Ocular optical system and mass production manufacturing method thereof

Abstract

An eyepiece optical system is configured to allow imaging light from a display screen to pass through the eyepiece optical system and enter an observer's eye to form an image. The eyepiece optical system sequentially includes a first optical element and a second optical element along an optical axis from the eye side to the display side. Each of the first and second optical elements includes an eye-side surface and a display-side surface. The eyepiece optical system also includes a reflective polarizing film and a quarter-wave plate. The eye-side surface and the display-side surface of the first optical element satisfy the following condition: PV ≤ 160 μm, where PV is a peak-to-valence value of a surface. Furthermore, the present invention also provides a method for mass-producing the eyepiece optical system.

Description

Technical Field

[0001] The present invention relates to an optical system and a manufacturing method thereof, and in particular to an eyepiece optical system and a mass production method thereof. Prior Art

[0002] Currently available VR eyepiece optical systems can be categorized into three main types: aspherical, Fresnel, and pancake. Aspherical optical elements offer advantages such as low manufacturing cost and minimal stray light issues like flare and ghosting, but they are also heavy and bulky. Fresnel optical elements offer advantages such as lower weight and improved viewing angle, but their manufacturing cost is approximately twice that of aspherical elements. However, they can suffer from significant flare issues. Pancake optical elements offer advantages such as less than half the weight and volume of aspherical elements, and no flare. However, because the cost of optical film materials is half that of the lens, and the film application process and assembly adjustments are more complex, the manufacturing cost ranges from 10 to 40 times that of aspherical elements, and they are prone to ghosting.

[0003] Due to the weight, volume, stray light, and manufacturing cost issues associated with the three main types of optical components, VR has not been as widely adopted as smartphones. Furthermore, VR users demand not only excellent image quality but also high magnification. Therefore, designing eyepiece optical systems that offer high magnification at low manufacturing costs while meeting consumer demand for image quality remains a challenge that the industry must address. Summary of the Invention

[0004] The present invention provides an eyepiece optical system and a mass production method thereof, which have low manufacturing costs and meet consumers' demands for image quality and magnification.

[0005] The present invention provides an eyepiece optical system configured to allow imaging light from a display screen to pass through the eyepiece optical system and enter an observer's eye to form an image, wherein the side facing the eye is an eye side, and the side facing the display screen is a display side. The eyepiece optical system includes a first optical element and a second optical element, sequentially along an optical axis from the eye side to the display side. The first optical element and the second optical element each include an eye side surface facing the eye side and through which the imaging light passes, and a display side surface facing the display side and through which the imaging light passes. The eyepiece optical system also includes a reflective polarizing film and a quarter-wave plate. The eye side surface and the display side surface of the first optical element satisfy the following condition: PV ≤ 160 μm, where PV is a peak-to-valley value of a surface. The reflective polarizing film is disposed on the eye side of the first optical element. The quarter-wave plate is disposed on the display side of the first optical element or between the reflective polarizing film and the eye side of the first optical element. The eyepiece optical system satisfies the following conditional formula: 35≤|ObjD| / ImgH≤200, where ObjD is the distance from the observer's eye to the image formed by the eyepiece optical system on the optical axis, and ImgH is the maximum image height of the eyepiece optical system.

[0006] The present invention further provides an eyepiece optical system configured to allow imaging light from a display screen to pass through the eyepiece optical system and enter an observer's eye to form an image, wherein the side facing the eye is an eye side, and the side facing the display screen is a display side. The eyepiece optical system includes a first optical element and a second optical element, sequentially along an optical axis from the eye side to the display side. The first optical element and the second optical element each include an eye-side surface facing the eye side and through which the imaging light passes, and a display-side surface facing the display side and through which the imaging light passes. The eyepiece optical system also includes a reflective polarizing film and a quarter-wave plate. The eye-side surface of the first optical element, the display-side surface of the first optical element, and the eye-side surface of the second optical element satisfy the following condition: PV ≤ 160 μm, where PV is a peak-to-valley value of a surface. The reflective polarizing film is disposed on the eye side of the first optical element. The quarter-wave plate is disposed on the display-side surface of the first optical element or between the reflective polarizing film and the eye side of the first optical element. There is no air gap between the display side surface of the first optical element and the eye side surface of the second optical element.

[0007] The present invention further provides a method for mass-producing eyepiece optical systems, comprising: manufacturing a large-scale first optical element using a low-birefringence plastic or glass material, wherein an eye-side surface of the large-scale first optical element and a display-side surface of the large-scale first optical element satisfy the following equation: PV ≤ 160 μm, where PV is the peak-to-valley value of the surface; disposing a large-scale reflective polarizing film on the eye-side surface of the large-scale first optical element, and disposing a large-scale quarter-wave plate on the display-side surface of the large-scale first optical element or between the large-scale reflective polarizing film and the eye-side surface of the large-scale first optical element to form an optical film on the large-scale first optical element; bonding a plurality of second optical elements to the display-side surface of the large-scale first optical element using an adhesive having a refractive index that matches the refractive index of the large-scale first optical element and the refractive index of the second optical elements to form a collection of a plurality of eyepiece optical systems arranged in an array; and cutting the collection of the eyepiece optical systems to form separate eyepiece optical systems.

[0008] Based on the above, the beneficial effects of the eyepiece optical system of the embodiment of the present invention are: by satisfying the optical design conditions, the manufacturing cost of the eyepiece optical system is reduced, and the consumer's demand for image quality and magnification is met.

[0009] To make the above features and advantages of the present invention more clearly understood, embodiments are given below and described in detail with reference to the accompanying drawings. Simple diagram description

[0010] FIG1 is a schematic diagram illustrating how imaging light emitted from a display screen enters the eye through an eyepiece optical system. FIG2 is a schematic diagram illustrating the surface structure of a lens. FIG3 is a schematic diagram illustrating the concave-convex structure of a lens and the intersection of light rays. FIG4 is a schematic diagram illustrating the surface structure of a lens in Example 1. FIG5 is a schematic diagram illustrating the surface structure of a lens in Example 2. FIG6 is a schematic diagram illustrating the surface structure of a lens in Example 3. FIG7 is a schematic diagram of the eyepiece optical system of the first embodiment of the present invention. 8A to 8D are diagrams showing longitudinal spherical aberration and various aberrations of the eyepiece optical system of the first embodiment. FIG9 shows detailed optical data and aspheric parameters of the eyepiece optical system of the first embodiment of the present invention. FIG. 10 is a schematic diagram of an eyepiece optical system according to a second embodiment of the present invention. 11A to 11D are diagrams showing longitudinal spherical aberration and various aberrations of the eyepiece optical system of the second embodiment. FIG12 shows detailed optical data and aspheric parameters of the eyepiece optical system of the second embodiment of the present invention. FIG. 13 is a schematic diagram of an eyepiece optical system according to a third embodiment of the present invention. 14A to 14D are diagrams showing longitudinal spherical aberration and various aberrations of the eyepiece optical system of the third embodiment. FIG15 shows detailed optical data and aspheric parameters of the eyepiece optical system of the third embodiment of the present invention. FIG. 16 is a schematic diagram of an eyepiece optical system according to a fourth embodiment of the present invention. 17A to 17D are diagrams showing longitudinal spherical aberration and various aberrations of the eyepiece optical system of the fourth embodiment. FIG18 shows detailed optical data and aspheric parameters of the eyepiece optical system of the fourth embodiment of the present invention. FIG. 19 is a schematic diagram of an eyepiece optical system according to a fifth embodiment of the present invention. 20A to 20D are diagrams showing the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the fifth embodiment. FIG21 shows detailed optical data and aspheric parameters of the eyepiece optical system of the fifth embodiment of the present invention. FIG. 22 is a schematic diagram of an eyepiece optical system according to a sixth embodiment of the present invention. 23A to 23D are diagrams showing the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the sixth embodiment. FIG24 shows detailed optical data and aspheric parameters of the eyepiece optical system of the sixth embodiment of the present invention. FIG. 25 is a schematic diagram of an eyepiece optical system according to a seventh embodiment of the present invention. 26A to 26D are diagrams showing the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the seventh embodiment. FIG27 shows detailed optical data and aspheric parameters of the eyepiece optical system of the seventh embodiment of the present invention. FIG. 28 is a schematic diagram of an eyepiece optical system according to an eighth embodiment of the present invention. 29A to 29D are diagrams showing the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the eighth embodiment. FIG30 shows detailed optical data and aspheric parameters of the eyepiece optical system of the eighth embodiment of the present invention. FIG31 is a schematic diagram of an eyepiece optical system according to a ninth embodiment of the present invention. 32A to 32D are diagrams showing the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the ninth embodiment. FIG33 shows detailed optical data and aspheric parameters of the eyepiece optical system of the ninth embodiment of the present invention. FIG34 is a schematic diagram of an eyepiece optical system according to a tenth embodiment of the present invention. 35A to 35D are diagrams showing the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the tenth embodiment. FIG36 shows detailed optical data and aspheric parameters of the eyepiece optical system of the tenth embodiment of the present invention. FIG37 and FIG38 show the numerical values of the relationship between the important parameters of the eyepiece optical system of the first to fifth embodiments of the present invention. FIG39 and FIG40 show the numerical values of the relationship between the important parameters of the eyepiece optical system of the sixth to tenth embodiments of the present invention. Figure 41 shows a step flow chart of the mass production manufacturing method of the eyepiece optical system of the present invention. FIG42 is a schematic diagram showing a method for mass-producing the eyepiece optical system of the present invention. Implementation Method

