CN113960751B - Low-cost day and night high-low temperature confocal lens - Google Patents

Low-cost day and night high-low temperature confocal lens Download PDF

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CN113960751B
CN113960751B CN202111144822.3A CN202111144822A CN113960751B CN 113960751 B CN113960751 B CN 113960751B CN 202111144822 A CN202111144822 A CN 202111144822A CN 113960751 B CN113960751 B CN 113960751B
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CN113960751A (en
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马宏博
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Jiangxi Phoenix Optical Technology Co ltd
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    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B13/00Optical objectives specially designed for the purposes specified below
    • G02B13/001Miniaturised objectives for electronic devices, e.g. portable telephones, webcams, PDAs, small digital cameras
    • G02B13/0015Miniaturised objectives for electronic devices, e.g. portable telephones, webcams, PDAs, small digital cameras characterised by the lens design
    • G02B13/002Miniaturised objectives for electronic devices, e.g. portable telephones, webcams, PDAs, small digital cameras characterised by the lens design having at least one aspherical surface
    • G02B13/0045Miniaturised objectives for electronic devices, e.g. portable telephones, webcams, PDAs, small digital cameras characterised by the lens design having at least one aspherical surface having five or more lenses
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B1/00Optical elements characterised by the material of which they are made; Optical coatings for optical elements
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B1/00Optical elements characterised by the material of which they are made; Optical coatings for optical elements
    • G02B1/04Optical elements characterised by the material of which they are made; Optical coatings for optical elements made of organic materials, e.g. plastics
    • G02B1/041Lenses
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B13/00Optical objectives specially designed for the purposes specified below
    • G02B13/001Miniaturised objectives for electronic devices, e.g. portable telephones, webcams, PDAs, small digital cameras
    • G02B13/0055Miniaturised objectives for electronic devices, e.g. portable telephones, webcams, PDAs, small digital cameras employing a special optical element
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B13/00Optical objectives specially designed for the purposes specified below
    • G02B13/001Miniaturised objectives for electronic devices, e.g. portable telephones, webcams, PDAs, small digital cameras
    • G02B13/008Miniaturised objectives for electronic devices, e.g. portable telephones, webcams, PDAs, small digital cameras designed for infrared light
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B13/00Optical objectives specially designed for the purposes specified below
    • G02B13/18Optical objectives specially designed for the purposes specified below with lenses having one or more non-spherical faces, e.g. for reducing geometrical aberration

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Abstract

The invention discloses a low-cost day-night high-low temperature confocal lens, which comprises a first lens L1, a second lens L2, a third lens L3, a fourth lens L4, a fifth lens L5 and an optical filter which are sequentially arranged from an object space to an image space along an optical axis, wherein: the first lens L1 is a convex-concave aspheric plastic lens with positive focal power; the second lens L2 is a concave-convex aspheric plastic lens with negative focal power; the third lens L3 is a biconvex spherical glass lens having positive optical power; the fourth lens L4 is a biconvex aspheric plastic lens with positive focal power; the fifth lens L5 is a concave-convex aspheric plastic lens with negative optical power. The lens has a large aperture, can clearly image in weak light, meets the requirements of day and night sharing, has low distortion, has imaging effect of 500 ten thousand pixels, has stable working performance in an environment of-40 ℃ to +80 ℃, and has low cost and wide application range.

Description

Low-cost day and night high-low temperature confocal lens
Technical Field
The invention belongs to the technical field of optical lenses, and particularly relates to a low-cost day-night high-low temperature confocal lens.
Background
Along with the development of science and technology, intelligent high-definition cameras are widely applied in various fields, and higher requirements are put on optical lenses. At present, domestic monitoring equipment is developed towards miniaturization, multifunction and multi-scene application, and in some application scenes with complex environments, the monitoring equipment is required to have stronger environment adaptability. When the monitoring equipment is applied to a scene with a large temperature difference between high temperature and low temperature, the security lens is required to be prevented from defocusing in the high-temperature environment and the low-temperature environment. Meanwhile, the monitoring equipment works day and night, the security lens is required to be clear in imaging in the daytime, and the security lens is also clear in imaging at night under the infrared light filling, and is high in brightness. Moreover, in the situation that the domestic security protection lens is very competitive, the cost of the lens is also important to control. Therefore, the security lens with low cost, suitability for different temperature scenes and clear imaging in the day and night is necessary.
