CN109270607B - Single-chip broadband achromatic refraction and diffraction mixed lens and design method - Google Patents

Single-chip broadband achromatic refraction and diffraction mixed lens and design method Download PDF

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CN109270607B
CN109270607B CN201811453680.7A CN201811453680A CN109270607B CN 109270607 B CN109270607 B CN 109270607B CN 201811453680 A CN201811453680 A CN 201811453680A CN 109270607 B CN109270607 B CN 109270607B
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许峰
陈昱杰
郑鹏磊
陈旭
胡正文
邢春蕾
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Suzhou University
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B3/00—Simple or compound lenses
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    • G02B3/08—Simple or compound lenses with non-spherical faces with discontinuous faces, e.g. Fresnel lens
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
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    • G02—OPTICS
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Abstract

The invention belongs to the field of optics, and provides a single-chip broadband achromatic refraction and diffraction mixed lens and a design method thereof for solving the problems of large chromatic aberration and poor imaging quality of the traditional single-chip lens. The single-chip refraction and diffraction mixed lens designed by the method effectively reduces chromatic dispersion, enhances imaging quality and realizes lightness and thinness of the device.

Description

Single-chip broadband achromatic refraction and diffraction mixed lens and design method
Technical Field
The invention belongs to the field of optics, and particularly relates to a design method of an achromatic lens, in particular to a design method of a single-chip broadband achromatic refraction and diffraction hybrid lens.
Background
With the development of science and technology, wearable equipment is more and more popular in people's daily life. The mobile phone has gained wide attention of science and technology personnel as a wearable device which is most widely applied at present. The length of the lens of the mobile phone determines how thin the mobile phone can be in the future. At present, the mobile phone lens is commonly provided with 5-piece or 6-piece structures and the like, so that the mobile phone is limited to be thinned in one step.
VR (Virtual Reality) technology was proposed in the eighties of the twentieth century, which is a technology for creating an immersion in a three-dimensional environment, generated on a computer, using a computer hardware structure and a software control system. With the development of computer technology and the improvement of sensor performance in recent years, various head-mounted virtual reality displays are on the market, which basically comprise a display screen or a mobile phone and a pair of eyepieces, wherein human eyes can see enlarged images on the screen through the eyepieces, and the sensor senses the change of human head to adjust the images in the left and right screens, so that the human eyes can see three-dimensional and interactive visual images.
Traditional VR glasses often adopt a set of camera lens for the colour difference, the distortion etc. that correct the eyepiece and bring, can make VR glasses whole too heavy like this and influence the comfort level of wearing. In order to reduce the weight of VR glasses, the current solution is a single-piece spherical mirror, an aspherical mirror or a refractive fresnel lens. The chromatic aberration problem caused by the single-chip spherical mirror, the aspherical mirror or the refraction type Fresnel lens cannot be eliminated by the lens, at this time, the image needs to be processed in advance and then displayed by a display, so that the image definition is reduced, the vertigo is caused, and the watching experience is influenced. The existing refraction type Fresnel lens inevitably introduces a lot of stray light into the virtual reality equipment, so that when a user uses the virtual reality equipment, the edge of a visual virtual image is seen to be fuzzy, even a smear or a ghost appears, the visual effect of the virtual reality equipment is seriously reduced, and the user experience is influenced.
Disclosure of Invention
The invention aims to solve the problems of large chromatic aberration and poor imaging quality of the traditional single-chip lens. A monolithic broadband achromatic diffractive-refractive hybrid lens and a design method therefor are disclosed. The specific scheme is as follows:
a single-chip broadband achromatic refraction and diffraction hybrid lens comprises a first optical surface and a second optical surface, wherein the first optical surface and the second optical surface share an optical axis; wherein the first optical surface is a high-order aspheric surface, and the second optical surface is a harmonic diffraction surface; the harmonic diffraction surface consists of a substrate and a Fresnel zone superposed on the substrate, wherein the substrate comprises a plane, a spherical surface, an aspheric surface or a high-order aspheric surface;
the difference between the focal powers of the first optical surface and the second optical surface is as follows:
Figure BDA0001887220370000021
the surface rise equation of the Fresnel zone is
Figure BDA0001887220370000022
Figure BDA0001887220370000023
Wherein: f' is the focal length of the single-chip type broadband achromatic refraction-diffraction mixed lens, gammadifAbbe number, gamma, of Fresnel ring surfacerefIs the abbe number of the refractive material, and n is the refractive index of the lens material; k is the Fresnel zone number of the harmonic diffraction surface, k is 1, 2 … …, xk，ykIs the substrate coordinate of the harmonic diffraction surface in the k-th zone, and p is the harmonic diffraction parameter.
The design method of the single-chip broadband achromatic refraction and diffraction hybrid lens is as follows;
