JP5612972B2 - Projection optical device - Google Patents

Description

  The present invention relates to an optical system including a projection optical system, and particularly to a projection optical apparatus capable of projecting a high-resolution image without image distortion on a curved projection surface (screen). It is.

  Regarding a projection optical system that projects a real image onto a cylindrical screen using a projection optical system, Patent Document 1 discloses a small-sized flare light in an optical system that projects an image having an angle of view of 360 ° in all directions. It is disclosed to provide an optical system having a small resolution and good resolution.

JP 2007-334019 A

  According to the optical system described in Patent Document 1, by projecting an image around the entire periphery, the observer can observe the image spreading in a panoramic shape around the entire periphery, thereby immersing the observer in the image. Become. However, in order to project such a 360 ° image, it is necessary to provide a certain amount of space around the optical system.

  Therefore, with the optical system described in Patent Document 1, it is difficult to enjoy an immersive image in a limited space such as in an airplane. Here, in the situation where the observer is seated on a chair, sofa, etc., it is not necessary to project an image up to 360 °, and it is understood that an immersive feeling can be obtained even with a projected image close to 180 °. Yes. This is because the viewpoint range of the observer is limited by sitting.

  The present invention projects a high-resolution projection image with reduced distortion and almost in focus on the entire surface in an optical system that projects a wide-angle image onto such a curved projection surface (curved screen). It is an object of the present invention to provide a projection optical apparatus characterized by being capable of doing so.

The projection optical apparatus according to the present invention is a projection optical system that projects an image displayed on a two-dimensional image display element, and is decentered with respect to the projection optical system, and the image projected by the projection optical system is projected. A projection optical apparatus comprising: a correction optical system including a reflection surface including a curved surface that reflects an image projected from the projection optical system and projects the image onto the screen. The plane containing the central principal ray of the light beam traveling from the screen to the screen is perpendicular to the YZ section, the projection center at which the central principal ray intersects the screen, and the normal of the screen at the projection center. The screen has an XZ cross section, the screen has a concave surface facing the correction optical system side in the XZ cross section, and the reflection surface is on the screen side in a plane parallel to the XZ cross section. A convex surface, and satisfies the following conditional expression (4).
αsr <20 ° (4)
However,
αsr is an angle formed by a perpendicular of the reflecting surface at a position where the central principal ray hits the reflecting surface and a perpendicular of the screen at a position where the central principal ray hits the screen
It is.

  The reflecting surface is formed by bending a plane mirror.

  The reflecting surface is formed by a back mirror.

  Further, the reflecting surface is characterized in that a power in a plane parallel to the YZ section differs from a power in a plane parallel to the XZ section.

  Further, the reflecting surface is formed so as to be a straight curve in the YZ section and a convex curve on one side in a plane parallel to the XZ section.

  The reflection surface may be a straight line in the YZ section and a parabola in the XZ section.

  The reflection surface may be a suspension curve in a plane parallel to the XZ cross section.

  Further, the reflecting surface is formed by curving a trapezoidal plane mirror so that the curvature in a plane parallel to the XZ section becomes stronger as it goes to the projection optical system side in the direction along the Y axis. Features.

  Further, the distance between both ends when the reflecting surface is curved and fixed so that the curvature in the plane parallel to the XZ cross section becomes stronger as it goes to the projection optical system side in the direction along the Y axis. A plane mirror is curved and formed so as to be shorter on the projection optical system side.

  The reflective surface includes a flat surface portion and a spherical convex reflective surface portion manufactured by vacuum forming.

  Further, the reflection surface has a flat surface portion and a convex reflection surface portion of a toric surface manufactured by vacuum forming.

  Further, the reflection surface is characterized in that the convex reflection surface portion is formed in an ellipse.

  Further, the reflection surface is formed to be curved so that the curvature increases in a plane parallel to the XZ section as it goes to the projection optical system side in the direction along the Y axis.

  The screen may be a spherical surface.

  The correction optical system further includes an optical element that is rotationally asymmetric with respect to the optical axis.

Moreover, the following conditional expression (2) is satisfied.
0 <α <70 ° (2)
Where α is an angle formed by the central principal ray of the projected light beam and the normal of the screen.

Further, the following conditional expression (7) is satisfied.
αs> 30 ° (7)
However,
αs is the angle of the arc of the screen in the XZ section,
It is.

Moreover, the following conditional expression (6) is satisfied.
40 <R1 <800 (6)
However,
R1 is the radius of curvature of the reflecting surface in the XZ section.

Moreover, the following conditional expression (5) is satisfied.
100 <Rs (5)
However,
Rs is the radius of curvature in the XZ section of a cylindrical or spherical screen,
It is.

Moreover, the following conditional expression (1) is satisfied.
−5 <z / R1 <5 (1)
However,
R1 is a radius of curvature of the reflecting surface in a plane parallel to the XZ cross section,
z is the distance from the center of the screen to the reflecting surface in the XZ cross section,
It is.

Moreover, the following conditional expression (3) is satisfied.
L2 / L1 <5.0 (3)
However,
L1 is the optical path length of the central principal ray from the reflecting surface to the rotationally asymmetric optical element,
L2 is the optical path length of the central principal ray from the stop of the projection optical system to the rotationally asymmetric optical element,
It is.

The reflection surface is formed by a curved surface satisfying the following equation (9) when approximated by the following equation (8) in a plane parallel to the XZ cross section.
^{Z = cX 2 / [1+ {} 1- (1 + k) c 2 X 2} 1/2] (8)
−1 <k <0 (9)
Where Z is the Z coordinate,
X is the X coordinate,
c is the curvature at the top,
k is an aspheric coefficient.

  As described above, according to the present invention, there is provided a projection optical apparatus capable of projecting a high-resolution image with no distortion on a curved projection surface (curved screen) with a simple configuration. It becomes possible to do.

It is a figure explaining the coordinate system and YZ section of an embodiment concerning the present invention. It is a figure explaining the coordinate system and XZ section of an embodiment concerning the present invention. It is the figure which showed the cross section in the YZ cross section about the optical system of Example 1, and its periphery structure. It is a top view in a XZ section about an optical system of Example 1, and its peripheral composition. 2 is a transverse aberration diagram for the whole optical system of Example 1. FIG. 2 is a transverse aberration diagram for the whole optical system of Example 1. FIG. FIG. 3 is a diagram illustrating image distortion of the entire optical system of Example 1. It is the figure which showed the cross section in the YZ cross section about the optical system of Example 2, and its periphery structure. It is a top view in a XZ section about an optical system of Example 2, and its peripheral composition. 6 is a lateral aberration diagram for the whole optical system of Example 2. FIG. 6 is a lateral aberration diagram for the whole optical system of Example 2. FIG. 6 is a diagram illustrating image distortion of the entire optical system according to Example 2. FIG. It is the figure which showed the cross section in the YZ cross section about the optical system of Example 3, and its periphery structure. It is a top view in the XZ section about the optical system of Example 3, and its periphery structure. FIG. 6 is a transverse aberration diagram for the whole optical system of Example 3. FIG. 6 is a transverse aberration diagram for the whole optical system of Example 3. 6 is a diagram illustrating image distortion of the entire optical system according to Example 3. FIG. It is the figure which showed the cross section in the YZ cross section about the optical system of Example 4, and its periphery structure. It is a top view in the XZ section about the optical system of Example 4, and its periphery structure. FIG. 6 is a transverse aberration diagram for the whole optical system of Example 4. FIG. 6 is a transverse aberration diagram for the whole optical system of Example 4. 10 is a diagram illustrating image distortion of the entire optical system according to Example 4. FIG. It is the figure which showed the cross section in the YZ cross section about the optical system of Example 5, and its periphery structure. It is a top view in an XZ section about an optical system of Example 5, and its peripheral composition. FIG. 6 is a lateral aberration diagram for the whole optical system of Example 5. FIG. 6 is a lateral aberration diagram for the whole optical system of Example 5. 10 is a diagram illustrating image distortion of the entire optical system of Example 5. FIG. It is the figure which showed the mode of observation by the cross section in a YZ cross section, and the observer about the optical system which concerns on embodiment of this invention, and its periphery structure. It is a figure which shows the curve before Example 1 of a reflective surface. It is a figure which shows Example 1 of a reflective surface. It is a figure which shows the curve before Example 2 of a reflective surface. It is a figure which shows Example 2 of a reflective surface. It is a figure which shows Example 3 of a reflective surface. It is a figure which shows Example 5 of a reflective surface. It is a figure which shows Example 6 of a reflective surface. It is a figure which shows Example 7 of a reflective surface.

  The projection optical apparatus of the present invention will be described below based on examples.

  First, a coordinate system according to an embodiment of the present invention will be described. FIG. 1 is a diagram illustrating a coordinate system and a YZ section according to an embodiment of the present invention, and FIG. 2 is a diagram illustrating a coordinate system and an XZ section according to an embodiment of the present invention.

