Patent Publication Number: US-2023161238-A1

Title: Optical element, illumination apparatus, and projective display apparatus

Description:
TECHNICAL FIELD 
     The present disclosure relates to an optical element, an illumination apparatus including the optical element, and a projective display apparatus including the illumination apparatus (projector). 
     BACKGROUND ART 
     In recent years, projective display apparatuses (projectors) using semiconductor laser elements as a light source have increasingly frequently been used. However, semiconductor laser elements have the problems of a high coherency and a high speckle contrast. For example, PTL 1 discloses a projector in which a rotating diffusion element has a two-layer structure. In the technology disclosed in PTL 1, a second light diffusion layer has a higher diffusive power than a first light diffusion layer, and the technology is intended to reduce backscattering, increase light usage efficiency, and reduce speckle noise. Additionally, for example, PTL 2 discloses a projector using a rotating hologram element as a first diffusion section. 
     CITATION LIST 
     Patent Literature 
     
         
         [PTL 1] 
       
    
     Japanese Patent Laid-open No. 2014-182207
     [PTL 2]   

     Japanese Patent Laid-open No. 2012-159823 
     SUMMARY 
     Technical Problems 
     Incidentally, the technology disclosed in PTL 1 uses diffusion plates, but a diffusion angle distribution formed by the diffusion plates is typically a circular distribution, a flat Gaussian distribution, or the like. Specifically, when the shape of light obtained by cutting the light along a virtual plane orthogonal to a traveling direction of the light is hereinafter referred to as a “cross-sectional shape of the light,” the cross-section shape of light emitted from the diffusion plate is like a circle. Additionally, the intensity distribution of light emitted from the diffusion plate has a flat Gaussian distribution on the virtual plane. Accordingly, the reduction of the speckle contract is limited. Additionally, the hologram element depends strongly on wavelength, and it is difficult to design, in the technology disclosed in PTL 2, a hologram element having diffraction characteristics that are equivalent with respect to all of red/green/blue colors. Accordingly, a hologram element needs to be disposed for each of the red/green/blue colors, leading to high costs and an increased size of the apparatus. 
     Consequently, an object of the present disclosure is to enable the speckle contrast to be significantly reduced and provide an illumination apparatus having a configuration and a structure that allow the use of a light source that emits light with multiple wavelengths, a projective display apparatus (projector) including the illumination apparatus, an optical element that is suitably used in the illumination apparatus. 
     Solution to Problems 
     An illumination apparatus of the present disclosure configured to achieve the object includes a light source, an optical member including a first surface on which light from the light source is incident and a second surface facing the first surface, and an integrator on which light emitted from the optical member is incident, in which the optical member is rotatable around a rotation axis extending parallel to a direction in which light from the light source is incident and is emitted, a planar shape of the optical member (the planar shape of the optical member obtained by cutting the optical member along a virtual plane orthogonal to the rotation axis) is annular around the rotation axis, multiple recessed and protruding structure units each having a fan-surface-like planar shape and including a recessed and protruding portion are consecutively formed on the first surface or the second surface of the optical member, an extended line of a boundary between adjacent recessed and protruding structure units intersects the rotation axis, when the boundary between the adjacent recessed and protruding structure units is a mirror plane, the adjacent recessed and protruding structure units are in a mirror symmetry relation, and recessed and protruding portions of the adjacent recessed and protruding structure units are smoothly connected together, and recessed portions and protruding portions of the recessed and protruding portion of each recessed and protruding structure unit are smoothly connected together, and an area occupied by the recessed and protruding portion of each recessed and protruding structure unit is larger in size than incident light from the light surface. 
     To achieve the above-described object, a projective display apparatus (projector) of the present disclosure includes an illumination apparatus including a light source, an optical member on and from which light from the light source is incident and is emitted, and an integrator on which light from the optical member is incident, an optical modulation apparatus configured to modulate light emitted from the illumination apparatus on a basis of image information to generate an image, and a projective optical system configured to receive an image projected from the optical modulation apparatus, in which the illumination apparatus includes the illumination apparatus of the present disclosure. 
     An optical element of the present disclosure configured to achieve the above-described object includes a first surface and a second surface facing the first surface, in which light from a light source emitting light with multiple wavelengths is incident on the first surface, the first surface or the second surface is provided with a recessed and protruding portion configured to refract incident light from the light source, an area occupied by the recessed and protruding portion is larger in size than incident light from the light source, 
     the recessed portions and the protruding portions of the recessed and protruding portion are smoothly connected together, and, when a shape of light obtained by cutting the light along a virtual plane orthogonal to a traveling direction of the light is referred to as a cross-sectional shape of the light, the cross-sectional shape of light emitted from the optical element is like a rectangle, a polygon, or a shape with one or more angles. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a conceptual drawing of an illumination apparatus of Example 1. 
         FIG.  2    is a conceptual drawing of an illumination apparatus of Example 2. 
         FIG.  3    is a conceptual drawing of an illumination apparatus of Example 3. 
         FIG.  4    is a conceptual drawing of a projective display apparatus (projector) of the present disclosure. 
         FIG.  5    is a conceptual drawing of a modified example of the projective display apparatus (projector) of the present disclosure. 
         FIG.  6 A  and  FIG.  6 B  are a schematic plan view and a schematic cross-sectional view of an optical member constituting an illumination apparatus of Example 1. 
         FIG.  7    is a partly enlarged, schematic partial plan view of the optical member constituting the illumination apparatus of Example 1. 
         FIG.  8 A  and  FIG.  8 B  are a partly enlarged schematic partial plan view and a partly enlarged schematic plan view of the optical member constituting the illumination apparatus of Example 1. 
       
         FIG.  9   
       
       (a) of  FIG.  9    depicts a light position distribution on an integrator in an illumination apparatus of a reference example provided with no recessed and protruding structure units or rotary diffusion plate, (b) and (c) of  FIG.  9    depict a light position distribution on an integrator in an illumination apparatus of Example 1 provided with recessed and protruding structure units, and (d) and (e) of  FIG.  9    depict a light position distribution on an integrator in an illumination apparatus of Comparative Example 1 provided with a typical rotary diffusion plate. 
         FIG.  10 A  depicts simulation results for a light emission angle distribution from recessed and protruding structure units in the illumination apparatus of Example 1 provided with the recessed and protruding structure units,  FIG.  10 B  depicts simulation results for a light emission angle distribution from a typical rotary diffusion plate in the illumination apparatus of Comparative Example 1 provided with the rotary diffusion plate. 
         FIG.  11 A ,  FIG.  11 B , and  FIG.  11 C  are diagrams schematically depicting light incident on a recessed and protruding structure unit in a rotating optical member. 
         FIG.  12 A ,  FIG.  12 B , and  FIG.  12 C  are diagrams continued from  FIG.  11 C  and schematically depicting light incident on the recessed and protruding structure unit in the rotating optical member. 
         FIG.  13    is a diagram illustrating a Gerchberg-Saxton method. 
         FIG.  14    is a schematic plan view of an optical member in a case where a recessed and protruding structure unit having a depth distribution of a recessed and protruding portion obtained by the Gerchberg-Saxton method has a rectangular planar shape. 
         FIG.  15    is a schematic plan view of the optical member depicted in  FIG.  14    and rotated by 45 degrees. 
         FIG.  16    is a schematic plan view of the optical member depicted in  FIG.  14    and rotated by 90 degrees. 
         FIG.  17 A  is a conceptual drawing of the reference example of the recessed and protruding structure unit having a rectangular planar shape, and  FIG.  17 B  is a conceptual drawing of a reference example of a fan-surface-like recessed and protruding structure unit obtained from the reference example of the recessed and protruding structure unit having the rectangular planar shape. 
         FIG.  18 A  is a conceptual drawing of a recessed and protruding structure unit corresponding to the recessed and protruding structure unit of Example 1 having an isosceles-trapezoidal planar shape, and  FIG.  18 B  is a conceptual drawing of the recessed and protruding structure unit of Example 1 and having a fan surface shape, the recessed and protruding structure unit being obtained from the recessed and protruding structure unit depicted in  FIG.  18 A  and having the isosceles-trapezoidal planar shape. 
         FIG.  19 A  is a schematic diagram depicting a light emission angle distribution of light having passed through the fan-surface-like recessed and protruding structure unit depicted in  FIG.  17 B , and  FIG.  19 B  is a schematic diagram depicting a light emission angle distribution of light having passed through the fan-surface-like recessed and protruding structure unit of Example 1 depicted in  FIG.  18 B . 
       
         FIG.  20   
       
       (a) of  FIG.  20    is a plan view of one fan-surface-like recessed and protruding structure unit in Example 1, (b) and (c) of  FIG.  20    are diagrams depicting ∂Z/∂X=[∂f(X, Y)/∂X] Y  and ∂Z/∂Y=[∂f(X, Y)/∂Y] X , and (d) of  FIG.  20    and (e) of  FIG.  20    are diagrams depicting ∂Z/∂X and ∂Z/∂Y and respectively obtained by extracting parts of (b) of  FIG.  20    and (c) of  FIG.  20    in the shape of a rectangle. 
         FIG.  21    is a diagram depicting a histogram distribution obtained by converting ∂Z/∂X and ∂Z/∂Y depicted in (d) of  FIG.  20    and (e) of  FIG.  20   . 
         FIG.  22 A  and  FIG.  22 B  are diagrams depicting results of determination of a spatial frequency by Fourier transform on the basis of the value of ∂Z/∂X and the value of ∂Z/∂Y in (d) and (e) of  FIG.  20   . 
         FIG.  23    is a diagram depicting the average value F X′-ave  of the spatial frequency of the recessed and protruding portion along a straight line satisfying Y=X, and  FIG.  24    is a diagram depicting the average value F Y′-ave  of the spatial frequency of the recessed and protruding portion along a straight line satisfying Y=−X. 
       
         FIG.  24   
       
       (a) of  FIG.  24    is a diagram schematically depicting arrangement of a light source in the illumination apparatus of Example  3 , (b) of  FIG.  24    is a diagram depicting a light emission angle distribution of light emitted from the recessed and protruding structure unit toward the integrator, and (c) of  FIG.  24    is a diagram depicting a light position distribution on the integrator. 
         FIG.  25 A  and  FIG.  25 B  are respectively a diagram schematically depicting a configuration in which multiple light emitting elements are arrayed at intersections in an orthogonal grid and a diagram schematically depicting the cross-sectional shape of light emitted from the recessed and protruding structure unit. 
         FIG.  26 A  and  FIG.  26 B  are respectively a diagram schematically depicting a configuration in which multiple light emitting elements are arrayed at intersections in a honeycomb lattice and a diagram schematically depicting the cross-sectional shape of light emitted from the recessed and protruding structure unit. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     With reference to the drawings, the present disclosure will be described below on the basis of embodiments. However, the present disclosure is not limited to the embodiments, and various numeral values and materials in the embodiments are illustrative. Note that the description is in the following order.
       1 . Description of Optical Element, Illumination Apparatus, and Projective Display Apparatus of Present Disclosure in General   2. Example 1 (Optical Element, Illumination Apparatus, and Projective Display Apparatus of Present Disclosure)   3. Example 2 (Modification of Example 1)   4. Example 3 (Another Modification of Example 1)   5. Others   

