Optical system, imaging apparatus, and projection apparatus

Abstract

To provide an optical system that is compact, can support a large aperture and has high optical performance.SOLUTION: An optical system includes, in order from the magnification side toward the reduction side, a first transmission reflection surface (HM1), a 1 / 4 wavelength plate (QWP), and a second transmission reflection surface (HM2). Light from the magnification side sequentially transmits through the first transmission reflection surface and the 1 / 4 wavelength plate, is reflected by the second transmission reflection surface toward the magnification side, transmits through the 1 / 4 wavelength plate, is reflected by the first transmission reflection surface toward the reduction side, and then transmits through the 1 / 4 wavelength plate and the second transmission reflection surface in this order toward the reduction side. The first and second transmission reflection surfaces each face a convex surface with the magnification side. In addition, a first lens (101) formed by a lens surface different from the first and second transmission reflection surfaces, and a second lens (102) disposed on the reduction side relative to the first lens are arranged.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] The present invention relates to an optical system, an imaging device, and a projection device.

Background Art

[0002] Conventionally, an optical system that uses a reflecting surface to control the incident light ray angle of light rays in front of the imaging point is known. Patent Document 1 discloses a configuration of an optical system having about 1 to 3 lenses and using surface reflection within the lens. Patent Document 2 discloses a configuration of an eyepiece lens for a head-mounted display that has about 2 lenses, one of which has a transmissive reflecting surface, and performs thinning by using reflection within the lens.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0004] In the configuration disclosed in Patent Document 1, thinning and miniaturization are possible by using reflection. However, since the reflection area is a perfect reflecting surface, light rays do not pass through the reflecting surface, and light rays do not reach the entire surface of the imaging element. Specifically, on-axis light rays are blocked by the reflecting surface and do not reach the imaging element. Further, since the optical system is designed to handle narrow light rays with a small Fno, the number of lenses is small, and it is difficult to ensure good optical performance when applied to a large-aperture optical system.

[0005] In the configuration disclosed in Patent Document 2, in order to correspond to the observation system, the aperture stop (pupil position: eye point) is arranged away from the first lens toward the subject side. When it is used for the imaging system or the projection system, the lens diameter becomes large and it is difficult to miniaturize. Further, when the aperture is increased in this configuration, the off-axis rays become thicker, so that the outer diameter of the lens becomes large.

[0006] Therefore, an object of the present invention is to provide an optical system having high optical performance that can cope with small size and large aperture.

Means for Solving the Problems

[0007] An optical system according to one aspect of the present invention is an optical system having a first transmissive-reflective surface, a quarter-wave plate, and a second transmissive-reflective surface arranged in order from the magnifying side to the reducing side. Light from the magnifying side passes through the first transmissive-reflective surface and the quarter-wave plate in order, is reflected toward the magnifying side by the second transmissive-reflective surface, passes through the quarter-wave plate, is reflected toward the reducing side by the first transmissive-reflective surface, passes through the quarter-wave plate and the second transmissive-reflective surface in order and goes toward the reducing side. The first transmissive-reflective surface and the second transmissive-reflective surface each face the convex surface toward the magnifying side, and a first lens composed of a lens surface different from the first transmissive-reflective surface and the second transmissive-reflective surface and a second lens arranged on the reducing side of the first lens are arranged.

[0008] Other objects and features of the present invention will be described in the following examples.

Advantages of the Invention

[0009] According to the present invention, it is possible to provide an optical system having high optical performance that can cope with small size and large aperture.

Brief Description of the Drawings

[0010]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19

Figure 20

Figure 21

Figure 22

Figure 23

Figure 24

Figure 25

Figure 26

Figure 27

Figure 28

Figure 29

Figure 30

Figure 31

Embodiments for Carrying Out the Invention

[0011] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In each figure, the same members are denoted by the same reference numerals, and overlapping descriptions are omitted.

[0012] The imaging optical system of each example is an optical system that forms an image of an object on an image plane, and is an optical system for acquiring an image by a solid-state imaging device or a photosensitive film arranged on the image plane. Further, it can also be used for a projection optical system that projects an image onto the subject side with the imaging point as the emission surface.

[0013] The imaging optical systems of the embodiments can be used in imaging devices such as the imaging cameras of smartphones, distance detection cameras, lens-fixed cameras, and disposable film cameras, which have image sensors that receive images formed by the imaging optical systems. Also, the imaging optical systems of the embodiments can be used in interchangeable lenses of video cameras, digital still cameras, and lens-interchangeable cameras. Further, they can also be used in projection lenses of projection systems having light-emitting panels.

[0014] The imaging optical systems of the embodiments may be used, for example, for line-of-sight detection, biometric recognition, expression recognition, etc. in camera finders and XR devices. Also, they may be used for external world recognition applications such as XR devices and automatic robots. Further, they can also be used in the projection systems of AR glasses as projection optical systems.

[0015] The imaging optical systems of the embodiments have a first transmissive-reflective surface, a quarter-wave plate QWP, and a second transmissive-reflective surface, which are arranged in order from the magnifying side to the reducing side. Light from the magnifying side passes through the first transmissive-reflective surface and the quarter-wave plate QWP in order, and is reflected by the second transmissive-reflective surface. Then, the light passes through the QWP and is reflected by the first transmissive-reflective surface, and then passes through the quarter-wave plate QWP and the second transmissive-reflective surface, and heads towards an imaging unit such as a solid-state image sensor or a photosensitive film. When this imaging optical system is used as a projection optical system, light rays are emitted from the image sensor as a light-emitting panel, follow a route opposite to that of the imaging optical system, and are projected to the magnifying side.

[0016] Here, the first transmissive-reflective surface and the second transmissive-reflective surface do not necessarily have a transmittance of 50% and a reflectance of 50%. The ratio of the transmittance to the reflectance for random polarization is preferably in the range of 1:3 to 3:1. Random polarization is light with Stokes parameters S0 = 1, S1 = S2 = S3 = 0. Also, the first transmissive-reflective surface and the second transmissive-reflective surface may absorb light. Also, lenses may be formed or joined on both sides or one side of each transmissive-reflective surface.

[0017] As the quarter-wave plate QWP, for example, a polymer film having birefringence or a liquid crystal alignment layer can be used. Further, a laminate of such a polymer film and a liquid crystal alignment layer can also be used as the QWP. By appropriately laminating these, a retardation close to a quarter of the wavelength can be obtained in a wide wavelength range. In addition to the above, as the quarter-wave plate QWP, for example, an inorganic wavelength plate of Dexerials Corporation can be used.

[0018] The quarter-wave plate QWP can be arranged, for example, in adhesion with the first transmission-reflection surface or the second transmission-reflection surface. Further, the quarter-wave plate QWP can also be arranged separately from these transmission-reflection surfaces. For example, the film may be directly inserted into the optical path, or a film bonded to a glass plate may be inserted into the optical path. Further, lenses may be formed or joined on both sides or one side of the quarter-wave plate QWP. For example, using wafer-level optics technology with an inorganic wavelength plate as a substrate, lenses can be formed on one side or both sides of the inorganic wavelength plate.

[0019] Hereinafter, the characteristic configurations in the optical systems of the respective embodiments will be described.

[0020] The first transmission-reflection surface or the second transmission-reflection surface of the optical system of each embodiment is preferably convex on the magnification side. Off-axis light rays traveling from the magnification side to the reduction side are transmitted through the first reflection surface, reflected by the second transmission-reflection surface, reflected again by the first transmission-reflection surface, and transmitted through the second transmission-reflection surface to become telecentric light rays.

[0021] Making the light rays transmitted through the second transmission-reflection surface telecentric after reflection by the first transmission-reflection surface and the second transmission-reflection surface means that the point of transmission through the second transmission-reflection surface and the imaging position are substantially at the same position in a position perpendicular to the optical axis. That is, the distance from the point of transmission through the first transmission-reflection surface to the point of transmission through the second transmission-reflection surface is reflected and moved by the distance in the direction perpendicular to the optical axis.

[0022] By making the first transmissive-reflective surface and the second transmissive-reflective surface convex toward the magnification side, it is possible to move in a direction perpendicular to the optical axis from the transmission point of the first transmissive-reflective surface to the transmission point of the second transmissive-reflective surface. Therefore, the point passing through the second transmissive-reflective surface and the imaging position can be made to be approximately the same position in a direction perpendicular to the optical axis. That is, telecentric light rays can be obtained.

[0023] Since the light rays pass through the first transmissive-reflective surface, are reflected by the second transmissive-reflective surface, and return to the first transmissive-reflective surface again, the optical path during this period will be reciprocated, resulting in the effect of bending the light rays. The originally required length of the light rays is folded, and the overall length of the lens can be shortened.

[0024] By making the shapes of the first transmissive-reflective surface and the second transmissive-reflective surface convex toward the magnification side, the distance in the direction perpendicular to the optical axis from the transmission point of the first transmissive-reflective surface to the transmission point of the second transmissive-reflective surface can be adjusted greatly. For example, even if the transmission point of the first transmissive-reflective surface of the most off-axis light ray passing through the optical system passes near the optical axis, by adjusting the convex shapes of the first transmissive-reflective surface and the second transmissive-reflective surface on the magnification side, the transmission position of the second transmissive-reflective surface can be set to pass through the same position as the outermost peripheral position of the imaging device. If the transmission point of the first transmissive-reflective surface can be set near the optical axis, the lens diameter of the object can be made smaller than that of the first transmissive-reflective surface, so miniaturization becomes possible.

[0025] The reflections of the first transmissive-reflective surface and the second transmissive-reflective surface have the effect of adjusting the positions in the direction perpendicular to the optical axis of the transmission points of the first transmissive-reflective surface and the second transmissive-reflective surface. However, even if the lens system is composed only of this surface, it is impossible to satisfy the optical performance in a large-aperture thick light beam. In the optical systems of the embodiments, it is preferable that at least two lenses (a plurality of lenses including the first lens and the second lens arranged on the reduction side with respect to the first lens), which are composed of lens surfaces different from the first transmissive-reflective surface and the second transmissive-reflective surface, are arranged. With such a configuration, good optical performance can be ensured by having an effect on aberration correction. Since the first transmissive-reflective surface and the second transmissive-reflective surface are reflective structures, chromatic aberration does not occur, and since the refractive power and the Petzval sum can be manipulated, if there are two refractive power lenses separate from the reflective surfaces, high performance can be realized with a small number of lenses and a large-aperture specification.

[0026] Next, in the optical systems of the embodiments, configurations that are preferably satisfied will be described.

[0027] One of the first transmissive-reflective surface and the second transmissive-reflective surface is preferably a surface that separates incident light into reflected light and transmitted light according to the polarization state. Specifically, as will be described later, it is preferable to use a polarization-selective transmissive-reflective element as one of the first transmissive-reflective surface and the second transmissive-reflective surface. Examples of the polarization-selective transmissive-reflective element include those manufactured by Asahi Kasei Corporation under the trade name "WGF" and those manufactured by 3M Company under the trade name "IQPE". Also, as the polarization-selective transmissive-reflective element, an optical element created by forming a grid on the lens reflective surface during lens molding and then depositing, printing, or lithographing a metal or dielectric thereon may be used. As the other, a half mirror, a cholesteric liquid crystal, a holographic optical element, etc. can be used. When a half mirror is used, the amount of randomly polarized light incident from the enlargement side becomes 12.5% or less by the time it reaches the image plane. By using a cholesteric liquid crystal or a holographic optical element, the amount of light on the image plane can be significantly increased, about twice that when a half mirror is used.

[0028] Preferably, at least one of the lenses disposed separately from the first transmissive reflecting surface and the second transmissive reflecting surface has a positive refractive power. A positive refractive power is required to converge a large light beam. Further, at least one lens having a negative refractive power is required to correct spherical aberration and field curvature generated with a positive refractive power. If at least two lenses having a positive refractive power and a negative refractive power can be disposed, spherical aberration and field curvature can be corrected while correcting field curvature at the first transmissive reflecting surface and the second transmissive reflecting surface.

[0029] Also, it is preferable to dispose a lens having a negative refractive power adjacent to the magnifying side of the first transmissive reflecting surface. By disposing a negative refractive power, the off-axis light beam after passing through the lens having a negative refractive power can be made at a large angle with respect to the optical axis, and the light beam can be moved in a direction perpendicular to the optical axis from the reflections of the first transmissive reflecting surface and the second transmissive reflecting surface, making it easier to configure telecentricity.

[0030] Also, by disposing a lens having a positive refractive power on the magnifying side of the lens having a negative refractive power and arranging them in the order of positive refractive power, negative refractive power, and the first transmissive reflecting surface, spherical aberration and field curvature correction of a large-diameter light beam can be achieved.

[0031] The optical system of each embodiment has an open aperture. The open aperture means the state where the aperture stop is fully open. In each embodiment, the state where the aperture stop is fully open is used as the value of the open aperture. At that time, the width of the on-axis light beam is determined by the open aperture diameter. In an optical system without an aperture whose aperture opening can be changed, the aperture that determines the on-axis light beam may be determined as the open aperture. If there is an aperture that determines the on-axis light beam within the range of conditional expression (2) described later, that aperture is determined as the open aperture.

[0032] The optical system of each embodiment is preferably rotationally symmetric with respect to the optical axis. Further, in the optical system of each embodiment, the second transmission reflection surface is preferably a surface having a refractive power disposed on the most reduced side of the optical system. By the reflection of the first transmission reflection surface and the second transmission reflection surface, it is possible to move in a direction perpendicular to the optical axis from the transmission point of the first transmission reflection surface to the transmission point of the second transmission reflection surface, and the transmitted light beam preferably forms an image at a point (sensor surface, panel surface) that travels substantially parallel to the optical axis as it is. If a surface having another refractive power enters between the transmission point of the second transmission reflection surface and the image surface, unnecessary aberrations such as chromatic aberration will occur.

[0033] Next, the conditions that the optical system of each embodiment preferably satisfies will be described. The optical system of each embodiment preferably satisfies at least one of the following conditional expressions (1) to (16).

[0034] 0.50 ≦ fp / f ≦ 10.00 (1) 0.00 ≦ Ls / L ≦ 1.00 (2) 0.03 ≦ D / LD ≦ 1.50 (3) -2.00 ≦ fF / fR ≦ 10.00 (4) 0.15 ≦ Ld / La ≦ 0.80 (5) 0.50 ≦ La / f ≦ 3.00 (6) 0.10 ≦ Lh / L ≦ 1.00 (7) 0.30 ≦ Lh / f ≦ 3.00 (8) 1.40 ≦ nd ≦ 2.30 (9) -10.00 ≦ fN / f ≦ -0.50 (10) -0.50 ≦ f / fR ≦ 2.00 (11) 0.05 ≦ Li / L ≦ 1.00 (12) -1.00 ≦ (R1 - R2) / (R1 + R2) ≦ 1.00 (13) 0.10 ≦ Ld / f ≦ 2.00 (14) 0.10 ≦ Oe / Ie ≦ 2.00 (15) 0.50 ≦ Fno ≦ 15.00 (16) Here, fp is the focal length of a positive refractive power lens disposed on the magnifying side of a negative refractive power lens disposed on the magnifying side of the first transmissive reflection surface. f is the focal length of the optical system (the entire system). Ls is the distance on the optical axis from the aperture stop to the first transmissive reflection surface. L is the overall optical length, which is the distance on the optical axis including a member G such as a glass block from the first lens surface (the magnifying side surface of the lens on the most magnifying side of the optical system) to the image surface (panel surface). D is the diameter of the aperture stop (aperture diameter). LD is the distance on the optical axis from the aperture stop to the image surface (panel surface).

