Optical system

Abstract

The present application discloses an optical system, which includes, in sequence from a first side to a second side along an optical axis, a first element group with positive optical power and a second element group with positive optical power, wherein the first element group includes a reflective polarizing element, a quarter-wave plate, a first lens, and a partially reflecting element, and the second element group includes a second lens and a third lens, which are cemented together; wherein the curvature radius R3 of the first side surface of the second lens, the curvature radius R6 of the second side surface of the third lens, and the effective focal length FG2 of the second element group satisfy the following relationship: 0.4<|R3+R6| / FG2<1.9.

Description

Technical Field

[0001] The present application relates to the field of optical devices, and in particular to a catadioptric optical system. Background Art

[0002] As the application scenarios of virtual reality devices continue to expand, higher technical requirements are being placed on their performance, color rendering, and wearing experience. While existing catadioptric optical systems offer significant advantages in overall size, they still require multiple lens combinations to correct for edge aberrations. This inevitably increases the load on the optical system, impacting the user experience while wearing the system. Summary of the Invention

[0003] The present application provides an optical system that can at least solve or partially solve at least one problem or other problems existing in the prior art.

[0004] One aspect of the present application provides an optical system, which includes, in sequence from a first side to a second side along an optical axis, a first element group with positive optical power and a second element group with positive optical power, wherein the first element group includes a reflective polarizing element, a quarter-wave plate, a first lens, and a partially reflecting element, and the second element group includes a second lens and a third lens, and the second lens and the third lens are cemented together; wherein a curvature radius R3 of a first side surface of the second lens, a curvature radius R6 of a second side surface of the third lens, and an effective focal length FG2 of the second element group satisfy the following relationship: 0.4<|R3+R6| / FG2<1.9.

[0005] According to an exemplary embodiment of the present application, the effective focal length FG1 of the first element group, the effective focal length FG2 of the second element group, and the on-axis distance TD from the first side surface of the first lens to the second side surface of the third lens satisfy: 1.3<(FG2-FG1) / TD<2.0.

[0006] According to an exemplary embodiment of the present application, the total effective focal length f of the optical system satisfies: 25 mm <f<28mm。

[0007] According to an exemplary embodiment of the present application, the total effective focal length f of the optical system, the entrance pupil diameter EPD of the optical system, the refractive index N2 of the second lens and the refractive index N3 of the third lens satisfy: 5.0<(f / EPD)×(N2 / N3)<6.0.

[0008] According to an exemplary embodiment of the present application, the sum ΣCT of the central thicknesses of the first lens, the second lens, and the third lens on the optical axis, the total effective focal length f of the optical system, and the maximum field of view FOV of the optical system satisfy the following conditions: 0.6<ΣCT / (f×tan(FOV / 2))<0.9.

[0009] According to an exemplary embodiment of the present application, the center thickness CT1 of the first lens on the optical axis, the air interval T12 between the first lens and the second lens on the optical axis, and the entrance pupil diameter EPD of the optical system satisfy: 2.5<(CT1+T12) / EPD<3.1.

[0010] According to an exemplary embodiment of the present application, the effective focal length FG1 of the first element group, the center thickness CTR of the reflective polarizing element on the optical axis, the center thickness CTQ of the quarter-wave plate on the optical axis, and the center thickness CT1 of the first lens on the optical axis satisfy: 1.8 <FG1 / (CTR+CTQ+CT1)<3.2。

[0011] According to an exemplary embodiment of the present application, the center thickness CT1 of the first lens on the optical axis, the center thickness CT2 of the second lens on the optical axis, and the center thickness CT3 of the third lens on the optical axis satisfy the following conditions: 0.8 <CT1 / (CT2+CT3)<1.3。

[0012] According to an exemplary embodiment of the present application, the effective focal length FG2 of the second element group, the Abbe number V2 of the second lens and the Abbe number V3 of the third lens satisfy: 0.7 mm <FG2 / (V2+V3)<1.1mm。

[0013] According to an exemplary embodiment of the present application, the refractive index N1 of the first lens, the Abbe number V1 of the first lens, the center thickness CTR of the reflective polarizer on the optical axis, and the center thickness CTQ of the quarter-wave plate on the optical axis satisfy: 0<(N1 / V1)×(CTR / CTQ)<0.1.

[0014] According to an exemplary embodiment of the present application, a central thickness CT2 of the second lens on the optical axis and a curvature radius R3 of the first side surface of the second lens satisfy: 0.2<10×CT2 / R3<0.5.

[0015] The optical system provided by the present application is configured as a catadioptric optical system. By ensuring that both the first element group and the second element group have positive focal length, the two element groups can be used to fully converge the light beam, and the reflective polarizing element in the first element group can fold the light path, effectively shortening the total axial length of the optical system and improving the user's experience of wearing the optical system. The second lens and the third lens are glued together to form a double-cemented lens. On the basis of gapless assembly to save the total axial length of the optical system, they can compensate for chromatic aberrations with each other, which is beneficial to the color performance of the optical system's external field of view. When paired with the first lens, it can fully regulate the aberrations of the optical system and optimize the imaging performance of the optical system. At the same time, by controlling the ratio of the sum of the curvature radii of the two surfaces of the double-cemented lens to the effective focal length of the second element group, it is beneficial to the evaluation of lens strength and shape preset during processing, and the marginal light is regulated to improve the processability and assembly stability of the double-cemented lens. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Other features, objects and advantages of the present application will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings, in which:

[0017] Figure 1 1 shows a schematic structural diagram of an optical system according to Example 1 of the present application;

[0018] Figures 2A to 2C axial chromatic aberration curve, astigmatism curve, and distortion curve of the optical system according to Example 1 of the present application are respectively shown;

[0019] Figure 3 1 shows a schematic structural diagram of an optical system according to Example 2 of the present application;

[0020] Figures 4A to 4C axial chromatic aberration curve, astigmatism curve, and distortion curve of the optical system according to Example 2 of the present application are respectively shown;

[0021] Figure 5 1 shows a schematic structural diagram of an optical system according to Example 3 of the present application;

[0022] Figures 6A to 6C axial chromatic aberration curve, astigmatism curve, and distortion curve of the optical system according to Example 3 of the present application are respectively shown;

[0023] Figure 7 1 shows a schematic structural diagram of an optical system according to Example 4 of the present application;

[0024] Figures 8A to 8C axial chromatic aberration curve, astigmatism curve, and distortion curve of the optical system according to Example 4 of the present application are respectively shown;

[0025] Figure 9shows a schematic structural diagram of an optical system according to embodiment 5 of the present application; and

[0026] 10A to 10C The axial chromatic aberration curve, astigmatism curve and distortion curve of the optical system according to Example 5 of the present application are respectively shown. DETAILED DESCRIPTION

[0027] In order to better understand the present application, various aspects of the present application will be described in more detail with reference to the accompanying drawings. It should be understood that these detailed descriptions are merely descriptions of exemplary embodiments of the present application and are not intended to limit the scope of the present application in any way. Throughout the specification, the same reference numerals refer to the same elements.

