PATENT ABSTRACT
Provided is a small size optical system having functions of a luminous flux splitting optical system or those of a luminous flux integrating optical system and functions of a fly&#39;s eye integrator. The integrator is provided with two surfaces. A first surface ( 111 ) is composed of a first unit surface, i.e., a positive refractive surface, and a second surface ( 113 ) is composed of a second unit surface, i.e., a positive refractive surface. Prescribed n number of second unit surfaces ( 113   a,    113   b ) correspond to a prescribed first unit surface ( 111   a ). Light which entered the n number of second unit surfaces and parallel to the optical axis of the prescribed first unit surface is collected to the center of the prescribed first unit surface. The n number of second unit surfaces are arranged not to be adjacent to each other on a refractive surface having substantially the same diffractive power as that of the refractive surface of the prescribed first unit surface.

PATENT DESCRIPTION
FIELD OF THE INVENTION 
       [0001]    The present invention relates to an integrator that splits or integrates a beam and an illuminating apparatus using the integrator. 
       BACKGROUND OF THE INVENTION 
       [0002]    In the illuminating apparatus, a fly&#39;s eye integrator is used in order to uniformize illuminance of an illuminating target region. In the illuminating apparatus, sometimes a beam splitting optical system that splits a beam emitted from a light source into plural beams or a beam integrating optical system that integrates plural beams emitted from plural light sources into a single beam is used in addition to the fly&#39;s eye integrator that uniformizes the illuminance of the illuminating target region. 
         [0003]    For example, in a projection exposure apparatus that is used in a lithography process such as that of a semiconductor device, a quadrupole type modified illuminating apparatus in which a pupil of illumination is formed into a four-hole shape is used to improve a depth of focus or a resolution. In the quadrupole type modified illuminating apparatus, a beam splitting optical system such as a diffraction optical element and a pyramidal prism and a fly&#39;s eye integrator that uniformizes pupil illuminance are used according to the pupil having the four-hole shape (for example, Patent Document 1). 
         [0004]    For example, a beam integrating optical system such as a dichroic prism that integrates beams from RGB three-color light sources and a fly&#39;s eye integrator that improves the illumination uniformity of the projection image are used in an image projector (for example, Patent Document 2).
   Patent Document 1: Japanese Patent Application Laid-Open No. 2000-182933   Patent Document 2: Japanese Patent Application Laid-Open No. 2006-39495   
 
         [0007]    However, in the optical system including the beam splitting optical system or beam integrating optical system and the fly&#39;s eye integrator, a size of the optical system is enlarged. A size of the illuminating apparatus including the optical system is also enlarged. 
         [0008]    Accordingly, there is the need for a compact optical system having the function of the beam splitting optical system or beam integrating optical system and the function of the fly&#39;s eye integrator, and there is also the need for a compact illuminating apparatus including the optical system. 
       SUMMARY OF THE INVENTION 
       [0009]    In accordance with a first aspect of the invention, an integrator includes first and second surfaces. The first surface includes a first unit surface that is of a positive refractive surface, and the second surface includes a second unit surface that is of a positive refractive surface. Predetermined n second unit surfaces correspond to a predetermined first unit surface, and light that is parallel to the optical axis of the predetermined first unit surface and incident to each of the predetermined n second unit surfaces is collected in a center of the predetermined first unit surface. The predetermined n second unit surfaces are disposed so as not to be adjacent to one another on a refractive surface having a refractive power substantially identical to that of the refractive surface of the predetermined first unit surface. 
         [0010]    The integrator in accordance with the first aspect of the invention acts as an integrator, and the integrator splits the light into the n beams traveling in predetermined directions after the light that is parallel to the optical axis of the predetermined first unit surface and incident to each of the predetermined n second unit surfaces is collected in the center of the predetermined first unit surface. Further, the integrator in accordance with the first aspect of the invention acts as an integrator, and the integrator integrates the n beams that travel in predetermined directions to be incident to the predetermined first unit surface into a beam parallel to the optical axis of the predetermined first unit surface. 
         [0011]    In accordance with a second aspect of the invention, an integrator includes first and second members. The first member includes a first unit portion having a positive refractive power, and the second member includes a second unit portion having a positive refractive power. Predetermined n second unit portions correspond to a predetermined first unit portion, and light that is parallel to the optical axis of the predetermined first unit portion and incident to a surface on an incident side in each of the predetermined n second unit portions is collected in a center of a surface on an output side in the predetermined first unit portion. The predetermined n second unit portions are disposed so as not to be adjacent to one another on a member having a refractive power substantially identical to the refractive power of the predetermined first unit portion. 
         [0012]    The integrator in accordance with the second aspect of the invention acts as an integrator, and the integrator splits the light into the n beams traveling in predetermined directions after the light that is parallel to the optical axis of the predetermined first unit portion and incident to the surface on the incident side in each of the predetermined n second unit portions is collected in the center of the surface on the output side in the predetermined first unit portion. Further, the integrator in accordance with the second aspect of the invention acts as an integrator, and the integrator integrates the n beams that travel in predetermined directions to be incident to the predetermined first unit portion into a beam parallel to the optical axis of the predetermined first unit portion. 
         [0013]    In accordance with a third aspect of the invention, an integrator includes first and second surfaces. The first surface includes a first unit surface that is of a positive refractive surface, and the second surface includes a second unit surface that is of a positive refractive surface. Predetermined m first unit surfaces correspond to predetermined n second unit surfaces, the predetermined m first unit surfaces are disposed on a first refractive surface so as not to be adjacent to one another, the predetermined n second unit surfaces are disposed on a second refractive surface so as not to be adjacent to one another, and the first refractive surface and the second refractive surface have a substantially identical refractive power and each of the first refractive surface and the second refractive surface is disposed near the focal point on the optical axe of the other. 
         [0014]    The integrator in accordance with the third aspect of the invention acts as an integrator, and the integrator splits the light into the m beams traveling in different directions after the n beams that travel in different directions to be incident to the predetermined m first unit surfaces at the predetermined angle are collected and integrated into the predetermined n second unit surfaces. 
         [0015]    In accordance with a fourth aspect of the invention, an integrator includes first and second members. The first member includes a first unit portion having a positive refractive surface, and the second member includes a second unit portion having a positive refractive surface. Predetermined m first unit portions correspond to predetermined n second unit portions, the predetermined m first unit portions are disposed on the first member so as not to be adjacent to one another, and the predetermined n second unit portions are disposed on the second member so as not to be adjacent to one another. Refractive surfaces of the predetermined m first unit portions are parts of a first refractive surface, and refractive surfaces of the predetermined n second unit portions are parts of a second refractive surfaces. The first refractive surface and the second refractive surface have a substantially identical refractive power and each of the first refractive surface and the second refractive surface is disposed near the focal point on the optical axe of the other, where n and m represent positive integers. 
         [0016]    The integrator in accordance with the fourth aspect of the invention acts as an integrator, and the integrator splits the light into the m beams traveling in different directions after the n beams that travel in different directions and are incident to the predetermined m first unit portions at the predetermined angle are collected and integrated in the predetermined n second unit portions. 
         [0017]    Accordingly, a compact integrator having the function of the beam splitting optical system or beam integrating optical system is obtained in the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]      FIG. 1  is a view illustrating a configuration of an optical system according to an embodiment of the invention. 
           [0019]      FIG. 2  is a view illustrating configuration of an optical element that includes a first surface having plural first unit surfaces and a second surface having plural second unit surfaces. 
           [0020]      FIG. 3  is a view illustrating an optical system in which a first unit surface is used as an incident surface, the optical system being identical to the optical system of  FIG. 1 . 
           [0021]      FIG. 4  is a view illustrating a configuration of an optical element in which a first surface is used as an incident surface, the optical element being identical to the optical element of  FIG. 2 . 
           [0022]      FIG. 5  is a view illustrating a configuration of an optical system according to another embodiment of the invention. 
           [0023]      FIG. 6  is a view illustrating configurations of a first optical element that includes a first surface having plural first unit surfaces and a second optical element that includes a second surface having plural second unit surfaces. 
           [0024]      FIG. 7  is a view illustrating an optical system in which a first unit surface is used as an incident surface, the optical system being identical to the optical system of  FIG. 5 . 
           [0025]      FIG. 8  is a view illustrating a configuration of an optical element in which a first surface is used as an incident surface, the optical element being identical to the optical element of  FIG. 6 . 
           [0026]      FIG. 9  is a view illustrating a configuration of an optical system according to another embodiment of the invention. 
           [0027]      FIG. 10  is a view illustrating a configuration of a first optical element that includes a first surface having plural first unit surfaces and a second optical element that includes a second surface having plural second unit surfaces. 
           [0028]      FIG. 11  is a view illustrating an optical system in which a first unit surface is used as an incident surface, the optical system being identical to the optical system of  FIG. 9 . 
           [0029]      FIG. 12  is a view illustrating a configuration of an optical element in which a first unit surface is used as an incident surface, the optical element being identical to the optical element of  FIG. 10 . 
           [0030]      FIG. 13  is a view illustrating sections including first and second surfaces when viewed from an optical axis direction and a section including an optical axis in an optical element according to a first embodiment. 
           [0031]      FIG. 14  is a view illustrating a second surface ( FIG. 14(   a ) and a first surface ( FIG. 14(   b )) of the optical element of the first embodiment. 
           [0032]      FIG. 15  is a view illustrating a second surface ( FIG. 15(   a )) and a first surface ( FIG. 15(   b )) of an optical element according to a second embodiment. 
           [0033]      FIG. 16  is a view illustrating a second surface ( FIG. 16(   a )) and a first surface ( FIG. 16(   b )) of an optical element according to a third embodiment. 
           [0034]      FIG. 17  is a view illustrating a second surface ( FIG. 17(   a )) and a first surface ( FIG. 17(   b )) of an optical element according to a fourth embodiment. 
           [0035]      FIG. 18  is a view illustrating a configuration of an illuminating apparatus according to a first embodiment in which optical element is used. 
           [0036]      FIG. 19  is a view illustrating a configuration of an illuminating apparatus according to a second embodiment in which optical element is used. 
           [0037]      FIG. 20  is a view illustrating a configuration of an illuminating apparatus according to a third embodiment in which optical element is used. 
           [0038]      FIG. 21  is a view illustrating a configuration of an illuminating apparatus according to a fourth embodiment in which optical element is used. 
           [0039]      FIG. 22  is a view illustrating a configuration of an illuminating apparatus of an image projector in which reflection type optical modulation element is used in the illuminating apparatus of  FIG. 21 . 
           [0040]      FIG. 23  is a view illustrating a configuration of an optical system according to another embodiment of the invention. 