[0035] fR is the focal length in the range between the first transmissive reflection surface and the second transmissive reflection surface, and fF is the focal length in the range on the object side of the first transmissive reflection surface. La is the total lens thickness, which is the thickness on the optical axis from the lens surface on the most magnifying side (the magnifying side surface of the most magnifying lens) to the lens surface on the most reducing side (the reducing side surface of the most reducing lens) of the optical system. Ld is the distance on the optical axis from the first transmissive reflection surface to the second transmissive reflection surface. Lh is the distance on the optical axis including the glass block from the first transmissive reflection surface to the image surface (panel surface).

[0036] nd is the refractive index for the d-line of a material other than air filling the region between the first transmissive reflection surface and the second transmissive reflection surface. fN is the focal length of the negative lens disposed adjacent to the magnifying side of the first transmissive reflection surface. Li is the distance on the optical axis from the second transmissive reflection surface to the image surface (panel surface). R1 is the radius of curvature of the first transmissive reflection surface, and R2 is the radius of curvature of the second transmissive reflection surface. Oe is the outer diameter of the lens disposed on the most magnifying side of the optical system, and Ie is the outer diameter of the lens disposed on the most reducing side of the optical system. In each embodiment, the outer diameter of the lens is a value obtained by adding 2 mm to the effective diameter of the lens.

[0037] Conditional expression (1) is a conditional expression that defines the focal length of a lens with a positive refractive power arranged on the further enlarged side of a lens with a negative refractive power arranged on the enlarged side of the first transmission-reflection surface. By appropriately setting the positive refractive power, it is possible to satisfactorily correct spherical aberration and field curvature generated by a large-diameter light beam. If it is below the lower limit value of conditional expression (1), the refractive power of the positive lens becomes too strong, so that a large amount of spherical aberration is generated on the under side and cannot be fully corrected, which is not preferable. On the other hand, if it exceeds the upper limit value of conditional expression (1), the refractive power of the positive lens becomes weak, so that spherical aberration is generated on the over side, which is not preferable.

[0038] Conditional expression (2) is a conditional expression that defines how far the aperture stop is separated from the first transmission-reflection surface toward the enlarged side. The aperture stop is set at a location where the on-axis light beam and the off-axis light beam respectively pass through the optical axis. Therefore, usually, the outer diameter of the lens becomes large at a position separated from the aperture stop toward the enlarged side or the reduced side. When the distance between the aperture stop and the first transmission-reflection surface increases, the diameter of the lens arranged between the aperture stop and the first transmission-reflection surface becomes large. Therefore, the size of the entire lens system is defined by conditional expression (2).

[0039] If it is below the lower limit value of conditional expression (2), the aperture stop will be arranged between the first transmission-reflection surface and the second transmission-reflection surface and cannot be arranged realistically, which is not preferable. On the other hand, if it exceeds the upper limit value of conditional expression (2), the position of the aperture stop will be arranged significantly on the subject side rather than on the enlarged side surface of the first lens. Therefore, the diameter of the lens arranged between the aperture stop and the first transmission-reflection surface becomes large, which is not preferable. Further, it becomes so large that telecentricity can be ensured without using the reflections between the first transmission-reflection surface and the second transmission-reflection surface, which is not preferable.

[0040] Conditional expression (3) is a conditional expression that defines the aperture diameter of the aperture stop that determines the on-axis Fno light beam diameter and the distance on the optical axis from the aperture stop to the image plane. If it is below the lower limit value of conditional expression (3), the F-number that can be set in terms of specifications becomes darker and the amount of light becomes insufficient, which is not preferable. On the other hand, if it exceeds the upper limit value of conditional expression (3), the light beam diameter becomes large and it becomes too bright. As a result, in order to correct aberrations, it becomes larger depending on the number of lens elements for imaging, which is not preferable.

[0041] Conditional expression (4) is a conditional expression that defines the focal length of the range surrounded by the first transmission-reflection surface and the second transmission-reflection surface and the focal length of the entire lens on the subject side with respect to the first transmission-reflection surface. The light rays in the range surrounded by the first transmission-reflection surface and the second transmission-reflection surface are structured to be reflected so as to move in a direction perpendicular to the optical axis between the first transmission-reflection surface and the second transmission-reflection surface. In order to move the light rays, it is preferably substantially similar in shape. Considering the element between the first transmission-reflection surface and the second transmission-reflection surface as an element with an integral refractive power, a strong refractive power is not required. Also, the shape between the first transmission-reflection surface and the second transmission-reflection surface is a similar shape, and the focal length can be a weak positive refractive power or a negative refractive power.

[0042] If it is below the lower limit value of conditional expression (4), the focal length of the entire lens on the subject side with respect to the first transmission-reflection surface becomes too loose with respect to the distance between the first transmission-reflection surface and the second transmission-reflection surface, and the aberration correction for spherical aberration and field curvature becomes insufficient, which is not preferable. On the other hand, if it exceeds the upper limit value of conditional expression (4), similarly, the focal length of the entire lens on the subject side with respect to the first transmission-reflection surface becomes too loose, and the aberration correction for spherical aberration and field curvature becomes insufficient, which is not preferable.

[0043] Conditional expression (5) is a conditional expression that defines the distance (interval) between the first transmission-reflection surface and the second transmission-reflection surface with respect to the total thickness of the lenses of the optical system, that is, the thickness from the surface with the largest magnification having curvature to the surface with the smallest magnification in the so-called entire lens system. If the interval between the first transmission-reflection surface and the second transmission-reflection surface is large, the light ray distance passing through between them can be increased, so miniaturization can be achieved.

[0044] If it is less than the lower limit of conditional expression (5), the distance between the first transmissive-reflective surface and the second transmissive-reflective surface becomes too narrow, so the light beam has to be moved in a direction perpendicular to the optical axis within the narrow space. As a result, it becomes difficult to ensure telecentricity when passing through the second transmissive-reflective surface. To ensure telecentricity, it is necessary to strengthen the convex shape toward the magnification side, which is not preferable because an unnecessary air gap is formed from the second transmissive-reflective surface to the imaging point, leading to an increase in size. On the other hand, if it exceeds the upper limit of conditional expression (5), the distance between the first transmissive-reflective surface and the second transmissive-reflective surface becomes too large for the entire optical system, making it difficult to arrange lenses for aberration correction and thus making aberration correction difficult, which is not preferable.

[0045] Conditional expression (6) is a conditional expression that defines the total lens thickness of the optical system (the overall thickness on the optical axis of the lenses constituting the optical system). Since it is an optical system using the first transmissive-reflective surface and the second transmissive-reflective surface, significant miniaturization can be achieved for an optical system of a type that does not perform normal reflection.

[0046] If it is less than the lower limit of conditional expression (6), it is advantageous for the overall thinning and miniaturization of the optical system. However, if it becomes too thin, the distance (interval) between the first transmissive-reflective surface and the second transmissive-reflective surface becomes small. It is necessary to gain a distance for movement in a direction perpendicular to the optical axis between the first transmissive-reflective surface and the second transmissive-reflective surface within this small range. As a result, the shapes of the first transmissive-reflective surface and the second transmissive-reflective surface become strongly convex toward the magnification side, and an unnecessary air gap is formed from the second transmissive-reflective surface to the imaging point, leading to an increase in size, which is not preferable. On the other hand, if it exceeds the upper limit of conditional expression (6), the total lens thickness of the optical system becomes thick, resulting in an increase in size, which is not preferable.

[0047] Conditional expression (7) is a conditional expression that defines the position of the first transmissive-reflective surface with respect to the overall optical length. The more the first transmissive-reflective surface is arranged toward the magnification side, the more the reflection distance between the first transmissive-reflective surface and the second transmissive-reflective surface can be gained, making it easier to achieve miniaturization.

[0048] When it is below the lower limit of conditional expression (7), the first transmissive reflecting surface approaches too close to the imaging point side, so the distance (spacing) between the first transmissive reflecting surface and the second transmissive reflecting surface becomes substantially narrow. Since the light rays have to be moved in a direction perpendicular to the optical axis within this narrow space, it becomes difficult to ensure telecentricity when passing through the second transmissive reflecting surface. Also, to ensure telecentricity, it is necessary to strengthen the convex shape toward the magnifying side, which results in a useless air space from the second transmissive reflecting surface to the imaging point and an increase in size, which is not preferable. On the other hand, when it exceeds the upper limit of conditional expression (7), it becomes easier to ensure the distance (spacing) between the first transmissive reflecting surface and the second transmissive reflecting surface with respect to the optical system (the entire system). However, it becomes difficult to arrange lenses that can correct aberrations with lenses arranged on the magnifying side of the first transmissive reflecting surface, making aberration correction difficult, which is not preferable.

[0049] Conditional expression (8) is a conditional expression that defines the position of the first transmissive reflecting surface. The more the first transmissive reflecting surface is arranged on the magnifying side, the more the reflection distance between the first transmissive reflecting surface and the second transmissive reflecting surface can be obtained, making it easier to achieve miniaturization.

[0050] When it is below the lower limit of conditional expression (8), it is advantageous for the overall thinning and miniaturization of the optical system. However, since the optical system becomes too thin, the distance (spacing) between the first transmissive reflecting surface and the second transmissive reflecting surface becomes small. To obtain the distance moved in a direction perpendicular to the optical axis between the first transmissive reflecting surface and the second transmissive reflecting surface within this small range, the shapes of the first transmissive reflecting surface and the second transmissive reflecting surface become strongly convex toward the magnifying side. As a result, a useless air space is created from the second transmissive reflecting surface to the imaging point, leading to an increase in size, which is not preferable. On the other hand, when it exceeds the upper limit of conditional expression (8), it becomes easier to ensure the distance (spacing) between the first transmissive reflecting surface and the second transmissive reflecting surface with respect to the optical system (the entire system). However, it becomes difficult to arrange lenses that can correct aberrations with lenses arranged on the magnifying side of the first transmissive reflecting surface, making aberration correction difficult, which is not preferable.

[0051] The conditional expression (9) indicates that the space between the first transmissive-reflective surface and the second transmissive-reflective surface is filled with a refractive index medium other than air. When there is no refractive index medium and it is composed of only air, it is difficult to determine the relative position accuracy between the first transmissive-reflective surface and the second transmissive-reflective surface, which becomes a factor for performance degradation such as vignetting. The accuracy of the relative positional relationship can be ensured with a configuration that can be integrally processed such as a lens. If it is below the lower limit value of the conditional expression (9), it cannot be processed with a glass material, so the relative positional relationship between the first transmissive-reflective surface and the second transmissive-reflective surface is likely to shift, which affects optical performance such as vignetting and is not preferable. On the other hand, if it exceeds the upper limit value of the conditional expression (9), there is no glass material and it becomes an air gap, and it is necessary to be composed of a reflective surface or the like. For this reason, it is necessary to suppress it with a mechanical structure, and the relative positional relationship between the first transmissive-reflective surface and the second transmissive-reflective surface is likely to shift, which affects optical performance such as vignetting and is not preferable.

[0052] The conditional expression (10) is a conditional expression that defines the focal length of the negative lens arranged adjacent to the magnifying side of the first transmissive-reflective surface. When the focal length of the negative lens becomes longer below the lower limit value of the conditional expression (10), the correction of the field curvature is insufficient, and it is necessary to bear the insufficient negative refractive power by the lens on the magnifying side rather than the negative lens. At this time, since the number of lenses increases and the size becomes larger, it is not preferable. On the other hand, when the focal length of the negative lens becomes shorter above the upper limit value of the conditional expression (10), it is advantageous for the correction of the field curvature. However, the correction of the field curvature becomes excessive, and the amount of movement in the direction perpendicular to the optical axis between the first transmissive-reflective surface and the second transmissive-reflective surface becomes too large, and the telecentricity cannot be ensured, so it is not preferable.

[0053] The conditional expression (11) is a conditional expression that defines the focal length between the first transmissive-reflective surface and the second transmissive-reflective surface. The light rays within the range surrounded by the first transmissive-reflective surface and the second transmissive-reflective surface are reflected so as to move in a direction perpendicular to the optical axis between the first transmissive-reflective surface and the second transmissive-reflective surface, and it is preferable that they have substantially similar shapes for moving the light rays. Considering the space between the first transmissive-reflective surface and the second transmissive-reflective surface as an integral refractive element, a strong refractive power is not required. Also, the shapes between the first transmissive-reflective surface and the second transmissive-reflective surface are similar, and the focal length can be either a weak positive refractive power or a negative refractive power. Therefore, it has a large focal length with respect to the focal length of the optical system (the entire system).

[0054] When it is below the lower limit value of the conditional expression (11), it becomes easier to ensure the amount of movement in the direction perpendicular to the optical axis between the first transmissive-reflective surface and the second transmissive-reflective surface. However, since the focal length of the optical system (the entire system) becomes too short and cannot meet the specifications, it is not preferable. On the other hand, when it exceeds the upper limit value of the conditional expression (11), the focal length between the first transmissive-reflective surface and the second transmissive-reflective surface becomes too short, and the amount of movement in the direction perpendicular to the optical axis becomes short, making it impossible to ensure telecentricity, so it is not preferable.

[0055] The conditional expression (12) is a conditional expression that defines the distance on the optical axis from the second transmissive-reflective surface to the image plane. Since the first transmissive-reflective surface and the second transmissive-reflective surface have convex shapes, if the distance on the optical axis from the second transmissive-reflective surface to the image plane becomes too large, useless space will be generated. When the interval from the second transmissive-reflective surface to the image plane becomes short by falling below the lower limit value of the conditional expression (12), interference occurs in the effective part of the second transmissive-reflective surface, which is not preferable. On the other hand, when the distance from the second transmissive-reflective surface to the image plane becomes long by exceeding the upper limit value of the conditional expression (12), there is no space to arrange the lens on the enlarged side of the first transmissive-reflective surface for realizing miniaturization, and it becomes difficult to correct spherical aberration and field curvature, so it is not preferable.

[0056] The conditional expression (13) defines the shape factor of the structure surrounded by the first transmissive-reflective surface and the second transmissive-reflective surface. Specifically, it defines that the first transmissive-reflective surface and the second transmissive-reflective surface face the same direction. The light ray is reflected so as to move between the first transmissive-reflective surface and the second transmissive-reflective surface in a direction perpendicular to the optical axis. In order to move the light ray, it is preferable that they have substantially similar shapes. If it exceeds the upper limit value or is below the lower limit value of the conditional expression (13), the first transmissive-reflective surface and the second transmissive-reflective surface will face each other with convex surfaces or concave surfaces. As a result, the light ray cannot reach the imaging device due to the reflection of the first transmissive-reflective surface and the second transmissive-reflective surface, which is not preferable.

[0057] The conditional expression (14) is a conditional expression that defines the interval (distance) between the first transmissive-reflective surface and the second transmissive-reflective surface. If it is below the lower limit value of the conditional expression (14), the interval between the first transmissive-reflective surface and the second transmissive-reflective surface becomes too narrow. As a result, since the light ray has to be moved in a direction perpendicular to the optical axis within the narrow interval, it is difficult to ensure telecentricity when passing through the second transmissive-reflective surface. In order to ensure telecentricity, it is necessary to strengthen the convex shape toward the enlargement side, and an unnecessary air interval is formed from the second transmissive-reflective surface to the imaging point, resulting in an increase in size, which is not preferable. On the other hand, if it exceeds the upper limit value of the conditional expression (14), the interval (distance) between the first transmissive-reflective surface and the second transmissive-reflective surface becomes too large for the entire optical system, making it difficult to arrange lenses for aberration correction and difficult to perform aberration correction, which is not preferable.