  As shown in FIGS. 1 and 2, the projection optical apparatus using the optical system according to the present embodiment includes a projection optical system 13, a correction optical system 12, and a screen 11. The image projected from the projection optical system 13 is reflected by the correction optical system 12 such as a curved mirror and projected onto the screen 11.

  In the coordinate system of the optical system of this embodiment, the center principal ray C emitted from the projection optical system 13 passes through the correction optical system 12 and intersects the screen 11 as the projection center SO, and the rotation center of the screen 11 from the projection center SO. When the perpendicular line A1 to the axis 11a is drawn, the intersection point of the rotation center axis 11a and the perpendicular line A1 is set as the origin O. When the screen 11 is a spherical surface or the like, the center of the screen 11 is set as the origin O.

  Further, as shown in FIG. 1, a plane including the rotation center axis 11 a and the central principal ray C of the screen 11 is a YZ cross section 101. Further, as shown in FIG. 2, a plane including the projection center SO perpendicular to the YZ section 101 and the central principal ray C intersecting the screen 11 and the perpendicular line A1 of the screen 11 at the projection center SO is defined as an XZ section 102. To do.

  Next, based on Example 1, the projection optical apparatus of this embodiment will be described. FIG. 3 is a diagram showing a cross section of the optical system of Example 1 and its peripheral configuration in the YZ section, and FIG. 4 is a plan view of the optical system of Example 1 and its peripheral structure in the XZ section. .

  The projection optical apparatus according to the present embodiment projects the image displayed on the two-dimensional image display element, the projection optical system 13 and the projection optical system 13, and the image projected by the projection optical system 13 is projected. A correction optical system 12 including a reflection surface 12 formed of a curved surface that reflects the image projected from the projection optical system 13 and projects it onto the screen 11. A plane including the central principal ray C of the light beam traveling from the projection optical system 13 toward the screen 11 is perpendicular to the YZ cross section 101, the YZ cross section 101, and the projection center SO and the projection center SO at which the central principal ray C intersects the screen 11. The plane including the perpendicular line A1 of the screen 11 is defined as an XZ cross section 102, and the screen 11 is reflected in the XZ cross section 102 with the concave surface facing the rotation center O side of the screen 11. 12, it is preferable that a convex surface facing the screen 11 side in a plane parallel with the XZ cross-section 102.

  For example, as shown in FIGS. 1 and 2, the case where the screen 11 is a cylindrical screen 11 and a cylindrical reflecting surface 12 having a rotation center axis 11 a that is vertical to the observer will be described.

  In general, when an image is projected onto the cylindrical reflecting surface 12 from an obliquely upward direction, the image is reflected by the convex surface of the cylinder and the projection angle of view widens, but the line segment that hits the horizontal direction of the image seems to cut the cylinder obliquely. Therefore, the horizontal line segment of the image is projected in a bow shape so as to have a convex shape upward on the cylindrical reflecting surface 12, and becomes an arc-shaped reflected light having a convex shape upward. .

  On the other hand, since the horizontal line segment projected obliquely on the cylindrical screen 11 from the upper side first hits the screen from both ends of the horizontal line, it is bent and projected in a bow shape so as to have a convex shape downward.

  The present invention has succeeded in eliminating the distortion of the horizon by making these two states appropriate. 1 and 2, the case where the screen 11 and the reflecting surface 12 are cylindrical has been described. However, the screen 11 and the reflecting mirror 12 may be spherical, toric, anamorphic, free curved, rotationally symmetric free curved, Needless to say, it is possible to correct the image distortion generated in a bow shape, which is the gist of the present invention.

  Further, the reflecting surface 12a is different in power in a plane parallel to the YZ section 101 and in a plane parallel to the XZ section 102, and the correction optical system 12 further includes an optical element 12b that is rotationally asymmetric with respect to the optical axis. Is preferred.

  Astigmatism generated on the reflecting surface 12 can be corrected by the rotationally asymmetric optical element 12b. A cylindrical lens is preferably disposed as the rotationally asymmetric optical element 12b. It is also possible to correct with a second reflecting mirror composed of an anamorphic surface, a free-form surface, a rotationally symmetric free-form surface, or the like. Furthermore, it goes without saying that the rotationally asymmetric optical element 12b is not necessary when the reflecting surface 12a is spherical or when astigmatism is small.

  The correction optical system is preferably a reflecting surface that is a parabola in the XZ section and a straight line in the YZ section.

  By making it a parabola, there is a feature that the inclination does not become larger than the spherical surface as it goes from the YZ section in the positive and negative directions of the X axis. Therefore, it is possible to reduce image distortion in which a portion having a large angle of view in the X-axis direction (lateral direction) is trapezoidally distorted as compared to a spherical surface or a cylindrical surface.

  The reflecting surface of the correction optical system is preferably a plastic back mirror.

  Since there are off-the-shelf plastic flat mirrors, it can be manufactured at low cost. In addition, the cross-sectional shape of a back mirror made of a curved surface obtained by bending a flat back mirror is closer to a parabola than a circle, and the effect of reducing the image distortion can be expected.

Moreover, it is preferable that the following conditional expression (1) is satisfied.
−5 <z / R1 <5 (1)
However,
R1 is the radius of curvature of the reflecting surface in a plane parallel to the XZ cross section,
z is the distance from the center of the screen to the reflecting surface in the XZ section,
It is.
Here, R1 also includes an effective radius of curvature of the reflecting surface that can be calculated from a sphere in the XZ cross section near the intersection where the central principal ray C hits the reflecting surface.

  Conditional expression (1) relates to image distortion that occurs in a bow-like manner. If the lower limit of conditional expression (1) is not reached, the occurrence of upward convex image distortion that occurs on the reflecting surface 12a is small, and the screen 11 It is impossible to correct the downwardly generated image distortion. If the upper limit of conditional expression (1) is exceeded, excessively convex image distortion will occur excessively on the reflective surface 12a with the convex surface facing the screen 11 side.

Further, it is more preferable that the following conditional expression (1 ′) is satisfied.
0 <z / R1 <5 (1 ′)

Moreover, it is preferable that the following conditional expression (2) is satisfied.
0 <α <70 ° (2)
Where α is an angle formed by the central principal ray of the projected light beam and the perpendicular of the screen.

  Conditional expression (2) relates to the angle of oblique projection of the projection optical system 13. If the lower limit of the conditional expression (2) is not reached, the projection optical system 13 and the reflecting surface 12 a become obstructive and from the front of the screen 11. The observer will not be able to observe. If the upper limit of conditional expression (2) is exceeded, the occurrence of decentration aberrations increases, which places a burden on the design of the projection optical system 13 and makes it impossible to obtain a wide projection area.

Further, it is more preferable that the following conditional expression (2 ′) is satisfied.
5 ° <α <60 ° (2 ')

Moreover, it is preferable that the following conditional expression (3) is satisfied.
L2 / L1 <5.0 (3)
However,
L1 is the optical path length of the central principal ray from the reflecting surface to the rotationally asymmetric optical element,
L2 is the optical path length of the central principal ray from the stop of the projection optical system to the rotationally asymmetric optical element,
It is.

  If the upper limit of conditional expression (3) is exceeded, the rotationally asymmetric optical element 12b will be too close to the reflecting surface 12a, making it difficult to correct astigmatism well.

Further, it is more preferable that the following conditional expression (3 ′) is satisfied.
L2 / L1 <0.5 (3 ′)

Further, it is more preferable that the following conditional expression (3 ″) is satisfied.
L2 / L1 <0.1 (3 ″)

Moreover, it is preferable that the following conditional expression (4) is satisfied.
αsr <20 ° (4)
However,
αsr is an angle formed by a perpendicular of the reflecting surface at a position where the central principal ray hits the reflecting surface and a perpendicular of the screen at a position where the central principal ray hits the screen.

  Conditional expression (4) is a condition that cancels the upward convex image distortion generated by the convex reflecting surface and the concave screen along the traveling direction of the central principal ray in the cross section parallel to the XZ cross section. is there. If the upper limit of the conditional expression (4) is exceeded, an upward or downward convex bow-like image distortion may remain, and the observed image may become uncomfortable.

Further, it is more preferable that the following conditional expression (4 ′) is satisfied.
αsr <10 ° (4 ')

Moreover, it is preferable that the following conditional expression (5) is satisfied.
100 <Rs (5)
However,
Rs is the radius of curvature in the XZ section of a cylindrical or spherical screen,
It is.

  If the lower limit of conditional expression (5) is not reached, the screen becomes small and observation by an observer becomes difficult.

Further, it is more preferable that the following conditional expression (5 ′) is satisfied.
500 <Rs (5 ′)

Further, it is more preferable that the following conditional expression (5 ″) is satisfied.
1000 <Rs (5 '')

Moreover, it is preferable that the following conditional expression (6) is satisfied.
40 <R1 <800 (6)
However,
R1 is the radius of curvature of the correction optical system in the XZ section.

