CN113514425A

CN113514425A - Calibration device and calibration method for refractive index of planar medium with equal thickness

Info

Publication number: CN113514425A
Application number: CN202111071946.3A
Authority: CN
Inventors: 不公告发明人
Original assignee: Suzhou Gaoshi Semiconductor Technology Co ltd
Current assignee: Suzhou Gaoshi Semiconductor Technology Co ltd
Priority date: 2021-09-14
Filing date: 2021-09-14
Publication date: 2021-10-19
Anticipated expiration: 2041-09-14
Also published as: CN113514425B

Abstract

The embodiment of the application discloses a calibration device and a calibration method for the refractive index of a plane uniform-thickness medium, wherein the calibration device comprises a spectrum confocal sensor spectrometer and a distance adjusting mechanism, wherein the spectrum confocal sensor comprises a white light point light source, a semi-transparent semi-reflecting mirror and a dispersion objective lens; the semi-transparent and semi-reflective mirror and the dispersive objective lens are sequentially arranged between the white light point light source and the measured medium along an optical axis, the semi-transparent and semi-reflective mirror is close to the white light point light source, and the dispersive objective lens is close to the side of the measured medium; and calculating a refractive index curve of the measured medium according to the refractive indexes of the middle 4 wavelengths in the 6 different wavelengths obtained by detection, and then calibrating by using the refractive indexes of the two wavelengths. According to the invention, the precision of the predicted refractive index curve can be improved by correcting the wavelength term coefficient in the apochromatic characteristic formula, so that the accurate refractive index formula of the tested sample is obtained, and the accurate refractive index curve of the sample is obtained at the same time.

Description

Calibration device and calibration method for refractive index of planar medium with equal thickness

Technical Field

The invention relates to the field of transparent material refractive index calibration, in particular to a device and a method for calibrating a plane uniform-thickness medium refractive index.

Background

The refractive index is one of the basic parameters of optical materials, and the refractive index of a material generally decreases with increasing wavelength of incident light, and the difference in refractive index at different wavelengths is called dispersion. The research on the refractive index and the dispersion of the glass is significant for understanding the properties of the glass material and is also an indispensable parameter in the design of an optical system, and the size of the glass directly influences the imaging quality of the system. The accurate obtaining of the refractive index of the optical material in the visible and near infrared bands is very important to the production, use and optical design of the optical material.

The refractive index of the conventional transparent medium is fitted by using a Schott formula or a Sellmeier formula, and although the fitting result is more accurate, the fitting data is more. If the Conrady formula or Cauchy formula can be used under the condition that only a small number of points exist, the calculation accuracy of the two formulas is not high, the applicable waveband range is short, and the method is not suitable for accurately calculating the refractive index curve.

The refractive index curve is usually only a monotonous curve, theoretically, the refractive index curve can be very accurately represented in a longer wave band range by using an apochromatic property formula (ACF formula), and the ACF formula can be calculated by only needing a small amount of data, and has very important value in actual measurement. The VNIR band of 400-1100 nm is a very common band in optics, but the ACF formula is a formula set, which is described in "research on typical transmission system multi-wavelength wavefront detection method (university of vinpocetine, 2019), wherein the coefficient of the wavelength term is not uniquely determined, and for refractive indices of different materials, the ACF formula with different coefficient of the wavelength term is required to obtain a very precise refractive index curve. And plane medium such as glass with equal thickness can be provided by a plurality of manufacturers, and each manufacturer can provide hundreds to thousands of mediums, and many glasses can not use the same standard ACF formula, namely, the refractive index of the material in the wave band of 400-1100 nm is calculated by using a determined ACF formula, so that the refractive index accuracy of some calculated materials is higher, and the refractive index accuracy of some calculated materials is not high.

In order to more accurately obtain the ACF formula for representing the refractive index of a known or unknown material and to more accurately measure the refractive index of the corresponding known or unknown material, it is necessary to develop a calibration apparatus and a calibration method for the refractive index of a planar uniform-thickness medium, so as to solve the above problems.

Disclosure of Invention

The embodiment of the application provides a calibration device, a calibration method and a calibration method for the refractive index of a plane medium with the same thickness, which can improve the precision of a predicted refractive index curve by correcting a wavelength term coefficient in an ACF formula, further obtain an accurate refractive index formula of a measured sample, and simultaneously obtain an accurate refractive index curve of the sample.

