Reflective geometric holographic display system

Abstract

The present invention relates to the field of 3D display, and discloses a reflective geometric holographic display system, comprising at least one projector, an auxiliary imaging screen, one reflective geometric holographic screen located on one side of the auxiliary imaging screen or two reflective geometric holographic screens located on both sides of the auxiliary imaging screen, a supporting structure and a controller, wherein the reflective geometric holographic screen is used to reversely reflect the light irradiated thereon; the reflective geometric holographic display system has n viewpoints, the average value of the diameter of the light-transmitting part of the outermost lens of the projector is D decimeters, and the average value of the projection light source power of the projector is P watts, which satisfies: by introducing the reflective geometric holographic screen capable of modulating light at any angle to realize reverse reflection, the incident light is modulated, other optical modules are omitted, the cost is saved to a certain extent, the occupied space of the system is reduced, and at the same time, an optimized design parameter configuration is provided, so as to achieve the purpose of taking into account both the display effect and the system reliability.

Description

Technical Field

[0001] The present invention relates to the field of 3D display, and in particular to a reflective geometric holographic display system. Background Art

[0002] Compared with traditional 2D display technology, 3D display technology can provide depth information, thereby displaying more visual information and making the displayed image more realistic. Therefore, 3D display technology is a very popular technology in academic research. Among them, the 3D display solution based on holographic technology can, in principle, restore the light field distribution of the real physical world, thereby completely restoring all the optical characteristics of the 3D scene. Traditional holographic display technology uses the wave characteristics of light to simultaneously record the light intensity information and phase information of the scene, thereby achieving the recording of the light intensity, color and depth of field of the scene. However, this method requires coherent light for shooting and display, and the optical path setting during the shooting and display process is very harsh. Slight disturbances in the environment will cause shooting failures, so it has never been truly applied in life.

[0003] At present, mainstream 3D display solutions (such as 3D movies in theaters) are based on pseudo 3D display images of parallax image pairs (stereoscopic image pairs), which cannot display real 3D images. The physical focal depth of the display screen is fixed, and it is impossible to display scenes with different focal depths. Although many 3D display technologies have been proposed, there is no technology that can truly display large-scale, stable, and high-quality 3D images.

[0004] The patent with application number 201910875975.1 discloses a new holographic display solution, which fully utilizes the principles of geometric optics to reproduce depth of field information. However, very precise eye tracking methods are required to achieve 3D display, and the structural limitations of the display system are relatively large. In many application scenarios, it is impossible to provide sufficient system layout space for it. The system is complex and costly. In addition, the optical parameter setting of this display system needs to be carefully designed to ensure the ideal display effect and the reliability of the display system. Otherwise, the display system may not achieve the ideal display effect or cannot guarantee reliability due to inappropriate display parameters. In addition, this transmissive imaging system also has the problem of low light source utilization. After being refracted, the projection light is divided into four beams of light, of which only one beam of light participates in imaging, and the three non-imaging beams are easy to interfere with the formed image, reducing the imaging quality.

[0005] An aerial floating display system with publication number CN108269511A discloses a two-dimensional plane air imaging solution and a retro-reflective right-angled triangle prism array, which includes a series of right-angled triangle prism light reflection screens. This right-angled triangle prism can only realize the retro-reflective imaging function of the light parallel to its cross-section. When the light is not parallel to the cross-section, the retro-reflective function cannot be realized. It does not have the function of modulating these light rays that are not parallel to its cross-section, and needs to use other optical modules to modulate the light to realize retro-reflective imaging. At the same time, the display solution of this application is a fixed display. The user can only view the off-screen picture in the space in a specific external place. Dynamic display cannot be realized, and the limitation is relatively large. Summary of the invention

[0006] In order to solve or partially solve the deficiencies of the prior art, a reflective geometric holographic display system is provided. By introducing a reflective geometric holographic screen capable of modulating light at any angle to achieve retroreflection, the incident light is modulated, and other optical modules are eliminated, which saves costs to a certain extent and reduces the space occupied by the system. At the same time, the system uses two reflective geometric holographic screens to improve the utilization rate of the light source, avoid interference from non-imaging light beams, and greatly improve the imaging quality. In addition, an optimized design parameter configuration is provided to achieve the purpose of taking into account both display effect and system reliability.

[0007] In order to solve the above technical problems, the present invention provides a reflective geometric holographic display system, comprising:

[0008] At least one projector, used to project image information in space;

[0009] Auxiliary imaging screen for light splitting;

[0010] A reflective geometric holographic screen located on one side of the auxiliary imaging screen or two reflective geometric holographic screens located on both sides of the auxiliary imaging screen, used for retro-reflecting the light irradiated thereon;

[0011] The supporting structure is matched with the projector, the auxiliary imaging screen and the reflective geometric holographic screen respectively to provide physical structural support for the three;

[0012] A controller, electrically connected to the projector, for controlling the projector to adjust the depth of field and display content of the projected image;

[0013] The number of viewpoints of the reflective geometric holographic display system is n, the average value of the diameter of the light-transmitting part of the outermost lens of the projector is D decimeters, and the average value of the projection light source power of the projector is P watts, satisfying:

[0014]

[0015] Furthermore, the average value of the display luminous flux of the projector is L lumens, which satisfies the following relationship with the number of viewpoints n of the reflective geometric holographic display system:

[0016] n 1.27 ·L≤24000.

[0017] Furthermore, the viewpoint number n of the reflective geometric holographic display system satisfies the following relationship:

[0018]

[0019] Furthermore, the reflective geometric holographic screen is a flexible holographic screen, which is provided with a series of columnar elementary prisms with a right-angled triangle or a pentagonal shape of a combination of a rectangle and a right-angled triangle in cross section, and the columnar elementary prisms are provided with a plurality of transparent layers and reflective layers arranged alternately along the length direction, and a reflective film is provided on the inclined surface where the right-angled side of the right-angled triangle included in the cross section of the columnar elementary prism is located, for performing specular reflection on light;

[0020] The cross section of the columnar primitive prism is a right triangle or a pentagon formed by a combination of a rectangle and a right triangle, and the error range of the right angle included in the cross section and the angle formed by the transparent layer and the reflective layer with the length direction of the columnar primitive prism is within ±5°.