  If the lower limit of conditional expression (6) is not reached, the relative size of the projection optical system with respect to the size of the reflecting surface increases, and the occurrence of decentration aberrations increases. And it becomes impossible to correct on other surfaces, and it becomes difficult to observe a clear observation image. If the upper limit of conditional expression (6) is exceeded, the size of the reflecting surface becomes too large, making it difficult to secure a free observation region, and it is difficult for the observer to observe the observation image in a comfortable posture. It becomes.

Further, it is more preferable that the following conditional expression (6 ′) is satisfied.
50 <R1 <800 (6 ′)

It is more preferable that the following conditional expression (6 ″) is satisfied.
200 <R1 <500 (6 ″)

Moreover, it is preferable that the following conditional expression (7) is satisfied.
αs> 30 ° (7)
However,
αs is the angle of the arc of the screen in the XZ section,
It is.

  When the conditional expression (7) is satisfied, a high sense of realism can be obtained.

Further, it is more preferable that the following conditional expression (7 ′) is satisfied.
αs> 60 ° (7 ')

Further, it is more preferable that the following conditional expression (7 ″) is satisfied.
αs> 90 ° (7 ″)

  In addition, the reflection surface has a cross section parallel to the XZ cross section, and the curvature radius of the convex surface decreases from the position where the central principal ray hits the reflection surface to the projection optical system side, and the opposite side of the projection optical system. It is preferable that the radius of curvature increases as it goes to.

  Since the light beam in the XZ sectional direction on the projection optical system side hits the reflecting surface in a state where it does not spread sufficiently with respect to the position where the central principal ray hits the reflecting surface, the length in the XZ sectional direction is projected short. On the other hand, on the side opposite to the projection optical system with respect to the position where the central principal ray hits the reflecting surface, the light beam hits the reflecting surface after sufficiently spreading in the XZ sectional direction, so the length in the XZ sectional direction is also projected long. A trapezoidal image distortion with a short upper side occurs.

  The shape of the reflecting surface is a section parallel to the XZ section, and the curvature radius of the convex surface is decreased from the position where the central principal ray hits the reflecting surface to the projection optical system side, and the curvature is increased toward the opposite side of the projection optical system. By increasing the radius, it is possible to correct such trapezoidal image distortion in which the image sizes in the direction parallel to the upper and lower XZ sections of the projected image are different.

  In addition, the reflection surface is a cross section parallel to the YZ cross section, and the curvature radius of the convex surface decreases from the position where the central principal ray hits the reflection surface to the projection optical system side, and the opposite side of the projection optical system. It is preferable that the radius of curvature increases as it goes to.

  In a section parallel to the YZ section, the size of the image in the Y direction on the projection optical system side is shortened, and image distortion occurs on the opposite side to the projection optical system.

  The shape of the reflecting surface is a section parallel to the YZ section, and the curvature radius of the convex surface is reduced as it goes from the position where the central principal ray hits the reflecting surface to the projection optical system side, and the curvature as it goes to the opposite side of the projection optical system. By increasing the radius, it is possible to correct such image distortion in which the image sizes in the direction parallel to the upper and lower YZ sections of the projected image are different.

  The screen is preferably made of a spherical surface.

  Design becomes easy and the manufacturing cost can be reduced.

  Moreover, it is preferable that the reflecting surface is a spherical surface.

  Design becomes easy and the manufacturing cost can be reduced.

  Hereinafter, examples of the optical system of the projection optical apparatus 1 will be described. The configuration parameters of these optical systems will be described later. The configuration parameters of these examples and the like are tracked by back ray tracing from the screen 11 toward the image display element 13b.

  As shown in FIG. 1 and FIG. 2, the coordinate system is a projection center SO where the central principal ray C emitted from the projection optical system 13 intersects the screen 11 via the correction optical system 12, and the screen from the projection center SO to the screen. When the perpendicular line A1 to the rotation center axis 11a of 11 is drawn, the intersection of the rotation center axis 11a and the perpendicular line A1 is set as the origin O of the decentered optical system. In addition, the direction from the origin O toward the rotation optical axis 11a toward the projection optical system 13 is defined as the Y-axis positive direction, and the direction toward the opposite side of the projection center SO is defined as the Z-axis positive direction. The axes constituting the Y-axis and Z-axis and the right-handed orthogonal coordinate system are defined as the X-axis positive direction.

  Further, as shown in FIG. 1, a plane including the rotation center axis 11 a and the central principal ray C of the screen 11 is a YZ cross section 101. Further, as shown in FIG. 2, a plane orthogonal to the rotation center axis 11 a of the screen 11 and including the projection center SO is defined as an XZ cross section 102. Further, XYZ coordinates are defined by the YZ cross section 101 and the ZX plane 102.

  For the decentered surface, the amount of decentering from the center of the origin of the optical system in the coordinate system in which the surface is defined (X-axis direction, Y-axis direction, and Z-axis direction are X, Y, and Z, respectively) and the optical system The inclination angles (α, β, γ (°), respectively) of the coordinate system defining each surface centered on the X axis, Y axis, and Z axis of the coordinate system defined at the origin are given. In this case, positive α and β mean counterclockwise rotation with respect to the positive direction of each axis, and positive γ means clockwise rotation with respect to the positive direction of the Z axis. Note that the α, β, and γ rotations of the central axis of the surface are performed by rotating the coordinate system defining each surface counterclockwise around the X axis of the coordinate system defined at the origin of the optical system. Then rotate it around the Y axis of the new rotated coordinate system by β and then rotate it around the Z axis of another rotated new coordinate system by γ. It is.

  Further, among the optical action surfaces constituting the optical system of each embodiment, when a specific surface and a subsequent surface constitute a coaxial optical system, a surface interval is given, in addition, the curvature radius of the surface, The refractive index and Abbe number of the medium are given according to conventional methods. The coefficient term for which no data is described is zero. The refractive index and Abbe number are for d-line (wavelength 587.56 nm). In addition, the unit of length not particularly described is mm.

  Moreover, the shape of the surface of the free-form surface used in the embodiment according to the present invention is defined by the following formula (a). Note that the Z axis of the defining formula is the axis of the free-form surface.

Z = (r ² / R) / [1 + √ {1- (1 + k) (r / R) ² }]
∞
+ Σ C _j X ^m Y ⁿ (a)
^{j = 1}
Here, the first term of the equation (a) is a spherical term, and the second term is a free-form surface term.

In the spherical term,
R: radius of curvature of apex k: conic constant (conical constant)
r = √ (X ² + Y ² )
It is.

The free-form surface term is
₆₆
ΣC _j X ^m Y ^{n
j = 1}
= C ₁
+ C ₂ X + C ₃ Y
+ C ₄ X ² + C ₅ XY + C ₆ Y ²
+ C ₇ X ³ + C ₈ X ² Y + C ₉ XY ² + C ₁₀ Y ³
+ C ₁₁ X ⁴ + C ₁₂ X ³ Y + C ₁₃ X ² Y ² + C ₁₄ XY ³ + C ₁₅ Y ⁴
+ C ₁₆ X ⁵ + C ₁₇ X ⁴ Y + C ₁₈ X ³ Y ² + C ₁₉ X ² Y ³ + C ₂₀ XY ⁴
+ C ₂₁ Y ⁵
+ C ₂₂ X ⁶ + C ₂₃ X ⁵ Y + C ₂₄ X ⁴ Y ² + C ₂₅ X ³ Y ³ + C ₂₆ X ² Y ⁴
+ C ₂₇ XY ⁵ + C ₂₈ Y ⁶
+ C ₂₉ X ⁷ + C ₃₀ X ⁶ Y + C ₃₁ X ⁵ Y ² + C ₃₂ X ⁴ Y ³ + C ₃₃ X ³ Y ⁴
+ C ₃₄ X ² Y ⁵ + C ₃₅ XY ⁶ + C ₃₆ Y ⁷
・ ・ ・ ・ ・ ・
However, C _j (j is an integer of 1 or more) is a coefficient.

In general, the free-form surface does not have a symmetric surface in both the XZ cross section and the YZ cross section, but in the present invention, by setting all odd-order terms of X to 0, there is one symmetric surface parallel to the YZ cross section. It becomes only a free-form surface. For example, in the above defining equation _{(a), C 2, C} 5, C 7, C 9, C 12, C 14, C 16, C 18, C 20, C 23, C 25, C 27, C 29, This is possible by setting the coefficient of each term of C ₃₁ , C ₃₃ , C ₃₅ .