[0028] It should be noted that in this specification, the terms "first," "second," "third," etc., are used solely to distinguish one feature from another and do not limit the features. Thus, the first lens discussed below could also be referred to as the second lens or the third lens without departing from the teachings of this application.

[0029] In the drawings, the thickness, size, and shape of the lenses are slightly exaggerated for ease of illustration. Specifically, the shapes of the spherical and aspherical surfaces shown in the drawings are provided by way of example. That is, the shapes of the spherical and aspherical surfaces are not limited to those shown in the drawings. The drawings are for illustration only and are not drawn strictly to scale.

[0030] In this document, the paraxial region refers to the region near the optical axis. If a lens surface is convex and the position of the convex surface is undefined, it means that the lens surface is convex at least in the paraxial region. If a lens surface is concave and the position of the concave surface is undefined, it means that the lens surface is concave at least in the paraxial region. The surface of each lens closest to the first side (e.g., the eye side) is called the first side surface of the lens, and the surface of each lens closest to the second side (e.g., the display side) is called the second side surface of the lens.

[0031] It should also be understood that the terms "comprise," "including," "having," "include," and / or "comprising," when used in this specification, indicate the presence of the stated features, elements, and / or components, but do not preclude the presence or addition of one or more other features, elements, components, and / or combinations thereof. Furthermore, when describing embodiments of the present application, the term "may" is used to mean "one or more embodiments of the present application." Furthermore, the term "exemplary" is intended to refer to an example or illustration.

[0032] Unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by those skilled in the art to which this application belongs. It should also be understood that terms (such as those defined in commonly used dictionaries) should be interpreted as having a meaning consistent with their meaning in the context of the relevant technology and will not be interpreted in an idealized or overly formal sense unless expressly defined as such herein.

[0033] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0034] The features, principles and other aspects of the present application are described in detail below.

[0035] refer to Figure 1 、 Figure 3 、 Figure 5 、 Figure 7 and Figure 9 In a first aspect, the present application provides an optical system that may include a first element group and a second element group arranged sequentially along an optical axis from a first side to a second side. The first element group may have positive optical power and include a reflective polarizing element, a quarter-wave plate, a first lens, and a partially reflecting element. The second element group may have positive optical power and include a second lens and a third lens. The second lens and the third lens are cemented together, i.e., the air gap between the second lens and the third lens on the optical axis is 0 mm.

[0036] In an exemplary embodiment, the first side may be, for example, the side closest to the human eye, and the second side may be, for example, the side closest to the display. Accordingly, the first side of each element (the first lens, the second lens, the third lens, the reflective polarizer, the quarter-wave plate, and the partially reflective element) may be referred to as the side closest to the human eye, and the second side may be referred to as the side closest to the display.

[0037] In an exemplary embodiment, the optical system may further include an aperture, which may be disposed, for example, between the first side and the first lens. Image light from the display is refracted and reflected multiple times through the third lens, the second lens, the first lens, the reflective polarizer, the quarter-wave plate, the partially reflective element, and ultimately projected into the user's eyes.

[0038] In an exemplary embodiment, the second side of the optical system may be provided with an imaging surface, which may, for example, be provided with a display. The image light from the display may sequentially pass through the third lens, the second lens, the first lens, and the quarter-wave plate to reach the reflective polarizing element, and then be reflected at the reflective polarizing element to form a first reflection of the image light. The first reflection of the image light passes through the quarter-wave plate and reaches the partially reflective element on the second side of the first lens, and then is reflected at the partially reflective element to form a second reflection of the image light. The second reflection of the image light sequentially passes through the first lens, the quarter-wave plate, the reflective polarizing element to the aperture and is finally projected into the user's eyes. The optical system provided in the present application folds the required optical path without affecting the projection quality through a combination of light reflection and refraction, thereby effectively shortening the main body length of the optical system.

[0039] In an exemplary embodiment, a reflective polarizing element and a quarter-wave plate are laminated to form a single film layer, which is then attached to the first side surface of the first lens. The reflective polarizing element is located on the first side surface of the quarter-wave plate. By laminating the reflective polarizing element and the quarter-wave plate to form a single film layer, the number of film layers to which the film layer is attached can be reduced, thereby improving the film layer attachment yield.

[0040] As an example, the first side surface of the first lens is configured as a flat surface, and a film layer formed by laminating a reflective polarizer and a quarter-wave plate is attached to the first side surface of the first lens. Using a planar lamination method to attach the composite film layer to the flat surface improves the stability of the film layer after attachment, thereby enhancing the optical system's field of view performance.

[0041] As an example, the second side surface of the first lens is configured as a plane, and a partially reflective element is attached to the second side surface of the first lens. The partially reflective element has a semi-transmissive and semi-reflective effect on light. By providing a partially reflective element on the second side surface of the first lens, combined with a reflective polarizing element and a quarter-wave plate on the first side surface of the first lens, light can be refracted multiple times, effectively reducing the main length of the optical system. At the same time, the partially reflective element is attached to the plane using a flat film, which helps to improve the stability of the partially reflective element after attachment, thereby improving the external field of view performance of the optical system.

[0042] In an exemplary embodiment, the radius of curvature R3 of the first side surface of the second lens, the radius of curvature R6 of the second side surface of the third lens, and the effective focal length FG2 of the second element group may satisfy: 0.4 < |R3 + R6| / FG2 < 1.9. Both the first element group and the second element group have positive optical powers. The two element groups with positive optical powers can fully converge the light beam, and the reflective polarizing element in the first element group can fold the optical path, effectively shortening the total axial length of the optical system and improving the user experience of wearing the optical system. The second lens and the third lens are cemented to form a doublet lens. On the basis of assembling without gaps to save the total axial length of the optical system, chromatic aberration can be mutually compensated, which is beneficial to the color performance of the outer field of view of the optical system. When paired with the first lens, it can fully control the aberration of the optical system and optimize the imaging performance of the optical system. At the same time, by controlling the ratio of the sum of the radii of curvature of the two surfaces of the doublet lens to the effective focal length of the second element group, it is beneficial to evaluate the lens strength and preset the shape during processing, and to control the marginal rays, improving the processability and assembly stability of the doublet lens.