           [0041]      FIG. 24  is a view illustrating a configuration of an optical element that includes a first surface having plural first unit surfaces and a second surface having plural second unit surfaces. 
           [0042]      FIG. 25  is a view illustrating a configuration of an optical system according to another embodiment of the invention. 
           [0043]      FIG. 26  is a view illustrating a configuration of a first optical element that includes a first surface having plural first unit surfaces and a second optical element that includes a second surface having plural second unit surfaces. 
           [0044]      FIG. 27  is a view illustrating a configuration of an optical system according to another embodiment of the invention. 
           [0045]      FIG. 28  is a view illustrating a configuration of a first optical element that includes a first surface having plural first unit surfaces and a second optical element that includes a second surface having plural second unit surfaces. 
           [0046]      FIG. 29  is a view illustrating a section including first and second surfaces and an optical axis when viewed from an optical axis direction in an optical element according to a fifth embodiment. 
           [0047]      FIG. 30  is a view illustrating a first surface ( FIG. 30(   a )) and a second surface ( FIG. 30(   b )) of an optical element of the fifth embodiment. 
           [0048]      FIG. 31  is a view illustrating a first surface ( FIG. 31(   a )) and a second surface ( FIG. 31(   b )) of an optical element according to a sixth embodiment. 
           [0049]      FIG. 32  is a view illustrating a configuration of an illuminating apparatus of a fifth embodiment in which the optical element is used. 
       
    
    
     EXPLANATIONS OF LETTERS OR NUMERALS 
       [0000]    
       
           110 ,  120 ,  130 , and  140  optical element 
           111 ,  1111 ,  1113 , and  1115  first surface 
           113 ,  1131 ,  1133 , and  1135  second surface 
           111   a,    1111   a,    1113   a,  and  1115   a  first unit surface 
           113   a,    113   b,    1131   a,    1131   b,    1133   a,    1133   b,    1135   a,  and  1135   b  second unit surface 
       
     
       DETAILED DESCRIPTION 
       [0055]      FIG. 1  is a view illustrating a configuration of an optical system according to an embodiment of the invention. The optical system includes a first unit surface  111   a  and second unit surfaces  113   a  and  113   b  corresponding to the first unit surface  111   a.  The first unit surface and the second unit surfaces are positive refractive surfaces.  FIG. 1  is a sectional view including an optical axis of the first unit surface  111   a.  In  FIG. 1  illustrating the section of the optical system, the two second unit surfaces correspond to the first unit surface  111   a.  However, actually there are four second unit surfaces corresponding to the first unit surface  111   a.    
         [0056]    Both the second unit surfaces  113   a  and  113   b  are partial regions on a spherical surface of a focal length f, and the second unit surfaces  113   a  and  113   b  are symmetrically disposed in relation to the optical axis of the first unit surface  111   a.  The first unit surface  111   a  is also the spherical surface of the focal length f. Gaps between the first unit surface  111   a  and the second unit surfaces  113   a  and  113   b  are filled with a medium having a refractive index n. An interval d between the first unit surface  111   a  and the second unit surfaces  113   a  and  113   b  satisfies Equation (1), and the first unit surface  111   a  is located on the focal point of each of the second unit surfaces  113   a  and  113   b  and each of the second unit surfaces  113   a  and  113   b  is located on the focal point of the first unit surface  111   a.   
         [0000]      f=d/n  (1) 
         [0057]    A beam L 1  is parallel to the optical axis of the first unit surface  111   a  (hereinafter simply referred to as optical axis) and incident to the second unit surface  113   a.  The beam L 1  is collected in the center of the first unit surface  111   a  by a refractive power of the second unit surface  113   a,  and the beam L 1  exits from the first unit surface  111   a  at an angle θ 1  formed with the optical axis diverging at a spread angle φ 1 . Similarly, a beam L 2 , which is parallel to the optical axis and incident to the second unit surface  113   b  and, is collected in the center of the first unit surface  111   a  by a refractive power of the second unit surface  113   b.  On the side opposite to the beam L 1  in relation to the optical axis, the beam L 2  exits from the first unit surface  111   a  at the angle θ 1  formed with the optical axis as light that is divergent at the spread angle φ 1 . 
         [0058]    At this point, in  FIG. 1 , assuming that hi is a distance between the center of the second unit surface  113   a  and the optical axis and w 1  is a width perpendicular to the optical axis in the second unit surface  113   a,  the angle θ 1  and the spread angle φ 1  substantially satisfy Equations (2) and (3) (sine condition): 
         [0000]      sin θ 1   =h   1   /f   (2) 
         [0000]      sin φ 1   =w   1 /2 f   (3) 
         [0059]    It is not always necessary that the first unit surface  111   a  have the spherical surface, but the first unit surface  111   a  may have an aspherical surface (including a parabolic surface). It is not always necessary that the second unit surfaces  113   a  and  113   b  be the partial regions on the spherical surface, but the second unit surfaces  113   a  and  113   b  may be partial regions on an aspherical surface. It is not always necessary that a focal length (refractive power) of the first unit surface  111   a  be identical to focal length (refractive power) of the second unit surfaces  113   a  and  113   b,  but the first unit surface  111   a  and the second unit surfaces  113   a  and  113   b  may be deviated from a focal position of a paraxial to improve a function as the integrator in consideration of aberration. However, in such cases, it is assumed that the first unit surface  111   a  and the second unit surfaces  113   a  and  113   b  have the substantially same refractive power. 
         [0060]      FIG. 2  is a view illustrating configuration of an optical element (integrator)  110  that includes a first surface  111  having plural first unit surfaces and a second surface  113  having plural second unit surfaces.  FIG. 2  is a sectional view including the optical axis of the first unit surface. 
         [0061]      FIG. 14  is a view illustrating the first surface  111  ( FIG. 14(   b )) and the second surface  113  ( FIG. 14(   a )) when viewed from above the optical axis of the first unit surface. As described above, four second unit surfaces  113   a,    113   b,    113   c,  and  113   d  in the second surface  113  correspond to the first unit surface  111   a  in the first surface  111 . The four second unit surfaces  113   a,    113   b,    113   c,  and  113   d  are partial regions of a sole refractive surface. The focal length of the refractive surface is equal to that of the refractive surface of the first unit surface  111   a,  and the optical axes of the two refractive surfaces are matched with each other. The four second unit surfaces  113   a,    113   b,    113   c,  and  113   d  are disposed so as not to be adjacent to one another, and the second unit surfaces  113   a,    113   b,    113   c,  and  113   d  are distant from the optical axis of the first unit surface  111   a.  As illustrated in  FIG. 14 , an area of the first unit surface  111   a  in a section perpendicular to the optical axis of the first unit surface  111   a  is four times an area of the second unit surfaces  113   a,    113   b,    113   c,  or  113   d  in a section perpendicular to the optical axis of the first unit surface  111   a.    
         [0062]    In  FIG. 2 , the beam, which is parallel to the optical axis of the first unit surface and incident to the second surface  113 , is split into two beams. Actually the beam, which is parallel to the optical axis of the first unit surface and incident to the second surface  113 , is split into four beams. As illustrated in  FIG. 14 , the second unit surfaces in the second surface  113  are classified into one (first group, for example,  113   a ) located in the upper left of the optical axis of the corresponding first unit surface, one (second group, for example,  113   b ) located in the lower left, one (third group, for example,  113   c ) located in the upper right, and one (fourth group, for example,  113   d ) located in the lower right. For example, the second unit surfaces of the first group are scattered on the second surface  113 . The beams, which are parallel to the optical axis of the first unit surface and incident to the second unit surfaces of the first group scattered on the second surface  113 , are collected in the center of the first unit surface, and then the beams exit as one beam traveling in a predetermined direction at the angle θ 1  formed with the optical axis of the first unit surface from the first surface  111 , diverging at the spread angle φ 1 . Therefore, the illuminance is uniformized in the beam. Thus, the optical element  110  uniformizes the illuminance of the beam, which is parallel to the optical axis of the first unit surface and incident to the second unit surfaces, and splits the beam into plural beams, so that the optical element  110  acts as the integrator and the beam splitting means. 
         [0063]      FIG. 3  is a view illustrating an optical system in which the first unit surface  111   a  is used as the incident surface, the optical system being identical to the optical system of  FIG. 1 . In  FIG. 3 , parallel beams L 3  and L 4  are incident to the first unit surface  111   a  that is of the incident surface from two directions that are symmetrical in relation to the optical axis of the first unit surface  111   a.  When the angle θ 1  formed between the parallel beams L 3  and L 4  and the optical axis satisfies Equation (2), the parallel beams L 3  and L 4  are respectively collected in the centers of the second unit surfaces  113   a  and  113   b  that are of the output surface, and exit in directions parallel to the optical axe of the first unit surface  111   a  as lights diverging at a spread angle φ 2 . 
         [0064]    At this point, assuming that w 2  is a width of a refractive surface  1   x,  the spread angle φ 2  substantially satisfies Equation (4) (sine condition): 
         [0000]      sin φ 2   =w   2 /2 f   (4) 
         [0065]      FIG. 4  is a view illustrating a configuration of the optical element  110  in which the first surface  111  is used as the incident surface, the optical element  110  being identical to the optical element of  FIG. 2 .  FIG. 4  is a sectional view including the optical axis of the first unit surface. 
         [0066]    In  FIG. 4 , the two parallel beams, which are incident to the first unit surface  111  that is of the incident surface at the angle θ 1  formed with the optical axis of the first unit surface, are integrated into one beam that exits from the second surface  113  that is of the output surface in the direction parallel to the optical axis, diverging at the spread angle φ 2 . Actually the four parallel beams incident to the first surface  111  that is of the incident surface are integrated into one beam. After the light beams incident to the first unit surfaces distributed in the first surface  111  are collected on the second unit surface, the light beams are integrated into one beam that exits in the direction parallel to the optical axis of the first unit surface, diverging at the spread angle φ 2 , so that the illuminance of the beam is uniformized. Thus, the optical element  110  uniformizes the illuminance of plural beams incident at a predetermined angle to the first unit surface and integrates the plural beams into one beam, so that the optical element  110  acts as the integrator and the beam integrating means. 
         [0067]      FIG. 5  is a view illustrating a configuration of an optical system according to another embodiment of the invention. The optical system of  FIG. 5  includes a first unit surface  1111   a  and second unit surfaces  1131   a  and  1131   b  corresponding to the first unit surface  1111   a.  The first unit surface and the second unit surfaces are positive refractive surfaces.  FIG. 5  is a sectional view including the optical axis of the first unit surface  1111   a.  In  FIG. 5 , the two second unit surfaces correspond to the first unit surface  1111   a.  However, actually there are four second unit surfaces corresponding to the first unit surface  1111   a.    