according to the following formula:
Figure BDA0001887220370000024
and respectively carrying out optical power distribution of the first optical surface and the second optical surface substrate on the R wave band, the G wave band and the B wave band, and realizing achromatism in the R wave band, the G wave band and the B wave band, wherein: r wave band, G wave band and B wave band respectively represent red light wave band, green light wave band and blue light wave band f 'in the incident light source of the single-chip type wide wave band achromatic refraction and diffraction mixed lens'difIs the focal length, f 'of the Fresnel zone of the second optical surface'refIs the focal length of the first optical surface, f' is the focal length of the single-piece broadband achromatic refraction and diffraction mixed lens, gammadifAbbe number, gamma, of Fresnel ring surfacerefIs the abbe number of the refractive material;
then according to the following formula:
Figure BDA0001887220370000025
selecting harmonic diffraction parameter p to make central wavelengths of R wave band, G wave band and B wave band be confocal, in which lambdaR、λG、λBCentral wavelengths of R, G and B bands, p is harmonic diffraction parameter of harmonic diffraction surface, and lambda0Is the center wavelength of the harmonic diffraction plane;
and adjusting the high-order term of the first optical surface and the high-order term of the second optical surface to enlarge the field of view, reduce the thickness of the lens and correct the rest aberration.
The first optical surface is an even-order term aspheric surface, and the surface equation is as follows:
Figure BDA0001887220370000031
Figure BDA0001887220370000032
where c is the curvature of the aspheric surface, r is the distance from a point on the lens surface to the optical axis, k is the degree of the cone, a2，a4，a6Is a polynomial coefficient.
The first optical surface is an odd-order aspheric surface, and the surface equation of the first optical surface is as follows:
Figure BDA0001887220370000033
Figure BDA0001887220370000034
where c is the curvature of the aspheric surface, r is the distance from a point on the lens surface to the optical axis, k is the degree of the cone, a1，a2，a3，a4，a5Is a polynomial coefficient.
The working principle of the achromatic lens is as follows: distributing focal power through the substrate of the first optical surface and the harmonic diffraction surface to realize achromatization of an R wave band, a G wave band and a B wave band, and then realizing the confocal of the central wavelengths of the R wave band, the G wave band and the B wave band through a diffraction microstructure on the harmonic diffraction surface; the high-order terms of the first optical surface or the second optical surface and the high-order terms of the harmonic diffraction surface are used for expanding the field of view, reducing the thickness of the lens and correcting the effects of other aberrations.
Due to the application of the technical scheme, compared with the prior art, the invention has the following advantages:
1. the single-chip type broadband achromatic refraction and diffraction mixed lens can realize RGB three-waveband achromatism.
2. The single-chip broadband achromatic refraction and diffraction hybrid lens is thin in thickness, light in weight and low in manufacturing cost.
3. When the color-reducing agent is used for VR glasses and mobile phone lenses, the three wave bands of RGB can be achromatized without preprocessing the image, so that the definition of the image is not reduced; the thicknesses of VR glasses and mobile phone lenses can be shortened, and the weight of the VR glasses and the mobile phone lenses is reduced.
Drawings
Figure 1 is a schematic diagram of a monolithic broadband achromatic hybrid diffractive refractive lens,
figure 2 is a plot of the R-band dot alignment,
figure 3 is a plot of the G-band dot alignment,
figure 4 is a B-band dot diagram,
figure 5 is an R-band full field MTF,
figure 6 is a G-band full field MTF,
figure 7 is a B-band full field MTF,
figure 8 is a 60 field of view lenticular VR lens optical path diagram,
figure 9 is a 60 field-of-view lenticular VR lens imaging MTF plot,
figure 10 is a 60 field of view hybrid lens optical path diagram,
FIG. 11 is a 60 field hybrid lens imaging MTF plot;
wherein: 1 is a first optical surface and 2 is a second optical surface.
Detailed Description
The invention is further described with reference to the following figures and examples:
the first embodiment is as follows: a single-piece broadband achromatic refraction and diffraction hybrid lens is shown in FIG. 1, and comprises a first optical surface 1 and a second optical surface 2, wherein the first optical surface and the second optical surface share an optical axis; wherein the first optical surface is a high-order aspheric surface, and the second optical surface is a harmonic diffraction surface; the harmonic diffraction surface consists of a substrate and a Fresnel zone superposed on the substrate, wherein the substrate comprises a plane, a spherical surface, an aspheric surface or a high-order aspheric surface;
the surface shape equation of the first optical surface is as follows:
Figure BDA0001887220370000041
Figure BDA0001887220370000042
wherein x1，y1The bottom coordinates of the first optical surface.
The base of the second optical surface is a high-order aspheric surface, and the high-order aspheric surface equation of the base is as follows:
Figure BDA0001887220370000043
wherein x2，y2The bottom coordinate of the second optical surface.
The rise equation of the Fresnel zone on the second optical surface is as follows:
Figure BDA0001887220370000044
where k is the number of fresnel zones on the second optical surface, k is 1, 2 … …, xk，ykIs the base coordinate of the second optical surface in the k-th ring zone.
Example two: a design method of a single-chip broadband achromatic refraction and diffraction hybrid lens is provided, according to the following formula:
Figure BDA0001887220370000051