[0043] In an exemplary embodiment, the effective focal length FG1 of the first element group, the effective focal length FG2 of the second element group, and the on-axis distance TD from the first side surface of the first lens to the second side surface of the third lens satisfy: 1.3 < (FG2 - FG1) / TD < 2.0. By controlling the ratio of the difference between the effective focal lengths of the second element group and the first element group to the on-axis distance from the first side surface of the first lens to the second side surface of the third lens, it is beneficial to reasonably distribute the focal length of the optical system and restrict the virtual image distance of the optical system, avoiding the problem that the virtual image is too far or too close, which causes the virtual image to exceed the human visual regulation range and affects the actual visual experience.

[0044] In an exemplary embodiment, the total effective focal length f of the optical system may satisfy: 25 mm < f < 28 mm. By restricting the total effective focal length of the optical system within the range of 25 mm to 28 mm, the field angle and the body length of the optical system can be reasonably configured, facilitating the presetting of the mechanism and optical elements, and facilitating the estimation of the display size and the design of the virtual image position.

[0045] In an exemplary embodiment, the total effective focal length f of the optical system, the entrance pupil diameter EPD of the optical system, the refractive index N2 of the second lens, and the refractive index N3 of the third lens may satisfy: 5.0 < (f / EPD) × (N2 / N3) < 6.0. By controlling the mutual relationship among the total effective focal length of the optical system, the entrance pupil diameter of the optical system, and the refractive indices of the second lens and the third lens, it is beneficial to increase the brightness of the entrance pupil light, enhance the entrance pupil imaging effect of the optical system in a dark environment, and reduce the problem of marginal field vignetting; at the same time, it is also beneficial to control the angle of the light rays emitted from the display, facilitating the selection of reasonable doublet lens materials and curvatures.

[0046] In an exemplary embodiment, the sum ∑CT of the central thicknesses of the first lens, the second lens, and the third lens on the optical axis, the total effective focal length f of the optical system, and the maximum field angle FOV of the optical system may satisfy: 0.6 < ∑CT / (f × tan(FOV / 2)) < 0.9. By controlling the relationship among the sum of the central thicknesses of the first lens, the second lens, and the third lens on the optical axis, the total effective focal length of the optical system, and the maximum field angle of the optical system, it is beneficial to constrain the image height of the optical system, indirectly limit the object height of the display, and ensure that the overall size of the optical system is within a reasonable range to meet the basic wearing requirement of being lightweight.

[0047] In an exemplary embodiment, the central thickness CT1 of the first lens on the optical axis, the air gap T12 between the first lens and the second lens on the optical axis, and the entrance pupil diameter EPD of the optical system may satisfy: 2.5 < (CT1 + T12) / EPD < 3.1. By controlling the ratio of the sum of the central thickness of the first lens on the optical axis and the air gap between the first lens and the second lens on the optical axis to the entrance pupil diameter of the optical system, it is beneficial to ensure the forming and processing strength of the first lens, avoid interference during the assembly of the first lens and the second lens; and it is also beneficial to indirectly limit the exit pupil distance, facilitating the evaluation of parameters such as the eye movement range.

[0048] In an exemplary embodiment, the effective focal length FG1 of the first element group, the central thickness CTR of the reflective polarizing element on the optical axis, the central thickness CTQ of the quarter-wave plate on the optical axis, and the central thickness CT1 of the first lens on the optical axis may satisfy: 1.8 < FG1 / (CTR + CTQ + CT1) < 3.2. By controlling the ratio of the effective focal length of the first element group to the sum of the central thicknesses of the first lens, the reflective polarizing element, and the quarter-wave plate, it is beneficial to compress the total length of the refractive and reflective optical paths, reserve a light optimization space for the transmission optical path, and facilitate the limitation of the overall size of the optical system; at the same time, it is also beneficial to limit the field angle of the entrance pupil light rays to meet the basic usage requirement of a large field angle.

[0049] In an exemplary embodiment, the central thickness CT1 of the first lens on the optical axis, the central thickness CT2 of the second lens on the optical axis, and the central thickness CT3 of the third lens on the optical axis may satisfy: 0.8 < CT1 / (CT2 + CT3) < 1.3. By controlling the ratio of the central thickness of the first lens to that of the doublet lens, it is beneficial to reasonably distribute the lens thicknesses in the optical system, ensure the processing and assembly strength of the lenses, and avoid the problem of poor actual productivity of the lenses caused by extreme optimization of the lenses.

[0050] In an exemplary embodiment, the effective focal length FG2 of the second element group, the Abbe number V2 of the second lens, and the Abbe number V3 of the third lens may satisfy: 0.7 mm < FG2 / (V2 + V3) < 1.1 mm. By controlling the ratio of the effective focal length of the second element group to the sum of the Abbe numbers of the second lens and the third lens, while ensuring that the second element group has a reasonable focal length range, it is beneficial to reasonably distribute the dispersion coefficients of the second lens and the third lens, facilitate the adjustment of chromatic aberration compensation of the optical system, avoid abnormal phenomena such as large-field color distortion and purple fringing in the optical system, and optimize the visual experience.

[0051] In an exemplary embodiment, the refractive index N1 of the first lens, the Abbe number V1 of the first lens, the central thickness CTR of the reflective polarizing element on the optical axis, and the central thickness CTQ of the quarter-wave plate on the optical axis may satisfy: 0 < (N1 / V1) × (CTR / CTQ) < 0.1. By controlling the ratio of the refractive index of the first lens to the Abbe number and the ratio of the central thicknesses of the reflective polarizing element and the quarter-wave plate, and constraining the product of the two ratios within a reasonable range, it is beneficial for the material selection of the first lens and the thickness control of the reflective polarizing element and the quarter-wave plate, reducing the influence of the reflective polarizing element and the quarter-wave plate on the light transmission of the first element group, and improving the feasibility of optimization adjustment in design and actual production.