[0011] Generally speaking, the light direction of the eyepiece optical system V100 is as follows: an imaging light ray VI is emitted from the display screen V50, passes through the eyepiece optical system V100, enters the eye V60, focuses on the retina of the eye V60, and forms a magnified virtual image VV at the visual distance VD, as shown in FIG1 . The following description of the optical specifications of this embodiment assumes that the light direction is reversely tracked, with a parallel imaging light ray passing from the eye side through the eyepiece optical system to the display screen, where it forms a focused image.

[0012] The terms "optical axis region", "circumferential region", "concave surface" and "convex surface" used in this specification and the claims should be interpreted based on the definitions listed in this specification.

[0013] The optical system described herein includes at least one lens that receives imaging light from the incident optical system parallel to the optical axis and within a half-field of view (HFOV) relative to the optical axis. The imaging light forms an image on an imaging surface through the optical system. "A lens having a positive (or negative) refractive power" refers to a lens having a positive (or negative) paraxial refractive power calculated using Gaussian optics theory. The "eye-side (or display-side) of the lens" is defined as the specific area of the lens surface where the imaging light passes. Imaging light includes at least two types of light: chief rays Lc and marginal rays Lm (as shown in Figure 2). The eye-side (or display-side) of the lens can be divided into different regions based on different locations, including the optical axis region, the circumferential region, or, in some embodiments, one or more intermediate regions. These regions are described in detail below.

[0014] Figure 2 is a radial cross-sectional view of lens 100. Two reference points are defined on the surface of lens 100: a center point and a transition point. The center point of a lens surface is the intersection of the surface and the optical axis I. As shown in Figure 2, the first center point CP1 is located on the eye-side surface 110 of lens 100, and the second center point CP2 is located on the display-side surface 120 of lens 100. A transition point is a point on the lens surface whose tangent is perpendicular to the optical axis I. The optical boundary OB of a lens surface is defined as the point where the radially outermost marginal ray Lm passing through the lens surface intersects the lens surface. All transition points are located between the optical axis I and the optical boundary OB of the lens surface. Alternatively, the surface of lens 100 may have no transition points or at least one. If a single lens surface has multiple transition points, the transition points are named sequentially, starting with the first transition point, in a radially outward direction. For example, the first transition point TP1 (closest to the optical axis I), the second transition point TP2 (as shown in Figure 5), and the Nth transition point (farthest from the optical axis I).

[0015] When the lens surface has at least one transition point, the range from the center point to the first transition point TP1 is defined as the optical axis region, where the optical axis region includes the center point. The region radially outward from the transition point farthest from the optical axis I (the Nth transition point) to the optical boundary OB is defined as the circumferential region. In some embodiments, intermediate regions between the optical axis region and the circumferential region may be included, with the number of intermediate regions depending on the number of transition points. When the lens surface does not have a transition point, the optical axis region is defined as 0% to 50% of the distance from the optical axis I to the optical boundary OB of the lens surface, and the circumferential region is defined as 50% to 100% of the distance from the optical axis I to the optical boundary OB of the lens surface.

[0016] When a light ray parallel to the optical axis I passes through an area, if the ray is deflected toward the optical axis I and its intersection with the optical axis I is located on the lens's display side A2, the area is considered convex. When a light ray parallel to the optical axis I passes through an area, if the extension of the ray intersects the optical axis I on the lens's eye side A1, the area is considered concave.

[0017] In addition, as shown in FIG2 , lens 100 may also include an assembly portion 130 extending radially outward from optical boundary OB. Assembly portion 130 is generally used to assemble lens 100 to a corresponding component (not shown) in an optical system. Imaging light does not reach assembly portion 130. The structure and shape of assembly portion 130 are merely illustrative of the present invention and do not limit the scope of the present invention. The assembly portion 130 of the lens discussed below may be partially or entirely omitted from the drawings.

[0018] Referring to Figure 3 , the area between the center point CP and the first transition point TP1 is defined as the optical axis region Z1. The area between the first transition point TP1 and the optical boundary OB of the lens surface is defined as the circumferential region Z2. As shown in Figure 3 , after passing through the optical axis region Z1, the parallel light ray 211 intersects the optical axis I on the display side A2 of the lens 200. That is, the focus of the parallel light ray 211 passing through the optical axis region Z1 is located at point R on the display side A2 of the lens 200. Because the light ray intersects the optical axis I on the display side A2 of the lens 200, the optical axis region Z1 is convex. Conversely, the parallel light ray 212 diverges after passing through the circumferential region Z2. As shown in Figure 3 , the extension line EL of the parallel light ray 212 after passing through the circumferential region Z2 intersects the optical axis I on the eye side A1 of the lens 200. That is, the focus of the parallel light ray 212 passing through the circumferential region Z2 is located at point M on the eye side A1 of the lens 200. Because the extended line EL of the light ray intersects the optical axis I at the eye side A1 of lens 200, the circumferential region Z2 is concave. In lens 200 shown in FIG3 , the first transition point TP1 is the boundary between the optical axis region and the circumferential region, i.e., the first transition point TP1 is the point where the convex surface transitions to the concave surface.

[0019] Alternatively, the optical axis area's surface convexity can be determined using a method commonly used by those skilled in the art. This involves determining the convexity of the lens' optical axis area based on the sign of the paraxial radius of curvature (abbreviated as the R value). R values are commonly used in optical design software such as Zemax or CodeV. R values are also commonly found in lens data sheets within optical design software. For the eye-side surface, a positive R value indicates that the optical axis area on the eye-side surface is convex; a negative R value indicates that the optical axis area on the eye-side surface is concave. Conversely, for the display-side surface, a positive R value indicates that the optical axis area on the display-side surface is concave; a negative R value indicates that the optical axis area on the display-side surface is convex. The results of this method are consistent with the previously described method of determining surface convexity based on the intersection of a ray / ray extension line with the optical axis. This method uses the focus of a ray parallel to the optical axis on either the eye-side or the display-side of the lens to determine surface convexity. The terms “a region is convex (or concave)”, “a region is convex (or concave)” or “a convex (or concave) region” described in this specification can be used interchangeably.

[0020] 4 to 6 provide examples of determining the surface shape and area boundaries of lens areas in various situations, including the aforementioned optical axis area, circumferential area, and relay area.

[0021] Figure 4 is a radial cross-sectional view of lens 300. Referring to Figure 4 , the display side surface 320 of lens 300 has only one transition point TP1 within optical boundary OB. The optical axis region Z1 and circumferential region Z2 of the display side surface 320 of lens 300 are shown in Figure 4 . The R value of this display side surface 320 is positive (i.e., R>0), and therefore, the optical axis region Z1 is concave.

[0022] Generally speaking, the surface shape of each area bounded by a transition point is opposite to that of the adjacent areas. Therefore, the transition point can be used to define the transition of surface shape, that is, from concave to convex or vice versa. In Figure 4, since the optical axis area Z1 is concave, the surface shape changes at transition point TP1, so the circumferential area Z2 is convex.

[0023] Figure 5 is a radial cross-sectional view of lens 400. Referring to Figure 5 , the eye-side surface 410 of lens 400 has a first transition point TP1 and a second transition point TP2. The area between the optical axis I and the first transition point TP1 is defined as the optical axis region Z1 of eye-side surface 410. The R value of this eye-side surface 410 is positive (i.e., R>0), and therefore, the optical axis region Z1 is convex.