[0021] Furthermore, in the pentagonal columnar elementary prism whose cross section is a combination of a rectangle and a right-angled triangle, the interior of the prism of the right-angled triangle portion does not contain a reflective layer.

[0022] Furthermore, it also comprises at least one optical path folding mirror group arranged on one side or both sides of the auxiliary imaging screen for adjusting the optical path.

[0023] Furthermore, the projector is a common projection device capable of projecting a two-dimensional image, or a holographic projection device capable of projecting a three-dimensional image or a group of two-dimensional images distributed at different depths of field in space.

[0024] Furthermore, the projection focal depth of the projector is adjustable within a space of 0.1 m and beyond 0.1 m from the outermost lens of the projector lens.

[0025] Furthermore, the supporting structure is a structure that can be deformed or moved and is electrically connected to a controller. The controller can control the deformation or movement of the supporting structure, thereby realizing relative movement and / or overall movement among the projector, the auxiliary imaging screen and the reflective geometric holographic screen.

[0026] Furthermore, it also includes an interactive action capture unit electrically connected to the controller, the interactive action capture unit is used to identify the user's interactive actions and send the user's interactive action information to the controller, and the controller adjusts the display screen content according to the user interactive action information received by the interactive action capture unit.

[0027] Furthermore, it also includes a human eye tracking unit electrically connected to the controller, wherein the human eye tracking unit is used to track the position of the human eye and send the positioning information of the human eye to the controller. The controller controls the supporting structure to make corresponding action responses according to the human eye positioning information obtained by the human eye tracking unit, so as to adjust the relative position and / or the overall spatial position of the projector, the auxiliary imaging screen and the reflective geometric holographic screen, so that the user's eyes are always in the visible space of the system.

[0028] Furthermore, the visual space is a space that satisfies the following relationship in an optical conjugate coordinate system (X′, Y′, Z′) after a series of optical transformations, with the center of the outermost lens of the projector lens as the origin, the outer normal of the lens center as the Y-axis direction, the straight line passing through the origin and perpendicular to the horizontal plane as the X-axis, and the straight line passing through the origin and perpendicular to the X-axis and the Y-axis as the Z-axis:

[0029]

[0030] Where K is an expansion constant, the unit is decimeter, and the range of K is 0<K<0.08;

[0031] m is the conjugate deviation constant, and the range of m is 0≤m≤5.

[0032] Compared with the prior art, the advantages of the present invention are:

[0033] 1. By introducing a reflective geometric holographic screen that can modulate light at any angle to achieve retroreflection, the incident light is modulated, eliminating other optical modules, saving costs to a certain extent and reducing the space occupied by the system;

[0034] 2. The display system of the present invention adopts two reflective geometric holographic screens, which are respectively arranged on both sides of the auxiliary imaging screen. There is no interference from non-imaging light beams during the imaging process, thereby greatly improving the imaging quality and achieving high light source utilization;

[0035] 3. By setting the supporting structure as a deformable or movable structure, relative movement and / or overall movement between the projector, the auxiliary imaging screen and the reflective geometric holographic screen can be achieved to realize dynamic display;

[0036] 4. Reasonable optical parameter settings can effectively improve the display effect and reliability of the holographic display system. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0038] Figure 1 is a schematic diagram of an existing holographic display system;

[0039] Figure 2 The schematic diagram and optical path diagram of the system of the present invention in which a projector 6 and a reflective geometric holographic screen 8 are located on the same side of an auxiliary imaging screen 7;

[0040] Figure 3 It is a system schematic diagram and optical path diagram of the present invention in which a projector 6 and a reflective geometric holographic screen 8 are respectively located on both sides of an auxiliary imaging screen 7;

[0041] Figure 4 It is a schematic diagram and optical path diagram of the system of the present invention in which two reflective geometric holographic screens 8 are respectively located on both sides of the auxiliary imaging screen 7;

[0042] Figure 5 is Figure 2 A schematic diagram of a system with an interactive motion capture unit 31 and an eye tracking unit 32 added thereto;

[0043] Figure 6 is Figure 2 Based on the above, a schematic diagram of the system of the present invention is provided in which an optical path folding lens group 11 is added on the same side of the projector 6;

[0044] Figure 7 is Figure 6 A schematic diagram of the system of the present invention in which an optical path folding lens group 11 is added to the other side of the auxiliary imaging screen 7 on the basis of FIG.

[0045] Figure 8 It is a schematic diagram of the reflected light path of light on mutually perpendicular surfaces, i.e. right-angle reflection walls;

[0046] Fig. 9 A schematic diagram of the structure of a reflective geometric holographic screen 8 with a right-angled triangle cross section after partially hiding the reflective film 84;

[0047] Fig.10 for Figure 8 The retroreflective optical path diagram of the columnar elementary prism 81 included therein for the light which is not parallel to the cross section;

[0048] Fig.11A schematic diagram of the structure of a reflective geometric holographic screen 8 with a cross section of a pentagon composed of a rectangle and a right-angled triangle after partially hiding the reflective film 84;

[0049] Fig.12 for Fig.10 The retroreflective optical path diagram of the columnar elementary prism 81 included therein for the light which is not parallel to the cross section;

[0050] Fig.13 Schematic diagram of several viewpoint configurations for off-screen display of the present invention;

[0051] Fig.14 A schematic diagram of a multi-view system configuration of the present invention;

[0052] Fig.15 This is a schematic diagram of the space 0.1m away from the outermost lens of the projection lens;

[0053] Fig.16 It is a schematic diagram of the coordinate system (X′, Y′, Z′) where the ellipsoid visual space is located;

[0054] The reference numerals are as follows:

[0055] Holographic projector 1, projection screen 2, interactive response unit 3, processor 4, motion actuator 5, projector 6, auxiliary imaging screen 7, reflective geometric holographic screen 8, columnar elementary prism 81, transparent layer 82, reflective layer 83, reflective film 84, supporting structure 9, controller 10, optical path folding mirror group 11, interactive motion capture unit 31, human eye tracking unit 32. DETAILED DESCRIPTION

[0056] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is described in detail below in conjunction with the accompanying drawings. The description in this part is only exemplary and explanatory and should not have any limiting effect on the protection scope of the present invention.