[0058] The conditional expression (15) is a conditional expression regarding the outer diameter of the lens arranged on the most enlarged side and the outer diameter of the lens arranged on the most reduced side, and is a conditional expression that defines miniaturization. In each embodiment, the outer diameter of the lens is a value obtained by adding 2 mm to the effective diameter of the lens. Since the light ray is reflected so as to move between the first transmissive-reflective surface and the second transmissive-reflective surface in a direction perpendicular to the optical axis to form a telecentric light ray, the effective diameter of the light ray between the first transmissive-reflective surface and the second transmissive-reflective surface becomes large. However, by setting the position of the aperture stop, miniaturization can be achieved with respect to the effective diameter of the lens on the enlargement side of the first transmissive-reflective surface.

[0059] If it is less than the lower limit value of conditional expression (15), the outer diameter of the lens arranged on the most enlarged side becomes too small, a predetermined Fno light beam cannot enter, and it becomes difficult to increase the aperture diameter, which is not preferable. On the other hand, if it exceeds the upper limit value of conditional expression (15), the outer diameter of the lens arranged on the most enlarged side becomes too large and it becomes heavy, which is not preferable.

[0060] In the optical systems of each embodiment, light quantity loss occurs due to the first transmission reflection surface and the second transmission reflection surface. For this reason, when the F number is large, the amount of light reaching the imaging element becomes small. Therefore, it is preferable that the optical systems of each embodiment satisfy conditional expression (16).

[0061] More preferably, at least one numerical range of conditional expressions (1) to (16) is set as the following conditional expressions (1a) to (16a).

[0062] 0.80 ≦ fp / f ≦ 8.00 (1a) 0.02 ≦ Ls / L ≦ 0.80 (2a) 0.05 ≦ D / LD ≦ 1.20 (3a) -1.00 ≦ fF / fR ≦ 5.00 (4a) 0.20 ≦ Ld / La ≦ 0.70 (5a) 0.60 ≦ La / f ≦ 2.80 (6a) 0.20 ≦ Lh / L ≦ 0.90 (7a) 0.40 ≦ Lh / f ≦ 2.50 (8a) 1.45 ≦ nd ≦ 1.80 (9a) -7.00 ≦ fN / f ≦ -0.70 (10a) -0.20 ≦ f / fR ≦ 1.00 (11a) 0.10 ≦ Li / L ≦ 0.85 (12a) -0.90 ≦ (R1 - R2) / (R1 + R2) ≦ 0.80 (13a) 0.20 ≦ Ld / f ≦ 1.50 (14a) 0.15 ≦ Oe / Ie ≦ 1.20 (15a) 0.70 ≦ Fno ≦ 12.00 (16a) More preferably, at least one numerical range of the conditional expressions (1) to (16) is set as the following conditional expressions (1b) to (16b).

[0063] 1.00 ≦ fp / f ≦ 5.00 (1b) 0.03 ≦ Ls / L ≦ 0.60 (2b) 0.07 ≦ D / LD ≦ 1.00 (3b) 0.00 ≦ fF / fR ≦ 1.00 (4b) 0.24 ≦ Ld / La ≦ 0.60 (5b) 0.70 ≦ La / f ≦ 2.60 (6b) 0.30 ≦ Lh / L ≦ 0.80 (7b) 0.50 ≦ Lh / f ≦ 2.00 (8b) 1.48 ≦ nd ≦ 1.60 (9b) -5.00 ≦ fN / f ≦ -1.00 (10b) -0.05 ≦ f / fR ≦ 0.30 (11b) 0.15 ≦ Li / L ≦ 0.70 (12b) -0.80 ≦ (R1 - R2) / (R1 + R2) ≦ 0.60 (13b) 0.30 ≦ Ld / f ≦ 0.90 (14b) 0.20 ≦ Oe / Ie ≦ 1.00 (15b) 0.90 ≦ Fno ≦ 10.0 (16b) [Configuration 1 Utilizing Polarization] With reference to FIG. 1, a configuration (Configuration 1) utilizing polarization will be described. FIG. 1 is a schematic diagram showing the optical path of the optical system in each embodiment. The optical system of this configuration has two transmission-reflection surfaces. Here, the transmission-reflection surface arranged on the magnification side of the optical system of this configuration is configured by arranging a polarization-selective transmission-reflection element (PBS): A. The transmission-reflection surface arranged on the image plane side of the optical system of this configuration is configured by arranging a half mirror (HM): C. Further, a first quarter-wave plate (QWP1): B is arranged between the polarization-selective transmission-reflection element PBS and the half mirror HM. Furthermore, between the half mirror HM and the image plane (imaging plane) IM, in order from the magnification side to the reduction side, a second quarter-wave plate (QWP2): D and a linear polarizer (POL): E are arranged.

[0064] Here, the polarization-selective transmission and reflection element A is an element configured to reflect linearly polarized light polarized in the same direction as when passing through the linear polarizer E and transmit linearly polarized light orthogonal thereto. The polarization-selective transmission and reflection element A is, for example, a wire grid polarizer or a reflective polarizer having a configuration in which retardation films are laminated. At this time, the wire grid formation surface or the retardation film surface of the polarization-selective transmission and reflection element A functions as a transmission and reflection surface. Note that the wire grid polarizer does not necessarily have to have metal wires aligned, and it may have thin metal or dielectric layers at predetermined intervals and function as a polarization-selective transmission and reflection element. For example, an element in which metal or dielectric layers are aligned by vapor deposition can be used.

[0065] Also, the first quarter-wave plate B and the second quarter-wave plate D are arranged such that their slow axes are inclined by 45° with respect to the polarization transmission axis of the linear polarizer E. Here, it is preferable that the first quarter-wave plate B and the second quarter-wave plate D are arranged such that their slow axes are inclined by 90°. According to this arrangement, when light passes through the first quarter-wave plate B and the second quarter-wave plate D, the wavelength dispersion characteristics of the wave plates are canceled out. The half mirror C is, for example, a half mirror formed by a dielectric multilayer film or metal vapor deposition, and the mirror surface of the half mirror C functions as a transmission and reflection surface. The linear polarizer E is, for example, an absorption-type linear polarizer.

[0066] Next, the optical path selection and operation in the polarization utilization configuration will be described. Light incident on the optical system from the magnification side becomes linearly polarized light by the polarization-selective transmission and reflection element A, becomes circularly polarized light by the first quarter-wave plate B, and enters the half mirror C. A part of the light that reaches the half mirror C is reflected and becomes counterclockwise circularly polarized light, and returns to the first quarter-wave plate B.

[0067] The light with counterclockwise circular polarization that has returned to the first quarter-wave plate B becomes linearly polarized light polarized in a direction orthogonal to that when it first passed through the polarization selective transmission reflection element A by the first quarter-wave plate B and returns to the polarization selective transmission reflection element A. The light that has returned to the polarization selective transmission reflection element A is reflected by the polarization selective transmission reflection element A. Here, due to the polarization selectivity of the polarization selective transmission reflection element A, linearly polarized light polarized in a direction orthogonal to that when it first passed through the polarization selective transmission reflection element A is reflected.

[0068] On the other hand, a part of the light that has reached the half mirror C is transmitted and becomes linearly polarized light polarized in the same direction as when it passed through the polarization selective transmission reflection element A by the second quarter-wave plate D, enters the linear polarizer E, and is absorbed by the linear polarizer E.

[0069] The light reflected by the polarization selective transmission reflection element A becomes circularly polarized by the first quarter-wave plate B and enters the half mirror C. A part of the light that has reached the half mirror C is transmitted and enters the second quarter-wave plate D. By the second quarter-wave plate D, the incident light becomes linearly polarized light in a direction parallel to the linearly polarized light reflected by the polarization selective transmission reflection element A. The light that has passed through the second quarter-wave plate D enters the linear polarizer E. Here, since the polarization of the light coincides with the transmission axis of the linear polarizer E, most of the light is transmitted and guided to the image plane IM.

[0070] Due to the above actions, only the light that has passed through the polarization selective transmission reflection element PBS, been reflected by the half mirror C, been reflected by the polarization selective transmission reflection element PBS, and passed through the half mirror C is guided to the image plane IM.

[0071] In addition, when a cholesteric liquid crystal is used instead of the half mirror C, it is preferable to install the cholesteric liquid crystal so that it greatly reflects the polarization of the circular polarization in the direction of the incident light during the first reflection of the cholesteric liquid crystal. By doing so, it is possible to increase the amount of light in the normal optical path while reducing ghost light.

[0072] In addition, solid-state imaging devices, CCDs (Charge Coupled Devices), etc. that can be used as the image plane IM generally have a high surface reflectance. In this configuration, the light reflected by the image plane IM passes through the linear polarizer E again and is converted into circular polarization by the second quarter-wave plate D. Then, the light emerging from the second quarter-wave plate D is reflected by the half mirror C to become circular polarization in the reverse direction and passes through the second quarter-wave plate D again. At this time, the circular polarization is converted into linear polarization in a direction perpendicular to that immediately after passing through the linear polarizer E by the second quarter-wave plate D. Since the direction of this linear polarization is orthogonal to the transmission axis of the linear polarizer E, most of the light is absorbed by the linear polarizer E. Thus, in this configuration, the light reflected in sequence by the image plane IM and the half mirror C is almost cut off, so that ghosts and flares related to the image plane IM are less noticeable. Note that in order to obtain such a reflection reduction effect, it is preferable that an optical low-pass filter using birefringence does not exist between the image plane IM and the linear polarizer plate. This is because the polarization state deviates from the desired polarization state due to the optical low-pass filter.

[0073] Also, in this configuration, a quarter-wave plate may be disposed between the polarization selective transmission and reflection element A and the object. At this time, it is arranged such that the angle formed by the fast axis or slow axis of the quarter-wave plate and the transmission axis of the polarization selective transmission and reflection element A is 45°. By doing so, even if the light incident from the magnification side is linearly polarized, imaging can be performed regardless of the polarization direction. Also, a depolarizing element may be disposed instead of the quarter-wave plate. As the depolarizing element, for example, "Cosmo Shine SRF" of Toyobo Co., Ltd. can be used.

[0074] [Configuration 2 Utilizing Polarization] Referring to FIG. 2, a configuration using polarization (Configuration 2) will be described. FIG. 2 is a schematic diagram showing the optical path of the optical system in each embodiment. The optical system of this configuration has two transmissive and reflective surfaces. Here, the transmissive and reflective surface arranged on the magnifying side of the optical system of this configuration is configured by arranging a half mirror (HM): C. The transmissive and reflective surface arranged on the image plane side of the optical system of this configuration is configured by arranging a polarization selective transmissive and reflective element (PBS): A. Further, a first quarter-wave plate (QWP1): B is arranged between the polarization selective transmissive and reflective element PBS and the half mirror HM. Furthermore, between the half mirror HM and the object plane, a linear polarizer (POL): E and a second quarter-wave plate (QWP2): D are arranged in order from the magnifying side to the reducing side. Here, the configuration of each polarization element and the preferred arrangement of the optical axis orientation are the same as those of Configuration 1 using polarization.

[0075] Next, the optical path selection and operation in the polarization utilization configuration will be described. The light incident on the optical system from the magnifying side becomes linearly polarized by the linear polarizer E, becomes circularly polarized by the second quarter-wave plate D, and is incident on the half mirror C. A part of the light that reaches the half mirror C is reflected and becomes counterclockwise circularly polarized, and returns to the second quarter-wave plate D. The light that reaches the half mirror C and is reflected becomes circularly polarized in the opposite direction to the incident direction. This light becomes linearly polarized in a direction orthogonal to that when passing through the linear polarizer E by the second quarter-wave plate D, is incident on the linear polarizer E, and is absorbed by the linear polarizer E.

[0076] On the other hand, the light transmitted through the half mirror C becomes linearly polarized in the same direction as immediately after passing through the linear polarizer E by the first quarter-wave plate B. This linearly polarized light is reflected by the polarization selective transmissive and reflective element A and returns to the first quarter-wave plate B. Thereafter, the light is converted into circularly polarized light by the first quarter-wave plate B, and a part of it is reflected by the half mirror C. The light reflected by the half mirror C is incident on the first quarter-wave plate B again and is converted into linearly polarized light whose polarization direction is orthogonal to that when reflected by the polarization selective transmissive and reflective element A. This linearly polarized light passes through the polarization selective transmissive and reflective element A and is guided to the image plane IM.

[0077] Due to the above actions, only the light that passes through the half mirror C, is reflected by the polarization selective transmission and reflection element PBS, is reflected by the half mirror C, and then passes through the polarization selective transmission and reflection element PBS is guided to the image plane IM.

[0078] In this arrangement, a linear polarizer A' may be arranged between the polarization selective transmission and reflection element A and the image plane IM. At this time, the transmission axes of the linear polarizer A' and the polarization selective transmission and reflection element A are made to coincide. By doing so, it is possible to absorb the light that is reflected at the image plane IM, reflected by the polarization selective transmission and reflection element A, and then incident on the image plane IM again to become ghost flare.

[0079] Also, in this configuration, a quarter-wave plate may be arranged between the linear polarizing plate E and the object. At this time, it is arranged such that the angle formed by the fast axis or slow axis of the quarter-wave plate and the transmission axis of the linear polarizing plate E is 45°. By doing so, even if the light incident from the magnification side is linearly polarized, imaging can be performed regardless of the polarization direction. Also, a depolarizing element may be arranged instead of the quarter-wave plate. As the depolarizing element, for example, "Cosmo Shine SRF" of Toyobo Co., Ltd. can be used.

[0080] In the description of the above configuration, terms such as orthogonal, parallel, and 45° are used, but these do not necessarily have to be exactly 90°, 0°, and 45°. However, these should be within ±5° from the desired angle, more preferably within ±2°, and even more preferably within ±1°.

[0081] In the optical system of each embodiment, as the constituent material of the lens, either a polymer material or a glass material may be used. However, for the lens arranged between the first transmission and reflection surface and the second transmission and reflection surface, it is preferably of low birefringence.

[0082] [Configuration 3 Utilizing Polarization] Referring to FIG. 3, the configuration using polarization (Configuration 3) will be described. FIG. 3 is a schematic diagram showing the optical path of the optical system in each embodiment. This configuration assumes a configuration in which a light source panel is arranged instead of an image sensor on the image plane IM, and is an optical system that projects the light from the light source panel to the magnification side. The image plane IM is the panel surface of a light-emitting panel such as an LCOS (Liquid Crystal On Silicon) panel or a DMD (Digital Micromirror Device) panel. The configuration in FIG. 3 is the same as the configuration in FIG. 1, but the direction in which the light passes is reversed.

[0083] The optical system of this configuration has two transmissive-reflective surfaces. Here, the transmissive-reflective surface arranged on the magnification side of the optical system of this configuration is configured by arranging a polarization-selective transmissive-reflective element (PBS): A. The transmissive-reflective surface arranged on the image plane side of the optical system of this configuration is configured by arranging a half mirror (HM): C. Also, a first quarter-wave plate (QWP1): B is arranged between the polarization-selective transmissive-reflective element PBS and the half mirror HM. Further, between the half mirror HM and the image plane IM, in order from the magnification side to the reduction side, a second quarter-wave plate (QWP2): D and a linear polarizer (POL): E are arranged.

