Image-forming optical system, projection-type display device, and imaging device

Abstract

This image-forming optical system comprises a first optical system and a second optical system in the stated order from the enlargement side toward the reduction side along the optical path, and an intermediate image is formed at least twice between an enlargement-side image-forming surface and a reduction-side image-forming surface. The first optical system includes at least two reflective surfaces each having a curvature. The surface of the first optical system closest to the enlargement side on the optical path is a first refraction surface that refracts light beams reflected by the reflection surfaces of the first optical system. The surface of the first optical system closest to the reduction side on the optical path is the surface on the most reduced side on the optical path among the surfaces through which light beams pass a plurality of times.

Description

Imaging optical system, projection display device, and imaging device

[0001] The technology of the present disclosure relates to an imaging optical system, a projection display device, and an imaging device.

[0002] Conventionally, imaging optical systems that can be used in projection display devices, imaging devices, and the like are known from Japanese Patent Application Laid-Open Nos. 2008-250296, 2017-040849, and 2020-024359.

[0003] In recent years, there has been a demand for an imaging optical system that is compact and has a small number of optical elements, yet has a wide angle and good optical performance.

[0004] The present disclosure has been made in consideration of the above circumstances, and provides an imaging optical system that is compact and made up of a small number of optical elements, yet has a wide angle and good optical performance, as well as a projection display device and an imaging device that include this imaging optical system.

[0005] A first aspect of the present disclosure is an imaging optical system comprising, in order along an optical path from the enlargement side to the reduction side, a first optical system and a second optical system, wherein an intermediate image is formed at least twice between the enlargement side image forming surface and the reduction side image forming surface, the first optical system includes at least two reflective surfaces having curvature, the most enlargement side surface on the optical path of the first optical system is a first refracting surface that refracts light rays reflected by the reflective surface of the first optical system, and the most reduction side surface on the optical path of the first optical system is the most reduction side surface on the optical path among the surfaces through which the light rays pass multiple times.

[0006] In the first aspect, when the distance on the optical axis from the first refractive surface to the most enlargement side reflecting surface on the optical path of the first optical system is L1, and the distance on the optical axis from the most enlargement side reflecting surface on the optical path of the first optical system to the most reduction side surface on the optical path of the second optical system is L2, it is preferable to satisfy conditional expression (1) expressed as 0.1<|L1 / L2|<0.8 (1), and it is more preferable to satisfy conditional expression (1-1) expressed as 0.2<|L1 / L2|<0.7 (1-1).

[0007] In the first aspect, if the distance on the optical axis from the first refractive surface to the most reduction-side reflecting surface on the optical path of the first optical system is L3, and the distance on the optical axis from the most reduction-side reflecting surface on the optical path of the first optical system to the most reduction-side surface on the optical path of the second optical system is L4, it is preferable to satisfy conditional expression (2) expressed as 0.1<|L3 / L4|<0.8 (2), and it is more preferable to satisfy conditional expression (2-1) expressed as 0.2<|L3 / L4|<0.7 (2-1).

[0008] In the first aspect, it is preferable that the light ray is reflected three times by a reflective surface having a curvature inside the first optical system.

[0009] In the first aspect, it is preferable that the reflecting surface on the most enlargement side in the optical path of the first optical system and the reflecting surface on the most reduction side in the optical path of the first optical system have a concave shape.

[0010] In the first aspect, it is preferable that an intermediate image is formed twice inside the first optical system.

[0011] In the first aspect, the first refracting surface preferably has a free-form surface shape.

[0012] In the first aspect, it is preferable that the optical system includes a display element or an image sensor arranged on the reduction-side image plane, and that at least one of the optical axis of the first optical system and the optical axis of the second optical system is shifted in a direction perpendicular to the optical axis relative to the center of the display element or image sensor.

[0013] In the first aspect, it is preferable that the optical axis of the first optical system is shifted in a direction perpendicular to the optical axis relative to the optical axis of the second optical system and the center of the display element or image sensor, and that the optical axis of the second optical system is shifted in a direction perpendicular to the optical axis relative to the center of the display element or image sensor.

[0014] In the first aspect, it is preferable that the first refracting surface transmits the light ray twice.

[0015] In the first aspect, it is preferable that the first refractive surface and the one reflecting surface are formed on the same optical member.

[0016] In the first aspect, it is preferable that the first optical system is made up of one optical member.

[0017] In the first aspect, it is preferable that the optical element includes a first refractive surface that transmits a light ray twice and reflects the light ray once, and a surface that is opposite to the first refractive surface and reflects the light ray twice.

[0018] In the first aspect, it is preferable that the reflecting surface on the most enlargement side in the optical path of the first optical system and the reflecting surface on the most reduction side in the optical path of the first optical system are formed on the same surface.

[0019] A second aspect of the present disclosure is an imaging optical system in which an intermediate image is formed at least twice between an enlargement-side imaging surface and a reduction-side imaging surface, and an optical element arranged on the most enlargement side on the optical path includes a PA surface, which is the most enlargement-side surface on the optical path, that transmits light rays twice and reflects the light rays once, and a PB surface, which is the surface opposite the PA surface and reflects the light rays twice.

[0020] In the second aspect, it is preferable that the intermediate image is formed twice inside the optical member.

[0021] A third aspect of the present disclosure is a projection display device, comprising the imaging optical system according to the first or second aspect.

[0022] A fourth aspect of the present disclosure is an imaging device including the imaging optical system according to the first or second aspect.

[0023] In this specification, the terms "consisting of" and "consisting of" are intended to mean that, in addition to the listed components, other optical elements than lenses, such as lenses that have substantially no refractive power, apertures, masks, filters, cover glasses, plane mirrors, and prisms, as well as mechanical parts such as lens flanges, lens barrels, image sensors, and image stabilization mechanisms, may also be included.

[0024] In this specification, "light rays" refers to light rays used for forming an image on the magnification-side image forming surface or the reduction-side image forming surface. "The reflective surface on the most magnification side on the optical path" refers to the reflective surface on the most magnification side on the optical path among all the reflective surfaces in the optical system. "The reflective surface on the most reduction side on the optical path" refers to the reflective surface on the most reduction side on the optical path among all the reflective surfaces in the optical system.

[0025] Unless otherwise specified, the sign of the refractive power and the surface shape of the aspherical surface are considered in the paraxial region. The "distance on the optical axis" used in the conditional expressions is a geometric distance unless otherwise specified.

[0026] According to the present disclosure, it is possible to provide an imaging optical system that is compact and made up of a small number of optical elements, yet has a wide angle and good optical performance, as well as a projection display device and an imaging device that include this imaging optical system.

