 1s From the intersection point with M on the mirror's reflecting surface A The distance to the point is calculated by first calculating the incident ray and the sagittal light source ray S s Intersection point P s From M A The distance to the point is calculated, and the intersection point P is calculated. s From the equiphase surface A 1s The arc B defines 1s The distance to, i.e., P s From arc B 1s The foot of the perpendicular line to H 1s As P s H 1s The distance between the incident length f is calculated by adding or subtracting (subtracting in this example). 1s A is expressed by equation (17). The reason why this equation is an approximation is that point H 1s is the line P s M A However, it is of course possible to use calculations other than these approximate expressions. s From arc B 1s The foot of the perpendicular line to H 1s As P s H 1s The distance between arcs B and C is approximated by adding / subtracting the distance between arcs B and C. 1s P s From the above, the incident light and the equiphase surface A 1s The meridional light ray S is one of the two intersection points with m Alternatively, the distance to the intersection point closer to the center of the intersection may be used for more accurate calculation.

[0079]

number

[0080] To this t' 1xA , t' 1y A By introducing the above, it can be transformed into the following equation (18).

[0081]

number

[0082] Next, on the incident side of the first reflecting surface, the meridional light source ray S m The intersection point P mentioned above m Consider the equiphase surface in the vicinity of the meridional light ray S m Now, the sagittal light source ray S s Under this assumption, we should observe a wavefront diverging from S m Although it is not possible to define the phase above precisely, we use S s The intersection point with the z1 axis is P s0 Tooki, S m Above is P. s0 In other words, before the beam enters the mirror (reflecting surface), it is a sagittal light source line S in the x1-axis direction. s Based on this concept, as shown in Figure 8, the sagittal light source line S s and z1 axis intersection point P s0 The meridional light source line S m and z1 axis intersection point P m0 Circular arc B extends perpendicular to the y1 axis through 1m , the meridional light source ray S m The rotational arc surface formed by rotating around the axis is called the equiphase surface A. 1m From the light source position in the meridional direction, M A The length of incidence to the point is the incident ray and the equiphase surface A 1m Of the two intersections with the sagittal light source line S s From the intersection point closest to A It is calculated as the distance to a point.

[0083] Incident light and equiphase surface A 1m From the intersection with MA The distance to a point is calculated by first calculating the incident ray and the meridional light source ray S m Intersection point P m From M A The distance to the point is calculated, and the intersection point P is calculated. m From the equiphase surface A 1m The arc B defines 1m The distance to, i.e., P m From arc B 1m The foot of the perpendicular line to H 1m As P m H 1m The distance between the incident length f is calculated by adding or subtracting (adding in this example). 1m A is expressed by equation (19).

[0084]

number

[0085] To this t' 1x A , t' 1y A By introducing the above, it can be transformed into the following equation (20).

[0086]

number

[0087] (Compensation of the optical path length on the exit side of the first reflecting surface) On the exit side, as on the entrance side, the sagittal virtual focusing ray F s A Above intersection point Q s A The equiphase surface and meridional virtual focusing line F m A Above intersection point Q m A Consider the equiphase surfaces in the vicinity of the sagittal virtual focusing ray F s A So, the meridional virtual focusing ray F m AUnder this assumption, a diverging wavefront should be virtually observed. s A Although it is not possible to define the phase above precisely, here we use F m A The intersection point of the output optical axis z2 is Q m0 A Toki, F s A Above is Q m0 A It is assumed that there exists a phase distribution according to the distance from the m A Then, the sagittal virtual focusing ray F s A Under this assumption, a wavefront converging toward F m A Although it is not possible to define the above topology precisely, here we use F s A The intersection point of the output optical axis z2 is Q s0 A Tooki, F m A Above is Q s0 A It is assumed that there exists a phase distribution according to the distance from .

[0088] Based on these considerations, a more accurate exit length is calculated, as in the case of the incident side. Specifically, although not shown in the figure, the intersection point Q s A Arc B that defines the equiphase surface from 2s A The distance to, i.e., Q s A From arc B 2s A The foot of the perpendicular line to H 2s A H 2s A Q s A Distance between and intersection point Q m A Arc B that defines the equiphase surface from 2m A The distance to, i.e., Q m A From arc B2m A The foot of the perpendicular line to H 2m A Q m A H 2m A The virtual exit length in the sagittal direction f is calculated by adding or subtracting the distance between the two points as shown in equations (21) and (22). 2s A , the virtual exit length in the meridional direction f 2m A For each of these, a more accurate exit length can be obtained.

[0089]

number

[0090]

number

[0091] f 2s A t' 2x A , t' 2y A By introducing the above, it can be transformed into the following equation (23).

[0092]

number

[0093] f 2m A t' 2x A , t' 2y A By introducing the above, it can be transformed into the following equation (24).

[0094]

number

[0095] (Compensation of the optical path length on the incident side of the second reflecting surface) The incident side of the second reflecting surface has the same sagittal virtual light source ray S s B Above intersection point P s B The equiphase surface and meridional virtual light ray S m B Above intersection point P m B Consider the equiphase surfaces in the vicinity of the sagittal virtual light source ray S s B So, the meridional virtual light source ray S m B Under this assumption, a diverging wavefront should be virtually observed. s B Although it is not possible to define the phase above precisely, we use S m B The intersection point of the incident optical axis z2 is P m0 B Toki, S s B Above is P. m0 B It is assumed that there exists a phase distribution according to the distance from the m B So, the sagittal virtual light source ray S s B Under this assumption, a wavefront converging toward S m B Although it is not possible to define the above topology precisely, we will use S s B The intersection point of the incident optical axis z2 is P s0 B Tooki, S m B Above is P. s0 B It is assumed that there exists a phase distribution according to the distance from .

[0096] Based on these considerations, a more accurate incidence length is calculated. Specifically, although not shown in the figure, the intersection point P s BArc B that defines the equiphase surface from 1s B The distance to, i.e., P s B From arc B 1s B The foot of the perpendicular line to H 1s B H 1s B P s B Distance between and intersection point P m B Arc B that defines the equiphase surface from 1m B The distance to, i.e., P m B From arc B 1m B The foot of the perpendicular line to H 1m B P m B H 1m B The compensation is performed by adding or subtracting the distance between the two points, and the virtual entrance length in the sagittal direction f is calculated as shown in Eqs. (25) and (26). 1s B , the imaginary incidence length in the meridional direction f 1m B For each of these, a more accurate entrance length can be obtained. 2s A >0 and L 2m A >0 when L 1s B <0 and L 1m B <0, and f 1s B < 0 and f 1m B <0.

[0097]

number

[0098]

number

[0099] f 1s B t' 1x B , t' 1y B By introducing the above, it can be transformed into the following equation (27).

[0100]

number

[0101] f 1m B t' 1x B , t' 1y B By introducing the above, it can be transformed into the following equation (28).

[0102]

number

[0103] (Compensation of the optical path length at the exit side of the second reflecting surface) On the exit side, as on the entrance side, the sagittal focusing ray F s Above intersection point Q s The corresponding equiphase surface and meridional focusing line F m Above intersection point Q m Consider the equiphase surfaces in the vicinity of the sagittal focusing ray F s So, the meridional ray F m Under this assumption, we should observe a wavefront emanating from F s Although it is not possible to define the phase above precisely, here we use F m The intersection point of the output optical axis z3 is Q m0 Toki, F s Above is Q m0 It is assumed that there is a phase distribution according to the distance from the m Now, the sagittal focusing ray F s Under this assumption, we should observe a wavefront converging toward F mAlthough it is not possible to define the above topology precisely, here we use F s The intersection point of the output optical axis z3 is Q s0 Tooki, F m Above is Q s0 It is assumed that there exists a phase distribution according to the distance from .

[0104] Based on these considerations, a more accurate exit length is calculated. Specifically, although not shown in the figure, the intersection point Q s Arc B that defines the equiphase surface from 2s B The distance to, i.e., Q s From arc B 2s B The foot of the perpendicular line to H 2s B H 2s B Q s Distance between and intersection point Q m Arc B that defines the equiphase surface from 2m B The distance to, i.e., Q m From arc B 2m B The foot of the perpendicular line to H 2m B Q m H 2m B The compensation is performed by adding or subtracting the distance between the two points, and the sagittal exit length f 2s B , the exit length in the meridional direction f 2m B For each of these, a more accurate entrance length can be obtained.

[0105]

number

[0106]

number

[0107] f 2s B t'2x B , t' 2y B By introducing the above, it can be transformed into the following equation (31).

[0108]

number

[0109] f 2m B t' 2x B , t' 2y B By introducing the above, it can be transformed into the following equation (32).

[0110]

number

[0111] (Calculation of optical path length) Using the entrance length and exit length thus determined, the optical path length for the light collection in each of the sagittal and meridional directions is calculated for each of the first and second reflecting surfaces.

[0112] In the sagittal direction of the first reflecting surface, the reference optical path length from the light source point to the virtual focusing point is L. s A =L 1s A +L 2s A Then, the condition required for focusing in the sagittal direction is derived as follows:

[0113]

number

[0114] Similarly, for the meridional direction of the first reflecting surface, the reference optical path length from the light source point to the virtual focusing point is L m A =L 1m A +L2m A Then, the condition required for focusing in the meridional direction is derived as follows:

[0115]

number

[0116] Similarly, for the sagittal direction of the second reflecting surface, the reference optical path length from the virtual light source point to the focal point is L s B =L 1s B +L 2s B Then, the condition required for focusing in the sagittal direction is derived as follows:

[0117]

number

[0118] Similarly, for the meridional direction of the second reflecting surface, the reference optical path length from the virtual light source point to the focusing point is L m B =L 1m B +L 2m B Then, the condition required for focusing in the meridional direction is derived as follows:

[0119]

number

[0120] Ideally, the first reflecting surface is located at a point (u A ,v A ,w A ) is the desired shape of the reflecting surface. If the solution of such a simultaneous equation is used as the design formula, then "L 1s A =L 1m A And L2s A =L 2m A Similarly, the second reflecting surface is also at a point (u B ,v B ,w B ) is the desired shape of the reflecting surface. If the solution of such a simultaneous equation is used as the design formula, then "L 1s B =L 1m B And L 2s B =L 2m B " It becomes something that is under special conditions such as.

[0121] Therefore, in order to obtain a design formula that represents a more generalized shape of the reflecting surface that can be applied under other conditions, the inventors have weighted the formulas (33) and (34) for the first reflecting surface, and have obtained a new formula f shown in formula (37). A (u A ,v A ,w A ) = 0 is used as the design equation for the reflecting surface. Similarly, for the second reflecting surface, equations (35) and (36) are weighted to obtain the new equation f B (u B ,v B ,w B )=0 was used as the design formula for the reflecting surface.