and respectively carrying out optical power distribution of the first optical surface and the second optical surface substrate on the R wave band, the G wave band and the B wave band, and realizing achromatism in the R wave band, the G wave band and the B wave band, wherein: r band, G band and B band respectively representRed light wave band, green light wave band and blue light wave band f 'in single-chip type wide wave band achromatic refraction and diffraction mixed lens incident light source'difIs the focal length, f 'of the Fresnel zone of the second optical surface'refIs the focal length of the first optical surface, f' is the focal length of the single-piece broadband achromatic refraction and diffraction mixed lens, gammadifAbbe number, gamma, of Fresnel ring surfacerefIs the abbe number of the refractive material;
then according to the following formula:
Figure BDA0001887220370000052
selecting harmonic diffraction parameter p to make central wavelengths of R wave band, G wave band and B wave band be confocal, in which lambdaR、λG、λBCentral wavelengths of R, G and B bands, p is harmonic diffraction parameter of harmonic diffraction surface, and lambda0Is the center wavelength of the harmonic diffraction plane;
and adjusting the high-order term of the first optical surface and the high-order term of the second optical surface to enlarge the field of view, reduce the thickness of the lens and correct the rest aberration.
Taking VR glasses as an example, the design method of the single-chip broadband achromatic refraction and diffraction mixed lens is as follows: the LCD display screen in VR glasses is 5.5 inches, the resolution is 1440 x 2560, the size of the pixel is 47.25 μm, the arrangement mode of red, green and blue sub-pixels is RGB stripe arrangement, and the size of the sub-pixels is 15.75 x 47.25 μm. The VR lens material is PMMA, and the processing mode is a precision diamond turning method.
The three bandwidths of the LCD display screen are 481-491nm, 582-592nm and 651-661nm respectively, and the central wavelengths of the three wave bands are respectively: lambda [ alpha ]R＝656nm，λG＝587nm，λB486 nm. According to the following formula:
Figure BDA0001887220370000053
Figure BDA0001887220370000061
Figure BDA0001887220370000062
and selecting proper harmonic diffraction parameters to enable the three central wavelengths to be apochromatically achromatized. In this embodiment, the harmonic diffraction parameter P is 19, and the design wavelength λ0＝587nm。λR，λG，λBWhich is exactly the harmonic wavelength of the harmonic diffraction surface.
According to the following formula:
Figure BDA0001887220370000063
Figure BDA0001887220370000064
Figure BDA0001887220370000065
the power distribution is performed for each of the three wavelength bands. For 481-491nm,. gammaBdif＝-48.61，γBref＝629.3，f′Bdif＝551mm，f′Bref42.55 mm. For 582-Gdif＝-58.76，γGref＝1140.72，f′Gdif＝806mm，f′Gref41.53 mm. For 651-661nm, gammaRdif＝-65.63，γRref＝1532.14，f′Rdif＝962mm，f′Rref41.19 mm. And finally, finding the optimal solution which minimizes the color difference in the three wave bands as an initial structure.
After the initial structure is selected, the high-order term of the first optical surface and the high-order term of the second optical surface are adjusted to enlarge the field of view, reduce the thickness of the lens and correct the rest aberrations.
The finally designed single VR-type broadband achromatic refraction and diffraction hybrid lens has the center thickness of 5.8mm, the back focal length of 37.8mm, three-waveband dot diagrams as shown in figures 2-4, and the root-mean-square radius of the three-waveband achromatic refraction and diffraction hybrid lens is less than half of the size of a pixel. The MTF curves are shown in fig. 5-7, and the MTF for each field is greater than 0.8 at the nyquist frequency.
Example three: a VR glasses comprises a glass frame and a single-chip broadband achromatic refraction and diffraction mixed lens in the first embodiment, wherein the single-chip broadband achromatic refraction and diffraction mixed lens is installed on the glass frame, and a clamping component for clamping a display screen is arranged on the glass frame.
In this example, the present invention is compared with a patent "a VR spectacle lens" (Authority publication No.: CN 105785487B) issued in 2018.
CN 105785487B discloses a VR glasses lenticular lens, which sets the exit pupil diameter to 4mm, the exit pupil distance to 15mm, the wavelength to F, d, C light, and the full field of view to 60 °. The lenticular lens was optimized according to the description in CN 105785487B, and the final optimized optical path diagram is shown in fig. 8. The optimized central thickness of the lenticular lens is 14.926mm, the distance from the pupil of the human eye to the display screen is 64.87mm, the mtf curve of the optimized lenticular lens is shown in fig. 9, and as can be seen from fig. 9, the VR lens only has higher resolution in the on-axis field of view.
The lens provided by the invention is used for replacing the double-convex lens for VR glasses disclosed in CN 105785487B, so that the imaging quality of VR eyes is improved. Similarly, the diameter of the exit pupil is set to be 4mm, the exit pupil distance is set to be 15mm, the wavelengths are set to be F, d and C light, the full field of view is 60 degrees, and the finally optimized optical path diagram is shown in FIG. 10. The optimized mixed lens has the central thickness of 5.8mm, the distance from the pupil of the human eye to the display screen is 58.6mm, the mtf curve is shown in fig. 11, and as can be seen from fig. 10, mtf of each field of view reaches 0.9, so that the imaging quality is extremely high. When the hybrid lens is used in a VR device, the weight of the device can be greatly reduced, the length of the device can be shortened, the chromatic aberration can be eliminated, and the imaging quality can be improved.
The technical scheme is not described in detail and belongs to the known technology in the field.