     &lt;Description of Optical Element, Illumination Apparatus, and Projective Display Apparatus of Present Disclosure in General&gt; 
     An illumination apparatus of the present disclosure, or an illumination apparatus of the present disclosure constituting a projective display apparatus of the present disclosure (the illumination apparatus and the projective display apparatus may hereinafter be collectively referred to as the “illumination apparatus of the present disclosure and the like”) can be configured such that a recessed and protruding section refracts incident light from a light source. This also applies to an optical element of the present disclosure. 
     The illumination apparatus of the present disclosure and the like including the above-described preferred forms can be configured such that the light source emits light with multiple wavelengths. This also applies to the optical element of the present disclosure. 
     The illumination apparatus of the present disclosure and the like including the above-described preferred forms can be configured such that, when the shape of light obtained by cutting the light along a virtual plane orthogonal to the traveling direction of the light is referred to as the cross-sectional shape of the light, the cross-sectional shape of light incident on the recessed and protruding structure unit from the light source differs from the cross-sectional shape of light emitted from the recessed and protruding structure unit. Specifically, the illumination apparatus of the present disclosure and the like including the above-described preferred forms can be configured such that the cross-sectional shape of light emitted from the recessed and protruding structure unit is like a rectangle, a polygon, or a shape having one or more angles. In other words, the cross-sectional shape of light emitted from the recessed and protruding structure unit can be a shape other than a circle or an ellipse. This also applies to the optical element of the present disclosure. 
     Furthermore, the illumination apparatus of the present disclosure and the like including the above-described preferred forms can be configured such that 
     the light source includes multiple light emitting elements arrayed in a two-dimensional matrix, 
     when the shape of light obtained by cutting the light along a virtual plane orthogonal to the traveling direction of the light is referred to as the cross-sectional shape of the light, the cross-sectional shape of light emitted from the recessed and protruding structure unit is approximate to the arrangement shape of the light emitting elements arranged in the outermost portion of the light source. 
     In this case, the illumination apparatus of the present disclosure including the above-described preferred forms can be configured such that 
     the multiple light emitting elements are arrayed on intersections in an orthogonal grid, 
     the arrangement shape of multiple the light emitting elements arranged at an outer edge portion of the light source is like a rectangle, and 
     the cross-sectional shape of light emitted from the recessed and protruding structure unit is like a rectangle, or 
     the multiple light emitting elements are arrayed on intersections in a honeycomb lattice, 
     the arrangement shape of multiple the light emitting elements at the outer edge portion of the light source is like a regular hexagon, and 
     the cross-sectional shape of light emitted from the recessed and protruding structure unit is a regular hexagon. 
     Alternatively, the illumination apparatus of the present disclosure including the above-described preferred forms can be configured such that 
     the light source includes multiple light emitting elements arrayed in a two-dimensional matrix, and 
     the cross-sectional shape of light emitted from the recessed and protruding structure unit is approximate to the external shape of the integrator. 
     In this case, the illumination apparatus of the present disclosure including the above-described preferred forms can be configured such that 
     the multiple light emitting elements are arrayed on intersections in an orthogonal grid, and 
     the external shape of the integrator is like a square or a rectangle. 
     Furthermore, the illumination apparatus of the present disclosure and the like including the above-described preferred forms can be configured such that the recessed and protruding portion of the recessed and protruding structure unit is designed in compliance with a Gerchberg-Saxton method (hereinafter sometimes referred to as the “GS method” for convenience) or a repeated Fourier method. 
     Furthermore, the illumination apparatus of the present disclosure and the like including the above-described preferred forms can be configured such that, when an X axis refers to an axis passing through the center of the recessed and protruding structure unit and through a rotation axis and located in a surface of the recessed and protruding structure unit provided with the recessed and protruding portion, a Z axis refers to an axis passing through the center of the recessed and protruding structure unit and that is parallel to the rotation axis, and a Y axis refers to an axis that is orthogonal to the X axis and the Z axis and that is located in a surface of the recessed and protruding structure unit provided with the recessed and protruding portion, 
     the average value F x-ave  of the spatial frequency of the recessed and protruding portion along the X axis is 1×10 3  mm −1  or less, preferably 1×10 2  mm −1  or less, and 
     the average value F Y-ave  of the spatial frequency of the recessed and protruding portion along the Y axis is 1×10 3  mm −1  or less, preferably 1×10 2  mm −1  or less. In this case, the illumination apparatus of the present disclosure and the like including the above-described preferred forms can be configured such that, when F X′-ave  denotes the average value of the spatial frequency of the recessed and protruding portion along a straight line satisfying Y=X and F Y′-ave  denotes the average value of the spatial frequency of the recessed and protruding portion along a straight line satisfying Y=−X, 
     F X′-ave &gt;F X-ave , 
     F X′-ave &gt;F Y-ave , 
     F Y′-ave &gt;F X-ave , and 
     F Y′-ave &gt;F Y-ave  are satisfied. Note that the center of light incident on the recessed and protruding structure unit is defined as the area center of gravity of the cross-sectional shape of the incident light in a case where the cross-sectional shape of the incident light is not a circle or an ellipse or is an odd shape. 
     Furthermore, the illumination apparatus of the present disclosure and the like including the above-described preferred forms can be configured such that, when L X-0  denotes the length along the X axis of the recessed and protruding structure unit on which light from the light source is incident and L Y-0  denotes the length, along the Y axis, of the recessed and protruding structure unit on which light from the light source is incident, 
       L X-0 ×F X-ave ≥10
 
     and 
       L Y-0 ×F Y-ave ≥10,
 
     preferably 
       L X-0 ×F X-ave ≥15
 
     and 
     L Y-0 ×F Y-ave ≥15 are satisfied. 
     Furthermore, the illumination apparatus of the present disclosure and the like including the above-described preferred forms can be configured such that F X-ave ≠F Y-ave . 
     Furthermore, the illumination apparatus of the present disclosure and the like including the above-described preferred forms can be configured such that the recessed and protruding structure unit has a kurtosis β (kurtosis β X  along the X axis and kurtosis β Y  along the Y axis) of −0.5 or less, preferably −0.8 or less. Note that the kurtosis is defined in JIS Z8101-1: 2015 (ISO 3534-1: 2006). 
     Furthermore, the illumination apparatus of the present disclosure and the like including the above-described preferred forms can be configured such that 
     light from the light source is incident on each recessed and protruding structure unit in a rotating state from a first surface of each recessed and protruding structure unit, the light from the light source is emitted from a second surface of each recessed and protruding structure unit toward the integrator, and 
     the first surface of each recessed and protruding structure unit is provided with the recessed and protruding portion, whereas 
     the second surface of each recessed and protruding structure unit is flat, or such that 
     the first surface of each recessed and protruding structure unit is flat, and 
     the second surface of each recessed and protruding structure unit is provided with the recessed and protruding portion, or such that 
     the first surface of each recessed and protruding structure unit is provided with the recessed and protruding portion, and 
     the second surface of each recessed and protruding structure unit is also provided with the recessed and protruding portion. 
     Alternatively, the illumination apparatus of the present disclosure and the like including the above-described preferred forms can be configured such that: 
     light from the light source is incident on each recessed and protruding structure unit in the rotating state from the first surface of each recessed and protruding structure unit, the light from the light source is emitted from the second surface of each recessed and protruding structure unit toward the integrator, 
     the first surface of each recessed and protruding structure unit is provided with the recessed and protruding portion, and 
     the second surface of each recessed and protruding structure unit is flat and constitutes a light reflection surface, and such that 
     in this case, 
     the illumination apparatus further includes a polarization beam splitter ad a quarter wavelength plate, and 
     light from the light source enters the polarization beam splitter, exits the polarization beam splitter along a first direction, passes through the quarter wavelength plate, is reflected at the recessed and protruding structure unit, passes through the quarter wavelength plate, enters the polarization beam splitter, exits the polarization beam splitter along a second direction different from the first direction, and enters the integrator. 
     The illumination apparatus or the optical element of the present disclosure can be configured such that the cross-sectional shape of light incident on the recessed and protruding structure unit or the optical element is, though not limited to, a circle or an ellipse. 
     Examples of a material constituting the optical member or the optical element or a substrate described below can include polyethylene terephthalate, polyethylene naphthalate, polycarbonate, a cellulose ester such as cellulose acetate, a fluorine polymer such as a copolymer of polyvinylidene fluoride or polytetrafluoroethylene and hexafluoro propylene, a polyether of polyoxymethylene or the like, polyacetal, polystyrene, polyethylene, polypropylene, polyolefin such as a methylpentene polymer, polyimide such as polyamide-imide or polyetherimide, polyamide, polyether sulfone, polyphenylene sulfide, polyvinylidene fluoride, tetraacetylcellulose, bromized phenoxy, polyarylate, polysulfone, a silicone-based resin (for example, a methyl silicone resin, a methylphenyl silicone resin, or a propylphenyl silicone resin), and the like. In a case where the optical member or the optical element includes glass, the glass can be transparent glass such as soda lime glass or a white glass plate. 
     The first surface of each recessed and protruding structure unit and/or the second surface facing the first surface is provided with the recessed and protruding portion. However, the recessed and protruding portion is only required to be formed on one of the surfaces (for example, the first surface) of the material constituting the optical member (recessed and protruding structure unit) or the optical element. Examples of a formation method for the recessed and protruding portion include various printing methods including a screen printing method, an ink-jet printing method, and a metal mask printing method; a transfer method using a mold or the like; a nanoimprint method; a 3D printing technology (for example, a 3D printing technology using a stereolithography 3D printer or a two-photon absorption micro 3D printer; a physical vapor deposition method (for example, a PVD method including a vacuum deposition method such as an electron beam deposition method or a hot filament deposition method, a sputtering method, an ion plating method, and a laser ablation method); various chemical vapor deposition method (CVD method); a liftoff method; microfabrication technology using a pulse laser, and the like, and also include combinations of these methods with an etching method. 
     In the illumination apparatus of the present disclosure and the like, the recessed and protruding portions of adjacent recessed and protruding structure units are smoothly connected together, and the recessed portions and the protruding portions are smoothly connected together, or in the optical element of the present disclosure, the recessed and protruding portions are smoothly connected together. In this case, “smooth” is an analytical term. For example, in a case where the real variable function f(x) is differentiable for a&lt;x&lt;b and f′(x) is continuous, the function is described as continuously differentiable or expressed as smooth. Here, when the recessed and protruding portion is expressed as Z=f(X, Y), a differential value for the recessed and protruding portion (the inclination of a surface of the recessed and protruding portion obtained by cutting the surface along the X axis or an XZ virtual plane parallel to the X axis and the inclination of the surface of the recessed and protruding portion obtained by cutting the surface along the Y axis or a YZ virtual plane parallel to the Y axis) can be obtained by 
       ∂Z/∂X=[∂f(X, Y)/∂X] Y  
 
       ∂Z/∂Y=[∂f(X, Y)/∂Y] X .
 