[0122] (Design formula for the first reflecting surface) That is, the design formula for the first reflecting surface is the first formula (the formula for the sagittal focusing condition) derived from the fact that the optical path length from the light source point to the virtual focusing point is constant for sagittal focusing, f s A (u A ,v A ,w A )=0 (Equation (33)) and the second equation (the meridional focusing condition equation) f m A (uA ,v A ,w A )=0 (Equation (34)) and α A , β A Using the above, the weighted formula f A (u A ,v A ,w A )=0. α A is the weighting factor for the meridional concentration, β A is the weighting factor for sagittal focusing. 0≦α A ≦1, β A =1-α A It is.

[0123]

number

[0124] Equation (37) is the design equation for the first reflecting surface. 1x ,t' 1y ,t' 2x ,t' 2y U A v A w A When rewritten based on the coordinate system, we get the following equations (38) to (41).

[0125]

number

[0126] As can be seen from equation (37), we can confirm that we have obtained an equation with good symmetry for the sagittal and meridional focusing directions. 1s A >L 1m A >0 and L 2s A >L 2m A> 0' has been assumed, but even if this assumption is not made, that is, even if the magnitude relationship is reversed or each setting value takes a negative value, the same equation (design equation) shown in equation (37) can be derived. However, L 1m A , L 1s A , L 2m A , L 2s A All four constants above can be positive or negative and cannot be zero.

[0127] (Design formula for the second reflecting surface) Similarly, the design formula for the second reflecting surface is the first formula (the formula for the sagittal focusing condition) f, which is derived from the fact that the optical path length from the virtual light source point to the focusing point is constant for sagittal focusing. s B (u B ,v B ,w B )=0 (Equation (35)) and the second equation (the meridional focusing condition equation) f m B (u B ,v B ,w B )=0 (Equation (36)) and α B , β B Using the above, the weighted formula f B (u B ,v B ,w B )=0. α B is the weighting factor for the meridional concentration, β B is the weighting factor for sagittal focusing. 0≦α B ≦1, β B =1-α B It is.

[0128]

number

[0129] Equation (42) is the design equation for the second reflecting surface. 1x B ,t' 1y B ,t' 2x B ,t' 2y B U B v B w B When rewritten based on the coordinate system, we get the following equations (43) to (46).

[0130]

number

[0131] As can be seen from equation (42), we can confirm that we have obtained an equation with good symmetry for the sagittal and meridional focusing directions. 1s B <L 1m B <0 and L 2s B >L 2m B > 0' has been assumed, but even if this assumption is not made, that is, even if the magnitude relationship is reversed or the positive and negative of each set value is reversed, the same equation (design equation) shown in equation (42) can be derived. However, L 1m B , L 1s B , L 2m B , L 2s B All four constants above can be positive or negative and cannot be zero.

[0132] (Design equation in common coordinate system (uvw coordinate system)) As mentioned above, A v A w A The design equation of the first reflector expressed in the coordinate system and u B v B w BThe design equations of the second reflecting surface expressed in a coordinate system are expressed in a common uvw coordinate system. That is, each reflecting surface of the mirror of the present invention is expressed in a common coordinate system (u, v, w) as shown in FIG.

[0133] The intersection of the incident beam optical axis z1 and the outgoing beam optical axis z3 is the origin O(0,0,0) of the Cartesian coordinate system uvw. The rotation center of the mirror installation mechanism is also aligned with this point. The intersection of the incident beam optical axis and the first reflecting surface is M0. A , and the intersection point M0 between the output beam optical axis and the second reflecting surface B Let the line M0 A M0 B The longitudinal u-axis is set to be parallel to the θ axis. The transverse v-axis is set to be perpendicular to both the incident beam axis and the outgoing beam axis. The w-axis is perpendicular to both the u-axis and the v-axis.

[0134] Point M0 on the first reflecting surface A The glancing angle at θ0 A and the point M0 on the second reflecting surface B The glancing angle at θ0 B Also, set the line segment M0 A M0 B Set the length of the point M0 as L. A ,M0 B The coordinates of are expressed by the following equations (47) and (48).

[0135]

number

[0136] Longitudinal unit vector e of the first reflecting surface u A , the short-axis unit vector e v A ,Normal direction unit vector e w A are expressed by the following equation (49).

[0137]

number

[0138] Similarly, the longitudinal unit vector e of the second reflecting surface u B , the short-axis unit vector e v B ,Normal direction unit vector e w B are also expressed by the following equation (50).

[0139]

number

[0140] By the above steps, the positions and orientations of the first and second reflecting surfaces are determined in the uvw coordinate system. Next, the entrance and exit lengths required to determine the shape of each reflecting surface are calculated. The cross section of the mirror in the uw plane is shown in Figure 10.

[0141] The entrance length and exit length based on the mirror origin O are defined as L in both the meridional and sagittal directions. 1m , L 1s , L 2m , L 2s The light source line S for the entire mirror is defined as m and S s Since the light must be a light source ray for the first reflecting surface as described above, the incident length L 1m A and L 1s A is determined as shown in the following equations (51) and (52).

[0142]

number

[0143] Similarly, the focal ray F for the entire mirror m and F s is synonymous with the focusing ray for the second reflecting surface. The exit length L 2m B and L 2s A L 2m , L2s Using these, it is expressed as the following equations (53) and (54).

[0144]

number

[0145] For the mirror of the present invention to function properly, the sagittal virtual focusing ray F of the first reflecting surface must be s A is the sagittal virtual source line S of the second reflecting surface s B and the meridional virtual focusing ray F of the first reflecting surface m A is the meridional virtual light source ray S of the second reflecting surface m B Therefore, the meridional incidence length L of the second reflecting surface must be equal to 1m B and the sagittal entrance length L 1s B is the meridional exit length L of the first reflecting surface 2m A and the sagittal exit length L 2s A From this, the following equations (55) and (56) are derived.

[0146]

number

[0147] From the above, the constants required to design the mirror according to the present invention are L 1m , L 1s , L 2m , L 2s , L 2m A ,L 2s A , L, θ0 A ,θ0 B It has been shown that there are nine types of spheres. And, the coordinates (u A ,v A ,w A ) is expressed in the uvw coordinate system as follows:

[0148]

number

[0149] By substituting the above formula (57) into formula (37), the design formula (isosurface) f representing the first reflecting surface is obtained as the following formula (58). A This leads to (u,v,w)=0.

[0150]

number

[0151] Similarly, the coordinates (u B ,v B ,w B ) is expressed in the uvw coordinate system as follows:

[0152]

number

[0153] By substituting the above formula (59) into formula (42), the design formula (isosurface) f representing the second reflecting surface is obtained as the following formula (60). B This leads to (u,v,w)=0.

[0154]

number

[0155] (Examples of mirrors that can be designed) In the condition setting of equation (58) and equation (60), L 1s A and L 1m A Set the value of to different values ​​and 2s B and L 2m BBy setting the values ​​of to the same value, it is possible to design an astigmatism control mirror that can obtain an output beam that is focused to a single point from an input beam with astigmatism by reflecting twice at the first and second reflecting surfaces. 1s A and L 1m A Set the value of to the same value and set L 2s B and L 2m B By setting the value of different values, it is possible to design an astigmatism control mirror that can obtain an astigmatism-bearing output beam from an input beam diverging from a single point. 1m A and L 2m A and L 2m B Set the value of to positive or negative infinity and L 1s A and L 2s A and L 2s B is a given value (where L 1s A +L 2s A ≠0, L 1s B +L 2s B ≠ 0), it is possible to design an astigmatism control mirror that has light-collecting performance only in the sagittal direction.

[0156] Also, L 1s A and L 1m A Match the value of L 2s A and L 2m A The values ​​of are different from each other, and L 1s B and L 1m B The values ​​of L 2s B and L 2m BBy matching the values ​​of , it is possible to design an astigmatism control mirror that imparts astigmatism to an incident beam diverging from a single point at the first reflecting surface and eliminates the astigmatism at the second reflecting surface, thereby providing different reduction ratios in the vertical and horizontal directions.

[0157] Also, L 1s =L 1m = L1, and L 2s =L 2m = L2, and L 2s A =L 2m A =L2 A By setting the light source and focus positions in both the meridional and sagittal directions to coincide, the first reflecting surface A of the mirror is aligned with the light source point S and the virtual focus point F, as shown in Figure 11. A The second reflecting surface B is a virtual focusing point F A It becomes a hyperboloid of revolution (paraboloid of revolution, ellipsoid of revolution) with the focal point F at two foci.

[0158] In addition, for sagittal focusing, the source line S s and z1 axis intersection point P s0 , virtual focusing line F s A and the intersection point Q of the z2 axis S0 A , focusing ray F s and the intersection point Q of the z3 axis s0 The three points are on the same line, and the light source line S is focused in the meridional direction. m and z1 axis intersection point P m0 , virtual focusing line F m A and the intersection point Q of the z2 axis m0 A , focusing ray F m and the intersection point Q of the z3 axis m0 So that the three points of are on the same line, L 2s A and L 2m A By setting L, it is possible to make a mirror that expands the allowable installation angle range. 1s =L 1m , L2s =L 2m , L 2s A =L 2m A By satisfying the above condition, a Wolter type I mirror is formed, as shown in FIG.

[0159] Also, L 2m A and L 2s A By setting the length L of the first reflecting surface, it is possible to design a mirror that controls the vertical to horizontal ratio of the beam size at the focusing point, or the ratio of the vertical to horizontal divergence angles of the focusing beam. 2m A and L 2s A Determine the magnification of the meridional focusing and the sagittal focusing, respectively. The magnification in a focusing optical system is defined as the ratio of the focusing size to the source size. The magnification of the meridional focusing is M m、 The sagittal focusing magnification is M s These are roughly calculated from the ratio of the entrance length and exit length of the optical system as shown in the following formula (3).

[0160]

number

[0161] In the formula, d m S and d m F represents the source size and the focal size in the meridional direction. Also, d s S and d s F express the source size and focal size in the sagittal direction. Equation (3) shows that the overall magnification of the double-reflection mirror can be estimated by the product of the magnification given to the beam by the first reflecting surface and the magnification given to the beam by the second reflecting surface. Here, M m and M s can be negative. For example, L 1m >0 and L1s >0 and L 2m >0 and L 2s >0, L 2m A and L 2s A If you set to a positive value, L 1m B and L 1s B becomes negative, resulting in M m and M. s Both have negative values, but the size of the focused beam does not disappear. The image formed at the focusing position is inverted with respect to the reflecting surface, and the effective magnification that determines the focused size is |M|. The desired magnification M m and M. s L required to obtain 2m and L 2s The requirement is expressed by the following formula (4).