[0027] FIG. 1 is a cross-sectional view showing the configuration and light beam of an imaging optical system according to an embodiment, corresponding to the imaging optical system of Example 1. FIG. 2 is a view for explaining a shift of an optical axis. FIG. 3 is a view showing a display surface. FIG. 4 is a view showing a spot diagram of Example 1. FIG. 5 is a view showing a distortion grating of Example 1. FIG. 6 is a cross-sectional view showing the configuration and light beam of an imaging optical system of Example 2. FIG. 7 is a view showing a spot diagram of Example 2. FIG. 8 is a view showing a distortion grating of Example 2. FIG. 9 is a cross-sectional view showing the configuration and light beam of an imaging optical system of Example 3. FIG. 10 is a view showing a spot diagram of Example 3. FIG. 11 is a cross-sectional view showing the configuration and light beam of an imaging optical system of Example 4. FIG. 12 is a view showing a spot diagram of Example 4. FIG. 13 is a view showing a distortion grating of Example 4. FIG. 14 is a schematic configuration diagram of a projection display device according to an embodiment. FIG. 15 is a schematic configuration diagram of a projection display device according to another embodiment. FIG. 16 is a schematic configuration diagram of a projection display device according to yet another embodiment. FIG. 17 is a perspective view of the front side of an imaging device according to an embodiment. FIG. 18 is a perspective view of the rear side of an imaging device according to an embodiment.

[0028] An example of an embodiment of the technology of the present disclosure will be described in detail below with reference to the drawings. Fig. 1 shows a cross-sectional view of a configuration of an imaging optical system according to an embodiment of the present disclosure and a light beam. The configuration example shown in Fig. 1 corresponds to Example 1, which will be described later. Fig. 1 also shows light beams LF0, LF1, and LF2.

[0029] The imaging optical system according to the technique of the present disclosure can be mounted in a projection display device as a projection optical system in which a display element is arranged on the reduction-side image plane, or can be mounted in a digital camera or the like as an imaging optical system in which an imaging element is arranged on the reduction-side image plane. The imaging optical system according to the technique of the present disclosure will be described below assuming that it is used as a projection optical system.

[0030] FIG. 1 shows an example in which optical elements PP1-PP3 and a light valve display surface Sim are arranged on the reduction side of the imaging optical system, assuming that the imaging optical system is installed in a projection display device. The light valve is a display element that outputs an optical image, and this optical image is displayed as an image on the display surface Sim. The light valve may be, for example, a liquid crystal display element or an image display element such as a DMD (Digital Micromirror Device: registered trademark). The optical elements PP1-PP3 are elements that are intended to include various filters, cover glasses, color synthesis prisms, etc. The optical elements PP1-PP3 are elements that do not have refractive power. The materials, lengths, and number of components of the optical elements PP1-PP3 can be changed as appropriate, and a configuration in which some or all of the optical elements PP1-PP3 are omitted is also possible.

[0031] The imaging optical system is mounted, for example, on a projection display device and projects an image displayed on a display surface Sim of a reduction-side display element onto a projection surface on an enlargement-side. In a projection display device, a light beam imparted with image information on the display surface Sim is incident on the imaging optical system via optical members PP1 to PP3, and is projected by the imaging optical system onto a screen (see, for example, reference numeral 105 in FIG. 15 ), which is a projection surface. In other words, the display surface Sim and the screen are optically conjugate. The screen is an example of an "enlargement-side image surface" in the present disclosure, and the display surface Sim is an example of a "reduction-side image surface" in the present disclosure. Note that, in this specification, "screen" refers to an object onto which a projection image formed by the imaging optical system is projected. The screen may be, for example, a dedicated screen, or a wall, floor, ceiling, or exterior wall of a room.

[0032] In the description of this specification, the "magnification side" means the screen side on the optical path, and the "reduction side" means the display surface Sim side on the optical path. In this specification, the "magnification side" and "reduction side" are determined along the optical path. For example, in an imaging optical system that forms a folded optical path, "lens A is on the magnification side of lens B" has the same meaning as "lens A is on the optical path on the magnification side of lens B." Therefore, in an imaging optical system that forms a folded optical path, "the side closest to the magnification side" means the side closest to the magnification side in terms of order on the optical path, and does not mean the side closest to the screen in terms of distance.

[0033] The imaging optical system of the present disclosure is configured so that an intermediate image is formed at least twice between the magnification-side image plane and the reduction-side image plane. By forming an intermediate image within the optical system, the focal length of the entire system can be shortened, making it suitable for a wide angle of view. Furthermore, by forming an intermediate image two or more times, it is possible to achieve a wide angle of view and high performance while reducing the diameter of the optical element located on the furthest magnification side of the optical path.

[0034] The imaging optical system of the present disclosure preferably comprises, in order from the enlargement side to the reduction side along the optical path, a first optical system G1 and a second optical system G2, as described below. As an example, the imaging optical system of FIG. 1 is configured as follows: The first optical system G1 comprises an optical element P1. The second optical system G2 comprises, in order from the enlargement side to the reduction side, a lens L1, an aperture stop St, and lenses L2 to L4. Intermediate images M1 and M2 are formed within the optical element P1 of the first optical system G1. Note that the aperture stop St shown in FIG. 1 does not indicate its size or shape, but rather its position in the direction of the optical axis Z. Furthermore, the intermediate images M1 and M2 are conceptually shown by dashed lines in FIG. 1, and the shapes of the intermediate images M1 and M2 shown in FIG. 1 are not accurate.

[0035] It is preferable that the first optical system G1 include at least two reflective surfaces having a curvature. Generally, chromatic aberration becomes an issue when widening the angle of view. However, by including a reflective surface in the first optical system G1, which is located on the magnification side of the entire optical system, chromatic aberration does not occur during reflection, thereby reducing the occurrence of chromatic aberration throughout the entire optical system. Furthermore, by reflecting light multiple times, the optical system can be configured compactly while ensuring the necessary optical path length, contributing to miniaturization. Furthermore, by including multiple reflective surfaces, the power of each reflective surface can be reduced, thereby reducing the occurrence of various aberrations and the power of each optical element. In particular, the burden of aberration correction, etc., on the second optical system G2 can be reduced, thereby reducing the number of optical components of the second optical system G2 and contributing to miniaturization.

[0036] It is preferable that the surface on the magnification side on the optical path of the first optical system G1 be configured to refract light rays reflected by the reflecting surface of the first optical system G1. By configuring in this way, it is possible to both reduce the size of the reflecting surface of the first optical system G1 and correct distortion aberrations and the like, which become an issue when attempting to achieve a wider angle of view. Hereinafter, such a surface that is on the magnification side on the optical path of the first optical system G1 and also has the function of refracting light rays reflected by the reflecting surface will be referred to as the "first refracting surface."