         [0068]    Both the second unit surfaces  1131   a  and  1131   b  are partial regions on the spherical surface, and the second unit surfaces  1131   a  and  1131   b  are symmetrically disposed in relation to the optical axis of the first unit surface  1111   a.  The first unit surface  1111   a  is a spherical surface having the same shape as the spherical surface of the second unit surfaces  1131   a  and  1131   b.    
         [0069]    It is not always necessary that the second unit surfaces  1131   a  and  1131   b  be partial regions on a spherical surface, but the second unit surfaces  1131   a  and  1131   b  may be partial regions on an aspherical surface (including a parabolic surface). It is not always necessary that the first unit surface  1111   a  have a spherical surface, but the first unit surface  111   a  may have an aspherical surface. It is not always necessary that the second unit surfaces  1131   a  and  1131   b  and the first unit surface  1111   a  have the same shape provided that the first unit surface  1111   a  and the second unit surfaces  1131   a  and  1131   b  have the substantially same refractive power. 
         [0070]    The beam L 1  is parallel to the optical axis of the first unit surface  1111   a  and incident to the second unit surface  1131   a.  The beam L 1  is collected in the center of the first unit surface  1111   a  by the refractive power of the second unit surface  1131   a.  Similarly a beam L 2 , which is parallel to the optical axis of the first unit surface  1111   a  and incident to the second unit surface  1131   b,  is collected in the center of the first unit surface  1111   a  by the refractive power of the second unit surface  1131   b.    
         [0071]      FIG. 6  is a view illustrating configurations of a first optical element  110   a  including a first surface  1111  having plural first unit surfaces and a second optical element  110   b  including a second surface  1131  having plural second unit surfaces.  FIG. 6  is a sectional view including the optical axis of the first unit surface. A surface  1113  of the first optical element  110   a  on the side opposite to the first surface  1111  and a surface  1133  of the second optical element  110   b  on the side opposite to the second surface  1131  are flat. 
         [0072]    In  FIG. 6 , the beam, which is parallel to the optical axis of the first unit surface and incident to the second surface  1131 , is split into two beams. Actually the beam, which is parallel to the optical axis of the first unit surface and incident to the second surface  1131 , is split into four beams. Thus, the optical elements  110   a  and  110   b  act as an integrator and beam splitting means. 
         [0073]      FIG. 7  is a view illustrating an optical system in which a first unit surface  1111   a  is used as the incident surface, the optical system being identical to the optical system of  FIG. 5 . In  FIG. 7 , the first unit surface  1111   a  is the incident surface. In  FIG. 7 , parallel beams L 3  and L 4 , which are incident to the first unit surface  1111   a  that is of the incident surface from predetermined two directions that are symmetrical in relation to the optical axis of the first unit surface  1111   a,  are collected in the centers of the second unit surfaces  1131   a  and  1131   b  that are of the output surface, and the parallel beams L 3  and L 4  exit in the directions parallel to the optical axes of the first unit surface  1111   a.    
         [0074]      FIG. 8  is a view illustrating a configuration of an optical element in which a first surface  1111  is used as the incident surface, the optical element being identical to the optical element of  FIG. 6 .  FIG. 8  is a sectional view including the optical axis of the first unit surface. 
         [0075]    In  FIG. 8 , two parallel beams incident at a predetermined angle to the first surface  1111  that is of the incident surface are integrated into one beam exiting in the direction parallel to the optical axis from the second surface  1131  that is of the output surface. Actually four parallel beams incident to the first surface  1111  that is of the incident surface are integrated into one beam. Thus, the optical elements  110   a  and  110   b  act as an integrator and beam integrating means. 
         [0076]      FIG. 9  is a view illustrating a configuration of an optical system according to another embodiment of the invention. The optical system includes a first unit portion  110   cp  and a second unit portion  110   dp.  The first unit portion  110   cp  includes a unit surface  1115   a  and a unit surface  1117   a.  The second unit portion  110   dp  corresponds to the first unit portion  110   cp,  and the second unit portion  110   dp  includes a unit surface  1135   a  and a unit surface  1137   a  (or second unit portion  110   dp  includes a unit surface  1135   b  and a unit surface  1137   b ). The first unit portion  110   cp  and the second unit portion  110   dp  have positive refractive powers.  FIG. 9  is a sectional view including the optical axis of the first unit portion. In  FIG. 9 , the two second unit portions  110   dp  correspond to the first unit portion  110   cp.  However, actually there are four second unit portions corresponding to the first unit portion  110   cp.    
         [0077]    The unit surfaces  1135   a  and  1135   b  and the unit surfaces  1137   a  and  1137   b  are respectively partial regions of a spherical surface, and the second unit portions  110   dp  are symmetrically disposed in relation to the optical axis of the first unit portion  110   cp.  The unit surfaces  1115   a  and  1117   a  are spherical surfaces having the same shape as the spherical surfaces of the unit surfaces  1135   a  and  1135   b  and unit surfaces  1137   a  and  1137   b.    
         [0078]    It is not always necessary that the unit surfaces  1135   a  and  1135   b  and the unit surfaces  1137   a  and  1137   b  be partial regions on a spherical surface, but the unit surfaces  1135   a  and  1135   b  and the unit surfaces  1137   a  and  1137   b  may be partial regions on an aspherical surface (including a parabolic surface). It is not always necessary that the unit surfaces  1115   a  and  1117   a  have the spherical surfaces, but the unit surfaces  1115   a  and  1117   a  may have the aspherical surfaces. It is not always necessary that the unit surface  1135   a  ( 1135   b ), the unit surface  1137   a  ( 1137   b ), and the unit surfaces  1117   a  and  1115   a  have the same shape provided that the first unit portion  110   cp  and the second unit portion  110   dp  have the substantially same refractive power. 
         [0079]    The beam L 1 , which is incident to the unit surface  1135   a  of the second unit portion  110   dp  and parallel to the optical axis of the first unit portion  110   cp,  is collected in the center of the unit surface  1115   a  by the refractive power of the second unit portion  110   dp.  Similarly the beam L 2 , which is parallel to the optical axis of the first unit portion  110   cp  and incident to the unit surface  1135   b  of the second unit portion  110   dp,  is collected in the center of the unit surface  1115   a.    
         [0080]      FIG. 10  is a view illustrating a configuration of an integrator that includes a first optical element  110   c  and a second optical element  110   d.  The first optical element  110   c  includes a surface  1115  having plural unit surfaces and a surface  1117  having plural unit surfaces. The second optical element  110   d  includes a surface  1135  having plural unit surfaces and a surface  1137  having plural unit surfaces.  FIG. 10  is a sectional view including the optical axis of the first unit portion  110   cp.    
         [0081]    In  FIG. 10 , the beam, which is parallel to the optical axis of the first unit portion and incident to the surface  1135  of the second optical element  110   d,  is split into the two beams. Actually the beam, which is parallel to the optical axis of the first unit portion and incident to the surface  1135 , is split into the four beams. Thus, the optical elements  110   c  and  110   d  act as an integrator and beam splitting means. 
         [0082]      FIG. 11  is a view illustrating an optical system in which the unit surface  1115   a  of the first unit portion  110   cp  is used as the incident surface, the optical system being identical to the optical system of  FIG. 9 . In  FIG. 11 , the parallel beams L 3  and L 4 , which are in predetermined two directions that are symmetrical in relation to the optical axis of the first unit portion  110   cp  and incident to the unit surface  1115   a  that is of the incident surface, are collected in the centers of the unit surfaces  11135   a  and  1135   b  of the second unit portions  110   dp  that are of the output surface, and the parallel beams L 3  and L 4  exit in the directions parallel to the optical axe of the first unit portion  110   cp.    
         [0083]      FIG. 12  is a view illustrating a configuration of an optical element in which the surface  1115  of the first optical element  110   c  is used as the incident surface, the optical element being identical to the optical element of  FIG. 10 .  FIG. 12  is a sectional view including the optical axis of the first unit portion. 
         [0084]    In  FIG. 12 , two parallel beams, which are incident at a predetermined angle to the surface  1115  that is of the incident surface, are integrated into one beam exiting in the direction parallel to the optical axis from the surface  1135  that is of the output surface. Actually four parallel beams incident to the surface  1115  that is of the incident surface are integrated into one beam. Thus, the optical elements  110   c  and  110   d  act as an integrator and beam integrating means. 
         [0085]      FIG. 23  is a view illustrating a configuration of an optical system according to another embodiment of the invention. The optical system includes first unit surfaces  511   a  and  511   b  and second unit surfaces  513   a  and  513   b  corresponding to the first unit surfaces  511   a  and  511   b.  The first unit surfaces and the second unit surfaces are positive refractive surfaces. 
         [0086]    Both the first unit surfaces  511   a  and  511   b  are partial regions on a spherical surface C 1  having a focal length f. Both the second unit surfaces  513   a  and  513   b  are partial regions on a spherical surface C 2  having the focal length f.  FIG. 23  is a sectional view including an optical axis that is defined by a straight line connecting the centers of the spherical surfaces C 1  and C 2  (hereinafter simply referred to as optical axis). In  FIG. 23  illustrating the section of the optical system, the two first unit surfaces and the two second unit surfaces are provided. However, actually there are four first unit surfaces and four second unit surfaces. 
         [0087]    The first unit surfaces  511   a  and  511   b  are symmetrically disposed in relation to the optical axis. Similarly the second unit surfaces  513   a  and  513   b  are symmetrically disposed in relation to the optical axis. Gaps between the first unit surfaces  511   a  and  511   b  and the second unit surfaces  513   a  and  513   b  are filled with a medium having a refractive index n. An interval d between the first unit surfaces  511   a  and  511   b  and the second unit surfaces  513   a  and  513   b  satisfies following Equation (1), and the first unit surfaces  511   a  and  511   b  are located in focal points of the second unit surfaces  513   a  and  513   b  while the second unit surfaces  513   a  and  513   b  are located in focal points of the first unit surfaces  511   a  and  511   b.   
         [0000]        f=d/n   (1) 
         [0088]    At this point, in  FIG. 23 , assuming that hi is a distance between the center of the first unit surface  511   a  and the optical axis and w 1  is a width in a direction perpendicular to the optical axis in the first unit surface  511   a,  the angle θ 1  and the spread angle φ 1  substantially satisfy Equations (2) and (3) (sine condition), respectively. 