[0024] The area between the second transition point TP2 and the optical boundary OB of the eye-side surface 410 of the lens 400 is defined as a circumferential region Z2. This circumferential region Z2 of the eye-side surface 410 is also convex. Furthermore, the area between the first transition point TP1 and the second transition point TP2 is defined as a relay region Z3. This relay region Z3 of the eye-side surface 410 is concave. Referring again to FIG. 5 , the eye-side surface 410 includes, radially outward from the optical axis I, the optical axis region Z1 between the optical axis I and the first transition point TP1, the relay region Z3 between the first transition point TP1 and the second transition point TP2, and the circumferential region Z2 between the second transition point TP2 and the optical boundary OB of the eye-side surface 410 of the lens 400. Since the optical axis region Z1 is convex, the surface shape changes to concave at the first transition point TP1, so the relay region Z3 is concave. Since the surface shape changes again to convex at the second transition point TP2, the circumferential region Z2 is convex.

[0025] Figure 6 is a radial cross-sectional view of lens 500. Eye-side surface 510 of lens 500 lacks a transition point. For a lens surface without a transition point, such as eye-side surface 510 of lens 500, the optical axis region is defined as 0% to 50% of the distance from optical axis I to optical boundary OB of the lens surface, and the circumferential region is defined as 50% to 100% of the distance from optical axis I to optical boundary OB of the lens surface. Referring to the lens 500 shown in Figure 6, optical axis region Z1 of eye-side surface 510 is defined as the distance from optical axis I to 50% of the distance from optical axis I to optical boundary OB of the lens surface. The R value of this eye-side surface 510 is positive (i.e., R>0), and therefore, optical axis region Z1 is convex. Since eye-side surface 510 of lens 500 lacks a transition point, the circumferential region Z2 of eye-side surface 510 is also convex. Lens 500 may further include an assembly portion (not shown) extending radially outward from circumferential region Z2.

[0026] Figure 7 is a schematic diagram of the eyepiece optical system of the first embodiment of the present invention. Figures 8A to 8D are diagrams of the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the first embodiment. Referring first to Figure 7 , the eyepiece optical system 10 of the first embodiment of the present invention includes, in order from the eye side A1 to the display side A2, a linear polarizing film plus a reflective polarizing film 4, a first optical element 1, a quarter-wave plate 5, and a second optical element 2 along an optical axis I of the eyepiece optical system 10. When light emitted from a display image to be captured (such as the display image 99 shown in Figure 7 ), passes through the eyepiece optical system 10 and enters an eye (such as the observer's pupil 0 shown in Figure 7 ), an image is formed, and this image is a magnified virtual image.

[0027] In this embodiment, the first optical element 1, the second optical element 2, the polarizing film plus reflective polarizing film 4, and the quarter-wave plate 5 each have an eye-side surface 15, 25, 45, or 55 facing the eye side A1 through which imaging light passes, and a display-side surface 16, 26, 46, or 56 facing the display side A2 through which imaging light passes. In this embodiment, the first optical element 1 is positioned between the pupil O and the second optical element 2. Furthermore, the display-side surface 26 of the second optical element 2 includes a partial reflector 6 for reflecting a portion of the energy of the imaging light. The partial reflector 6 has an average optical reflectivity of at least 30% across multiple desired wavelengths, and in this embodiment, the partial reflector 6 is a half-mirror.

[0028] The first optical element 1 is a flat plate. The optical axis region 151 of the eye-side surface 15 of the first optical element 1 is a flat surface, and its circumferential region 153 is also a flat surface. The optical axis region 161 of the display-side surface 16 of the first optical element 1 is also a flat surface, and its circumferential region 163 is also a flat surface.

[0029] The second optical element 2 is a lens with positive refractive power. The optical axis region 251 of the eye-side surface 25 of the second optical element 2 is flat, and its circumferential region 253 is also flat. The optical axis region 261 of the display-side surface 26 of the second optical element 2 is convex, and its circumferential region 263 is also convex. In this embodiment, both the eye-side surface 25 and the display-side surface 26 of the second optical element 2 are aspherical surfaces, but the present invention is not limited to this. The peak-to-valley values of the eye-side surface 15 of the first optical element 1, the display-side surface 16 of the first optical element 1, and the eye-side surface 25 of the second optical element 2 satisfy PV = 0 μm. However, in practice, the peak-to-valley values are affected by tolerances during the manufacturing process, resulting in PV ≤ 5 μm.

[0030] A reflective polarizing film is disposed on the eye-side A1 of the first optical element 1 to reflect imaging light having one linear polarization state and allow imaging light having another linear polarization state to pass through. Specifically, a linear polarizing film plus a reflective polarizing film 4 is disposed on the eye-side surface 15 of the first optical element 1.

[0031] The quarter-wave plate 5 is positioned between the display side A2 of the first optical element 1 or the linear polarization film plus reflective polarization film 4 and the eye side A1 of the first optical element 1 to convert circularly polarized imaging light into linearly polarized imaging light, or vice versa. Specifically, the quarter-wave plate 5 is positioned between the display side 16 of the first optical element 1 and the eye side 25 of the second optical element 2.

[0032] Specifically, in this embodiment, a display screen (such as display screen 99 shown in FIG7 ) provides imaging light having one of the circular polarization states. This imaging light passes through the second optical element 2 and the quarter-wave plate 5 to form imaging light having one of the linear polarization states. The imaging light having one of the linear polarization states passes through the first optical element 1 and the reflective polarizing film, which reflects imaging light having one of the linear polarization states. The imaging light having one of the linear polarization states passes through the first optical element 1 and the quarter-wave plate 5 again to form imaging light having the other of the circular polarization states. The imaging light having the other of the circular polarization states passes through the second optical element 2 and the display side surface 26 of the second optical element 2, which includes a partial reflector 6, to reflect imaging light having the other of the circular polarization states. The imaging light having the other of the circular polarization states passes through the second optical element 2 and the quarter-wave plate 5 again to form imaging light having the other of the linear polarization states. Finally, the imaging light having the other of the linear polarization states passes through the first optical element 1 and the linear polarization film plus the reflective polarizing film 4, entering the observer's eye (the observer's pupil 0 shown in FIG7 ) to form an image.

[0033] Other detailed optical data of the first embodiment are shown in FIG9 . The eyepiece optical system 10 of the first embodiment has an effective focal length (EFL) of 23.906 mm, a half field of view (HFOV) of 45.000 degrees, a TTL of 21.685 mm, an aperture value (F-number, Fno) of 5.976, and an image height of 17.196 mm. TTL refers to the distance from the eyepiece side surface 15 of the first optical element 1 to the display screen 99 on the optical axis I.

[0034] In addition, in this embodiment, the display side surface 26 of the second optical element 2 is an aspheric surface, wherein the display side surface 26 is a general even asphere surface. These aspheric surfaces are defined according to the following formula (1): (1) in: R: radius of curvature of the lens surface near the optical axis I; Z: Depth of the aspheric surface (the vertical distance between a point on the aspheric surface that is Y away from the optical axis I and the tangent plane that is tangent to the vertex on the aspheric surface on the optical axis I); Y: the vertical distance between the point on the aspheric curve and the optical axis I; K:conic constant; ai: i-th order aspheric coefficient.

[0035] The various aspheric coefficients of the display side surface 26 of the second optical element 2 in formula (1) are shown in FIG9 . Column number 26 in FIG9 indicates the aspheric coefficient of the display side surface 26 of the second optical element 2, and the same applies to the other columns. In this embodiment and the following embodiments, the second-order aspheric coefficient a2 is 0.