Disclosure of Invention
The invention aims to solve the problems, and provides a low-cost day-night high-low temperature confocal lens which is provided with a large aperture, can clearly image in weak light, meets the day-night sharing requirement, is low in distortion, has an imaging effect of 500 ten thousand pixels, is stable in working performance in an environment of-40 ℃ to +80 ℃, and is low in cost and wide in application range.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
the invention provides a low-cost day-night high-low temperature confocal lens, which comprises a first lens L1, a second lens L2, a third lens L3, a fourth lens L4, a fifth lens L5 and an optical filter, wherein the first lens L1, the second lens L2, the third lens L3, the fourth lens L4, the fifth lens L5 and the optical filter are sequentially arranged from an object side to an image side along an optical axis, wherein:
the first lens L1 is a convex-concave aspheric plastic lens with positive focal power;
the second lens L2 is a concave-convex aspheric plastic lens with negative focal power;
the third lens L3 is a biconvex spherical glass lens having positive optical power;
the fourth lens L4 is a biconvex aspheric plastic lens with positive focal power;
the fifth lens L5 is a concave-convex aspheric plastic lens with negative optical power.
Preferably, a STOP is provided between the second lens L2 and the third lens L3.
Preferably, the low cost day and night high and low temperature confocal lens satisfies the following conditions:
f1/f0>1
wherein f1 is the effective focal length of the first lens L1, and f0 is the effective focal length of the lens.
Preferably, the low cost day and night high and low temperature confocal lens also satisfies the following conditions:
5<|f1/f3|<15
wherein f1 is an effective focal length of the first lens L1, and f3 is an effective focal length of the third lens L3. Preferably, the low cost day and night high and low temperature confocal lens also satisfies the following conditions:
0.1<f0/TTL<1.5
wherein f0 is the effective focal length of the lens, and TTL is the total optical length of the lens.
Preferably, the working wave bands of the low-cost day-night high-low temperature confocal lens are 436 n-656 nm of visible light wavelength and 830-870 nm of infrared wavelength.
Preferably, the mirror surface of the aspherical lens satisfies the following formula:
Figure GDA0004139683290000021
wherein z is sagittal height, c=1/r, r is surface curvature radius, h is radial coordinate, k is conical coefficient, a is fourth order coefficient, B is sixth order coefficient, C is eighth order coefficient, D is tenth order coefficient, E is twelfth order coefficient, and F is fourteenth order coefficient.
Preferably, the first lens L1, the second lens L2, the fourth lens L4 and the fifth lens L5 are mirror surfaces sequentially arranged from the object side to the image side, k corresponds to-1.21, 0.21, -0.95, -0.87, 3.25, -8.32, -6.8, -12.6 in sequence, A corresponds to 1.1e-3, 3.3e-3, 0.011, 0.022, 6.5e-3, 1.1e-3, -3.4e-3, 9.3e-4 in sequence, B corresponds to-6.8 e-5, -2.5e-4, -6.2e-4, 2.8e-4, -8.8e-4, -8.6e-4, 6.7e-4, 2.4e-4, C corresponds to 1.9e-5, 6.3e-5, -9.8e-5, -2.3e-4, 6.6e-5, 5.2e-5, 2.1e-5 in sequence, D corresponds to-1.1 e-6, -4.3.5, 2.8 e-5, -2.8 e-5, 2.7 e-5, 2.9-7 e-5, 2.9.7 e-5, 2.9-7 e-5, 6.9.9 e-5, 6.9-9, 3.9-5, 3.9-4 in sequence.