     The integrator is referred to as an integrator lens or a fly eye lens, and is a lens that improves uniformity of illuminance for an irradiated surface. As the integrator in the present disclosure, an integrator with a known configuration and a known structure can be used, and specifically the integrator includes, for example, multiple lenses arranged in an array or in a two-dimensional matrix. Alternatively, the integrator includes a rod integrator. 
     The light source includes multiple light emitting elements with a known configuration and a known structure, for example, multiple semiconductor laser elements. The number of light emitting elements constituting the light source may be one or may be multiple. For multiple light emitting elements, the light source may be configured by arranging multiple semiconductor laser elements in an array or may be configured by using multiple semiconductor laser element units each obtained by bringing together multiple semiconductor laser elements. The semiconductor laser elements include, for example, a semiconductor laser element that emits red, a semiconductor laser element that emits green, and a semiconductor laser element that emits blue. Alternatively, the semiconductor laser elements include, for example, a semiconductor laser element that emits yellow and a semiconductor laser element that emits blue, or for example, a semiconductor laser element that emits blue and a wavelength conversion member. The array of semiconductor laser elements in the semiconductor laser element unit can include the semiconductor laser elements arranged in a straight line or on the vertexes of an equilateral triangle. The multiple semiconductor laser elements may be arrayed on the vertexes of a rectangle or on the vertexes of a regular hexagon. The semiconductor laser element can be a semiconductor laser element (edge-emitting semiconductor laser element) configured to emit laser light from an end face or can include a surface emitting laser (VCSEL). 
     The optical member is only required to be rotated using, for example, a driving motor. 
     To provide light emitted from the recessed and protruding structure unit with, for example, a rectangular external shape, in other words, to provide light emitted from the recessed and protruding structure unit in the rotating state, with a rectangular cross-sectional shape, the recessed and protruding portions are only required to be designed such that light emitted from the recessed and protruding structure unit in a non-rotating state, with a trapezoidal cross-sectional shape. In other words, the recessed and protruding portion is only required to be designed such that the external shape of light emitted from the recessed and protruding structure unit in the non-rotating state is like an isosceles trapezoid including a bottom side (rotation axis side) longer than a top side, the top side and the bottom side extending parallel to the Y axis. The relation between the value A 1  of (length of the bottom side)/(length of the top side) and the value A 2  of (outer diameter)/(inner diameter) of a fan-surface-like recessed and protruding structure unit desirably satisfies, for example, 0.85≤A 1 /A 2 ≤ 1 . 15 , preferably A 1 /A 2 =1.0. 
     Additionally, the illumination apparatus of the present disclosure and the like can be configured such that, when an XZ virtual plane in the recessed and protruding structure unit is a mirror plane, two areas of the recessed and protruding structure unit located across the XZ virtual surface are in a mirror symmetry relation, and the recessed and protruding portions in the two areas are smoothly connected together. 
     EXAMPLE 1 
     Example 1 relates to the optical element, the illumination apparatus (light source apparatus), and the projective display apparatus (projector) of the present disclosure.  FIG.  1    depicts a conceptual drawing of the illumination apparatus of Example 1,  FIGS.  4  and  5    depict conceptual drawings of the projective display apparatus (projector) of Example 1 and a modified example of the projective display apparatus,  FIGS.  6 A and  6 B  depict a schematic plan view and a schematic cross-sectional view of an optical member constituting the illumination apparatus of Example 1,  FIG.  7    depicts a partly enlarged schematic partial plan view of the optical member constituting the illumination apparatus of Example 1, and  FIGS.  8 B and  8 A  depict a schematic plan view and a partly enlarged schematic partial plan view of the optical member constituting the illumination apparatus of Example 1. 
     Note that, in the illumination apparatus of the embodiment, the X axis refers to an axis extending through the center and the rotation axis of the recessed and protruding structure unit and located in the surface of the recessed and protruding structure unit provided with the recessed and protruding portion, the Z axis refers to an axis extending through the center of the recessed and protruding structure unit and that is parallel to the rotation axis, and the Y axis refers to an axis that is orthogonal to the X axis and the Z axis and that is located in the surface of the recessed and protruding structure unit provided with the recessed and protruding portion. In the optical member, the number of X axes, the number of Y axes, and the number of Z axes are each equal to the number of the recessed and protruding structure units. Additionally, a ζ axis refers to any axis that is orthogonal to the rotation axis and that is located in the surface of the recessed and protruding structure unit provided with the recessed and protruding portion, and a η axis refers to any axis that is orthogonal to the rotation axis AR and the ζ axis and that is located in the surface of the recessed and protruding structure unit provided with the recessed and protruding portion. 
     The illumination apparatus of Example 1 depicted in  FIG.  1    includes 
     a light source  10 , 
     an optical member  20  including a first surface  20 A on which light from the light source  10  is incident and a second surface  20 B facing the first surface  20 A, and 
     an integrator  30  on which light emitted from the optical member  20  is incident. 
     As depicted in  FIGS.  6 A and  8 B , the optical member  20  is rotatable around the rotation axis AR extending parallel to a direction in which light from the light source  10  is incident on the optical member  20  and is emitted from the optical member  20 , 
     as depicted in  FIGS.  6 A and  8 B , the planar shape of the optical member  20  (planar shape of the optical member  20  obtained by cutting the optical member  20  along a virtual plane orthogonal to the rotation axis AR) is annular around the rotation axis AR, 
     as depicted in  FIG.  6 B , the first surface  20 A or the second surface  20 B of the optical member  20  (the first surface  20 A in the depicted example) is provided with multiple recessed and protruding structure units  21  each having a fan-surface-like planar shape and including a recessed and protruding portion  21 ′, 
     as depicted in  FIG.  6 A , an extended line of a boundary BL between adjacent recessed and protruding structure units  21  intersects the rotation axis AR, 
     as depicted in  FIGS.  6 A,  7 , and  8 B , when the boundary BL between the adjacent recessed and protruding structure units  21  is a mirror plane, the adjacent recessed and protruding structure units  21  are in a mirror symmetry relation, that is, the recessed and protruding portions in the adjacent recessed and protruding structure units  21  are in the mirror symmetry relation, and the recessed and protruding portions  21 ′ of the adjacent recessed and protruding structure units  21  are smoothly connected together, 
     the recessed portions and the protruding portions in the recessed and protruding portion  21 ′ of each recessed and protruding structure unit  21  are smoothly connected together, and 
     an area of each recessed and protruding structure unit  21  occupied by the recessed and protruding portion  21 ′ is larger in size than incident light from the light source  10 . 
     Note that  FIG.  8 B  depicts half of one recessed and protruding structure unit  21  by sandwiching the half between white dotted lines and that  FIG.  8 A  depicts this portion in an enlarged manner. 
     Here, as depicted in  FIG.  7   , a part of the recessed and protruding portion  21 ′ with a predetermined shape is formed in each of an area A, an area B, an area C, an area D, an area E, an area F, an area G, an area H, and an area J of the recessed and protruding structure unit  21 .  FIG.  7   , depicting two recessed and protruding structure units  21 , schematically illustrates the arrangement of the area A, the area B, the area C, the area D, the area E, the area F, the area G, the area H, and the area J. In the depicted example, the optical member  20  is provided with  24  recessed and protruding structure units  21 . The optical member  20  includes a disc-shaped substrate  22  including a polymethylmethacrylate (PMMA) resin with a refractive index n d =1.5, and the optical member  20  (recessed and protruding structure unit  21 ) is formed on an outer circumferential portion of the substrate  22 . The center of the substrate  22  is attached to a driving motor  23 , and rotation of the driving motor  23  rotates the optical member  20  (recessed and protruding structure unit  21 ) formed on the outer circumferential portion of the substrate  22 . A rotation axis of the driving motor  23  corresponds to the rotation axis AR. In the examples, the substrate  22  has a diameter of 40 mm, and the annular optical member  20  has an outer diameter of 40 mm and an inner diameter of 32 mm. The fan-surface-like recessed and protruding structure unit  21  has a central angle (Θ) of 15 degrees and a width (W) of 4 mm. For the recessed and protruding portion  21 ′ of the recessed and protruding structure unit  21 , a mold is produced by 3D printing or laser lithography, and the recessed and protruding portion  21 ′ is formed on the basis of an injection molding method. The recessed and protruding portion  21 ′ has a maximum depth of 27 μm. Light (with a circular cross-sectional shape) incident on the recessed and protruding portion  21 ′ in the recessed and protruding structure unit  21  has a diameter of 1.5 mm. 
     Note that, when an XZ virtual plane in the recessed and protruding structure unit  21  is a mirror plane, two areas  21   a  and  21   b  (see  FIG.  7   ) of the recessed and protruding structure unit  21 , located across the XZ virtual plane, are in the mirror symmetry relation, that is, in the two areas  21   a  and  21   b,  the recessed and protruding portions  21 ′ are in the mirror symmetry relation and are smoothly connected together. Specifically, between the area A and the area G, between the area B and the area H, and between the area C and the area J, the recessed and protruding portions  21 ′ are in the mirror symmetry relation when the XZ virtual plane is a mirror plane. Additionally, in the area D, the area E, and the area F, the recessed and protruding portions  21 ′ are smoothly connected together across the XZ virtual plane. In addition, the area G, area H, and area J in the area  21   b  of a certain recessed and protruding structure unit  21  are in the mirror symmetry relation with the area A, area B, and area C in the area  21   a  of the recessed and protruding structure unit  21  adjacent to the certain recessed and protruding structure unit  21  when the boundary BL in the recessed and protruding structure unit  21  is a mirror plane, and the area A and the area G are smoothly connected together, the area B and the area H are smoothly connected together, and the area C and the area J are smoothly connected together. 
     A projective display apparatus (projector) of Example 1 or Examples 2 and 3 described below includes, as depicted in  FIG.  4    or  FIG.  5   , 
     an illumination apparatus  110  including the light source  10 , the optical member  20  on and from which light from the light source  10  is incident and is emitted, and the integrator  30  on which light from the optical member  20  is incident, 
     an optical modulation apparatus (image forming unit  130 ) that modulates light emitted from the illumination apparatus  110  on the basis of image information, and 
     a projective optical system  140  that projects an image from the optical modulation apparatus (image forming unit  130 ). 
     The illumination apparatus includes an illumination apparatus of Example 1 or Examples 2 and 3 described below. The projective display apparatus (projector) will be described below. 
     Furthermore, an optical element of Example 1 or Example 2 described below corresponds to one recessed and protruding structure unit  21  in the illumination apparatus of Example 1 or Example 2 described below, and includes 
     a first surface  20 A and a second surface  20 B facing the first surface  20 A, light being incident on the first surface  20 A, the light being applied by the light source  10  emitting light with multiple wavelengths, 
     the first surface  20 A or the second surface  20 B (specifically, the first surface  20 A) is provided with the recessed and protruding portion  21 ′ that refracts incident light from the light source  10 , 
     an area occupied by the recessed and protruding portion  21 ′ is larger in size than the incident light from the light source  10 , 
     recessed portions and protruding portions on the recessed and protruding portion  21 ′ are smoothly connected together, and 
     when the shape of light obtained by cutting the light along a virtual plane orthogonal to a traveling direction of light is referred to as the cross-sectional shape of light (this also applies to the description below), the cross-sectional shape of light emitted from the optical element is like a rectangle or a polygon or a shape with one or more angle (shape with one or more point for which differential is impossible). In other words, the cross-sectional shape of light emitted from the optical element is a shape other than a circle or an ellipse, or in other words, light incident on the optical element from the light source  10  has a cross-sectional shape different from that of light emitted from the optical element. 
     The light source  10  includes multiple light emitting elements emitting red (specifically, semiconductor laser elements  10 R), multiple light emitting elements emitting green (specifically, semiconductor laser elements  10 G), multiple light emitting elements emitting blue (specifically, semiconductor laser elements  10 B), a dichroic prism  12  that brings together red laser light, green laser light, and blue laser light emitted from the light emitting elements (semiconductor laser elements  10 R,  10 G, and  10 B), and a lens system  13  that condenses white light from the dichroic prism  12  into a partial area of the recessed and protruding structure unit  21 . Note that red laser light emitted from the multiple red semiconductor laser elements  10 R is temporarily collimated into substantially parallel beams by a lens  11 R, green laser light emitted from the multiple green semiconductor laser elements  10 G is temporarily collimated into substantially parallel beams by a lens  11 G, and blue laser light emitted from the multiple blue semiconductor laser elements  10 B is temporarily collimated into substantially parallel beams by a lens  11 B. Then, the laser light beams are color-multiplexed in the dichroic prism  12 , and the resultant white laser light is condensed into the recessed and protruding structure unit  21  in a rotating state via the lens system  13 . 
     The laser light incident on the recessed and protruding structure unit  21  is subjected to predetermined refraction in the recessed and protruding structure unit  21  in the rotating state, and the resultant laser light is emitted from the recessed and protruding structure unit  21 . The white laser light beams emitted from the recessed and protruding structure unit  21  pass through a condenser lens  24  to reduce the incident angle to an integrator  30 , and the resultant white laser light beams are incident on the integrator  30  at the resultant incident angle. The integrator  30  is also referred to as an integrator lens or a fly eye lens and includes multiple lenses arrayed in a two-dimensional matrix. Then, the white laser light emitted from the integrator  30  travels toward a light valve (optical modulation apparatus or image forming unit  130  described below). 
     In the illumination apparatus of Example 1 depicted in  FIG.  1    or the illumination apparatus of Example 3 depicted in  FIG.  3    described below, 
     light from the light source  10  is incident on each recessed and protruding structure unit  21  in the rotating state from the first surface  20 A of each recessed and protruding structure unit  21  and is emitted from the second surface  20 B of each recessed and protruding structure unit  21  toward the integrator  30 , 
     the first surface  20 A of each recessed and protruding structure unit  21  is provided with the recessed and protruding portion  21 ′, and 
     the second surface  20 B of each recessed and protruding structure unit  21  is flat. Note that the recessed and protruding portion  21 ′ may be formed on the second surface  20 B of the optical member  20  or may be formed on the first surface  20 A and the second surface  20 B of the optical member  20 . 
     As described above, in the illumination apparatus of Example 1, the recessed and protruding portion  21 ′ refracts incident light from the light source  10 . Additionally, the light source  10  emits light with multiple wavelengths. Furthermore, light incident on the recessed and protruding structure unit  21  from the light source  10  has a cross-sectional shape different from that of light emitted from the recessed and protruding structure unit  21 . Specifically, the cross-sectional shape of light emitted from the recessed and protruding structure unit  21  is like a rectangle or a polygon or a shape with one or more angles. In other words, the cross-sectional shape of light emitted from the recessed and protruding structure unit  21  is a shape other than a circle or an ellipse. 
     Additionally, in the illumination apparatus or the optical element of Example 1, the cross-sectional shape of light incident on the recessed and protruding structure unit  21  or the optical element from the light source  10  is a circle or an ellipse, and the cross-sectional shape of light emitted from the optical element is like a rectangle. 
     Furthermore, in the illumination apparatus of Example 1, as depicted in  FIG.  25 A , 
     the light source  10  includes multiple light emitting elements  10 ′ (specifically, semiconductor laser elements) arrayed in a two-dimensional matrix, and 
     the cross-sectional shape of light emitted from the recessed and protruding structure unit  21  is approximate to the arrangement shape of the light emitting elements  10 ′ arranged in an outermost portion of the light source  10 . 
     Here, in Example 1, as depicted in  FIG.  25 A , 
     the multiple light emitting elements  10 ′ are arrayed on intersections in an orthogonal grid, 
     the arrangement shape of the multiple light emitting elements  10 ′ arranged at the outer edge portion of the light source  10  is like a rectangle (depicted by dotted lines in  FIG.  25 A ), and 
     the cross-sectional shape of light emitted from the recessed and protruding structure unit  21  is like a rectangle (see  FIG.  25 B ). 
     (a) of  FIG.  9    depicts a light position distribution of green light on the integrator  30  in an illumination apparatus in a reference example in which no recessed and protruding structure unit  21  or rotary diffusion plate is provided. The multiple green semiconductor laser elements  10 G emitting green light, specifically, a semiconductor laser element unit including the multiple green semiconductor laser elements  10 G emitting green light is arrayed in a two-dimensional matrix, and more specifically, the semiconductor laser elements are arrayed on intersections in an orthogonal grid. The cross-sectional shape of light emitted from one semiconductor laser element unit is like an ellipse. 
     Additionally, (b) and (c) of  FIG.  9    depict a light position distribution of green light on the integrator  30  in the illumination apparatus in Example 1 provided with the recessed and protruding structure unit  21 . (b) and (c) of  FIG.  9    indicate that the optical member  20  makes the light position distribution on the integrator  30  as uniform as possible (see (c) of  FIG.  9   ) to distribute light substantially all over the integrator  30  (see (b) of  FIG.  9   ). In other words, the cross-sectional shape of light emitted from the recessed and protruding structure unit  21  is approximate to the arrangement shape of the light emitting elements  10 ′ arranged in the outermost portion of the light source  10 . Additionally, in the optical system, the relation described below is established. Thus, the distribution of the light emission angle from the recessed and protruding structure unit  21  is similar to the light position distribution on the integrator  30 , and the distribution of the light emission angle from the recessed and protruding structure unit can be considered as the light position distribution on the integrator  30 . The light position distribution on the integrator≈the distribution of the light emission angle from the recessed and protruding structure unit, where a proportionality coefficient depends on the distance from the recessed and protruding structure unit to the integrator (focal length f). In a case where parallel beams are made incident on the optical member  20 , simulation results indicate a rectangular distribution of light emission angle as depicted in  FIG.  10 A . Note that green light corresponding to light depicted in (a) of  FIG.  9   , distributing the light position distribution on the integrator  30 , is incident on the optical member  20 . (c) and (e) of  FIG.  9    are light position distributions along the X axis direction corresponding to the light position distributions on the integrator  30  depicted in (b) and (d) of  FIG.  9   . 
     Here, the horizontal axis “X angle (unit: deg)” in  FIG.  10 A  and  FIG.  10 B  indicates the emission angle of light emitted from the center of the recessed and protruding structure unit  21  in the X axis direction, and the vertical axis “Y angle (unit: deg)” indicates the emission angle of light emitted from the center of the recessed and protruding structure unit  21  in the Y axis direction. 
     Furthermore, (d) of  FIG.  9    depicts a light position distribution of green light on the integrator  30  in an illumination apparatus in Comparative Example 1 which is provided with a typical rotary diffusion plate instead of the optical member  20  for comparison. In a case where parallel beams are made incident on a typical rotary diffusion plate, simulation results indicate a circular distribution of light emission angle as depicted in  FIG.  10 B . Note that green light corresponding to light depicted in (a) of  FIG.  9   , depicting the light position distribution on the integrator  30 , is incident on the optical member  20 . Note that green light corresponding to light depicted in (a) of  FIG.  9   , depicting the light position distribution on the integrator  30 , is incident on the rotary diffusion plate. In a case where a typical rotary diffusion plate is used, the light position distribution is a Gaussian distribution (see (e) of  FIG.  9   ). Thus, the distribution of light on the integrator  30  is elongate in the vertical direction and is biased in the central portion (see (d) of  FIG.  9   ). 
     Results similar to those depicted in (a) of  FIG.  9   , (b) of  FIG.  9   , (c) of  FIG.  9   , (d) of  FIG.  9   , (e) of  FIG.  9 ,  10 A , and  10 B were obtained when the multiple red semiconductor laser elements  10 R emitting red and the multiple blue semiconductor laser elements  10 B emitting blue were used. 
     Table 1 indicates simulation results for a speckle contrast level in the illumination apparatus in Example 1 and the illumination apparatus in Comparative Example 1. Note that the speckle contrast level in the illumination apparatus in Comparative Example 1 is “ 100 .” 
     &lt;Table 1&gt; 
     Simulation Results for Speckle Contrast Level 
     Example 1: 85 
     Comparative Example 1: 100 
     Table 1 indicates that the use of the illumination apparatus in Example 1 enables the speckle contrast to be significantly reduced. The results indicate that the use of the illumination apparatus in Example 1 made the light position distribution on the integrator  30  more uniform. Furthermore, illumination simulation indicates that loss of light passing through the illumination apparatus in Example 1 is 0.1% and that as depicted in (b) of  FIG.  9   , speckle noise can be further reduced with light vignetting prevented and with an appropriate light amount maintained. In addition, the light distribution on the integrator  30  is more uniform, enabling color unevenness in the illumination of the light valve to be reduced. 
     As depicted in  FIGS.  11 A,  11 B,  11 C,  12 A,  12 B, and  12 C , the position of the incidence, on the optical member  20 , of light from the light source  10  remains unchanged, but rotation of the optical member  20  sequentially changes the recessed and protruding structure unit  21  on which light traveling from the light source  10  to the optical member  20  is incident, from the recessed and protruding structure unit  21 D to the recessed and protruding structure unit  21 E and then to the recessed and protruding structure unit  21 F. Note that the position of light incidence on the recessed and protruding structure unit  21  is depicted by a filled circle but that light is incident on a trajectory resulting from relative rotation of the filled circle around the rotation axis AR. However, light emitted from the recessed and protruding structure unit  21  has a cross-sectional shape as depicted in (b) of  FIG.  9   , leading to no change in the light position distribution on the integrator  30 . This is because a desired light emission angle distribution is obtained by sufficient overlap between light emission angle distributions in each recessed and protruding structure unit  21  or across the recessed and protruding structure units  21 , the overlap being caused by refraction. 
     In the illumination apparatus of Example 1, the recessed and protruding portion  21 ′ of the recessed and protruding structure unit  21  is designed in accordance with a Gerchberg-Saxton method (GS method), which is known as a design method for diffraction grating. In Example 1, unwrapping processing and smoothing processing are added to a known GS method.  FIG.  13    depicts a conceptual drawing of the design method. Specifically, a light electric field A is given as follows by multiplying an incident light intensity I with a random phase Φ. 
       A=I 1/2 ·exp(i·Φ)
 