[0036] In addition, the relationship between the important parameters of the eyepiece optical system 10 of the first embodiment is shown in Figures 37 and 38. in, EPD is the exit pupil diameter of the eyepiece optical system 10, corresponding to the diameter of the observer's pupil 0; ER is the exit pupil distance, that is, the distance from the observer's pupil 0 to the first optical element 1 on the optical axis I; ER11 is the maximum distance from the center of the eye side surface 15 of the first optical element 1 to the mounting portion; ER12 is the maximum distance from the center of the display side 16 of the first optical element 1 to the mounting portion; ER21 is the maximum distance from the center of the object side surface 25 of the second optical element 2 to the mounting portion; ER22 is the maximum distance from the center of the display side 26 of the second optical element 2 to the mounting portion; PV is the peak-to-valley value of the surface, in other words, the difference between the highest point and the lowest point of the surface; ω is the half visual angle, that is, the maximum angle of half the observer's visual field; ObjH is the maximum height of the image formed in the eyepiece optical system 10, and this image is a virtual image; ObjD is the distance on the optical axis I from the observer's pupil 0 to the image formed by the eyepiece optical system 10; T1 is the thickness of the first optical element 1 on the optical axis I; T2 is the thickness of the second optical element 2 on the optical axis I; Tlp + Trp is the sum of the thickness of the linear polarizing film and the reflective polarizing film 4 on the optical axis I; Tqwp is the thickness of the quarter-wave plate 5 on the optical axis I; Toca is the thickness of the optically transparent adhesive 8 on the optical axis I; G12 is an air gap 7 on the optical axis I from the first optical element 1 to the second optical element 2; BFL is the distance from the display side 26 of the second optical element 2 to the display screen 99 on the optical axis I; ImgH is the maximum image height of the eyepiece optical system 10, which is half the diameter of the image circle; ALT is the sum of the thicknesses of the first optical element 1 and the second optical element 2 on the optical axis I; TL is the distance from the eye side of the optical element closest to the eye side A1 to the display side 26 of the second optical element 2 on the optical axis I; TTL is the distance from the eye side of the optical element closest to the eye side A1 to the display screen 99 on the optical axis I; SL is the system length of the eyepiece optical system 10, that is, the distance from the observer's eye to the display screen 99 on the optical axis I; EFL is the effective focal length of the eyepiece optical system 10 . In addition, redefine: f1 is the focal length of the first optical element 1; f2 is the focal length of the second optical element 2; f3 is the focal length of the third optical element 3; Nd1 is the refractive index of the first optical element 1; Nd2 is the refractive index of the second optical element 2; Nd3 is the refractive index of the third optical element 3; V1 is the Abbe number of the first optical element 1; V2 is the Abbe number of the second optical element 2; V3 is the Abbe number of the third optical element 3 .

[0037] 8A to 8D , FIG8A illustrates the longitudinal spherical aberration of the first embodiment on the display screen 99 when the wavelength is 486 nm, 588 nm, and 656 nm. FIG8B and FIG8C illustrate the field curvature aberration in the sagittal direction and the field curvature aberration in the tangential direction on the display screen 99 when the wavelength is 486 nm, 588 nm, and 656 nm, respectively. FIG8D illustrates the distortion aberration of the first embodiment on the display screen 99 when the wavelength is 486 nm, 588 nm, and 656 nm. The longitudinal spherical aberration of the first embodiment is shown in FIG8A . The curves for each wavelength are very close together and converge toward the center, indicating that off-axis light rays of different heights for each wavelength are concentrated near the image point. The deviation of the curves for each wavelength indicates that the deviation of the image points for off-axis light rays of different heights is controlled within a range of ±0.08 mm. Therefore, the first embodiment significantly improves spherical aberration for the same wavelength. Furthermore, the distances between the three representative wavelengths are also very close, indicating that the image positions of light rays of different wavelengths are relatively concentrated, thus significantly improving chromatic aberration.

[0038] In the field curvature aberration diagrams of Figures 8B and 8C , the focal length variation for the three representative wavelengths across the entire field of view falls within ±1.00 mm, demonstrating that the optical system of the first embodiment effectively eliminates aberrations. The distortion aberration diagram of Figure 8D shows that the distortion aberration of this embodiment remains within ±30%, indicating that the distortion aberration of this embodiment meets the imaging quality requirements of the optical system. This demonstrates that, compared to conventional optical systems, this first embodiment can still provide good imaging quality even when the TTL has been shortened to 21.685 mm. Therefore, this first embodiment can achieve a larger aperture, larger image height, superior imaging quality, and lower manufacturing costs while maintaining good optical performance.

[0039] Figure 10 is a schematic diagram of the eyepiece optical system of the second embodiment of the present invention. Figures 11A to 11D are diagrams of the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the second embodiment. Referring first to Figure 10 , the second embodiment of the eyepiece optical system 10 of the present invention is generally similar to the first embodiment, with the following differences: various optical data, aspheric coefficients, and parameters of the first optical element 1, the second optical element 2, the linear polarizing film plus the reflective polarizing film 4, and the quarter-wave plate 5 are somewhat different. Furthermore, in this embodiment, the linear polarizing film plus the reflective polarizing film 4 is disposed on the quarter-wave plate 5, facilitating the stacking of the three optical films. It should be noted that for clarity, the labels of some optical axis and circumferential regions with similar surface shapes to those of the first embodiment have been omitted in Figure 10 .

[0040] Detailed optical data of the eyepiece optical system 10 of the second embodiment are shown in FIG12 , and the effective focal length of the eyepiece optical system 10 of the second embodiment is 23.906 mm, the half angle of view is 45.000 degrees, the TTL is 21.685 mm, the aperture value is 5.976, and the image height is 17.196 mm.

[0041] FIG12 also shows the various aspheric coefficients of the display side surface 26 of the second optical element 2 in the second embodiment in the above formula (1).

[0042] In addition, the relationship between the important parameters of the eyepiece optical system 10 of the second embodiment is shown in Figures 37 and 38.

[0043] Figure 11A shows the longitudinal spherical aberration of the second embodiment. The image point deviations for off-axis light rays at different heights are controlled within a range of ±0.08 mm. In the field curvature aberration diagrams of Figures 11B and 11C, the focal length variation for three representative wavelengths across the entire field of view falls within ±1.00 mm. The distortion diagram of Figure 11D shows that the distortion of this embodiment is maintained within a range of ±30%.

[0044] From the above description, it can be seen that the second embodiment is easy to manufacture. Therefore, compared with the first embodiment, the second embodiment has a higher yield rate.

[0045] Figure 13 is a schematic diagram of the eyepiece optical system of the third embodiment of the present invention. Figures 14A to 14D are diagrams of the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the third embodiment. Referring first to Figure 13 , the third embodiment of the eyepiece optical system 10 of the present invention is generally similar to the first embodiment, with the following differences: various optical data, aspheric coefficients, and parameters of the first optical element 1, second optical element 2, linear polarization film plus reflective polarization film 4, and quarter-wave plate 5 are somewhat different. Furthermore, in this embodiment, the material of the first optical element 1 is replaced with a low-birefringence plastic material, which facilitates the use of low-stress optical plastic materials and reduces the occurrence of ghosting. It should be noted that for clarity, the labels for the optical axis and circumferential regions with similar surface shapes to the first embodiment are omitted in Figure 13 .

[0046] Detailed optical data of the eyepiece optical system 10 of the third embodiment are shown in FIG15 , and the effective focal length of the eyepiece optical system 10 of the third embodiment is 23.920 mm, the half angle of view is 44.999 degrees, the TTL is 21.609 mm, the aperture value is 5.980, and the image height is 17.204 mm.

[0047] FIG. 15 also shows various aspheric coefficients of the display side surface 26 of the second optical element 2 according to the third embodiment in the above formula (1).

[0048] In addition, the relationship between the important parameters of the eyepiece optical system 10 of the third embodiment is shown in Figures 37 and 38.

[0049] Figure 14A shows the longitudinal spherical aberration of the third embodiment. The image point deviations for off-axis light rays at different heights are controlled within a range of ±0.08 mm. In the field curvature aberration diagrams of Figures 14B and 14C, the focal length variation for three representative wavelengths across the entire field of view falls within ±1.00 mm. The distortion diagram of Figure 14D shows that the distortion of this embodiment is maintained within a range of ±30%.

[0050] As can be seen from the above description, the TTL of the third embodiment is shorter than that of the first embodiment. Therefore, compared to the first embodiment, the third embodiment has a smaller size. The image height of the third embodiment is greater than that of the first embodiment. Therefore, compared to the first embodiment, the third embodiment has better sensitivity.

[0051] Figure 16 is a schematic diagram of the eyepiece optical system of the fourth embodiment of the present invention. Figures 17A to 17D are diagrams of the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the fourth embodiment. Referring first to Figure 16 , the fourth embodiment of the eyepiece optical system 10 of the present invention is generally similar to the first embodiment, with the following differences: various optical data, aspheric coefficients, and parameters of the first optical element 1, the second optical element 2, the linear polarization film plus reflective polarization film 4, and the quarter-wave plate 5 are somewhat different. Furthermore, in this embodiment, the material is replaced with a low-birefringence glass material, which facilitates the use of low-stress optical glass materials and reduces the occurrence of ghosting. It should be noted that for clarity, the labels of some optical axis and circumferential regions with similar surface shapes to the first embodiment are omitted in Figure 16 .