[0037] Specifically, it is preferable that the surface on the most reduction side on the optical path of the first optical system G1 is the surface on the most reduction side on the optical path among the surfaces through which the light ray passes multiple times. In other words, it is preferable that, of the optical surfaces included in the entire optical system, all optical surfaces through which the light ray passes multiple times are included in the first optical system G1, and that each optical surface included in the second optical system G2 is one through which the light ray passes only once.

[0038] The imaging optical system of the present disclosure is preferably configured so that light rays are reflected three times by reflective surfaces having curvatures within the first optical system G1. In this case, the above-described effect achieved by including at least two reflective surfaces having curvatures in the first optical system G1 can be more effectively achieved. However, if light rays are to be reflected four or more times, it may become difficult to arrange the reflective surfaces, which may be disadvantageous for miniaturization.

[0039] As an example, the first optical system G1 in Fig. 1 reflects light rays three times within itself by two surfaces PA and PB of the optical member P1. Specifically, the first optical system G1 is configured such that a light ray traveling from the magnification side to the reduction side is refracted a first time in region A1 of surface PA, reflected a first time in region R1 of surface PB, reflected a second time in region R2 of surface PA, reflected a third time in region R3 of surface PB, and refracted a second time in region A2 of surface PA. Surface PA of optical member P1 is an example of a "first refractive surface" in the present disclosure. Hereinafter, PA will be used as the reference symbol for the first refractive surface.

[0040] The first refracting surface PA preferably has a free-form shape. By making the first refracting surface PA, i.e., the refracting surface on the magnification side on the optical path, a free-form shape, it becomes easy to control the aspect ratio of the image at the reduction-side conjugate plane and the image at the magnification-side conjugate plane. Furthermore, by making the first refracting surface PA a free-form shape, it becomes advantageous for correcting distortion, and it becomes possible to achieve both compactness and high performance.

[0041] It is also preferable that the first refractive surface PA transmits a light ray twice, which can reduce the time and man-hours required for the relative alignment of the optical surfaces during manufacturing, thereby contributing to cost reduction.

[0042] It is preferable that the first refractive surface PA and one reflecting surface are formed on the same optical element. That is, it is preferable that the optical element including the first refractive surface PA is configured to perform at least one reflection on the first refractive surface PA or another surface. This configuration is advantageous for ensuring performance because it can suppress performance degradation (e.g., degradation of distortion and curvature of field) that may occur due to misalignment of the relative positions of each refractive surface and each reflecting surface during manufacturing. Furthermore, it can reduce the time and labor required for relative alignment of each optical surface during manufacturing, contributing to cost reduction.

[0043] It is preferable that the reflective surface on the most enlargement side on the optical path of the first optical system G1 and the reflective surface on the most reduction side on the optical path of the first optical system G1 have a concave shape. By making the reflective surface on the most enlargement side on the optical path a concave shape with a converging effect, the reflective surface can be made smaller while also making the refractive surface on the enlargement side of the reflective surface smaller, compared to when the reflective surface is a convex shape with a diverging effect. Furthermore, by making the reflective surface on the most reduction side on the optical path a concave shape, it is possible to prevent the optical system on the enlargement side of the reflective surface from becoming larger, contributing to the miniaturization of the entire optical system. The surface PB in Figure 1 is an example of the "reflective surface on the most enlargement side on the optical path of the first optical system G1" and the "reflective surface on the most reduction side on the optical path of the first optical system G1."

[0044] It is preferable that the reflective surface on the magnification side in the optical path of the first optical system G1 and the reflective surface on the reduction side in the optical path of the first optical system G1 are formed on the same surface. By configuring the reflection to occur twice on the same surface (e.g., surface PB in FIG. 1), it is possible to suppress performance degradation (e.g., degradation of distortion and curvature of field) that may occur due to misalignment of the relative positions of the reflective surfaces during manufacturing, which is advantageous for ensuring performance. Furthermore, it is possible to reduce the time and labor required for tasks such as aligning the relative positions of the optical surfaces during manufacturing, which contributes to cost reduction.

[0045] The term "same surface" refers to a continuous surface having a shape formed based on the same design data. In the case of a spherical shape, the same radius of curvature is used. In the case of an aspherical shape, the same aspherical formula and aspherical coefficients are used. In the case of a free-form surface shape, the same free-form surface formula and free-form coefficients are used.

[0046] 1, when the first optical system G1 is made up of a single optical member P1, it is possible to more effectively prevent performance degradation (e.g., degradation of distortion and curvature of field) that may occur due to misalignment of the respective refractive surfaces and reflecting surfaces during manufacturing, which is advantageous for ensuring performance. Furthermore, it is possible to reduce the time and man-hours required for the relative alignment of the respective optical surfaces during manufacturing, which contributes to cost reduction.

[0047] Specifically, the optical element P1 includes a surface PA, which is the most magnified surface on the optical path and transmits light rays twice and reflects them once, and a surface PB, which is opposite to the surface PA and reflects light rays twice. Because a total of three reflections occur within the optical element P1, chromatic aberration does not occur during reflection, thereby reducing the occurrence of chromatic aberration throughout the optical system. Furthermore, by reflecting light three times, the optical system can be configured compactly while ensuring the necessary optical path length, contributing to miniaturization. Furthermore, by reflecting light three times, the power of each reflective surface can be reduced, thereby reducing the occurrence of various aberrations and the power of each optical element. Furthermore, since light enters and exits the optical element P1 through a single surface PA, this contributes to miniaturization of the optical element P1. The surface PA of the optical element P1 is an example of a "PA surface" in the present disclosure, and the surface PB of the optical element P1 is an example of a "PB surface" in the present disclosure.

[0048] 1 illustrates an example in which the optical element positioned on the most magnified side of the optical path is composed of a single optical element P1, but the imaging optical system of the present disclosure is not limited to this. For example, two or more optical elements bonded together may be used instead of the single optical element P1. Furthermore, the material of these optical elements may be resin or glass.

[0049] Furthermore, the imaging optical system of the present disclosure is preferably configured so that an intermediate image is formed twice inside the first optical system G1. When the first optical system G1 is configured to consist of a single optical member P1, as in the example of Figure 1, the imaging optical system may be configured so that an intermediate image is formed twice inside the optical member P1. In these cases, the above-mentioned effect of forming an intermediate image at least twice between the enlargement-side image forming surface and the reduction-side image forming surface can be more effectively obtained.