[0162]

number

[0163] This makes it possible, for example, to design a mirror that focuses a beam that diverges from a single point in both the vertical and horizontal directions back to a single point after two reflections, and then circularizes the beam at the focusing point (a mirror that makes the beam circular at the focusing point), or to design a mirror that focuses a beam that diverges from a single point in both the vertical and horizontal directions back to a single point after two reflections, and then circularizes the beam at the divergence point downstream (a mirror that makes the beam circular at the divergence point).

[0164] Finally, we will show the mutual relationships between the x1y1z1 coordinate system, the x2y2z2 coordinate system, and the x3y3z3 coordinate system. Here, the relationships are derived via the above-mentioned uvw coordinate system, but they can be derived without being limited to this. First, the x1y1z1 coordinate system can be expressed by equation (61) using uvw, and from this equation (62) is derived.

[0165]

number

[0166] On the other hand, the x2y2z2 coordinate system can be expressed by the following equation (63) using uvw, and by substituting the above equation (62) into this, equation (64) is obtained.

[0167]

number

[0168] In addition, the x3y3z3 coordinate system can be expressed by equation (65) using uvw, and by substituting the above equation (62) into this, equation (66) is obtained.

[0169]

number

[0170] As described above, the mutual relationships between the x1y1z1 coordinate system, the x2y2z2 coordinate system, and the x3y3z3 coordinate system are expressed by equations (64) and (66).

[0171] Although the embodiment of the present invention has been described above, the present invention is not limited to these examples, and can be embodied in various forms without departing from the scope of the present invention. In this embodiment, the light source line, the condenser line, the virtual light source line, and the virtual condenser line are each treated as a straight line, and the distance between the straight line and the equiphase surface in the vicinity thereof is compensated for, but such compensation is not necessarily required. It is also preferable to determine an arc line or other curved line as the light source line, the condenser line, the virtual light source line, and the virtual condenser line without compensation or by a compensation method or approximation method other than the compensation described above. The positions of the origins of the design equations of the first and second reflecting surfaces may also be different. Of course, coordinate transformation may be performed. EXAMPLES

[0172] (Verification of expansion of installation angle tolerance range) In this invention, for sagittal focusing and meridional focusing, a mirror (called an "installation angle tolerance expanding mirror") is set so that the light source line, virtual focusing line, and intersection points of the focusing line and the optical axes z1, z2, and z3 are collinear, respectively, and is shown to be effective as a mirror that expands the installation angle tolerance range by suppressing the effects of angle errors (gliding angle error, in-plane rotation error, and rotation around the axis).

[0173] Generally, the radius of curvature ρ differs between the sagittal and meridional directions. s , ρ m For a reflecting surface with a design glancing angle of θ0 and incident length of L 1s , L 1m , the exit length is L 2s , L 2m Then, the radius of curvature ρ s , ρ m The response of the exit length to the increment δ of the glancing angle is expressed by equations (69) and (70), which are obtained by partially differentiating equations (67) and (68). Comparing equations (69) and (70), it can be seen that the exit length of meridional focusing and sagittal focusing show different changes in positive and negative directions with respect to the change in the glancing angle.

[0174]

number

[0175] In a mirror that reflects only once, glancing angle error not only shifts the optical axis of the output beam but also generates unwanted astigmatism in the focused beam. Figure 13 shows the position shift of the meridional focusing point Fm and the sagittal focusing point Fs when the glancing angle is increased in the focusing of a spheroidal mirror that focuses light from one point to another. Both focusing points Fm and Fs move away from the reflecting surface from the designed focusing point F, and at the same time, move symmetrically in the optical axis direction.

[0176] In contrast, FIG. 14 is a schematic diagram showing the response of a two-time reflection mirror (integral type) when a glancing angle error is input. AThe glancing angle of the downstream reflecting surface is θ0 B When both reflecting surfaces rotate together, if the glancing angle of the first reflecting surface increases by a small angle δ, the glancing angle of the second reflecting surface decreases by δ. As a result, the angle between the incident optical axis and the outgoing optical axis is 2θ0 A +2θ0 B = constant, and it can be seen that this is an optical system in which the direction of the exit beam is difficult to move. In this case, the exit length of the first reflecting surface responds with a positive / negative inversion in the meridional and sagittal directions as described above. In contrast, at the second reflecting surface, not only does the glancing angle δ become shallower, but the incident lengths in the meridional and sagittal directions also change due to the shift in the focusing position of the first reflecting surface. The exit length L of the entire mirror 2m and L 2s shows the response to the glancing angle error δ as shown in the following equations (71) and (72).

[0177]

number

[0178] Here, when the partial differential coefficient of the exit length with respect to the glancing angle error becomes 0, that is, when the right-hand sides of equations (71) and (72) become 0, the exit length becomes stable regardless of the slight change in the glancing angle. By substituting equations (55) and (56) into equations (71) and (72), the following equations (73) and (74) are obtained. Adding L given by equations (51) to (54), 1m A ,L 1s A ,L 2m B ,L 2s B Substituting the above, the exit length of the first reflecting surface L 2m A ,L 2s A By solving the above equation, the condition for stabilizing the exit length can be obtained, resulting in an optical system that is robust against glancing angle errors.

[0179]

number

[0180] The exit length L2 of the first reflecting surface is derived from the condition that the partial differential coefficient of the exit length with respect to the installation angle is 0, and the condition that the light source line, the virtual light condensing line, and the intersection points of the light condensing line and the optical axis z1, z2, z3 are located on the same straight line for the sagittal direction and the meridional direction, respectively, required by the design of the Wolter type I mirror, which is a type of "installation angle tolerance expansion mirror". A The optimum values ​​of were compared. The calculation conditions are shown in Table 1. The results are shown in Figure 15. This is a comparison of the optimum values ​​of L2 while changing the exit length L2 of the entire reflecting surface. A The optimal values ​​of are calculated and plotted in the graph. The results obtained from both conditions are roughly the same.

[0181] [Table 1]

[0182] Furthermore, a mirror was designed under the condition of a given exit length L2, and the response to glancing angle errors was confirmed. When the exit length L2 = 250 mm, the L2 calculated under the condition of the partial differential coefficient being 0 was A The value of L2 calculated for the Wolter type I mirror is 590.333 mm, and 507.590 mm for the Wolter type I mirror. The mirror was designed using this condition, and ray tracing was used for the calculation. The light beam was emitted uniformly from the light source beam over the entire effective area of ​​the first reflecting surface, and the scattering of the light beam on the designed focusing surface was obtained by calculating the RMS blur radius. The results are shown in Figure 16. Within the range of ±1 mrad, the L2 calculated for the Wolter type I mirror is A It was found that the mirror using the value of is a better design because it suppresses the increase in the focal size due to the glancing angle error.

[0183] The above results are comparisons made under conditions where there is no astigmatism in the design of the incident and exit beams of both the first and second reflecting surfaces. However, even if astigmatism is present in the incident beam, by satisfying the above-mentioned "mirror with expanded installation angle tolerance" condition (three-point collinear condition), a focusing optical system that is robust against installation angle errors can be obtained. Expressed as a design formula, this is L that satisfies the following formulas (75) and (76). 2m A , L 2s A The following will be set:

[0184]

number

[0185] Next, among the above "Installation angle tolerance expansion mirrors", 1s ≠L 1m , L 2s =L 2m , L 2s A ≠L 2m A (Example 1), L 1s =L 1m , L 2s =L 2m , L 2s A =L 2m A This section describes the results of a comparison of the response of the focusing size and position to the installation angle error calculated based on ray tracing for a Wolter type I mirror (Example 2) with the same entrance length and exit length as in Example 1 for focusing in the meridional direction and focusing in the sagittal direction, respectively.

[0186] The design conditions of the mirror in the first embodiment are shown in Table 2. The mirror reflecting surface is a vertical deflection surface, with the meridional direction handling vertical focusing and the sagittal direction handling horizontal focusing. The exit length L of the first reflecting surface 2m A L 1m and L 2m From L 2s AL 1s and L 2s , and are calculated independently so as to satisfy the three-point collinear condition. The arrangement of the optical system is shown in FIG. 17, and the calculated mirror shape is shown in FIG. 18. The first and second reflecting surfaces have concave shapes in both the meridional and sagittal directions. Table 3 shows the design conditions for the Wolter type I mirror of Example 2. Table 4 shows the design conditions for the flat-plate type single-reflection astigmatism control mirror of Comparative Example 1.

[0187] [Table 2]

[0188] [Table 3]

[0189] [Table 4]

[0190] The astigmatism control mirrors of Example 1 and Comparative Example 1 have an incidence length of 20 m in the vertical (meridional) direction and 5 m in the horizontal (sagittal) direction. In contrast, the incidence length of Example 2 (Wolter type I mirror) is 10 m in both the vertical and horizontal directions. The focal points of each mirror of Examples 1 and 2 and Comparative Example 1 are fixed at a position 250 mm from the mirror reference position, and the angle between the optical axis of the incident beam and the optical axis of the outgoing beam is fixed at 40 mrad. The installation angle errors to be input are the pitch (oblique incidence) angle error, the yaw (in-plane rotation) angle error, and the roll (rotation around an axis) angle error. A list of these is shown in FIG. 19.

[0191] The increase in the focal size (RMS value) in the meridional and sagittal directions and the deviation in the focal position were calculated for each of Examples 1 and 2 and Comparative Example 1. The response to the pitch angle error is shown in Fig. 20, the response to the yaw angle error in Fig. 21, and the response to the roll angle error in Fig. 22.

[0192] It can be seen that the installation angle response of Example 1 is almost equivalent to that of Example 2 (Wolter type I mirror), and in particular, the suppression of increase in focused light size due to pitch angle error and yaw angle error is far superior to Comparative Example 1. It can be seen that in sub-μm focusing by Example 1, there is a tolerance range of 100 μrad or more for various installation angle errors.

[0193] (Verification of mirror that circularizes beam intensity 1) Next, a mirror that circularizes the beam at the focusing position (Example 3) will be described. The light source conditions (illumination conditions) are shown in Table 5. It is assumed that the light source size has a ratio of 5 times between the vertical and horizontal directions. In order to circularize the focused beam, the magnification of the reflecting mirror must be given an inverse ratio between the vertical and horizontal directions. The design conditions for Example 3 are shown in Table 6.