     Then, Fourier transform (FET) is applied to the light electric field A to determine a light electric field A′ obtained during emission from the recessed and protruding structure. 
     Then, only a light phase Φ′ is taken out from the light electric field A′ determined and is multiplied by a desired light intensity distribution I′ TGT  for emission to determine a light electric field A′ obtained during emission as follows. 
       A′=I′ 1/2   TGT ·exp(I·Φ′)
 
     Then, inverse Fourier transform (IFET) is applied to the light electric field A′ determined to obtain a phase Φ″. The known GS method provides a discontinuous phase amount. On the other hand, in design of the recessed and protruding portion  21 ′ of the recessed and protruding structure unit  21  in Example 1, unwrapping processing and phase smoothing processing (see steps (A) and (B) in  FIG.  13   ) are subsequently introduced into the GS method to obtain a continuous phase Φ UW2 . Then, the light intensity I and the phase Φ are replaced using the phase Φ UW2  subjected to unwrapping processing and phase smoothing processing, and Fourier transform (FET), inverse Fourier transform (IFET), unwrapping processing, and phase smoothing processing are repeated to gradually change the phase amount. Then, a design phase (specifically, the recessed and protruding portion  21 ′ of the recessed and protruding structure unit  21 ) is finally obtained. Thus, wavelength dependence can be suppressed, and substantially equivalent light emission angle control can be performed on all of red light, green light, and blue light. 
     However, even in a case where the cross-sectional shape of light emitted from the recessed and protruding structure unit  21  can be controlled to a rectangle by using the above-described method, the following problem is caused by rotation of the recessed and protruding structure unit  21 . Specifically, the planar shape of a recessed and protruding structure unit  41  with the depth distribution of the recessed and protruding portion  21 ′ obtained by the GS method is assumed to be like, for example, as depicted in  FIG.  14   , a rectangle with two opposite sides a and b extending in a direction and two other opposite sides c and d extending in a η direction. The recessed and protruding structure unit  41  is assumed to be disposed in an outer circumferential portion of the substrate  22 , shaped like a disc. However, in all the recessed and protruding structure units  41 , the two sides a and b extend in the ζdirection, and the two other opposite sides c and d extend in the η direction. Light is assumed to be incident on a position on the substrate  22  indicated by a filled circle and on a trajectory obtained by rotating the filled circle around the rotation axis AR. Additionally, the recessed and protruding structure unit located at an angle of 45 degrees to a certain recessed and protruding structure unit  41 A is denoted by the reference numeral  41 B, and the recessed and protruding structure unit located at an angle of 90 degrees to the certain recessed and protruding structure unit  41 A is denoted by the reference numeral  41 C. In this case, even in a case where the cross-sectional shape of light emitted from the certain recessed and protruding structure unit  41 A (see  FIG.  14   ) is like a rectangle, when light is incident on the recessed and protruding structure unit  41 B, the cross-sectional shape of light emitted from the recessed and protruding structure unit  41 B (see  FIG.  15   ) is like a rectangle inclined at 45 degrees to the ζ direction. Additionally, when light is incident on the recessed and protruding structure unit  41 C, the cross-sectional shape of light emitted from the recessed and protruding structure unit  41 C (see  FIG.  16   ) is like a rectangle inclined at 90 degrees to the ζ direction. In other words, the cross-sectional shape of light emitted from the recessed and protruding structure unit  41  is rotated. 
     On the other hand, in the optical member of Example 1 depicted in  FIGS.  6 A and  8 B , the recessed and protruding structure unit located at 45 degrees to the certain recessed and protruding structure unit  21 A is denoted by the reference numeral  21 B, and the recessed and protruding structure unit located at 90 degrees to the certain recessed and protruding structure unit  21 A is denoted by the reference numeral  21 C. In this case, when light is incident on the recessed and protruding structure unit  21 A, the cross-sectional shape of light emitted from the recessed and protruding structure unit  21 A is like a rectangle as depicted in (b) of  FIG.  9   , when light is incident on the recessed and protruding structure unit  21 B, the cross-sectional shape of light emitted from the recessed and protruding structure unit  21 B is the same as that of light emitted from the recessed and protruding structure unit  21 A as depicted in (b) of  FIG.  9   , and the cross-sectional shape of light emitted from the recessed and protruding structure unit  21 C is the same as that of light emitted from the recessed and protruding structure unit  21 A as depicted in (b) of  FIG.  9   . In other words, the cross-sectional shape of light emitted from the recessed and protruding structure unit  21  is not rotated and remains the same. 
     Incidentally, the planar shape of a recessed and protruding structure unit  21 α in which the recessed and protruding portion has a depth distribution obtained by the GS method is assumed to like, for example, as depicted in  FIG.  17 A , a rectangle with two opposite sides a and b extending in the X direction and two other opposite sides c and d extending in the Y direction. It is assumed that  24  fan-surface-like recessed and protruding structure units  21 α′ are obtained by taking out the fan-surface-like recessed and protruding structure unit  21 α′ from the recessed and protruding structure unit  21 α as described above with the recessed and protruding portions unchanged as depicted in  FIG.  17 B  and that the  24  fan-surface-like recessed and protruding structure units  21 α′ are then placed in the outer circumferential portion of the disc-like substrate  22  as depicted in  FIG.  6 A . In this case, the cross-sectional shape of light emitted from the recessed and protruding structure unit  21 α′ in the rotating state is not like a rectangle but is like an isosceles trapezoid including a bottom side c′ (side closer to the rotation axis AR) shorter than a top side d′ as depicted in  FIG.  19 A . 
     To solve such a problem, the planar shape of the recessed and protruding structure unit  21 β in which the recessed and protruding portion  21 ′ has a depth distribution obtained by the GS method is assumed to be like, for example, as depicted in  FIG.  18 A , an isosceles trapezoid including two opposite sides e and f extending substantially in the X direction and two other opposite sides g and h extending in the Y direction. Then, such an isosceles trapezoid is deformed into a fan surface shape, and at this time, as depicted in  FIG.  18 B , the formation state of the recessed and protruding portion  21 ′ is more heavily compressed at a position closer to the rotation axis AR along the Y axis or parallel to the Y axis. In some cases, the formation state of the recessed and protruding portion  21 ′ is more significantly elongated at a position farther from the rotation axis AR along the Y axis or parallel to the Y axis. Specifically, to externally shape light emitted from the recessed and protruding structure unit  21  in the rotating state like a rectangle, in other words, to form the cross-sectional shape of light emitted from the recessed and protruding structure unit  21  like a rectangle, the recessed and protruding portion  21 ′ in a recessed and protruding structure unit  21 β′ is only required to be designed in such a manner as to execute the above-described compression processing (optionally the elongation processing) such that the cross-sectional shape of light emitted from the recessed and protruding structure unit  21 β in a non-rotating state is like an isosceles trapezoid. In other words, light emitted from the recessed and protruding structure unit  21 β in the non-rotating state is only required to be externally shaped like an isosceles trapezoid including a bottom side g (side closer to the rotation axis) longer than a top side h, the top side h and the bottom side g extending parallel to the Y axis. The relation between the value A 1  of (length of the bottom side g)/(length of the top side h) and the value A 2  of (outer diameter)/(inner diameter) of the fan-surface-like recessed and protruding structure unit  21  preferably satisfies, for example, 0.85≤A 1 /A 2 ≤1.15. In Example 1, A 1 /A 2 =1.0 is set. Thus, as depicted in  FIG.  19 B , the cross-sectional shape of light emitted from the recessed and protruding structure unit  21  in the rotating state is like a rectangle with two sides e′ and f′ extending in the X direction and two other opposite sides g′ and h′ extending in the Y direction. 
     (a) of  FIG.  20    depicts a plan view of the structure of one fan-surface-like recessed and protruding structure unit  21 . In addition, (b) of  FIG.  20    and (c) of  FIG.  20    depict ∂Z/∂X=[∂ f(X, Y)/∂X] Y  and ∂Z/∂Y=[∂f(X, Y)/∂Y] X . The area of the recessed and protruding structure unit  21  on which light is incident is shaped like a circle with a diameter of 1.5 mm, and (d) and (e) of  FIG.  20    each depict a part of the area which is extracted in the form of a rectangle depicted by dotted lines, the part corresponding to each of ∂Z/∂X and ∂Z/∂Y. Furthermore,  FIG.  21    depicts a histogram distribution obtained by converting ∂Z/∂X and ∂Z/∂Y depicted in (d) and (e) of  FIG.  20    into histograms. As seen in  FIG.  21   , the recessed and protruding structure unit  21  involves a rectangular gradient distribution (rectangular distribution of ∂Z/∂X and ∂Z/∂Y). Consequently, on the basis of the Snell&#39;s law, the light emission angle distribution is as depicted in  FIG.  10 A . In other words,  FIG.  10 A  is approximately 1/1.5 times (=1/n d ) of  FIG.  21   . Thus, the optical member  20  and the recessed and protruding structure unit  21  are designed in accordance with the GS method, but actually exhibit a refraction effect. 
       FIG.  22 A  depicts the result of determination of a spatial frequency using the Fourier conversion method on the basis of the value of ∂Z/∂X in (d) of  FIG.  20   , and  FIG.  22 B  depicts the result of determination of a spatial frequency using the Fourier conversion method on the basis of the value of ∂Z/∂X in (e) of  FIG.  20   . Note that the horizontal axis in  FIGS.  22 A and  22 B  indicates the value of ∂Z/∂X and the value of ∂Z/∂Y in the X axis direction and that the vertical axis in  FIGS.  22 A and  22 B  indicates the value of ∂Z/∂X and the value of ∂Z/∂Y in the Y axis direction. Typical diffusion plates are isotropic, and thus distributions corresponding to  FIGS.  22 A and  22 B  are point-symmetric in the vertical direction (Y axis direction) and in the horizontal direction (X axis direction). On the other hand, for the recessed and protruding structure unit  21 , the distributions are point-asymmetric in the vertical direction (Y axis direction) and in the horizontal direction (X axis direction). In other words, ∂Z/∂X and ∂Z/∂Y that are angular distributions of the recessed and protruding portion  21 ′ are point-asymmetric when the intersection between the X axis and the Y axis is a point of symmetry. Additionally, calculation results for the average spatial frequency are as indicated in Table 2 below. The average value of the average spatial frequency is obtained by multiplying each spatial frequency (absolute value) by the distributions in  FIGS.  22 A and  22 B . Table 2 below also indicates N X =L X-0 ×F X-ave  and N Y =L Y-0 ×F Y-ave  when F x-ave  is the average value of the spatial frequency of the recessed and protruding portion  21 ′ along the X axis, F Y-ave  is the average value of the spatial frequency of the recessed and protruding portion  21 ′ along the Y axis, L X-0  is the length along the X axis of the recessed and protruding structure unit  21  on which light from the light source  10  is incident, and L Y-0  is the length, along the Y axis, of the recessed and protruding structure unit  21  on which light from the light source  10  is incident. However, L X-0 =L Y-0 =1.5 mm is set. 
     Here, in  FIG.  21   , the horizontal axis indicates a histogram distribution obtained by converting, into a histogram, ∂Z/∂X at a position corresponding to the emission angle, in the X axis direction, of light emitted from the center of the recessed and protruding structure unit  21 , and the vertical axis indicates a histogram distribution obtained by converting, into a histogram, ∂Z/∂Y at a position corresponding to the emission angle, in the Y axis direction, of light emitted from the center of the recessed and protruding structure unit  21 . 
     &lt;Table 2&gt; 
     