Claims (4)

1. A single-piece broadband achromatic refraction and diffraction hybrid lens is characterized in that: the single-chip broadband achromatic refraction and diffraction hybrid lens comprises a first optical surface and a second optical surface, wherein the first optical surface and the second optical surface are coaxial; wherein the first optical surface is a high-order aspheric surface, and the second optical surface is a harmonic diffraction surface; the harmonic diffraction surface consists of a substrate and a Fresnel zone superposed on the substrate, wherein the substrate comprises a plane, a spherical surface and an aspheric surface;
the difference between the focal powers of the first optical surface and the second optical surface is as follows:
Figure FDA0002354812610000011
the surface rise equation of the Fresnel zone is
Figure FDA0002354812610000012
Wherein: f' is the focal length of the single-chip type broadband achromatic refraction-diffraction mixed lens, gammadifAbbe number, gamma, of Fresnel ring surfacerefIs the abbe number of the refractive material, and n is the refractive index of the lens material; k is the Fresnel zone number of the harmonic diffraction surface, k is 1, 2 … …, xk，ykIs the substrate coordinate of the harmonic diffraction surface in the k-th zone, and p is the harmonic diffraction parameter.
2. A design method of a single-chip broadband achromatic refraction and diffraction hybrid lens is characterized by comprising the following steps of: the single-chip broadband achromatic refraction and diffraction hybrid lens comprises a first optical surface and a second optical surface, wherein the first optical surface and the second optical surface are coaxial; wherein the first optical surface is a high-order aspheric surface, and the second optical surface is a harmonic diffraction surface; the harmonic diffraction surface consists of a substrate and a Fresnel zone superposed on the substrate, wherein the substrate comprises a plane, a spherical surface and an aspheric surface; according to the following formula:
Figure FDA0002354812610000013
and respectively carrying out optical power distribution of the first optical surface and the second optical surface substrate on the R wave band, the G wave band and the B wave band, and realizing achromatism in the R wave band, the G wave band and the B wave band, wherein: the R wave band, the G wave band and the B wave band respectively represent the single-chip type wide-wave-band achromatic refraction and diffraction mixed lensRed light band, green light band, blue light band, f 'of incident light source'difIs the focal length, f 'of the Fresnel zone of the second optical surface'refIs the focal length of the first optical surface, f' is the focal length of the single-piece broadband achromatic refraction and diffraction mixed lens, gammadifAbbe number, gamma, of Fresnel ring surfacerefIs the abbe number of the refractive material;
then according to the following formula:
Figure FDA0002354812610000014
selecting harmonic diffraction parameter p to make central wavelengths of R wave band, G wave band and B wave band be confocal, in which lambdaR、λG、λBCentral wavelengths of R, G and B bands, p is harmonic diffraction parameter of harmonic diffraction surface, and lambda0Is the center wavelength of the harmonic diffraction plane;
the high-order terms of the first optical surface and the second optical surface are adjusted to enlarge the field of view, reduce the thickness of the lens and correct the aberration.
3. The method of claim 2, wherein the design method comprises: the first optical surface is an even-order term aspheric surface, and the surface equation is as follows:
Figure FDA0002354812610000015
where c is the curvature of the aspheric surface, r is the distance from a point on the lens surface to the optical axis, k is the degree of the cone, a2，a4，a6Is a polynomial coefficient.
4. The method of claim 2, wherein the design method comprises: the first optical surface is an odd-order aspheric surface, and the surface equation of the first optical surface is as follows:
Figure FDA0002354812610000021
Figure FDA0002354812610000022
where c is the curvature of the aspheric surface, r is the distance from a point on the lens surface to the optical axis, k is the degree of the cone, a1，a2，a3，a4，a5Is a polynomial coefficient.
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