[0194] [Table 5]

[0195] [Table 6]

[0196] As can be seen from the table, the mirror of Example 3 is designed to reflect light from a light source located 5 m from the mirror origin horizontally and focus it on a focusing point located 0.5 m away. The longer side is responsible for horizontal focusing, and the shorter side is responsible for vertical focusing. The additional astigmatism that the first reflecting surface (mirror A) imparts to the beam is eliminated by the second reflecting surface (mirror B).

[0197] The mirror shape (height distribution) of Example 3 is shown in Figure 23. The first reflecting surface (mirror A) on the upstream side has a profile that is convex in the longitudinal direction and concave in the lateral direction. The second reflecting surface (mirror B) on the downstream side has a profile that is concave in the longitudinal direction and convex in the lateral direction.

[0198] 24 shows the distribution of light rays at the focal point by ray tracing calculation for the mirror of Example 3. The focal size in the vertical direction is 0.506 μm (σ), and in the horizontal direction is 0.490 μm (σ), and it can be confirmed that the beam is roughly circularized.

[0199] (Verification of mirror that circularizes beam intensity 2) Next, we will explain a mirror that circularizes the beam at the divergence position, that is, a mirror that focuses a beam that diverges from a single point both vertically and horizontally to a single point again after two reflections, and then circularizes the beam at the divergence position further downstream (Example 4). The light source conditions (illumination conditions) are shown in Table 7. It is assumed that the divergence angle has a ratio of 2 in the vertical and horizontal directions. In order to circularize the divergence angle of the focused beam, the magnification of the reflecting mirror must be given the same ratio in the vertical and horizontal directions. The design conditions for Example 4 are shown in Table 8.

[0200] [Table 7]

[0201] [Table 8]

[0202] As can be seen from the table, the mirror of Example 4 is designed to reflect light from a light source located 5 m from the mirror origin horizontally and focus it on a focusing point located 0.5 m away. The longer side is responsible for horizontal focusing, and the shorter side is responsible for vertical focusing. The additional astigmatism that the first reflecting surface (mirror A) imparts to the beam is eliminated by the second reflecting surface (mirror B).

[0203] The mirror shape (height distribution) of Example 4 is shown in Figure 25. The first reflecting surface on the upstream side (mirror A) has a profile that is convex in the longitudinal direction and concave in the lateral direction. The second reflecting surface on the downstream side (mirror B) has a profile that is concave in the longitudinal direction and concave in the lateral direction.

[0204] For the mirror of Example 4, the results of outputting the distribution of light rays at the focal point by ray tracing calculation are shown in Fig. 26(a), and the results of outputting the distribution of light rays at a position 10 m downstream from the focal point are shown in Fig. 26(b). The focal size is less than 1 nm both vertically and horizontally, and it can be seen that the light from the light source, which has no size, is focused to a single point. In addition, the dispersion of the light rays at a position 10 m downstream is 10.201 mm (σ) in the vertical direction and 10.198 mm (σ) in the horizontal direction, and it can be seen that the beam is roughly circularized at the divergence position. [Explanation of symbols]

[0205] A 1st reflective surface B Second reflective surface

Claims

1. A method for designing a mirror having a first reflecting surface and a second reflecting surface from which light is sequentially reflected, comprising the steps of: The optical axis of the beam incident on the first reflecting surface is z １ axis, and the cross section perpendicular to it is x １ y １ A plane is formed. The optical axis of the beam emitted from the first reflecting surface, which becomes the beam incident on the second reflecting surface, is z ２ axis, and the cross section perpendicular to it is x ２ y ２ A plane is formed. The optical axis of the beam emitted from the second reflecting surface is z ３ axis, and the cross section perpendicular to it is x ３ y ３ A plane is formed. x １ axis, x ２ and x ３ The axis is parallel to the sagittal direction of the first and second reflecting surfaces, The incident beam on the first mirror surface is z １ On-axis z １ Axis and z ２ Intersection M of the first reflecting surface with the axis ０ Ａ From Z １ Along the axial direction L １ｓ Ａ A light source for sagittal focusing at a displaced position, and １ The intersection point M on the axis ０ Ａ From Z １ Along the axial direction L １ｍ Ａ A light source for focusing in the meridional direction is provided at the displaced position. The beam emitted from the second reflecting surface has a sagittal focusing angle of z ３ On-axis z ２ Axis and z ３ Intersection point M on the second reflecting surface with the axis ０ Ｂ From Z ３ Along the axial direction L ２ｓ Ｂ The light is focused at a displaced position, and the z ３ The intersection point M on the axis ０ Ｂ From Z ３ Along the axial direction L ２ｍ Ｂ The light is focused at the displaced position, All incident rays via the first reflecting surface pass through the position of the light source in the sagittal focus at x １ Axis and z １ A sagittal light source line extending in a direction perpendicular to both axes and a y line passing through the position of the light source in the convergence in the meridional direction １ Axis and z １ Passing through meridional light rays extending in a direction perpendicular to both axes, All the rays of light emitted from the second reflecting surface pass through the focusing position in the sagittal focusing direction x ３ Axis and z ３ A sagittal focusing line extending in a direction perpendicular to both axes and a meridional focusing line passing through the focusing position in the y direction ３ Axis and z ３ It is assumed that the light passes through a meridional condensing ray extending in a direction perpendicular to both axes, Furthermore, when it is assumed that the beam emitted from the first reflecting surface travels straight without being reflected by the second reflecting surface, the beam is focused in the sagittal direction by z ２ The intersection point M on the axis ０ Ａ From Z ２ Along the axial direction L ２ｓ Ａ The light is focused at a displaced position, and the z ２ The intersection point M on the axis ０ Ａ From Z ２ Along the axial direction L ２ｍ Ａ The light is focused at the displaced position, The light beam emitted from the first reflecting surface passes through the focusing position in the sagittal direction, and reaches a point x ２ Axis and z ２ A sagittal virtual focusing line extending in a direction perpendicular to both axes and a meridional direction focusing line passing through the focusing position ２ Axis and z ２ It is assumed that the light passes through a meridional virtual focusing ray extending in a direction perpendicular to both axes. All incident rays passing through the second reflecting surface intersect, on their extension lines, with the sagittal virtual focusing line in the sagittal direction focusing for the first reflecting surface as a sagittal virtual light source line, and the meridional virtual focusing line in the meridional direction focusing for the first reflecting surface as a meridional virtual light source line, Let any point on the first reflecting surface be M Ａ As the sagittal light source line and M Ａ Intersection of the incident ray to the point, and the meridional light source line and M Ａ The coordinates of the intersection points with the incident ray to the point are １ｓ Ａ , L １ｍ Ａ and the M Ａ The intersection of the outgoing ray from the point and the sagittal virtual focusing ray, and M Ａ The coordinates of the intersections of the outgoing ray from the point and the meridional virtual condensed ray are expressed as ２ｓ Ａ , L ２ｍ Ａ It is expressed using Let any point on the second reflecting surface be M Ｂ As the sagittal virtual light source line and M Ｂ Intersection of the incident ray to the point, and the meridional virtual light source line and M Ｂ The coordinates of the intersection points with the incident ray to the point are ２ｓ Ａ , L ２ｍ Ａ , and M ０ Ａ M ０ Ｂ The distance between the Ｂ The intersection of the outgoing ray from the point and the sagittal convergent ray, and M Ｂ The coordinates of the intersections of the outgoing ray from the point and the meridional condensed ray are expressed as ２ｓ Ｂ , L ２ｍ Ｂ It is expressed using A mirror design method characterized by determining design equations representing the first reflecting surface and the second reflecting surface based on these coordinates, the optical path length from the light source position to the virtual focusing position for any point on the reflecting surface for sagittal focusing and meridional focusing on the first reflecting surface being constant, and the optical path length from the virtual light source position to the focusing position for any point on the reflecting surface for sagittal focusing and meridional focusing on the second reflecting surface being constant.