         
         Average value F X-ave  of the spatial frequency based on the value of ∂Z/∂X: 13.3 mm −1    
         Average value F Y-ave  of the spatial frequency based on the value of ∂Z/∂Y: 17.1 mm −1    
       
    
         N   X   =L   X-0   ×F   X-ave : 19.9 
         N   Y   =L   Y-0   ×F   Y-ave : 25.6 
     Here, N X  and N Y  mean how many increases and decreases in ∂Z/∂X and ∂Z/∂T are present within the light irradiation range on average. In other words, N X  and N Y  indicate the average number of recesses and protrusions present. N X  and N Y  having extremely low values lead to reduced (insufficient) overlap between light emission angle distributions caused by refraction, preventing the desired light emission angle distribution from being maintained. Thus, the following are desirably satisfied: 
         N   X   =L   X-0   ×F   X-ave ≥10 and
 
         N   Y   =L   Y-0   ×F   Y-ave ≥10.
 
     For a more desirable light emission angle distribution, preferably the following are desirably satisfied. 
         N   X   =L   X-0   ×F   X-ave ≥15 and
 
         N   Y   =L   Y-0   ×F   Y-ave ≥15.
 
     Additionally, an excessively large average value of the spatial frequency leads to an intense diffraction effect and also degrades productivity. Accordingly, desirably, F X-ave  is equal to or less than 1×10 3  mm −1 , preferably equal to or less than 1×10 2  mm −1 , and F Y-ave  is equal to or less than 1×10 3  mm −1 , preferably equal to or less than 1×10 2  mm −1 . Note that, for example, F X-ave  being 1×10 3  mm −1  means that the length of one period of the recessed and protruding portion  21 ′ along the X axis is 1 μm and that F X-ave  being 1×10 2  mm −1  means that the length of one period of the recessed and protruding portion  21 ′ along the X axis is 10 μm. Furthermore, F X-ave ≠F Y-ave . 
     Additionally, as illustrated in  FIG.  23   , when F X′-ave  is the average value of the spatial frequency of the recessed and protruding portion  21 ′ along a straight line satisfying Y=X, and F Y′-ave  is the average value of the spatial frequency of the recessed and protruding portion  21 ′ along a straight line satisfying Y=−X, the distribution is more approximate to a rectangle in diagonal directions, and thus 
       F X′-ave &gt;F X-ave    
       F X′-ave &gt;F Y-ave    
         F   Y′-ave &gt;F X-ave    
     and
 
F Y′-ave &gt;F Y-ave  are satisfied. Specifically, Table 3 below indicates the values of F X′-ave , F Y′-ave , N X ′=L X-0 ×F X′-ave , and N Y ′=L Y-0 ×F Y′-ave .
 