Further, by setting all odd-numbered terms of Y to 0, a free-form surface having only one symmetry plane parallel to the XZ section is obtained. For example, in the above definition formula, C ₃ , C ₅ , C ₈ , C ₁₀ , C ₁₂ , C ₁₄ , C ₁₇ , C ₁₉ , C ₂₁ , C ₂₃ , C ₂₅ , C ₂₇ , C ₃₀ , C ₃₂ , This is possible by setting the coefficient of each term of C ₃₄ , C ₃₆ .

  Further, any one of the directions of the symmetry plane is a symmetry plane, and the eccentricity in the corresponding direction, for example, the eccentric direction of the optical system is parallel to the Y-axis direction and parallel to the XZ section with respect to the symmetry plane parallel to the YZ section By making the decentering direction of the optical system in the X axis direction with respect to such a symmetrical plane, it becomes possible to improve the manufacturability at the same time while effectively correcting the rotationally asymmetric aberration caused by the decentering.

  The definition formula (a) is shown as an example as described above, and the free curved surface of the present invention is generated by eccentricity by using a rotationally asymmetric surface having only one symmetric surface. It is characterized by correcting rotationally asymmetric aberrations and improving the manufacturability at the same time, and it goes without saying that the same effect can be obtained for any other defining formula.

  Example 1 will be described. FIG. 3 is a diagram showing a cross section of the optical system of Example 1 and its peripheral configuration in the YZ section, and FIG. 4 is a plan view of the optical system of Example 1 and its peripheral structure in the XZ section. . 5 and 6 are lateral aberration diagrams of the entire optical system, and FIG. 7 is a diagram showing image distortion.

  The projection optical apparatus according to the first embodiment projects the image displayed on the two-dimensional image display element, the projection optical system 13 and the projection optical system 13, and the image projected by the projection optical system 13 is projected. A correction optical system 12 including a reflection surface 12 formed of a curved surface that reflects the image projected from the projection optical system 13 and projects it onto the screen 11. The plane including the central principal ray C of the light beam traveling from the projection optical system 13 toward the screen 11 is perpendicular to the YZ cross section, the YZ cross section, and the screen at the projection center SO and the projection center SO where the central principal ray C intersects the screen 11. The plane including the perpendicular line A1 of 11 is the XZ cross section, the screen 11 has a concave surface facing the origin O side of the screen 11 in the XZ cross section 102, and the reflective surface 12 is parallel to the XZ cross section. And a convex surface facing the screen 11 side in the plane.

  Further, the reflecting surface 12a is different in power in a plane parallel to the YZ section and in a plane parallel to the XZ section, and the correction optical system 12 further includes an optical element 12b that is rotationally asymmetric with respect to the optical axis.

  The screen 11 is a reflecting surface having a curvature in the XZ section with the rotation center axis 11a as the center. The mirror 12a is a reflecting surface having a curvature in the XZ cross section, which is different from the screen 11 in the length of the radius of curvature and the center position.

  A line A1 connecting the projection center SO of the screen 11 and the coordinate origin O is decentered in the Y-axis direction with respect to the central axis A2 of the ideal lens 13a and the central axis A3 of the image display element 13b in the projection optical system 13. ing. Further, assuming that the point where the central principal ray C is reflected by the mirror 12a is the reflection center RO, the position of the reflection center RO in the Y-axis direction is arranged between the line A1, the central axis A2, and the central axis A3. As a result, the projected image projected obliquely from the projection optical system 13 onto the mirror 12a is reflected by the mirror 12a and projected onto the screen 11 to become a projected image that is observed by the observer.

  3 and 4 also show enlarged views of a portion surrounded by a broken line. The projection optical system 13 includes an image display element 13b for displaying an image, such as an LCD, and an ideal lens 13a. A diaphragm is provided on the cylindrical surface r4 of the cylindrical lens 12b.

  As shown in FIG. 3, the central axis A2 of the ideal lens 13a of the projection optical system 13 of Example 1 is arranged eccentrically with respect to the central axis A3 of the video display element 13b. Therefore, the image irradiated from the image display element 13b is projected using the periphery of the ideal lens 13a, and is projected obliquely to the eccentrically arranged mirror 12a, just like using the shift lens.

  As described above, it is preferable that the image display element 13b is shifted in eccentricity and oblique projection is performed, since no distortion is generated. Note that when the projection optical system 13 is tilted and tilted, trapezoidal image distortion occurs. Such image distortion can be corrected electronically.

  In the embodiment, the mirror 12a (reflective surface) is used as means for enlarging the projection angle of view in the X-axis direction. However, the use of the mirror 12a causes astigmatism and degrades the image formed on the screen 11. Therefore, this astigmatism is corrected using an optical element composed of the cylindrical lens 12b.

  In the reverse ray tracing, the light beam emitted from the screen 11 (r1) as the object surface is reflected by the mirror 12a (r3) of the correction optical system 12 and enters the cylindrical surface (r4) of the cylindrical lens 12b provided with a stop. Thereafter, the light beam that has passed through the cylindrical lens 12b and has exited from the opposite surface (r5) enters the ideal lens 13a (r6) of the projection optical system 13. The light beam emitted from the ideal lens 13a (r6) reaches a predetermined position of the video display element 13b (r7). Note that the coordinate origin O is r2.

  The screen 11 according to the first embodiment is on the inside of a cylindrical surface having a radius of 1 m and having the origin O at the center position. The ideal lens 13 has a focal length of 23 mm and an exit pupil diameter of 15 mm.

  FIG. 7 is a diagram illustrating image distortion in the first embodiment. The outer approximate quadrilateral represents the distortion on the image plane with the maximum image height, and the inner approximate quadrilateral represents the distortion on the image plane with the maximum image height × 0.7. It can be seen that the upper and lower sides of the substantially quadrilateral are nearly horizontal, and the image distortion that forms a bow is corrected.

  Example 2 will be described. FIG. 8 is a diagram showing a cross section of the optical system of Example 2 and its peripheral configuration in the YZ section, and FIG. 9 is a plan view of the optical system of Example 2 and its peripheral structure in the XZ section. . 10 and 11 are lateral aberration diagrams of the entire optical system, and FIG. 12 is a diagram showing image distortion.

  The projection optical apparatus according to the second embodiment has a projection optical system 13 that projects an image displayed on a two-dimensional image display element, and is decentered with respect to the projection optical system 13, and the image projected by the projection optical system 13 is projected. A correction optical system 12 including a reflection surface 12 formed of a curved surface that reflects the image projected from the projection optical system 13 and projects it onto the screen 11. The plane including the central principal ray C of the light beam traveling from the projection optical system 13 toward the screen 11 is perpendicular to the YZ cross section, the YZ cross section, and the screen at the projection center SO and the projection center SO where the central principal ray C intersects the screen 11. The plane including the perpendicular line A1 of 11 is the XZ cross section, the screen 11 has a concave surface facing the origin O side of the screen 11 in the XZ cross section, and the reflective surface 12 is in a plane parallel to the XZ cross section. And a convex surface facing the screen 11 side.

  Further, the reflecting surface 12a is different in power in a plane parallel to the YZ section and in a plane parallel to the XZ section, and the correction optical system 12 further includes an optical element 12b that is rotationally asymmetric with respect to the optical axis.

  The screen 11 is a reflecting surface having a curvature in the XZ section with the rotation center axis 11a as the center. The mirror 12a is a reflecting surface having a curvature in the XZ cross section, which is different from the screen 11 in the length of the radius of curvature and the center position.

  A line A1 connecting the projection center SO of the screen 11 and the coordinate origin O is decentered in the Y-axis direction with respect to the central axis A2 of the ideal lens 13a and the central axis A3 of the image display element 13b in the projection optical system 13. ing. Further, assuming that the point where the central principal ray C is reflected by the mirror 12a is the reflection center RO, the position of the reflection center RO in the Y-axis direction is arranged between the line A1, the central axis A2, and the central axis A3. As a result, the projected image projected obliquely from the projection optical system 13 onto the mirror 12a is reflected by the mirror 12a and projected onto the screen 11 to become a projected image that is observed by the observer.

  8 and 9 also show enlarged views of a portion surrounded by a broken line. The projection optical system 13 includes an image display element 13b for displaying an image, such as an LCD, and an ideal lens 13a. Further, a stop is provided on the cylindrical surface r4 of the cylindrical lens 12b.

  As shown in FIG. 8, the central axis A2 of the ideal lens 13a of the projection optical system 13 of Example 2 is arranged eccentrically with respect to the central axis A3 of the video display element 13b. Therefore, the image irradiated from the image display element 13b is projected using the periphery of the ideal lens 13a, and is projected obliquely to the eccentrically arranged mirror 12a, just like using the shift lens.

  As described above, it is preferable that the image display element 13b is shifted in eccentricity and oblique projection is performed, since no distortion is generated. Note that when the projection optical system 13 is tilted and tilted, trapezoidal image distortion occurs. Such image distortion can be corrected electronically.