2. The sagittal light source line and the meridional light source line are respectively defined as y １ A straight line S extending in the axial direction ｓ , x １ A straight line S extending in the axial direction ｍ year, The sagittal virtual condensing line and the meridional virtual condensing line are respectively defined as y ２ A straight line F extending in the axial direction ｓ Ａ , x ２ A straight line F extending in the axial direction ｍ Ａ year, The sagittal virtual light source line and the meridional virtual light source line are respectively defined as the straight line F ｓ Ａ A straight line S that coincides with ｓ Ｂ , the straight line F ｍ Ａ A straight line S that coincides with ｍ Ｂ year, The sagittal condensed ray and the meridional condensed ray are respectively defined as y ３ A straight line F extending in the axial direction ｓ , x ３ A straight line F extending in the axial direction ｍ year, 2. A method for designing a mirror according to claim 1, wherein the optical path length is calculated for the focusing of light in the meridional direction or the focusing of light in the sagittal direction on the first reflecting surface or the second reflecting surface by the following (i) to (iv): (i) Calculation of the optical path length of the sagittal focusing light at the first reflecting surface: M from the light source position for sagittal direction focusing on the first reflecting surface Ａ The length of incidence to the point is the meridional light source line S ｍ and z １ Intersection point P with axis ｍ０ The sagittal light source line S ｓ and z １ Intersection point P with axis ｓ０ Through x １ The arc extending perpendicular to the axis is called the sagittal light source line S ｓ The rotational arc surface rotated around the axis is called equiphase surface A. １ｓ The incident light and the equiphase surface A １ｓ Among the two intersection points with the meridional light source ray S ｍ From the intersection closest to M Ａ Calculate the distance to the point, M for sagittal focusing on the first reflecting surface Ａ The exit length from the point to the virtual focusing position is the meridional virtual focusing line F ｍ Ａ and z ２ Intersection point Q with axis ｍ０ Ａ A virtual sagittal focusing line F ｓ Ａ and z ２ Intersection point Q with axis ｓ０ Ａ Through x ２ The arc extending perpendicular to the axis is called the sagittal virtual focusing line F ｓ Ａ The rotational arc surface rotated around the axis is called equiphase surface A. ２ｓ Ａ The emitted light ray and the equiphase surface A ２ｓ Ａ Among the two intersections with the meridional virtual focusing line F ｍ Ａ From the intersection closest to M Ａ Calculate the distance to the point, In this way, the optical path length for the light collected in the sagittal direction on the first reflecting surface is calculated. (ii) Calculation of the optical path length of the light focused in the meridional direction on the first reflecting surface: M from the light source position for light collection in the meridional direction on the first reflecting surface Ａ The incident length to the point is the sagittal light source line S ｓ and z １ Intersection point P with axis ｓ０ The meridional light source line S ｍ and z １ Intersection point P with axis ｍ０ Through y １ The arc extending in a direction perpendicular to the axis is called the meridional light source line S ｍ The rotational arc surface rotated around the axis is called equiphase surface A. １ｍ The incident light and the equiphase surface A １ｍ Of the two intersections with the sagittal light source line S ｓ From the intersection closest to M Ａ Calculate the distance to the point, M for the light collection in the meridional direction on the first reflecting surface Ａ The exit length from the point to the virtual focusing position is the sagittal virtual focusing line F ｓ Ａ and z ２ Intersection point Q with axis ｓ０ Ａ A meridional virtual focusing line F ｍ Ａ and z ２ Intersection point Q with axis ｍ０ Ａ Through y ２ The arc extending in a direction perpendicular to the axis is called the meridional virtual focusing line F. ｍ Ａ The rotational arc surface rotated around the axis is called equiphase surface A. ２ｍ Ａ The emitted light ray and the equiphase surface A ２ｍ Ａ Of the two intersections with the sagittal virtual focusing line F ｓ Ａ From the intersection closest to M Ａ Calculate the distance to the point, In this way, the optical path length for the light collected in the meridional direction on the first reflecting surface is calculated. (iii) Calculation of the optical path length of the sagittal focusing light at the second reflecting surface: M from the virtual light source position for sagittal direction focusing on the second reflecting surface Ｂ The incident length to the point is the meridional virtual light source ray S ｍ Ｂ and z ２ Intersection point P with axis ｍ０ Ｂ A virtual light source line S ｓ Ｂ and z ２ Intersection point P with axis ｓ０ Ｂ Through x ２ The arc extending perpendicular to the axis is called the sagittal virtual light source line S ｓ Ｂ The rotational arc surface rotated around the axis is called equiphase surface A. １ｓ Ｂ The incident light and the equiphase surface A １ｓ Ｂ Among the two intersections with the meridional virtual light source line S ｍ Ｂ From the intersection closest to M Ｂ Calculate the distance to the point, M for sagittal focusing on the second reflecting surface Ｂ The exit length from the point to the focusing position is the meridional focusing line F ｍ and z ３ Intersection point Q with axis ｍ０ The sagittal focusing line F ｓ and z ３ Intersection point Q with axis ｓ０ Through x ３ The arc extending perpendicular to the axis is called the sagittal focusing line F ｓ The rotational arc surface rotated around the axis is called equiphase surface A. ２ｓ The emitted light ray and the equiphase surface A ２ｓ Of the two intersections with the meridional condensing ray F ｍ From the intersection closest to M Ｂ Calculate the distance to the point, In this way, the optical path length for the light collected in the sagittal direction on the second reflecting surface is calculated. (iv) Calculation of the optical path length of the light focused in the meridional direction on the second reflecting surface: The second reflecting surface is focused in the meridional direction from the virtual light source position M Ｂ The incident length to the point is the sagittal virtual light source line S ｓ Ｂ and z ２ Intersection point P with axis ｓ０ Ｂ A meridional virtual light source line S ｍ Ｂ and z ２ Intersection point P with axis ｍ０ Ｂ Through y ２ The arc extending in a direction perpendicular to the axis is called the meridional virtual light source ray S ｍ Ｂ The rotational arc surface rotated around the axis is called equiphase surface A. １ｍ Ｂ The incident light and the equiphase surface A １ｍ Ｂ Of the two intersections with the sagittal virtual light source line S ｓ Ｂ From the intersection closest to M Ｂ Calculate the distance to the point, M for the light collection in the meridional direction on the second reflecting surface Ｂ The exit length from the point to the focusing position is the sagittal focusing line F ｓ and z ３ Intersection point Q with axis ｓ０ The meridional focusing line F ｍ and z ３ Intersection point Q with axis ｍ０ Through y ３ The arc extending perpendicular to the axis is called the meridional focusing line F. ｍ The rotational arc surface rotated around the axis is called equiphase surface A. ２ｍ The emitted light ray and the equiphase surface A ２ｍ Of the two intersections with the sagittal focusing ray F ｓ From the intersection closest to M Ｂ Calculate the distance to the point, In this way, the optical path length for the light collected in the meridional direction on the second reflecting surface is calculated.

3. Regarding the calculation of the optical path length of (i) (sagittal direction focusing of the first reflecting surface), A surface A having an equal phase to the incident light on the first reflecting surface １ｓ Among the two intersection points with the meridional light source ray S ｍ From the intersection closest to M Ａ The distance to the point is the distance between the incident light ray and the sagittal light source line S ｓ Intersection point P ｓ From the above M Ａ The distance to the point is calculated, and the distance is multiplied by the intersection point P ｓ From the equiphase surface A １ｓ Add or subtract the distance to the arc that defines A surface A having an equal phase to the emitted light beam on the first reflecting surface ２ｓ Ａ Among the two intersections with the meridional virtual focusing line F ｍ Ａ From the intersection closest to M Ａ The distance to the point is the distance between the exit ray and the sagittal virtual focusing ray F ｓ Ａ Intersection Q with ｓ Ａ From the above M Ａ The distance to the point is calculated, and the distance is multiplied by the intersection point Q ｓ Ａ From the equiphase surface A ２ｓ Ａ Add or subtract the distance to the arc that defines Regarding the calculation of the optical path length of (ii) (meridional direction focusing of the first reflecting surface), The incident light beam on the first reflecting surface and the equiphase surface A １ｍ Of the two intersections with the sagittal light source line S ｓ From the intersection closest to M Ａ The distance to the point is the distance between the incident ray and the meridional light source ray S ｍ Intersection point P ｍ From the above M Ａ The distance to the point is calculated, and the distance is multiplied by the intersection point P ｍ From the equiphase surface A １ｍ Add or subtract the distance to the arc that defines The emitted light beam on the first reflecting surface and the equiphase surface A ２ｍ Ａ Of the two intersections with the sagittal virtual focusing line F ｓ Ａ From the intersection closest to M Ａ The distance to the point is the distance between the exit ray and the meridional virtual focusing ray F ｍ Ａ Intersection Q with ｍ Ａ From the above M Ａ The distance to the point is calculated, and the distance is multiplied by the intersection point Q ｍ Ａ From the equiphase surface A ２ｍ Ａ Add or subtract the distance to the arc that defines Regarding the calculation of the optical path length of (iii) (sagittal direction focusing of the second reflecting surface), The incident light beam on the second reflecting surface and the equiphase surface A １ｓ Ｂ Among the two intersections with the meridional virtual light source line S ｍ Ｂ From the intersection closest to M Ｂ The distance to the point is the distance between the incident ray and the sagittal virtual light source ray S ｓ Ｂ Intersection point P ｓ Ｂ From the above M Ｂ The distance to the point is calculated, and the distance is multiplied by the intersection point P ｓ Ｂ From the equiphase surface A １ｓ Ｂ Add or subtract the distance to the arc that defines The emitted light beam and the equiphase surface A on the second reflecting surface ２ｓ Of the two intersections with the meridional condensing ray F ｍ From the intersection closest to M Ｂ The distance to the point is the distance between the exit ray and the sagittal focusing ray F ｓ Intersection Q with ｓ From the above M Ｂ The distance to the point is calculated, and the distance is multiplied by the intersection point Q ｓ From the equiphase surface A ２ｓ Add or subtract the distance to the arc that defines Regarding the calculation of the optical path length of (iv) (meridional direction focusing of the second reflecting surface), The incident light beam on the second reflecting surface and the equiphase surface A １ｍ Ｂ Of the two intersections with the sagittal virtual light source line S ｓ Ｂ From the intersection closest to M Ｂ The distance to the point is the distance between the incident ray and the meridional virtual light source ray S ｍ Ｂ Intersection point P ｍ Ｂ From the above M Ｂ The distance to the point is calculated, and the distance is multiplied by the intersection point P ｍ Ｂ From the equiphase surface A １ｍ Ｂ Add or subtract the distance to the arc that defines The emitted light beam and the equiphase surface A on the second reflecting surface ２ｍ Of the two intersections with the sagittal focusing ray F ｓ From the intersection closest to M Ｂ The distance to the point is the distance between the emitted ray and the meridional convergent ray F ｍ Intersection Q with ｍ From the above M Ｂ The distance to the point is calculated, and the distance is multiplied by the intersection point Q ｍ From the equiphase surface A ２ｍ Add or subtract the distance to the arc that defines 3. The method for designing a mirror according to claim 2.

4. Z １ Axis and z ３ The intersection of the axes is the origin, Z ２ The direction parallel to the axis is the u axis, x １ axis, x ２ axis and x ３ The direction parallel to the axis is the v axis, Define an orthogonal coordinate system uvw with the w axis perpendicular to both the u axis and the v axis, The uvw coordinate system is expressed as x １ y １ Z １ Coordinate system, x , which is based on the optical axis of the exit beam from the first reflecting surface, which is the incident beam on the second reflecting surface ２ y ２ Z ２ coordinate system and the optical axis of the exit beam from the second reflecting surface as a reference x ３ y ３ Z ３ Transform each into a coordinate system, The design equation is expressed in a uvw coordinate system. The method for designing a mirror according to any one of claims 1 to 3.