[0050] Fig. 2 is a diagram for explaining the shift of the optical axis Z1 of the first optical system G1 and the optical axis Z2 of the second optical system G2, and corresponds to the imaging optical system of Fig. 1. The optical axis Zv indicated by the two-dot chain line in Fig. 2 is a virtual optical axis based on lens data, which will be described later. The optical axis Z shown in Fig. 1 collectively represents the optical axis Z1 of the first optical system G1, the optical axis Z2 of the second optical system G2, and the virtual optical axis Zv between the surface of the second optical system G2 on the most reduction side and the display surface Sim.

[0051] Fig. 3 shows the display surface Sim in an XY coordinate system in which the point through which the virtual optical axis Zv (see Fig. 2) on the lens data passes is the origin. In Fig. 3, the interior of the display surface Sim is conveniently divided into eight grid squares. The grid point S0 is the center of the display surface Sim, and is shifted downward in Figs. 2 and 3 from the origin (the virtual optical axis Zv). The light beam LF0 shown in Fig. 1 passes through the grid point S0 in Fig. 3, the light beam LF1 shown in Fig. 1 passes through the grid point S1 in Fig. 3, and the light beam LF2 shown in Fig. 1 passes through the grid point S2 in Fig. 3.

[0052] In the imaging optical system of the present disclosure, at least one of the optical axis Z1 of the first optical system G1 and the optical axis Z2 of the second optical system G2 is preferably shifted in a direction perpendicular to the optical axes Z1 and Z2 relative to the center (lattice point S0) of the display element arranged on the reduction-side image forming surface (display surface Sim). Specifically, the optical axis Z1 of the first optical system G1 is preferably shifted in a direction perpendicular to the optical axis Z1 relative to the optical axis Z2 of the second optical system G2 and the center of the display element, and the optical axis Z2 of the second optical system G2 is preferably shifted in a direction perpendicular to the optical axis Z2 relative to the center of the display element. That is, as shown in FIG. 2 , in the imaging optical system of the present disclosure, the optical axis Z1, the optical axis Z2, and the center (lattice point S0) of the display element may be shifted relative to each other. Note that when the imaging optical system of the present disclosure is used as an imaging optical system, an imaging element is arranged on the reduction-side image forming surface instead of a display element, and a similar configuration may also be used in that case.

[0053] When the optical axis Z2 of the second optical system G2 and the center of the display element (or image sensor) are shifted, the degree of freedom of the position of the display element (or image sensor) in the direction perpendicular to the optical axis Z2 is improved, making it easier to avoid interference of light rays within the optical system. Furthermore, when the optical axis Z1 of the first optical system G1 and the optical axis Z2 of the second optical system G2 are shifted, in addition to the effect of avoiding the above-mentioned interference of light rays, the degree of freedom of the positions of the first optical system G1 and the second optical system G2 in the direction perpendicular to the optical axes Z1 and Z2 is improved, thereby improving design performance.

[0054] Next, preferred and possible configurations for the conditional expressions of the imaging optical system of the present disclosure will be described. In the following description of the conditional expressions, to avoid redundant explanation, the same symbols are used for elements with the same definitions, and duplicate explanations of symbols will be omitted. The "optical axis" used in the conditional expressions is the virtual optical axis Zv (see FIG. 2) on the lens data.

[0055] In the imaging optical system of the present disclosure, it is preferable to satisfy the following conditional expression (1), where L1 is the distance on the optical axis from the first refractive surface PA to the magnification-side reflective surface on the optical path of the first optical system G1, and L2 is the distance on the optical axis from the magnification-side reflective surface on the optical path of the first optical system G1 to the reduction-side surface on the optical path of the second optical system G2. In the example of FIG. 1 , the "magnification-side reflective surface on the optical path of the first optical system G1" is surface PB, and the "reduction-side surface on the optical path of the second optical system G2" is the reduction-side surface of lens L4. By ensuring that L1 is not equal to or greater than the upper limit of conditional expression (1), the length of L1 relative to L2 does not become too large, thereby preventing an increase in the diameter of the first refractive surface PA (i.e., the magnification-side reflective surface on the optical path). By ensuring that L2 is not equal to or less than the lower limit of conditional expression (1), the length of L2 relative to L1 does not become too large, thereby preventing the entire optical system from becoming large. In order to obtain better characteristics, it is more preferable that the imaging optical system of the present disclosure satisfy the following conditional expression (1-1): 0.1<|L1 / L2|<0.8 (1) 0.2<|L1 / L2|<0.7 (1-1)

[0056] Furthermore, in the imaging optical system of the present disclosure, it is preferable to satisfy the following conditional expression (2), where L3 is the distance on the optical axis from the first refractive surface PA to the most reduction-side reflective surface on the optical path of the first optical system G1, and L4 is the distance on the optical axis from the most reduction-side reflective surface on the optical path of the first optical system G1 to the most reduction-side surface on the optical path of the second optical system G2. In the example of FIG. 1 , the "most reduction-side reflective surface on the optical path of the first optical system G1" is surface PB. By ensuring that L3 is not equal to or greater than the upper limit of conditional expression (2), the length of L3 relative to L4 does not become too large, thereby preventing an increase in the diameter of the first refractive surface PA (i.e., the most magnification-side reflective surface on the optical path). By ensuring that L4 is not equal to or less than the lower limit of conditional expression (2), the length of L4 relative to L3 does not become too large, thereby preventing the entire optical system from becoming too large. In order to obtain better characteristics, it is more preferable that the imaging optical system of the present disclosure satisfy the following conditional expression (2-1). 0.1<|L3 / L4|<0.8 (2) 0.2<|L3 / L4|<0.7 (2-1)

[0057] The above-described preferred and possible configurations, including those related to the conditional expressions, can be arbitrarily combined, and are preferably selectively adopted as appropriate according to the required specifications. Various modifications are possible within the scope of the gist of the technology of the present disclosure. For example, in the technology of the present disclosure, the number of lenses and optical elements included in the imaging optical system, as well as the shapes of the lenses and optical elements, may be different from those in the example of FIG. 1.

[0058] As an example, a preferred aspect of the imaging optical system of the present disclosure comprises, in order along the optical path from the enlargement side to the reduction side, a first optical system G1 and a second optical system G2, wherein an intermediate image is formed at least twice between the enlargement side image forming surface and the reduction side image forming surface, the first optical system G1 includes at least two reflective surfaces having curvature, the most enlargement side surface on the optical path of the first optical system G1 is a first refracting surface PA that refracts light rays reflected by the reflective surface of the first optical system G1, and the most reduction side surface on the optical path of the first optical system G1 is the most reduction side surface on the optical path among the surfaces through which the light rays pass multiple times.