         [0000]      sin θ 1     32  h   1   /f   (2) 
         [0000]      sin φ 1   =w   1 /2 f   (3) 
         [0089]    Parallel beams L 6  and L 5  which travel in two directions that are symmetrical in relation to the optical axis and are incident to the first unit surfaces  511   a,  are collected in the centers of the second unit surfaces  513   a  and  513   b  that are of the output surface, respectively when the angle θ 2  formed between the beams L 6  and L 5  and the optical axis satisfies Equation (2-1). Then the parallel beams L 6  and L 5  exit from the second unit surfaces  513   a  and  513   b  at the angle θ 1  formed with the optical axis, diverging at the spread angle φ 1 , Similarly parallel beams L 8  and L 7  which travel in two directions that are symmetrical in relation to the optical axis and are incident to the first unit surfaces  511   b,  exit from the second unit surfaces  513   a  and  513   b  at the angle θ 1  formed with the optical axis, diverging at the spread angle φ 1 , respectively. 
         [0000]      sin θ 2   =h   1   /f   (2-1) 
         [0090]    It is not always necessary that the first unit surfaces  511   a  and  511   b  be a spherical surface, but the first unit surfaces  511   a  and  511   b  may be an aspherical surface (including a parabolic surface). It is not always necessary that the second unit surfaces  513   a  and  513   b  be partial regions on a spherical surface, but the second unit surfaces  513   a  and  513   b  may be partial regions on an aspherical surface. It is not always necessary that the focal length (refractive power) of the first unit surfaces  511   a  and  511   b  be identical to the focal length (refractive power) of the second unit surfaces  513   a  and  513   b,  but the first unit surfaces  511   a  and  511   b  and the second unit surfaces  513   a  and  513   b  may be deviated from a focal position of a paraxial to improve a function as the integrator (described later) in consideration of the aberration. However, in such cases, it is assumed that the first unit surfaces  511   a  and  511   b  and the second unit surfaces  513   a  and  513   b  have the substantially same refractive power. 
         [0091]      FIGS. 30(   a ) and  30 ( b ) are views illustrating the first surface  511  and the second surface  513  when viewed from above the optical axis, The first surface  511  includes four first unit surfaces  511   a,    511   b,    511   c,  and  511   d,  and the second surface  513  includes four second unit surfaces  513   a,    513   b,    513   c,  and  513   d.  The four first unit surfaces  511   a,    511   b,    511   c,  and  511   d  are partial regions of the same refractive surface. Similarly the four second unit surfaces  513   a,    513   b,    513   c,  and  513   d  are partial regions of the same refractive surface. The four first unit surfaces  511   a,    511   b,    511   c,  and  511   d  are disposed so as not to be adjacent to one another, and the first unit surfaces  511   a,    511   b,    511   c,  and  511   d  are distant from the optical axis. Similarly the four second unit surfaces  513   a,    513   b,    513   c,  and  513   d  are disposed so as not to be adjacent to one another, and the second unit surfaces  513   a,    513   b,    513   c,  and  513   d  are distant from the optical axis. 
         [0092]      FIG. 24  is a view illustrating a configuration of an optical element (integrator)  510  that includes the first surface  511  having plural first unit surfaces and the second surface  513  having plural second unit surfaces.  FIG. 24  is a sectional view including the optical axis. 
         [0093]    In  FIG. 24 , two parallel beams incident to the first surface  511  at the angle θ 2  formed with the optical axis are integrated in the second surface  513  that is of the output surface, and then the integrated beam is split again into the two beams exiting at the angle θ 1  formed with the optical axis, diverging at the spread angle φ 1  Actually, after four beams incident to the first surface  511  that is of the incident surface are integrated, the integrated beam is split into four beams again. 
         [0094]    In  FIG. 30 , the first unit surfaces in the first surface  511  are classified into one (first group, for example,  511   a ) located in the upper left of the optical axis, one (second group, for example,  511   b ) located in the lower left of the optical axis, one (third group, for example,  511   c ) located in the upper right of the optical axis, and one (fourth group, for example,  511   d ) located in the lower right of the optical axis. For example, the first unit surfaces of the first group are distributed on the first surface  511 . Similarly, in  FIG. 30 , the second unit surfaces on the second surface  513  are classified into one (fifth group, for example,  513   a ) located in the upper left of the optical axis, one (sixth group, for example,  513   b ) located in the lower left of the optical axis, one (seventh group, for example,  513   c ) located in the upper right of the optical axis, and one (eighth group, for example,  513   d ) located in the lower right of the optical axis. For example, the second unit surfaces of the fifth group are distributed on the second surface  513 . After the four beams incident to the first unit surfaces of the first group at the angle θ 2  formed with the optical axis are collected in the second unit surfaces of the fifth group, sixth group, seventh group, and eighth group, respectively, and the four beams exit from the second surface  513  in a predetermined direction at the angle θ 1  formed with the optical axis, diverging at the spread angle φ 1 , so that the illuminance is uniformized in the beam. Generally, after n beams which travel in different directions and are incident to m first unit surfaces at a predetermined angle, are collected and integrated in n second unit surfaces, and the integrated beam is split into m beams traveling in different directions, where n and m represent positive integers. The optical element  510  uniformizes the illuminance of the beam incident to the first unit surface, the optical element  510  integrates plural beams, and the optical element  510  splits the integrated beam again. Therefore, the optical element  510  acts as an integrator and beam integrating and splitting means. 
         [0095]      FIG. 25  is a view illustrating a configuration of an optical system according to another embodiment of the invention. The optical system includes first unit surfaces  5111   a  and  5111   b  and second unit surfaces  5131   a  and  5131   b  corresponding to the first unit surfaces  5111   a  and  5111   b.    
         [0096]    Both the first unit surfaces  5111   a  and  5111   b  are partial regions on the spherical surface C 1  having the focal length f. Both the second unit surfaces  5131   a  and  5131   b  are partial regions on the spherical surface C 2  having the focal length f.  FIG. 25  is a sectional view including an optical axis that is defined by a straight line connecting the centers of the spherical surfaces C 1  and C 2  (hereinafter simply referred to as optical axis). In  FIG. 25 , the two first unit surfaces and the two second unit surfaces corresponding to the two first unit surfaces are provided. However, actually there are four first unit surfaces and four second unit surfaces. 
         [0097]    The first unit surfaces  5111   a  and  5111   b  are symmetrically disposed in relation to the optical axis. Similarly the second unit surfaces  5131   a  and  5131   b  are symmetrically disposed in relation to the optical axis. 
         [0098]    It is not always necessary that the first unit surfaces  5111   a  and  5111   b  be partial regions on a spherical surface, but the first unit surfaces  5111   a  and  5111   b  may be partial regions on an aspherical surface (including a parabolic surface). It is not always necessary that the second unit surfaces  5131   a  and  5131   b  be partial regions on a spherical surface, but the second unit surfaces  5131   a  and  5131   b  may be partial regions on an aspherical surface (including a parabolic surface). It is not always necessary that the first unit surfaces  5111   a  and  5111   b  and the second unit surfaces  5113   a  and  5113   b  have the same shape provided that the first unit surfaces  5111   a  and  5111   b  and the second unit surfaces  5131   a  and  5131   b  have the substantially same refractive power. 
         [0099]    The parallel beams L 6  and L 5  which travel in two directions that are symmetrical in relation to the optical axis and are incident to the first unit surfaces  5111   a,  are collected in the centers of the second unit surfaces  5131   a  and  5131   b,  respectively by the refractive power of the first unit surface  5111   a.  Similarly the parallel beams L 8  and L 7  which travel in two directions that are symmetrical in relation to the optical axis and are incident to the first unit surfaces  5111   b,  are collected in the centers of the second unit surfaces  5131   a  and  5131   b,  respectively by the refractive power of the first unit surface  5111   b.    
         [0100]      FIG. 26  is a view illustrating configurations of a first optical element  510   a  that includes a first surface  5111  having plural first unit surfaces and a second optical element  510   b  that includes a second surface  5131  having plural second unit surfaces.  FIG. 26  is a sectional view including the optical axis. A surface  5113  of the first optical element  510   a  on the side opposite to the first surface  5111  and a surface  5133  of the second optical element  510   b  on the side opposite to the second surface  5131  are flat. 
         [0101]    In  FIG. 26 , after two parallel beams which are incident at a predetermined angle formed with the optical axis to the first surface  5111 , are integrated in the second surface  5131  that is of the output surface, the integrated beam is split again into two beams exiting at a predetermined angle formed with the optical axis. Actually, after four beams incident to the first surface  5111  that is of the incident surface are integrated into one beam, the integrated beam is split again into four beams. Generally, after n beams which travel in different directions and are incident to m first unit surfaces at a predetermined angle, are collected and integrated in n second unit surfaces, the integrated beam is split into m beams traveling in different directions, where n and m represent positive integers. Thus, the optical elements  510   a  and  510   b  act as an integrator and beam integrating and splitting means. 
         [0102]      FIG. 27  is a view illustrating a configuration of an optical system according to another embodiment of the invention. The optical system includes a first unit portion  510   cp   1 , a first unit portion  510   cp   2 , a second unit portion  510   dp   1 , and a second unit portion  510   dp   2 . The first unit portion  510   cp   1  includes a unit surface  5115   a  and a unit surface  5117   a.  The first unit portion  510   cp   2  includes a unit surface  5115   b  and a unit surface  5117   b.  The second unit portion  510   dp   1  includes a unit surface  5135   a  and a unit surface  5137   a.  The second unit portion  510   dp   2  includes a unit surface  5135   b  and a unit surface  5137   b.  The second unit portions correspond to the first unit portions. The first unit portions  510   cp   1  and  510   cp   2  and the second unit portions  510   dp   1  and  510   dp   2  have positive refractive powers.  FIG. 27  is a sectional view including the optical axis of the first unit portion. In  FIG. 27 , the two first unit portions and the two second unit portions corresponding to the first unit portions are provided. However, actually there are four first unit portions and four second unit portions. 
         [0103]    The unit surfaces  5115   a  and  5115   b  and the unit surfaces  5117   a  and  5117   b  are partial regions on spherical surfaces, and the first unit portions  510   cp   1  and  510   cp   2  are symmetrically disposed in relation to the optical axis. The unit surfaces  5135   a  and  5135   b  and the unit surfaces  5137   a  and  5137   b  are partial regions on spherical surfaces, and the second unit portions  510   dp   1  and  510   dp   2  are symmetrically disposed in relation to the optical axis. 
         [0104]    It is not always necessary that the unit surfaces  5115   a  and  5115   b  and the unit surfaces  5117   a  and  5117   b  be partial regions on spherical surfaces, but the unit surfaces  5115   a  and  5115   b  and the unit surfaces  5117   a  and  5117   b  may be partial regions on aspherical surfaces (including parabolic surfaces). It is not always necessary that the unit surfaces  5135   a  and  5135   b  and the unit surfaces  5137   a  and  5137   b  be partial regions on spherical surfaces, but the unit surfaces  5135   a  and  5135   b  and the unit surfaces  5137   a  and  5137   b  may be partial regions on aspherical surfaces (including parabolic surfaces). It is not always necessary that the unit surface  5115   a  ( 5115   b ), the unit surface  5117   a  ( 5117   b ), the unit surface  5135   a  ( 5135   b ), and the unit surface  5137   a  ( 5137   b ) have the same shape provided that the first unit portions  510   cp   1  and  510   cp   2  and the second unit portions  510   dp   1  and  510   dp   2  have the substantially same refractive power. 