[0057] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0058] It should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inside", "outside", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the drawings, or are the orientation or positional relationship in which the invented product is usually placed when in use. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", "third", etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0059] In addition, the terms "horizontal", "vertical", "overhanging" and the like do not mean that the components are required to be absolutely horizontal or overhanging, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0060] In the description of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms "set", "install", "connect", and "connect" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0061] like Figures 2 to 7 , the present invention provides a reflective geometric holographic display system, comprising at least one projector 6, an auxiliary imaging screen 7, a reflective geometric holographic screen 8, a supporting structure 9 and a controller 10;

[0062] The projector 6 is used to project image information in space. The present invention can directly use a holographic projector as the projector 6 to achieve 3D display;

[0063] Ordinary projection equipment capable of projecting two-dimensional images can also be used to realize projecting a two-dimensional image on a focal plane in the space, and then the depth of field and image content of the two-dimensional image can be adjusted through the controller 10. Usually, the 3D film sources in theaters are in the form of stereoscopic image pairs, which show the 3D effect through binocular parallax, but the actual image focal depth is fixed in one position, so it will cause visual fatigue. Since the projection and focal depth of the system of the present invention are adjustable, the equivalent focal depth of the image can be moved to a reasonable position, thereby avoiding the problem of the 3D focal depth being different from the actual focal depth, and presenting a more realistic 3D effect. Compared with the holographic projector as the projector 6, this method can effectively reduce the cost. Specifically, the above-mentioned ordinary projection equipment can use a common ordinary projector;

[0064] A holographic projection device of a two-dimensional picture group at different depths of field in space can also be used to realize 3D display. For example, an ordinary projection device can be further optically designed so that it can realize 3D display on the basis of a single projector. Reference can be made to a fully solid-state holographic projector with application number 202010029144.5, which realizes a technical solution of three-dimensional picture display by adding some optical elements inside the projector for optical design. No specific limitation is made here.

[0065] The auxiliary imaging screen 7 is used for light splitting, and is preferably a semi-transparent and semi-reflective film. After the projection light of the projector 6 is irradiated to the auxiliary imaging screen 7, part of the light is reflected to the reflective geometric holographic screen 8. Through the modulation of the light by the reflective geometric holographic screen 8, any light irradiated on the reflective geometric holographic screen 8 is reversely reflected and returned to the original direction. The reversely reflected light part passes through the auxiliary imaging screen 7 and forms an off-screen projection picture in the air.

[0066] The reflective geometric holographic screen 8 is used to retroreflect the incident light rays that are not parallel to the cross section and are irradiated thereon. These light rays can be retroreflected after being offset by a distance dmm, where d is the distance from the intersection of the outgoing light ray and the incident surface of the reflective geometric holographic film to the incident light ray, and d≤2mm (usually for giant screen movies like those in movie theaters, since the user is far away from the screen, a 2mm deviation of the image point is not easy for the human eye to distinguish, and a relatively clear picture can still be displayed. However, if the deviation is too large, the image quality will be affected). A flexible holographic screen is preferably used, and the number of reflective geometric holographic screens 8 is one or two: when there is one reflective geometric holographic screen 8, it is set on any side of the auxiliary imaging screen 7; when there are two reflective geometric holographic screens 8, they are respectively set on both sides of the auxiliary imaging screen 7. When the system includes two reflective geometric holographic screens 8, the system has high light energy utilization and imaging quality.

[0067] Preferably, if Figures 9 to 12 The interior of the reflective geometric holographic screen 8 is provided with a series of columnar elementary prisms 81 with a cross section of a right triangle or a pentagonal shape of a combination of a rectangle and a right triangle, wherein the above-mentioned right triangle is preferably an isosceles right triangle;

[0068] Inside the columnar elementary prism 81, a plurality of transparent layers 82 and reflective layers 83 are arranged alternately along the length direction. This structure can be obtained by a top-down two-dimensional processing method. The processing technology is extremely simple, the processing accuracy is very high, and the imaging quality is excellent.

[0069] The bottom surface of the columnar elementary prism 81 is the light incident surface, the reflective layer 83, the end surface of the columnar elementary prism 81 and the inclined surface where the right-angled side of the cross section is located are the reflective surfaces, and a layer of reflective film 84 is provided on the inclined surface where the right-angled side of the right-angled triangle included in the cross section of the columnar elementary prism 81 is located, for performing specular reflection on the light;

[0070] As another solution, a reflective film 84 for reflecting light may also be provided on the end face of the columnar elementary prism 81 serving as a reflective surface. It should be noted that if during the processing, the end face of the columnar elementary prism 81 is a reflective layer 83, there is no need to plate the reflective film 84 on the end face of the reflective layer 83, as the reflective layer 83 itself has the function of specularly reflecting light.

[0071] In addition, in the pentagonal columnar elementary prism 81 whose cross section is a combination of a rectangle and a right-angled triangle, the interior of the prism in the right-angled triangle part may not contain the reflective layer 83, and this structure can also achieve reverse reflection of light.

[0072] The angle error range involved in the cross section of the above-mentioned columnar primitive prism is within ±5°, including the right angles of the right triangle and pentagon of the cross section and the angles formed by the transparent layer 82 and the reflective layer 83 with the length direction of the columnar primitive prism 81. Although the above principle is based on ideal geometric shapes, in actual situations, the processing process may not be able to produce completely ideal geometric shapes, and there will be certain errors in the angles. The vertex cannot be an ideal geometric point but a fillet with a very small radius. When the manufacturing error is relatively small, the direction of the reflected light deviates slightly from the ideal situation of retroreflection. These deviations cannot be distinguished by the human eye, and the aberrations caused by these errors are also very small, so very good imaging effects can also be achieved.

[0073] For example, when the right angle error of the cross section of the columnar elementary prism 81 is within ±5°, the user experience is relatively satisfactory. When it exceeds this range, the user begins to feel that the imaging effect is unacceptable. Similarly, the geometric vertex is allowed to be a relatively small fillet (for example, the radius is less than 0.1mm), then a relatively good imaging function can also be achieved. Of course, the smaller the error, the higher the user evaluation, so the error should be minimized during production.