[0052] Detailed optical data of the eyepiece optical system 10 of the fourth embodiment is shown in FIG. 18 , and the effective focal length of the eyepiece optical system 10 of the fourth embodiment is 23.913 mm, the half angle of view is 44.999 degrees, the TTL is 21.647 mm, the aperture value is 5.978, and the image height is 17.200 mm.

[0053] FIG18 also shows the various aspheric coefficients of the display side surface 26 of the second optical element 2 in the fourth embodiment in the above formula (1).

[0054] In addition, the relationship between the important parameters of the eyepiece optical system 10 of the fourth embodiment is shown in Figures 37 and 38.

[0055] Figure 17A shows the longitudinal spherical aberration of the fourth embodiment. The deviation of the image point for off-axis light rays at different heights is controlled within a range of ±0.08 mm. In the field curvature aberration diagrams of Figures 17B and 17C, the focal length variation for three representative wavelengths across the entire field of view falls within ±1.00 mm. The distortion diagram of Figure 17D shows that the distortion aberration of this embodiment is maintained within a range of ±30%.

[0056] As can be seen from the above description, the TTL of the fourth embodiment is shorter than that of the first embodiment. Therefore, compared to the first embodiment, the fourth embodiment has a smaller size. The image height of the fourth embodiment is greater than that of the first embodiment. Therefore, compared to the first embodiment, the fourth embodiment has better sensitivity.

[0057] Figure 19 is a schematic diagram of the eyepiece optical system of the fifth embodiment of the present invention. Figures 20A to 20D are diagrams of the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the fifth embodiment. Referring first to Figure 19, the fifth embodiment of the eyepiece optical system 10 of the present invention is generally similar to the first embodiment, with the following differences: various optical data, aspheric coefficients, and parameters of the first optical element 1, second optical element 2, linear polarization film plus reflective polarization film 4, and quarter-wave plate 5 are somewhat different. Furthermore, in this embodiment, anti-reflection coatings are applied to both the display side 16 of the first optical element 1 and the eye side 25 of the second optical element 2, which helps reduce ghosting. Furthermore, an air gap 7 is provided between the first and second optical elements 1, 2, which helps reduce TTL and eases the difficulty of the bonding process between the first and second optical elements 1, 2. It should be noted that for clarity, the reference numbers of the optical axis and circumferential regions with similar surface shapes to those of the first embodiment have been omitted in Figure 19.

[0058] Detailed optical data of the eyepiece optical system 10 of the fifth embodiment is shown in FIG. 21 , and the effective focal length of the eyepiece optical system 10 of the fifth embodiment is 24.259 mm, the half angle of view is 50.385 degrees, the TTL is 20.968 mm, the aperture value is 6.065, and the image height is 19.120 mm.

[0059] FIG21 also shows the various aspheric coefficients of the display side surface 26 of the second optical element 2 of the fifth embodiment in the above formula (1).

[0060] In addition, the relationship between the important parameters of the eyepiece optical system 10 of the fifth embodiment is shown in Figures 37 and 38.

[0061] Figure 20A shows the longitudinal spherical aberration of the fifth embodiment. The image point deviations for off-axis light rays at different heights are controlled within a range of ±0.08 mm. In the field curvature aberration diagrams of Figures 20B and 20C, the focal length variation for three representative wavelengths across the entire field of view falls within ±1.00 mm. The distortion diagram of Figure 20D shows that the distortion of this embodiment is maintained within a range of ±30%.

[0062] As can be seen from the above description, the half-angle of view of the fifth embodiment is greater than that of the first embodiment. Therefore, compared to the first embodiment, the fifth embodiment has a wider angular range of image reception. The TTL of the fifth embodiment is shorter than that of the first embodiment. Therefore, compared to the first embodiment, the fifth embodiment has a smaller size. The image height of the fifth embodiment is greater than that of the first embodiment. Therefore, compared to the first embodiment, the fifth embodiment has better sensitivity.

[0063] Figure 22 is a schematic diagram of the eyepiece optical system of the sixth embodiment of the present invention. Figures 23A to 23D are diagrams of the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the sixth embodiment. Referring first to Figure 22, the sixth embodiment of the eyepiece optical system 10 of the present invention is generally similar to the first embodiment, with the following differences: various optical data, aspheric coefficients, and parameters of the first optical element 1, second optical element 2, linear polarizing film plus reflective polarizing film 4, and quarter-wave plate 5 are somewhat different. Furthermore, in this embodiment, the thickness of the first optical element 1 is reduced, which helps reduce the weight of the eyepiece optical system 10 and shortens the injection molding time of the first optical element 1, thereby increasing production capacity. It should be noted that for clarity, the labels for the optical axis and circumferential regions with similar surface shapes to the first embodiment are omitted in Figure 22.

[0064] Detailed optical data of the eyepiece optical system 10 of the sixth embodiment is shown in FIG. 24 , and the effective focal length of the eyepiece optical system 10 of the sixth embodiment is 23.191 mm, the half angle of view is 44.999 degrees, the TTL is 21.876 mm, the aperture value is 5.798, and the image height is 16.741 mm.

[0065] FIG24 also shows the various aspheric coefficients of the display side surface 26 of the second optical element 2 in the sixth embodiment in the above formula (1).

[0066] In addition, the relationship between the important parameters of the eyepiece optical system 10 of the sixth embodiment is shown in Figures 39 and 40.

[0067] Figure 23A shows the longitudinal spherical aberration of the sixth embodiment. The image point deviations for off-axis light rays at different heights are controlled within a range of ±0.12 mm. In the field curvature aberration diagrams of Figures 23B and 23C, the focal length variation for three representative wavelengths across the entire field of view falls within ±1.00 mm. The distortion diagram of Figure 23D shows that the distortion of this embodiment is maintained within a range of ±30%.

[0068] From the above description, it can be seen that the aperture of the sixth embodiment is larger than that of the first embodiment. Therefore, compared with the first embodiment, the sixth embodiment allows for greater light intake.

[0069] Figure 25 is a schematic diagram of the eyepiece optical system of the seventh embodiment of the present invention. Figures 26A to 26D are diagrams of the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the seventh embodiment. Referring first to Figure 25 , the seventh embodiment of the eyepiece optical system 10 of the present invention is generally similar to the first embodiment, with the following differences: various optical data, aspheric coefficients, and parameters of the first optical element 1, second optical element 2, linear polarizing film plus reflective polarizing film 4, and quarter-wave plate 5 vary to varying degrees. Furthermore, in this embodiment, the thickness of the first optical element 1 is reduced, which facilitates shortening the TTL of the eyepiece optical system 10. It should be noted that for clarity, the labels of some optical axis and circumferential regions with similar surface shapes to those of the first embodiment have been omitted in Figure 25 .

[0070] Detailed optical data of the eyepiece optical system 10 of the seventh embodiment are shown in FIG. 27 . The effective focal length of the eyepiece optical system 10 of the seventh embodiment is 25.391 mm, the half angle of view is 45.000 degrees, the TTL is 21.027 mm, the aperture value is 6.348, and the image height is 18.052 mm.

[0071] FIG27 also shows the various aspheric coefficients of the display side surface 26 of the second optical element 2 of the seventh embodiment in the above formula (1).

[0072] In addition, the relationship between the important parameters of the eyepiece optical system 10 of the seventh embodiment is shown in Figures 39 and 40.

[0073] Figure 26A shows the longitudinal spherical aberration of the seventh embodiment. The image point deviations for off-axis light rays at different heights are controlled within a range of ±0.05 mm. In the field curvature aberration diagrams of Figures 26B and 26C, the focal length variation for three representative wavelengths across the entire field of view falls within ±1.20 mm. The distortion diagram of Figure 26D demonstrates that the distortion of this embodiment is maintained within a range of ±30%.

[0074] As can be seen from the above description, the TTL of the seventh embodiment is shorter than that of the first embodiment. Therefore, the seventh embodiment has a smaller size compared to the first embodiment. The image height of the seventh embodiment is greater than that of the first embodiment. Therefore, the seventh embodiment has better sensitivity than the first embodiment. Furthermore, the longitudinal spherical aberration of the seventh embodiment is less than that of the first embodiment.

