Samsung Patent | Lens based on human visual system, video see-through apparatus employing the lens, and method of designing the lens
Patent: Lens based on human visual system, video see-through apparatus employing the lens, and method of designing the lens
Patent PDF: 20240027768
Publication Number: 20240027768
Publication Date: 2024-01-25
Assignee: Samsung Electronics
Abstract
A lens includes at least one lens element configured to interface with a user's pupil along an optical-axis direction from a side of the user's pupil to a side of a display surface. The at least one lens element defines an aperture stop that is configured to be at least a portion of an area for facing the user's pupil. The aperture stop defines a plurality of sub-stop areas corresponding to a plurality of gaze directions within an entire viewing angle of the user with respect to the optical-axis direction. An orientation of the plurality of sub-stop areas are based on a human visual system.
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Description
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation application of International Application No. PCT/KR2023/010570 designating the United States, filed on Jul. 21, 2023, in the Korean Intellectual Property Receiving Office, which claims priority from Korean Patent Application No. 10-2022-0090576, filed on Jul. 21, 2022, in the Korean Intellectual Property Office and from Korean Patent Application No. 10-2022-0143021, filed on Oct. 31, 2022, in the Korean Intellectual Property Office, the disclosures of which are hereby incorporated by reference herein in their entireties.
TECHNICAL FIELD
The disclosed embodiments relate to a lens, a video see-through apparatus employing the lens, and a method of designing the lens, and more particularly, to a lens according to the human visual system, a video see-through apparatus employing the lens, and a method of designing the lens.
BACKGROUND
Interest in video see-through (VST) apparatuses has increased. A video see-through method allows enjoying virtual reality (VR) or augmented reality (AR) by wearing a head-mounted display (HMD) with a camera attached thereto.
A video see-through apparatus is desired to be lightweight and compact, and an optical system employed in the video see-through apparatus is desired to have a wide viewing angle and transmit a high-quality image. The optical system includes a lens including one or more lens elements arranged in an optical-axis direction from the side of a user's pupil to the side of a display surface. Lenses have been designed to have the maximum performance for the maximum viewing angle at a fixed viewpoint, and the performance thereof has been improved by adding optical elements, sharing the characteristics of light, or using new structures.
SUMMARY
Provided are a lens capable of providing a wide viewing angle and transmitting a high-quality image, a video see-through apparatus employing the lens, and a method of designing the lens.
Provided are a lens according to a movement of a human gaze, a video see-through apparatus employing the lens, and a method of designing the lens.
Technical objects to be achieved by the disclosed embodiments are not limited to the above technical objects and there may be other technical objects.
A lens may include at least one lens element configured to interface with a user's pupil along an optical-axis direction from a side of the user's pupil to a side of a display surface. The at least one lens element may define an aperture stop that is configured to be at least a portion of an area for facing the user's pupil. The aperture stop may define a plurality of sub-stop areas corresponding to a plurality of gaze directions within an entire viewing angle of the user with respect to the optical-axis direction. An orientation of the plurality of sub-stop areas may be based on a human visual system.
A radial width of each sub-stop area with respect to the optical-axis direction may be based on a human pupil size.
Each of the plurality of sub-stop areas may be rotationally symmetrical about an optical axis in the optical-axis direction.
The plurality of sub-stop areas may be separated from each other or at least partially overlap each other.
A sub-field range may be allocated according to each sub-stop area.
The sub-field range may be based on a change in visual acuity according to a human corneal eccentricity.
A central sub-stop area of the plurality of sub-stop areas may correspond to a front gaze direction to provide the entire viewing angle.
A size of an entire stop area of the stop surface may be based on a total rotation angle (α) of a human eye.
A video see-through apparatus may include: an electronic display configured to display an image; and a lens including at least one lens element configured to interface with a user's pupil along an optical-axis direction from a side of the user's pupil to a side of a display surface. The at least one lens element may define an aperture stop that is configured to be at least a portion of an area for facing the user's pupil. The aperture stop may define a plurality of sub-stop areas corresponding to a plurality of gaze directions within an entire viewing angle of the user with respect to the optical-axis direction. An orientation of the plurality of sub-stop areas may be based on a human visual system. The lens may be configured to direct the image generated by the electronic display to a user's pupil.