Preferably, the first lens L1, the second lens L2, the fourth lens L4 and the fifth lens L5 are mirror surfaces sequentially arranged from the object side to the image side, k corresponds to-0.54, 0.83, -1.12, -0.98, 5.45, -10.65, -4.56, -9.21 in sequence, A corresponds to 1.6e-3, 3.1e-3, 0.019, 0.012, 5.3e-3, 1.4e-3, -2.4e-3, 5.9e-4 in sequence, B corresponds to-5.1 e-5, -2.3e-4, -9.8e-4, 1.3e-4, -9.1e-4, -5.6e-4, 1.1e-3, 3.6e-4 in sequence, C corresponds to 1.5e-5, 9.3e-5, -1.1e-4, -1.5e-4, 7.9e-5, 4.8e-5, 4-1.5 e-4, 5.5e-6,D, in turn, -1.4e-6, -1.5e-5, 1.1e-5, 1.2e-5, -6.4e-6, -3.4e-6, 5.7e-6, -1.6e-6,E, in turn, -4.4 e-8, -6.1 e-7, -6.3e-8, -2.5e-7, 1.9e-7, 1.1e-7, -1.2e-7, 4.8e-8,F, in turn, -2.7e-9, -2.3e-10, -1.2e-9, -4.2e-9, -1.2e-9, -9.2e-10, -5.2e-9, -3.1e-10.
Compared with the prior art, the invention has the beneficial effects that: the lens has a large aperture, the relative illuminance is greater than 50% and less than or equal to 1.6, and can clearly image in weak light, confocal in visible light wavelength and infrared wavelength ranges, and the day-night sharing requirement is met; by reasonably adopting the aspheric lens to correct various aberrations, the imaging quality is greatly improved, and the imaging effect can reach 500 ten thousand pixels; the lens is prevented from defocusing in the environment of minus 40 ℃ to +80 ℃ by reasonably distributing the focal length, so that the application in the environment of different temperatures is satisfied, the imaging quality is good, and the working performance is stable; the 1G4P glass-plastic mixed structure is simple in structure and low in cost, and can be used in the fields of intelligent traffic, intelligent security and the like.
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FIG. 1 is a schematic diagram of a low cost day-night high and low temperature confocal lens of the present invention;
fig. 2 is a graph of the MTF of visible light according to the first embodiment of the present invention;
FIG. 3 is an infrared light MTF graph of a first embodiment of the present invention;
FIG. 4 is a graph showing the MTF at low temperature of-40℃for an embodiment of the present invention;
FIG. 5 is a graph of MTF at high temperature +80℃;
fig. 6 is a graph of the MTF of visible light for the second embodiment of the present invention;
FIG. 7 is an infrared light MTF graph of a second embodiment of the present invention;
FIG. 8 is a graph showing MTF at low temperature of-40℃for example two of the present invention;
FIG. 9 is a graph showing MTF at high temperature +80℃.
Detailed Description
The following description of the technical solutions in the embodiments of the present application will be made clearly and completely with reference to the drawings in the embodiments of the present application, and it is apparent that the described embodiments are only some embodiments of the present application, not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present disclosure.
It is noted that unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein in the description of the present application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.
As shown in fig. 1, a low-cost day-night high-low temperature confocal lens includes a first lens L1, a second lens L2, a third lens L3, a fourth lens L4, a fifth lens L5 and an optical filter sequentially disposed from an object side to an image side along an optical axis, wherein:
the first lens L1 is a convex-concave aspheric plastic lens with positive focal power;
the second lens L2 is a concave-convex aspheric plastic lens with negative focal power;
the third lens L3 is a biconvex spherical glass lens having positive optical power;
the fourth lens L4 is a biconvex aspheric plastic lens with positive focal power;
the fifth lens L5 is a concave-convex aspheric plastic lens with negative optical power.