[0075] Figure 28 is a schematic diagram of the eyepiece optical system of the eighth embodiment of the present invention. Figures 29A to 29D are diagrams of the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the eighth embodiment. Referring first to Figure 28 , the eighth embodiment of the eyepiece optical system 10 of the present invention is generally similar to the first embodiment, with the following differences: various optical data, aspheric coefficients, and parameters of the first optical element 1, the second optical element 2, the linear polarizing film plus reflective polarizing film 4, and the quarter-wave plate 5 are somewhat different. Furthermore, in this embodiment, the first optical element 1 has a positive refractive power. The optical axis region 151 of the eyepiece side surface 15 of the first optical element 1 is convex, the circumferential region 153 of the eyepiece side surface 15 of the first optical element 1 is convex, the optical axis region 161 of the display side surface 16 of the first optical element 1 is convex, and the circumferential region 163 of the display side surface 16 of the first optical element 1 is convex. The optical axis region 251 of the eyepiece side surface 25 of the second optical element 2 is concave, and the circumferential region 253 of the eyepiece side surface 25 of the second optical element 2 is concave. Furthermore, the PV values of the eye-side surface 15 of the first optical element 1, the display-side surface 16 of the first optical element 1, and the eye-side surface 25 of the second optical element 2 are designed to be 156 microns. It should be noted that for clarity, the reference numbers for the optical axis and circumferential regions similar to those in the first embodiment have been omitted in FIG. 28 .

[0076] Detailed optical data of the eyepiece optical system 10 of the eighth embodiment are shown in FIG. 30 . The effective focal length of the eyepiece optical system 10 of the eighth embodiment is 22.448 mm, the half angle of view is 47.500 degrees, the TTL is 19.944 mm, the aperture value is 5.612, and the image height is 16.845 mm.

[0077] FIG30 also shows the various aspheric coefficients of the display side surface 26 of the second optical element 2 of the eighth embodiment in the above formula (1).

[0078] In addition, the relationship between the important parameters of the eyepiece optical system 10 of the eighth embodiment is shown in Figures 39 and 40.

[0079] Figure 29A shows the longitudinal spherical aberration of the eighth embodiment. The deviation of the image point for off-axis light rays at different heights is controlled within a range of ±0.07 mm. In the field curvature aberration diagrams of Figures 29B and 29C, the focal length variation for three representative wavelengths across the entire field of view falls within ±1.00 mm. The distortion diagram of Figure 29D shows that the distortion of this embodiment is maintained within a range of ±30%.

[0080] The above description shows that the half-angle of view of the eighth embodiment is greater than that of the first embodiment. Therefore, compared to the first embodiment, the eighth embodiment has a wider angular range of image reception. The TTL of the eighth embodiment is shorter than that of the first embodiment. Therefore, compared to the first embodiment, the eighth embodiment has a smaller size. The aperture of the eighth embodiment is greater than that of the first embodiment. Therefore, compared to the first embodiment, the eighth embodiment allows for greater light intake. Furthermore, the longitudinal spherical aberration of the eighth embodiment is less than that of the first embodiment.

[0081] Figure 31 is a schematic diagram of the eyepiece optical system of the ninth embodiment of the present invention. Figures 32A to 32D are diagrams of the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the ninth embodiment. Referring first to Figure 31 , the ninth embodiment of the eyepiece optical system 10 of the present invention is generally similar to the first embodiment, with the following differences: various optical data, aspheric coefficients, and parameters of the first optical element 1, the second optical element 2, the linear polarizing film plus reflective polarizing film 4, and the quarter-wave plate 5 are somewhat different. Furthermore, in this embodiment, the magnification of the eyepiece optical system 10 is increased to reduce observer fatigue during continuous use. It should be noted that for clarity, the labels of some optical axis and circumferential regions with similar surface shapes to the first embodiment are omitted in Figure 31 .

[0082] Detailed optical data of the eyepiece optical system 10 of the ninth embodiment are shown in FIG. 33 . The eyepiece optical system 10 of the ninth embodiment has an effective focal length of 23.847 mm, a half angle of view of 45.000 degrees, a TTL of 21.891 mm, an aperture value of 5.962, and an image height of 17.181 mm.

[0083] FIG33 also shows the various aspheric coefficients of the display side surface 26 of the second optical element 2 of the ninth embodiment in the above formula (1).

[0084] In addition, the relationship between the important parameters of the eyepiece optical system 10 of the ninth embodiment is shown in Figures 39 and 40.

[0085] Figure 32A shows the longitudinal spherical aberration of the ninth embodiment. The image point deviations for off-axis light rays at different heights are controlled within a range of ±0.09 mm. In the field curvature aberration diagrams of Figures 32B and 32C, the focal length variation for three representative wavelengths across the entire field of view falls within ±1.00 mm. The distortion diagram of Figure 32D demonstrates that the distortion of this embodiment is maintained within a range of ±30%.

[0086] The above description demonstrates that the aperture of the ninth embodiment is larger than that of the first embodiment. Therefore, compared to the first embodiment, the ninth embodiment allows for greater light intake. Furthermore, the longitudinal spherical aberration of the ninth embodiment is smaller than that of the first embodiment.

[0087] Figure 34 is a schematic diagram of the eyepiece optical system of the tenth embodiment of the present invention. Figures 35A to 35D are diagrams of the longitudinal spherical aberration and various aberrations of the eyepiece optical system of the tenth embodiment. Referring first to Figure 34 , the tenth embodiment of the eyepiece optical system 10 of the present invention is generally similar to the first embodiment, with the following differences: various optical data, aspheric coefficients, and parameters of the first optical element 1, second optical element 2, linear polarizing film plus reflective polarizing film 4, and quarter-wave plate 5 vary to varying degrees. Furthermore, the addition of the third optical element 3 and optically transparent adhesive 8 in this embodiment improves imaging quality, including MTF. It should be noted that for clarity, the labels for the optical axis and circumferential regions, which have similar surface shapes to those of the first embodiment, have been omitted in Figure 34 .

[0088] The third optical element 3 has a positive refractive power. The optical axis region 351 of the eye-side surface 35 of the third optical element 3 is convex, and its circumferential region 353 is also convex. The optical axis region 361 of the display-side surface 36 of the third optical element 3 is flat, and its circumferential region 363 is also flat. In this embodiment, the eye-side surface 35 of the third optical element 3 is aspherical, but the present invention is not limited to this.

[0089] Detailed optical data of the eyepiece optical system 10 of the tenth embodiment are shown in FIG. 36 , and the effective focal length of the eyepiece optical system 10 of the tenth embodiment is 21.771 mm, the half angle of view is 45.000 degrees, the TTL is 24.031 mm, the aperture value is 4.354, and the image height is 15.044 mm.

[0090] FIG36 also shows the various aspheric coefficients of the display side surface 26 of the second optical element 2 and the eye side surface 36 of the third optical element 3 in the above formula (1) according to the tenth embodiment.

[0091] In addition, the relationship between the important parameters of the eyepiece optical system 10 of the tenth embodiment is shown in Figures 39 and 40.

[0092] Figure 35A shows the longitudinal spherical aberration of the tenth embodiment. The image point deviations for off-axis light rays at different heights are controlled within a range of ±0.14 mm. In the field curvature aberration diagrams of Figures 35B and 35C, the focal length variation for three representative wavelengths across the entire field of view falls within ±0.18 mm. The distortion diagram of Figure 35D demonstrates that the distortion of this embodiment is maintained within a range of ±35%.

[0093] As can be seen from the above description, the aperture of the tenth embodiment is larger than that of the first embodiment. Therefore, compared to the first embodiment, the tenth embodiment allows for greater light intake. Furthermore, the field curvature aberration of the tenth embodiment is smaller than that of the first embodiment.

[0094] In the embodiment of the present invention, the eye-side surface 15 and the display-side surface 16 of the first optical element 1 meet the following condition: PV ≤ 160 μm. Therefore, the eyepiece optical system 10, utilizing a double-reflection optical effect, facilitates reducing the thickness of the second optical element 2, which primarily provides refractive power. Since plastic injection molding time is proportional to the square of the element thickness, a thinner second optical element 2 can shorten its production cycle, increasing product productivity and reducing manufacturing costs. Furthermore, since the eye-side surface 15 and the display-side surface 16 of the first optical element 1 meet the PV ≤ 160 μm requirement, this reduces the difficulty of the film lamination process, thereby improving yield and reducing manufacturing costs. To achieve optimal optical performance, the optimal PV limit is ≤ 5 μm.

[0095] The embodiment of the present invention further limits the air gap between the display side surface 16 of the first optical element 1 and the eyepiece side surface 25 of the second optical element 2, which is conducive to mass production of the eyepiece optical system 10 and reduces manufacturing costs.