[0074] Of course, the smaller the error, the higher the user evaluation, so the error should be minimized during production. Similar processing errors also apply to the cutting direction and bonding direction.

[0075] In specific applications, when the angle error of living room applications is within ±2.5°, the user experience is relatively satisfactory;

[0076] When the angle error of desktop applications is within ±1°, the user experience is relatively satisfactory;

[0077] When the angle error of mobile terminal applications is within ±0.5°, the user experience is relatively satisfactory.

[0078] The support structure 9 is matched with the projector 6, the auxiliary imaging screen 7 and the reflective geometric holographic screen 8 respectively, and provides physical structural support for the three. Specifically, the support structure 9 can be made into a support frame with a fixed structure. In this case, the display system of the present invention is fixed as a whole, and the user needs to be in a fixed position to observe the picture;

[0079] The controller 10 is electrically connected to the projector 6, and the projector 6 can adjust the depth of field and the content of the projection image according to the control signal of the controller 10;

[0080] Retroreflection principle description: Figure 8 , when a ray of light hits two reflective walls that form a right angle, after two reflections, the outgoing ray will propagate in a direction parallel to the incident ray. When the right-angle reflective wall is small enough, the distance between the outgoing ray and the incident ray will also be very small, so small that the human eye cannot distinguish, and visually it looks like the ray is returning along the original path. Of course, a right-angle reflective wall in a two-dimensional plane can only reflect the light in the plane along the original path. If a reflective wall with a right-angle triangular pyramid structure can be formed in space, the light in space can be reflected along the original path.

[0081] Regardless of whether the cross-section is a right-angled triangle or a pentagon that is a combination of a rectangle and a right-angled triangle, it has multiple right-angled reflection walls, including right-angled reflection walls formed by the two inclined surfaces of the columnar elementary prism 81 and right-angled reflection walls formed by the inclined surfaces and the reflective layer 83 or the end faces of the columnar elementary prism 81. Therefore, this microstructure unit has the function of reflecting the light in the space along the original path. Therefore, if many such microstructures are densely arranged on a plane, a large area of ​​incident light can be reflected along the original path.

[0082] like Fig.10 As shown, when any light that is not parallel to the cross section of the columnar elementary prism 81 is incident on the reflective layer 83 or the end reflective film 84 of the columnar elementary prism 81, it is reflected once to an adjacent inclined surface, and then reflected twice by the reflective film 84 coated on the inclined surface, and then reflected to another inclined surface, and then reflected three times by the reflective film 84 coated on the inclined surface, the light can be reflected back in the direction parallel to the incident light after being offset by dmm, and these reversely reflected lights can be used for 3D imaging;

[0083] Similarly, if Fig.12 As shown, any light that is not parallel to the cross section of the columnar elementary prism 81 can be reflected back after multiple reflections to perform 3D imaging when it is incident on the reflection layer 83 or the reflection film 84 on the end face of the columnar elementary prism 81;

[0084] For incident light parallel to the cross section of the columnar elementary prism 81, Figure 8 The optical path principle is that light can be reflected twice on two inclined surfaces to achieve retroreflective 3D imaging.

[0085] like Figure 5 As a preferred solution, the holographic display system of the present invention further includes an interactive action capture unit 31 electrically connected to the controller 10, the interactive action capture unit 31 is used to identify the user's interactive action and send the user's interactive action information to the controller 10, the controller 10 adjusts the display screen content according to the user's interactive action information received by the interactive action capture unit 31, and realizes the interactive action between the user and the screen. Specifically, it can be to use a camera combined with machine vision technology to identify the user's gesture action to obtain the user's interactive information, so as to control the movement of the support structure 9 to adjust the spatial position and posture of the projection device and / or the auxiliary imaging screen 7. The controller 10 can also adjust the display screen content in real time according to the user's interactive action information received by the interactive action capture unit 31, and realize the interactive action between the user and the screen, such as controlling the screen to translate according to the translation gesture signal, or controlling the zooming, zooming in, zooming out, touching, etc. of the screen according to other corresponding interactive actions;

[0086] The setting of the interactive motion capture unit 31 has positive significance for application scenarios such as wearable applications where the spatial position of the user relative to the display system is fixed;

[0087] In addition, for application scenarios in which the spatial position of the user relative to the display system changes in real time, it is necessary to set up a human eye tracking unit 32 electrically connected to the controller 10. The human eye tracking unit 32 is used to track the position of the human eye and send the positioning information of the human eye to the controller 10. The controller 10 controls the support structure 9 to make corresponding action responses based on the human eye positioning information obtained by the human eye tracking unit 32, so as to adjust the relative position and / or the overall spatial position of the projector 6 and the auxiliary imaging screen 7, so that the user's eyes are always in the visible space of the system. In this way, the user's eyes can always receive the projection information and watch the picture normally even when the user is in motion.

[0088] In practical applications, the human eye tracking unit 32 and the interactive motion capturing unit 31 can be integrated into the same device, such as using a machine vision camera device.

[0089] In order to increase the flexibility of the display system, we can also set the support structure 9 to a structure that can move or deform, and electrically connect the support structure 9 to the controller 10. The support structure 9 makes corresponding response actions according to the control information of the controller 10, thereby realizing the relative movement and / or overall movement among the projector 6, the auxiliary imaging screen 7 and the reflective geometric holographic screen 8, so that the visible window of the system always covers the user's eyes, so that the user can watch the picture normally in different directions. It should be noted that the support structure 9 is a general existing technology, and technicians in this field can design it according to the spatial conditions of actual application. For example, using some hinge structures and structures similar to umbrella shafts can easily design a deformable structure, which is not specifically limited here;

[0090] like Figure 6 and Figure 7 In order to further improve the flexibility of the system, a light path folding mirror group 11 can be set on one side or both sides of the auxiliary imaging screen 7, and the light path folding mirror group 11 includes at least one reflector, so that the imaging light path can be adjusted to adapt to various application space scenes. For the holographic display system including the light path folding mirror group 11, the relative or overall movement between the projector 6, the auxiliary imaging screen 7, the reflective geometric holographic screen 8 and the light path folding mirror group 11 can also be controlled by the support structure 9 to adjust in real time to ensure that the user can watch normally.