[0059] In addition, another preferred aspect of the imaging optical system of the present disclosure is one in which an intermediate image is formed at least twice between the enlargement-side image plane and the reduction-side image plane, and the optical element P1 arranged on the most enlargement side on the optical path includes a PA surface which is the most enlargement-side surface on the optical path and transmits light rays twice and reflects the light rays once, and a PB surface which is the surface opposite the PA surface and reflects the light rays twice.

[0060] Next, examples of the imaging optical system of the present disclosure will be described with reference to the drawings. The reference symbols attached to the cross-sectional views of each example are used independently for each example to avoid cluttering the explanations and drawings due to the increased number of digits in the reference symbols. Therefore, even if common reference symbols are attached in drawings of different examples, they do not necessarily have the same configuration. Hereinafter, the "optical axis" in the description of each example refers to the virtual optical axis Zv on the lens data (see FIG. 2).

[0061] [Example 1] The configuration of the imaging optical system of Example 1 and a cross-sectional view of the light beam are shown in Figure 1. The illustration method and configuration are as described above, so some overlapping explanations will be omitted here. The imaging optical system of Example 1 comprises, in order along the optical path from the enlargement side to the reduction side, a first optical system G1 and a second optical system G2. The first optical system G1 comprises an optical member P1. The optical member P1 of Example 1 is a resin lens. The second optical system G2 comprises, in order from the enlargement side to the reduction side, a lens L1, an aperture stop St, and lenses L2 to L4. Intermediate images M1 and M2 are formed inside the optical member P1 of the first optical system G1.

[0062] The first optical system G1 and the second optical system G2 are each shifted in a direction perpendicular to the optical axis. If the upward direction in FIG. 2 is the positive direction and the downward direction is the negative direction, the shift amounts relative to the virtual optical axis Zv are as follows: The first optical system G1 is shifted by 3.3223 mm (millimeters) in the positive direction, and the second optical system G2 is shifted by 1.4537 mm (millimeters).

[0063] 3, the display surface Sim is a horizontally long rectangle with a width of 5.184 mm (millimeters) and a height of 2.916 mm (millimeters). The center (lattice point S0) of the display surface Sim is located at coordinates (X, Y) = (0, -2.45) (unit: mm (millimeters)) in the XY coordinate system with the virtual optical axis Zv as the origin.

[0064] For the imaging optical system of Example 1, basic lens data is shown in Table 1, free-form surface coefficients are shown in Tables 2A and 2B, and aspherical surface coefficients are shown in Table 3. The free-form surface coefficients are shown in two tables to avoid making one table too long.

[0065] The table of basic lens data is written as follows. The Sn column indicates the surface number, with the surface closest to the enlargement side designated as surface 1 and the numbers increasing by one toward the reduction side. Aspherical surface numbers are marked with an *, and free-form surface surface numbers are marked with **. The R column indicates the radius of curvature of each surface, and the free-form surface column indicates the paraxial radius of curvature. The D column indicates the surface spacing along the optical axis Zv between each surface and its adjacent surface on the reduction side. The Nd column indicates the refractive index of each component with respect to the d-line. The νd column indicates the Abbe number of each component based on the d-line. Surface 20 in Table 1 corresponds to surface Sim. In this specification, the "d-line" refers to an emission line, and the wavelength of the d-line is treated as 587.56 nm (nanometers).

[0066] In the table of basic lens data, the sign of the radius of curvature of a surface that is convex on the enlargement side is positive, and the sign of the radius of curvature of a surface that is convex on the reduction side is negative. In the column Sn, the terms (PA), (PB), and (St) are also written for the surfaces that correspond to the first refracting surface PA, the surface PB arranged opposite the first refracting surface PA, and the aperture stop St, respectively.

[0067] The margins of Table 1 show the values ​​of the projection distance, full angle of view, and aperture diameter. The projection distance is the distance from the first refractive surface PA to the screen. The aperture diameter is the opening diameter (radius) of the aperture diaphragm St when the aperture diaphragm St is in the fully open state. The margins of the rows corresponding to each reflecting surface are marked "Reflecting surface."

[0068] In Tables 2A and 2B, for each free-form surface, the Sn row shows the surface number, and the C(i, j) row shows the numerical value of the free-form surface coefficient for each free-form surface. The "E±n" (n: integer) of the numerical value of the free-form surface coefficient in Tables 2A and 2B is "×10 ±ｎ The free-form surface coefficients shown in Tables 2A and 2B are the values ​​of the rotationally asymmetric free-form surface coefficients C(i, j) in the free-form surface formula expressed by the following formula: Z = ΣΣC(i, j) X ｉ ・Y ｊ Here, X, Y, and Z are coordinates with the surface vertex as the origin. In the above formula, the value of X is an absolute value. In the above formula, the first Σ is the summation with respect to i, and the second Σ is the summation with respect to j.

[0069] Table 3 shows the surface number and aspherical coefficient for each aspherical surface. In Table 3, the Sn row shows the surface number of the aspherical surface, and the KA and Am rows show the numerical value of the aspherical coefficient for each aspherical surface. Note that m in Am is an integer of 3 or more and varies depending on the surface. For example, for the 12th surface in Example 1, m = 3, 4, 5, ..., 10. The numerical value of the aspherical coefficient in Table 3, "E±n" (n: integer), is expressed as "×10 ±ｎ " KA and Am are aspherical coefficients in the aspherical formula expressed as follows: Zd = C × h ２ / {1 + (1 - KA × C ２ ×h ２ ) １ / ２} + ΣAm × h ｍ where Zd: aspherical depth (length of perpendicular line dropped from a point on the aspherical surface at height h to a plane perpendicular to the optical axis Z where the aspherical vertex is in contact) h: height (distance from the optical axis Z to the lens surface) C: reciprocal of the paraxial radius of curvature KA, Am: aspherical coefficients, and Σ in the aspherical formula represents the summation over m.

[0070] In the data in each table, the angle unit is degrees and the length unit is mm (millimeters), but since the optical system can be used with proportional magnification or reduction, other appropriate units can also be used. Also, in each table below, values ​​are listed rounded to a certain number of decimal places.

[0071]

[0072]

[0073]

[0074]

[0075] Fig. 4 shows spot diagrams obtained by tracing rays from the enlargement side to the reduction side in Example 1. Each spot diagram in Fig. 4 is a spot diagram at each of the 15 grid points indicated by black circles on the display surface Sim in Fig. 3 .

[0076] 5 shows the distortion grid of Example 1. The distortion grid shows the distorted shape of the grid pattern formed on the screen when an image made of a grid pattern is projected using the imaging optical system of Example 1.

[0077] The symbols, meanings, notation and illustration methods of each data item related to the above-mentioned first embodiment are basically the same in the following embodiments unless otherwise specified, and therefore, redundant explanations will be omitted below.