The third lens L3 of the lens is a glass spherical lens, the first lens L1, the second lens L2, the fourth lens L4 and the fifth lens L5 are all plastic aspheric lenses, the first lens L1 has a light receiving effect, the second lens L2 can reduce a deflection angle of light, the third lens L3 can well correct on-axis aberration and is favorable for compensating height Wen Lijiao, the fourth lens L4 is used for compensating distortion, the fifth lens L5 can effectively correct curvature of field, and a Chief Ray Angle (CRA) can be reduced to match a photosensitive chip to improve light energy receiving efficiency of the photosensitive chip. The optical filter can filter other stray light of a non-working wave band, and the imaging resolution of the lens is improved. The lens has a large aperture, the relative illuminance is greater than 50% and the lens can clearly image in weak light, wherein the aperture is smaller than or equal to 1.6; by reasonably adopting the aspheric lens to correct various aberrations, the aberration is low, the imaging quality of the lens is greatly improved, and the imaging effect can reach 500 ten thousand pixels; by reasonably distributing the focal length, the lens is prevented from defocusing in the environment of minus 40 ℃ to +80 ℃, the application in the environment of different temperatures is satisfied, the imaging quality is good, and the working performance is stable; adopt 1G4P glass to mould mixed structure, rationally select the glass material, make this camera lens confocal in visible light wavelength and infrared wavelength range, satisfy day night sharing demand, simple structure, with low costs can be used to fields such as wisdom traffic, intelligent security protection.
In one embodiment, a STOP is provided between the second lens L2 and the third lens L3. Used for limiting the light transmission aperture of the on-axis light beam and helping to improve the image quality.
In one embodiment, the low cost day and night high and low temperature confocal lens satisfies the following conditions:
f1/f0>1
wherein f1 is the effective focal length of the first lens L1, and f0 is the effective focal length of the lens.
In one embodiment, the low cost day and night high and low temperature confocal lens also satisfies the following conditions:
5<|f1/f3|<15
wherein f1 is an effective focal length of the first lens L1, and f3 is an effective focal length of the third lens L3.
By defining f1/f0>1,5< |f1/f3| <15, the aberration can be well corrected, imaging quality is improved, and lens assembly tolerances are made insensitive.
In one embodiment, the low cost day and night high and low temperature confocal lens also satisfies the following conditions:
0.1<f0/TTL<1.5
wherein f0 is the effective focal length of the lens, and TTL is the total optical length of the lens.
By defining 0.1< f0/TTL <1.5, the total length of the lens can be defined, contributing to miniaturization of the lens.
In one embodiment, the low cost day and night high and low temperature confocal lens operates in the wavelength range of 436 nm to 656nm visible light and 830nm to 870nm infrared. The requirement of day and night sharing of monitoring equipment is met.
In one embodiment, the specular surface of the aspherical lens satisfies the following formula:
Figure GDA0004139683290000051
wherein z is sagittal height, c=1/r, r is surface curvature radius, h is radial coordinate, k is conical coefficient, a is fourth order coefficient, B is sixth order coefficient, C is eighth order coefficient, D is tenth order coefficient, E is twelfth order coefficient, and F is fourteenth order coefficient.
Specific parameters of the lens are further disclosed by the detailed description of the embodiments below.
Example 1:
in this embodiment, the relevant parameters of each lens are shown in table 1:
TABLE 1
Surface serial number Surface type Radius of curvature Thickness of (L) Refractive index Abbe number
Object plane Spherical surface Infinity distance
S1 Aspherical surface 6.5 2.2 1.58 50.2
S2 Aspherical surface 7.8 1.8
S3 Aspherical surface -2.3 1.6 1.5 61.5
S4 Aspherical surface -2.5 -0.5
Stop Spherical surface Infinity distance 3.1
S6 Spherical surface 10.2 2.8 1.45 95
S7 Spherical surface -15.2 0.4
S8 Aspherical surface -23.4 2.8 1.5 61.5
S9 Aspherical surface -2.7 1.1
S10 Aspherical surface -2.6 3.1 1.67 28.5
S11 Aspherical surface -6.3 1
S12 Spherical surface Infinity distance 0.8 1.52 64.2
S13 Spherical surface Infinity distance 3.2
Image plane (IMA) Spherical surface Infinity distance
In table 1, S1 and S2 correspond to the object side surface and the image side surface of the first lens element L1, S3 and S4 correspond to the object side surface and the image side surface of the second lens element L2, S6 and S7 correspond to the object side surface and the image side surface of the third lens element L3, S8 and S9 correspond to the object side surface and the image side surface of the fourth lens element L4, S10 and S11 correspond to the object side surface and the image side surface of the fifth lens element L5, and S12 and S13 correspond to the object side surface and the image side surface of the optical filter, respectively.