5. Z １ Axis and z ２ Intersection point M of the axis on the first reflecting surface ０ Ａ and the surface in contact with the reflecting surface is u Ａ v Ａ Let us assume that the plane is u Ａ v Ａ The plane M ０ Ａ The direction of the normal passing through Ａ axis, v Ａ Axis z １ axis and z ２ A direction perpendicular to both axes, u Ａ Axis v Ａ Axis and w Ａ The direction is perpendicular to both axes, and the intersection point M ０ Ａ is the origin, u Ａ v Ａ Plane and optical axis z １ The oblique incidence angle between ０ Ａ The orthogonal coordinate system u Ａ v Ａ W Ａ Define Z ２ Axis and z ３ Intersection point M of the axis on the second reflecting surface ０ Ｂ and the surface in contact with the reflecting surface is u Ｂ v Ｂ Let us assume that the plane is u Ｂ v Ｂ The plane M ０ Ｂ The direction of the normal passing through Ｂ axis, v Ｂ Axis z ２ axis and z ３ A direction perpendicular to both axes, u Ｂ Axis v Ｂ Axis and w Ｂ The direction is perpendicular to both axes, and the intersection point M ０ Ｂ is the origin, u Ｂ v Ｂ Plane and optical axis z ２ The oblique incidence angle between ０ Ｂ The orthogonal coordinate system u Ｂ v Ｂ W Ｂ Define Said u Ａ v Ａ W Ａ Coordinate system and u Ｂ v Ｂ W Ｂ The coordinate system is defined as x １ y １ Z １ Coordinate system, x , which is based on the optical axis of the exit beam from the first reflecting surface, which is the incident beam on the second reflecting surface ２ y ２ Z ２ coordinate system and the optical axis of the exit beam from the second reflecting surface as a reference x ３ y ３ Z ３ Convert to the coordinate system, The design formula is Ａ v Ａ W Ａ Coordinate system and u Ｂ v Ｂ W Ｂ Expressed in the coordinate system, This is further expressed in the uvw coordinate system:

5. The method for designing a mirror according to claim 4.

6. The design formula is The first formula f is derived from the fact that the optical path length from the light source point to the virtual focusing point is constant for the focusing in the sagittal direction on the first reflecting surface. ｓ Ａ (u A , v A , w A )=0, and the optical path length from the light source point to the virtual light collecting point is constant for the light collecting in the meridional direction on the first reflecting surface. ｍ Ａ (u A , v A , w A ) = 0, the following formula (1) A third formula f is derived from the fact that the optical path length from the virtual light source point to the light collection point is constant for the light collection in the sagittal direction on the second reflecting surface. ｓ Ｂ (u B , v B , w B )=0, and the optical path length from the virtual light source point to the light collection point is constant for the light collection in the meridional direction on the second reflecting surface. ｍ Ｂ (u B , v B , w B 6. The method for designing a mirror according to claim 5, comprising the following equation (2) with weighting: [0010]

7. According to the following formula, the light source line S ｓ From the focused ray F ｓ Any magnification M for sagittal focusing up to ｓ and the light source line S ｍ From the focused ray F ｍ Any magnification M for meridional focusing up to ｍ Using L ２ｍ Ａ , L ２ｓ Ａ The method for designing a mirror according to any one of claims 1 to 6, further comprising setting [0025]

8. The optical axis of the beam incident on the first reflecting surface is defined as the z 1 axis, and the cross section perpendicular to the z 1 axis is defined as the x 1 y 1 plane, The optical axis of the output beam from the first reflecting surface, which becomes the incident beam on the second reflecting surface, is defined as the z 2 axis, and a cross section perpendicular to the z 2 axis is defined as the x 2 y 2 plane, The optical axis of the beam emitted from the second reflecting surface is defined as the z 3 axis, and a cross section perpendicular to the z 3 axis is defined as the x 3 y 3 plane, The x 1 , x 2 and x 3 axes are assumed to be parallel to the sagittal directions of the first and second reflecting surfaces, a light source for focusing a beam incident on the first opposite surface in a sagittal direction is located at a position displaced by L 1s A along the z 1 axis direction from an intersection M 0 A on the z 1 axis of the z 1 axis and the z 2 axis on the first reflecting surface, and a light source for focusing a beam in a meridional direction is located at a position displaced by L 1m A along the z 1 axis direction from the intersection M 0 A on the z 1 axis; the outgoing beam from the second reflecting surface is focused at a position displaced by L 2s B along the z 3 axis direction from an intersection M 0 B on the z 3 axis between the z 2 axis and the z 3 axis on the second reflecting surface in the sagittal direction, and is focused at a position displaced by L 2m B along the z 3 axis direction from the intersection M 0 B on the z 3 axis in the meridional direction; All incident light rays passing through the first reflecting surface pass through a sagittal light source line passing through the position of the light source in the sagittal direction focusing and extending in a direction perpendicular to both the x 1 axis and the z 1 axis, and a meridional light source line passing through the position of the light source in the meridional direction focusing and extending in a direction perpendicular to both the y 1 axis and the z 1 axis; All of the light rays emitted from the second reflecting surface pass through a sagittal focusing line that passes through the focusing position in the sagittal direction and extends in a direction perpendicular to both the x 3 axis and the z 3 axis, and a meridional focusing line that passes through the focusing position in the meridional direction and extends in a direction perpendicular to both the y 3 axis and the z 3 axis, Furthermore, assuming that the exit beam from the first reflecting surface travels straight without being reflected by the second reflecting surface, the exit beam is focused in the sagittal direction at a position displaced by L 2s A from the intersection point M 0 A on the z 2 axis along the z 2 axis direction, and is focused in the meridional direction at a position displaced by L 2m A from the intersection point M 0 A on the z 2 axis along the z 2 axis direction, The light beam emitted from the first reflecting surface passes through a sagittal virtual focusing line that passes through the focusing position in the sagittal direction and extends in a direction perpendicular to both the x 2 axis and the z 2 axis, and a meridional virtual focusing line that passes through the focusing position in the meridional direction and extends in a direction perpendicular to both the y 2 axis and the z 2 axis; All incident rays passing through the second reflecting surface intersect, on their extension lines, with the sagittal virtual focusing line in the sagittal direction focusing for the first reflecting surface as a sagittal virtual light source line, and the meridional virtual focusing line in the meridional direction focusing for the first reflecting surface as a meridional virtual light source line, A surface including an intersection M 0 A of the z 1 axis and the z 2 axis on the first reflecting surface and tangent to the reflecting surface is defined as a u A v A plane, a direction of a normal to the u A v A plane passing through the M 0 A is defined as a w A axis, the v A axis is defined as a direction perpendicular to both the z 1 axis and the z 2 axis, the u A axis is defined as a direction perpendicular to both the v A axis and the w A axis, the intersection M 0 A is defined as the origin, and the oblique incidence angle between the u A v A plane and the optical axis z 1 is defined as θ 0 A , Let the surface including the intersection M 0 B of the z 2 axis and the z 3 axis on the second reflecting surface be the u B v B plane, the direction of the normal to the u B v B plane passing through M 0 B be the w B axis, the v B axis be a direction perpendicular to both the z 2 axis and the z 3 axis, the u B axis be a direction perpendicular to both the v B axis and the w B axis, the intersection M 0 B be the origin, and the oblique incidence angle between the u B v B plane and the optical axis z 2 be θ 0 B , a first reflecting surface expressed by the following formula (37) (wherein t'1xA, t'1yA, t'2xA, and t'2yA are the following formulas (38) to (41) respectively) and a second reflecting surface expressed by the following formula (42) (wherein t'1xB, t'1yB, t'2xB, and t'2yB are the following formulas (43) to (46) respectively), Said L １ｓ Ａ and L １ｍ Ａ The values ​​of L are different. ２ｓ Ｂ and L ２ｍ Ｂ The reflecting surface has a first reflecting surface and a second reflecting surface, and An astigmatism control mirror that can obtain an output beam that is focused to a single point from an input beam that has astigmatism. [0030] [0045] [0050] [006]

9. The optical axis of the beam incident on the first reflecting surface is defined as the z 1 axis, and the cross section perpendicular to the z 1 axis is defined as the x 1 y 1 plane, The optical axis of the output beam from the first reflecting surface, which becomes the incident beam on the second reflecting surface, is defined as the z 2 axis, and a cross section perpendicular to the z 2 axis is defined as the x 2 y 2 plane, The optical axis of the beam emitted from the second reflecting surface is defined as the z 3 axis, and a cross section perpendicular to the z 3 axis is defined as the x 3 y 3 plane, The x 1 , x 2 and x 3 axes are assumed to be parallel to the sagittal directions of the first and second reflecting surfaces, a light source for focusing a beam incident on the first opposite surface in a sagittal direction is located at a position displaced by L 1s A along the z 1 axis direction from an intersection M 0 A on the z 1 axis of the z 1 axis and the z 2 axis on the first reflecting surface, and a light source for focusing a beam in a meridional direction is located at a position displaced by L 1m A along the z 1 axis direction from the intersection M 0 A on the z 1 axis; the outgoing beam from the second reflecting surface is focused at a position displaced by L 2s B along the z 3 axis direction from an intersection M 0 B on the z 3 axis between the z 2 axis and the z 3 axis on the second reflecting surface in the sagittal direction, and is focused at a position displaced by L 2m B along the z 3 axis direction from the intersection M 0 B on the z 3 axis in the meridional direction; All incident light rays passing through the first reflecting surface pass through a sagittal light source line passing through the position of the light source in the sagittal direction focusing and extending in a direction perpendicular to both the x 1 axis and the z 1 axis, and a meridional light source line passing through the position of the light source in the meridional direction focusing and extending in a direction perpendicular to both the y 1 axis and the z 1 axis; All of the light rays emitted from the second reflecting surface pass through a sagittal focusing line that passes through the focusing position in the sagittal direction and extends in a direction perpendicular to both the x 3 axis and the z 3 axis, and a meridional focusing line that passes through the focusing position in the meridional direction and extends in a direction perpendicular to both the y 3 axis and the z 3 axis, Furthermore, assuming that the exit beam from the first reflecting surface travels straight without being reflected by the second reflecting surface, the exit beam is focused in the sagittal direction at a position displaced by L 2s A from the intersection point M 0 A on the z 2 axis along the z 2 axis direction, and is focused in the meridional direction at a position displaced by L 2m A from the intersection point M 0 A on the z 2 axis along the z 2 axis direction, The light beam emitted from the first reflecting surface passes through a sagittal virtual focusing line that passes through the focusing position in the sagittal direction and extends in a direction perpendicular to both the x 2 axis and the z 2 axis, and a meridional virtual focusing line that passes through the focusing position in the meridional direction and extends in a direction perpendicular to both the y 2 axis and the z 2 axis; All incident rays passing through the second reflecting surface intersect, on their extension lines, with the sagittal virtual focusing line in the sagittal direction focusing for the first reflecting surface as a sagittal virtual light source line, and the meridional virtual focusing line in the meridional direction focusing for the first reflecting surface as a meridional virtual light source line, A surface including an intersection M 0 A of the z 1 axis and the z 2 axis on the first reflecting surface and tangent to the reflecting surface is defined as a u A v A plane, a direction of a normal to the u A v A plane passing through the M 0 A is defined as a w A axis, the v A axis is defined as a direction perpendicular to both the z 1 axis and the z 2 axis, the u A axis is defined as a direction perpendicular to both the v A axis and the w A axis, the intersection M 0 A is defined as the origin, and the oblique incidence angle between the u A v A plane and the optical axis z 1 is defined as θ 0 A , Let the surface including the intersection M 0 B of the z 2 axis and the z 3 axis on the second reflecting surface be the u B v B plane, the direction of the normal to the u B v B plane passing through M 0 B be the w B axis, the v B axis be a direction perpendicular to both the z 2 axis and the z 3 axis, the u B axis be a direction perpendicular to both the v B axis and the w B axis, the intersection M 0 B be the origin, and the oblique incidence angle between the u B v B plane and the optical axis z 2 be θ 0 B , a first reflecting surface expressed by the following formula (37) (wherein t'1xA, t'1yA, t'2xA, and t'2yA are the following formulas (38) to (41) respectively) and a second reflecting surface expressed by the following formula (42) (wherein t'1xB, t'1yB, t'2xB, and t'2yB are the following formulas (43) to (46) respectively), Said L １ｓ Ａ and L １ｍ Ａ The values ​​of are the same, and the L ２ｓ Ｂ and L ２ｍ Ｂ The first and second reflecting surfaces have different values ​​of An astigmatism control mirror that produces an astigmatism-bearing output beam from an input beam diverging from a single point. [0070] [0080] [0097] [0010]