A method of making a lens including at least one lens element configured to interface with a user's pupil along an optical-axis direction from a side of the user's pupil to a side of a display surface, may include: setting at least a portion of an area of the lens facing the user's pupil as an aperture stop; dividing the aperture stop into a plurality of sub-stop areas corresponding to a plurality of gaze directions within an entire viewing angle of the user with respect to the optical-axis direction; allocating a plurality of sub-field ranges to the plurality of sub-stop areas, respectively; and optimizing each sub-stop area based on a corresponding gaze direction.
A radial width of each of the plurality of sub-stop areas with respect to the optical-axis direction may be based on a human pupil size.
Each of the plurality of sub-stop areas may be rotationally symmetrical about an optical axis in the optical-axis direction.
The plurality of sub-stop areas may be separated from each other or at least partially overlap each other.
The sub-field range may be based on a change in visual acuity according to a human corneal eccentricity.
The sub-field range may be based on a human macula range.
The at least one lens element may include a first lens element, a second lens element, and a third lens element. The first lens element, the second lens element, and the third lens element may be oriented sequentially along the optical-axis direction.
At least one surface of each of the first lens element, the second lens element, and the third lens element may include a polarization-selective reflection layer.
The sub-field range may be nine degrees.
The at least one lens element may include a first lens element, a second lens element, and a third lens element. The first lens element, the second lens element, and the third lens element may be oriented sequentially along the optical-axis direction.
At least one surface of each of the first lens element, the second lens element, and the third lens element may include a polarization-selective reflection layer.
The lens, the video see-through apparatus employing the lens, and the method of designing the lens may provide a wide viewing angle and transmit a high-quality image.
The lens, the video see-through apparatus employing the lens, and the method of designing the lens may suppress the image quality of the screen from degrading due to the movement of the gaze.
BRIEF DESCRIPTION OF DRAWINGS
FIG. 1 schematically illustrates a video see-through apparatus according to an embodiment of the disclosure.
FIG. 2 illustrates an area on a display surface corresponding to a sub-stop area.
FIG. 3 is a diagram describing the human perceptible levels depending on viewing angles.
FIG. 4 is a diagram describing the classification of visual fields according to viewing angles (eccentricity).
FIG. 5 is a diagram describing the human visual acuity depending on viewing angles.
FIG. 6 is a flowchart of a method of designing a lens according to an embodiment of the disclosure.
FIG. 7 illustrates ray diagrams in a plurality of sub-stop areas divided according to gaze directions.
FIG. 8 illustrates a ray diagram corresponding to an overlap of all ray diagrams in a plurality of sub-stop areas divided according to gaze directions.
FIG. 9 is a diagram schematically illustrating a lens manufactured by a design method according to an embodiment of the disclosure.
FIG. 10 is a graph illustrating the optical performance of the lens of FIG. 9 in a gaze direction of 0°, a sub-field of ±9°, and a viewing angle of ±9°.
FIG. 11 is a graph illustrating the optical performance of the lens of FIG. 9 in a gaze direction of 10°, a sub-field of ±9°, and a viewing angle of about 1° to about 19°.
FIG. 12 is a graph illustrating the optical performance of the lens of FIG. 9 in a gaze direction of 20°, a sub-field of ±9°, and a viewing angle of about 11° to about 29°.
FIG. 13 is a graph illustrating the optical performance of the lens of FIG. 9 in a gaze direction of 30°, a sub-field of ±9°, and a viewing angle of about 21° to about 45°.
FIG. 14 is a graph illustrating the optical performance for an entire viewing angle when the lens of FIG. 9 is viewed at the front.
DETAILED DESCRIPTION
Hereinafter, embodiments will be described in detail with reference to the accompanying drawings so that those of ordinary skill in the art may easily implement the embodiments. However, the disclosed embodiments may be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein. Also, portions irrelevant to the description will be omitted in the drawings for a clear description of the disclosed embodiments, and like reference numerals will denote like elements throughout the specification.