  In the second embodiment, the mirror 12a (reflection surface) is used as a means for enlarging the projection angle of view in the X-axis direction. However, the use of the mirror 12a causes astigmatism and degrades the image formed on the screen 11. Therefore, this astigmatism is corrected using a second optical element composed of the cylindrical lens 12b.

  In the reverse ray tracing, the light beam emitted from the screen 11 (r1) as the object surface is reflected by the mirror 12a (r3) of the correction optical system 12 and enters the cylindrical surface (r4) of the cylindrical lens 12b provided with a stop. Thereafter, the light beam that has passed through the cylindrical lens 12b and has exited from the opposite surface (r5) enters the ideal lens 13a (r6) of the projection optical system 13. The light beam emitted from the ideal lens 13a (r6) reaches a predetermined position of the video display element 13b (r7). Note that the coordinate origin O is r2.

  The screen 11 according to the second embodiment is on the inner side of a cylindrical surface having a radius of 180 mm with the origin O at the center. The ideal lens 13 has a focal length of 23 mm and an exit pupil diameter of 5 mm.

  FIG. 12 is a diagram illustrating image distortion in the second embodiment. The outer approximate quadrilateral represents the distortion on the image plane with the maximum image height, and the inner approximate quadrilateral represents the distortion on the image plane with the maximum image height × 0.7. It can be seen that the upper and lower sides of the substantially quadrilateral are nearly horizontal, and the image distortion that forms a bow is corrected.

  Example 3 will be described. FIG. 13 is a diagram showing a cross section of the optical system of Example 3 and its peripheral configuration in the YZ section, and FIG. 14 is a plan view of the optical system of Example 3 and its peripheral structure in the XZ section. . 15 and 16 are lateral aberration diagrams of the entire optical system, and FIG. 17 is a diagram showing image distortion.

  The projection optical apparatus according to the third embodiment projects the image displayed on the two-dimensional image display element, the projection optical system 13 and the projection optical system 13, and the image projected by the projection optical system 13 is projected. A correction optical system 12 including a reflection surface 12 formed of a spherical surface that reflects an image projected from the projection optical system 13 and projects the image projected onto the screen 11. The plane including the central principal ray C of the light beam traveling from the projection optical system 13 toward the screen 11 is perpendicular to the YZ cross section, the YZ cross section, and the screen at the projection center SO and the projection center SO where the central principal ray C intersects the screen 11. The plane including the perpendicular line A1 of 11 is the XZ cross section, the screen 11 has a concave surface facing the origin O side of the screen 11 in the XZ cross section, and the reflective surface 12 is in a plane parallel to the XZ cross section. And a convex surface facing the screen 11 side.

  The screen 11 is a reflecting surface made of a spherical surface with the origin O as the center. The mirror 12a differs from the screen 11 in the length of the radius of curvature and the center position, and is a reflecting surface made of a spherical surface.

  A line A1 connecting the projection center SO of the screen 11 and the coordinate origin O is decentered in the Y-axis direction with respect to the central axis A2 of the ideal lens 13a and the central axis A3 of the image display element 13b in the projection optical system 13. ing. Further, assuming that the point where the central principal ray C is reflected by the mirror 12a is the reflection center RO, the position of the reflection center RO in the Y-axis direction is arranged between the line A1 and the center axis A2. As a result, the projected image projected obliquely from the projection optical system 13 onto the mirror 12a is reflected by the mirror 12a and projected onto the screen 11 to become a projected image that is observed by the observer.

  13 and 14 also show enlarged views of a portion surrounded by a broken line. The projection optical system 13 includes an image display element 13b for displaying an image, such as an LCD, and an ideal lens 13a. A stop S is provided on the mirror 12a side of the ideal lens 13a.

  As shown in FIG. 13, the central axis A2 of the ideal lens 13a of the projection optical system 13 of Example 3 is arranged eccentric with respect to the central axis A3 of the video display element 13b. Therefore, the image irradiated from the image display element 13b is projected using the periphery of the ideal lens 13a, and is projected obliquely to the eccentrically arranged mirror 12a, just like using the shift lens.

  As described above, it is preferable that the image display element 13b is shifted in eccentricity and oblique projection is performed, since no distortion is generated. Note that when the projection optical system 13 is tilted and tilted, trapezoidal image distortion occurs. Such image distortion can be corrected electronically.

  In the third embodiment, a spherical mirror 12a (reflection surface) is used as a means for enlarging the projection angle of view in the X-axis direction. Astigmatism can be reduced by using the spherical mirror 12a, and an image can be formed on the screen 11 without using an optical element as in the other embodiments.

  In the reverse ray tracing, the light beam emitted from the screen 11 as the object surface r1 is reflected by the mirror 12a (r3) of the correction optical system 12, passes through the stop S (r4), and the ideal lens 13a (r5) of the projection optical system 13 ). The light beam emitted from the ideal lens 13a (r5) reaches a predetermined position of the image display element 13b (r6). Note that the coordinate origin O is r2.

  The screen 11 of Example 3 is a spherical inner surface with a radius of 1 m having the origin O at the center position. The ideal lens 13 has a focal length of 23 mm and an exit pupil diameter of 15 mm.

  FIG. 17 is a diagram illustrating image distortion in the third embodiment. The outer approximate quadrilateral represents the distortion on the image plane with the maximum image height, and the inner approximate quadrilateral represents the distortion on the image plane with the maximum image height × 0.7. It can be seen that the image distortion that becomes a bow is corrected.

  Example 4 will be described. 18 is a diagram showing a cross section of the optical system of Example 4 and its peripheral configuration in the YZ section, and FIG. 19 is a plan view of the optical system of Example 4 and its peripheral structure in the XZ section. . 20 and 21 are lateral aberration diagrams of the entire optical system, and FIG. 22 is a diagram showing image distortion.

  The projection optical apparatus according to the fourth embodiment projects the image displayed on the two-dimensional image display element, the projection optical system 13 and the projection optical system 13, and the image projected by the projection optical system 13 is projected. And a correction optical system 12 including a reflection surface 12 having a free-form surface that reflects an image projected from the projection optical system 13 and projects the image onto the screen 11. The plane including the central principal ray C of the light beam traveling from the projection optical system 13 toward the screen 11 is perpendicular to the YZ section, the YZ section, and the projection center SO and the projection center SO where the central principal ray C intersects the screen 11. The plane including the perpendicular line A1 of the screen 11 is defined as an XZ cross section, the screen 11 faces a concave surface toward the origin O of the screen 11 in the XZ cross section, and the reflective surface 12 And a convex surface facing the screen 11 side in such a plane.

  Further, the reflecting surface 12a is different in power in a plane parallel to the YZ section and in a plane parallel to the XZ section, and the correction optical system 12 further includes an optical element 12b that is rotationally asymmetric with respect to the optical axis.

  The screen 11 is a reflecting surface having a curvature in the XZ section with the rotation center axis 11a as the center. The first free-form surface mirror 12a is a rotationally asymmetric reflecting surface.

  A line A1 connecting the projection center SO of the screen 11 and the coordinate origin O is arranged to be decentered in the Y-axis direction with respect to the ideal lens 13a and the center axis A2 of the image display element 13b in the projection optical system 13. Further, assuming that the point at which the central principal ray C is reflected by the first free-form curved mirror 12a is the first reflection center RO1, the position of the first reflection center RO1 in the Y-axis direction is between the line A1 and the center axis A2. Arranged between. Further, assuming that the point at which the central principal ray C is reflected by the second free-form curved mirror 12b is the second reflection center RO2, the position of the second reflection center RO2 in the Y-axis direction is the center of the first reflection center RO1. It arrange | positions between axis | shafts A2. As a result, a projected image projected obliquely from the projection optical system 13 onto the second free-form surface mirror 12b is reflected by the second free-form surface mirror 12a, reflected by the first free-form surface mirror 12a, and reflected on the screen 11. The projected image is projected to be observed by an observer.

  18 and 19 also show enlarged views of a portion surrounded by a broken line. The projection optical system 13 includes an image display element 13b for displaying an image, such as an LCD, and an ideal lens 13a. An aperture S is provided between the second free-form curved mirror 12b and the ideal lens 13a.

  As shown in FIG. 18, the central axis A2 of the ideal lens 13a of the projection optical system 13 of Example 4 is arranged eccentrically with respect to the central axis A3 of the video display element 13b. For this reason, the image irradiated from the image display element 13b is projected using the periphery of the ideal lens 13a, and is inclined with respect to the second free-form curved mirror 12b arranged eccentrically just like using the shift lens. Projected on. In addition, the image reflected by the second free-form curved mirror 12b is projected obliquely to the first free-form curved mirror 12a.

  As described above, it is preferable that the image display element 13b is shifted in eccentricity and oblique projection is performed, since no distortion is generated. Note that when the projection optical system 13 is tilted and tilted, trapezoidal image distortion occurs. Such image distortion can be corrected electronically.