10. The optical axis of the beam incident on the first reflecting surface is defined as the z 1 axis, and the cross section perpendicular to the z 1 axis is defined as the x 1 y 1 plane, The optical axis of the output beam from the first reflecting surface, which becomes the incident beam on the second reflecting surface, is defined as the z 2 axis, and a cross section perpendicular to the z 2 axis is defined as the x 2 y 2 plane, The optical axis of the beam emitted from the second reflecting surface is defined as the z 3 axis, and a cross section perpendicular to the z 3 axis is defined as the x 3 y 3 plane, The x 1 , x 2 and x 3 axes are assumed to be parallel to the sagittal directions of the first and second reflecting surfaces, a light source for focusing a beam incident on the first opposite surface in a sagittal direction is located at a position displaced by L 1s A along the z 1 axis direction from an intersection M 0 A on the z 1 axis of the z 1 axis and the z 2 axis on the first reflecting surface, and a light source for focusing a beam in a meridional direction is located at a position displaced by L 1m A along the z 1 axis direction from the intersection M 0 A on the z 1 axis; the outgoing beam from the second reflecting surface is focused at a position displaced by L 2s B along the z 3 axis direction from an intersection M 0 B on the z 3 axis between the z 2 axis and the z 3 axis on the second reflecting surface in the sagittal direction, and is focused at a position displaced by L 2m B along the z 3 axis direction from the intersection M 0 B on the z 3 axis in the meridional direction; All incident light rays passing through the first reflecting surface pass through a sagittal light source line passing through the position of the light source in the sagittal direction focusing and extending in a direction perpendicular to both the x 1 axis and the z 1 axis, and a meridional light source line passing through the position of the light source in the meridional direction focusing and extending in a direction perpendicular to both the y 1 axis and the z 1 axis; All of the light rays emitted from the second reflecting surface pass through a sagittal focusing line that passes through the focusing position in the sagittal direction and extends in a direction perpendicular to both the x 3 axis and the z 3 axis, and a meridional focusing line that passes through the focusing position in the meridional direction and extends in a direction perpendicular to both the y 3 axis and the z 3 axis, Furthermore, assuming that the exit beam from the first reflecting surface travels straight without being reflected by the second reflecting surface, the exit beam is focused in the sagittal direction at a position displaced by L 2s A from the intersection point M 0 A on the z 2 axis along the z 2 axis direction, and is focused in the meridional direction at a position displaced by L 2m A from the intersection point M 0 A on the z 2 axis along the z 2 axis direction, The light beam emitted from the first reflecting surface passes through a sagittal virtual focusing line that passes through the focusing position in the sagittal direction and extends in a direction perpendicular to both the x 2 axis and the z 2 axis, and a meridional virtual focusing line that passes through the focusing position in the meridional direction and extends in a direction perpendicular to both the y 2 axis and the z 2 axis; All incident rays passing through the second reflecting surface intersect, on their extension lines, with the sagittal virtual focusing line in the sagittal direction focusing for the first reflecting surface as a sagittal virtual light source line, and the meridional virtual focusing line in the meridional direction focusing for the first reflecting surface as a meridional virtual light source line, A surface including an intersection M 0 A of the z 1 axis and the z 2 axis on the first reflecting surface and tangent to the reflecting surface is defined as a u A v A plane, a direction of a normal to the u A v A plane passing through the M 0 A is defined as a w A axis, the v A axis is defined as a direction perpendicular to both the z 1 axis and the z 2 axis, the u A axis is defined as a direction perpendicular to both the v A axis and the w A axis, the intersection M 0 A is defined as the origin, and the oblique incidence angle between the u A v A plane and the optical axis z 1 is defined as θ 0 A , Let the surface including the intersection M 0 B of the z 2 axis and the z 3 axis on the second reflecting surface be the u B v B plane, the direction of the normal to the u B v B plane passing through M 0 B be the w B axis, the v B axis be a direction perpendicular to both the z 2 axis and the z 3 axis, the u B axis be a direction perpendicular to both the v B axis and the w B axis, the intersection M 0 B be the origin, and the oblique incidence angle between the u B v B plane and the optical axis z 2 be θ 0 B , a first reflecting surface expressed by the following formula (37) (wherein t'1xA, t'1yA, t'2xA, and t'2yA are the following formulas (38) to (41) respectively) and a second reflecting surface expressed by the following formula (42) (wherein t'1xB, t'1yB, t'2xB, and t'2yB are the following formulas (43) to (46) respectively), Said L １ｓ Ａ and L １ｍ Ａ The values ​​of match, Said L ２ｓ Ａ and L ２ｍ Ａ The values ​​of are different, And the L ２ｓ Ｂ and L ２ｍ Ｂ The reflecting surface has a first reflecting surface and a second reflecting surface, and An astigmatism control mirror that imparts astigmatism to an incident beam diverging from a single point at a first reflecting surface and eliminates the astigmatism at a second reflecting surface, thereby providing different reduction magnifications in the vertical and horizontal directions. ##EQU00011## ##EQU00012## ##EQU00013## ##EQU14##

11. The optical axis of the beam incident on the first reflecting surface is defined as the z 1 axis, and the cross section perpendicular to the z 1 axis is defined as the x 1 y 1 plane, The optical axis of the output beam from the first reflecting surface, which becomes the incident beam on the second reflecting surface, is defined as the z 2 axis, and a cross section perpendicular to the z 2 axis is defined as the x 2 y 2 plane, The optical axis of the beam emitted from the second reflecting surface is defined as the z 3 axis, and a cross section perpendicular to the z 3 axis is defined as the x 3 y 3 plane, The x 1 , x 2 and x 3 axes are assumed to be parallel to the sagittal directions of the first and second reflecting surfaces, a light source for focusing a beam incident on the first opposite surface in a sagittal direction is located at a position displaced by L 1s A along the z 1 axis direction from an intersection M 0 A on the z 1 axis of the z 1 axis and the z 2 axis on the first reflecting surface, and a light source for focusing a beam in a meridional direction is located at a position displaced by L 1m A along the z 1 axis direction from the intersection M 0 A on the z 1 axis; the outgoing beam from the second reflecting surface is focused at a position displaced by L 2s B along the z 3 axis direction from an intersection M 0 B on the z 3 axis between the z 2 axis and the z 3 axis on the second reflecting surface in the sagittal direction, and is focused at a position displaced by L 2m B along the z 3 axis direction from the intersection M 0 B on the z 3 axis in the meridional direction; All incident light rays passing through the first reflecting surface pass through a sagittal light source line passing through the position of the light source in the sagittal direction focusing and extending in a direction perpendicular to both the x 1 axis and the z 1 axis, and a meridional light source line passing through the position of the light source in the meridional direction focusing and extending in a direction perpendicular to both the y 1 axis and the z 1 axis; All of the light rays emitted from the second reflecting surface pass through a sagittal focusing line that passes through the focusing position in the sagittal direction and extends in a direction perpendicular to both the x 3 axis and the z 3 axis, and a meridional focusing line that passes through the focusing position in the meridional direction and extends in a direction perpendicular to both the y 3 axis and the z 3 axis, Furthermore, assuming that the exit beam from the first reflecting surface travels straight without being reflected by the second reflecting surface, the exit beam is focused in the sagittal direction at a position displaced by L 2s A from the intersection point M 0 A on the z 2 axis along the z 2 axis direction, and is focused in the meridional direction at a position displaced by L 2m A from the intersection point M 0 A on the z 2 axis along the z 2 axis direction, The light beam emitted from the first reflecting surface passes through a sagittal virtual focusing line that passes through the focusing position in the sagittal direction and extends in a direction perpendicular to both the x 2 axis and the z 2 axis, and a meridional virtual focusing line that passes through the focusing position in the meridional direction and extends in a direction perpendicular to both the y 2 axis and the z 2 axis; All incident rays passing through the second reflecting surface intersect, on their extension lines, with the sagittal virtual focusing line in the sagittal direction focusing for the first reflecting surface as a sagittal virtual light source line, and the meridional virtual focusing line in the meridional direction focusing for the first reflecting surface as a meridional virtual light source line, A surface including an intersection M 0 A of the z 1 axis and the z 2 axis on the first reflecting surface and tangent to the reflecting surface is defined as a u A v A plane, a direction of a normal to the u A v A plane passing through the M 0 A is defined as a w A axis, the v A axis is defined as a direction perpendicular to both the z 1 axis and the z 2 axis, the u A axis is defined as a direction perpendicular to both the v A axis and the w A axis, the intersection M 0 A is defined as the origin, and the oblique incidence angle between the u A v A plane and the optical axis z 1 is defined as θ 0 A , Let the surface including the intersection M 0 B of the z 2 axis and the z 3 axis on the second reflecting surface be the u B v B plane, the direction of the normal to the u B v B plane passing through M 0 B be the w B axis, the v B axis be a direction perpendicular to both the z 2 axis and the z 3 axis, the u B axis be a direction perpendicular to both the v B axis and the w B axis, the intersection M 0 B be the origin, and the oblique incidence angle between the u B v B plane and the optical axis z 2 be θ 0 B , a first reflecting surface expressed by the following formula (37) (wherein t'1xA, t'1yA, t'2xA, and t'2yA are the following formulas (38) to (41) respectively) and a second reflecting surface expressed by the following formula (42) (wherein t'1xB, t'1yB, t'2xB, and t'2yB are the following formulas (43) to (46) respectively), The magnification of the beam from the light source line to the focusing line is the sagittal magnification M defined by the following formula (3): ｓ , and the meridional magnification M ｍ According to the formula (4) using L ２ｍ Ａ , L ２ｓ Ａ and a first reflecting surface and a second reflecting surface, An astigmatism control mirror designed to focus a beam that diverges both vertically and horizontally from a single point onto a single point again through two reflections, so that the beam becomes circular at the focusing point or at the divergence point further downstream. ##EQU00015## ##EQU00016## ##EQU00017## [0018] [0019] [0020]