The terms used herein are those general terms currently widely used in the art in consideration of functions, but the terms may vary according to the intentions of those of ordinary skill in the art, precedents, or new technology in the art. Also, in some cases, there may be terms that are optionally selected by the applicant, and the meanings thereof will be described in detail in the corresponding portions of the disclosed embodiments. Thus, the terms used herein should be understood not as simple names but based on the meanings of the terms and the overall description of the disclosed embodiments.
As used herein, the singular forms “a”, “an”, and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. When a part “includes” or “comprises” a component, unless there is a particular description contrary thereto, the part may further include other components, not excluding the other components.
As used herein, the term “lens” may refer to not only a single lens but also a lens including a plurality of lens elements. For clarity, each individual lens may also be referred to as a lens element.
Hereinafter, the disclosed embodiments will be described in detail with reference to the accompanying drawings.
FIG. 1 schematically illustrates a video see-through apparatus according to an embodiment of the disclosure, and FIG. 2 illustrates an area on a display surface corresponding to a sub-stop area.
Referring to FIGS. 1 and 2, an electronic apparatus may include a lens 100 and an electronic display 200.
The electronic apparatus may be, for example, a video see-through apparatus configured to allow the user to see an image displayed on the electronic display 200 while wearing the same, such as a head-mounted display (HMD). The lens 100 may direct an image generated by the electronic display 200 to the user's pupil, and when the user wears the electronic apparatus, the lens 100 may be located adjacent to the user's pupil. In that the lens 100 is located adjacent to the user's pupil, the electronic apparatus may be understood as a near-eye display apparatus. Also, in that the user may wear the electronic apparatus, the electronic apparatus may be understood as a wearable device. Although not illustrated, the electronic apparatus may be configured to include a separate camera to photograph a real scene and provide the real scene to the user through the electronic display 200. The electronic apparatus may be a virtual reality device providing virtual reality or an augmented reality device providing augmented reality. Although the lens 100 and the electronic display 200 for one eyeball E are illustrated, the lens 100 and the electronic display 200 may be provided for each of the user's left and right eyes.
The lens 100 may include, for example, first to third lens elements 110, 120, and 130. A case where the lens 100 includes three lens elements (i.e., the first to third lens elements 110, 120, and 130) is described as an example; however, this is merely an example, and the lens 100 may include only one lens element or two lens elements or may include four or more lens elements.
The first to third lens elements 110, 120, and 130 may be sequentially arranged from the side of an object where the user is located to the side of a display surface 201 of the electronic display 200 where an image is formed (i.e., to an image side). The lens 100 may be a catadioptric lens; however, the disclosed embodiments are not limited thereto. For example, a second surface S3 (see FIG. 9) of the first lens 110, first and second surfaces S4 and S5 (see FIG. 9) of the second lens 120, and a second surface S7 (see FIG. 9) of the third lens 130 may have a polarization-selective reflection layer.
The lens 100 may further include an aperture stop 140. For example, the aperture stop 140 may be located at the front end (i.e., the object side) of the lens 100; however, the disclosed embodiments are not limited thereto. The aperture stop 140 may have a circular opening in consideration of the rotation of the eyeball E.
The electronic display 200 may be, for example, a liquid crystal panel, a micro light emitting diode (micro LED) panel, or an organic light emitting diode (OLED) panel; however, the disclosed embodiments are not limited thereto.
The lens 100 may have a stop surface that is at least a portion of an area facing the pupil of the user's eyeball E.
The size of an entire stop area may be determined based on a total rotation angle a of the human eyeball E. In other words, the user may not gaze only at the front while wearing the electronic apparatus and may change the gaze direction according to usage environments and provided images. Thus, the lens 100 may be designed to have a stop area corresponding to the total rotation angle a by which the user may rotate the eyeball E.
The stop surface may include a plurality of sub-stop areas Z1, Z2, . . . , Zn divided according to a plurality of gaze directions GD1, GD2, GDn within an entire viewing angle. The number “n” of the plurality of sub-stop areas Z1, Z2, . . . , Zn may be two or more. The plurality of sub-stop areas Z1, Z2, . . . , Zn may be determined based on the human visual system. FIG. 2 illustrates an area corresponding to the plurality of sub-stop areas Z1, Z2, . . . , Zn on the display surface 201 of the electronic display 200.