[0091] When a common projector is used as the projector 6, the controller 10 sends the picture and the average focal depth information of the picture to the projector, and the projector adjusts the projection focal depth by itself, so that the projector can project the picture to a specific focal depth position for human eyes to watch.

[0092] It should be noted that ordinary projectors generally have an autofocus function. When the projector is turned on, the projector will measure the distance between the screen and the projector based on the built-in distance sensor, and then drive the lens to adjust to a suitable position so that the projection focal depth coincides with the screen. In the system of the present invention, the built-in distance sensor can also be removed, so that the controller 10 directly sends the focal depth data to the projector to achieve control of the projection focal depth. The specific implementation method is the existing mature hardware communication technology, which will not be repeated here.

[0093] The present invention is described by taking a projector 6 as an example:

[0094] like Figure 2, the projector 6 and a reflective geometric holographic screen 8 are located on the same side of the auxiliary imaging screen 7, and part of the projection light of the projector 6 is irradiated onto the reflective geometric holographic screen 8 after being split by the auxiliary imaging screen 7, and after being reversely reflected by the reflective geometric holographic screen 8, the light is reflected back in the original direction and passes through the auxiliary imaging screen 7, and then an off-screen display image is formed on the other side of the auxiliary imaging screen 7, and the human eye can see it through the window shown in the figure;

[0095] like Figure 3 , a projector 6 and a reflective geometric holographic screen 8 are respectively located on both sides of the auxiliary imaging screen 7. A portion of the projection light from the projector 6 passes through the auxiliary imaging screen 7 and then irradiates the reflective geometric holographic screen 8. After the light is reversely reflected by the reflective geometric holographic screen 8, it is reflected in the original direction and split by the auxiliary imaging screen 7 to form an off-screen display image in space, which can be viewed by human eyes through the window shown in the figure;

[0096] from Figure 2 and Figure 3 The optical path principle is easy to find. When the auxiliary imaging screen 7 is a semi-transparent and semi-reflective film, the energy utilization rate of the light is only 1 / 4. In order to improve the light energy utilization rate, some special optical designs such as polarization + wave plate can be used, which can greatly improve the light energy utilization rate. The specific design scheme is generally known in this field and will not be described here. In addition, if Figure 4 As shown, a solution of two reflective geometric holographic screens 8 can also be adopted, that is, two reflective geometric holographic screens 8 are respectively arranged on both sides of the auxiliary imaging screen 7, which can effectively improve the light energy utilization rate of the system (doubled) and the imaging quality.

[0097] It should be noted that the above is only an example of the present invention and is not intended to limit the present invention. Fig.14 The same applies when there are multiple projectors 6.

[0098] The reflective geometric holographic display system of the present invention has a very special feature compared to the traditional display system. It cannot be viewed by a large number of users at the same time like the traditional 2D display device. For the convenience of description, the concept of viewpoint is introduced here:

[0099] If the display system can provide a viewing window for one eye, then the system has one viewpoint. For a binocular display system, it can be viewed by two eyes at the same time, so the number of viewpoints is 2. When the display system can be viewed by n eyes at the same time, the number of viewpoints is n. In actual design, it is also necessary to reasonably set the system structure while considering practicality.

[0100] like Fig.13As shown, in case a, corresponding to the use of a large-aperture projector, the optical conjugate area (also a mirror-symmetrical area, which can be called a viewing window) of the outermost lens of the projector relative to the auxiliary imaging screen 7 can cover the user's two eyes. At this time, although the area between the two eyes can also view images in principle, it is impossible to use it under practical conditions. It can only be viewed by two eyes at the same time, so this situation is equivalent to having two viewpoints;

[0101] In cases b to d, two small-aperture projectors are used, and the projection lenses of the two projectors form two separate sub-areas relative to the optical conjugate area of ​​the auxiliary imaging screen 7. When the spacing between the two sub-areas just matches the spacing of human eyes, two eyes can watch at the same time (case b), so there are two viewpoints;

[0102] When the distance between the two sub-areas is smaller than the distance between human eyes (case c) or larger than the distance between human eyes (case d), only one of the two eyes can see the image, and therefore there is only one viewpoint.

[0103] like Fig.14 When the number of projectors increases, the number of viewpoints of the system will increase accordingly. The specific number depends on the specific circumstances a to d. The number of viewpoints of the display system is n, which is related to the size and number of the lenses of the projectors used.

[0104] Similarly, when designing a multi-user system, it is even more necessary to consider the spatial position relationship between users in the usage scenario, and reasonably design the spatial distribution between each window to avoid the situation where the actual available viewpoint of the system is smaller than the designed viewpoint. An effective design strategy is to reasonably design the support structure 9 so that it has a structural adjustment function, such as being able to adjust the distance or spatial position between the two projectors, so that when in use, the geometric shape of the support structure 9 can be flexibly adjusted according to the user's pupil distance and the application site to adapt to actual needs.

[0105] It should be noted that when the projection system is switched to the 2D projection mode for backward compatibility (such as adjusting the projection focal plane of the projector to directly project a 2D image on the reflective geometric holographic screen 8, or replacing it with an ordinary projection receiving screen or placing it on the front or rear surface of the reflective geometric holographic screen 8 for receiving and displaying the 2D projection image), the image focal plane coincides with the screen, and the number of viewpoints will increase greatly. However, these viewpoints have great viewing limitations. Only the images on the screen can be seen, and the off-screen images output by the display system cannot be viewed. Therefore, they cannot be counted in the actual number of viewpoints. The actual effective viewpoints should be viewpoints that can view the images in all modes of the system.

[0106] Traditional 2D display devices, such as televisions, projectors, computers, etc., have a very large number of viewpoints and can be viewed by many users simultaneously. This is because the light emitted by their light sources has a high divergence and no directivity. Therefore, a relatively high brightness is also required. However, for the holographic display system of the present invention, the number of viewpoints is relatively small, and the light emitted by its display device (such as a holographic projector or an ordinary projector) will be very efficiently concentrated at the viewing window position and received by the human eye. Therefore, if the light intensity is too strong, it is easy to cause dizziness, the image is not clear, and even damage to the human eye. At the same time, too high a light flux often requires the light source (such as the bulb or LED lamp inside the projector) to operate at a high power, and the service life of the light source will be significantly reduced when it operates in a high-power mode for a long time. Therefore, the light flux cannot be designed too high. However, as the number of viewpoints increases, the total light flux of the display system also needs to be increased to ensure that each viewpoint can provide a clear picture. Due to the complexity of the optical path of the display system of the present invention, the relationship between the viewpoint and the light flux is not a simple linear relationship.