[0096] Because the distance on the optical axis between the observer's eye and the image of the eyepiece optical system 10 is proportional to the system length of the eyepiece optical system 10, the eye-side surface 15 of the first optical element 1 and the display side surface 16 of the first optical element 1 satisfy PV ≤ 160 μm. Therefore, the eyepiece optical system 10 satisfies the conditional equation: 35 ≤ |ObjD| / ImgH ≤ 200, which helps to increase the magnification of the eyepiece optical system 10 (i.e., ObjH / ImgH).

[0097] This embodiment of the present invention further restricts the eye-side surface 25 of the second optical element 2 to satisfy a PV of ≤160 μm, and eliminates any air gap between the display side 16 of the first optical element 1 and the eye-side surface 25 of the second optical element 2. Therefore, it is advantageous to use an adhesive that matches the refractive index of the first optical element 1 and the refractive index of the second optical element 2 (Nd = 1.492-1.543), such as optical adhesive (Nd = 1.540), to bond the second optical element 2 to the display side 16 of the first optical element 1. This reduces reflections from light entering the optical adhesive from the second optical element 2 and from the optical adhesive to the first optical element 1, thereby preventing ghost images. Furthermore, this structure facilitates mass production of the eyepiece optical system 10, reducing manufacturing costs.

[0098] The first optical element 1 and the second optical element 2 are made of low-birefringence plastic or glass materials, such as APEL, PMMA or BK7, which is beneficial to reducing the stress of the optical elements and thus reducing the chance of ghosting.

[0099] The first optical element 1 is a flat plate, which facilitates mass production of the eyepiece optical system, reduces the difficulty of the film-mounting process, and reduces manufacturing costs.

[0100] The second optical element 2 is a lens, the eye-side surface 25 of the second optical element 2 is a plane, and the optical axis region 261 of the display side surface 26 of the second optical element 2 is a convex surface. Therefore, this helps improve the yield rate of the injection molding of the second optical element 2.

[0101] A linear polarizing film is disposed on the reflective polarizing film, and an anti-reflective film is disposed on the reflective polarizing film to help reduce stray light of the eyepiece optical system 10 .

[0102] The present invention further restricts the magnification of the eyepiece optical system 10 to 18≦|ObjD| / SL≦85, 30≦|ObjD| / TTL≦140, and 60≦|ObjD| / TL≦300. Therefore, the magnification of the eyepiece optical system 10 can be increased by increasing the distance and height of the virtual image, so that the magnification satisfies 40≦ObjH / ImgH≦200.

[0103] The present invention further restricts the values to 1.6≦SL / ImgH≦2.8, 1.6≦ImgH / T1≦10.0, or 2.5≦ImgH / T2≦3.7. Therefore, by reducing the image height, the magnification of the eyepiece optical system 10 can be increased while reducing the size and weight of the display.

[0104] Embodiments of the present invention further restrict the optical element to: 2.5 ≤ ER12 / T1 ≤ 17.0, 3.0 ≤ ER22 / T2 ≤ 7.0, 2.0 ≤ (ER11 + ER21) / ALT ≤ 10.0, or 1.5 ≤ (ER21 + ER22) / TTL ≤ 3.0. This helps reduce the ratio of the effective radius to thickness of optical components and improves yield and production capacity.

[0105] The eyepiece optical system 10 has an eye relief range of 5 to 20 mm. Further limiting the range to 1.2 ≤ ER / T1 ≤ 30.0 or 2.0 ≤ ER / T2 ≤ 4.0 can help maintain an appropriate distance between the eyepiece optical system 10 and the eyeball, reducing observer fatigue.

[0106] The embodiment of the present invention further limits the range of 2.0≦SL / TL≦6.0 or 1.4≦EFL / TL≦3.6. Therefore, it is helpful to reduce the volume and weight of the eyepiece optical system 10.

[0107] Figure 41 is a flow chart of the steps of the mass production method for the eyepiece optical system 10 of the present invention. Figure 42 is a schematic diagram of the mass production method for the eyepiece optical system 10 of the present invention. Please refer to Figures 41 and 42. In this embodiment, step S100 is first performed to manufacture a large-sized first optical element 11 using a low-birefringence plastic or glass material. The eye-side surface 115 and the display-side surface 116 of the large-sized first optical element 11 meet the following condition: PV ≤ 160 μm, where PV is the peak-to-valley value of the surface. Both the eye-side surface 115 and the display-side surface 116 of the large-sized first optical element 11 are flat. The definition of large size is, for example, an area of 21 cm × 30 cm, but the present invention is not limited thereto. Furthermore, to achieve better optical performance, the PV is preferably limited to PV ≤ 5 μm.

[0108] Next, step S101 is performed to dispose a large-scale reflective polarizing film 14 on the eye-side surface 115 of the large-scale first optical element 11, and a large-scale quarter-wave plate 15 on the display side 116 of the large-scale first optical element 11 or between the large-scale reflective polarizing film 14 and the eye-side surface 115 of the large-scale first optical element 11, thereby forming an optical film on the large-scale first optical element 11. In this way, a large-area coating of the eyepiece optical system 10 to be produced can be completed in one step.

[0109] Next, step S102 is performed, where the plurality of second optical elements 2, for example, manufactured by injection molding, are bonded to the display side 116 of the large-sized first optical element 11 using an adhesive having a refractive index that matches the refractive index of the large-sized first optical element 11 and the refractive index of the plurality of second optical elements 2, thereby forming an assembly 20 consisting of a plurality of eyepiece optical systems 10 arranged in an array. This minimizes material waste.

[0110] Next, step S103 is performed to cut the aggregate 20 consisting of the plurality of eyepiece optical systems 10 to form a plurality of separate eyepiece optical systems 10. In this way, production efficiency can be improved and manufacturing costs can be reduced.

[0111] The contents disclosed in various embodiments of the present invention include, but are not limited to, optical parameters such as focal length, lens thickness, and Abbe number. For example, each embodiment of the present invention discloses an optical parameter A and an optical parameter B. The ranges covered by these optical parameters, the comparative relationships between the optical parameters, and the conditional ranges covered by various embodiments are specifically explained as follows: (1) The range covered by the optical parameters, for example: α 2 ≦ A ≦ α 1 or β 2 ≦ B ≦ β 1, α 1 is the maximum value of the optical parameter A in multiple embodiments, α 2 is the minimum value of the optical parameter A in multiple embodiments, β 1 is the maximum value of the optical parameter B in multiple embodiments, and β 2 is the minimum value of the optical parameter B in multiple embodiments. (2) The comparative relationship between optical parameters, for example: A is greater than B or A is less than B. (3) The range of conditional expressions covered by multiple embodiments, specifically, the combination relationship or proportional relationship obtained by possible calculation of multiple optical parameters of the same embodiment, these relationships are defined as E. E can be, for example: A+B or AB or A / B or A*B or (A*B) 1 / 2, and E satisfies the conditional expression E≦γ1 or E≧γ2 or γ2≦E≦γ1, γ1 and γ2 are the values obtained by calculation of optical parameters A and optical parameters B of the same embodiment, and γ1 is the maximum value among multiple embodiments of the present invention, and γ2 is the minimum value among multiple embodiments of the present invention. The ranges encompassed by the aforementioned optical parameters, the comparative relationships between the optical parameters, and the maximum and minimum values, as well as the numerical ranges within these conditional expressions, are all features that enable the present invention to be implemented and fall within the scope disclosed herein. The above is merely illustrative and should not be construed as limiting.

[0112] All embodiments of the present invention are applicable, and some feature combinations can be extracted from the same embodiment. These feature combinations can achieve unexpected benefits compared to prior art. These feature combinations include, but are not limited to, combinations of features such as face shape, refractive index, and conditional formula. The disclosure of the embodiments of the present invention is intended to illustrate the principles of the present invention and should not be construed as limiting the present invention to the disclosed embodiments. Furthermore, the embodiments and accompanying figures are intended for illustrative purposes only and are not intended to limit the present invention.