Because the human eyeball E may substantially rotate along the circumference around the front, each of the sub-stop areas Z1, Z2, . . . , Zn may be rotationally symmetrical about an optical axis. In this case, the optical axis may be the same as the first gaze direction GD1 when the user gazes at the front; however, the disclosed embodiments are not limited thereto. In this case, the width of each of the sub-stop areas Z1, Z2, . . . , Zn may be understood as a width in a radial direction.
The plurality of sub-stop areas Z1, Z2, . . . , Zn may be separated from each other or may at least partially overlap each other. In FIG. 2, a portion where the first sub-stop area Z1 and the second sub-stop area Z2 partially overlap each other is shaded.
The width of each of the sub-stop areas Z1, Z2, . . . , Zn may be determined based on the human pupil size. The human pupil size may vary from person to person and may also vary depending on the surrounding brightness. For example, the electronic apparatus such as a virtual reality device may provide a brightness of about 150 nits to about 200 nits, and in this case, it is known that the human pupil size is about 3 mm to about 4 mm. Thus, the width of each sub-stop area may be determined based on a size of about 3 mm to about 4 mm. Because the brightness provided by the electronic apparatus may vary depending on the usage environment thereof, the performance of, for example, the electronic display 200, the width of each of the sub-stop areas Z1, Z2, . . . , Zn is not limited to the above values.
As an example, all of the widths of the sub-stop areas Z1, Z2, . . . , Zn may be equal to each other.
As an example, the widths of the sub-stop areas Z1, Z2, . . . , Zn may be different from each other. For example, a width wi of the first sub-stop area Z1 corresponding to the first gaze direction GD1 in which the user gazes at the front may be different from a width w2 of the second sub-stop area Z2 corresponding to the second gaze direction GD2 different from the first gaze direction G11.
Each of the sub-stop areas Z1, Z2, . . . , Zn may have each sub-field range. The sub-field may be an angle range (i.e., a visual field) that is clearly visible in each of the gaze directions GD1, GD2, . . . , GDn corresponding to each of the sub-stop areas Z1, Z2, . . . , Zn. The sub-field range may be determined by considering a change in visual acuity according to the human corneal eccentricity. With respect to each of the gaze directions GD1, GD2, GDn, at least some of the sub-fields may have different ranges or all of the sub-fields may have the same range. For example, the sub-field may be an angle range of ±9° corresponding to a macula range in each of the gaze directions GD1, GD2, . . . , GDn.
When a first sub-field is allocated θ1 with respect to a central sub-stop corresponding to the first gaze direction GD1 at the front, that is, the first sub-stop area Z1, a clearly visible viewing angle of the first sub-stop area Z1 may be in the range of ±θ1. Likewise, when a second sub-field is allocated θ2 with respect to the second sub-stop area Z2 corresponding to the second gaze direction GD2, a clearly visible viewing angle of the second sub-stop area Z2 may be in the range of ±θ2 with respect to the second gaze direction GD2.
Moreover, even when the clearly visible viewing angle of the central sub-stop, that is, the first sub-stop area Z1, is in the range of ±θ1, the central sub-stop may provide the entire viewing angle.
Next, the characteristics of the lens 100 will be described in relation to the human visual system.
FIG. 3 is a diagram describing the human perceptible levels depending on viewing angles, FIG. 4 is a diagram describing the classification of visual fields according to viewing angles (eccentricity), and FIG. 5 is a diagram describing the human visual acuity depending on viewing angles.
The human visual system applied to the lens 100 will be described with reference to FIGS. 3 to 5.
As illustrated in FIGS. 3 to 5, the human visual system may be a highly-foveated system. In other words, the human visual system may have a visual field where only a central portion is clearly visible and the other portions are barely visible. The maximum visual acuity may appear in a viewing angle period of about 3° to about 5°, only an approximate shape of the object may be detected at a viewing angle of up to about 30° to about 40°, only the color of the object may be detected at a viewing angle of up to 60°, and only the movement of the object may be detected in a subsequent period.