[0078] [Example 2] Figure 6 shows a cross-sectional view of the configuration of an imaging optical system of Example 2 and a light beam. The imaging optical system of Example 2 comprises, in order along the optical path from the enlargement side to the reduction side, a first optical system G1 and a second optical system G2. The first optical system G1 comprises an optical element P1. The optical element P1 of Example 2 is a glass lens. The second optical system G2 comprises, in order from the enlargement side to the reduction side, a lens L1, an aperture stop St, and lenses L2 to L4. Intermediate images M1 and M2 are formed inside the optical element P1 of the first optical system G1.

[0079] The first optical system G1 and the second optical system G2 are each shifted in a direction perpendicular to the optical axis. When the upward direction in FIG. 2 is the positive direction and the downward direction is the negative direction, the shift amounts relative to the virtual optical axis Zv are as follows: The first optical system G1 is shifted by 2.2243 mm (millimeters) in the positive direction, and the second optical system G2 is shifted by 1.1443 mm (millimeters). The size of the display surface Sim and its position relative to the virtual optical axis Zv are the same as in Example 1.

[0080] For the imaging optical system of Example 2, basic lens data is shown in Table 4, free-form surface coefficients are shown in Tables 5A and 5B, aspherical surface coefficients are shown in Table 6, a spot diagram is shown in FIG. 7, and a distortion grating is shown in FIG.

[0081]

[0082]

[0083]

[0084]

[0085] [Example 3] Figure 9 shows a cross-sectional view of the configuration of an imaging optical system and a light beam of Example 3. The imaging optical system of Example 3 comprises, in order along the optical path from the enlargement side to the reduction side, a first optical system G1 and a second optical system G2. The first optical system G1 comprises an optical member P2 and a reflecting surface RR. The second optical system G2 comprises, in order from the enlargement side to the reduction side, a lens L1, an aperture stop St, and lenses L2 to L4. Intermediate images M1 and M2 are formed within the first optical system G1.

[0086] The first optical system G1 and the second optical system G2 are each shifted in a direction perpendicular to the optical axis. When the upward direction in FIG. 2 is defined as the positive direction and the downward direction as the negative direction, the shift amounts relative to the virtual optical axis Zv are as follows: The first optical system G1 is shifted by 0.6206 mm (millimeters) in the positive direction, and the second optical system G2 is shifted by 0.2961 mm (millimeters). The size of the display surface Sim and its position relative to the virtual optical axis Zv are the same as in Example 1.

[0087] For the imaging optical system of Example 3, basic lens data is shown in Table 7, free-form surface coefficients are shown in Tables 8A and 8B, aspherical surface coefficients are shown in Table 9, a spot diagram is shown in FIG. 10, and a distortion grating is shown in FIG.

[0088]

[0089]

[0090]

[0091]

[0092] [Embodiment 4] Figure 12 shows a cross-sectional view of the configuration of an imaging optical system of embodiment 4 and a light beam. The imaging optical system of embodiment 4 comprises, in order from the enlargement side to the reduction side along the optical path, a first optical system G1 and a second optical system G2. The first optical system G1 comprises an optical member P1. The second optical system G2 comprises, in order from the enlargement side to the reduction side, lenses L1 to L5, an aperture stop St, and lenses L6 to L9. Intermediate images M1 and M2 are formed within the first optical system G1.

[0093] The size of the display surface Sim is the same as in Example 1. The center (lattice point S0) of the display surface Sim is located at coordinates (X, Y) = (0, -2.1) (unit: mm (millimeter)) in the XY coordinate system with the virtual optical axis Zv as the origin.

[0094] For the imaging optical system of Example 4, basic lens data is shown in Table 10, aspherical coefficients are shown in Table 11, a spot diagram is shown in FIG. 13, and a distortion grating is shown in FIG.

[0095]

[0096]

[0097] Table 12 shows the corresponding values ​​of conditional expressions (1) and (2) for the imaging optical systems of Examples 1 to 4.

[0098]

[0099] The imaging optical systems of Examples 1 to 4 are compact and made with a small number of optical elements, yet achieve high optical performance with excellent correction of aberrations. In addition, the total angle of view is wider than 130 degrees.

[0100] Next, a projection display device according to an embodiment of the present disclosure will be described. FIG. 15 is a schematic diagram illustrating the configuration of a projection display device according to an embodiment of the present disclosure. The projection display device 100 shown in FIG. 15 includes an imaging optical system 10 according to an embodiment of the present disclosure, a light source 15, transmissive display elements 11a to 11c as light valves corresponding to the respective color lights, dichroic mirrors 12 and 13 for color separation, a cross dichroic prism 14 for color synthesis, condenser lenses 16a to 16c, and total reflection mirrors 18a to 18c for deflecting the optical path. Note that FIG. 15 only illustrates the imaging optical system 10. An integrator is disposed between the light source 15 and the dichroic mirror 12, but is not shown in FIG. 15.

[0101] White light from the light source 15 is separated into three colored light beams (green light, blue light, and red light) by the dichroic mirrors 12 and 13, and then passes through condenser lenses 16a to 16c to enter and be modulated by the transmissive display elements 11a to 11c corresponding to the colored light beams, and is color-synthesized by the cross dichroic prism 14 before entering the imaging optical system 10. The imaging optical system 10 projects an optical image formed by the modulated light by the transmissive display elements 11a to 11c onto a screen 105.

[0102] FIG. 16 is a schematic diagram of a projection display device according to another embodiment of the present disclosure. The projection display device 200 shown in FIG. 16 includes an imaging optical system 210 according to an embodiment of the present disclosure, a light source 215, DMD elements 21a to 21c as light valves corresponding to the respective color lights, TIR (Total Internal Reflection) prisms 24a to 24c for color separation and color synthesis, and a polarization separation prism 25 that separates the illumination light and the projection light. Note that FIG. 16 only shows a schematic diagram of the imaging optical system 210. An integrator is disposed between the light source 215 and the polarization separation prism 25, but is not shown in FIG. 16.

[0103] White light from light source 215 is reflected by a reflective surface inside polarization separation prism 25, and then separated into three colored light beams (green light, blue light, and red light) by TIR prisms 24a to 24c. Each separated colored light beam enters and is modulated by a corresponding DMD element 21a to 21c, travels again in the opposite direction through TIR prisms 24a to 24c, and is color-synthesized. Then, it passes through polarization separation prism 25 and enters imaging optical system 210. Imaging optical system 210 projects an optical image formed by the modulated light by DMD elements 21a to 21c onto screen 205.