[0107] In the reflective geometric holographic display system of the present invention, the number of viewpoints is n, the average value of the diameter of the light-transmitting part of the outermost lens of the projector 6 is D decimeters (dm), the average display light flux of the projector 6 is L lumens (lm), and the display light flux viewpoint product is n 1.27 ·L. In summary, combined with the actual test results, the display light flux viewpoint product satisfies: n 1.27 ·L ≤ 24000 can ensure better display effects and system reliability.

[0108] Among them, the measurement method of the display light flux L (lm) of the projector 6 can refer to the test method of ANSI lumens:

[0109] 1) Set the distance between the projector and the screen in the display system to: 2.4 meters;

[0110] 2) The screen is 60 inches;

[0111] 3) Use an illuminance meter to measure the illuminance at each point of the nine intersection points of the "field" shape on the screen and obtain the average illuminance of the 9 points;

[0112] 4) The average illuminance multiplied by the projected image area is ANSI lumens, that is, the display light flux described in the present invention.

[0113] For displaying different pictures, the measured value of L may vary greatly. In actual tests, it is preferably to display a full-white picture for testing, that is, the case where each pixel is displayed as white;

[0114] When the illumination area of ​​the projector cannot be well matched with the screen, the illumination test is performed according to the actual illumination area. It is preferred to evenly select 8 points in the light band about 10cm to 30cm away from the outer boundary of the illumination area and 1 point in the illumination area no more than 20cm away from the center of the screen, for a total of 9 points for illumination test. Then multiply the average of the 9 illumination values ​​by the actual area of ​​the illumination area to obtain the displayed luminous flux value.

[0115] For application cases that only include one projector 6, the display luminous flux can be tested in the above manner (the display luminous flux of a single projector is the same as the average display luminous flux value). When multiple projectors are used, the luminous flux of each projection unit can be tested separately and the average value can be taken as the display luminous flux value.

[0116] In addition, in actual tests, different design structures (such as differences in sealing and heat dissipation) will also have a more obvious impact on the life of the system. Therefore, different design structures in the actual test process may cause certain fluctuations in the measured data, but the overall trend will not change, and the optimal value of the display configuration parameters will not change.

[0117] The present invention will be further described below with examples:

[0118] In the systems of the following embodiments, the projector 6 is a common projector, and the reflective geometric holographic screen 8 is located on the same side of the auxiliary imaging screen 7 as the projector 6;

[0119] Embodiment 1: A projector with a lens diameter of 0.5 dm is used as the projector 6, and the number of viewpoints n=1, which can be viewed by a single household using a single eye;

[0120] Usually the number of user eyes is even, and the number of viewpoints n is set to an even number:

[0121] Embodiments 2 to 24: Using one projector with a lens diameter greater than 6.5 dm or two projectors with lens diameters less than 6.5 dm as the projector 6, the number of viewpoints n = 2, which can be viewed by both eyes of a single household;

[0122] Embodiment 25: Four projectors with a lens diameter of 0.4 dm are used as projectors 6, and the number of system viewpoints n=4, which can be used for two users to watch at the same time;

[0123] Embodiment 26: Six projectors with lens diameters of 0.3 dm are used as projectors 6, and the number of viewpoints n=6, so that a family of three can watch at the same time;

[0124] Example 27: Eight projectors with a lens diameter of 0.2 dm are used as projectors 6, and a family of four watches at the same time;

[0125] Comparative Example 1: A projector with a lens diameter of 8 dm is used as the projector 6 for viewing by both eyes of a single household, as shown in the following table:

[0126]

[0127] The data of Examples 1 to 27 show that: the display luminous flux viewpoint product n 1.27 When L≤24000, the display effect is good, and the user rating is above 80 points. The display luminous flux viewpoint product n in Example 1 is 1.27 ·L is 31351, the user rating is low, the picture is dazzling, and the actual display effect is poor.

[0128] In actual use, in addition to considering the design relationship between the number of viewpoints n and the luminous flux L, the projector aperture size and the luminous flux need to be matched. When the projector aperture is large, the visual utilization rate of the display light will be low, and many lights can only reach areas outside the human eye. Therefore, the luminous flux needs to be appropriately increased. According to the application of the above embodiments 1 to 27, the actual application can refer to the following expression for design:

[0129]

[0130] Based on the influence of light source power on the display effect and reliability of the system. When the internal light source of projector 6 works in high-power mode, its lifespan tends to be greatly reduced, so it is best to work in low-power mode. However, when there are a large number of viewpoints or when the aperture of a single projector is large, the visual utilization rate of the display light will be low, and many rays can only reach areas outside the human eye. Therefore, it is necessary to increase the power of the light source appropriately to increase the luminous flux. The average power of the projector projection light source included in projector 6 is P watts (W). Tests have found that when the following relationship is met, the system can operate under a better condition:

[0131]

[0132] The measurement of the light source power P of the projection device can directly test the voltage across the light source and the current passing through the light source under normal working conditions, and then multiply them to obtain the power value.

[0133] On the basis of Examples 1 to 27, the light source power P (W) is introduced for illustration, as shown in the following table:

[0134]

[0135] Data shows: Power View Product When the display effect is good, the user rating is above 80 points, while the power viewpoint product in Example 1 The user rating is 679, the picture is glaring, and the actual display effect is poor. In addition, the light source power is less than 400W, which can generally meet the 5-year design life.

[0136] The common projector used in the above implementation can also be replaced by a holographic projector or other projection equipment capable of realizing three-dimensional image display. At the same time, the above design formulas involving the number of viewpoints, light source power and display luminous flux are also applicable to the holographic projector.