         [0105]    The parallel beams L 6  and L 5 , which travel in two directions that are symmetrical in relation to the optical axis and are incident to the unit surfaces  5115   a  of the first unit portion  510   cp   1 , are collected in the centers of the unit surfaces  5135   a  and  5135   b,  respectively by the refractive powers of the first unit portion  510   cp   1  and the second unit portions. Similarly the parallel beams L 8  and L 7  which travel in two directions that are symmetrical in relation to the optical axis and are incident to the unit surfaces  5115   b  of the first unit portion  510   cp   2 , are collected in the centers of the unit surfaces  5135   a  and  5135   b,  respectively. 
         [0106]      FIG. 28  is a view illustrating a configuration of an integrator that includes a first optical element  510   c  and a second optical element  510   d.  The first optical element  510   c  includes a surface  5115  having plural unit surfaces and a surface  5117  having plural unit surfaces. The second optical element  510   d  includes a surface  5135  having plural unit surfaces and a surface  5137  having plural unit surfaces.  FIG. 28  is a sectional view including the optical axis. 
         [0107]    In  FIG. 28 , after two parallel beams incident to the surface  5115  of the first optical element  510   c  at a predetermined angle formed with the optical axis of the first unit portion are integrated in the surface  5135  of the second optical element  510   d,  the integrated beam is split again into two beams exiting at a predetermined angle formed with the optical axis. Actually, after four beams incident to the surface  5115  at a predetermined angle formed with the optical axis of the first unit portion are integrated, the integrated beam is split again into four beams. Generally, after n beams which travel in different directions and are incident to m first unit surfaces at a predetermined angle, are collected and integrated in n second unit surfaces, the integrated beam is split into m beams traveling in different directions, where n and m represent positive integers. Thus, the optical elements  510   c  and  510   d  act as an integrator and beam integrating and splitting means. 
       Optical Element (Integrator) of First Embodiment 
       [0108]      FIG. 13  is a view illustrating sections including first and second surfaces when viewed from an optical axis direction and a section including an optical axis in an optical element according to a first embodiment. As used herein the optical axis shall mean an optical axis of the first unit surface.  FIG. 13(   a ) is a view illustrating a section including the first surface  111  when viewed from the optical axis direction, a section including the second surface  113  when viewed from the optical axis direction, and a section including the optical axis in the optical element  110 .  FIG. 13(   b ) is a view illustrating a section AA′ of the optical element  110 . 
         [0109]    The optical element  110  used in a visible ray wavelength band can be produced at low cost as an injection-molded component of thermoplastic resin. In the first embodiment, ZEONEX 480R having a refractive index n of 1.525 (product of ZEON corporation) is used as a material for the optical element  110 . 
         [0110]    The second surface  113  of the optical element  110  includes second unit surfaces. The second unit surface includes a convex spherical surface having a curvature radius r of 5.25 and a focal length f of 10. The first surface  111  of the optical element  110  includes first unit surfaces. The first unit surface also includes the convex spherical surface having the curvature radius r of 5.25 and the focal length f of 10. An interval (that is, a thickness of the optical element  110 ) between the first surface  111  and the second surface  113  is d of 15.25. The first surface  111  is disposed in the focal position of the second surface  113  while the second surface  113  is disposed in the focal position of the first surface  111 . 
         [0111]      FIG. 14  is a view illustrating the second surface  113  ( FIG. 14(   a )) and the first surface  111  ( FIG. 14(   b )) of the optical element  110  of the first embodiment. In the second surface  113 , four second unit surfaces  113   a,    113   b,    113   c,  and  113   d  that are not adjacent to one another correspond to the first unit surface  111   a  of the first surface  111 . In  FIG. 14 , the second unit surface is formed into a square whose one side has a length w 1  of 1.5. The second unit surfaces adjacent to each other are separated by 4.5 (a size of three unit surfaces), and a distance h 1  from the optical axis (center axis) of the optical element to the centers of the second unit surfaces  113   a,    113   b,    113   c,  and  113   d  is given by Equation (5). 
         [0000]        h   1 =1.5√{square root over (2)} w   1 =3.18  (5) 
         [0112]    In  FIG. 14 , the first unit surface  111   a  of the first surface  111  is formed into a square whose one side has a length w 2  of 3 (=2×w 1 ), and the center of one of the first unit surfaces  111   a  (indicated in black of  FIG. 14(   b )) is disposed so as to be matched with the center axis of the optical element. When the first unit surfaces are arranged with no gap therebetween in the first surface  111 , the second unit surfaces corresponding to the first unit surfaces can also be arranged with no gap therebetween in the second surface  113 . 
         [0113]    In the optical element  110  thus configured, when the second surface  113  is used as the incident surface, the parallel beam that is perpendicularly incident to the second surface  113  of the optical element  110  can be split into four beams, each of which travels at the angle θ 1  formed with the optical axis, diverging at the spread angle φ 1 . 
         [0114]    When the second surface  113  is used as the output surface, the four beams each of which is incident to the optical element  110  at the angle θ 1  formed with the optical axis, can be integrated in the beam that exits in the optical axis direction, diverging at the spread angle φ 2 . At this point, the angle θ 1  and the spread angles φ 1  and φ 2  are obtained as follows by Equations (1) to (3). 
         [0000]      θ 1 = 18 . 6 ° 
         [0000]      φ 1 = 4 . 3 ° 
         [0000]      φ 2 = 8 . 5 ° 
       Optical Element (Integrator) of Second Embodiment 
       [0115]      FIG. 15  is a view illustrating a second surface  123  ( FIG. 15(   a )) and a first surface  121  ( FIG. 15(   b )) of an optical element  120  according to a second embodiment. In the second surface  123 , nine second unit surfaces (indicated in black of  FIG. 15(   a )) that are not adjacent to one another correspond to the first unit surface (indicated in black of  FIG. 15(   b )) of the first surface  121 . In  FIG. 15 , the second unit surface is formed into a square whose one side has a length w 1  of 1.0. The second unit surfaces adjacent to each other are separated by 2.0 (size of two unit surfaces). 
         [0116]    In  FIG. 15 , the first unit surface of the first surface  121  is formed into a square whose one side has a length w 2  of 3 (=3×w 1 ), and the center of one of the first unit surfaces (indicated in black of  FIG. 15(   b )) is disposed so as to be matched with the center axis of the optical element. When the first unit surfaces are arranged with no gap therebetween in the first surface  121 , the second unit surfaces corresponding to the first unit surfaces can also be arranged with no gap therebetween in the second surface  123 . 
         [0117]    In the optical element  120  thus configured, when the second surface  123  is used as the incident surface, the parallel beam that is perpendicularly incident to the second surface  123  of the optical element  120  can be split into nine beams each of which travels at a predetermined angle formed with the optical axis. 
         [0118]    When the second surface  123  is used as the output surface, the nine beams each of which is incident to the optical element  120  at a predetermined angle formed with the optical axis can be integrated into a beam that exits in the optical axis direction. 
         [0119]    When the optical element of the second embodiment is used as the beam splitting means, the number of second unit surfaces corresponding to one first unit surface becomes equal to the number of split beams. When the optical element of the second embodiment is used as the beam integrating means, the number of second unit surfaces corresponding to one first unit surface becomes equal to the number of integrated beams. Accordingly, the number of second unit surfaces corresponding to one first unit surface can be determined according to the number of split or integrated beams. 
       Optical Element (Integrator) of Third Embodiment 
       [0120]      FIG. 16  is a view illustrating a second surface  133  ( FIG. 16(   a )) and a first surface  131  ( FIG. 16(   b )) of an optical element  130  according to a third embodiment. In the second surface  133 , four second unit surfaces (indicated in black of  FIG. 16(   a )) that are not adjacent to one another correspond to the first unit surface (indicated in black of  FIG. 16(   b )) of the first surface  131 . In  FIG. 16 , the first unit surface and the second unit surface are formed into rectangles. 
         [0121]    As illustrated in  FIG. 16 , when the first unit surfaces are arranged with no gap therebetween in the first surface  131 , the second unit surfaces corresponding to the first unit surfaces can also be arranged with no gap therebetween in the second surface  133 . 
         [0122]    In the optical element  130  thus configured, when the second surface  133  is used as the incident surface, the parallel beam that is perpendicularly incident to the second surface  133  of the optical element  130  can be split into four beams each of which travels at a predetermined angle formed with the optical axis. 
         [0123]    When the second surface  133  is used as the output surface, four beams each of which is incident to the optical element  130  at a predetermined angle formed with the optical axis can be integrated into a beam that exits in the optical axis direction. 
         [0124]    Because the incident surface of the optical element is disposed in a position conjugate with the illuminated region, desirably an end face of the incident surface has a shape close to the shape of an actually required illuminated region. For example, in cases where the optical element is used in an apparatus in which an image of the illuminated region is taken with a CCD camera or in a liquid crystal projector, the end face of the incident surface is formed into a rectangle having an aspect ratio close to that of an image pickup device or an image modulation device as illustrated in  FIG. 16 , which allows efficient illumination. 
       Optical Element (Integrator) of Fourth Embodiment 
       [0125]      FIG. 17  is a view illustrating a second surface  143  ( FIG. 17(   a )) and a first surface  141  ( FIG. 17(   b )) of an optical element  140  according to a fourth embodiment. In the second surface  143 , seven second unit surfaces (indicated in black of  FIG. 17(   a )) that are not adjacent to one another correspond to the first unit surface (indicated in black of  FIG. 17(   b )) of the first surface  141 . In  FIG. 17 , the first unit surface and the second unit surface are formed into regular hexagons. 
         [0126]    As illustrated in  FIG. 17 , when the first unit surfaces are arranged with no gap therebetween in the first surface  141 , the second unit surfaces corresponding to the first unit surfaces can also be arranged with no gap therebetween in the second surface  143 . 
         [0127]    In the optical element  140  thus configured, when the second surface  143  is used as the incident surface, the parallel beam that is perpendicularly incident to the second surface  143  of the optical element  140  can be split into the seven beams each of which travels at a predetermined angle formed with the optical axis. 
         [0128]    When the second surface  143  is used as the output surface, the seven beams each of which is incident to the optical element  140  at a predetermined angle formed with the optical axis can be integrated into a beam that exits in the optical axis direction. 