[0084] Here, the polarization-selective transmissive-reflective element A is an element configured to reflect linearly polarized light polarized in the same direction as when passing through the linear polarizer E and transmit linearly polarized light orthogonal to this. The polarization-selective transmissive-reflective element A is, for example, a wire grid polarizer or a reflective polarizer having a retardation film laminated structure. At this time, the wire grid formation surface or the retardation film surface of the polarization-selective transmissive-reflective element A functions as the transmissive-reflective surface. Note that the wire grid polarizer does not necessarily have to have metal wires aligned, and it may have thin metal or dielectric layers at a predetermined interval and function as a polarization-selective transmissive-reflective element. For example, an element in which metal or dielectric layers are aligned by vapor deposition can be used.

[0085] Further, the first quarter-wave plate B and the second quarter-wave plate D are arranged such that their slow axes are inclined by 45° with respect to the polarization transmission axis of the linear polarizer E. Here, it is preferable that the first quarter-wave plate B and the second quarter-wave plate D are arranged such that their slow axes are inclined by 90°. According to this arrangement, when light passes through the first quarter-wave plate B and the second quarter-wave plate D, the wavelength dispersion characteristics of the wave plates cancel each other out.

[0086] Also, the half mirror C is, for example, a half mirror formed by a dielectric multilayer film or metal evaporation, and the mirror surface of the half mirror C functions as a transmission reflection surface. The linear polarizer E is, for example, an absorption type linear polarizer.

[0087] Next, the optical path selection and operation in the polarization utilization configuration will be described. The image plane IM is the panel surface of a light-emitting panel such as an LCOS panel or a DMD panel, and uses the light reflected by the laser light source on the panel surface. Since the deflection directions of the laser light rays are aligned, light with aligned polarization is emitted from the image plane IM which is the panel surface.

[0088] The linearly polarized light emitted from the image plane IM passes through the linear polarizer E and is transmitted as linearly polarized light. The light transmitted as linearly polarized light becomes circularly polarized by the second quarter-wave plate D and enters the half mirror C. A part of the light that reaches the half mirror C is transmitted, becomes linearly polarized by the first quarter-wave plate B, is reflected by the polarization selective transmission reflection element PBS, becomes circularly polarized again by the first quarter-wave plate B, and enters the half mirror C. A part of the light that reaches the half mirror C is reflected and becomes counterclockwise circularly polarized light, and returns to the first quarter-wave plate B. The counterclockwise circularly polarized light that returns to the first quarter-wave plate B becomes linearly polarized by the first quarter-wave plate B, passes through the polarization selective transmission reflection element A, and is emitted to the expansion side in a linearly polarized state. On the other hand, a part of the light that reaches the half mirror C is reflected and becomes counterclockwise circularly polarized light, is converted into linearly polarized light by the second quarter-wave plate D, enters the linear polarizer E, and is absorbed by the linear polarizer E.

[0089] Due to the above actions, the light emitted from the image plane IM is reflected by the polarization selective transmission and reflection element PBS, reflected by the half mirror C, and guided to the subject. When a cholesteric liquid crystal is used instead of the half mirror C, it is preferable to arrange the cholesteric liquid crystal so that the polarization of the circularly polarized light in the incident light direction is largely reflected during the first reflection of the cholesteric liquid crystal. By doing so, it is possible to increase the amount of light in the normal optical path while reducing ghost light.

[0090] Hereinafter, the configuration of the optical system in each embodiment will be described.

[0091] (Example 1) First, the optical system 100 in Example 1 will be described. FIG. 4 is a cross-sectional view of the optical system 100 at infinity focus. The optical system 100 includes a diaphragm (aperture diaphragm) SP, a first positive lens (first lens) 101, and a second negative lens (second lens) 102 arranged in order from the magnification side to the reduction side. The optical system 100 also includes a third lens 103 having a first transmission and reflection surface HM1 and a second transmission and reflection surface HM2 arranged in order from the magnification side to the reduction side, and members G such as a glass block such as a prism and a sensor protection glass. The third lens 103 includes a quarter-wave plate QWP on the reduction side of the first transmission and reflection surface HM1.

[0092] The first positive lens 101, the second negative lens 102, and the third lens 103 constitute a focusing group f. Focusing is performed by integrally moving each lens constituting the focusing group f in the optical axis direction. Ry1 is an on-axis ray, and Ry2 is the most off-axis ray. The optical system 100 is configured to guide the on-axis ray Ry1 to the image plane IM.

[0093] FIG. 5 is an aberration diagram of the optical system 100 at infinity focus. In the spherical aberration diagram, Fno is the F-number, indicating the amount of spherical aberration with respect to the d-line (wavelength 587.6 nm) and the g-line (wavelength 435.8 nm). In the astigmatism diagram, S indicates the amount of astigmatism on the sagittal image plane, and M indicates the amount of astigmatism on the meridional image plane. In the distortion aberration diagram, it indicates the amount of distortion aberration with respect to the d-line. In the chromatic aberration diagram, it indicates the amount of chromatic aberration at the g-line. ω is the semi-field angle (degrees).

[0094] When the optical system 100 is used as a projection optical system (an optical system used in a projection apparatus), the enlarged side is the projection side, and the reduced side is the light source panel side. When the optical system 100 is used as an imaging optical system, the enlarged side is the object side, and the reduced side is the image side.

[0095] (Example 2) Next, the optical system 200 in Example 2 will be described. FIG. 6 is a cross-sectional view of the optical system 200 at infinity focus. The optical system 200 includes an aperture stop (aperture diaphragm) SP, a first positive lens (first lens) 201, and a second negative lens (second lens) 202, which are arranged in order from the enlarged side to the reduced side. The optical system 200 also includes a third lens 203 having a first transmissive reflection surface HM1 and a second transmissive reflection surface HM2, which are arranged in order from the enlarged side to the reduced side, and members G such as a glass block like a prism and a sensor protection glass. The third lens 203 is provided with a quarter-wave plate QWP on the reduced side of the first transmissive reflection surface HM1. The first positive lens 201, the second negative lens 202, and the third lens 203 constitute a focusing group f. Focusing is performed by integrally moving each lens constituting the focusing group f in the optical axis direction. Ry1 is the on-axis ray, and Ry2 is the outermost off-axis ray. The optical system 200 is configured to guide the on-axis ray Ry1 to the image plane IM.

[0096] FIG. 7 is an aberration diagram of the optical system 200 at infinite focus. In the spherical aberration diagram, Fno is the F number, and it shows the spherical aberration amounts for the d line (wavelength 587.6 nm) and the g line (wavelength 435.8 nm). In the astigmatism diagram, S shows the astigmatism amount on the sagittal image plane, and M shows the astigmatism amount on the meridional image plane. In the distortion aberration diagram, it shows the distortion aberration amount for the d line. In the chromatic aberration diagram, it shows the chromatic aberration amount for the g line. ω is the semi-field angle (degrees).

[0097] When the optical system 200 is used as a projection optical system, the magnifying side is the projection side, and the reducing side is the light source panel side. When the optical system 200 is used as an imaging optical system, the magnifying side is the object side, and the reducing side is the image side.

[0098] (Example 3) Next, the optical system 300 in Example 3 will be described. FIG. 8 is a cross-sectional view of the optical system 300 at infinite focus. The optical system 300 includes, in order from the magnifying side to the reducing side, a first negative lens 301, a second positive lens 302, an aperture stop (iris diaphragm) SP, a third positive lens 303, and a fourth negative lens 304. The optical system 300 also includes a fifth lens 305 having a first transmissive reflection surface HM1 and a second transmissive reflection surface HM2 arranged in order from the magnifying side to the reducing side, and members G such as a glass block like a prism and a sensor protection glass. The fifth lens 305 is provided with a quarter-wave plate QWP on the reducing side of the first transmissive reflection surface HM1. The first negative lens 301, the second positive lens 302, the third positive lens 303, the fourth negative lens 304, and the fifth lens 305 constitute a focusing group f. Focusing is performed by moving each lens constituting the focusing group f integrally in the optical axis direction. Ry1 is the on-axis ray, and Ry2 is the outermost off-axis ray. The optical system 300 is configured to guide the on-axis ray Ry1 to the image plane IM.

[0099] In this embodiment, the first lens is one of a first negative lens 301, a second positive lens 302, or a third positive lens 303. The second lens is one of a second positive lens 302, a third positive lens 303, or a fourth negative lens 304, which is arranged on the reduction side with respect to the first lens.

[0100] FIG. 9 is an aberration diagram of the optical system 300 at infinity focus. In the spherical aberration diagram, Fno is the F number, and it shows the amount of spherical aberration with respect to the d line (wavelength 587.6 nm) and the g line (wavelength 435.8 nm). In the astigmatism diagram, S shows the amount of astigmatism on the sagittal image plane, and M shows the amount of astigmatism on the meridional image plane. In the distortion aberration diagram, it shows the amount of distortion aberration with respect to the d line. In the chromatic aberration diagram, it shows the amount of chromatic aberration at the g line. ω is the semi-field angle (degrees).

[0101] When the optical system 300 is used as a projection optical system, the enlargement side is the projection side, and the reduction side is the light source panel side. When the optical system 300 is used as an imaging optical system, the enlargement side is the object side, and the reduction side is the image side.

[0102] (Example 4) Next, the optical system 400 in Example 4 will be described. FIG. 10 is a cross-sectional view of the optical system 400 at infinity focus. The optical system 400 includes a first negative lens 401, a second positive lens 402, an aperture stop (iris diaphragm) SP, a third positive lens 403, and a fourth negative lens 404, which are arranged in order from the magnification side to the reduction side. The optical system 400 also includes a fifth lens 405 having a first transmissive reflecting surface HM1 and a second transmissive reflecting surface HM2, which are arranged in order from the magnification side to the reduction side, and members G such as a glass block like a prism and a sensor protection glass. The fifth lens 405 includes a quarter-wave plate QWP on the reduction side of the first transmissive reflecting surface HM1. The first negative lens 401, the second positive lens 402, the third positive lens 403, the fourth negative lens 404, and the fifth lens 405 constitute a focusing group f. Focusing is performed by integrally moving each lens constituting the focusing group f in the optical axis direction. Ry1 is an on-axis ray, and Ry2 is the outermost off-axis ray. The optical system 400 is configured to guide the on-axis ray Ry1 to the image plane IM.

[0103] In this embodiment, the first lens is one of the first negative lens 401, the second positive lens 402, and the third positive lens 403. The second lens is one of the second positive lens 402, the third positive lens 403, and the fourth negative lens 404, which is arranged on the reduction side of the first lens.

[0104] FIG. 11 is an aberration diagram of the optical system 400 at infinity focus. In the spherical aberration diagram, Fno is the F-number, and it shows the spherical aberration amounts for the d-line (wavelength 587.6 nm) and the g-line (wavelength 435.8 nm). In the astigmatism diagram, S shows the astigmatism amount at the sagittal image plane, and M shows the astigmatism amount at the meridional image plane. In the distortion aberration diagram, it shows the distortion aberration amount for the d-line. In the chromatic aberration diagram, it shows the chromatic aberration amount for the g-line. ω is the semi-field angle (degrees).

[0105] When the optical system 400 is used as a projection optical system, the magnifying side is the projection side and the reducing side is the light source panel side. When the optical system 400 is used as an imaging optical system, the magnifying side is the object side and the reducing side is the image side.

[0106] (Example 5) Next, the optical system 500 in Example 5 will be described. FIG. 12 is a cross-sectional view of the optical system 500 at infinity focus. The optical system 500 includes a first negative lens 501, a second positive lens 502, an aperture stop (iris diaphragm) SP, a third positive lens 503, and a fourth negative lens 504, which are arranged in order from the magnifying side to the reducing side. The optical system 500 also includes a fifth lens 505 having a first transmissive-reflective surface HM1 and a second transmissive-reflective surface HM2, which are arranged in order from the magnifying side to the reducing side, and members G such as a glass block like a prism and a sensor protection glass. The fifth lens 505 is provided with a quarter-wave plate QWP on the reducing side of the first transmissive-reflective surface HM1. The first negative lens 501, the second positive lens 502, the third positive lens 503, the fourth negative lens 504, and the fifth lens 505 constitute a focusing group f. Focusing is performed by moving each lens constituting the focusing group f integrally in the optical axis direction. Ry1 is an on-axis ray, and Ry2 is the most off-axis ray. The optical system 500 is configured to guide the on-axis ray Ry1 to the image plane IM.

[0107] In this example, the first lens is one of the first negative lens 501, the second positive lens 502, and the third positive lens 503. The second lens is one of the second positive lens 502, the third positive lens 503, and the fourth negative lens 504, which is arranged on the reducing side of the first lens.

[0108] FIG. 13 is an aberration diagram of the optical system 500 at infinity focus. In the spherical aberration diagram, Fno is the F number, and it shows the amount of spherical aberration with respect to the d line (wavelength 587.6 nm) and the g line (wavelength 435.8 nm). In the astigmatism diagram, S represents the amount of astigmatism on the sagittal image plane, and M represents the amount of astigmatism on the meridional image plane. In the distortion aberration diagram, it shows the amount of distortion aberration with respect to the d line. In the chromatic aberration diagram, it shows the amount of chromatic aberration at the g line. ω is the semi-field angle (degrees).

[0109] When the optical system 500 is used as a projection optical system, the enlarged side is the projection side, and the reduced side is the light source panel side. When the optical system 500 is used as an imaging optical system, the enlarged side is the object side, and the reduced side is the image side.

[0110] (Example 6) Next, the optical system 600 in Example 6 will be described. FIG. 14 is a cross-sectional view of the optical system 600 at infinity focus. The optical system 600 includes a first negative lens 601, a second positive lens 602, an aperture stop (iris diaphragm) SP, a third positive lens 603, and a fourth negative lens 604, which are arranged in order from the enlarged side to the reduced side. The optical system 600 also includes a fifth lens 605 having a first transmissive-reflective surface HM1 and a second transmissive-reflective surface HM2, which are arranged in order from the enlarged side to the reduced side, and members G such as a glass block like a prism and a sensor protection glass. The fifth lens 605 is provided with a quarter-wave plate QWP on the reduced side of the first transmissive-reflective surface HM1. The first negative lens 601, the second positive lens 602, the third positive lens 603, the fourth negative lens 604, and the fifth lens 605 constitute a focusing group f. Focusing is performed by moving each lens constituting the focusing group f integrally in the optical axis direction. Ry1 is the on-axis ray, and Ry2 is the most off-axis ray. The optical system 600 is configured to guide the on-axis ray Ry1 to the image plane IM.

[0111] In this embodiment, the first lens is one of the first negative lens 601, the second positive lens 602, and the third positive lens 603. The second lens is one of the second positive lens 602, the third positive lens 603, and the fourth negative lens 604, which is arranged on the reduction side with respect to the first lens.

[0112] FIG. 15 is an aberration diagram of the optical system 600 at infinity focus. In the spherical aberration diagram, Fno is the F-number, and it shows the amount of spherical aberration with respect to the d-line (wavelength 587.6 nm) and the g-line (wavelength 435.8 nm). In the astigmatism diagram, S shows the amount of astigmatism on the sagittal image plane, and M shows the amount of astigmatism on the meridional image plane. In the distortion aberration diagram, it shows the amount of distortion aberration with respect to the d-line. In the chromatic aberration diagram, it shows the amount of chromatic aberration at the g-line. ω is the semi-field angle (degrees).