     &lt;Table 3&gt; 
       F X′-ave : 23.7 mm −1    
       F Y′-ave : 23.7 mm −1    
         N   X   ′=L   X-0   ×F   X′-ave =35.6 
         N   Y   ′=L   Y-0   ×F   Y′-ave =35.6 
     Furthermore, Table 4 indicates the results of calculation of kurtosis β of ∂Z/∂X and ∂Z/∂Y within the light irradiation range. The kurtosis is defined as the ratio μ 4 /σ 4  of the fourth moment μ 4  around the average value and the fourth power of a standard deviation σ, and the distribution becomes more round with decreasing kurtosis. It is known that kurtosis=0 indicates a normal distribution and that kurtosis is −1.2 in a uniform distribution. In the recessed and protruding structure unit  21  constituting the illumination apparatus of Example 1, the value of ∂Z/∂X and the value of ∂Z/∂Y are preferably closer to the uniform distribution than to the Gaussian distribution, and specifically, desirably β (kurtosis along the X axis β X  and kurtosis along the Y axis β Y )≤−0.5,preferably β (kurtosis along the X axis β X  and kurtosis along the Y axis β Y )≤−0.8. 
     &lt;Table 4&gt; 
     Kurtosis of ∂Z/∂X β X : −1.1 
     Kurtosis of ∂Z/∂Y β Y : −1.1 
     A configuration of a projective display apparatus (projector) will be described with reference to  FIG.  4   .  FIG.  4    is a schematic diagram illustrating a general configuration of a projective display apparatus  100  including an illumination apparatus (light source apparatus)  110 . Note that, by way of example, a projective display apparatus based on a 3LCD reflective 3LCD technology will be described that modulates light using a reflective liquid crystal panel (LCD). The illumination apparatus  110  can include the illumination apparatus described in Examples 1 to 3. 
     The projective display apparatus  100  includes the illumination apparatus  110  including a fly eye lens  121  ( 121 A and  121 B) [integrator  30 ], an illumination optical system  120 , an image forming unit  130 , and a projective optical system  140  in this order. 
     The illumination optical system  120  includes, for example, a polarization conversion element  122 , a lens  123 , dichroic mirrors  124 A and  124 B, reflection mirrors  125 A and  125 B, lenses  126 A and  126 B, a dichroic mirror  127 , and polarizing plates  128 A,  128 B, and  128 C in order of increasing distance from the illumination apparatus  110 . 
     The fly eye lens  121  ( 121 A and  121 B) is intended to homogenize the illuminance distribution of white light from the illumination apparatus  110  (specifically, the optical member  20 ). The polarization conversion element  122  functions to align a polarizing axis of incident light with a predetermined direction, and for example, converts light other than p polarized light into the p polarized light. The lens  123  condenses light from the polarization conversion element  122  toward the dichroic mirrors  124 A and  124 B. The dichroic mirrors  124 A and  124 B selectively reflect light in a predetermined wavelength region, while selectively transmitting light in the other wavelength regions. For example, the dichroic mirror  124 A mainly reflects red light toward the reflection mirror  125 A. Additionally, the dichroic mirror  124 B mainly reflects blue light toward the reflection mirror  125 B. Consequently, green light is mainly transmitted through both dichroic mirrors  124 A and  124 B toward a reflective polarizing plate  131 C of the image forming unit  130 . The reflection mirror  125 A reflects light (mainly red light) from the dichroic mirror  124 A toward the lens  126 A, and the reflection mirror  125 B reflects light (mainly blue light) from the dichroic mirror  124 B toward the lens  126 B. The lens  126 A transmits light (mainly red light) from the reflection mirror  125 A and condenses the light onto the dichroic mirror  127 . The lens  126 B transmits light (mainly blue light) from the reflection mirror  125 B and condenses the light onto the polarizing plate  128 B. The dichroic mirror  127  selectively reflects green light, while selectively transmitting light in the other wavelength regions. Here, red light components of the light from the transmission lens  126 A are transmitted. In a case where the light from the transmission lens  126 A includes green light components, the dichroic mirror  127  reflects the green light components toward the polarizing plate  128 C. The polarizing plates  128 A,  128 B, and  128 C each include a polarizer with a polarizing axis in a predetermined direction. For example, in a case where the polarization conversion element  122  has performed conversion into p polarized light, the polarizing plates  128 A,  128 B, and  128 C transmits the p polarized light, while reflecting s polarized light. 
     The image forming unit  130  includes reflective polarizing plates  131 A,  131 B, and  131 C, reflective liquid crystal panels  132 A,  132 B, and  132 C, and a dichroic prism  133 . 
     The reflective polarizing plates  131 A,  131 B, and  131 C transmit light (for example, p polarized light) with the same polarizing axis as that of polarized light from a respective one of the polarizing plates  128 A,  128 B, and  128 C, while reflecting light with the other polarizing axes (s polarized light). Specifically, the reflective polarizing plate  131 A transmits red light of p polarized light from the polarizing plate  128 A toward the reflective liquid crystal panel  132 A. The reflective polarizing plate  131 B transmits blue light of p polarized light from the polarizing plate  128 B toward the reflective liquid crystal panel  132 B. The reflective polarizing plate  131 C transmits green light of p polarized light from the polarizing plate  128 C toward the reflective liquid crystal panel  132 C. Additionally, green light of p polarized light entering the reflective polarizing plate  131 C after passing through both the dichroic mirrors  124 A and  124 B is directly transmitted through the reflective polarizing plate  131 C and enters the dichroic prism  133 . Furthermore, the reflective polarizing plate  131 A reflects red light of s polarized light from the reflective liquid crystal panel  132 A, and the reflected light enters the dichroic prism  133 . The reflective polarizing plate  131 B reflects blue light of s polarized light from the reflective liquid crystal panel  132 B, and the reflected light enters the dichroic prism  133 . The reflective polarizing plate  131 C reflects green light of s polarized light from the reflective liquid crystal panel  132 C, and the reflected light enters the dichroic prism  133 . 
     The reflective liquid crystal panels  132 A,  132 B, and  132 C respectively spatially modulate red light, blue light, and green light. 
     The dichroic prism  133  synthesizes incident red light, blue light, and green light, and emits the resultant light toward the projective optical system  140 . The projective optical system  140  includes lenses  142  to  146  and a mirror  141 . The projective optical system  140  enlarges light emitted from the image forming unit  130  and projects the resultant light on a screen (not depicted) or the like. 
       FIG.  5    depicts a schematic diagram of a projective display apparatus (projector) with another configuration. The projective display apparatus is a projective display apparatus based on a transmissive 3LCD technology and which modulates light using a transmissive liquid crystal panel (LCD). 
     The projective display apparatus (projector)  200  includes the illumination apparatus  110  including an integrator  221 , an optical modulation apparatus (including an image forming unit  220  and an illumination optical system) that generates an image using light emitted from the illumination apparatus  110  (specifically, the optical member  20 ), and a projective optical system  240  that projects image light generated by the image forming unit  220 . 
     The image forming unit  220  including the illumination optical system includes a polarization conversion element  222 , a condenser lens  223 , dichroic mirrors  224  and  225 , mirrors  226 ,  227 , and  228 , and relay lenses  231  and  232 . Additionally, the image forming unit  220  includes a field lens  233  ( 233 R,  233 G, and  233 B), liquid crystal light valves  234 R,  234 G, and  234 B, and a dichroic prism  235 . 
     The integrator  221  includes a function to generally arrange, into a uniform luminance distribution, incident light from the illumination apparatus  110  (specifically, the optical member  20 ) with which the liquid crystal light valves  234 R,  234 G, and  234 B are irradiated. For example, the integrator  221  includes a first fly eye lens  221 A including multiple microlenses (not depicted) arrayed in a two-dimensional manner and a second fly eye lens  221 B including multiple microlenses arrayed corresponding to the respective microlenses of the first fly eye lens  221 A. 
     Parallel beams incident on the integrator  221  from the illumination apparatus  110  are split into multiple light fluxes by the microlenses of the first fly eye lens  221 A, and each of the light fluxes is formed into an image on the corresponding microlens in the second fly eye lens  221 B. Each of the microlenses of the second fly eye lens  221 B functions as a secondary light source to irradiate the polarization conversion element  222  with multiple parallel beams as incident light. 
     The polarization conversion element  222  includes a function to uniformize the polarization state of incident light incident via the integrator  221  and the like. The polarization conversion element  222 , for example, emits emitted light including blue light B 3 , green light G 3 , and red light R 3 , via the condenser lens  223  positioned on the emission side of the illumination apparatus  110 . 
     The dichroic mirrors  224  and  225  have the property of selectively reflecting light in a predetermined wavelength region, while transmitting light in the other wavelength regions. For example, the dichroic mirror  224  selectively reflects the red light R 3 . In the green light G 3  and blue light B 3  transmitted through the dichroic mirror  224 , the dichroic mirror  225  selectively reflects the green light G 3 . The remaining blue light B 3  is transmitted through the dichroic mirror  225 . Thus, light emitted from the illumination apparatus  110  is separated into multiple light beams of different colors. 
     The red light R 3  resulting from the separation is reflected by the mirror  226  and collimated by passing through the field lens  233 R, and then enters the liquid crystal light valve  234 R for modulation of red light. The green light G 3  is collimated by passing through the field lens  233 G, and then enters the liquid crystal light valve  234 G for modulation of green light. The blue light B 3  passes through the relay lens and is reflected by the mirror  227 , and passes through the relay lens  232  and is reflected by the mirror  228 . The blue light B 3  reflected by the mirror  228  passes through the field lens  233 B and is collimated by passing through the field lens  233 B, and the light then enters the liquid crystal light valve  234 B for modulation of blue light. 
     The liquid crystal light valves  234 R,  234 G, and  234 B are electrically connected to a signal source (for example, a personal computer or the like) that supplies image signals including image information. On the basis of supplied image signals in the respective colors, the liquid crystal light valves  234 R,  234 G, and  234 B modulate incident light for each pixel to respectively generate a red image, a green image, and a blue image. The modulated light beams in the respective colors (images formed) are incident on the dichroic prism  235  for synthesis. The dichroic prism  235  overlaps light beams in the respective colors incident from three directions for synthesis, and the resultant light is emitted toward the projective optical system  240 . 
     The projective optical system  240  includes multiple lenses  241  and the like and irradiates the screen (not depicted) with light resulting from the synthesis performed by the dichroic prism  235 . Thus, a full-color image is displayed. 
     As described above,
     (A) The optical member is rotatable around a rotation axis extending parallel to the direction in which light from the light source is incident and is emitted,   (B) The planar shape of the optical member is annular around the rotation axis, and   (C) The first surface or the second surface of the optical member is provided with multiple recessed and protruding structure units consecutively formed and each having a fan-surface-like planar shape and including a recessed and protruding portion.   Accordingly, even in a case where the optical member is rotated, light emitted from the rotating recessed and protruding portion can maintain a desired cross-sectional shape, for example, a rectangle approximate to the external shape of the integrator. Furthermore,   (D) An extension of the boundary between adjacent recessed and protruding structure units intersects the rotation axis,   (E) When the boundary between the adjacent recessed and protruding structure units is a mirror plane, the adjacent recessed and protruding structure units are in a mirror symmetry relation, and the recessed and protruding portions of the adjacent recessed and protruding structure units are smoothly connected together, and   (F) The recesses and protrusions in the recessed and protruding portion of each recessed and protruding structure unit are smoothly connected together.   Accordingly, even in a case where the optical member is rotated, light emitted from the rotating recessed and protruding portion can constantly and reliably maintain a desired cross-sectional shape, for example, a rectangle approximate to the external shape of the integrator. In addition,   (G) The area occupied by the recessed and protruding portion of each recessed and protruding structure unit is larger in size than light incident from the light source.   This allows prevention of the problem of unwanted diffracted light resulting from a light diffraction effect. Note that, unlike a lens array, the recessed and protruding structure unit includes no repeated structures smaller than the light irradiation area. The lens array can provide a similar light emission angle distribution, but an actual combination with very coherent light such as laser light leads to high-order diffracted light depending on repetition periodicity. The recessed and protruding structure unit is relatively highly random and generates no diffracted light. Additionally, rotation of the optical member enables speckle noise to be reduced. Furthermore, light emitted from the optical member can be provided with a desired cross-sectional shape.   

     Additionally, a recessed and protruding structure unit can be designed that includes a recessed and protruding shape with a flexible refraction angle, thus allowing, for example, possible distortion in the condenser lens to be corrected. Accordingly, a light position distribution more uniform than a known light position distribution (≈light emission angle distribution) can be formed on the integrator. Additionally, there is a problem in that, in a case where few semiconductor laser elements constitute the light source, the use of a diffusion plate leads to difficult light distribution control on the integrator. However, appropriate design of the recessed and protruding structure unit allows the light position distribution (≈light emission angle distribution) on the integrator to be uniformized. This enables color unevenness and speckle noise to be reduced with no decrease in the quantity of light. Furthermore, auxiliary arrangement of a cylindrical lens in addition to the collimator lens enables a light position distribution (≈light emission angle distribution) similar to a circle to be formed on the integrator. 
     Incidentally, depolarization may occur depending on the type of the diffusion plate. The use of an element with polarization dependence [for example, LCOS (Liquid Crystal on Silicon), an LCD (Liquid Crystal Display) or the like] requires a polarization rectifier element. On the other hand, the optical element in Examples 1 to 3 spreads light in accordance with the law of reflection, preventing depolarization. This eliminates the need for a polarization rectifier element (for example, a P wave-S wave conversion apparatus, a P-S converter, or the like), allowing the whole system to be compactified. The polarization rectifier element also degrades efficiency. However, Examples  1  to  3  eliminate the need for the polarization rectifier element, leading to high light utilization efficiency. 
     EXAMPLE 2 
     Example 2 is a variation of Example 1. In an illumination apparatus in Example 2 depicted in  FIG.  2   , light from the light source  10  is incident on each recessed and protruding structure unit  21  in the rotating state from the first surface  20 A of each recessed and protruding structure unit  21  and is emitted from the first surface  20 A of each recessed and protruding structure unit  21  toward the integrator  30 , 
     the first surface  20 A of each recessed and protruding structure unit  21  is provided with the recessed and protruding portion  21 ′, and 
     the second surface  20 B of each recessed and protruding structure unit  21  is flat and constitutes a light reflection surface. Specifically, the second surface  20 B is provided with a light reflection layer including, for example, silver (Ag), aluminum (Al), or the like. 
     The illumination apparatus further includes a polarization beam splitter  25  and a quarter wavelength plate  26 , and light from the light source  10  enters the polarization beam splitter  25  and exits the polarization beam splitter  25  along the first direction (reflected by the polarization beam splitter  25  in the illustrated example), passes through the quarter wavelength plate  26 , is reflected at the recessed and protruding structure unit  21 , passes through the quarter wavelength plate  26 , enters the polarization beam splitter  25 , exits the polarization beam splitter  25  along the second direction different from the first direction (passing through the polarization beam splitter  25  in the illustrated example), and enters the integrator  30 . 
     Example 1 includes a transmissive recessed and protruding structure unit, whereas Example 2 includes a reflective recessed and protruding structure unit. In a case of the transmissive recessed and protruding structure unit, the emission angle of light from the recessed and protruding structure unit can be expressed as: 
       (emission angle of light from recessed and protruding structure unit)≈(incident angle of light on recessed and protruding structure unit)/(refractive index n d )
 
     On the other hand, in a case of the reflective recessed and protruding structure unit, in the recessed and protruding structure unit, light is subjected to two refraction actions, and thus the emission angle of light from the recessed and protruding structure unit is approximately twice the incident angle of light on the recessed and protruding structure unit. Consequently, in a case where the recessed and protruding portion  21 ′ in the transmissive recessed and protruding structure unit has a maximum depth of 27 μm, the recessed and protruding portion  21 ′ in the reflective recessed and protruding structure unit is only required to have a maximum depth obtained by multiplying the maximum depth of the recessed and protruding portion  21 ′ in the transmissive recessed and protruding structure unit by 1/(2×n d ). Specifically, in the reflective recessed and protruding structure unit, the recessed and protruding portion  21 ′ is only required to have a maximum depth of 9 μm. Accordingly, compared to Example 1, Example 2 further facilitates manufacture of the recessed and protruding structure unit. 
     EXAMPLE 3 
     Example 3 is a variation of Examples 1 and 2. In Examples 1 and 2, once light from the light source  10  is condensed into the recessed and protruding structure unit  21 , the desired light position distribution (≈light emission angle distribution) is formed on the integrator  30  via the condenser lens  24 . On the other hand, a sufficient distance between the optical member  20  and the integrator  30  allows the desired light position distribution (≈light emission angle distribution) to be formed on the integrator  30  with no light from the light source  10  condensed into the recessed and protruding structure unit  21 .  FIG.  3    depicts such a configuration. In Example 3, substantially parallel light beams are incident on the condenser lens  27 . The recessed and protruding structure unit  21  is disposed upstream of (on the light source side of) the condenser lens  27 . No lens system  13  is provided. The focal length f of the condenser lens  27  satisfies the following equations. Here, IH LD  is the maximum image height from the optical axis of laser light, and IG INT  is the maximum image height on the integrator  30 . θ (unit: rad) is the maximum incident angle on the integrator  30 , and φ (unit: rad) is the maximum emission angle in the recessed and protruding structure unit  21 . 
       IH LD =f·θ
 