[0052] In an exemplary embodiment, the central thickness CT2 of the second lens on the optical axis and the radius of curvature R3 of the first side of the second lens may satisfy: 0.2 < 10 × CT2 / R3 < 0.5. By controlling the ratio of the central thickness of the second lens on the optical axis to the radius of curvature of the first side of the second lens, it is beneficial to constrain the forming strength and surface shape of the second lens, optimize the outgoing light of the doublet lens, and facilitate the control of the aberration and vignetting of the optical system.

[0053] The optical system according to the above embodiment of the present application may employ multiple lenses, such as the three lenses described above. By reasonably distributing the parameters of the reflective polarizing element, the quarter-wave plate, and each lens, the body length of the optical system can be reduced, and the processability and imaging quality of the optical system can be improved. The optical system configured as above can control the overall machine size while correcting off-axis aberration and chromatic aberration as much as possible, taking into account both performance and wearing experience, and can well meet the usage requirements of various portable electronic products in the projection scenario.

[0054] In an embodiment of the present application, at least one of the surfaces of each of the first through third lenses is an aspheric surface. Aspheric lenses are characterized by a continuously varying curvature from the center to the periphery. Unlike spherical lenses, which have a constant curvature from the center to the periphery, aspheric lenses have a better curvature radius characteristic, with the advantages of reducing distortion and astigmatism. The use of aspheric lenses can minimize aberrations that occur during imaging, thereby improving image quality.

[0055] However, it should be understood by those skilled in the art that, without departing from the technical solution claimed in the present application, the number of lenses constituting the optical system can be changed to obtain the various results and advantages described in this specification.

[0056] refer to Figure 1 、 Figure 3 、 Figure 5 、 Figure 7 and Figure 9 According to a second aspect of the present application, an optical system may include a first element group and a second element group arranged sequentially along an optical axis from a first side to a second side. The first element group may have positive optical power and include a reflective polarizing element, a quarter-wave plate, a first lens, and a partially reflecting element. The second element group may have positive optical power and include a second lens and a third lens. The second lens and the third lens are cemented together, i.e., the air gap between the second lens and the third lens on the optical axis is 0 mm.

[0057] The effective focal length FG1 of the first element group, the effective focal length FG2 of the second element group, and the on-axis distance TD from the first side surface of the first lens to the second side surface of the third lens can satisfy the following requirement: 1.3 < (FG2 - FG1) / TD < 2.0. Both the first and second element groups have positive optical power. Utilizing these two positive optical power element groups can fully converge the light beam, and the reflective polarizing element in the first element group can fold the light path, effectively shortening the total axial length of the optical system. The second and third lenses are cemented together to form a doublet. While being assembled without gaps to save the total axial length of the optical system, they can compensate for chromatic aberrations, which is beneficial to the optical system's out-of-field color performance. In combination with the first lens, they can fully regulate the aberrations of the optical system and optimize its imaging performance. At the same time, by controlling the ratio of the difference between the effective focal lengths of the second element group and the first element group to the on-axis distance from the first side surface of the first lens to the second side surface of the third lens, it is beneficial to reasonably distribute the focal length of the optical system and constrain the virtual image distance of the optical system, thereby avoiding the problem that the virtual image is too far or too close, which causes the virtual image to exceed the human visual control range and affect the actual viewing experience.

[0058] refer to Figure 1 、 Figure 3 、 Figure 5 、 Figure 7 and Figure 9 According to a third aspect of the present application, an optical system may include a first element group and a second element group arranged sequentially along an optical axis from a first side to a second side. The first element group may have positive optical power and include a reflective polarizing element, a quarter-wave plate, a first lens, and a partially reflecting element. The second element group may have positive optical power and include a second lens and a third lens. The second lens and the third lens are cemented together, i.e., the air gap between the second lens and the third lens on the optical axis is 0 mm.

[0059] The total effective focal length f of the optical system, the entrance pupil diameter (EPD) of the optical system, the refractive index N2 of the second lens, and the refractive index N3 of the third lens can satisfy the following conditions: 5.0 < (f / EPD) × (N2 / N3) < 6.0. Both the first and second lens groups have positive optical power. These two positive optical power groups can fully converge the light beam, and the reflective polarizing element in the first lens group can fold the optical path, effectively shortening the total axial length of the optical system. The second and third lenses are cemented together to form a doublet. While seamlessly assembled to reduce the total axial length of the optical system, they can compensate for chromatic aberration, which is beneficial to the system's out-of-field color rendering. Combined with the first lens, they can fully control the optical system's aberrations and optimize its imaging performance. At the same time, by controlling the total effective focal length of the optical system, the entrance pupil diameter of the optical system, and the relationship between the refractive indices of the second lens and the third lens, it is beneficial to improve the brightness of the entrance pupil light, enhance the entrance pupil imaging effect of the optical system in a dark environment, reduce the problem of vignetting at the edge of the field of view, and also facilitate the control of the angle of the output light of the display, so as to facilitate the selection of a reasonable double-cemented lens material and curvature.

[0060] Specific embodiments of the optical system applicable to the above-mentioned embodiments will be further described below with reference to the accompanying drawings.

[0061] Example 1

[0062] The following reference Figures 1 to 2C An optical system according to Example 1 of the present application is described.

[0063] like Figure 1As shown, the optical system 100 includes a first element group G1 and a second element group G2, arranged in sequence from the first side to the second side along the optical axis. The first element group G1 includes a reflective polarizer RP, a quarter-wave plate QWP, a first lens E1, and a partially reflective element BS. The second element group G2 includes a second lens E2 and a third lens E3, which are cemented together. In this embodiment, the first side refers to the human eye side, and the second side refers to the display side. The first side of each element (the first lens E1, the second lens E2, the third lens E3, the reflective polarizer RP, the quarter-wave plate QWP, and the partially reflective element BS) is referred to as the side proximal to the human eye, and the second side is referred to as the side proximal to the display.

[0064] The first lens E1 has positive optical power. Its eye-side surface S1 is concave, and its display-side surface S2 is convex. A partially reflective element BS is attached to it. A reflective polarizer RP is laminated to a quarter-wave plate QWP and attached to the eye-side surface S1 of the first lens E1 after the lamination. Compared to the quarter-wave plate QWP, the reflective polarizer RP is further away from the eye-side surface S1 of the first lens E1. The second lens E2 has positive optical power. Its eye-side surface S3 is convex, and its display-side surface S4 is convex. The third lens E3 has positive optical power. Its eye-side surface S5 is concave, and its display-side surface S6 is convex. The display-side surface S4 of the second lens E2 is laminated to the eye-side surface S5 of the third lens E3.