[0113] When the optical system 600 is used as a projection optical system, the enlargement side is the projection side, and the reduction side is the light source panel side. When the optical system 600 is used as an imaging optical system, the enlargement side is the object side, and the reduction side is the image side.

[0114] (Example 7) Next, the optical system 700 in Example 7 will be described. FIG. 16 is a cross-sectional view of the optical system 700 at infinity focus. The optical system 700 includes an aperture stop (iris diaphragm) SP, a first positive lens (first lens) 701, and a second negative lens (second lens) 702, which are arranged in order from the enlargement side to the reduction side. The optical system 700 also includes a third lens 703 having a first transmissive-reflective surface HM1 and a second transmissive-reflective surface HM2, which are arranged in order from the enlargement side to the reduction side, and members G such as a glass block like a prism and a sensor protection glass. The third lens 703 is provided with a quarter-wave plate QWP on the reduction side of the first transmissive-reflective surface HM1. Ry1 is the on-axis ray, and Ry2 is the outermost off-axis ray. The optical system 700 is configured to guide the on-axis ray Ry1 to the image plane IM.

[0115] The focusing group f is composed of a first positive lens 701, a second negative lens 702, and a third lens 703. Focusing is performed by moving each lens constituting the focusing group f integrally in the optical axis direction.

[0116] FIG. 17 is an aberration diagram of the optical system 700 at infinity focus. In the spherical aberration diagram, Fno is the F-number, and it shows the amount of spherical aberration with respect to the d-line (wavelength 587.6 nm) and the g-line (wavelength 435.8 nm). In the astigmatism diagram, S shows the amount of astigmatism on the sagittal image plane, and M shows the amount of astigmatism on the meridional image plane. In the distortion aberration diagram, it shows the amount of distortion aberration with respect to the d-line. In the chromatic aberration diagram, it shows the amount of chromatic aberration at the g-line. ω is the semi-field angle (degrees).

[0117] When the optical system 700 is used as a projection optical system, the enlarged side is the projection side, and the reduced side is the light source panel side. When the optical system 700 is used as an imaging optical system, the enlarged side is the object side, and the reduced side is the image side.

[0118] (Example 8) Next, the optical system 800 in Example 8 will be described. FIG. 18 is a cross-sectional view of the optical system 800 at infinity focus. The optical system 800 includes a first positive lens 801, an aperture stop (aperture diaphragm) SP, a second positive lens 802, and a third negative lens 803, which are arranged in order from the enlarged side to the reduced side. The optical system 800 also includes a fourth lens 804 having a first transmissive reflection surface HM1 and a second transmissive reflection surface HM2, which are arranged in order from the enlarged side to the reduced side, and members G such as a glass block like a prism and a sensor protection glass. The fourth lens 804 is provided with a quarter-wave plate QWP on the reduced side of the first transmissive reflection surface HM1. The focusing group f is composed of the first positive lens 801, the second positive lens 802, the third negative lens 803, and the fourth lens 804. Focusing is performed by moving each lens constituting the focusing group f integrally in the optical axis direction. Ry1 is the on-axis ray, and Ry2 is the most off-axis ray. The optical system 800 is configured to guide the on-axis ray Ry1 to the image plane IM.

[0119] In this embodiment, the first lens is one of the first positive lens 801 or the second positive lens 802. The second lens is one of the second positive lens 802 or the third negative lens 803, which is arranged on the reduction side relative to the first lens.

[0120] FIG. 19 is an aberration diagram when the optical system 800 is focused at infinity. In the spherical aberration diagram, Fno is the F-number, showing the amount of spherical aberration with respect to the d-line (wavelength 587.6 nm) and the g-line (wavelength 435.8 nm). In the astigmatism diagram, S represents the amount of astigmatism on the sagittal image plane, and M represents the amount of astigmatism on the meridional image plane. In the distortion diagram, it shows the amount of distortion with respect to the d-line. In the chromatic aberration diagram, it shows the amount of chromatic aberration at the g-line. ω is the semi-field angle (degrees).

[0121] When the optical system 800 is used as a projection optical system, the enlargement side is the projection side, and the reduction side is the light source panel side. When the optical system 800 is used as an imaging optical system, the enlargement side is the object side, and the reduction side is the image side.

[0122] (Example 9) Next, the optical system 900 in Example 9 will be described. FIG. 20 is a cross-sectional view of the optical system 900 at infinity focus. The optical system 900 has a cemented lens formed by cementing a first positive lens 901, an aperture stop (iris diaphragm) SP, a second positive lens 902, and a third negative lens 903, which are arranged in order from the magnification side to the reduction side. The optical system 900 also includes a fourth lens 904 having a first transmissive-reflective surface HM1 and a second transmissive-reflective surface HM2, which are arranged in order from the magnification side to the reduction side, and members G such as a glass block like a prism and a sensor protection glass. The fourth lens 904 is provided with a quarter-wave plate QWP on the reduction side of the first transmissive-reflective surface HM1. The first positive lens 901, the second positive lens 902, the third negative lens 903, and the fourth lens 904 constitute a focusing group f. Focusing is performed by integrally moving each lens constituting the focusing group f in the optical axis direction. Ry1 is an on-axis ray, and Ry2 is the most off-axis ray. The optical system 900 is configured to guide the on-axis ray Ry1 to the image plane IM. e is a flare cut diaphragm for cutting unnecessary light.

[0123] In this embodiment, the first lens is one of the first positive lens 901 or the second positive lens 902. The second lens is one of the second positive lens 902 or the third negative lens 903, which is arranged on the reduction side of the first lens.

[0124] FIG. 21 is an aberration diagram of the optical system 900 at infinity focus. In the spherical aberration diagram, Fno is the F-number, and it shows the spherical aberration amount for the d-line (wavelength 587.6 nm) and the g-line (wavelength 435.8 nm). In the astigmatism diagram, S shows the astigmatism amount at the sagittal image plane, and M shows the astigmatism amount at the meridional image plane. In the distortion aberration diagram, it shows the distortion aberration amount for the d-line. In the chromatic aberration diagram, it shows the chromatic aberration amount for the g-line. ω is the semi-field angle (degrees).

[0125] When the optical system 900 is used as a projection optical system, the magnifying side is the projection side and the reducing side is the light source panel side. When the optical system 900 is used as an imaging optical system, the magnifying side is the object side and the reducing side is the image side.

[0126] (Example 10) Next, the optical system 1000 in Example 10 will be described. FIG. 22 is a cross-sectional view of the optical system 1000 at infinity focus. The optical system 1000 includes a first positive lens (first lens) 1001, an aperture stop (open aperture) SP, and a second negative lens (second lens) 1002, which are arranged in order from the magnifying side to the reducing side. The optical system 1000 also includes a third lens 1003 having a first transmissive reflection surface HM1 and a second transmissive reflection surface HM2, which are arranged in order from the magnifying side to the reducing side, and members G such as a glass block like a prism and a sensor protection glass. The third lens 1003 is provided with a quarter-wave plate QWP on the reducing side of the first transmissive reflection surface HM1. The first positive lens 701, the second negative lens 702, and the third lens 703 constitute a focusing group f. Focusing is performed by integrally moving each lens constituting the focusing group f in the optical axis direction. Ry1 is an on-axis ray, and Ry2 is the most off-axis ray. The optical system 1000 is configured to guide the on-axis ray Ry1 to the image plane IM. e is a flare cut aperture for cutting unnecessary light.

[0127] FIG. 23 is an aberration diagram of the optical system 1000 at infinity focus. In the spherical aberration diagram, Fno is the F-number, and it shows the amount of spherical aberration with respect to the d-line (wavelength 587.6 nm) and the g-line (wavelength 435.8 nm). In the astigmatism diagram, S shows the amount of astigmatism in the sagittal image plane, and M shows the amount of astigmatism in the meridional image plane. In the distortion aberration diagram, it shows the amount of distortion aberration with respect to the d-line. In the chromatic aberration diagram, it shows the amount of chromatic aberration in the g-line. ω is the semi-field angle (degrees).

[0128] When the optical system 1000 is used as a projection optical system, the magnifying side is the projection side, and the reducing side is the light source panel side. When the optical system 1000 is used as an imaging optical system, the magnifying side is the object side, and the reducing side is the image side.

[0129] (Example 11) Next, the optical system 1100 in Example 11 will be described. FIG. 24 is a cross-sectional view of the optical system 1100 at infinity focus. The optical system 1100 includes an aperture stop (iris diaphragm) SP, a first positive lens (first lens) 1101, and a second negative lens (second lens) 1102, which are arranged in order from the magnifying side to the reducing side. The optical system 1100 also includes a third lens 1103 having a first transmissive-reflective surface HM1 and a second transmissive-reflective surface HM2, which are arranged in order from the magnifying side to the reducing side, and members G such as a glass block like a prism and a sensor protection glass. The third lens 1103 is provided with a quarter-wave plate QWP on the reducing side of the first transmissive-reflective surface HM1. The first positive lens 1101, the second negative lens 1102, and the third lens 1103 constitute a focusing group f. Focusing is performed by integrally moving each lens constituting the focusing group f in the optical axis direction. Ry1 is an on-axis ray, and Ry2 is the most off-axis ray. The optical system 1100 is configured to guide the on-axis ray Ry1 to the image plane IM.

[0130] FIG. 25 is an aberration diagram of the optical system 1100 at infinity focus. In the spherical aberration diagram, Fno is the F-number, and it shows the amount of spherical aberration with respect to the d-line (wavelength 587.6 nm) and the g-line (wavelength 435.8 nm). In the astigmatism diagram, S shows the amount of astigmatism on the sagittal image plane, and M shows the amount of astigmatism on the meridional image plane. In the distortion aberration diagram, it shows the amount of distortion aberration with respect to the d-line. In the chromatic aberration diagram, it shows the amount of chromatic aberration at the g-line. ω is the semi-field angle (degrees).

[0131] When the optical system 1100 is used as a projection optical system, the magnifying side is the projection side, and the reducing side is the light source panel side. When the optical system 1100 is used as an imaging optical system, the magnifying side is the object side, and the reducing side is the image side.

[0132] (Example 12) Next, the optical system 1200 in Example 12 will be described. FIG. 26 is a cross-sectional view of the optical system 1200 at infinity focus. The optical system 1200 includes a first positive lens (first lens) 1201, an aperture stop (aperture diaphragm) SP, and a second negative lens (second lens) 1202, which are arranged in order from the magnifying side to the reducing side. The optical system 1200 also includes a third lens 1203 having a first transmissive-reflective surface HM1 and a second transmissive-reflective surface HM2, which are arranged in order from the magnifying side to the reducing side, and members G such as a glass block like a prism and a sensor protection glass. The third lens 1203 is provided with a quarter-wave plate QWP on the reducing side of the first transmissive-reflective surface HM1. The first positive lens 1201, the second negative lens 1202, and the third lens 1203 constitute a focusing group f. Focusing is performed by integrally moving each lens constituting the focusing group f in the optical axis direction. Ry1 is an on-axis ray, and Ry2 is the most off-axis ray. The optical system 1200 is configured to guide the on-axis ray Ry1 to the image plane IM. e is a flare cut diaphragm for cutting unnecessary light.

[0133] FIG. 27 is an aberration diagram of the optical system 1200 at infinity focus. In the spherical aberration diagram, Fno is the F-number, and it shows the amount of spherical aberration with respect to the d-line (wavelength 587.6 nm) and the g-line (wavelength 435.8 nm). In the astigmatism diagram, S shows the amount of astigmatism in the sagittal image plane, and M shows the amount of astigmatism in the meridional image plane. In the distortion aberration diagram, it shows the amount of distortion aberration with respect to the d-line. In the chromatic aberration diagram, it shows the amount of chromatic aberration in the g-line. ω is the semi-field angle (degrees).

[0134] When the optical system 1200 is used as a projection optical system, the magnifying side is the projection side, and the reducing side is the light source panel side. When the optical system 1200 is used as an imaging optical system, the magnifying side is the object side, and the reducing side is the image side.

[0135] (Example 13) Next, the optical system 1300 in Example 13 will be described. FIG. 28 is a cross-sectional view of the optical system 1300 when focused at infinity. The optical system 1300 has an aperture stop (iris diaphragm) SP, and a cemented lens formed by cementing a first positive lens (first lens) 1301 and a second negative lens (second lens) 1302, which are arranged in order from the magnification side to the reduction side. The optical system 1300 also includes a third lens 1303 having a first transmissive-reflective surface HM1 and a second transmissive-reflective surface HM2, which are arranged in order from the magnification side to the reduction side, and members G such as a glass block like a prism and a sensor protection glass. The third lens 1303 is provided with a quarter-wave plate QWP on the reduction side of the first transmissive-reflective surface HM1. The first positive lens 1301, the second negative lens 1302, and the third lens 1303 constitute a focusing group f. Focusing is performed by integrally moving each lens constituting the focusing group f in the optical axis direction. Ry1 is an on-axis ray, and Ry2 is the most off-axis ray. The optical system 1300 is configured to guide the on-axis ray Ry1 to the image plane IM.

[0136] FIG. 29 is an aberration diagram of the optical system 1300 when focused at infinity. In the spherical aberration diagram, Fno is the F-number, and it shows the amount of spherical aberration with respect to the d-line (wavelength 587.6 nm) and the g-line (wavelength 435.8 nm). In the astigmatism diagram, S shows the amount of astigmatism in the sagittal image plane, and M shows the amount of astigmatism in the meridional image plane. In the distortion diagram, it shows the amount of distortion with respect to the d-line. In the chromatic aberration diagram, it shows the amount of chromatic aberration in the g-line. ω is the semi-field angle (degrees).

[0137] When the optical system 1300 is used as a projection optical system, the magnification side is the projection side, and the reduction side is the light source panel side. When the optical system 1300 is used as an imaging optical system, the magnification side is the object side, and the reduction side is the image side.

[0138] The numerical Examples 1 to 13 corresponding to Examples 1 to 13 are shown below. In the surface data of each numerical example, r represents the radius of curvature of each optical surface, and d (mm) represents the axial interval (distance on the optical axis) between the m-th surface and the (m + 1)-th surface. Here, m is the surface number counted from the light incident side. Also, nd represents the refractive index with respect to the d-line of each optical member, and νd represents the Abbe number with respect to the d-line of the optical member. The Abbe number νd of a certain material is calculated as follows when the refractive indices at the d-line (587.6 nm), F-line (486.1 nm), and C-line (656.3 nm) of the Fraunhofer lines are Nd, NF, and NC: νd=(Nd-1) / (NF-NC) which is expressed as

[0139] Note that in each numerical example, d, focal length (mm), F-number, and half angle (degrees) are all values when the optical system of each example is focused on an infinitely distant object. "Back focus" is the distance on the optical axis from the final surface of the lens (the lens surface on the most reduced side) to the paraxial image plane, expressed in terms of the air equivalent length. "Total lens length" is the length obtained by adding the back focus, which is the distance on the optical axis from the frontmost surface (the lens surface on the most enlarged side) to the final surface of the optical system, converted to air equivalent. "Lens group" includes not only cases composed of multiple lenses but also cases composed of a single lens.