  In the fourth embodiment, the first free-form curved mirror 12a (reflecting surface) is used as means for enlarging the projection angle of view in the X-axis direction. However, astigmatism occurs due to the use of the first free-form curved mirror 12a, and the image formed on the screen 11 is deteriorated. Therefore, this astigmatism and trapezoidal distortion are corrected using an optical element composed of the second free-form curved mirror 12b.

  In the reverse ray tracing, the light beam emitted from the screen 11 (r1) as the object surface is reflected by the first free-form surface mirror 12a (r3) of the correction optical system 12, and reflected by the second free-form surface mirror 12b (r4). Then, the light passes through the stop S (r5) and enters the ideal lens 13a (r6) of the projection optical system 13. The light beam emitted from the ideal lens 13a (r6) reaches a predetermined position of the video display element 13b (r7). Note that the coordinate origin O is r2.

  The screen 11 of the fourth embodiment is on the inner side of a cylindrical surface having a radius of 2 m and having the origin O at the center position. The ideal lens 13 has a focal length of 50 mm and an exit pupil diameter of 15 mm.

  FIG. 22 is a diagram illustrating image distortion in the fourth embodiment. The outer approximate quadrilateral represents the distortion on the image plane with the maximum image height, and the inner approximate quadrilateral represents the distortion on the image plane with the maximum image height × 0.7. It can be seen that the upper and lower sides of the substantially quadrilateral are horizontal and the image distortion is corrected.

  Example 5 will be described. FIG. 23 is a view showing a cross section in the YZ section of the optical system of Example 5 and its peripheral configuration, and FIG. 24 is a plan view of the optical system of Example 5 and its peripheral structure in the XZ section. . 25 and 26 are lateral aberration diagrams of the entire optical system, and FIG. 27 is a diagram showing image distortion.

  The projection optical apparatus according to the fifth embodiment projects the image displayed on the two-dimensional image display element, the projection optical system 13 and the projection optical system 13, and the image projected by the projection optical system 13 is projected. A correction optical system 12 including a reflection surface 12a formed of a free-form surface that reflects an image projected from the projection optical system 13 and projects the image onto the screen 11. The plane containing the central principal ray C of the light beam traveling from the projection optical system 13 toward the screen 11 is perpendicular to the YZ cross section, the YZ cross section, and the central principal ray C intersects the screen 11 at the projection center SO and the projection center SO. A plane including the perpendicular line A1 of the screen 11 is an XZ section, the screen 11 has a concave surface facing the origin O side of the screen 11 in the XZ section, and the reflecting surface 12 is parallel to the XZ section. And a convex surface facing the screen 11 side in the plane.

  The screen 11 is a reflecting surface made of a spherical surface with the origin O as the center. The mirror 12a is a reflecting surface made of a free-form surface having a radius of curvature different from that of the screen 11 and a center position.

  A line A1 connecting the projection center SO of the screen 11 and the coordinate origin O is arranged to be decentered in the Y-axis direction with respect to the ideal lens 13a and the center axis A2 of the image display element 13b in the projection optical system 13. Further, assuming that the point where the central principal ray C is reflected by the mirror 12a is the reflection center RO, the position of the reflection center RO in the Y-axis direction is between the aperture center of the stop S and the perpendicular line A1 at the screen center of the screen 11. Has been placed. As a result, the projected image projected obliquely from the projection optical system 13 onto the mirror 12a is reflected by the mirror 12a and projected onto the screen 11 to become a projected image that is observed by the observer.

  13 and 14 also show enlarged views of a portion surrounded by a broken line. The projection optical system 13 includes an image display element 13b for displaying an image, such as an LCD, and an ideal lens 13a. A stop S is provided on the mirror 12a side of the ideal lens 13a.

  As shown in FIG. 13, the ideal lens 13a of the projection optical system 13 of Example 5 and the central axis A2 of the image display element 13b are arranged obliquely. Therefore, the image irradiated from the image display element 13b is projected using the ideal lens 13a, and is projected obliquely to the mirror 12a arranged eccentrically.

  Note that when the projection optical system 13 is tilted and tilted, trapezoidal image distortion occurs. Such image distortion can be corrected electronically.

  In the fifth embodiment, a free-form mirror 12a (reflection surface) is used as means for enlarging the projection angle of view in the X-axis direction. Astigmatism can be reduced by using the free-form mirror 12a, and an image can be formed on the screen 11 without using an optical element as in the other embodiments.

  In the reverse ray tracing, the light beam emitted from the screen 11 as the object surface r1 is reflected by the mirror 12a (r3) of the correction optical system 12, passes through the stop S (r4), and the ideal lens 13a (r5) of the projection optical system 13 ). The light beam emitted from the ideal lens 13a (r5) reaches a predetermined position of the image display element 13b (r6). Note that the coordinate origin O is r2.

  The screen 11 of Example 5 is a spherical inner surface with a radius of 1 m having the origin O at the center position. The ideal lens 13 has a focal length of 17 mm and an exit pupil diameter of 10 mm.

  FIG. 17 is a diagram illustrating image distortion in the fifth embodiment. The outer approximate quadrilateral represents the distortion on the image plane with the maximum image height, and the inner approximate quadrilateral represents the distortion on the image plane with the maximum image height × 0.7. It can be seen that the bow-shaped image distortion and the trapezoidal distortion are corrected.

The configuration parameters of Examples 1 to 5 are shown below. In the table below, “FFS” indicates a free-form surface.

Example 1
Surface number Curvature radius Surface spacing Eccentric Refractive index Abbe number
r1 (object surface) Cylindrical surface [1] 1000.00
r2 (coordinate origin) ∞ 0.00
r3 Cylindrical surface [2] 0.00 Eccentricity (1)
r4 (diaphragm) Cylindrical surface [3] 0.00 Eccentricity (2) 1.5163 64.1
r5 ∞ 0.00 Eccentricity (3)
r6 Ideal lens 0.00 Eccentricity (4)
r7 (image plane) ∞ 0.00 Eccentricity (5)

Cylindrical surface [1]
X direction radius of curvature 1000.00
Y direction radius of curvature ∞

Cylindrical surface [2]
X direction radius of curvature 455.24
Y direction radius of curvature ∞

Cylindrical surface [3]
X direction radius of curvature -1380.77
Y direction radius of curvature ∞

Eccentric [1]
X 0.00 Y 223.26 Z -250.61
α 0.00 β 0.00 γ 0.00

Eccentric [2]
X 0.00 Y 400.00 Z -843.83
α 0.00 β 0.00 γ 0.00

Eccentric [3]
X 0.00 Y 400.00 Z -848.83
α 0.00 β 0.00 γ 0.00

Eccentric [4]
X 0.00 Y 400.00 Z -871.83
α 0.00 β 0.00 γ 0.00

Eccentric [5]
X 0.00 Y 406.85 Z -895.33
α 0.00 β 0.00 γ 0.00

Example 2
Surface number Curvature radius Surface spacing Eccentric Refractive index Abbe number
r1 (object surface) Cylindrical surface [1] 180.00
r2 (coordinate origin) ∞ 0.00
r3 Cylindrical surface [2] 0.00 Eccentricity (1)
r4 (diaphragm) Cylindrical surface [3] 0.00 Eccentricity (2) 1.5163 64.1
r5 ∞ 0.00 Eccentricity (3)
r6 Ideal lens 0.00 Eccentricity (4)
r7 (image plane) ∞ 0.00 Eccentricity (5)

Cylindrical surface [1]
X direction radius of curvature 180.00
Y direction radius of curvature ∞

Cylindrical surface [2]
X direction radius of curvature 48.32
Y direction radius of curvature ∞

Cylindrical surface [3]
X direction radius of curvature -89.75
Y direction radius of curvature ∞

Eccentric [1]
X 0.00 Y 56.43 Z -36.10
α 0.00 β 0.00 γ 0.00

Eccentric [2]
X 0.00 Y 80.00 Z -96.19
α 0.00 β 0.00 γ 0.00

Eccentric [3]
X 0.00 Y 80.00 Z -101.19
α 0.00 β 0.00 γ 0.00

Eccentric [4]
X 0.00 Y 80.00 Z -124.19
α 0.00 β 0.00 γ 0.00

Eccentric [5]
X 0.00 Y 89.04 Z -150.48
α 0.00 β 0.00 γ 0.00

Example 3
Surface number Curvature radius Surface spacing Eccentric Refractive index Abbe number
r1 (object surface) 1000.00 1000.00
r2 (coordinate origin) ∞ 0.00
r3 931.25 0.00 Eccentricity (1)
r4 (diaphragm) ∞ 0.00 Eccentricity (2)
r5 Ideal lens 0.00 Eccentricity (3)
r6 (image plane) ∞ 0.00 Eccentricity (4)