The aspherical coefficients of each lens of this example are shown in table 2:
TABLE 2
Figure GDA0004139683290000061
Figure GDA0004139683290000071
In this embodiment, the effective focal length f1= -85.3mm of the first lens L1, the effective focal length f3=14.5 mm of the third lens L3, and the technical indexes of lens implementation are as follows:
1. focal length: f0 =9 mm;
2. f-number #f=1.6;
3. working wavelength: 436-656 nm/830-870 nm;
4. view angle 2ω:40 °;
5. optical distortion: <2%;
6. relative illuminance: 53%;
7. total optical length: <30mm.
According to the above data, the final imaging effect of the lens of this embodiment is evaluated by the MTF curve of fig. 2, and the MTF curves in each view field in fig. 2 gradually decrease, which indicates that the lens has better imaging effect and resolution in the whole view field. The MTF curves of fig. 3 in the infrared band under various fields of view also decrease gradually, which means that the lens has better imaging quality in the infrared band. Fig. 4 and 5 show MTF curves at-40 ℃ and +80 ℃ respectively, and it can be seen that the lens can still maintain better image quality in a temperature environment of-40 ℃ to +80 ℃.
Example 2:
in this embodiment, the relevant parameters of each lens are shown in table 3:
TABLE 3 Table 3
Figure GDA0004139683290000072
Figure GDA0004139683290000081
In table 3, S1 and S2 correspond to the object side surface and the image side surface of the first lens element L1, S3 and S4 correspond to the object side surface and the image side surface of the second lens element L2, S6 and S7 correspond to the object side surface and the image side surface of the third lens element L3, S8 and S9 correspond to the object side surface and the image side surface of the fourth lens element L4, S10 and S11 correspond to the object side surface and the image side surface of the fifth lens element L5, and S12 and S13 correspond to the object side surface and the image side surface of the optical filter, respectively.
The aspherical coefficients of each lens of this example are shown in table 4:
TABLE 4 Table 4
Figure GDA0004139683290000082
In this embodiment, the effective focal length f1= -57.6mm of the first lens L1, the effective focal length f3=12.1 mm of the third lens L3, and the technical indexes of lens implementation are as follows:
1. focal length: f0 =9 mm;
2. f-number #f=1.61;
3. working wavelength: 436-656 nm/830-870 nm;
4. view angle 2ω:35 °;
5. optical distortion: <2%;
6. relative illuminance: 58%;
7. total optical length: <26mm.
According to the above data, the final imaging effect of the lens of this embodiment is evaluated by the MTF curves of fig. 6, and the MTF curves under each field of view gradually decrease, which indicates that the lens has good imaging effect and resolution in the whole field of view. The MTF curves of fig. 7 in the infrared band at various fields also decrease smoothly, indicating that the lens has better imaging quality in the infrared band. Fig. 8 and 9 show MTF curves at-40 ℃ and +80 ℃ respectively, and it can be seen that the lens can still maintain better image quality in a temperature environment of-40 ℃ to +80 ℃.
The technical features of the above-described embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above-described embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above-described embodiments are merely representative of the more specific and detailed embodiments described herein and are not to be construed as limiting the claims. It should be noted that it would be apparent to those skilled in the art that various modifications and improvements could be made without departing from the spirit of the present application, which would be within the scope of the present application. Accordingly, the scope of protection of the present application is to be determined by the claims appended hereto.