[0065] In this example, an imaging surface IMG may be provided on the second side of the optical system. For example, a display may be provided on the imaging surface IMG. Image light from the display sequentially passes through the third lens E3, the second lens E2, the first lens E1, and the quarter-wave plate QWP, and reaches the reflective polarizer RP. It then undergoes a first reflection at the reflective polarizer RP. The first-reflected light then passes through the quarter-wave plate QWP and reaches the partially reflective element BS on the side of the first lens E1 near the display. It then undergoes a second reflection at the partially reflective element BS. The second-reflected light then sequentially passes through the first lens E1, the quarter-wave plate QWP, and the reflective polarizer RP, and is ultimately projected onto a target object in space. For example, the light from this optical system, after undergoing two reflections, is ultimately projected into the user's eyes.

[0066] Table 1 shows the basic parameters of the optical system of Example 1, where the units of curvature radius and thickness / distance are all millimeters (mm). Image light from the display passes through each element in the order of sequence number 13 to sequence number 1 and is finally projected into the human eye.

[0067]

[0068]

[0069] Table 1

[0070] In Example 1, the side surface S2 of the first lens E1 near the display, the side surface S3 of the second lens E2 near the human eye, and the side surface S6 of the third lens E3 near the display are all aspherical surfaces. The surface shape x of each aspherical lens can be defined by, but is not limited to, the following aspherical surface formula:

[0071]

[0072] Wherein, x is the distance vector height of the aspheric surface from the vertex of the aspheric surface at a height of h along the optical axis; c is the paraxial curvature of the aspheric surface, c = 1 / R (i.e., the paraxial curvature c is the reciprocal of the curvature radius R in Table 1 above); k is the conic coefficient; Ai is the correction coefficient of the i-th order of the aspheric surface. Table 2 shows the high-order coefficients A4, A6, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23, A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38, A39, 10 、A 12 、A 14 、A 16 、A 18 and A 20 .

[0073] Face number A4 A6 A8 A10 A12 A14 A16 A18 A20 S2 -1.4439E-01 -1.1917E-01 1.2143E-01 -6.4504E-02 2.3627E-02 -4.9825E-03 0.0000E+00 0.0000E+00 0.0000E+00 S3 5.7253E+00 1.9588E+00 -1.5607E+00 3.2402E-01 9.7913E-02 -2.8358E-02 -1.4678E-01 1.1857E-01 -2.8605E-02 S6 1.9789E+00 1.6020E+00 -8.1534E-02 -3.3916E-01 1.7534E-01 -7.0708E-02 2.7745E-01 -4.0489E-01 1.6410E-01

[0074] Table 2

[0075] Figure 2A The axial chromatic aberration curve of the optical system 100 of Example 1 is shown, which indicates the deviation of the convergence point of light of different wavelengths after passing through the optical system 100. Figure 2B The astigmatism curve of the optical system 100 of Example 1 is shown, which represents the meridional field curvature and sagittal field curvature corresponding to different field angles. Figure 2C The distortion curve of the optical system 100 of Example 1 is shown, which represents the distortion value corresponding to different field angles. Figures 2A to 2C It can be seen that the optical system 100 provided in Example 1 can achieve good imaging quality.

[0076] Example 2

[0077] The following reference Figures 3 to 4C An optical system according to Example 2 of the present application is described.

[0078] like Figure 3As shown, optical system 200 includes a first element group G1 and a second element group G2, arranged sequentially along the optical axis from the first side to the second side. The first element group G1 includes a reflective polarizer RP, a quarter-wave plate QWP, a first lens E1, and a partially reflective element BS. The second element group G2 includes a second lens E2 and a third lens E3, which are cemented together. In this embodiment, the first side refers to the human eye side, and the second side refers to the display side. The first side of each element (first lens E1, second lens E2, third lens E3, reflective polarizer RP, quarter-wave plate QWP, and partially reflective element BS) is referred to as the side proximal to the human eye, and the second side is referred to as the side proximal to the display.

[0079] The first lens E1 has positive optical power. Its eye-side surface S1 is convex, and its display-side surface S2 is flat and attached with a partially reflective element BS. A reflective polarizer RP is laminated to a quarter-wave plate QWP and, after lamination, is attached to the eye-side surface S1 of the first lens E1. Compared to the quarter-wave plate QWP, the reflective polarizer RP is further away from the eye-side surface S1 of the first lens E1. The second lens E2 has positive optical power. Its eye-side surface S3 is convex, and its display-side surface S4 is flat. The third lens E3 has positive optical power. Its eye-side surface S5 is flat, and its display-side surface S6 is convex. The display-side surface S4 of the second lens E2 is laminated to the eye-side surface S5 of the third lens E3.

[0080] In this example, an imaging surface IMG may be provided on the second side of the optical system. For example, a display may be provided on the imaging surface IMG. Image light from the display sequentially passes through the third lens E3, the second lens E2, the first lens E1, and the quarter-wave plate QWP, and reaches the reflective polarizer RP. It then undergoes a first reflection at the reflective polarizer RP. The first-reflected light then passes through the quarter-wave plate QWP and reaches the partially reflective element BS on the side of the first lens E1 near the display. It then undergoes a second reflection at the partially reflective element BS. The second-reflected light then sequentially passes through the first lens E1, the quarter-wave plate QWP, and the reflective polarizer RP, and is ultimately projected onto a target object in space. For example, the light from this optical system, after undergoing two reflections, is ultimately projected into the user's eyes.

[0081] Table 3 shows the basic parameters of the optical system of Example 2, where the units of curvature radius and thickness / distance are all millimeters (mm). Image light from the display passes through each element in the order of sequence number 13 to sequence number 1 and is finally projected into the human eye.

[0082]

[0083] Table 3

[0084] In Example 2, the side surface S1 of the first lens E1 near the human eye and the side surface S6 of the third lens E3 near the display are both aspherical. Table 4 lists the high-order coefficients A4, A6, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23, A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38, A39, A40, A41, A42, A43, A44, A45, A46, A47, A48, A49, A50, A51, A52, A53, A54, A55, A56, A57, 10 、A 12 、A 14 、A 16 、A 18 and A 20 .