[0137] In addition, it was found in actual tests that Examples 1 to 27 can still work normally after 3000 hours in the accelerated test in the high temperature and high humidity environment (85°C, relative humidity 85%), while the light source of Comparative Example 1 was damaged and could not emit light at 3000 hours, indicating that unreasonable design parameters will greatly reduce the service life. The above test is commonly known as the double 85 aging test, and the 3000-hour accelerated aging test is equivalent to the minimum service life standard of 5 years under actual working conditions.

[0138] The display principle of the present invention is that the projector 6 can project images at different depths in space, that is, it can provide additional depth of field information for the projected image, but the images projected by the projector 6 are all divergent light and cannot be directly viewed by the human eye. This is also the reason why a receiving screen must be used in conventional projection systems. The reflective geometric holographic screen 8 of the present invention has the function of making the light irradiated thereon reflect back along the original path. The auxiliary imaging screen 7 is a semi-transparent and semi-reflective film with a light splitting function. In this way, after the light emitted by the projector 6 irradiates the auxiliary imaging screen 7, part of the light is reflected onto the reflective geometric holographic screen 8. Due to the retro-reflective function of the reflective geometric holographic screen 8, the light will return along the original path (or approximately along the original path), and the returned light will pass through the auxiliary imaging screen 7 again, and part of the light will pass through the auxiliary imaging screen 7 to form a converged off-screen projection image in the air. At this time, if the human eye is in the mirror position of the projector 6 relative to the auxiliary imaging screen (the human eye can only normally see the complete projection image in a very small area of ​​the mirror position of the projector relative to the auxiliary imaging screen), the image can be observed.

[0139] From the analysis of the display principle of the present invention, it can be found that the image seen by the user when using the projector 6 is completely consistent with the image projected by the projector 6. The distance between the image projected by the projector 6 and the outermost lens is the distance between the image seen by the user and the eye. In life, the visual distance of the human eye is generally 25cm, and the nearest object is generally 10cm away. Therefore, when selecting the projector 6, it is preferred that the projection focal depth can be within a space greater than 0.1m from the outer surface of the outermost lens of the projection lens (such as Fig.15 ) is used to adjust the projector (ordinary projector or holographic projector).

[0140] When the user is static, as long as the system structure is adjusted so that the user's eyes are covered by the window, the user can watch the picture normally. However, if the user is in motion, it is easy for the eyes to leave the window and cannot watch the picture normally. Therefore, for application scenarios where the user cannot be completely static, it is very important to increase the user's eye positioning tracking and then adjust the spatial position of the window in real time so that it always covers the user's eyes. However, in actual scenarios, the parameters of the components of the display system are different, and it is difficult to find a tracking method that is suitable for all systems. In principle, if the user's eye movement trajectory can be located very accurately, then the relative position and overall spatial position between the projector and the transmissive geometric holographic screen are adjusted to drive the window to accurately track the user's eye movement trajectory. The most ideal solution is. However, it is very difficult to completely and accurately track the user's eyes and accurately control the window position. Even if it can be achieved, it will cost a relatively large price, and it is not very practical.

[0141] In fact, since the window itself has a certain size, the human eye can see the picture as long as it is within the window, so when the user moves, it is not necessary to track the movement trajectory of the user's eyes completely accurately. It is sufficient to track the user's eyes roughly to ensure that they are within the window. Even if they are slightly offset from the window, but the pupil intersects with the window, the picture can be viewed normally.

[0142] The above discussion is mainly for the situation where the user moves left, right, up, or down relative to the screen. In addition, when the user moves forward or backward, he or she can also watch the picture normally if he or she does not deviate too much from the center of the window. In summary, the tracking of the user's eyes does not need to be particularly precise, as long as it is guaranteed to be within a certain accuracy, it can meet the use requirements. There will be an intersecting diamond-shaped area for the light above and below the screen. In principle, as long as the support structure is adjusted in real time so that the user's eyes are always in the above-mentioned diamond-shaped visual space, the picture can be observed. However, near the corners of the diamond, it is easier to lose tracking, so a relatively small ellipsoidal visual area is further defined inside the prismatic area to reduce the probability of tracking loss.

[0143] The ellipsoid region is described below. Fig.16 The ellipsoidal visual space is the visual space that takes the center of the outermost lens of each projector 6 lens as the origin, the outer normal of the lens center as the Y-axis direction, the straight line passing through the origin and perpendicular to the horizontal plane as the x-axis, and the straight line passing through the origin and perpendicular to the X-axis and the Y-axis as the Z-axis. After optical transformation, the optical conjugate coordinate system (X′, Y′, Z′) satisfies the following relationship:

[0144]

[0145] Where K is an expansion constant, the unit is dm, and the range of K is 0<K<0.08;

[0146] m is the conjugate deviation constant, and the range of m is 0≤m≤5.

[0147] The above coordinate system (X′, Y′, Z′) is the conjugate image of the coordinate system (X, Y, Z) after the optical system transformation. The above expression is a space surrounded by an ellipsoid, where the value of m affects the length of the ellipsoid in the y-axis direction. Fig.16 It can be seen that the visual space has a certain extension in the Y' axis direction. The actual test found that the visual space has a certain extension length in the Y' axis direction of about 6 times the lens diameter D. A clear picture can be seen within this range. However, considering the actual tracking effect, it is relatively easy to achieve a better display effect within the range of less than 5 times the lens diameter in the Y' axis direction. In addition, the actual test found that:

[0148] When m is 5, the entire display area of ​​the picture can be clearly seen. Only in the local boundary area, the picture clarity is slightly worse, but the details can still be clearly distinguished.

[0149] When m is 3, the entire display area of ​​the picture can be clearly seen, even in the boundary area, the picture is relatively clear, and the tracking stability is also very good;

[0150] When m is 2, the entire display range of the picture is complete, the display details are very clear, the tracking stability is relatively good, and it is only occasionally lost, which is suitable for desktop office scenes;

[0151] When m is 1, the entire display range of the picture is complete, the display details are very clear, the tracking stability is slightly poor, and the tracking loss frequency increases, which is suitable for movie viewing and entertainment application scenarios;

[0152] K and D determine the cross-section of the visible space in the plane perpendicular to the Y′ axis. In principle, the image can be seen within the diameter range of the projection lens. In fact, as long as the optical conjugate area of ​​the human eye intersects with the projection lens, the image can be seen even if the person is not completely within the optical conjugate area of ​​the projection lens. Therefore, an expansion constant K is introduced, and its value depends on the diameter of the human eye. Usually, the maximum diameter of the human pupil is 0.08dm, so 0.08dm is taken here as the expansion constant.