Eccentric [1]
X 0.00 Y 244.23 Z -343.86
α 0.00 β 0.00 γ 0.00

Eccentric [2]
X 0.00 Y 550.00 Z-1165.35
α 0.00 β 0.00 γ 0.00

Eccentric [3]
X 0.00 Y 550.00 Z-1188.35
α 0.00 β 0.00 γ 0.00

Eccentric [4]
X 0.00 Y 558.58 Z-1211.88
α 0.00 β 0.00 γ 0.00

Example 4
Surface number Curvature radius Surface spacing Eccentric Refractive index Abbe number
r1 (object surface) Cylindrical surface [1] 2000.00
r2 (coordinate origin) ∞ 0.00
r3 FFS [1] 0.00 Eccentricity (1)
r4 FFS [2] 0.00 Eccentricity (2)
r5 (diaphragm) ∞ 0.00 Eccentricity (3)
r6 Ideal lens 0.00 Eccentricity (4)
r7 (image plane) ∞ 0.00 Eccentricity (5)

Cylindrical surface [1]
X direction radius of curvature 1000.00
Y direction radius of curvature ∞

FFS [1]
C4 2.5976E-003 C6 2.8258E-005 C8 -1.0779E-007
C10 3.4901E-009 C11 4.6733E-008 C13 1.7474E-009

FFS [2]
C4 3.9474E-004 C6 8.9780E-005 C8 -3.5485E-007
C10 -1.2841E-007

Eccentric [1]
X 0.00 Y 400.00 Z -100.00
α 0.00 β 0.00 γ 0.00

Eccentric [2]
X 0.00 Y 577.78 Z -500.00
α 0.00 β 0.00 γ 0.00

Eccentric [3]
X 0.00 Y 600.00 Z -450.00
α 0.00 β 0.00 γ 0.00

Eccentric [4]
X 0.00 Y 600.00 Z -400.00
α 0.00 β 0.00 γ 0.00

Eccentric [5]
X 0.00 Y 622.31 Z -348.73
α 0.00 β 0.00 γ 0.00

Example 5
Surface number Curvature radius Surface spacing Eccentric Refractive index Abbe number
r1 (object surface) spherical surface [1] 2000.00
r2 (coordinate origin) ∞ 0.00
r3 FFS [1] 0.00 Eccentricity (1)
r4 (diaphragm) ∞ 0.00 Eccentricity (2)
r5 Ideal lens 0.00 Eccentricity (3)
r6 (image plane) ∞ 0.00 Eccentricity (4)

Spherical [1]
Curvature radius 1000.00

FFS [1]
R 400
C8 3.1203e-006 C10 2.4651e-006

Eccentric [1]
X 0.00 Y 285.05 Z -44.69
α -9.02 β 0.00 γ 0.00

Eccentric [2]
X 0.00 Y 507.02 Z -365.72
α -34.66 β 0.00 γ 0.00

Eccentric [3]
X 0.00 Y 516.69 Z -379.70
α -34.66 β 0.00 γ 0.00

Eccentric [4]
X 0.00 Y 526.36 Z -393.68
α -34.66 β 0.00 γ 0.00

Next, the angle a of the central chief ray incident on the cylindrical screen in each embodiment and the values of conditional expressions (1) to (7) are shown.

Example 1 Example 2 Example 3 Example 4 Example 5
(1) z / R1 0.55 0.75 0.37 0.39 -0.11
(2) α 16.59 21.41 20.42 23.42 16.61
(3) L2 / L1 0.11 1.51 3.00
(4) αsr 0.00 0.00 0.00 0.00 -9.02
(5) Rs 1000 180 1000 2000 1000
(6) R1 455.24 48.32 931.25 384.97 400.00
(7) αs 160.00 155.00 118.00 149.0 121.73

  FIG. 28 is a diagram showing a cross section in the YZ cross section and a state of observation by the observer, regarding the optical system according to the embodiment of the present invention and its peripheral configuration.

  The configuration and light rays are the same as those in the fourth embodiment shown in FIG. In the apparatus of the present embodiment, the observer is observed in a situation where the observer is seated as illustrated, for example. For observation, it is preferable that the line-of-sight direction of the observer is in the sitting state along the Z axis. Therefore, by making the projection optical system 13 and the correction optical system 12 such as a projector movable and changing the position according to the seating state, it is possible to provide a projection image that can be easily observed according to the seating situation. It becomes. Moreover, in a reclining-type movable seat or the like, the entire apparatus may be tilted according to the reclining angle.

  Thus, according to the apparatus using the optical system of the present embodiment, it is possible to provide an immersive projection image in a state where an observer is seated. Furthermore, it is possible to project a high-resolution projection image on the screen 11 that is suppressed in distortion and focused on the entire surface.

  Next, the mirror 12a as a reflecting surface will be described.

FIG. 29 is a diagram illustrating a state of the mirror 12a according to the first embodiment before being bent, and FIG. In the first embodiment of the mirror 12a of the correction optical system 12, a plane mirror as shown in FIG. 29 is formed by being bent and fixed to the table 20 as shown in FIG.

  By forming the plane mirror by bending it, it becomes possible to manufacture it inexpensively and easily. Further, since the plane mirror can be manufactured smoothly with less surface roughness, it is possible to obtain a projected image with good contrast.

  Further, when the mirror 12a is curved, in the coordinate system shown in FIG. 1, the mirror 12a is preferably formed so as to be a straight curved surface on the YZ cross section and a convex curved surface on one side in a plane parallel to the XZ cross section.

  In the YZ section, the angle of view of the YZ section of the projection optical system is reflected as it is by the mirror 12a, and in the XZ section, the image is enlarged and projected in the lateral direction corresponding to the XZ section by the negative power of the mirror 12a. A close angle of view can be obtained.

  Further, the mirror 12a may be formed of a back mirror. When the mirror 12a is formed by a back mirror, the back surface 12a1 of the mirror 12a shown in FIG.

  For example, in the case where the mirror 12a is made of a material such as plastic, if a surface having a reflecting action such as an aluminum coat is disposed on the surface, the coating is easily peeled off due to dirt on the surface, which causes a problem in durability. By using a back mirror, this durability can be dramatically improved.

  Further, when the mirror 12a is curved, the mirror 12a may be formed to have a suspension curve in a plane parallel to the XZ section in the coordinate system shown in FIG.

  By using a catenary curve, it is possible to reduce the curvature change at the positions where the light rays having the angles of view at both ends in the XZ cross section strike, and to reduce the image distortion generated in the trapezoid.

Further, when the shape of the mirror 12a is approximated by the following formula (8) in a plane parallel to the XZ cross section, it may be formed by a curved surface that satisfies the following formula (9).
^{Z = cX 2 / [1+ {} 1- (1 + k) c 2 X 2} 1/2] (8)
−1 <k <0 (9)
Where Z is the Z coordinate,
X is the X coordinate,
c is the curvature at the top,
k is an aspheric coefficient.

In general, the suspension curve is defined by the following equation (10).
Y = acosh (x / a) (10)

  For example, when both ends of the mirror 12a having a width of 600 mm and a thickness of 3 mm are fixed to 528.82 mm, a in Expression (10) is 300. This suspension curve can be approximated to an aspherical expression of c = 1/300 and k = −0.6921 in Expression (8).

  Further, when both ends of the mirror 12a having a width of 400 mm and a thickness of 3 mm are fixed to 352.55 mm, a in Equation (10) is 200. This suspension curve can be approximated to an aspherical expression of c = 1/200 and k = −0.6894 in Expression (8).

  By curving a flat rear surface reflecting mirror as the mirror 12a and fixing both ends to the lens base 20, the curved shape becomes a suspended curve and is stabilized. A reflection surface composed of a hanging curve can be formed only by fixing both ends, and the manufacture is easy.

  Further, when the aspheric coefficient satisfies Expression (9), it is possible to reduce the image distortion of the surrounding video. If the lower limit of Expression (9) is not reached, the curvature around the reflection surface in the XZ cross-sectional direction becomes small, and as a result, the size of the projected image reflected in the XZ direction becomes small. If the upper limit of Expression (9) is exceeded, the curvature increases, and the reflected projected image is greatly enlarged.

  FIG. 31 is a diagram illustrating a state of the mirror 12a according to the second embodiment before bending, and FIG. 32 is a diagram illustrating the mirror according to the second embodiment. In Example 2 of the mirror 12a of the correction optical system 12, a trapezoidal plane mirror as shown in FIG. 31 is formed by bending as shown in FIG.

  In the second embodiment of the mirror 12a, the mirror 12a, which is a trapezoidal plane reflecting mirror, is curved so that the curvature in the plane parallel to the XZ section increases as it goes to the projection optical system side in the direction along the Y axis. Form.

  By increasing the curvature of the mirror 12a in the plane parallel to the XZ section as it goes to the projection optical system side in the direction along the Y axis, the image distortion generated in the trapezoid is increased on the short side of the mirror 12a. It becomes possible to shorten on the long side. Therefore, trapezoidal image distortion can be corrected by appropriately setting the length and curvature of the short side and long side of the mirror 12a.