[0085] Face number A4 A6 A8 A10 A12 A14 A16 A18 A20 S1 -4.3675E-07 2.0311E-10 1.1000E-13 -1.2564E-17 8.0673E-21 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 S6 1.5074E+00 -4.1403E+00 -8.7479E-01 -1.9012E-01 -1.7177E-01 -2.5510E+00 3.0057E+00 -1.2213E+00 2.2008E-02

[0086] Table 4

[0087] Figure 4A The axial chromatic aberration curve of the optical system 200 of Example 2 is shown, which indicates the deviation of the convergence point of light of different wavelengths after passing through the optical system 200. Figure 4B The astigmatism curve of the optical system 200 of Example 2 is shown, which represents the meridional field curvature and sagittal field curvature corresponding to different field angles. Figure 4C The distortion curve of the optical system 200 of Example 2 is shown, which represents the distortion value corresponding to different field angles. Figures 4A to 4C It can be seen that the optical system 200 provided in Example 2 can achieve good imaging quality.

[0088] Example 3

[0089] The following reference Figures 5 to 6C An optical system according to Example 3 of the present application is described.

[0090] like Figure 5 As shown, optical system 300 includes a first element group G1 and a second element group G2, arranged sequentially along the optical axis from the first side to the second side. The first element group G1 includes a reflective polarizer RP, a quarter-wave plate QWP, a first lens E1, and a partially reflective element BS. The second element group G2 includes a second lens E2 and a third lens E3, which are cemented together. In this embodiment, the first side refers to the human eye side, and the second side refers to the display side. The first side of each element (first lens E1, second lens E2, third lens E3, reflective polarizer RP, quarter-wave plate QWP, and partially reflective element BS) is referred to as the near-human eye side, and the second side is referred to as the near-display side.

[0091] The first lens E1 has positive optical power. Its eye-side surface S1 is planar, and its display-side surface S2 is convex and attached with a partially reflective element BS. A reflective polarizer RP is laminated to a quarter-wave plate QWP and, after lamination, is attached to the eye-side surface S1 of the first lens E1. Compared to the quarter-wave plate QWP, the reflective polarizer RP is further away from the eye-side surface S1 of the first lens E1. The second lens E2 has positive optical power. Its eye-side surface S3 is convex, and its display-side surface S4 is concave. The third lens E3 has positive optical power. Its eye-side surface S5 is convex, and its display-side surface S6 is convex. The display-side surface S4 of the second lens E2 is laminated to the eye-side surface S5 of the third lens E3.

[0092] In this example, an imaging surface IMG may be provided on the second side of the optical system. For example, a display may be provided on the imaging surface IMG. Image light from the display sequentially passes through the third lens E3, the second lens E2, the first lens E1, and the quarter-wave plate QWP, and reaches the reflective polarizer RP. It then undergoes a first reflection at the reflective polarizer RP. The first-reflected light then passes through the quarter-wave plate QWP and reaches the partially reflective element BS on the side of the first lens E1 near the display. It then undergoes a second reflection at the partially reflective element BS. The second-reflected light then sequentially passes through the first lens E1, the quarter-wave plate QWP, and the reflective polarizer RP, and is ultimately projected onto a target object in space. For example, the light from this optical system, after undergoing two reflections, is ultimately projected into the user's eyes.

[0093] Table 5 shows the basic parameters of the optical system of Example 3, where the units of curvature radius and thickness / distance are all in millimeters (mm). Image light from the display passes through each element in the order of sequence number 13 to sequence number 1 and is finally projected into the human eye.

[0094]

[0095]

[0096] Table 5

[0097] In Example 3, the side surface S2 of the first lens E1 near the display, the side surface S4 of the second lens E2 near the display, and the side surface S5 near the human eye and the side surface S6 near the display of the third lens E3 are all aspherical. Table 6 lists the high-order coefficients A4, A6, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23, A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38, A39, A40, A41, A42, A43, A44, A45, A46, A47, A48, A49, A50, A51 10 、A 12 、A 14 、A 16 、A 18 and A 20 .

[0098] Face number A4 A6 A8 A10 A12 A14 A16 A18 A20 S2 -3.3314E-01 2.7729E-02 4.4322E-04 -7.4259E-03 3.2047E-03 -3.7440E-04 0.0000E+00 0.0000E+00 0.0000E+00 S4 / S5 4.5871E-01 3.4243E-01 -1.9111E-01 3.0514E-01 -1.3126E-01 -1.4615E-01 1.2358E-01 -1.9061E-02 -4.4782E-03 S6 -1.5937E+00 6.7876E-01 -6.2734E-01 -1.8778E-01 5.9262E-01 -2.7318E-01 -1.0390E-01 1.2798E-01 -4.0585E-02

[0099] Table 6

[0100] Figure 6A The axial chromatic aberration curve of the optical system 300 of Example 3 is shown, which indicates the deviation of the convergence point of light of different wavelengths after passing through the optical system 300. Figure 6B The astigmatism curve of the optical system 300 of Example 3 is shown, which represents the meridional field curvature and sagittal field curvature corresponding to different field angles. Figure 6C The distortion curve of the optical system 300 of Example 3 is shown, which represents the distortion value corresponding to different field angles. Figures 6A to 6C It can be seen that the optical system 300 provided in Example 3 can achieve good imaging quality.

[0101] Example 4

[0102] The following reference Figures 7 to 8C An optical system according to Example 4 of the present application is described.

[0103] like Figure 7 As shown, optical system 400 includes a first element group G1 and a second element group G2, arranged in sequence from the first side to the second side along the optical axis. The first element group G1 includes a reflective polarizer RP, a quarter-wave plate QWP, a first lens E1, and a partially reflective element BS. The second element group G2 includes a second lens E2 and a third lens E3, which are cemented together. In this embodiment, the first side refers to the human eye side, and the second side refers to the display side. The first side of each element (first lens E1, second lens E2, third lens E3, reflective polarizer RP, quarter-wave plate QWP, and partially reflective element BS) is referred to as the side near the human eye, and the second side is referred to as the side near the display.