[0140] Also, when the optical surface is an aspherical surface, an asterisk "*" is attached to the right side of the surface number. The aspherical shape is expressed by the following formula when X is the displacement amount from the vertex of the surface in the optical axis direction, h is the height from the optical axis in the direction perpendicular to the optical axis, R is the paraxial radius of curvature, K is the conic constant, and A4, A6, A8, and A10 are the aspherical coefficients of each order:

[0141] X=(h 2 / R) / [1+{1-(1+K)(h / R) 2} 1 / 2 +A4×h 4 +A6×h 6 +A8×h 8 +A10×h 10 Note that "e±XX" in each aspherical coefficient means "×10 ±XXIt means "」".

[0142] Also, regarding the effective diameter, it is described for the first transmission - reflection surface and the second transmission - reflection surface. These transmission - reflection surfaces act on light rays multiple times, and the diameter with the largest effective diameter among them is described.

[0143] (Numerical Example 1) Unit: mm Surface data Surface number r d nd νd Effective diameter 1 (Aperture) ∞ 0.50 1.05 2* 4.813 0.62 1.53160 55.8 1.74 3* 7.689 0.33 2.01 4* 5.105 0.50 1.63550 23.9 2.17 5* 3.437 0.18 2.72 6* 6.082 2.12 1.53160 55.8 7.30 7* 5.328 -2.12 6.40 8* 6.082 2.12 7.30 9* 5.328 1.86 6.40 10 ∞ 3.00 1.51633 64.1 6.32 11 ∞ 1.00 6.49 Image plane ∞ Aspherical data The second surface K = 0.00000e+00 A 4= 1.59298e - 03 A 6= 1.44166e - 02 The third surface K = 0.00000e+00 A 4=-7.33771e - 02 A 6= 2.56412e - 02 The fourth surface K = 0.00000e+00 A 4=-1.54702e - 01 A 6=-9.51329e - 04 The fifth surface K = 0.00000e+00 A 4=-1.06994e-01 A 6= 1.54292e-02 A 8=-1.41224e-03 The 6th surface K = 0.00000e+00 A 4=-1.04799e-03 A 6= 4.63155e-05 A 8=-3.25879e-06 A10= 8.39518e-08 The 7th surface K = 0.00000e+00 A 4=-7.31119e-03 A 6= 1.14696e-03 A 8=-9.45610e-05 A10= 3.25001e-06 The 8th surface K = 0.00000e+00 A 4=-1.04799e-03 A 6= 4.63155e-05 A 8=-3.25879e-06 A10= 8.39518e-08 The 9th surface K = 0.00000e+00 A 4=-7.31119e-03 A 6= 1.14696e-03 A 8=-9.45610e-05 A10= 3.25001e-06 Various data Zoom ratio 1.00 Focal length 5.25 F-number 5.00 Half field angle 29.75 Image height 3.00 Overall lens length 9.09 BF 4.84 Single lens data Lens starting surface Focal length 1 1 22.52 2 4 -18.74 3 6 -3389.19 4 7 -3389.19 5 8 -3389.19 6 10 0.00 (Numerical Example 2) Unit: mm Surface data Surface number r d nd νd Effective diameter 1 (Diaphragm) ∞ 0.50 1.09 2* 4.348 0.89 1.53160 55.8 1.93 3* 12.536 1.57 2.40 4* 30.895 1.00 1.63550 23.9 3.98 5* 7.360 0.10 5.01 6* 11.996 3.40 1.53160 55.8 12.77 7* 13.360 -3.40 13.14 8* 11.996 3.40 12.77 9* 13.360 1.54 13.14 10 ∞ 3.00 1.51633 64.1 13.12 11 ∞ 1.00 13.09 Image plane ∞ Aspherical data Second surface K = 0.00000e+00 A 4= 1.05851e-03 A 6= 3.05162e-04 Third surface K = 0.00000e+00 A 4=-2.82512e-04 A 6= 5.82073e-04 Fourth surface K = 0.00000e+00 A 4=-8.97402e-03 A 6= 3.30996e-04 Fifth surface K = 0.00000e+00 A 4=-6.42629e-03 A 6= 5.18231e-04 A 8=-7.44003e-06 Sixth surface K = 0.00000e+00 A 4=-9.75536e-05 A 6=-1.78730e-06 A 8=-7.77142e-09 A10=-2.54424e-10 Seventh surface K = 0.00000e+00 A 4=-4.48515e-04 A 6=-5.24101e-06 A 8= 2.17552e-08 The 8th surface K = 0.00000e+00 A 4=-9.75536e-05 A 6=-1.78730e-06 A 8=-7.77142e-09 A10=-2.54424e-10 The 9th surface K = 0.00000e+00 A 4=-4.48515e-04 A 6=-5.24101e-06 A 8= 2.17552e-08 Various data Zoom ratio 1.00 Focal length 9.79 F-number 9.00 Half field angle 33.22 Image height 6.41 Overall lens length 11.98 BF 4.52 Single lens data Lens starting surface Focal length 1 1 12.07 2 4 -15.46 3 6 118.51 4 7 118.51 5 8 118.51 6 10 0.00 (Numerical Example 3) Unit: mm Surface data Surface number r d nd νd Effective diameter 1* 91.638 1.00 1.49700 81.6 43.80 2* 9.699 13.04 19.40 3* 34.045 1.75 1.82165 24.0 12.74 4 -519.385 2.62 11.61 5 (Aperture) ∞ 0.00 11.27 6 * 21.586 2.93 1.49700 81.6 11.32 7 -22.265 0.30 11.07 8 * 79.778 1.54 2.00178 19.3 10.47 9 * 22.876 0.12 10.56 10 * 29.334 9.70 1.49700 81.6 47.99 11 * 28.454 -9.70 45.39 12 * 29.334 9.70 47.99 13 * 28.454 9.55 45.39 14 ∞ 4.00 1.51633 64.1 45.11 15 ∞ 1.77 44.38 Image plane ∞ Aspherical data First surface K = 0.00000e+00 A4 = 1.06298e-05 A6 = -2.53750e-08 A8 = 3.17698e-11 A10 = -1.72216e-14 Second surface K = 0.00000e+00 A4 = 1.57119e-07 A6 = 9.83500e-08 A8 = -3.67081e-10 A10 = -2.17601e-12 Third surface K = 0.00000e+00 A4 = -2.06445e-05 A6 = 2.51199e-07 A8 = 1.26787e-09 Sixth surface K = 0.00000e+00 A4 = 1.45297e-04 A6 = -4.10421e-08 A8 = -3.05902e-08 Eighth surface K = 0.00000e+00 A4 = -2.22953e-04 A6 = 1.86379e-06 A8 = 2.28627e-08 Ninth surface K = 0.00000e+00 A 4=-1.51360e-04 A 6= 2.73312e-06 A 8= 5.62372e-09 The 10th surface K = 0.00000e+00 A 4=-1.94840e-06 A 6= 8.11131e-10 A 8=-7.48915e-12 A10=-1.59045e-15 The 11th surface K = 0.00000e+00 A 4=-8.28622e-06 A 6= 3.97937e-08 A 8=-8.50100e-11 The 12th surface K = 0.00000e+00 A 4=-1.94840e-06 A 6= 8.11131e-10 A 8=-7.48915e-12 A10=-1.59045e-15 The 13th surface K = 0.00000e+00 A 4=-8.28622e-06 A 6= 3.97937e-08 A 8=-8.50100e-11 Various data Zoom ratio 1.00 Focal length 13.43 F-number 2.00 Half field angle 58.16 Image height 21.63 Overall lens length 46.95 BF 13.95 Single lens data Lens starting surface Focal length 1 1 -21.91 2 3 38.94 3 6 22.55 4 8 -32.46 5 10 717.38 6 11 717.38 7 12 717.38 8 14 0.00 (Numerical Example 4) Unit: mm Surface data Surface number r d nd νd Effective diameter 1* 26.347 1.00 1.49700 81.6 27.79 2* 11.296 10.59 20.58 3* 58.068 3.50 1.85478 24.8 13.50 4 392.135 3.07 13.78 5 (Aperture stop) ∞ 0.00 14.38 6* 24.890 4.16 1.49700 81.6 14.64 7 -27.623 0.81 14.34 8* 34.547 2.26 2.00069 25.5 13.17 9* 17.639 0.35 12.26 10* 27.463 8.55 1.49700 81.6 38.56 11* 28.917 -8.55 38.46 12* 27.463 8.55 38.56 13* 28.917 4.71 38.46 14 ∞ 4.00 1.51633 64.1 38.33 15 ∞ 6.87 37.98 Image plane ∞ Aspherical surface data First surface K = 0.00000e+00 A 4= 2.82644e-05 A 6=-1.30278e-07 A 8= 9.27118e-10 A10=-1.95190e-12 Second surface K = 0.00000e+00 A 4= 1.55124e-05 A 6= 5.25719e-09 A 8=-1.57147e-09 A10= 1.85514e-11 Third surface K = 0.00000e+00 A 4=-2.85144e-05 A 6= 5.63775e-08 A 8=-8.46267e-11 Sixth surface K = 0.00000e+00 A 4= 9.82112e-05 A 6=-2.85734e-07 A 8= 1.89640e-09 The 8th surface K = 0.00000e+00 A 4=-1.87459e-04 A 6= 1.56461e-06 A 8=-8.81601e-09 The 9th surface K = 0.00000e+00 A 4=-1.91926e-04 A 6= 1.99746e-06 A 8=-7.81297e-09 The 10th surface K = 0.00000e+00 A 4=-3.15616e-06 A 6=-7.51703e-09 A 8=-3.55206e-12 A10=-3.61310e-14 The 11th surface K = 0.00000e+00 A 4=-1.45407e-05 A 6=-1.73107e-08 A 8=-3.99964e-11 The 12th surface K = 0.00000e+00 A 4=-3.15616e-06 A 6=-7.51703e-09 A 8=-3.55206e-12 A10=-3.67627e-14 The 13th surface K = 0.00000e+00 A 4=-1.45407e-05 A 6=-1.73107e-08 A 8=-3.99964e-11 Various data Zoom ratio 1.00 Focal length 16.00 F-number 1.50 Half field angle 49.16 Image height 18.51 Overall lens length 48.51 BF 14.22 Single lens data Lens starting surface Focal length 1 1 -40.68 2 3 79.36 3 6 27.06 4 8 -38.60 5 10 372.29 6 11 372.29 7 12 372.29 8 14 0.00 (Numerical Example 5) Unit: mm Surface data Surface No. r d nd νd Effective diameter 1 33.575 1.00 1.49700 81.6 25.47 2 14.325 7.68 20.71 3 38.285 3.72 1.85478 24.8 15.30 4 69.660 3.51 15.24 5 (Aperture) ∞ 0.00 15.72 6* 19.477 4.15 1.49700 81.6 16.01 7 -59.060 0.10 15.58 8* 41.854 1.83 2.00069 25.5 15.03 9* 21.273 0.82 14.17 10* 35.102 10.91 1.49700 81.6 41.49 11* 41.256 -10.91 38.61 12* 35.102 10.91 41.49 13* 41.256 5.29 38.61 14 ∞ 4.00 1.51633 64.1 38.46 15 ∞ 6.80 38.08 Image plane ∞ Aspherical data The 6th surface K = 0.00000e+00 A 4= 3.57108e-05 A 6=-1.39068e-07 A 8= 1.24007e-09 The 8th surface K = 0.00000e+00 A 4=-1.21991e-04 A 6= 1.26867e-06 A 8=-4.82759e-09 Face 9 K = 0.00000e+00 A 4=-1.19382e-04 A 6= 1.37944e-06 A 8=-3.61115e-09 Face 10 K = 0.00000e+00 A 4=-1.00209e-06 A 6=-1.74986e-09 A 8= 2.28712e-12 A10=-8.13336e-15 Face 11 K = 0.00000e+00 A 4=-3.29705e-06 A 6= 9.82698e-09 A 8=-2.96715e-11 Face 12 K = 0.00000e+00 A 4=-1.00209e-06 A 6=-1.74986e-09 A 8= 2.28712e-12 A10=-8.76500e-15 Face 13 K = 0.00000e+00 A 4=-3.29705e-06 A 6= 9.82698e-09 A 8=-2.96715e-11 Various data Zoom ratio 1.00 Focal length 20.00 F-number 1.50 Half field angle 42.78 Image height 18.51 Overall lens length 48.45 BF 14.73 Single lens data Lens starting surface Focal length 1 1 -51.15 2 3 94.29 3 6 30.00 4 8 -45.25 5 10 298.04 6 11 298.04 7 12 298.04 8 14 0.00 (Numerical Example 6) Unit: mm Surface data Surface number r d nd νd Effective diameter 1 19.037 1.00 1.49700 81.6 23.92 2 14.325 5.74 21.30 3 49.724 4.28 1.85478 24.8 19.48 4 62.429 3.89 19.30 5 (Aperture) ∞ 0.00 19.90 6* 23.387 5.34 1.49700 81.6 20.37 7 -96.813 0.10 19.83 8* 26.485 1.98 2.00069 25.5 18.94 9* 17.959 0.92 17.69 10* 37.252 10.83 1.49700 81.6 43.09 11* 46.119 -10.83 40.25 12* 37.252 10.83 43.09 13* 46.119 4.92 40.25 14 ∞ 4.00 1.51633 64.1 39.96 15 ∞ 6.71 39.18 Image plane ∞ Aspherical data The 6th surface K = 0.00000e+00 A 4= 1.55070e-05 A 6=-1.70885e-07 A 8= 1.07509e-09 The 8th surface K = 0.00000e+00 A 4=-1.10778e-04 A 6= 9.34434e-07 A 8=-2.97603e-09 The 9th surface K = 0.00000e+00 A 4=-1.33133e-04 A 6= 9.89656e-07 A 8=-2.80838e-09 The 10th surface K = 0.00000e+00 A 4=-8.91400e-07 A 6=-9.69094e-10 A 8= 1.07904e-12 A10=-5.10341e-15 The 11th surface K = 0.00000e+00 A 4=-2.87123e-06 A 6= 1.10285e-08 A 8=-3.60712e-11 The 12th surface K = 0.00000e+00 A 4=-8.91400e-07 A 6=-9.69094e-10 A 8= 1.07904e-12 A10=-5.73505e-15 The 13th surface K = 0.00000e+00 A 4=-2.87123e-06 A 6= 1.10285e-08 A 8=-3.60712e-11 Various data Zoom ratio 1.00 Focal length 24.00 F-number 1.24 Half field angle 37.64 Image height 18.51 Overall lens length 48.35 BF 14.27 Single lens data Lens starting surface Focal length 1 1 -125.27 2 3 247.42 3 6 38.47 4 8 -63.07 5 1O 277.38 6 11 277.38 7 12 277.38 8 14 0.00 (Numerical Example 7) Unit: mm Surface data Surface number r d nd νd Effective diameter 1 (aperture stop) ∞ 0.00 22.10 2* 25.408 3.35 1.49700 81.6 22.10 3 101.284 7.79 21.66 4* 87.435 1.73 2.00069 25.5 19.90 5* 49.167 0.10 21.36 6* 40.361 10.76 1.49700 81.6 46.62 7* 53.229 -10.76 41.57 8* 40.361 10.76 46.62 9* 53.229 5.63 41.57 10 ∞ 4.00 1.51633 64.1 41.15 11 ∞ 6.66 40.09 Image plane ∞ Aspherical data Second surface K = 0.00000e+00 A 4= 1.09150e-06 A 6= 1.46734e-08 A 8=-3.35318e-11 Fourth surface K = 0.00000e+00 A 4=-4.05227e-05 A 6=-5.52984e-08 A 8= 3.51679e-10 Fifth surface K = 0.00000e+00 A 4=-3.51461e-05 A 6=-5.98017e-08 A 8= 3.57095e-10 Sixth surface K = 0.00000e+00 A 4=-9.34775e-07 A 6= 1.45594e-09 A 8= 2.28776e-13 A10= 5.45402e-16 Seventh surface K = 0.00000e+00 A 4=-4.15347e-06 A 6= 2.14400e-08 A 8=-1.60773e-11 Page 8 K = 0.00000e+00 A 4=-9.34775e-07 A 6= 1.45594e-09 A 8= 2.28776e-13 A10=-8.62438e-17 Page 9 K = 0.00000e+00 A 4=-4.15347e-06 A 6= 2.14400e-08 A 8=-1.60773e-11 Various data Zoom ratio 1.00 Focal length 27.51 F-number 1.25 Half angle of view 33.93 Image height 18.51 Overall lens length 38.66 BF 14.93 Single lens data Lens starting surface Focal length 1 1 67.26 2 4 -114.85 3 6 262.94 4 7 262.94 5 8 262.94 6 10 0.00 (Numerical Example 8) Unit: mm Surface data Surface number r d nd νd Effective diameter 1* 43.704 4.51 1.49700 81.6 33.98 2 -395.892 8.81 33.75 3 (Aperture) ∞ 0.00 30.60 4* 55.166 6.84 1.53160 55.8 29.60 5 -54.815 0.10 28.38 6* -78.721 1.27 1.88202 37.2 27.67 7* 65.588 2.95 26.00 8 * 59.491 11.90 1.49700 81.6 46.09 9 * 116.270 -11.90 42.90 10 * 59.491 11.90 46.09 11 * 116.270 3.23 42.90 12 ∞ 4.00 1.51633 64.1 42.67 13 ∞ 6.39 42.07 Image plane ∞ Aspherical data First surface K = 0.00000e+00 A4=-4.67704e-06 A6=-3.08989e-09 A8=-7.97462e-13 Fourth surface K = 0.00000e+00 A4= 1.33099e-05 A6= 2.38224e-08 A8= 6.32849e-13 Sixth surface K = 0.00000e+00 A4=-1.53065e-05 A6= 4.67203e-08 A8=-4.58239e-11 Seventh surface K = 0.00000e+00 A4=-5.72119e-06 A6= 4.92699e-08 A8=-1.98994e-11 Eighth surface K = 0.00000e+00 A4=-5.20470e-07 A6= 6.26754e-10 A8= 5.98904e-13 A10= 9.49519e-16 Ninth surface K = 0.00000e+00 A4=-1.05024e-06 A6= 4.50479e-09 A8= 4.98171e-13 Tenth surface K = 0.00000e+00 A4=-5.20470e-07 A6= 6.26754e-10 A8= 5.98904e-13 A10= 3.17873e-16 Eleventh surface K = 0.00000e+00 A 4=-1.05024e-06 A 6= 4.50479e-09 A 8= 4.98171e-13 Various data Zoom ratio 1.00 Focal length 35.00 F number 1.03 Half angle of view 29.93 Image height 20.15 Overall lens length 48.64 BF 12.26 Single lens data Lens starting surface focal length 1 1 79.46 2 4 52.86 3 6 -40.40 4 8 229.17 5 9 229.17 6 10 229.17 7 12 0.00 (Numerical Example 9) Unit: mm Surface data Surface number r d nd νd Effective diameter 1* 51.457 5.51 1.49700 81.6 41.67 2 12231.122 19.66 41.33 3 (Aperture) ∞ 2.00 33.19 4* -254.989 2.79 1.72047 34.7 32.60 5 -61.810 1.56 1.92286 20.9 32.37 6* -167.224 9.05 32.06 7 ∞ -1.05 28.24 8* 96.179 17.18 1.49700 81.6 50.71 9* 255.697 -17.18 46.55 10* 96.179 17.18 50.71 11 * 255.697 2.31 46.55 12 ∞ 4.00 1.51633 64.1 46.27 13 ∞ 5.76 45.55 Image plane ∞ Aspherical data First surface K = 0.00000e+00 A 4=-3.48694e-07 A 6=-4.68927e-10 A 8= 2.20233e-13 Fourth surface K = 0.00000e+00 A 4=-8.66760e-07 A 6=-7.63502e-09 A 8= 2.91475e-11 Sixth surface K = 0.00000e+00 A 4=-5.78538e-07 A 6=-7.11577e-09 A 8= 2.63825e-11 Eighth surface K = 0.00000e+00 A 4= 1.84235e-07 A 6= 3.58581e-10 A 8=-4.20769e-13 A10= 3.13114e-16 Ninth surface K = 0.00000e+00 A 4= 6.79621e-07 A 6=-4.18462e-11 A 8= 5.74465e-13 Tenth surface K = 0.00000e+00 A 4= 1.84235e-07 A 6= 3.58581e-10 A 8=-4.20769e-13 A10= 3.13114e-16 Eleventh surface K = 0.00000e+00 A 4= 6.79621e-07 A 6=-4.18462e-11 A 8= 5.74465e-13 Various data Zoom ratio 1.00 Focal length 50.00 F-number 1.20 Half field angle 23.40 Image height 21.63 Overall lens length 67.40 BF 10.70 Single lens data Lens starting surface focal length 1 1 103.96 2 4 112.56 3 5 -107.01 4 8 299.49 5 9 299.49 6 10 299.49 7 12 0.00 (Numerical Example 10) Unit: mm Surface data Surface number r d nd νd Effective diameter 1* 27.471 3.84 1.49700 81.6 22.45 2 198.559 6.14 21.94 3 (Aperture) ∞ 2.01 19.62 4* 61.858 1.51 2.00069 25.5 18.76 5* 38.811 3.30 18.51 6 ∞ -1.10 19.09 7* 39.465 10.33 1.49700 81.6 43.56 8* 52.135 -10.33 39.86 9* 39.465 10.33 43.56 10* 52.135 5.13 39.86 11 ∞ 4.00 1.51633 64.1 39.60 12 ∞ 6.61 38.92 Image plane ∞ Aspherical data First surface K = 0.00000e+00 A 4= 1.68390e-06 A 6= 5.77125e-09 A 8= 1.67027e-12 Fourth surface K = 0.00000e+00 A 4=-8.42958e-05 A 6= 1.49208e-07 A 8=-1.11295e-10 The 5th surface K = 0.00000e+00 A 4=-8.57631e-05 A 6= 1.87591e-07 A 8=-2.50101e-10 The 7th surface K = 0.00000e+00 A 4=-5.17773e-07 A 6= 8.92860e-10 A 8= 1.85693e-14 A10= 1.16939e-16 The 8th surface K = 0.00000e+00 A 4=-1.86991e-06 A 6= 1.28414e-08 A 8=-1.38616e-11 The 9th surface K = 0.00000e+00 A 4=-5.17773e-07 A 6= 8.92860e-10 A 8= 1.85693e-14 A10=-5.14706e-16 The 10th surface K = 0.00000e+00 A 4=-1.86991e-06 A 6= 1.28414e-08 A 8=-1.38616e-11 Various data Zoom ratio 1.00 Focal length 27.96 F number 1.24 Half angle of view 33.51 Image height 18.51 Overall lens length 40.41 BF 14.38 Single lens data Lens starting surface Focal length 1 1 63.67 2 4 -107.62 3 7 257.14 4 8 257.14 5 9 257.14 6 11 0.00 (Numerical Example 11) Unit: mm Surface Data Surface Number r d nd νd Effective Diameter 1 (Aperture) ∞ 0.00 23.61 2* 26.343 10.43 1.53160 55.8 23.61 3* 674.385 2.70 20.91 4* 157.741 3.38 1.63550 23.9 19.41 5* 32.207 0.89 18.21 6* 44.567 12.72 1.53160 55.8 47.10 7* 50.665 -12.72 43.17 8* 44.567 12.72 47.10 9* 50.665 5.42 43.17 10 ∞ 3.38 1.51633 64.1 42.99 11 ∞ 10.38 42.59 Image Plane ∞ Aspherical Data Second Surface K = 0.00000e+00 A 4= 3.26025e-06 A 6= 4.22486e-09 Third Surface K = 0.00000e+00 A 4=-2.52001e-06 A 6=-3.34475e-08 Fourth Surface K = 0.00000e+00 A 4=-5.28388e-05 A 6= 5.93945e-08 Fifth Surface K = 0.00000e+00 A 4=-4.27604e-05 A 6= 9.75926e-08 A 8= 4.84214e-11 Sixth Surface K = 0.00000e+00 A 4=-6.02337e-07 A 6= 1.66776e-10 A 8=-1.70184e-13 A10=-5.24160e-16 Seventh Surface K = 0.00000e+00 A 4=-2.96823e-06 A 6= 6.05593e-09 A 8=-8.44780e-12 The 8th surface K = 0.00000e+00 A 4=-6.02337e-07 A 6= 1.66776e-10 A 8=-1.70184e-13 A10=-5.24160e-16 The 9th surface K = 0.00000e+00 A 4=-2.96823e-06 A 6= 6.05593e-09 A 8=-8.44780e-12 Various data Zoom ratio 1.00 Focal length 35.41 F-number 1.50 Half field angle 29.48 Image height 20.02 Overall lens length 48.15 BF 18.03 Single lens data Lens starting surface Focal length 1 1 51.28 2 4 -64.35 3 6 404.02 4 7 404.02 5 8 404.02 6 10 0.00 (Numerical Example 12) Unit: mm Surface data Surface number r d nd νd Effective diameter 1* 50.423 3.95 1.69680 55.5 34.48 2 691.944 9.87 34.15 3 (Aperture) ∞ 0.00 29.78 4* 87.463 1.00 1.94594 18.0 29.23 5 55.698 2.15 28.58 6 ∞ -1.20 28.50 7* 83.379 26.55 1.49700 81.6 51.88 8* 127.619 -26.55 45.63 9* 83.379 26.55 51.88 10* 127.619 3.48 45.63 11 ∞ 4.00 1.51633 64.1 45.38 12 ∞ 6.20 44.89 Image plane ∞ Aspherical data First surface K = 0.00000e+00 A 4=-3.97730e-07 A 6=-1.28949e-09 A 8= 1.64575e-12 Fourth surface K = 0.00000e+00 A 4=-2.89622e-07 A 6= 1.37573e-09 A 8=-2.98261e-12 Seventh surface K = 0.00000e+00 A 4=-1.95317e-09 A 6= 8.83267e-11 A 8=-1.08604e-13 A10= 5.44225e-17 Eighth surface K = 0.00000e+00 A 4= 1.37936e-07 A 6= 1.18914e-10 A 8= 1.72537e-13 Ninth surface K = 0.00000e+00 A 4=-1.95317e-09 A 6= 8.83267e-11 A 8=-1.08604e-13 A10= 5.44225e-17 Tenth surface K = 0.00000e+00 A 4= 1.37936e-07 A 6= 1.18914e-10 A 8= 1.72537e-13 Various data Zoom ratio 1.00 Focal length 50.00 F number 1.45 Half angle 23.40 Image height 21.63 Overall lens length 54.64 BF 12.32 Single lens data Lens starting surface focal length 1 1 77.85 2 4 -164.65 3 7 403.54 4 8 403.54 5 9 403.54 6 11 0.00 (Numerical Example 13) Unit mm Surface data Surface number r d nd νd Effective diameter 1 (Aperture) ∞ 0.00 18.75 2* 20.527 13.75 1.60562 43.7 18.75 3 -100.754 2.55 2.00178 19.3 14.66 4* 77.505 0.41 16.90 5* 71.203 11.45 1.51633 64.1 44.07 6* 457.607 -11.45 44.00 7* 71.203 11.45 44.07 8* 457.607 1.84 44.00 9 ∞ 1.00 1.51633 64.1 44.03 10 ∞ 1.00 44.04 Image plane ∞ Aspherical data The second surface K = 0.00000e+00 A 4= 2.34346e-06 A 6= 2.26090e-08 The fourth surface K = 0.00000e+00 A 4= 1.76035e-05 A 6= 3.34364e-08 A 8= 4.08744e-10 The 5th surface K = 0.00000e+00 A 4=-5.64718e-07 A 6= 6.77253e-10 A 8= 5.67978e-13 A10= 2.86767e-16 The 6th surface K = 0.00000e+00 A 4= 1.25166e-06 A 6= 4.37570e-09 A 8=-1.00957e-11 The 7th surface K = 0.00000e+00 A 4=-5.64718e-07 A 6= 6.77253e-10 A 8= 5.67978e-13 A10= 2.86767e-16 The 8th surface K = 0.00000e+00 A 4= 1.25166e-06 A 6= 4.37570e-09 A 8=-1.00957e-11 Various data Zoom ratio 1.00 Focal length 28.13 F-number 1.50 Half field angle 34.74 Image height 19.51 Overall lens length 31.66 BF 3.50 Single lens data Lens starting surface Focal length 1 1 29.41 2 3 -43.42 3 5 161.68 4 6 161.68 5 7 161.68 6 9 0.00 Table 1 shows the values of each conditional expression in each example.