Claims (6)

1. The utility model provides a low-cost day night high low temperature confocal camera lens which characterized in that: the low-cost day and night high-low temperature confocal lens comprises a first lens L1, a second lens L2, a third lens L3, a fourth lens L4, a fifth lens L5 and an optical filter which are sequentially arranged from an object side to an image side along an optical axis, wherein:
the first lens L1 is a convex-concave aspheric plastic lens with positive focal power;
the second lens L2 is a concave-convex aspheric plastic lens with negative focal power;
the third lens L3 is a biconvex spherical glass lens with positive focal power;
the fourth lens L4 is a biconvex aspheric plastic lens with positive focal power;
the fifth lens L5 is a concave-convex aspheric plastic lens with negative focal power;
and the low-cost day-night high-low temperature confocal lens meets the following conditions:
f1/f0>1,5<|f1/f3|<15,0.1<f0/TTL<1.5
wherein f1 is the effective focal length of the first lens L1, f0 is the effective focal length of the lens, f3 is the effective focal length of the third lens L3, and TTL is the total optical length of the lens.
2. The low cost day-night high and low temperature confocal lens of claim 1 wherein: a STOP is arranged between the second lens L2 and the third lens L3.
3. The low cost day-night high and low temperature confocal lens of claim 1 wherein: the working wave bands of the low-cost day-night high-low temperature confocal lens are 436 n-656 nm of visible light wavelength and 830-870 nm of infrared wavelength.
4. The low cost day-night high and low temperature confocal lens of claim 1 wherein: the mirror surface of the aspheric plastic lens meets the following formula:
Figure FDA0004139683270000011
wherein z is sagittal height, c=1/r, r is surface curvature radius, h is radial coordinate, k is conical coefficient, a is fourth order coefficient, B is sixth order coefficient, C is eighth order coefficient, D is tenth order coefficient, E is twelfth order coefficient, and F is fourteenth order coefficient.
5. The low cost day-night high and low temperature confocal lens of claim 4 wherein: mirror surfaces sequentially arranged from the object side to the image side on the first lens L1, the second lens L2, the fourth lens L4 and the fifth lens L5, k corresponds to-1.21, 0.21, -0.95, -0.87, 3.25, -8.32, -6.8, -12.6 in sequence, A corresponds to 1.1e-3, 3.3e-3, 0.011, 0.022, 6.5e-3, 1.1e-3, -3.4e-3, 9.3e-4 in sequence, B corresponds to-6.8 e-5, -2.5e-4, -6.2e-4, 2.8e-4, -8.8e-4, -8.6e-4, 6.7e-4, 2.4e-4, C corresponds to 1.9e-5, 6.3e-5, -9.8e-5, -2.3e-4, 6.6e-5, 5.2e-5, 2.1e-5 in sequence, D corresponds to-1.1 e-6, -4.3.5, 2.8 e-5, -2.8 e-5, 2.7 e-5, 2.9-7 e-5, 2.9.7 e-5, 2.9-7 e-5, 6.9.9 e-5, 6.9-9, 3.9-5, 3.9-4 in sequence.
6. The low cost day-night high and low temperature confocal lens of claim 4 wherein: mirror surfaces sequentially arranged from the object side to the image side on the first lens L1, the second lens L2, the fourth lens L4 and the fifth lens L5, k corresponds to-0.54, 0.83, -1.12, -0.98, 5.45, -10.65, -4.56, -9.21 in sequence, A corresponds to 1.6e-3, 3.1e-3, 0.019, 0.012, 5.3e-3, 1.4e-3, -2.4e-3, 5.9e-4 in sequence, B corresponds to-5.1 e-5, -2.3e-4, -9.8e-4, 1.3e-4, -9.1e-4, -5.6e-4, 1.1e-3, 3.6e-4 in sequence, C corresponds to 1.5e-5, 9.3e-5, -1.1e-4, -1.5e-4, 7.9e-5, 4.8e-5, 4-1.5 e-4, 5.5e-6,D, in turn, -1.4e-6, -1.5e-5, 1.1e-5, 1.2e-5, -6.4e-6, -3.4e-6, 5.7e-6, -1.6e-6,E, in turn, -4.4 e-8, -6.1 e-7, -6.3e-8, -2.5e-7, 1.9e-7, 1.1e-7, -1.2e-7, 4.8e-8,F, in turn, -2.7e-9, -2.3e-10, -1.2e-9, -4.2e-9, -1.2e-9, -9.2e-10, -5.2e-9, -3.1e-10.
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