         [0129]    Because the incident surface of the optical element is disposed in a position conjugate with an illuminated region, desirably an end face of the incident surface has a shape close to the shape of an actually required illuminated region. For example, in cases where the optical element is required to illuminate a circular region such as in a microscope, the end face of the incident surface is formed into a regular hexagon as illustrated in  FIG. 17 , which allows efficient illumination. 
       Optical Element (Integrator) of Fifth Embodiment 
       [0130]      FIG. 29  is a view illustrating sections including first and second surfaces respectively when viewed from an optical axis direction and a section including an optical axis in an optical element according to a fifth embodiment. As used herein, the optical axis shall mean an optical axis of the first unit surface.  FIG. 29(   a ) is a view illustrating a section including a first surface  511  when viewed from the optical axis direction, a section including a second surface  513  when viewed from the optical axis direction, and a section including the optical axis in an optical element  510 .  FIG. 29(   b ) is a view illustrating a section AA′ of the optical element  510 . In  FIG. 29 , the second unit surface is formed into a square whose one side has a length w 1  of 1.5. 
         [0131]      FIG. 30  is a view illustrating the first surface  511  ( FIG. 30(   a )) and the second surface  511  ( FIG. 30(   b )) of the optical element  510  of the fifth embodiment. In the second surface  513 , four second unit surfaces  513   a,    513   b,    513   c,  and  513   d  that are not adjacent to one another correspond to four first unit surfaces  511   a,    511   b,    511   c,  and  511   d  that are not adjacent to one another in the first surface  511 . In  FIG. 30 , the first unit surface and the second unit surface are formed into a square whose one side has a length w 1  of 1.5. Adjacent first unit surfaces are separated from each other by 3 (size of two unit surfaces), and adjacent second unit surface are separated from each other by 3 (size of two unit surfaces). 
         [0132]    In the fifth embodiment, the number of first unit surfaces becomes equal to the number of split beams. The number of second unit surfaces becomes equal to the number of integrated beams. In the optical element  510  thus configured, when the first surface  511  is used as the incident surface, after four parallel beams each of which is incident to the first surface  511  of the optical element  510  at a predetermined angle formed with the optical axis are integrated, the integrated beam can be split into four beams each of which travels at a predetermined angle formed with the optical axis. 
       Optical Element (Integrator) of Sixth Embodiment 
       [0133]      FIG. 31  is a view illustrating a first surface  521  ( FIG. 32(   a )) and a second surface  523  ( FIG. 31(   b )) of an optical element  520  according to a sixth embodiment. In the second surface  523 , two second unit surfaces (indicated in black of  FIG. 31(   b )) that are not adjacent to each other correspond to the four first unit surfaces (indicated in black of  FIG. 31(   a )) of the first surface  521  which are not adjacent to one another. In  FIG. 31 , the first unit surface is formed into a square whose one side has a length of 1, and the second unit surface is formed into a rectangular in which a short side has a length of 1 and a long side has a length of 2. 
         [0134]    As illustrated in  FIG. 31 , when the first unit surfaces are arranged with no gap therebetween in the first surface  521 , the second unit surfaces corresponding to the first unit surfaces can also be arranged with no gap therebetween in the second surface  523 . 
         [0135]    In the sixth embodiment, the number of first unit surfaces becomes equal to the number of split beams. The number of second unit surfaces becomes equal to the number of integrated beams. In the optical element  520  thus configured, when the first surface  521  is used as the incident surface, two parallel beams each of which is incident to the optical element  520  at a predetermined angle formed with the optical axis are integrated, and then the integrated beam can be split into four beams each of which travels at a predetermined angle formed with the optical axis. 
         [0136]    When the first surface  521  is used as the output surface, four beams each of which is incident to the optical element  520  at a predetermined angle formed with the optical axis are integrated, and then the integrated beam can be split into two beams each of which travels at a predetermined angle formed with the optical axis. 
       Illuminating Apparatus of First Embodiment 
       [0137]      FIG. 18  is a view illustrating a configuration of an illuminating apparatus according to a first embodiment in which optical element is used. The illuminating apparatus of the first embodiment is a quadrupole type modified illuminating apparatus that is used to improve a depth of focus or a resolution in a projection exposure apparatus used to produce a semiconductor device or the like. 
         [0138]    An illuminating beam emitted from a light source  21  such as a mercury vapor lamp is collected by an ellipsoidal mirror  22 , and the illuminating beam is formed into a substantially parallel beam by an input lens (collimator lens)  30 , and the parallel beam is incident to the optical element  110 . Four second unit surfaces correspond to the first unit surface of the optical element  110 . When the second surface  113  of the optical element  110  is disposed as the incident surface, the optical element  110  is used as beam splitting means and light uniformizing means. 
         [0139]    The illuminating beam is split into four beams by the optical element  110 , and the four beams are collected by a first collective lens  40 . Four secondary light sources are formed with uniform illuminance in a focal position on an exit side (back side) of the first collective lens  40 . 
         [0140]    Four fly&#39;s eye integrators  50  are provided in positions at which the secondary light sources are formed. The four fly&#39;s eye integrators  50  are a fly&#39;s eye integrator having a conventional shape. The beams emitted from the four fly&#39;s eye integrators  50  are collected by a second collective lens  60 , and a reticle  70  is uniformly illuminated at a predetermined inclination. 
         [0141]    A predetermined circuit pattern is formed in a surface of the reticle  70  opposite to the illuminated surface. Light of the inclined illumination that is transmitted and diffracted by the reticle pattern is collected to form a pattern image of the reticle  70  on a wafer  90  by a projection optical system  80 . 
         [0142]    As illustrated by dotted lines of  FIG. 18 , a light source image B 1  by the ellipsoidal mirror  22 , the first surface  111  of the optical element  110 , and an output side surface  50   x  of the fly&#39;s eye integrator  50  are provided in positions conjugate with an entrance pupil plane (aperture stop  80   a ) of the projection optical system. In other words, the light source image B 1 , the first surface  111  of the optical element  110 , and the output side surface  50   x  of the fly&#39;s eye integrator  50  become Fourier transform surface of object surfaces (reticle  70  and wafer  90 ). As illustrated by a solid line of  FIG. 18 , the second surface  113  of the optical element  110  and an incident-side side surface  50   a  of the fly&#39;s eye integrator  50  are provided in positions conjugate with the object surfaces (reticle  70  and wafer  90 ). 
         [0143]    As described above, the use of the optical element  110  that acts as a fly&#39;s eye integrator and beam splitting means eliminates the need for using independent beam splitting means, so that a compact optical system can be formed. 
       Illuminating Apparatus of Second Embodiment 
       [0144]      FIG. 19  is a view illustrating a configuration of an illuminating apparatus according to a second embodiment in which optical element is used. The illuminating apparatus of the second embodiment is an illuminating apparatus that is used to illuminate light receiving surfaces of plural solid-state image pickup devices with light in inspecting electric characteristics of the solid-state image pickup devices such as CCD (Charge-Coupled Device) and CMOS. 
         [0145]    The illuminating beam emitted from a light source  1020  such as a halogen lamp, a xenon lamp, and a metal halide lamp is formed into a substantially parallel beam by an input lens (collimator lens)  1030 , and the parallel beam passes through an ND filter turret  141  and a color filter turret  142 . 
         [0146]    The ND filter turret  141  having a circular shape is supported while being rotatable about a support shaft. The ND filter turret  141  retains plural kinds of ND (Neutral Density) filters along a circumferential direction. A ND filter attenuates the light emitted from the light source  1020  at a predetermined ratio without changing a spectral composition. The ND filter turret  141  is rotated to select a ND filter having a desired light attenuation amount, thereby performing adjustment to a light quantity suitable to the inspection. 
         [0147]    The color filter turret  142  having a circular shape is supported while being rotatable about a support shaft. The color filter turret  142  retains plural kinds of color filters along a circumferential direction. A color filter transmits only light having a predetermined wavelength in the light emitted from the light source  1020 . A wavelength of the transmitted light is selected by rotating the color filter turret  142 . 
         [0148]    The beam transmitted through the ND filter turret  141  and color filter turret  142  is incident to the optical element  110 . At this point, four second unit surfaces correspond to the first unit surface of the optical element  110 . The optical element  110  is used as a beam splitting means and light uniformizing means by disposing the second surface  113  of the optical element  110  as the incident surface. 
         [0149]    The illuminating beam is split into four beams by the optical element  110 , and the split beams are collected by a condenser lens  150 . Four solid-state image pickup devices  161  that are of inspection targets are disposed in a focal position on the exit side (back side) of the condenser lens  150 , and the solid-state image pickup devices  161  are illuminated with uniform illuminance by the split beams, respectively. 
         [0150]    In the second embodiment, four second unit surfaces correspond to one first unit surface of the optical element. However, the invention is not limited to four second unit surfaces. As described above, because the number of second unit surfaces corresponding to one first unit surface of the optical element becomes equal to the number of split beams, the number of second unit surfaces may appropriately be selected according to the number of simultaneously-inspected solid-state image pickup devices that are of the inspection targets. For example, the second optical element of  FIG. 15  (the number of splits is nine) may be used. 
         [0151]    Thus, the use of the optical element  110  that acts as a fly&#39;s eye integrator and beam splitting means eliminates the need for using independent beam splitting means, so that a compact optical system can be formed. 
       Illuminating Apparatus of Third Embodiment 
       [0152]      FIG. 20  is a view illustrating a configuration of an illuminating apparatus according to a third embodiment in which optical element is used. The illuminating apparatus of the third embodiment is an epi-fluorescent optical system of a microscope apparatus. 
         [0153]    As illustrated in  FIG. 20(   a ), the microscope apparatus includes a microscope main body M, an epi-fluorescent optical system L, an image pickup apparatus  280 , an image processing device  281 , and a display device  282 . A biological sample  271  previously labeled with a fluorescent material is set in the microscope apparatus. 
         [0154]    The microscope main body M includes an infinity objective lens  272  and an imaging lens  273 . 
         [0155]    The epi-fluorescent optical system L includes four kinds of light sources  221  to  224  having different illuminating light wavelengths, a collimator lens  230 , an optical element  110 , a relay lens  240 , a field stop  241 , and a dichroic mirror  250 . The dichroic mirror  250  is disposed between the objective lens  272  and the imaging lens  273  in the microscope main body M. A bandpass filter  260  is disposed between the dichroic mirror  250  and the imaging lens  273 . 
         [0156]      FIG. 20(   b ) is a view illustrating an arrangement of the light sources  221  to  223 . The light sources  221  to  224  are a solid-state light source that emits light having a center wavelength in waveband of an ultraviolet ray (wavelength of 340 nm to 400 nm) or a visible ray (wavelength of about 400 nm to about 700 nm). 