[0104] The first lens E1 has positive optical power. Its eye-side surface S1 is concave, and its display-side surface S2 is convex. A partially reflective element BS is attached to it. A reflective polarizer RP is laminated to a quarter-wave plate QWP and attached to the eye-side surface S1 of the first lens E1 after the lamination. Compared to the quarter-wave plate QWP, the reflective polarizer RP is further away from the eye-side surface S1 of the first lens E1. The second lens E2 has positive optical power. Its eye-side surface S3 is convex, and its display-side surface S4 is concave. The third lens E3 has positive optical power. Its eye-side surface S5 is convex, and its display-side surface S6 is convex. The display-side surface S4 of the second lens E2 is laminated to the eye-side surface S5 of the third lens E3.

[0105] In this example, an imaging surface IMG may be provided on the second side of the optical system. For example, a display may be provided on the imaging surface IMG. Image light from the display sequentially passes through the third lens E3, the second lens E2, the first lens E1, and the quarter-wave plate QWP, and reaches the reflective polarizer RP. It then undergoes a first reflection at the reflective polarizer RP. The first-reflected light then passes through the quarter-wave plate QWP and reaches the partially reflective element BS on the side of the first lens E1 near the display. It then undergoes a second reflection at the partially reflective element BS. The second-reflected light then sequentially passes through the first lens E1, the quarter-wave plate QWP, and the reflective polarizer RP, and is ultimately projected onto a target object in space. For example, the light from this optical system, after undergoing two reflections, is ultimately projected into the user's eyes.

[0106] Table 7 shows the basic parameters of the optical system of Example 4, where the units of curvature radius and thickness / distance are all in millimeters (mm). Image light from the display passes through each element in the order of sequence numbers 13 to 1 and is ultimately projected into the human eye.

[0107]

[0108] Table 7

[0109] In Example 4, the side surface S1 near the human eye and the side surface S2 near the display of the first lens E1, the side surface S4 near the display of the second lens E2, and the side surface S5 near the human eye and the side surface S6 near the display of the third lens E3 are all aspherical surfaces. Table 8 lists the high-order coefficients A4, A6, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23, A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38, A39, A40, A41, A42, A43, A44, A45, A46, A47, A48, 10 、A 12 、A 14 、A 16 、A 18 and A 20 .

[0110] Face number A4 A6 A8 A10 A12 A14 A16 A18 A20 S1 -4.3528E-07 7.2977E-11 1.5456E-13 7.6679E-17 -8.3088E-20 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 S2 2.2167E-01 5.3031E-02 1.2703E-02 -1.2593E-02 3.9783E-03 -4.7751E-04 0.0000E+00 0.0000E+00 0.0000E+00 S4 / S5 1.8697E+00 1.7162E-01 -6.5509E-01 3.4484E-01 1.1878E-01 5.8009E+00 2.4303E+00 -5.5140E-01 -3.1292E+00 S6 8.0957E-010 2.8222E-01 -1.7835E+00 1.0989E+00 7.9109E-03 -5.7604E-01 6.1331E-01 -3.0960E-01 1.2369E-01

[0111] Table 8

[0112] Figure 8A The axial chromatic aberration curve of the optical system 400 of Example 4 is shown, which indicates the deviation of the convergence point of light of different wavelengths after passing through the optical system 400. Figure 8B The astigmatism curve of the optical system 400 of Example 4 is shown, which represents the meridional field curvature and sagittal field curvature corresponding to different field angles. Figure 8C The distortion curve of the optical system 400 of Example 4 is shown, which represents the distortion magnitude values ​​corresponding to different field angles. Figures 8A to 8C It can be seen that the optical system 400 provided in Example 4 can achieve good imaging quality.

[0113] Example 5

[0114] The following reference Figures 9 to 10C An optical system according to Example 5 of the present application is described.

[0115] like Figure 9 As shown, optical system 500 includes a first element group G1 and a second element group G2, arranged sequentially along the optical axis from the first side to the second side. The first element group G1 includes a reflective polarizer RP, a quarter-wave plate QWP, a first lens E1, and a partially reflective element BS. The second element group G2 includes a second lens E2 and a third lens E3, which are cemented together. In this embodiment, the first side refers to the human eye side, and the second side refers to the display side. The first side of each element (first lens E1, second lens E2, third lens E3, reflective polarizer RP, quarter-wave plate QWP, and partially reflective element BS) is referred to as the side proximal to the human eye, and the second side is referred to as the side proximal to the display.

[0116] The first lens E1 has positive optical power. Its eye-side surface S1 is concave, and its display-side surface S2 is convex. A partially reflective element BS is attached to it. A reflective polarizer RP is laminated to a quarter-wave plate QWP and attached to the eye-side surface S1 of the first lens E1 after the lamination. Compared to the quarter-wave plate QWP, the reflective polarizer RP is further away from the eye-side surface S1 of the first lens E1. The second lens E2 has positive optical power. Its eye-side surface S3 is convex, and its display-side surface S4 is concave. The third lens E3 has positive optical power. Its eye-side surface S5 is convex, and its display-side surface S6 is convex. The display-side surface S4 of the second lens E2 is laminated to the eye-side surface S5 of the third lens E3.

[0117] In this example, an imaging surface IMG may be provided on the second side of the optical system. For example, a display may be provided on the imaging surface IMG. Image light from the display sequentially passes through the third lens E3, the second lens E2, the first lens E1, and the quarter-wave plate QWP, and reaches the reflective polarizer RP. It then undergoes a first reflection at the reflective polarizer RP. The first-reflected light then passes through the quarter-wave plate QWP and reaches the partially reflective element BS on the side of the first lens E1 near the display. It then undergoes a second reflection at the partially reflective element BS. The second-reflected light then sequentially passes through the first lens E1, the quarter-wave plate QWP, and the reflective polarizer RP, and is ultimately projected onto a target object in space. For example, the light from this optical system, after undergoing two reflections, is ultimately projected into the user's eyes.

[0118] Table 9 shows the basic parameters of the optical system of Example 5, where the units of curvature radius and thickness / distance are all in millimeters (mm). Image light from the display passes through each element in the order of sequence numbers 13 to 1 and is ultimately projected into the human eye.

[0119]

[0120]

[0121] Table 9

[0122] In Example 5, the side surface S2 of the first lens E1 near the display, the side surface S4 of the second lens E2 near the display, and the side surface S5 near the human eye and the side surface S6 near the display of the third lens E3 are all aspherical. Table 10 lists the high-order coefficients A4, A6, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23, A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38, A39, A40, A41, A42, A43, A44, A45, A46, A47, A48, A49, A50, A5 10 、A 12 、A 14 、A 16 、A 18 and A 20 .