  FIG. 33 shows a third embodiment of the mirror. In the third embodiment of the mirror 12a of the correction optical system 12, a plane mirror as shown in FIG. 29 is curved as shown in FIG.

  In the third embodiment of the mirror 12a, the distance between both ends when being curved and fixed is projected so that the curvature in the plane parallel to the XZ section increases as it goes to the projection optical system side in the direction along the Y axis. The planar reflecting mirror is curved and formed so as to be shorter on the optical system side. To shorten the distance between both ends when the rectangular flat reflector is bent and fixed on the projection optical system side, shorten the distance between the end faces of the flat reflector on the projection optical system side and increase it on the opposite side of the projection optical system. And fix it to the letter C.

  By increasing the curvature of the mirror 12a in the plane parallel to the XZ section as it goes to the projection optical system side in the direction along the Y axis, the image distortion generated in the trapezoid is increased on the short side of the mirror 12a. It becomes possible to shorten on the long side. Therefore, trapezoidal image distortion can be corrected by appropriately setting the length and curvature of the short side and long side of the mirror 12a.

  FIG. 34 is a diagram illustrating Example 5 of the reflecting surface. As shown in FIG. 34, the fifth embodiment of the mirror 12a of the correction optical system 12 includes a flat surface portion 12a2 and a spherical convex reflection surface portion 12a3 manufactured by vacuum forming.

  By forming the spherical convex reflection surface portion 12a3 manufactured by vacuum forming, the reflection surface can be manufactured at low cost.

  FIG. 35 is a diagram illustrating Example 6 of the reflecting surface. As shown in FIG. 35, the sixth embodiment of the mirror 12a of the correction optical system 12 includes a flat surface portion 12a2 and a convex reflection surface portion 12a4 having a toric surface manufactured by vacuum forming.

  By forming the convex reflection surface portion 12a4 of the toric surface manufactured by vacuum forming, the vertical and horizontal enlargement ratios can be arbitrarily selected, and the size of the projection screen can be flexibly supported. In addition, the reflecting surface can be manufactured at a low cost.

  Further, as shown in FIG. 35, the convex reflection surface portion 12a4 may be formed in an ellipse. By forming an ellipse, it is possible to form the convex reflection surface portion 12a4 having a toric surface having different curvatures on the ellipse side and the short circle side, and the enlargement / reduction ratio can be arbitrarily selected. It becomes possible to respond flexibly to the size.

  FIG. 36 is a diagram illustrating Example 7 of the reflecting surface. As shown in FIG. 36, the seventh embodiment of the mirror 12a of the correction optical system 12 includes a mirror 12a having a flat surface portion 12a2 shown in FIG. 34 and a spherical convex reflection surface portion 12a3 manufactured by vacuum forming. In the direction along the Y-axis, as it goes to the projection optical system side, it is curved and formed so that the curvature becomes stronger in a plane parallel to the XZ section.

  35. In contrast to Example 6 in which the convex reflection surface portion 12a4 of the toric surface shown in FIG. You may make it curve so that may become strong.

  By curving so that the curvature increases in a plane parallel to the XZ section as it goes to the projection optical system side in the direction along the Y axis, the curvature in the section parallel to the XZ section is strong on the projection optical system side, It is possible to correct the trapezoidal image distortion by weakening on the opposite side.

  Although various embodiments of the present invention have been described above, the present invention is not limited to these embodiments, and embodiments configured by appropriately combining the configurations of the respective embodiments also fall within the scope of the present invention. Is.

DESCRIPTION OF SYMBOLS 11 ... Screen, 12 ... Correction | amendment optical system, 12a ... Reflective surface, 12b ... Optical element, 13 ... Projection optical system, 13a ... Ideal lens, 13b ... Image display element, O ... Coordinate origin (rotation center of a screen)

Claims (22)

A projection optical system that projects an image displayed on a two-dimensional image display device; and a screen that is decentered with respect to the projection optical system and is formed of a curved surface onto which the image projected by the projection optical system is projected. In the projection optical device
A correction optical system including a reflecting surface composed of a curved surface that reflects and projects the image projected from the projection optical system onto the screen;
The plane including the central principal ray of the light beam traveling from the projection optical system toward the screen is perpendicular to the YZ section, the projection center where the central principal ray intersects the screen, and the screen at the projection center. The plane including the perpendicular of
The screen has a concave surface facing the correction optical system in the XZ cross section,
The reflective surface has a convex surface facing the screen in a plane parallel to the XZ cross section ,
A projection optical apparatus satisfying the following conditional expression (4):
αsr <20 ° (4)
However,
αsr is an angle formed by a perpendicular of the reflecting surface at a position where the central principal ray hits the reflecting surface and a perpendicular of the screen at a position where the central principal ray hits the screen
It is.   The projection optical apparatus according to claim 1, wherein the reflection surface is formed by bending a plane mirror.   The projection optical apparatus according to claim 1, wherein the reflecting surface is formed by a back mirror.   2. The projection optical apparatus according to claim 1, wherein the reflecting surface has different power in a plane parallel to the YZ cross section and power in a plane parallel to the XZ cross section.   5. The projection optical apparatus according to claim 4, wherein the reflection surface is formed so as to be a straight curve in the YZ section and a convex curve on one side in a plane parallel to the XZ section.   6. The projection optical apparatus according to claim 5, wherein the reflecting surface is a straight line in the YZ section and a parabola in the XZ section.   6. The projection optical apparatus according to claim 5, wherein the reflecting surface has a suspended curve in a plane parallel to the XZ cross section.   The reflecting surface is formed by curving a trapezoidal plane mirror so that the curvature in a plane parallel to the XZ section becomes stronger as it goes to the projection optical system side in the direction along the Y axis. The projection optical apparatus according to claim 2.   The distance between both ends when the reflecting surface is curved and fixed so that the curvature in the plane parallel to the XZ section becomes stronger as it goes toward the projection optical system in the direction along the Y axis. The projection optical apparatus according to claim 2, wherein the projection mirror is formed by curving the plane mirror so as to be short on the optical system side.   The projection optical apparatus according to claim 1, wherein the reflection surface includes a flat surface portion and a spherical convex reflection surface portion manufactured by vacuum forming.   The projection optical apparatus according to claim 1, wherein the reflection surface includes a flat portion and a convex reflection surface portion of a toric surface manufactured by vacuum forming.   The projection optical apparatus according to claim 11, wherein the reflection surface has the convex reflection surface portion formed in an ellipse.   11. The reflection surface according to claim 10, wherein the reflection surface is curved so as to have a strong curvature in a plane parallel to the XZ section as it goes toward the projection optical system in a direction along the Y axis. The projection optical apparatus according to any one of 12.   The projection optical apparatus according to claim 1, wherein the screen is a spherical surface.   The projection optical apparatus according to claim 1, wherein the correction optical system further includes an optical element that is rotationally asymmetric with respect to an optical axis. The projection optical system according to claim 1 or 2, characterized by satisfying the following conditional expression (2).
0 <α <70 ° (2)
Where α is an angle formed by the central principal ray of the projected light beam and the normal of the screen. The projection optical apparatus according to claim 16 , wherein the following conditional expression (7) is satisfied.
αs> 30 ° (7)
However,
αs is the angle of the arc of the screen in the XZ section,
It is. The projection optical apparatus according to claim 17 , wherein the following conditional expression (6) is satisfied.
40 <R1 <800 (6)
However,
R1 is the radius of curvature of the reflecting surface in the XZ section. The projection optical apparatus according to claim 18, wherein the following conditional expression (5) is satisfied.
100 <Rs (5)
However,
Rs is the radius of curvature in the XZ section of a cylindrical or spherical screen,
It is. The projection optical apparatus according to claim 19 , wherein the following conditional expression (1) is satisfied.
−5 <z / R1 <5 (1)
However,
R1 is a radius of curvature of the reflecting surface in a plane parallel to the XZ cross section,
z is the distance from the center of the screen to the reflecting surface in the XZ cross section,
It is. The projection optical apparatus according to claim 20 , wherein the following conditional expression (3) is satisfied.
L2 / L1 <5.0 (3)
However,
L1 is the optical path length of the central principal ray from the reflecting surface to the rotationally asymmetric optical element,
L2 is the optical path length of the central principal ray from the stop of the projection optical system to the rotationally asymmetric optical element,
It is. The projection optical system according to claim 6, wherein the reflecting surface is formed by a curved surface satisfying the following equation (9) when approximated by the following equation (8) in a plane parallel to the XZ section. apparatus.
^{Z = cX 2 / [1+ {} 1- (1 + k) c 2 X 2} 1/2] (8)
−1 <k <0 (9)
Where Z is the Z coordinate,
X is the X coordinate,
c is the curvature at the top,
k is an aspheric coefficient.

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