A general lens employed in a video see-through apparatus of the related art may be designed at a fixed viewpoint. The video see-through apparatus may require the lens to have a wide viewing angle for immersion, and the size of an entrance pupil (i.e., an eyebox) may decrease to optimize a steep incident light. The inventor found that the general lens designed at a fixed viewpoint failed to correspond to the rotation of the eyeball and the specifications of the central lens increased excessively for high image quality. Accordingly, the image quality of the screen may degrade greatly according to the movement of the user's gaze, and the screen may disappear according to the movement of the user's gaze due to a narrow eyebox.
The lens 100 may correspond to the rotation of the eyeball E, by trading off the image quality excessively wasted in the central portion, by designing the lens by considering the rotation of the eyeball E. That is, the lens 100 may correspond to the rotation of the eyeball E, by trading off the image quality excessively wasted in the central portion, by performing optimization only on a particular viewing angle range by using the fact that the human eye is foveated.
For example, when the user gazes at the front, a sub-field of ±9° corresponding to the macula range may be allocated to the first sub-stop area Z1 and optimization may be performed thereon. In this case, the size of the entrance pupil of the lens 100 corresponding to the first sub-stop area Z1 may be approximately equal to or greater than the size of the user's pupil (e.g., about 3 mm to about 4 mm).
As described above, by designing the lens 100 by performing optimization on each of the plurality of sub-stop areas Z1, Z2, . . . , Zn corresponding to the plurality of gaze directions GD1, GD2, . . . , GDn even when the eyeball E is rotated to change the gaze direction, the lens 100 may transmit a high-resolution image from the electronic display 200 to the user's pupil, maintain a uniform resolution throughout the screen, and simultaneously provide a high sense of immersion. Also, even when the size of the entrance pupil in each of the sub-stop areas Z1, Z2, . . . , Zn is about the size of the user's pupil, a practical eyebox provided by the lens 100 by corresponding to the rotation of the eyeball E The lens 100 may be sufficiently large and thus the lens 100 may provide a natural user experience by preventing the screen from being cut according to the gaze movement. Also, by using the fact that the peripheral resolution of the retina degrades, the lens 100 may provide a wide eyebox and high perceptual resolution.
FIG. 6 is a flowchart describing a method of designing a lens according to an embodiment of the disclosure, FIG. 7 illustrates ray diagrams in a plurality of sub-stop areas divided according to gaze directions, and FIG. 8 illustrates a ray diagram corresponding to an overlap of all ray diagrams in a plurality of sub-stop areas divided according to gaze directions. In FIG. 7, “θ” denotes an angle range of a clearly visible sub-field, “s” denotes the size of an eyebox for a given gaze direction, “h” denotes the height of an image, that is, half of the diagonal length of the display surface 201, and in FIG. 8, “Ω” represents a total viewing angle provided by the lens 100.
Referring to FIGS. 6 to 8, the method may first determine at least a portion of an area of the lens facing the user's pupil as a stop surface (S310). The size of an entire stop area may be determined based on a total rotation angle a of the human eyeball E. The total rotation angle a of the human eyeball E may be determined by various methods of evaluating the degree to which the human may comfortably move the pupil, and may be asymmetrically defined according to the left/right of both eyes.
Next, the method may divide the stop surface into a plurality of sub-stop areas Z1, Z2, . . . , Zn according to a plurality of gaze directions GD1, GD2, . . . , GDn within an entire viewing angle (S320). The stop surface may be divided by several particular rotation angles representing the total rotation angle a. For example, in FIG. 7, the first sub-stop area Zi may correspond to a gaze direction at the front, that is, a first gaze direction GD1 of 0°, the second sub-stop area Z2 may correspond to a second gaze direction GD2 of 10°, the (n-1)th sub-stop area Zn-2 may correspond to an (n-1)th gaze direction GDn-1 of 20°, and the n-th sub-stop area (Zn) may correspond to an n-th gaze direction GDn of 30°.
Each of the sub-stop areas Z1, Z2, . . . , Zn may be rotationally symmetrical about the optical axis. The plurality of sub-stop areas Z1, Z2, . . . , Zn may be separated from each other or may partially overlap each other. The width of each of the sub-stop areas Z1, Z2, . . . , Zn may be determined based on the human pupil size. The size “s” of the eyebox (i.e., the entrance pupil of the lens 100) for a given gaze direction may be about the size of the pupil of the eyeball E. For example, the size “s” of the eyebox for a given gaze direction may be determined to be slightly greater than the size of the pupil. For example, the size of the entrance pupil of the lens 100 may be approximately equal to or greater than the size of the user's pupil (e.g., about 3 mm to about 4 mm).