         [0157]    Desirably the light source is selected such that an exciting wavelength of the fluorescent material is matched with the center wavelength of the light source. For example, desirably a light source such as GaN LED is used when the fluorescent material has an exciting wavelength of an ultraviolet ray to a blue ray (300 nm to 500 nm). Because desirably a broadband white light source is used to observe a bright-field color image, a light source such as a white LED is desirably used. In the white LED, a GaN blue LED emitting the light having the exciting wavelength and YAG (Yttrium Aluminum Garnet) fluorescent emission are combined. 
         [0158]    In the collimator lens  230 , a front focus is disposed in the positions of the light sources  221  to  224  to collimate the beams exiting from the light sources  221  to  224 . 
         [0159]    The collimated beams are incident to the optical element  110  that is disposed in a back focus of the collimator lens  230  at an angle θ formed with the optical axis. At this point, assuming that h is an offset amount from the optical axis of the collimator lens  230  of the light sources  221  to  224  and f is a focal length of the collimator lens, the angle θ, the offset amount h, and the focal length f satisfy the following Equation (6). 
         [0000]      h=f sin θ  (6) 
         [0160]    As illustrated in  FIG. 14 , four second unit surfaces correspond to one first unit surface of the optical element  110 . When the second surface  113  of the optical element  110  is used as the output surface, the optical element  110  acts as light source switching means and light uniformizing means. One of the light sources  221  to  224  is lit on as one of plural exciting light sources or a color observation white light source, which allows switching of the beams. 
         [0161]    A secondary light source images S are formed in the second surface  113  of the optical element  110 . 
         [0162]    The relay lens  240  relays the secondary light source image S to a back focal surface (pupil plane) of the objective lens  272 . The dichroic mirror  250  reflects the excitation beam to guide the excitation beam toward the objective lens  272 . 
         [0163]    The beam (excitation beam) exiting from a light source image S′ formed in the pupil plane of the objective lens  272  is collimated by the objective lens  272 , and the beam is incident to an illuminated region E of the sample  271 . 
         [0164]    The field stop  241  is disposed in a position conjugate with the sample  271 , and the field stop  241  has a function of restricting the illuminated region E on the sample  271 . 
         [0165]    In the illuminated region E on the sample  271 , the fluorescent material is excited to generate fluorescence. The fluorescent wavelength is longer than the wavelength (500 nm or less) of the excitation beam and, for example, the fluorescent wavelength ranges from about 520 nm to about 590 nm. 
         [0166]    The beam including the fluorescence is converted by the objective lens  272  into such a beam as forms a fluorescent image of the sample  271  in the infinite distance. The fluorescent beam is transmitted through the dichroic mirror  250  and incident to the bandpass filter  260  and the imaging lens  273 . The bandpass filter  260  cuts excessive light having a wavelength different from that of the fluorescent beam (in this case, wavelength of 520 nm to 590 nm). 
         [0167]    An image pickup surface  280   a  of the image pickup apparatus  280  is disposed in a back focal surface of the imaging lens  273 , and the image (fluorescent image) of the sample  271  is formed on the image pickup surface  280   a  by the fluorescent beam. 
         [0168]    Dotted lines in  FIG. 20  indicate a conjugate relationship among the sample  271 , the image pickup surface  280   a,  and the field stop  241 . 
         [0169]    In the image pickup apparatus  280 , the fluorescent image formed on the image pickup surface  280   a  is taken, and the obtained image data is transmitted to the image display device  282  through the image processing device  281 . The image display device  282  displays the fluorescent image. 
         [0170]    In the third embodiment, four second unit surfaces correspond to one first unit surface of the optical element  110 . However, the invention is not limited to four second unit surfaces. As described above, because the number of second unit surfaces corresponding to one first unit surface of the optical element  110  becomes equal to the number of split beams, the number of second unit surfaces may appropriately be selected according to the number of light sources. For example, the second optical element of  FIG. 15  (the number of splits is nine) may be used. 
         [0171]    Thus, the use of the optical element  110  that acts as a fly&#39;s eye integrator and beam integrating means eliminates the need for using independent beam integrating means, so that a compact optical system can be formed. 
       Illuminating Apparatus of Fourth Embodiment 
       [0172]      FIG. 21  is a view illustrating a configuration of an illuminating apparatus according to a fourth embodiment in which optical element is used. The illuminating apparatus of the fourth embodiment is an illuminating apparatus of an image projector. 
         [0173]      FIG. 21(   b ) is a view illustrating an arrangement of light sources  320   r,    320   g,  and  320   b.  In  FIGS. 21(   a ) and  21 ( b ), the light sources  320   r,    320   g,  and  320   b  are red, green, and blue Light Emitting Diodes (LEDs), respectively. One red LED  320   r,  two green LEDs  320   g,  and one blue LED  320   b  are disposed in the fourth embodiment. Because the green LED has lower light emission efficiency than those of the other color LEDs, the two green LEDs are disposed such that a color balance is maintained. 
         [0174]    In a collimator lens  330 , a front focus is disposed in the positions of the light sources  320   r,    320   g,  and  320   b  to collimate the beams exiting from the light sources  320   r,    320   g,  and  320   b.    
         [0175]    The collimated beams are incident to the optical element  110  disposed in the back focus of the collimator lens  330  at the angle θ formed with the optical axis. At this point, assuming that h is an offset amount from the optical axis of the collimator lens  330  of in the light sources  320   r,    320   g,  and  320   b  and f is a focal length of the collimator lens, the angle θ, the offset amount h, and the focal length f satisfy Equation (6). 
         [0176]    As illustrated in  FIG. 14 , four second unit surfaces correspond to one first unit surface of the optical element  110 . When the second surface  113  of the optical element  110  is used as the output surface, the optical element  110  acts as light source switching means and light uniformizing means. 
         [0177]    RGB can be mixed by the configuration of  FIG. 21 . Particularly the illuminating apparatus of the fourth embodiment is suitable to an image projector apparatus in which color images are projected in time-shared manner by alternately lighting on the RGB light sources. 
         [0178]    An optical modulation element  350   a  is uniformly illuminated with the beams that are mixed by the optical element  110  and pass through a condenser lens  340 . 
         [0179]    An enlarged image of beam modulated by the optical modulation element  350   a  is formed on a screen  380  by a projection optical system  370 . 
         [0180]    In the fourth embodiment, the optical modulation element  350   a  is formed in a transmission type optical modulation element. 
         [0181]      FIG. 22  is a view illustrating a configuration of an illuminating apparatus of an image projector in which a reflection type optical modulation element  350   b  is used in the illuminating apparatus of  FIG. 21 . In the illuminating apparatus of  FIG. 22 , the optical element  110  is used in a manner similar to that of the illuminating apparatus of  FIG. 21 . 
       Illuminating Apparatus of Fifth Embodiment 
       [0182]      FIG. 32  is a view illustrating a configuration of an illuminating apparatus of a fifth embodiment in which the optical element is used. The illuminating apparatus of the fifth embodiment is an illuminating apparatus that is used to irradiate light receiving surfaces of plural solid-state image pickup devices with light in inspecting electric characteristics of the solid-state image pickup devices such as CCD (Charge-Coupled Device) and CMOS (Complementary Metal-Oxide Semiconductor). 
         [0183]      FIG. 32(   b ) is a view illustrating an arrangement of light sources  420   r,    420   g,  and  420   b.  In  FIGS. 32(   a ) and  32 ( b ), the light sources  420   r,    420   g,  and  420   b  are red, green, and blue Light Emitting Diodes (LEDs), respectively. One red LED  420   r,  two green LEDs  420   g,  and one blue LED  420   b  are disposed in the fifth embodiment. Because the green LED has a lower light emission efficiency than those of the other color LEDs, the two green LEDs are disposed such that a color balance is maintained. 
         [0184]    In a collimator lens  430 , a front focus is disposed in the positions of the light sources  420   r,    420   g,  and  420   b  to collimate the beams exiting from the light sources  420   r,    420   g,  and  420   b.    
         [0185]    The collimated beams are incident to the optical element  510  disposed in the back focus of the collimator lens  430  at the angle θ formed with the optical axis. At this point, assuming that h is an offset amount from the optical axis of the collimator lens  430  of the light sources  420   r,    420   g,  and  420   b,  and f is a focal length of the collimator lens, the angle θ, the offset amount h, and the focal length f satisfy the Equation (6). 
         [0000]      h=f sin θ  (6) 
         [0186]    The collimated beam is incident to the optical element  510 . At this point, in the optical element  510 , there are four first unit surfaces, and there are four second unit surfaces. Therefore, the optical element  510  is used as beam integrating means, beam splitting means, and light uniformizing means. 
         [0187]    The illuminating beam is split into the four beams by the optical element  510 , and each of the split beams is collected by the condenser lens  450 . Four solid-state image pickup devices  461  that are of the inspection targets are disposed in a focal position on the exit side (back side) of the condenser lens  450 , and the solid-state image pickup devices  461  are illuminated with uniform illuminance by the split beams, respectively. 
         [0188]    In the fifth embodiment, four unit surfaces are included in the set of first unit surface. However, the invention is not limited to four unit surfaces. As described above, because the number of unit surfaces included in the set of first unit surfaces becomes equal to the number of split beams, the number of unit surfaces may appropriately be selected according to the number of simultaneously-inspected solid-state image pickup devices that are of the inspection targets. 
         [0189]    In the fifth embodiment, four unit surfaces are included in the set of second unit surface. However, the invention is not limited to four unit surfaces. As described above, because the number of unit surfaces included in the set of second unit surfaces becomes equal to the number of integrated beams, the number of unit surfaces may appropriately be selected according to the number of light sources. 
         [0190]    Thus, the use of the optical element  510  that acts as a fly&#39;s eye integrator, beam splitting means, and beam integrating means eliminates the need for using independent beam splitting means and beam integrating means, so that a compact optical system can be formed. 
         [0191]    The features of embodiments of the invention will be described below. 
         [0192]    In an integrator according to one embodiment, a size of a section of the predetermined first unit surface is n times a size of a section of each of the predetermined n second unit surfaces. The section of the predetermined first unit surface is perpendicular to the optical axis of the predetermined first unit surface, and the section of each of the predetermined n second unit surfaces is perpendicular to the optical axis of the predetermined first unit surface. 
         [0193]    Accordingly, the size of the first surface is conveniently equalized to the size of the second surface. 
         [0194]    In an integrator according to another embodiment, the predetermined first unit surfaces are disposed in the first surface with no gap therebetween. 
         [0195]    The integrator of the embodiment is efficient because of no loss of the light incident to the first surface. 