12. The optical axis of the beam incident on the first reflecting surface is defined as the z 1 axis, and the cross section perpendicular to the z 1 axis is defined as the x 1 y 1 plane, The optical axis of the output beam from the first reflecting surface, which becomes the incident beam on the second reflecting surface, is defined as the z 2 axis, and a cross section perpendicular to the z 2 axis is defined as the x 2 y 2 plane, The optical axis of the beam emitted from the second reflecting surface is defined as the z 3 axis, and a cross section perpendicular to the z 3 axis is defined as the x 3 y 3 plane, The x 1 , x 2 and x 3 axes are assumed to be parallel to the sagittal directions of the first and second reflecting surfaces, a light source for focusing a beam incident on the first opposite surface in a sagittal direction is located at a position displaced by L 1s A along the z 1 axis direction from an intersection M 0 A on the z 1 axis of the z 1 axis and the z 2 axis on the first reflecting surface, and a light source for focusing a beam in a meridional direction is located at a position displaced by L 1m A along the z 1 axis direction from the intersection M 0 A on the z 1 axis; the outgoing beam from the second reflecting surface is focused at a position displaced by L 2s B along the z 3 axis direction from an intersection M 0 B on the z 3 axis between the z 2 axis and the z 3 axis on the second reflecting surface in the sagittal direction, and is focused at a position displaced by L 2m B along the z 3 axis direction from the intersection M 0 B on the z 3 axis in the meridional direction; All incident light rays passing through the first reflecting surface pass through a sagittal light source line passing through the position of the light source in the sagittal direction focusing and extending in a direction perpendicular to both the x 1 axis and the z 1 axis, and a meridional light source line passing through the position of the light source in the meridional direction focusing and extending in a direction perpendicular to both the y 1 axis and the z 1 axis; All of the light rays emitted from the second reflecting surface pass through a sagittal focusing line that passes through the focusing position in the sagittal direction and extends in a direction perpendicular to both the x 3 axis and the z 3 axis, and a meridional focusing line that passes through the focusing position in the meridional direction and extends in a direction perpendicular to both the y 3 axis and the z 3 axis, Furthermore, assuming that the exit beam from the first reflecting surface travels straight without being reflected by the second reflecting surface, the exit beam is focused in the sagittal direction at a position displaced by L 2s A from the intersection point M 0 A on the z 2 axis along the z 2 axis direction, and is focused in the meridional direction at a position displaced by L 2m A from the intersection point M 0 A on the z 2 axis along the z 2 axis direction, The light beam emitted from the first reflecting surface passes through a sagittal virtual focusing line that passes through the focusing position in the sagittal direction and extends in a direction perpendicular to both the x 2 axis and the z 2 axis, and a meridional virtual focusing line that passes through the focusing position in the meridional direction and extends in a direction perpendicular to both the y 2 axis and the z 2 axis; All incident rays passing through the second reflecting surface intersect, on their extension lines, with the sagittal virtual focusing line in the sagittal direction focusing for the first reflecting surface as a sagittal virtual light source line, and the meridional virtual focusing line in the meridional direction focusing for the first reflecting surface as a meridional virtual light source line, A surface including an intersection M 0 A of the z 1 axis and the z 2 axis on the first reflecting surface and tangent to the reflecting surface is defined as a u A v A plane, a direction of a normal to the u A v A plane passing through the M 0 A is defined as a w A axis, the v A axis is defined as a direction perpendicular to both the z 1 axis and the z 2 axis, the u A axis is defined as a direction perpendicular to both the v A axis and the w A axis, the intersection M 0 A is defined as the origin, and the oblique incidence angle between the u A v A plane and the optical axis z 1 is defined as θ 0 A , Let the surface including the intersection M 0 B of the z 2 axis and the z 3 axis on the second reflecting surface be the u B v B plane, the direction of the normal to the u B v B plane passing through M 0 B be the w B axis, the v B axis be a direction perpendicular to both the z 2 axis and the z 3 axis, the u B axis be a direction perpendicular to both the v B axis and the w B axis, the intersection M 0 B be the origin, and the oblique incidence angle between the u B v B plane and the optical axis z 2 be θ 0 B , a first reflecting surface expressed by the following formula (37) (wherein t'1xA, t'1yA, t'2xA, and t'2yA are the following formulas (38) to (41) respectively) and a second reflecting surface expressed by the following formula (42) (wherein t'1xB, t'1yB, t'2xB, and t'2yB are the following formulas (43) to (46) respectively), Said L １ｍ Ａ and L ２ｍ Ａ and L ２ｍ Ｂ The value of L is positive or negative infinity, and １ｓ Ａ and L ２ｓ Ａ and L ２ｓ Ｂ is a predetermined value (where L １ｓ Ａ +L ２ｓ Ａ ≠0 and (LL ２ｓ Ａ ) + L ２ｓ Ｂ ≠0), An astigmatism controlled mirror that has focusing performance only in the sagittal direction. ##EQU00021## [0022] [0023] ##EQU00024##

13. The optical axis of the beam incident on the first reflecting surface is defined as the z 1 axis, and the cross section perpendicular to the z 1 axis is defined as the x 1 y 1 plane, The optical axis of the output beam from the first reflecting surface, which becomes the incident beam on the second reflecting surface, is defined as the z 2 axis, and a cross section perpendicular to the z 2 axis is defined as the x 2 y 2 plane, The optical axis of the beam emitted from the second reflecting surface is defined as the z 3 axis, and a cross section perpendicular to the z 3 axis is defined as the x 3 y 3 plane, The x 1 , x 2 and x 3 axes are assumed to be parallel to the sagittal directions of the first and second reflecting surfaces, a light source for focusing a beam incident on the first opposite surface in a sagittal direction is located at a position displaced by L 1s A along the z 1 axis direction from an intersection M 0 A on the z 1 axis of the z 1 axis and the z 2 axis on the first reflecting surface, and a light source for focusing a beam in a meridional direction is located at a position displaced by L 1m A along the z 1 axis direction from the intersection M 0 A on the z 1 axis; the outgoing beam from the second reflecting surface is focused at a position displaced by L 2s B along the z 3 axis direction from an intersection M 0 B on the z 3 axis between the z 2 axis and the z 3 axis on the second reflecting surface in the sagittal direction, and is focused at a position displaced by L 2m B along the z 3 axis direction from the intersection M 0 B on the z 3 axis in the meridional direction; All incident light rays passing through the first reflecting surface pass through a sagittal light source line passing through the position of the light source in the sagittal direction focusing and extending in a direction perpendicular to both the x 1 axis and the z 1 axis, and a meridional light source line passing through the position of the light source in the meridional direction focusing and extending in a direction perpendicular to both the y 1 axis and the z 1 axis; All of the light rays emitted from the second reflecting surface pass through a sagittal focusing line that passes through the focusing position in the sagittal direction and extends in a direction perpendicular to both the x 3 axis and the z 3 axis, and a meridional focusing line that passes through the focusing position in the meridional direction and extends in a direction perpendicular to both the y 3 axis and the z 3 axis, Furthermore, assuming that the exit beam from the first reflecting surface travels straight without being reflected by the second reflecting surface, the exit beam is focused in the sagittal direction at a position displaced by L 2s A from the intersection point M 0 A on the z 2 axis along the z 2 axis direction, and is focused in the meridional direction at a position displaced by L 2m A from the intersection point M 0 A on the z 2 axis along the z 2 axis direction, The light beam emitted from the first reflecting surface passes through a sagittal virtual focusing line that passes through the focusing position in the sagittal direction and extends in a direction perpendicular to both the x 2 axis and the z 2 axis, and a meridional virtual focusing line that passes through the focusing position in the meridional direction and extends in a direction perpendicular to both the y 2 axis and the z 2 axis; All incident rays passing through the second reflecting surface intersect, on their extension lines, with the sagittal virtual focusing line in the sagittal direction focusing for the first reflecting surface as a sagittal virtual light source line, and the meridional virtual focusing line in the meridional direction focusing for the first reflecting surface as a meridional virtual light source line, A surface including an intersection M 0 A of the z 1 axis and the z 2 axis on the first reflecting surface and tangent to the reflecting surface is defined as a u A v A plane, a direction of a normal to the u A v A plane passing through the M 0 A is defined as a w A axis, the v A axis is defined as a direction perpendicular to both the z 1 axis and the z 2 axis, the u A axis is defined as a direction perpendicular to both the v A axis and the w A axis, the intersection M 0 A is defined as the origin, and the oblique incidence angle between the u A v A plane and the optical axis z 1 is defined as θ 0 A , Let the surface including the intersection M 0 B of the z 2 axis and the z 3 axis on the second reflecting surface be the u B v B plane, the direction of the normal to the u B v B plane passing through M 0 B be the w B axis, the v B axis be a direction perpendicular to both the z 2 axis and the z 3 axis, the u B axis be a direction perpendicular to both the v B axis and the w B axis, the intersection M 0 B be the origin, and the oblique incidence angle between the u B v B plane and the optical axis z 2 be θ 0 B , a first reflecting surface expressed by the following formula (37) (wherein t'1xA, t'1yA, t'2xA, and t'2yA are the following formulas (38) to (41) respectively) and a second reflecting surface expressed by the following formula (42) (wherein t'1xB, t'1yB, t'2xB, and t'2yB are the following formulas (43) to (46) respectively), For sagittal focusing, the source line S ｓ and z １ Axis intersection point P ｓ０、 Virtual focusing line F ｓ Ａ and z ２ Axis intersection point Q ｓ０ Ａ , focusing ray F ｓ and z ３ Axis intersection point Q ｓ０ The three points are on the same line, and at the same time, the light source line S ｍ and z １ Axis intersection point P ｍ０ , virtual focusing line F ｍ Ａ and z ２ Axis intersection point Q ｍ０ Ａ , focusing ray F ｍ and z ３ Axis intersection point Q ｍ０ So that the three points of are on the same line, ２ｓ Ａ and L ２ｍ Ａ and a first reflecting surface and a second reflecting surface, Astigmatism control mirror that expands the installation angle tolerance range. [0025] [0026] [0027] [0028]

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