[0104] FIG. 17 is a schematic diagram of a projection display device according to yet another embodiment of the present disclosure. The projection display device 300 shown in FIG. 17 includes an imaging optical system 310 according to an embodiment of the present disclosure, a light source 315, reflective display elements 31a to 31c as light valves corresponding to the respective color lights, dichroic mirrors 32 and 33 for color separation, a cross dichroic prism 34 for color synthesis, a total reflection mirror 38 for optical path deflection, and polarization separation prisms 35a to 35c. Note that FIG. 17 only shows the imaging optical system 310 in a simplified manner. An integrator is disposed between the light source 315 and the dichroic mirror 32, but is not shown in FIG. 17.

[0105] White light from the light source 315 is separated into three colored light beams (green light, blue light, and red light) by the dichroic mirrors 32 and 33. Each separated colored light beam passes through the polarization separation prisms 35a to 35c, enters the reflective display elements 31a to 31c corresponding to the colored light beam, is modulated, and is then color-synthesized by the cross dichroic prism 34 before entering the imaging optical system 310. The imaging optical system 310 projects an optical image formed by the modulated light by the reflective display elements 31a to 31c onto the screen 305.

[0106] 18 and 19 are external views of a camera 400, which is an imaging device according to an embodiment of the present disclosure. Fig. 18 shows a perspective view of the camera 400 as seen from the front side, and Fig. 19 shows a perspective view of the camera 400 as seen from the rear side. The camera 400 is a single-lens digital camera without a reflex viewfinder, to which an interchangeable lens 48 is removably attached. The interchangeable lens 48 has an imaging optical system 49 according to an embodiment of the present disclosure housed within a lens barrel.

[0107] The camera 400 includes a camera body 41, and a shutter button 42 and a power button 43 are provided on the top surface of the camera body 41. An operation unit 44, an operation unit 45, and a display unit 46 are provided on the back surface of the camera body 41. The display unit 46 displays a captured image and an image within the angle of view before the image was captured.

[0108] A photographic opening through which light from the subject to be photographed enters is provided in the center of the front of the camera body 41, and a mount 47 is provided at a position corresponding to the photographic opening, and an interchangeable lens 48 is attached to the camera body 41 via the mount 47.

[0109] The camera body 41 contains an imaging element (not shown) such as a CCD (Charge Coupled Device) or CMOS (Complementary Metal Oxide Semiconductor) that outputs an imaging signal corresponding to the subject image formed by the interchangeable lens 48, a signal processing circuit (not shown) that processes the imaging signal output from the imaging element to generate an image, and a recording medium (not shown) for recording the generated image. The camera 400 is capable of taking still images or videos by pressing the shutter button 42, and the image data obtained by this shooting is recorded on the recording medium.

[0110] Although the technology of the present disclosure has been described above using embodiments and examples, the technology of the present disclosure is not limited to the above embodiments and examples and can be modified in various ways. For example, the radius of curvature, surface spacing, refractive index, Abbe number, free-form surface coefficient, aspherical coefficient, etc. of each lens and optical member are not limited to the values ​​shown in the above examples and can take other values.

[0111] Furthermore, the projection display device according to the technology of the present disclosure is not limited to the above configuration, and for example, the optical members and light valves used for light beam separation or light beam combination can be modified in various ways. The light valve is not limited to a configuration in which light from a light source is spatially modulated by an image display element and output as an optical image based on image data, but may be a configuration in which light output from a self-luminous image display element itself is output as an optical image based on image data. Examples of self-luminous image display elements include image display elements in which light-emitting elements such as LEDs (Light Emitting Diodes) or OLEDs (Organic Light Emitting Diodes) are two-dimensionally arranged.

[0112] Furthermore, the imaging device according to the technology of the present disclosure is not limited to the above configuration, but can take various forms, such as a camera other than a non-reflex camera, a film camera, a video camera, and a camera for filming movies.

[0113] The following supplementary notes are further disclosed in relation to the above-described embodiments and examples: [Supplementary Note 1] An imaging optical system comprising, in order from the enlargement side to the reduction side along an optical path, a first optical system and a second optical system, wherein an intermediate image is formed at least twice between the enlargement-side image forming surface and the reduction-side image forming surface, the first optical system includes at least two reflective surfaces having a curvature, the surface on the optical path of the first optical system that is closest to the enlargement side is a first refracting surface that refracts light rays reflected by the reflective surfaces of the first optical system, and the surface on the optical path of the first optical system that is closest to the reduction side is the surface on the optical path that is closest to the reduction side among surfaces through which light rays pass multiple times. [Supplementary Note 2] The imaging optical system according to Supplementary Note 1, which satisfies conditional expression (1) expressed by: 0.1<|L1 / L2|<0.8 (1), where L1 is the distance on the optical axis from the first refracting surface to the most enlargement-side reflective surface on the optical path of the first optical system, and L2 is the distance on the optical axis from the most enlargement-side reflective surface on the optical path of the first optical system to the most reduction-side surface on the optical path of the second optical system. [Supplementary Note 3] The imaging optical system according to Supplementary Note 1 or Supplementary Note 2, which satisfies conditional expression (2) expressed by: 0.1<|L3 / L4|<0.8 (2), where L3 is the distance on the optical axis from the first refracting surface to the most reduction-side reflective surface on the optical path of the first optical system, and L4 is the distance on the optical axis from the most reduction-side reflective surface on the optical path of the first optical system to the most reduction-side surface on the optical path of the second optical system. [Supplementary Note 4] The imaging optical system according to any one of Supplementary Notes 1 to 3, wherein a light ray is reflected three times by a reflective surface having a curvature inside the first optical system. [Supplementary Note 5] The imaging optical system according to any one of Supplementary Notes 1 to 4, wherein a reflective surface on the magnification side on the optical path of the first optical system and a reflective surface on the reduction side on the optical path of the first optical system have concave shapes. [Supplementary Note 6] The imaging optical system according to any one of Supplementary Notes 1 to 5, wherein the intermediate image is formed twice inside the first optical system. [Supplementary Note 7] The imaging optical system according to any one of Supplementary Notes 1 to 6, wherein the first refracting surface has a free-form surface shape.[Supplementary Note 8] The imaging optical system according to any one of Supplementary Notes 1 to 7, including a display element or an image sensor arranged on the reduction-side image surface, wherein at least one of the optical axis of the first optical system and the optical axis of the second optical system is shifted in a direction perpendicular to the optical axis with respect to the center of the display element or the image sensor. [Supplementary Note 9] The imaging optical system according to Supplementary Note 8, wherein the optical axis of the first optical system is shifted in a direction perpendicular to the optical axis with respect to the optical axis of the second optical system and the center of the display element or the image sensor, respectively, and the optical axis of the second optical system is shifted in a direction perpendicular to the optical axis with respect to the center of the display element or the image sensor. [Supplementary Note 10] The imaging optical system according to any one of Supplementary Notes 1 to 9, wherein the first refractive surface transmits a light ray twice. [Supplementary Note 11] The imaging optical system according to any one of Supplementary Notes 1 to 10, wherein the first refractive surface and one of the reflecting surfaces are formed in the same optical member. [Supplementary Note 12] The imaging optical system according to any one of Supplementary Notes 1 to 11, wherein the first optical system is composed of one optical member. [Supplementary Note 13] The imaging optical system according to Supplementary Note 12, wherein the optical member includes: the first refracting surface that transmits a light ray twice and reflects the light ray once, and a surface that is opposed to the first refracting surface and is disposed opposite to the first refracting surface, and that reflects the light ray twice. [Supplementary Note 14] The imaging optical system according to any one of Supplementary Notes 1 to 13, wherein a reflecting surface on the most enlargement side in the optical path of the first optical system and a reflecting surface on the most reduction side in the optical path of the first optical system are formed on the same surface. [Supplementary Note 15] The imaging optical system according to Supplementary Note 2, which satisfies conditional expression (1-1) expressed by 0.2<|L1 / L2|<0.7 (1-1). [Supplementary Note 16] An imaging optical system according to Supplementary Note 3, which satisfies conditional expression (2-1) expressed by: 0.2<|L3 / L4|<0.7 (2-1) [Supplementary Note 17] An imaging optical system in which an intermediate image is formed at least twice between an enlargement-side image forming surface and a reduction-side image forming surface, and an optical element disposed on the most enlargement side on the optical path includes: a PA surface, which is the most enlargement-side surface on the optical path, that transmits a light ray twice and reflects the light ray once, and a PB surface, which is disposed opposite the PA surface and reflects the light ray twice.[Supplementary Note 18] The imaging optical system according to Supplementary Note 17, wherein the intermediate image is formed twice inside the optical member. [Supplementary Note 19] A projection display device including the imaging optical system according to any one of Supplementary Notes 1 to 18. [Supplementary Note 20] An imaging device including the imaging optical system according to any one of Supplementary Notes 1 to 18.