         [0196]    In an integrator according to another embodiment, the predetermined second unit surfaces are disposed in the second surface with no gap therebetween. 
         [0197]    The integrator of the embodiment is efficient because of no loss of the light incident to the second surface. 
         [0198]    In an integrator according to another embodiment, a shape of a section of the predetermined first unit surface and a section of each of the predetermined n second unit surfaces have square shapes. The section of the predetermined first unit surface is perpendicular to the optical axis of the predetermined first unit surface, and the section of each of the predetermined n second unit surfaces is perpendicular to the optical axis of the predetermined first unit surface. 
         [0199]    Accordingly, the square illuminated region is conveniently irradiated. 
         [0200]    In an integrator according to another embodiment, a section of the predetermined first unit surface and a section of each of the predetermined n second unit surfaces have rectangular shapes. The section of the predetermined first unit surface is perpendicular to the optical axis of the predetermined first unit surface, and the section of each of the predetermined n second unit surfaces is perpendicular to the optical axis of the predetermined first unit surface. 
         [0201]    Accordingly, the rectangular illuminated region is conveniently irradiated. The rectangle is formed into a rectangle having an aspect ratio close to that of the image pickup device or image modulation element, which allows the illuminated region to be efficiently irradiated. 
         [0202]    In an integrator according to another embodiment, a section of the predetermined first unit surface and a section of each of the predetermined n second unit surfaces have regular hexagonal shapes. The section of the predetermined first unit surface is perpendicular to the optical axis of the predetermined first unit surface, and the section of each of the predetermined n second unit surfaces is perpendicular to the optical axis of the predetermined first unit surface. 
         [0203]    Accordingly, the circular illuminated region is conveniently irradiated. In the microscope and the like, the circular illuminated region can conveniently be irradiated. 
         [0204]    An integrator according to another embodiment includes one optical element. 
         [0205]    Accordingly, the compact integrator in which the beam is split or integrated by one optical element is implemented in the integrator of the embodiment. 
         [0206]    An integrator according to another embodiment includes a first optical element including a surface in which the first unit surface is formed; and a second optical element including a surface in which the second unit surface is formed. 
         [0207]    Accordingly, the compact integrator in which the beam is split or integrated by two optical elements is implemented in the integrator of the embodiment. 
         [0208]    In an integrator according to another embodiment, after light that is incident to each of the predetermined n second unit surfaces and parallel to the optical axis of the predetermined first unit surface is collected on the predetermined first unit surface, the light is split into n beams traveling in different directions. 
         [0209]    Accordingly, the compact integrator having the beam splitting function is obtained. 
         [0210]    An illuminating apparatus according to one embodiment of the invention includes a light source; collimating means; and the integrator according to one embodiment. In the illuminating apparatus, after light emitted from the light source is formed into light parallel to the optical axis of the predetermined first unit surface by the collimating means, the light is incident to the predetermined n second unit surfaces, and the light is split into n beams traveling in different directions by the integrator. 
         [0211]    Accordingly, the compact illuminating apparatus having the illuminance uniformizing function and the beam splitting function is obtained. 
         [0212]    In an integrator according to another embodiment, after n beams that travel in different directions to be incident to the predetermined first unit surface at a predetermined angle are collected on the predetermined n second unit surfaces, the beams are integrated into a beam traveling in a direction parallel to the optical axis of the predetermined first unit surface. 
         [0213]    Accordingly, the compact integrator having the beam integrating function is obtained. 
         [0214]    An illuminating apparatus according to one embodiment of the invention includes n light sources; and the integrator according to one embodiment. In the illuminating apparatus, light beams emitted from n light sources are incident to the predetermined first unit surface at the predetermined angle as n beams traveling in different directions, and the light beams are integrated into a beam traveling in a direction parallel to the optical axis of the predetermined first unit surface by the integrator. 
         [0215]    Accordingly, the compact illuminating apparatus having the illuminance uniformizing function and the beam integrating function is obtained. 
         [0216]    In an illuminating apparatus according to another embodiment, the n light sources emit light beams having at least two wavelengths. 
         [0217]    Accordingly, the compact illuminating apparatus having the illuminance uniformizing function and the function of switching or mixing light beams having at least two wavelengths is obtained. 
         [0218]    In an integrator according to one embodiment, a size of a section of the predetermined first unit portion is n times a size of a section of each of the predetermined n second unit portions. The section of the predetermined first unit portion is perpendicular to the optical axis of the predetermined first unit portion, and the section of each of the predetermined n second unit portions is perpendicular to the optical axis of the predetermined first unit portion. 
         [0219]    Accordingly, the size of the first member is conveniently equalized to the size of the second member. 
         [0220]    In an integrator according to another embodiment, the predetermined first unit portions are disposed in the first member with no gap therebetween. 
         [0221]    The integrator of the embodiment is efficient because of no loss of the light incident to the first member. 
         [0222]    In an integrator according to another embodiment, the predetermined second unit portions are disposed in the second member with no gap therebetween. 
         [0223]    The integrator of the embodiment is efficient because of no loss of the light incident to the second member. 
         [0224]    In an integrator according to another embodiment, a section of the predetermined first unit portion and a section of each of the predetermined n second unit portions have square shapes. The section of the predetermined first unit portion is perpendicular to the optical axis of the predetermined first unit portion, and the section of each of the predetermined n second unit portions is perpendicular to the optical axis of the predetermined first unit portion. 
         [0225]    Accordingly, the square illuminated region is conveniently irradiated. 
         [0226]    In an integrator according to another embodiment, a section of the predetermined first unit portion and a section of each of the predetermined n second unit portions have rectangular shapes. The section of the predetermined first unit portion is perpendicular to the optical axis of the predetermined first unit portion, and the section of each of the predetermined n second unit portions is perpendicular to the optical axis of the predetermined first unit portion. 
         [0227]    Accordingly, the rectangular illuminated region is conveniently irradiated. The rectangle is formed into a rectangle having an aspect ratio close to that of the image pickup device or image modulation element, which allows the illuminated region to be efficiently irradiated. 
         [0228]    In an integrator according to another embodiment, a section of the predetermined first unit portion and a section of each of the predetermined n second unit portions have regular hexagonal shapes. The section of the predetermined first unit portion is perpendicular to the optical axis of the predetermined first unit portion, and the section of each of the predetermined n second unit portions is perpendicular to the optical axis of the predetermined first unit portion. 
         [0229]    Accordingly, the circular illuminated region is conveniently irradiated. In the microscope and the like, the circular illuminated region can conveniently be irradiated. 
         [0230]    In an integrator according to another embodiment, after light that is incident to a surface on an incident side in each of the predetermined n second unit portions and parallel to the optical axis of the predetermined first unit portion is collected on a surface on an output side in the predetermined first unit portion, the light is split into n beams traveling in different directions. 
         [0231]    Accordingly, the compact integrator having the beam splitting function is obtained. 
         [0232]    An illuminating apparatus according to one embodiment of the invention includes a light source; collimating means; and the integrator according to one embodiment. In the illuminating apparatus, after light emitted from the light source is formed into light parallel to the optical axis of the predetermined first unit portion by the collimating means, the light is incident to the predetermined n second unit portions, and the light is split into n beams traveling in different directions by the integrator. 
         [0233]    Accordingly, the compact illuminating apparatus having the illuminance uniformizing function and the beam splitting function is obtained. 
         [0234]    In an integrator according to another embodiment, after n beams that travel in different directions to be incident to a surface on an incident side in the predetermined first unit portion at a predetermined angle are collected in a surface on an output side in the predetermined n second unit portions, the beams are integrated into a beam traveling in a direction parallel to the optical axis of the predetermined first unit surface. 
         [0235]    Accordingly, the compact integrator having the beam integrating function is obtained. 
         [0236]    An illuminating apparatus according to one embodiment of the invention includes n light sources; and the integrator according to one embodiment. In the illuminating apparatus, light beams emitted from the n light sources are incident as n beams traveling in different directions to a surface on an incident side in the predetermined first unit portion at the predetermined angle, and the light beams are integrated into a beam traveling in a direction parallel to the optical axis of the predetermined first unit surface by the integrator. 
         [0237]    Accordingly, the compact illuminating apparatus having the illuminance uniformizing function and the beam integrating function is obtained. 
         [0238]    In an integrator according to one embodiment of the invention, a size of a section of each of the predetermined in first unit surfaces is n/m times a size of a section of each of the predetermined n second unit surfaces. The section of each of the predetermined m first unit surfaces is perpendicular to the optical axis of the first refractive surface, and the section of each of the predetermined n second unit surfaces is perpendicular to the optical axis of the second unit surface. 
         [0239]    Accordingly, the size of the first surface is conveniently equalized to the size of the second surface. 
         [0240]    In an integrator according to another embodiment, after n beams that travel in different directions to be incident to the predetermined m first unit surfaces at a predetermined angle are collected and integrated into the predetermined n second unit surfaces, the beams are split into m beams traveling in different directions. 
         [0241]    Accordingly, the compact integrator having the beam splitting function is obtained. 
         [0242]    An illuminating apparatus according to one embodiment of the invention includes n light sources; and the integrator according to one embodiment. In the illuminating apparatus, light beams emitted from the n light sources are incident as n beams traveling in different directions to the predetermined m first unit surfaces at the predetermined angle, and the light beams are split into m beams traveling in different directions by the integrator. 
         [0243]    Accordingly, the compact illuminating apparatus having the illuminance uniformizing function and the beam splitting function is obtained. 
         [0244]    In an integrator according to one embodiment, a size of a section of each of the predetermined m first unit portions is n/m times a size of a section of each of the predetermined n second unit portions. The section of each of the predetermined m first unit portions is perpendicular to the optical axis of the first member, and the section of each of the predetermined n second unit portions is perpendicular to the optical axis of the second member. 
         [0245]    Accordingly, the size of the section perpendicular to the optical axis of the first member is conveniently equalized to the size of the section perpendicular to the optical axis of the second member. 
         [0246]    In an integrator according to another embodiment, after n beams traveling in different directions that are incident to the predetermined m first unit portions at a predetermined angle are collected and integrated into the predetermined n second unit portions, the beams are split into m beams traveling in different directions. 
         [0247]    Accordingly, the compact integrator having the beam splitting function is obtained. 
         [0248]    An illuminating apparatus according to one embodiment of the invention includes n light sources; and the integrator according to one embodiment. In the illuminating apparatus, light beams emitted from the n light sources are incident as n beams traveling in different directions to the predetermined m first unit surfaces at the predetermined angle, and the light beams are split into m beams traveling in different directions by the integrator. 
         [0249]    Accordingly, the compact illuminating apparatus having the illuminance uniformizing function and the beam splitting function is obtained.