[0113] 0:Pupil 1: First optical element 10, V100: Eyepiece optical system 100,200,300,400,500: Lens 130: Assembly Department 15,25,35,45,55,85,110,410,510: side view 151,161,251,261,351,361,Z1: Optical axis area 153,163,253,263,353,363,Z2: Circumference area 16,26,36,46,56,86,120,320: Display side 2: Second optical element 211,212: Parallel rays 3: The third optical element 4: Linear polarizing film plus reflective polarizing film 5: Quarter Wavelength Plate 6: Partial reflector 7: Air gap 8: Optically transparent adhesive 99, V50: Display screen A1: Side of the eye A2: Display side CP: Center Point CP1: First Center Point CP2: Second center point EL: Extension line I: optical axis Lc: Chief ray Lm: marginal light M,R: intersection point OB: Optical Boundary TP1: First transition point TP2: Second transition point V60: Eyes VD: visual distance VI: Imaging Rays VV: magnified virtual image Z3: Relay Zone

Claims

1. An eyepiece optical system configured to allow imaging light from a display screen to pass through the eyepiece optical system into an observer's eye to form an image, wherein the side facing the eye is an eye side and the side facing the display screen is a display side, the eyepiece optical system sequentially including a first optical element and a second optical element along an optical axis from the eye side to the display side, each of the first and second optical elements including an eye side facing the eye side and allowing the imaging light to pass through, and a display side facing the display side and allowing the imaging light to pass through, the eyepiece optical system further including a reflective polarizing film and a quarter-wave plate; the eye side of the first optical element and the display side of the first optical element satisfy the following condition: PV ≤ 160 μm, where PV is a peak-to-valence value of a surface; the reflective polarizing film is disposed on the eye side of the first optical element; the quarter-wave plate is disposed on the display side of the first optical element or between the reflective polarizing film and the eye side of the first optical element; wherein, The eyepiece optical system satisfies the following condition: 35≤|ObjD| / ImgH≤200, where ObjD is the distance from the observer's eye to the image formed by the eyepiece optical system on the optical axis, and ImgH is the maximum image height of the eyepiece optical system.

2. An eyepiece optical system configured to allow imaging light from a display screen to pass through the eyepiece optical system into an observer's eye to form an image, wherein the side facing the eye is an eye side and the side facing the display screen is a display side, the eyepiece optical system sequentially includes a first optical element and a second optical element along an optical axis from the eye side to the display side, each of the first and second optical elements including an eye side facing the eye side and allowing the imaging light to pass through and a display side facing the display side and allowing the imaging light to pass through, the eyepiece optical system further including a reflective polarizing film and a quarter-wave plate; the eye side of the first optical element, the display side of the first optical element, and the eye side of the second optical element satisfy the following condition: PV ≤ 160 μm, where PV is a peak-to-valence value of a surface; the reflective polarizing film is disposed on the eye side of the first optical element; the quarter-wave plate is disposed on the display side of the first optical element or between the reflective polarizing film and the eye side of the first optical element; There is no air gap between the display side of the first optical element and the eye side of the second optical element.

3. The eyepiece optical system as claimed in claim 1 or 2, wherein a linear polarizing film is disposed on the reflective polarizing film, and an anti-reflective mode is disposed on the reflective polarizing film.

4. The eyepiece optical system as claimed in claim 1 or 2, wherein the eye side and the display side of the first optical element satisfy the following formula: PV ≤ 5 μm.

5. The eyepiece optical system as claimed in claim 2, wherein the eyepiece optical system further satisfies the following formula: 60 ≤ |ObjD| / ImgH ≤ 200, where ObjD is the distance from the observer's eye to the image formed by the eyepiece optical system on the optical axis, and ImgH is the maximum image height of the eyepiece optical system.

6. The eyepiece optical system as claimed in claim 2, wherein the eyepiece optical system further satisfies the following formula: 18 ≤ |ObjD| / SL ≤ 85, where ObjD is the distance from the observer's eye to the image formed by the eyepiece optical system on the optical axis, and SL is the distance from the observer's eye to the display screen on the optical axis.

7. The eyepiece optical system as claimed in claim 2, wherein the eyepiece optical system further satisfies the following formula: 1.6 ≤ SL / ImgH ≤ 2.8, where SL is the distance from the observer's eye to the display image on the optical axis, and ImgH is the maximum image height of the eyepiece optical system.

8. The eyepiece optical system as claimed in claim 1 or 2, wherein the eyepiece optical system further satisfies the following formula: 2.5≤ER12 / T1≤17.0, where ER12 is the maximum distance from the center of the display side of the first optical element to the mounting portion, and T1 is the thickness of the first optical element on the optical axis.

9. The eyepiece optical system as claimed in claim 1 or 2, wherein the eyepiece optical system further satisfies the following formula: 2.0 ≤ (ER11 + ER21) / ALT ≤ 10.0, where ER11 is the maximum distance from the center of the eyepiece side of the first optical element to the mounting portion, ER21 is the maximum distance from the center of the eyepiece side of the second optical element to the mounting portion, and ALT is the sum of the thicknesses of the first optical element and the second optical element on the optical axis.

10. The eyepiece optical system as claimed in claim 1 or 2, wherein the eyepiece optical system further satisfies the following formula: 1.2 ≤ ER / T1 ≤ 30.0, where ER is the distance from the observer's eye to the first optical element on the optical axis, and T1 is the thickness of the first optical element on the optical axis.

11. The eyepiece optical system as claimed in claim 1 or 2, wherein the eyepiece optical system further satisfies the following formula: 2.0 ≤ SL / TL ≤ 6.0, where SL is the distance from the observer's eye to the display image on the optical axis, and TL is the distance from the eye side of the optical element closest to the eye side to the display side of the second optical element on the optical axis.

12. The eyepiece optical system as claimed in claim 1 or 2, wherein the display side of the second optical element is convex.

13. The eyepiece optical system as claimed in claim 2, wherein the eyepiece optical system further satisfies the following formula: 30 ≤ |ObjD| / TTL ≤ 140, where ObjD is the distance on the optical axis from the observer's eye to the image formed by the eyepiece optical system, and TTL is the distance on the optical axis from the eye side of the optical element closest to the eye side to the display screen.

14. The eyepiece optical system of claim 2, wherein the eyepiece optical system further satisfies the following formula: 60 ≤ |ObjD| / TL ≤ 300, where ObjD is the distance on the optical axis from the observer's eye to the image formed by the eyepiece optical system, and TL is the distance on the optical axis from the eye side of the optical element closest to the eye side to the display side of the second optical element.

15. The eyepiece optical system as claimed in claim 2, wherein the eyepiece optical system further satisfies the following formula: 2.5 ≤ ImgH / T2 ≤ 3.7, where ImgH is the maximum image height of the eyepiece optical system and T2 is the thickness of the second optical element on the optical axis.

16. The eyepiece optical system as claimed in claim 1 or 2, wherein the eyepiece optical system further satisfies the following formula: 3.0≤ER22 / T2≤7.0, where ER22 is the maximum distance from the center of the display side of the second optical element to the mounting portion, and T2 is the thickness of the second optical element on the optical axis.

17. The eyepiece optical system as claimed in claim 1 or 2, wherein the eyepiece optical system further satisfies the following formula: 1.5 ≤ (ER21 + ER22) / TTL ≤ 3.0, where ER21 is the maximum distance from the center of the eye side of the second optical element to the mounting portion, ER22 is the maximum distance from the center of the display side of the second optical element to the mounting portion, and TTL is the distance from the eye side of the optical element closest to the eye side to the display screen on the optical axis.

18. The eyepiece optical system as claimed in claim 1 or 2, wherein the eyepiece optical system further satisfies the following formula: 2.0 ≤ ER / T2 ≤ 4.0, where ER is the distance from the observer's eye to the first optical element on the optical axis, and T2 is the thickness of the second optical element on the optical axis.

19. The eyepiece optical system as claimed in claim 1 or 2, wherein the eyepiece optical system further satisfies the following formula: 1.4 ≤ EFL / TL ≤ 3.6, where EFL is the effective focal length of the eyepiece optical system and TL is the distance on the optical axis from the eye side of the optical element closest to the eye side to the display side of the second optical element.

20. A method for mass-producing an eyepiece optical system, comprising: A large-size first optical element is manufactured using a low-birefringence plastic or glass material, wherein an eye-side and a display-side of the large-size first optical element satisfy the following formula: PV ≤ 160 μm, where PV is the peak-to-valence value of the surface; a large-size reflective polarizing film is disposed on the eye-side of the large-size first optical element, and a large-size quarter-wave plate is disposed on the display-side of the large-size first optical element or between the large-size reflective polarizing film and the eye-side of the large-size first optical element to form an optical film on the large-size first optical element; the second optical elements are bonded to the display-side of the large-size first optical element using an adhesive that matches the refractive index of the large-size first optical element and the refractive index of a plurality of second optical elements to form an assembly consisting of a plurality of eyepiece optical systems arranged in an array; and the assembly consisting of the eyepiece optical systems is cut to form the separate eyepiece optical systems.

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