       IH Int =f·φ
 
     The following equation is derived from the above-described two equations. 
       θ=φ·IH LD /IH INT  
 
     For example, 
     when θ=2 degrees, 
     IH INT =10 mm, and 
     IH LD =20 mm, 
     φ=4 degrees, and 
     f=143 mm. 
     are obtained. In Example 3, the integrator  30  is disposed at a position corresponding to the focus of the condenser lens  27 , and thus a light position distribution similar to that in Example 1 (see (b) of  FIG.  9   ) can be obtained by locating the integrator  30  approximately 143 mm away from the condenser lens  27 . The configuration of the recessed and protruding structure unit  21  in this case is only required to be substantially similar to the configuration in Example 1. However, the maximum emission angle φ in the recessed and protruding structure unit  21  is 4 degrees, and the maximum emission angle in  FIG.  10 A  is approximately 15 degrees, and thus Example 3 needs to be approximately (4/15=0.27) with respect to Example 1. 
     For this purpose, for example, the depth of the recessed and protruding portion  21 ′ in the recessed and protruding structure unit  21  is only required to be 0.27 times as large as the depth in Example 1. In Example 3, the number of components can be reduced, allowing cost reduction and manufacture simplification to be achieved. 
     Additionally, in Example 3, the area of the recessed and protruding structure unit  21  where light is incident varies with semiconductor laser element. Accordingly, by controlling, for each semiconductor laser element, the light emission angle in the area of the recessed and protruding structure unit corresponding to each semiconductor laser element, the distribution on the integrator  30  can be further uniformly approximated to the desired shape. For example, on the basis of light from an area of the light source  10  denoted by “1” in (a) of  FIG.  24   , the recessed and protruding structure unit  21  emits, toward the integrator  30 , light with a cross-sectional shape as denoted by “1” in (b) of  FIG.  24   . Additionally, on the basis of light from an area of the light source  10  denoted by “2” in (a) of  FIG.  24   , the recessed and protruding structure unit  21  emits, toward the integrator  30 , light with a cross-sectional shape as denoted by “2” in (b) of  FIG.  24   . By thus overlapping light emission angle distributions corresponding to different areas of the light source  10 , the light position distribution (≈light emission angle distribution) (see (c) of  FIG.  24   ) on the integrator  30  approximates, for example, a circle. For this purpose, by rotating the optical member  20  (recessed and protruding structure unit  21 ) in an oblique direction, or the like, the recessed and protruding structure units  21  to be irradiated with light need to be prevented from overlapping in spite of rotation of the optical member  20  (see (a) of  FIG.  24   ). Alternatively, the semiconductor laser element may be inclined with respect to the rotation axis AR. 
     The optical element, illumination apparatus, and projective display apparatus of the present disclosure have been described above on the basis of the preferred examples. However, the optical element, illumination apparatus, and projective display apparatus of the present disclosure are not intended to be limited to the examples. The light source, the optical system from the light source to the optical member, the optical member, the recessed and protruding structure unit, and the configuration and structure of the optical system from the optical member to the integrator are illustrative and can be appropriately modified. For example, the arrangement of the light emitting elements (semiconductor laser elements) constituting the light source, and the distribution of light emitted from the light source are optional, and the optimal design can be selected depending on the situation. 
     In the examples, the multiple light emitting elements  10 ′ are arrayed on the intersections in the orthogonal grid, the arrangement shape of the multiple light emitting elements  10 ′ arranged at the outer edge portion of the light source  10  is like a rectangle, and the cross-sectional shape of light emitted from the recessed and protruding structure unit  21  is like a rectangle. However, the present disclosure is not intended to be limited to these features. The cross-sectional shape of light emitted from the recessed and protruding structure unit  21  is approximate to the arrangement shape of the light emitting elements  10 ′ arranged in the outermost portion of the light source  10 . However, the present disclosure can be configured such that the multiple light emitting elements  10 ′ are arrayed on intersections in a honeycomb lattice, and the arrangement shape of the multiple light emitting elements  10 ′ arranged at the outer edge portion of the light source  10  is like a regular hexagon (depicted by dotted lines in  FIG.  26 A ), as depicted in  FIG.  26 A , and the cross-sectional shape of light emitted from the recessed and protruding structure unit  21  is like a regular hexagon, as depicted in  FIG.  26 B . 
     Additionally, (c) of  FIG.  9    depicts the light position distribution, along the X axis direction, of the light position distribution (≈light emission angle distribution) on the integrator  30 . However, in the recessed and protruding structure unit  21 , when the light emission angle distribution protrudes not only upward but also downward around the Z axis (that is, the light emission angle distribution is recessed around the Z axis, the light position distribution (≈light emission angle distribution) on the integrator  30  can be further uniformized. Additionally, light emitted from the optical member can be provided with a desired cross-sectional shape. 
     The light source may include a combination of semiconductor laser elements and a wavelength conversion member (wavelength conversion material layer and a color conversion material layer). The recessed and protruding structure unit is less dependent on wavelength, and can apply a similar light emission angle distribution to light with any wavelengths. In this case, the present disclosure can be configured such that white light can be emitted via the wavelength conversion material layer (color conversion material layer). Specifically, the wavelength conversion material layer through which laser light emitted from the semiconductor laser element passes is only required to be formed on a substrate. 
     In a case where blue light is emitted from the semiconductor laser element, a configuration in which white light is emitted via the wavelength conversion material layer can be provided by employing the following configuration.
     [A] By using a wavelength conversion material layer that converts blue light emitted from the semiconductor laser element into yellow light, white light including a mixture of blue and yellow is obtained as light emitted from the wavelength conversion material layer,   [B] By using a wavelength conversion material layer that converts blue light emitted from the semiconductor laser element into orange light, white light including a mixture of blue and orange is obtained as light emitted from the wavelength conversion material layer, and   [C] By using a wavelength conversion material layer that converts blue light emitted from the semiconductor laser element into green light, white light including a mixture of blue, green, and red is obtained as light emitted from the wavelength conversion material layer.   

     Alternatively, in a case where ultraviolet light is emitted from the semiconductor laser element, a configuration in which white light is emitted via the wavelength conversion material layer can be provided by employing the following configuration.
     [D] By using a wavelength conversion material layer that converts ultraviolet light emitted from the semiconductor laser element into blue light and a wavelength conversion material layer that converts the ultraviolet light into yellow light, white light including a mixture of blue and yellow is obtained as light emitted from the wavelength conversion material layer,   [E] By using a wavelength conversion material layer that converts ultraviolet light emitted from the semiconductor laser element into blue light and a wavelength conversion material layer that converts the ultraviolet light into orange light, white light including a mixture of blue and orange is obtained as light emitted from the wavelength conversion material layer, and   [F] By using a wavelength conversion material layer that converts ultraviolet light emitted from the semiconductor laser element into blue light and a wavelength conversion material layer that converts the ultraviolet light into green light, white light including a mixture of blue, green, and red is obtained as light emitted from the wavelength conversion material layer.   

     Here, a specific example of a wavelength conversion material that is excited by blue light to emit red light may be red light emitting phosphor particles, and more specific examples of the wavelength conversion material can include (ME:Eu)S [“ME” means at least one type of atoms selected from the group including Ca, Sr, and Ba, and this also applies to the description below], (M:Sm) x (Si, Al) 12 (O, N) 16  [“M” means at least one type of atoms selected from the group including Li, Mg, and Ca, and this also applies to the description below], ME 2 Si 5 N 8 :Eu, (Ca:Eu)SiN 2 , and (Ca:Eu)AlSiN 3 . Additionally, a specific example of a wavelength conversion material that is excited by blue light to emit green light may be green light emitting phosphor particles, and more specific examples of the wavelength conversion material can include (ME:Eu)Ga 2 S 4 , (M:RE) x (Si, Al) 12 (O, N) 15  [“RE” means Tb and Yb], (M:Tb) x (Si, Al) 12 (O,  N ) 16 , (M:Yb) x (Si, Al) 12 (O, N) 16 , and Si 6-Z Al Z O Z N 8-Z :Eu. Furthermore, a specific example of a wavelength conversion material that is excited by blue light to emit yellow light may be yellow light emitting phosphor particles, and more specific examples of the wavelength conversion material can include YAG (yttrium, aluminum, garnet)-based phosphor particles. Note that one type of wavelength conversion material may be used or two or more types of wavelength conversion materials may be mixed. Furthermore, the present disclosure can be configured such that a mixture of two or more types of wavelength conversion materials is used to cause emitted light in a color other than yellow, green, or red to be emitted from the wavelength conversion material mixture. Specifically, for example, the present disclosure can be configured to emit cyan light, and this configuration is only required to use a mixture of green light emitting phosphor particles (for example, LaO 4 :Ce, Tb, BaMgAl 10 O 17 :Eu, Mn, Zn 2 SiO 4 :Mn, MgAl 11 O 19 :Ce, Tb, Y 2 SiO 5 :Ce, Tb, MgAl 11 O 19 :CE, Tb, Mn) and blue light emitting phosphor particles (for example, BaMgAl 10 O 17 :Eu, BaMg 2 Al 16 O 27 :Eu, Sr 2 P 2 O 7 :Eu, Sr 5 (PO 4 ) 3 C 1  :Eu, (Sr, Ca, Ba, Mg) s (PO 4 ) 3 Cl:Eu, CaWO 4 , or CaWO 4 :Pb). 
     Additionally, a specific example of a wavelength conversion material that is excited by ultraviolet rays to emit red light may be red light emitting phosphor particles, and more specific examples of the wavelength conversion material can include Y 2 O 3 :Eu, YVO 4 :Eu, Y(P, V)O 4 :Eu, 3.5MgO 0.5MgF 2 .Ge2:Mn, CaSiO 3 :Pb, Mn, Mg 6 AsO 11 :Mn, (Sr, Mg) 3 (PO 4 ) 3 :Sn, La 2 O 2 S:Eu, and Y 2 O 2 S:Eu. Additionally, a specific example of a wavelength conversion material that is excited by ultraviolet rays to emit green light may be green light emitting phosphor particles, and more specific examples of the wavelength conversion material can include LaPO 4 :Ce, Tb, BaMgAl 10 O 17 :Eu, Mn, Zn 2 SiO 4 :Mn, MgAl 11 O 19 :Ce, Tb, Y 2 SiO 5 :Ce, Tb, MgAl 11 O 19 :CE, Tb, Mn, Si 6-Z Al Z O Z N 8-Z :Eu. Furthermore, a specific example of a wavelength conversion material that is excited by ultraviolet rays to emit blue light may be blue light emitting phosphor particles, and more specific examples of the wavelength conversion material can include BaMgAl 10 O 17 :Eu, BaMg 2 Al 16 O 27 :Eu, Sr 2 P 2 O 7 :Eu, Sr 5 (PO 4 ) 3 Cl:Eu, (Sr, Ca, Ba, Mg) 5 (PO 4 ) 3 Cl:Eu, CaWO 4 , and CaWO 4 :Pb. Moreover, a specific example of a wavelength conversion material that is excited by ultraviolet rays to emit yellow light may be yellow light emitting phosphor particles, and a more specific example of the wavelength conversion material may be YAG-based phosphor particles. Note that one type of wavelength conversion material may be used or two or more types of wavelength conversion materials may be mixed. Furthermore, the present disclosure can be configured such that a mixture of two or more types of wavelength conversion materials is used to cause emitted light in a color other than yellow, green, or red to be emitted from the wavelength conversion material mixture. Specifically, the present disclosure can be configured to emit cyan light, and this configuration is only required to use a mixture of green light emitting phosphor particles and blue light emitting phosphor particles described above. 
     However, the wavelength conversion material (color conversion material) is not limited to phosphor particles, and for example, light emitting particles may be used that include an indirect transition silicon-based material to which a two-dimensional quantum well structure, a one-dimensional quantum well structure (quantum wire), a zero-dimensional quantum well structure (quantum dot), or the like is applied, the two-, one-, or zero-dimensional quantum well structure using a localized wave function for carriers and using a quantum effect in order to efficiently convert carriers into light, as in a direct transition type. Additionally, rare earth atoms added to a semiconductor material are known to emit glittering light due to intra-shell transition, and light emitting particles to which such a technology is applied can be used. 
     Quantum dots can be used as the wavelength conversion material (color conversion material). A decrease in the size (diameter) of the quantum dot increases bandgap energy, while reducing the wavelength of light emitted from the quantum dot. In other words, a smaller quantum dot emits light with a smaller wavelength (blue light-side light), whereas a larger quantum dot emits light with a larger wavelength (red light-side light). Accordingly, by using the same material to form a quantum dot while adjusting the size of the quantum dot, quantum dots can be obtained that emit light with the desired wavelength (that perform color conversion in the desired light). Specifically, the quantum dot preferably has a core-shell structure. Examples of the material constituting quantum dots include, for example, but not limited to, Si; Se; CIGS(CuInGaSe), CIS(CuInSe 2 ), CuInS 2 , CuAlS 2 , CuAlSe 2 , CuGaS 2 , CuGaSe 2 , AgAlS 2 , AgAlSe 2 , AgInS 2 , and AgInSe 2 , which are chalcopyrite compounds; a perovskite material; GaAs, GaP, InP, InAs, InGaAs, AlGaAs, InGaP, AlGaInP, InGaAsP, and GaN, which are group III-V compounds; CdSe, CdSeS, CdS, CdTe, In 2 Se 3 , In 2 S 3 , Bi 2 Se 3 , Bi 2 S 3 , ZnSe, ZnTe, ZnS, HgTe, HgS, PbSe, PbS, and TiO 2 , and the like. 
     Note that the present disclosure can also provide the following configurations. 
     [A01] 
     «Illumination Apparatus» 
     An illumination apparatus including: 
     a light source; 
     an optical member including a first surface on which light from the light source is incident and a second surface facing the first surface; and 
     an integrator on which light emitted from the optical member is incident, in which 
     the optical member is rotatable around a rotation axis extending parallel to a direction in which light from the light source is incident and is emitted, 
     a planar shape of the optical member (the planar shape of the optical member obtained by cutting the optical member along a virtual plane orthogonal to the rotation axis) is annular around the rotation axis, 
     multiple recessed and protruding structure units each having a fan-surface-like planar shape and including a recessed and protruding portion are consecutively formed on the first surface or the second surface of the optical member, 
     an extended line of a boundary between adjacent recessed and protruding structure units intersects the rotation axis, 
     when the boundary between the adjacent recessed and protruding structure units is a mirror plane, the adjacent recessed and protruding structure units are in a mirror symmetry relation, and recessed and protruding portions of the adjacent recessed and protruding structure units are smoothly connected together, and 
     recessed portions and protruding portions of the recessed and protruding portion of each recessed and protruding structure unit are smoothly connected together, and 
     an area occupied by the recessed and protruding portion of each recessed and protruding structure unit is larger in size than incident light from the light surface. 
     [A02] 
     The illumination apparatus according to [A01], in which the recessed and protruding portion refracts incident light from the light source. 
     [A03] 
     The illumination apparatus according to [A01] or [A02], in which 
     the light source emits light with multiple wavelengths.
     [A04]   