[0123] Face number A4 A6 A8 A10 A12 A14 A16 A18 A20 S2 -2.1874E-01 -9.1719E-02 1.1293E-01 7.2432E-02 3.2980E-02 7.8982E-03 0.0000E+00 0.0000E+00 0.0000E+00 S4 / S5 6.9425E+00 4.0190E+00 -3.3095E+00 -1.4937E+00 1.5765E-01 8.1438E-01 -1.5417E-01 2.0167E-01 -8.7188E-02 S6 -3.4133E+00 3.2358E+00 -1.7123E+00 -1.5217E+00 2.9860E+00 -1.2729E+00 -4.7569E-01 7.9458E-01 -4.8167E-01

[0124] Table 10

[0125] Figure 10A The axial chromatic aberration curve of the optical system 500 of Example 5 is shown, which indicates the deviation of the convergence point of light of different wavelengths after passing through the optical system 500. Figure 10B The astigmatism curve of the optical system 500 of Example 5 is shown, which represents the meridional field curvature and sagittal field curvature corresponding to different field angles. Figure 10C The distortion curve of the optical system 500 of Example 5 is shown, which represents the distortion value corresponding to different field angles. 10A to 10C It can be seen that the optical system 500 provided in Example 5 can achieve good imaging quality.

[0126] Table 11 shows the values ​​of the basic parameters of each of Examples 1 to 5.

[0127] Basic parameters / embodiment 1 2 3 4 5 FG1(mm) 30.45 29.90 29.12 31.54 29.79 FG2(mm) 77.46 63.65 82.32 78.69 66.58 f(mm) 27.00 25.14 26.17 27.79 26.20 EPD(mm) 5.00 5.00 5.00 5.00 5.00 FOV(°) 100.00 100.00 106.00 100.00 100.00 TD(mm) 24.50 24.50 26.95 28.15 25.90 CTR(mm) 0.20 0.20 0.20 0.20 0.20 CTQ(mm) 0.20 0.20 0.20 0.20 0.20 ∑CT(mm) 24.30 19.51 26.71 28.05 25.80

[0128] Table 11

[0129] In summary, Table 12 shows the values ​​of the conditional expressions of each of Examples 1 to 5.

[0130]

[0131]

[0132] Table 12

[0133] The present application also provides an optical device, which can be an independent projection device such as a projector, or a projection module integrated into a mobile electronic device such as a virtual reality device. The optical device is equipped with the optical system described above.

[0134] The above description is merely a preferred embodiment of the present application and an illustration of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to the technical solutions formed by the specific combination of the above-mentioned technical features, but also encompasses other technical solutions formed by any combination of the above-mentioned technical features or their equivalents without departing from the inventive concept. For example, a technical solution formed by replacing the above-mentioned features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. An optical system, characterized in that The device comprises, in order from the first side to the second side along the optical axis: a first element group having positive optical power and consisting of, in order from the first side to the second side along the optical axis, a reflective polarizing element, a quarter-wave plate, a first lens having positive optical power, and a partially reflecting element; a second element group having positive refractive power and consisting of, in order from the first side to the second side along the optical axis, a second lens having positive refractive power and a third lens having positive refractive power, the second lens and the third lens being cemented together, the first side surface of the second lens being a convex surface, and the second side surface of the third lens being a convex surface; and Image surface; wherein the number of lenses having optical power in the optical system is three; The curvature radius R3 of the first side surface of the second lens, the curvature radius R6 of the second side surface of the third lens and the effective focal length FG2 of the second element group satisfy: 0.47≤ R3+R6 / FG2<1.9; The effective focal length FG1 of the first element group, the effective focal length FG2 of the second element group, and the on-axis distance TD from the first side surface of the first lens to the second side surface of the third lens satisfy the following: 1.38≤(FG2-FG1) / TD<2.

0.

2. The optical system according to claim 1, wherein: The total effective focal length f of the optical system satisfies: 25.14 mm ≤ f ≤ 27.79 mm.

3. The optical system according to claim 1, wherein: The total effective focal length f of the optical system, the entrance pupil diameter EPD of the optical system, the refractive index N2 of the second lens and the refractive index N3 of the third lens satisfy: 5.0<(f / EPD)×(N2 / N3)<6.

0.

4. The optical system according to claim 1, wherein: The sum ΣCT of the center thicknesses of the first lens, the second lens, and the third lens on the optical axis, the total effective focal length f of the optical system, and the maximum field of view FOV of the optical system satisfy the following conditions: 0.65≤ΣCT / (f×tan(FOV / 2))≤0.

85.

5. The optical system according to claim 1, wherein: The center thickness CT1 of the first lens on the optical axis, the air interval T12 between the first lens and the second lens on the optical axis, and the entrance pupil diameter EPD of the optical system satisfy the following: 2.58≤(CT1+T12) / EPD<3.

1.

6. The optical system according to any one of claims 1 to 5, characterized in that The effective focal length FG1 of the first element group, the center thickness CTR of the reflective polarizing element on the optical axis, the center thickness CTQ of the quarter-wave plate on the optical axis, and the center thickness CT1 of the first lens on the optical axis satisfy the following conditions: 1.88≤FG1 / (CTR+CTQ+CT1)<3.

2.

7. The optical system according to any one of claims 1 to 5, characterized in that A center thickness CT1 of the first lens on the optical axis, a center thickness CT2 of the second lens on the optical axis, and a center thickness CT3 of the third lens on the optical axis satisfy the following: 0.85≤CT1 / (CT2+CT3)<1.

3.

8. The optical system according to any one of claims 1 to 5, characterized in that The effective focal length FG2 of the second element group, the Abbe number V2 of the second lens and the Abbe number V3 of the third lens satisfy: 0.7 mm <FG2 / (V2+V3)≤1.02mm。 9. The optical system according to any one of claims 1 to 5, characterized in that The refractive index N1 of the first lens, the Abbe number V1 of the first lens, the center thickness CTR of the reflective polarizing element on the optical axis, and the center thickness CTQ of the quarter-wave plate on the optical axis satisfy the following conditions: 0<(N1 / V1)×(CTR / CTQ)<0.

1.

10. The optical system according to any one of claims 1 to 5, characterized in that A center thickness CT2 of the second lens on the optical axis and a curvature radius R3 of a first side surface of the second lens satisfy: 0.27≤10×CT2 / R3≤0.45.

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