Next, the method may allocate a plurality of sub-field ranges 8 to the plurality of sub-stop areas Z1, Z2, . . . , Zn respectively (S330). A sub-field for each of the sub-stop areas Z1, Z2, . . . , Zn may be determined as a clearly visible area based on a change in visual acuity according to the human corneal eccentricity. An upper angle limit of a sub-field in which the lens clearly transmits an image at a fixed viewpoint position may be determined by considering a given form factor and resources. Also, a lower angle limit of the sub-field may be determined by considering a phenomenon such as a tunnel vision of the user. With respect to each of the gaze directions GD1, GD2, . . . , GDn at least some of the sub-fields may have different ranges or all of the sub-fields may have the same range. For example, the sub-field range may be determined based on the human macula range. For example, a sub-field of ±9° corresponding to the average human macula range may be allocated.
Also, the central sub-stop corresponding to the front gaze direction may be designed to provide the entire viewing angle.
Next, the method may optimize the optical performance of each of the sub-stop areas Z1, Z2, . . . , Zn based on the corresponding gaze direction (S340) and may design the entire stop surface by overlapping the sub-stop areas Z1, Z2, . . . , Zn as illustrated in FIG. 8. In other words, the lens 100 may be optimized under the condition that the rotation angle of the eyeball E is set to be in different zoom states and the same lens is used.
Next, the lens 100 will be described with reference to FIG. 9 and a numerical example.
FIG. 9 is a diagram schematically illustrating a lens 100 manufactured by a design method according to an embodiment of the disclosure. The definition of an aspherical surface used in the lens 100 may be represented as follows. When the z-axis direction is set as the optical-axis direction, the aspherical shape may be represented by the following equation by using a Forbes Q-con polynomial in a cylindrical polar coordinate system with respect to the optical-axis direction.
Here, “a0” denotes a vertex position along the optical axis (measured from the display surface), “k” denotes a conic constant, δ=1/Y, “Y” denotes the radius of an apex, and “g2 i+4” denotes a coefficient of a Forbes Q-con polynomial Qi con (Forbes, Shape specification for axially symmetric optical surfaces, Optics Express, Vol. 15, Issue 8, pp. 5218-5226 (2007)).
Particular values of fitting parameters for the lens 100 in FIG. 9 are given in Tables 1 and 2 below. In the numerical example, lens surface numbers 2, 3, 4, 5, 6, and 7 are sequentially listed from the side of an object where the user is located to the side of the display surface 201 of the electronic display 200 on which an image is formed, and lens surface symbols S2, S3, S4, S5, S6, and S7 are illustrated. In Table 1, symbols S4-2, S3-2, S4-3, and S5-2 represent the time when a reflected ray is again incident and then refracted or reflected. Also, “Y” denotes a curvature radius, “T” denotes a lens thickness or an air gap between lenses, and all lengths are in units of mm.