[0144]

Table 1

[0145] [Imaging device] Referring to FIG. 30, an imaging device having the optical system of each embodiment will be described. FIG. 30 is a schematic diagram of a digital camera 10 which is an example of an imaging device. 20 is a digital camera body, 21 is an imaging optical system which is any one of the optical systems of each embodiment, and 22 is an imaging element such as a CCD which receives a subject image by the imaging optical system 21. 23 is a recording means for recording the subject image received by the imaging element 22, and 24 is a finder for observing the subject image displayed on a display element (not shown). The display element is constituted by a liquid crystal panel or the like, and the subject image formed on the imaging element 22 is displayed. 25 is a liquid crystal display panel having the same function as the finder 24.

[0146] 0]Thus, by applying the optical system of each embodiment to an imaging device, an imaging device having a small size and high optical performance can be realized.

[0147] [Projection device] Referring to FIG. 31, a projection device having the optical system of each embodiment will be described. FIG. 31 is a configuration diagram of a projector 30 which is an example of a projection device. As a light modulation element (display element) of the projector 30, a light emitting panel such as an LCOS or a DMD is used. In FIG. 31, 31 is a light source device, 32 is an illumination optical system, 33 is a color separation and synthesis optical system, and 34 is a projection optical system which is any one of the optical systems of each embodiment. The light source device 31 emits light toward the illumination optical system 32. The illumination optical system 32 illuminates the light from the light source device 3,1. The color separation and synthesis optical system 33 performs color separation and color synthesis on the illumination light from the illumination optical system 32. The projection optical system 34 projects the synthesized light from the color separation and synthesis optical system 33. The light emitted by the light emitting panel projects an image on the subject side rather than the projection optical system 34.

[0148] In the color separation and synthesis optical system 33, 331R, 331G, and 331B are each a light emitting panel unit provided with a light modulation element for red, green, and blue (a light emitting panel (display element) for red, green, and blue). 332R, 332G, and 332B are each a wavelength plate unit provided with a wavelength plate for red, green, and blue. Note that the number of light emitting panels is not limited to this, and it is applicable to any projector such as a single plate type or a three plate type.

[0149] According to each embodiment, it is possible to provide an optical system, an imaging device, and a projection device that are small in size, can handle a large aperture, and have high optical performance.