[0153] Although, mathematically m cannot be 0, taking it as 0 here has physical significance, that is, the point on the plane where Y′ is equal to 0.

[0154] When using multiple projectors (ordinary projectors or holographic projectors), the present invention can select completely the same model, or can select different models according to the requirements of actual application scenarios.

[0155] The display system of the present invention can avoid visual fatigue caused by users watching a fixed-depth image for a long time due to the adjustable depth of focus, thereby avoiding the occurrence of myopia and improving the visual acuity level.

[0156] The present invention can be used for fixed display, such as office, home audio and video, car display, etc., and can also be used for small mobile display and head-mounted display and other fields.

[0157] When the present invention is implemented, some optical elements such as anti-reflection films, light-absorbing films, filters, etc. can be appropriately added to further improve the effect of the system.

[0158] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A reflective geometric holographic display system, characterized in that: include: At least one projector (6) for projecting picture information in space; An auxiliary imaging screen (7) for light splitting; A reflective geometric holographic screen (8) located on one side of the auxiliary imaging screen (7) or two reflective geometric holographic screens (8) located on both sides of the auxiliary imaging screen (7); A support structure (9) is matched with the projector (6), the auxiliary imaging screen (7) and the reflective geometric holographic screen (8) respectively to provide physical structural support for the three; A controller (10) electrically connected to the projector (6); The number of viewpoints of the reflective geometric holographic display system is n, the average value of the diameter of the light-transmitting portion of the outermost lens of the projector (6) is D decimeters, and the average value of the projection light source power of the projector (6) is P watts, satisfying:

2. The reflective geometric holographic display system according to claim 1, characterized in that: The average value of the display luminous flux of the projector (6) is L lumens, which satisfies the following relationship with the number of viewpoints n of the reflective geometric holographic display system: n 1.27 ·L≤24000。 3. The reflective geometric holographic display system according to claim 2, characterized in that: The number of viewpoints n of the reflective geometric holographic display system, the average value L lumens of the display luminous flux of the projector (6), and the average value D decimeters of the diameter of the light-transmitting part of the outermost lens of the projector (6) satisfy the following relationship:

4. The reflective geometric holographic display system according to any one of claims 1 to 3, characterized in that: The reflective geometric holographic screen (8) is a flexible holographic screen, and is provided with a series of columnar elementary prisms (81) whose cross sections are right-angled triangles or pentagons that are a combination of rectangles and right-angled triangles. The columnar elementary prisms (81) are provided with a plurality of transparent layers (82) and reflective layers (83) arranged alternately along the length direction. A reflective film (84) is provided on the inclined surface where the right-angled side of the right-angled triangle included in the cross section of the columnar elementary prism (81) is located, and is used for specular reflection of light. The cross section of the columnar elementary prism (81) is a right-angled triangle or a pentagon formed by a combination of a rectangle and a right-angled triangle, and the error range of the right angle included in the angle formed by the transparent layer (82) and the reflective layer (83) and the length direction of the columnar elementary prism (81) is within ±5°.

5. The reflective geometric holographic display system according to claim 4, characterized in that: In the pentagonal columnar elementary prism (81) whose cross section is a combination of a rectangle and a right-angled triangle, the interior of the prism in the right-angled triangle portion does not contain a reflective layer (83).

6. The reflective geometric holographic display system according to claim 1, characterized in that: It also comprises at least one light path folding mirror group (11) arranged on one side or both sides of the auxiliary imaging screen (7) and used for adjusting the light path.

7. The reflective geometric holographic display system according to claim 1, characterized in that: The projector (6) is a common projection device capable of projecting a two-dimensional image, or a holographic projection device capable of projecting a three-dimensional image or a group of two-dimensional images distributed at different depths of field in space.

8. The reflective geometric holographic display system according to claim 7, characterized in that: The projection focal depth of the projector (6) is adjustable within a space 0.1 m away from the outermost lens of the projector (6) lens and a space beyond 0.1 m.

9. The reflective geometric holographic display system according to claim 1, characterized in that: The support structure (9) is a structure that can be deformed or moved and is electrically connected to a controller (10). The controller (10) can control the deformation or movement of the support structure (9), thereby achieving relative movement and / or overall movement among the projector (6), the auxiliary imaging screen (7) and the reflective geometric holographic screen (8).

10. The reflective geometric holographic display system according to claim 9, characterized in that: It also includes an interactive action capture unit (31) electrically connected to the controller (10), the interactive action capture unit (31) being used to identify the user's interactive actions and send the user's interactive action information to the controller (10), and the controller (10) adjusting the display screen content according to the user's interactive action information received by the interactive action capture unit (31).

11. The reflective geometric holographic display system according to claim 10, characterized in that: The system also includes an eye tracking unit (32) electrically connected to the controller (10), wherein the eye tracking unit (32) is used to track the position of the eye and send the positioning information of the eye to the controller (10). The controller (10) controls the support structure (9) to make a corresponding action response according to the eye positioning information received from the eye tracking unit (32), so as to adjust the relative position and / or the overall spatial position of the projector (6), the auxiliary imaging screen (7) and the reflective geometric holographic screen (8), so that the user's eyes are always within the visible space of the system.

12. The reflective geometric holographic display system according to claim 11, characterized in that: The visual space is a space that satisfies the following relationship in an optical conjugate coordinate system (X′, Y′, Z′) after a series of optical transformations, in which the center of the outermost lens of the projector (6) lens is taken as the origin, the outer normal of the lens center is taken as the Y-axis direction, the straight line passing through the origin and perpendicular to the horizontal plane is taken as the X-axis, and the straight line passing through the origin and perpendicular to the X-axis and the Y-axis is taken as the Z-axis: Where K is an expansion constant, the unit is decimeter, and the range of K is 0<K<0.08; m is the conjugate deviation constant, and the range of m is 0≤m≤5.

Images