| Abbe | Refract | |||||
| Surface | Surface Type | Y | T | Index | number | Mode |
| Object | Sphere | Infinity | −1000.000 | Refract | ||
| Stop | Sphere | Infinity | 13.000 | Refract | ||
| S2 | Qcon Asphere | 86.003 | 1.482 | 1.650 | 21.825 | Reflect |
| S3 | Sphere | Infinity | 0.100 | Refract | ||
| S4 | Qcon Asphere | 303.400 | 9.882 | 1.545 | 56.000 | Reflect |
| S5 | Qcon Asphere | −73.034 | −9.882 | 1.545 | 56.000 | Reflect |
| S4-2 | Qcon Asphere | 303.400 | −0.100 | Refract | ||
| S3-2 | Sphere | Infinity | 0.100 | Reflect | ||
| S4-3 | Qcon Asphere | 303.400 | 9.882 | 1.545 | 56.000 | Refract |
| S5-2 | Qcon Asphere | −73.034 | 0.100 | Reflect | ||
| S6 | Qcon Asphere | 18.325 | 6.100 | 1.671 | 19.200 | Refract |
| S7 | Qcon Asphere | −13.146 | 0.488 | Reflect | ||
| Image | Sphere | Infinity | 0.012 | |||
| Parameter | S2 | S4 | S5 | S6 | S7 |
| Y Radius | 86.00273 | 303.39952 | −73.03353 | 18.32469 | −13.14568 |
| Normalization Radius | 20.88971 | 27.32217 | 29.39824 | 18.19726 | 12.97647 |
| 4th Order Qcon | −3.38744 | 0.63833 | −1.01596 | −14.62959 | 10.75154 |
| Coefficient | |||||
| 6th Order Qcon | 0.09960 | −0.94522 | −0.22157 | 2.70179 | −0.81087 |
| Coefficient | |||||
| 8th Order Qcon | −0.17113 | −0.04808 | −0.21500 | −1.20896 | 1.23727 |
| Coefficient | |||||
| 10th Order Qcon | 0.05539 | −0.00715 | 0.02453 | 0.27459 | −0.24098 |
| Coefficient | |||||
| 12th Order Qcon | −0.00443 | −0.00594 | −0.02741 | −0.15955 | 0.41408 |
| Coefficient | |||||
| 14th Order Qcon | 0.01510 | −0.00356 | −0.00110 | 0.00958 | −0.09426 |
| Coefficient | |||||
| 16th Order Qcon | −0.00604 | 0.00165 | −0.00432 | −0.03491 | 0.16640 |
| Coefficient | |||||
| 18th Order Qcon | −0.00024 | 0.00163 | 0.00430 | −0.00154 | −0.07222 |
| Coefficient | |||||
| 20th Order Qcon | −0.00009 | 0.00038 | −0.00137 | 0.00049 | 0.04193 |
| Coefficient | |||||
| 22th Order Qcon | 0.00033 | −0.00026 | −0.00025 | −0.00229 | −0.02417 |
| Coefficient | |||||
| 24th Order Qcon | −0.00025 | −0.00014 | 0.00000 | 0.00000 | −0.00500 |
| Coefficient | |||||
| 26th Order Qcon | 0.00004 | 0.00000 | 0.00007 | −0.00002 | −0.01182 |
| Coefficient | |||||
| 28th Order Qcon | −0.00008 | 0.00000 | 0.00004 | −0.00141 | −0.00189 |
| Coefficient | |||||
| 30th Order Qcon | −0.00008 | 0.00000 | −0.00004 | 0.00063 | −0.00522 |
| Coefficient | |||||
FIGS. 10 to 13 are graphs illustrating the optical performances of the lens 100 of FIG. 9 in gaze directions of 0°, 10°, 20°, and 30°respectively, and FIG. 14 is a graph illustrating the optical performance for an entire viewing angle when the lens 100 of FIG. 9 is viewed at the front. In FIGS. 10 to 14, the horizontal axis represents a spatial frequency and the vertical axis represents a modulation size, and different curves are illustrated for the respective viewing angles.
Referring to FIG. 10, it may be seen that the resolution is good and uniform in a gaze direction of 0°, a sub-field of ±9°, and a viewing angle of ±9° of the lens 100. Likewise, FIG. 11 illustrates that the resolution is good and uniform in a gaze direction of 10°, a sub-field of ±9°, and a viewing angle of about 1° to about 19° of the lens 100, and FIG. 12 illustrates that the resolution is good and uniform in a gaze direction of 20°, a sub-field of ±9°, and a viewing angle of about 11° to about 29° of the lens 100, and FIG. 13 illustrates that the resolution is relatively good and uniform in a gaze direction of 30°, a sub-field of ±9°, and a viewing angle of about 21° to about 45° of the lens 100.
Moreover, referring to FIG. 14, it may be seen that the lens 100 provides the entire viewing angle when the user gazes at the front.
The lens, the video see-through apparatus employing the lens, and the method of designing the lens have been described above with reference to the embodiments illustrated in the drawings in order to facilitate an understanding thereof; however, this is merely an example, and those of ordinary skill in the art will understood that various modifications and other equivalent embodiments may be made therefrom. Thus, the true technical scope of the disclosed embodiments should be defined by the appended claims.