[0150] The disclosure of each embodiment includes the following configurations. (Configuration 1) An optical system having a first transmission reflection surface, a quarter wavelength plate, and a second transmission reflection surface arranged in order from the enlargement side to the reduction side, Light from the enlargement side passes through the first transmission reflection surface and the quarter wavelength plate in order, is reflected to the enlargement side by the second transmission reflection surface, passes through the quarter wavelength plate, is reflected to the reduction side by the first transmission reflection surface, and passes through the quarter wavelength plate and the second transmission reflection surface in order and heads toward the reduction side, The first transmission reflection surface and the second transmission reflection surface each face the convex surface toward the enlargement side, An optical system characterized in that a first lens composed of a lens surface different from the first transmission reflection surface and the second transmission reflection surface and a second lens arranged on the reduction side of the first lens are arranged. (Configuration 2) An optical system having an open aperture and a first transmission reflection surface, a quarter wavelength plate, and a second transmission reflection surface arranged in order from the enlargement side to the reduction side, Light from the enlargement side passes through the first transmission reflection surface and the quarter wavelength plate in order, is reflected to the enlargement side by the second transmission reflection surface, passes through the quarter wavelength plate, is reflected to the reduction side by the first transmission reflection surface, and passes through the quarter wavelength plate and the second transmission reflection surface in order and heads toward the reduction side, The first transmission reflection surface and the second transmission reflection surface each face the convex surface toward the enlargement side, When the distance from the magnifying side surface of the lens on the most magnifying side of the optical system to the panel surface is L, and the distance on the optical axis from the aperture stop to the first transmission-reflection surface is Ls, 0.00 ≦ Ls / L ≦ 1.00 An optical system characterized by satisfying the conditional expression. (Configuration 3) The optical system according to Configuration 1, wherein at least one of the first lens and the second lens has a positive refractive power. (Configuration 4) The optical system according to Configuration 1, wherein at least one of the first lens and the second lens has a negative refractive power. (Configuration 5) One of the first lens and the second lens has a positive refractive power, The other of the first lens and the second lens has a negative refractive power. The optical system according to Configuration 1, 3, or 4. (Configuration 6) The optical system according to any one of Configurations 1, 3 to 5, wherein the first lens and the second lens are arranged on the magnifying side with respect to the first transmission-reflection surface. (Configuration 7) The optical system according to any one of Configurations 1, 3 to 6, wherein one of the first lens and the second lens has a negative refractive power and is arranged on the magnifying side adjacent to the first transmission-reflection surface. (Configuration 8) The lens arranged on the magnifying side of one of the first lens and the second lens has a positive refractive power. When the focal length of the lens having the positive refractive power is fp and the focal length of the optical system is f, 0.50 ≦ fp / f ≦ 10.0 The optical system according to Configuration 7, characterized by satisfying the conditional expression. (Configuration 9) The optical system according to any one of Configurations 1 to 8, characterized in that it is configured to guide an on-axis ray to the panel surface. (Configuration 10) When the diameter of the aperture stop is D and the distance on the optical axis from the aperture stop to the panel surface is LD, 0.03 ≦ D / LD ≦ 1.50 The optical system according to Configuration 2, characterized by satisfying the conditional expression. (Configuration 11) The optical system according to Configuration 2 or 10, characterized in that the first transmission-reflection surface and the second transmission-reflection surface are arranged on the reduction side with respect to the aperture stop. (Configuration 12) When the focal length in the range between the first transmission-reflection surface and the second transmission-reflection surface is fR and the focal length in the range on the enlargement side with respect to the first transmission-reflection surface is fF, -2.00 ≦ fF / fR ≦ 10.00 The optical system according to any one of Configurations 1 to 11, characterized by satisfying the conditional expression. (Configuration 13) When the thickness on the optical axis from the enlargement side surface of the most enlarged lens to the reduction side surface of the most reduced lens in the optical system is La and the distance on the optical axis from the first transmission-reflection surface to the second transmission-reflection surface is Ld, 0.15 ≦ Ld / La ≦ 0.80 The optical system according to any one of Configurations 1 to 12, characterized by satisfying the conditional expression. (Configuration 14) When the thickness on the optical axis from the enlargement side surface of the most enlarged lens to the reduction side surface of the most reduced lens in the optical system is La and the focal length of the optical system is f, 0.50 ≦ La / f ≦ 3.00 The optical system according to any one of Configurations 1 to 13, characterized by satisfying the conditional expression. (Configuration 15) When the distance from the enlargement side surface of the most enlarged lens to the panel surface in the optical system is L and the distance on the optical axis from the first transmission-reflection surface to the panel surface is Lh, 0.10 ≦ Lh / L ≦ 1.00 The optical system according to any one of Configurations 1 to 14, characterized by satisfying the conditional expression. (Configuration 16) When the distance on the optical axis from the first transmissive-reflective surface to the panel surface is Lh and the focal length of the optical system is f, 0.30 ≦ Lh / f ≦ 3.00 The optical system according to any one of Configurations 1 to 15, characterized by satisfying the conditional expression. (Configuration 17) The region between the first transmissive-reflective surface and the second transmissive-reflective surface is filled with a material other than air, When the refractive index of the material with respect to the d-line is nd, 1.40 ≦ nd ≦ 2.30 The optical system according to any one of Configurations 1 to 16, characterized by satisfying the conditional expression. (Configuration 18) It has a negative lens disposed adjacent to the enlargement side of the first transmissive-reflective surface, When the focal length of the negative lens is fN, -10.00 ≦ fN / f ≦ -⁰.⁵⁰ The optical system according to any one of Configurations 1 to 17, characterized by satisfying the conditional expression. (Configuration 19) The second transmissive-reflective surface is disposed on the reduction side of the first transmissive-reflective surface, When the focal length of the optical system is f and the focal length in the range between the first transmissive-reflective surface and the second transmissive-reflective surface is fR, -0.5 ≦ f / fR ≦ 2.00 The optical system according to any one of Configurations 1 to 18, characterized by satisfying the conditional expression. (Configuration 20) When the distance on the optical axis from the second transmissive-reflective surface to the panel surface is Li and the distance from the enlargement side surface of the most enlarged lens in the optical system to the panel surface is L, 0.05 ≦ Li / L ≦ 1.00 The optical system according to any one of Configurations 1 to 19, characterized by satisfying the conditional expression. (Configuration 21) The optical system according to any one of Configurations 1 to 20, characterized in that the second transmissive-reflective surface is the reduction side surface of the lens disposed on the most reduction side in the optical system. (Configuration 22) When the radius of curvature of the first transmissive-reflective surface is R1 and the radius of curvature of the second transmissive-reflective surface is R2, -1.00 ≦ (R1 - R2) / (R1 + R2) ≦ 1.00 The optical system according to any one of Configurations 1 to 21, characterized by satisfying the conditional expression. (Configuration 23) When the distance on the optical axis from the first transmissive-reflective surface to the second transmissive-reflective surface is Ld and the focal length of the optical system is f, 0.10 ≦ Ld / f ≦ 2.00 The optical system according to any one of Configurations 1 to 22, characterized by satisfying the conditional expression. (Configuration 24) When the outer diameter of the lens disposed on the most magnifying side of the optical system is Oe and the outer diameter of the lens disposed on the most reducing side of the optical system is Ie, 0.10 ≦ Oe / Ie ≦ 2.00 The optical system according to any one of Configurations 1 to 23, characterized by satisfying the conditional expression. (Configuration 25) One of the first transmissive-reflective surface and the second transmissive-reflective surface is a surface that separates incident light into reflected light and transmitted light according to the polarization state, and the optical system according to any one of Configurations 1 to 24 is characterized thereby. (Configuration 26) The other of the first transmissive-reflective surface and the second transmissive-reflective surface is a surface of a half mirror or a cholesteric liquid crystal, and the optical system according to Configuration 25 is characterized thereby. (Configuration 27) The optical system is rotationally symmetric with respect to the optical axis, and the optical system according to any one of Configurations 1 to 26 is characterized thereby. (Configuration 28) When the F-number of the optical system is Fno, 0.50 ≦ Fno ≦ 15.00 The optical system according to any one of Configurations 1 to 27, characterized by satisfying the conditional expression. (Configuration 29) An imaging device comprising the optical system according to any one of Configurations 1 to 28 and an element that receives an image formed by the optical system. (Configuration 30) A projection device comprising the optical system according to any one of Configurations 1 to 28 and a display element.

[0151] As described above, the preferred embodiments of the present invention have been described. However, the present invention is not limited to these embodiments, and various modifications and changes are possible within the scope of the gist thereof.

Explanation of Reference Signs

[0152] HM1 First transmission-reflection surface QWP Quarter-wave plate HM2 Second transmission-reflection surface SP Aperture stop IM Image plane (panel plane)

Claims

1. An optical system having a first transmissive reflective surface, a quarter-wave plate, and a second transmissive reflective surface arranged in order from the magnifying side to the reducing side, wherein light from the magnifying side passes through the first transmissive reflective surface and the quarter-wave plate in order, is reflected toward the object side by the second transmissive reflective surface, passes through the quarter-wave plate, is reflected toward the reducing side by the first transmissive reflective surface, and passes through the quarter-wave plate and the second transmissive reflective surface in order and travels toward the reducing side, wherein the first transmissive reflective surface and the second transmissive reflective surface each face the object side with a convex surface, and wherein a first lens composed of a lens surface different from the first transmissive reflective surface and the second transmissive reflective surface and a second lens arranged on the reducing side of the first lens are arranged.

2. An optical system having an aperture stop, a first transmissive reflective surface, a quarter-wave plate, and a second transmissive reflective surface arranged in order from the magnifying side to the reducing side, wherein light from the magnifying side passes through the first transmissive reflective surface and the quarter-wave plate in order, is reflected toward the magnifying side by the second transmissive reflective surface, passes through the quarter-wave plate, is reflected toward the reducing side by the first transmissive reflective surface, and passes through the quarter-wave plate and the second transmissive reflective surface in order and travels toward the reducing side, wherein the first transmissive reflective surface and the second transmissive reflective surface each face the magnifying side with a convex surface, and wherein when the distance from the magnifying side surface of the lens on the most magnifying side of the optical system to the panel surface is L and the distance on the optical axis from the aperture stop to the first transmissive reflective surface is Ls, 0.00 ≦ Ls / L ≦ 1.00 and the optical system satisfies the conditional expression.

3. The optical system according to claim 1, wherein at least one of the first lens and the second lens has a positive refractive power.

4. The optical system according to claim 1, wherein at least one of the first lens and the second lens has a negative refractive power.

5. One of the first lens and the second lens has a positive refractive power, and the other of the first lens and the second lens has a negative refractive power, the optical system according to claim 1.

6. The optical system according to claim 1, wherein the first lens and the second lens are arranged on the magnifying side of the first transmissive reflective surface.

7. One of the first lens and the second lens has a negative refractive power and is arranged on the magnifying side adjacent to the first transmission-reflection surface. The optical system according to claim 1, characterized in that.

8. The lens arranged on the magnifying side of one of the first lens and the second lens has a positive refractive power. When the focal length of the lens having the positive refractive power is fp and the focal length of the optical system is f. 0.50 ≤ fp / f ≤ 10.0 The optical system according to claim 7, characterized in that the conditional expression is satisfied.

9. The optical system according to claim 1 or 2, characterized in that the optical system is configured to guide an on-axis ray to the panel surface.

10. When the diameter of the aperture stop is D and the distance on the optical axis from the aperture stop to the panel surface is LD. 0.03 ≤ D / LD ≤ 1.50 The optical system according to claim 2, characterized in that the conditional expression is satisfied.

11. The optical system according to claim 2, characterized in that the first transmission-reflection surface and the second transmission-reflection surface are arranged on the reducing side of the aperture stop.

12. When the focal length in the range between the first transmission-reflection surface and the second transmission-reflection surface is fR and the focal length in the range on the magnifying side of the first transmission-reflection surface is fF. -2.00 ≤ fF / fR ≤ 10.00 The optical system according to claim 1 or 2, characterized in that the conditional expression is satisfied.

13. When the thickness on the optical axis from the magnifying side surface of the most magnifying lens to the reducing side surface of the most reducing lens in the optical system is La and the distance on the optical axis from the first transmission-reflection surface to the second transmission-reflection surface is Ld. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ When the distance on the optical axis from the first transmissive reflection surface to the panel surface is Lh and the focal length of the optical system is f, 0.30 ≤ Lh / f ≤ 3.00 The optical system according to claim 1 or 2, characterized in that the conditional expression is satisfied.

17. The region between the first transmissive reflection surface and the second transmissive reflection surface is filled with a material other than air, When the refractive index of the material with respect to the d line is nd, 1.40 ≤ nd ≤ 2.30 The optical system according to claim 1 or 2, characterized in that the conditional expression is satisfied.

18. It has a negative lens disposed adjacent to the enlargement side of the first transmissive reflection surface, When the focal length of the negative lens is fN, -10.00 ≤ fN / f ≤ -0.50 The optical system according to claim 1 or 2, characterized in that the conditional expression is satisfied.

19. The second transmissive reflection surface is disposed on the reduction side of the first transmissive reflection surface, When the focal length of the optical system is f and the focal length in the range between the first transmissive reflection surface and the second transmissive reflection surface is fR, -0.5 ≤ f / fR ≤ 2.00 The optical system according to claim 1 or 2, characterized in that the conditional expression is satisfied.

20. When the distance on the optical axis from the second transmissive reflection surface to the panel surface is Li and the distance from the enlargement side surface of the lens on the most enlargement side of the optical system to the panel surface is L, 0.05 ≤ Li / L ≤ 1.00 The optical system according to claim 1 or 2, characterized in that the conditional expression is satisfied.

21. The optical system according to claim 1 or 2, characterized in that the second transmissive reflection surface is the reduction side surface of the lens disposed on the most reduction side of the optical system.

22. When the radius of curvature of the first transmissive reflection surface is R1 and the radius of curvature of the second transmissive reflection surface is R2, -1.00 ≤ (R1 - R2) / (R1 + R2) ≤ 1.00 The optical system according to claim 1 or 2, characterized in that the conditional expression is satisfied.

23. When the distance on the optical axis from the first transmissive reflection surface to the second transmissive reflection surface is Ld and the focal length of the optical system is f, 0.10 ≤ Ld / f ≤ 2.00 The optical system according to claim 1 or 2, characterized in that the conditional expression is satisfied.

24. When the outer diameter of the lens disposed on the most enlargement side of the optical system is Oe and the outer diameter of the lens disposed on the most reduction side of the optical system is Ie, 0.10 ≤ Oe / Ie ≤ 2.00 The optical system according to claim 1 or 2, characterized in that the conditional expression is satisfied.

25. The optical system according to claim 1 or 2, wherein one of the first transmissive reflecting surface and the second transmissive reflecting surface is a surface that separates incident light into reflected light and transmitted light according to the polarization state.

26. The optical system according to claim 25, wherein the other of the first transmissive reflecting surface and the second transmissive reflecting surface is a surface of a half mirror or a cholesteric liquid crystal.

27. The optical system according to claim 1 or 2, wherein the optical system is rotationally symmetric with respect to the optical axis.

28. When the F-number of the optical system is Fno, 0.50 ≤ Fno ≤ 15.00 The optical system according to claim 1 or 2, which satisfies the conditional expression.

29. An imaging device comprising the optical system according to claim 1 or 2 and an element that receives an image formed by the optical system.

30. A projection device comprising the optical system according to claim 1 or 2 and a display element.

Images