[0114] The disclosure of Japanese Patent Application No. 2023-116335, filed on July 14, 2023, is incorporated herein by reference in its entirety. All documents, patent applications, and technical standards described herein are incorporated herein by reference to the same extent as if each individual document, patent application, and technical standard was specifically and individually indicated to be incorporated by reference.

Claims

1. An imaging optical system comprising, in order from the enlargement side to the reduction side along an optical path, a first optical system and a second optical system, wherein an intermediate image is formed at least twice between the enlargement side image forming surface and the reduction side image forming surface, said first optical system includes at least two reflective surfaces having a curvature, said most enlargement side surface on the optical path of said first optical system is a first refracting surface that refracts a light ray reflected by the reflective surface of said first optical system, and said most reduction side surface on the optical path of said first optical system is the most reduction side surface on the optical path among surfaces through which a light ray passes multiple times.

2. The imaging optical system according to claim 1, which satisfies conditional expression (1) expressed by: 0.1<|L1 / L2|<0.8 (1), where L1 is the distance on the optical axis from the first refracting surface to the most enlargement-side reflecting surface on the optical path of the first optical system, and L2 is the distance on the optical axis from the most enlargement-side reflecting surface on the optical path of the first optical system to the most reduction-side surface on the optical path of the second optical system.

3. The imaging optical system according to claim 2, which satisfies conditional expression (2) expressed by: 0.1<|L3 / L4|<0.8 (2), where L3 is the distance on the optical axis from the first refracting surface to the most reduction-side reflecting surface on the optical path of the first optical system, and L4 is the distance on the optical axis from the most reduction-side reflecting surface on the optical path of the first optical system to the most reduction-side surface on the optical path of the second optical system.

4. The imaging optical system according to claim 3, wherein within said first optical system, a light ray is reflected three times by a reflective surface having a curvature.

5. The imaging optical system according to claim 4, wherein the reflecting surface on the most enlargement side in the optical path of said first optical system and the reflecting surface on the most reduction side in the optical path of said first optical system are concave in shape.

6. The imaging optical system according to claim 1, wherein the intermediate image is formed twice inside the first optical system.

7. The imaging optical system according to claim 1, wherein the first refracting surface has a free-form shape.

8. The imaging optical system according to claim 1, further comprising a display element or an image sensor arranged on the reduced-side image surface, wherein at least one of the optical axis of the first optical system and the optical axis of the second optical system is shifted in a direction perpendicular to the optical axis with respect to the center of the display element or the image sensor.

9. The imaging optical system described in claim 8, wherein the optical axis of the first optical system is shifted in a direction perpendicular to the optical axis relative to the optical axis of the second optical system and the center of the display element or the image sensor, respectively, and the optical axis of the second optical system is shifted in a direction perpendicular to the optical axis relative to the center of the display element or the image sensor.

10. The imaging optical system according to claim 1, wherein the first refractive surface transmits a light ray twice.

11. The imaging optical system according to claim 1, wherein the first refractive surface and one of the reflecting surfaces are formed on the same optical member.

12. The imaging optical system according to claim 1, wherein the first optical system is composed of a single optical member.

13. The imaging optical system according to claim 12, wherein the optical member comprises: the first refracting surface that transmits a light ray twice and reflects the light ray once; and a surface opposed to the first refracting surface that reflects the light ray twice.

14. The imaging optical system according to claim 12, wherein the reflecting surface on the most enlargement side in the optical path of the first optical system and the reflecting surface on the most reduction side in the optical path of the first optical system are formed on the same surface.

15. The imaging optical system according to claim 2, which satisfies the conditional expression (1-1) expressed as: 0.2<|L1 / L2|<0.7 (1-1).

16. The imaging optical system according to claim 3, which satisfies the conditional expression (2-1) expressed as: 0.2<|L3 / L4|<0.7 (2-1).

17. An imaging optical system in which an intermediate image is formed at least twice between an enlargement-side image surface and a reduction-side image surface, and an optical element arranged on the most enlargement side on the optical path includes: a PA surface which is the most enlargement side surface on the optical path, which transmits a light ray twice and reflects the light ray once, and a PB surface which is a surface opposite to the PA surface and reflects the light ray twice.

18. The imaging optical system according to claim 17, wherein the intermediate image is formed twice inside the optical member.

19. A projection display device comprising the imaging optical system according to any one of claims 1 to 18.

20. An imaging device comprising an imaging optical system according to any one of claims 1 to 18.

Images