     The illumination apparatus according to any one of [A01] to [A03], in which, 
     when a shape of light obtained by cutting the light along a virtual plane orthogonal to a traveling direction of the light is referred to as a cross-sectional shape of the light, the cross-sectional shape of light incident on the recessed and protruding structure unit from the light source is different from the cross-sectional shape of light emitted from the recessed and protruding structure unit.
     [A05]   

     The illumination apparatus according to any one of [A01] to [A04], in which 
     the light source includes multiple light emitting elements arrayed in a two-dimensional matrix, and, 
     when a shape of light obtained by cutting the light along a virtual plane orthogonal to a traveling direction of the light is referred to as a cross-sectional shape of the light, the cross-sectional shape of light emitted from the recessed and protruding structure unit is approximate to an arrangement shape of the light emitting elements arranged in an outermost portion of the light source.
     [A06]   

     The illumination apparatus according to [A05], in which 
     the multiple light emitting elements are arrayed on intersections in an orthogonal grid, 
     the arrangement shape of the multiple light emitting elements arranged at an outer edge portion of the light source is like a rectangle, and 
     the cross-sectional shape of the light emitted from the recessed and protruding structure unit is like a rectangle.
     [A07]   

     The illumination apparatus according to [A05], in which 
     the multiple light emitting elements are arrayed on intersections in a honeycomb lattice, 
     the arrangement shape of multiple the light emitting elements at the outer edge portion of the light source is like a regular hexagon, and 
     the cross-sectional shape of light emitted from the recessed and protruding structure unit is a regular hexagon.
     [A08]   

     The illumination apparatus according to any one of [A01] to [A05], in which 
     the light source includes multiple light emitting elements arrayed in a two-dimensional matrix, and 
     the cross-sectional shape of light emitted from the recessed and protruding structure unit is approximate to the external shape of the integrator.
     [A09]   

     The illumination apparatus according to [A08], in which 
     the multiple light emitting elements are arrayed on intersections in an orthogonal grid, and 
     the external shape of the integrator is like a square or a rectangle.
     [A10]   

     The illumination apparatus according to any one of [A01] to [A09], in which 
     the recessed and protruding portion of the recessed and protruding structure unit is designed in compliance with a Gerchberg-Saxton method.
     [A11]   

     The illumination apparatus according to any one of [A01] to [A10], in which, 
     when an X axis refers to an axis passing through a center of the recessed and protruding structure unit and through a rotation axis and located in a surface of the recessed and protruding structure unit provided with the recessed and protruding portion, a Z axis refers to an axis passing through the center of the recessed and protruding structure unit and that is parallel to the rotation axis, and a Y axis refers to an axis that is orthogonal to the X axis and the Z axis and that is located in a surface of the recessed and protruding structure unit provided with the recessed and protruding portion, 
     an average value F X-ave  of a spatial frequency of the recessed and protruding portion along the X axis is 1×10 3  mm −1  or less, and 
     an average value F Y-ave  of the spatial frequency of the recessed and protruding portion along the Y axis is 1×10 3  mm −1  or less.
     [A12]   

     The illumination apparatus according to [A11], in which 
     the average value F X-ave  of the spatial frequency of the recessed and protruding portion along the X axis is 1×10 2  mm −1  or less, and 
     the average value F Y-ave  of the spatial frequency of the recessed and protruding portion along the Y axis is 1×10 2  mm −1  or less.
     [A13]   

     The illumination apparatus according to [A11] or [A12], in which, 
     when F X′-ave  denotes the average value of the spatial frequency of the recessed and protruding portion along a straight line satisfying Y=X and F Y′-ave  denotes the average value of the spatial frequency of the recessed and protruding portion along a straight line satisfying Y=−X, 
     F X′-ave &gt;F X-ave , 
     F X′-ave &gt;F Y-ave , 
     F Y′-ave &gt;F X-ave , and 
     F Y′-ave &gt;F Y-ave  are satisfied.
     [A14]   

     The illumination apparatus according to any one of [A11] to [A13], in which, 
     when L X-0  denotes a length along the X axis of the recessed and protruding structure unit on which light from the light source is incident and L Y-0  denotes a length, along the Y axis, of the recessed and protruding structure unit on which light from the light source is incident, 
     L X-0 ×F X-ave ≥10, and 
     L Y-0 ×F Y-ave ≥10 are satisfied.
     [A15]   

     The illumination apparatus according to [A14], in which 
     L X-0 ×F X-ave ≥15, and 
     L Y-0 ×F Y-ave ≥15 are satisfied.
     [A16]   

     The illumination apparatus according to any one of [A11] to [A15], in which 
     F X-ave ≈F Y-ave  is obtained.
     [A17]   

     The illumination apparatus according to any one of [A01] to [A16], in which 
     the recessed and protruding structure unit has a kurtosis β of −0.5 or less.
     [A18]   

     The illumination apparatus according to any one of [A01] to [A17], in which 
     light from the light source is incident on each recessed and protruding structure unit in a rotating state from a first surface of each recessed and protruding structure unit and is emitted from a second surface of each recessed and protruding structure unit toward the integrator, 
     the first surface of each recessed and protruding structure unit is provided with the recessed and protruding portion, and 
     the second surface of each recessed and protruding structure unit is flat.
     [A19]   

     The illumination apparatus according to any one of [A01] to [A17], in which 
     light from the light source is incident on each recessed and protruding structure unit in a rotating state from a first surface of each recessed and protruding structure unit and is emitted from the first surface of each recessed and protruding structure unit toward the integrator, and 
     the first surface of each recessed and protruding structure unit is provided with the recessed and protruding portion, and 
     the second surface of each recessed and protruding structure unit is flat and constitutes a light reflection surface.
     [A20]   

     The illumination apparatus according to [A19], further including: 
     a polarization beam splitter; and 
     a quarter wavelength plate, in which 
     light from the light source enters the polarization beam splitter, exits the polarization beam splitter along a first direction, passes through the quarter wavelength plate, is reflected at the recessed and protruding structure unit, passes through the quarter wavelength plate, enters the polarization beam splitter, exits the polarization beam splitter along a second direction different from the first direction, and enters the integrator.
     [A21]   

     The illumination apparatus according to any one of [A01] to [A20], in which, 
     when an XZ virtual plane in the recessed and protruding structure unit is a mirror plane, two areas of the recessed and protruding structure unit located across the XZ virtual surface are in a mirror symmetry relation, and the recessed and protruding portions in the two areas are smoothly connected together.
     [A22]   

     The illumination apparatus according to any one of [A01] to [A21], in which 
     the recessed and protruding portion is designed such that the external shape of light emitted from the recessed and protruding structure unit in the non-rotating state is like an isosceles trapezoid including a bottom side (rotation axis side) longer than a top side, the top side and the bottom side extending parallel to the Y axis.
     [A23]   

     The illumination apparatus according to [A22], in which a relation between the value A 1  of (length of the bottom side)/(length of the top side) and the value A 2  of (outer diameter)/(inner diameter) of a fan-surface-like recessed and protruding structure unit satisfies: 
       0.85≤A 1 /A 2 ≤1.15.
     [A24]   

     The illumination apparatus according to [A23], in which 
     A 1 /A 2 =1.0 is satisfied.
     [A25]   

     The illumination apparatus according to any one of [A01] to [A24], in which, 
     when an XZ virtual plane in the recessed and protruding structure unit is a mirror plane, two areas of the recessed and protruding structure unit located across the XZ virtual surface are in a mirror symmetry relation, and the recessed and protruding portions in the two areas are smoothly connected together.
     [A26]   

     The illumination apparatus according to any one of [A01] to [A25], in which, 
     when the recessed and protruding portion is expressed as Z=f(X, Y), inclinations of the recessed and protruding portion in the X axis direction and the Y axis direction are obtained by: 
       ∂Z/∂X=[∂f(X, Y)/∂X] Y  
 
       ∂Z/∂Y=[∂f(X, Y)/∂Y] X , and
 
     ∂Z/∂Y and ∂Z/∂Y are not point-asymmetric when an intersection between the X axis and the Y axis is a point of symmetry.
     [B01]   

     «Projective Display Apparatus» 
     A projective display apparatus including: 
     an illumination apparatus including a light source, an optical member on and from which light from the light source is incident and is emitted, and an integrator on which light from the optical member is incident; 
     an optical modulation apparatus configured to modulate light emitted from the illumination apparatus on a basis of image information to generate an image; and 
     a projective optical system configured to receive an image projected from the optical modulation apparatus, in which 
     the illumination apparatus includes the illumination apparatus according to any one of [A01] to [A26].
     [C01]   

     «Optical Element» 
     An optical element including: 
     a first surface; and 
     a second surface facing the first surface, in which 
     light from a light source emitting light with multiple wavelengths is incident on the first surface, 
     the first surface or the second surface is provided with a recessed and protruding portion configured to refract incident light from the light source, 
     an area occupied by the recessed and protruding portion is larger in size than incident light from the light source, 
     recessed portions and protruding portions of the recessed and protruding portion are smoothly connected together, and, 
     when a shape of light obtained by cutting the light along a virtual plane orthogonal to a traveling direction of the light is referred to as a cross-sectional shape of the light, the cross-sectional shape of light emitted from the optical element is like a rectangle, a polygon or a shape with one or more angles.
     [C02]   

     The optical element according to [C01], in which 
     the cross-sectional shape of light incident on the optical element from the light source is like a circle or an ellipse. 
     REFERENCE SIGNS LIST 
       10 : Light source 
       10 R,  10 G,  10 B: Semiconductor laser element 
       11 R,  11 G,  11 B: Lens 
       12 : Dichroic prism 
       13 : Lens system 
       20 : Optical member 
       20 A: First surface of optical member (recessed and protruding structure unit) 
       20 B: Second surface of optical member (recessed and protruding structure unit) 
       21 : Recessed and protruding structure unit 
       22 : Substrate 
       23 : Driving motor 
       24 : Condenser lens 
       25 : Polarization beam splitter 
       26 : Quarter wavelength plate 
       27 : Condenser lens 
       30 : Integrator 
       110 : Illumination apparatus 
       130 : Optical modulation apparatus (image forming unit) 
       140 : Projective optical system 
     AR: Rotation axis 
     BL: Boundary between recessed and protruding structure units