In order to solve the above technical problem, an embodiment of the present application discloses the following technical solutions:

on one hand, the device for calibrating the plane uniform-thickness medium refractive index comprises a spectrum confocal sensor spectrometer and a distance adjusting mechanism, wherein the spectrum confocal sensor comprises a white light point light source, a semi-transparent semi-reflecting mirror and a dispersion objective lens; the semi-transparent and semi-reflective mirror and the dispersive objective lens are sequentially arranged between the white light point light source and the measured medium along an optical axis, the semi-transparent and semi-reflective mirror is close to the white light point light source, and the dispersive objective lens is close to the side of the measured medium; the distance adjusting mechanism drives the spectrum confocal sensor and the measured medium to be close to or far away from each other so that the distance between the dispersion objective lens and the measured medium changes 5 times along the optical axis; the spectrometer is opposite to the reflecting surface of the semi-transparent and semi-reflective mirror and is used for detecting the wavelength of the monochromatic light which is focused and reflected on the measured medium; detecting according to a spectrum confocal principle to obtain the refractive indexes of 6 monochromatic light wavelengths, sequencing the 6 monochromatic light wavelengths according to the wavelength, calculating a refractive index curve of a detected medium (13) by taking the refractive indexes of 4 monochromatic light wavelengths with the wavelengths in the middle position, and correcting a refractive index formula by using the refractive indexes of the remaining 2 monochromatic light wavelengths; and when the error between the residual 2 wavelength refractive indexes in the corrected refractive index curve and the actually measured residual 2 wavelength refractive indexes is smaller than a set threshold value, the calibration is considered to be successful.

Optionally, the set threshold is 0.003% -0.005%.

Optionally, defining:

the thickness of the plane uniform-thickness medium is H;

the plurality of monochromatic lights decomposed by the dispersion objective lens are composed of at least one monochromatic light subset, and each monochromatic light subset comprises an upper monochromatic light and a lower monochromatic light; the upper monochromatic light in each monochromatic photon set is focused on the upper surface of the measured medium, and the lower monochromatic light in each monochromatic photon set is focused on the lower surface of the measured medium;

the wavelength of the lower monochromatic light in each monochromatic photon set is lambda;

the incident angle of the lower monochromatic light of each monochromatic photon concentration is

；

The focal distance between the upper monochromatic light and the lower monochromatic light in each monochromatic photon concentration is

(ii) a The refractive index of the measured medium at the wavelength λ

Is derived from the following formula:

，

wherein the content of the first and second substances,

and

is a known parameter of dispersive objective lenses in spectroscopic confocal sensors.

Optionally, defining:

when the distance between the dispersion objective lens and the measured medium is not changed, the wavelength of the upper monochromatic light is lambda₁Wavelength of the lower monochromatic light is λ₂；

When the distance between the dispersion objective lens and the measured medium is changed for the first time, the wavelength of the upper monochromatic light is lambda₃Wavelength of the lower monochromatic light is λ₄；

When the distance between the dispersion objective lens and the measured medium changes for the second time, the wavelength of the upper monochromatic light is lambda₅Wavelength of the lower monochromatic light is λ₆；

When the distance between the dispersion objective lens and the measured medium changes for the third time, the wavelength of the upper monochromatic light is lambda₇Wavelength of the lower monochromatic light is λ₈；

The distance between the dispersive objective lens and the measured medium is changed for the fourth timeWhen in use, the wavelength of the upper monochromatic light is lambda₉Wavelength of the lower monochromatic light is λ₁₀

When the distance between the dispersion objective lens and the measured medium is changed for the fifth time, the wavelength of the upper monochromatic light is lambda₁₁Wavelength of the lower monochromatic light is λ₁₂(ii) a Then the incident angle of each monochromatic light can be obtained

And has the following components:

，

λ is a wavelength according to the wavelength₂、λ₄、λ₆、λ₈、λ₁₀And lambda₁₂The lower monochromatic light of (2) is sequenced and set

The range of the power series of the wavelength term in the formula is determined by using the wavelength corresponding to the 4 monochromatic lights with the wavelength being in the middle region according to the refractive index

Calculating a refractive index profile of the measured medium (13), wherein the wavelength term is a power series X₁、X₂And X₃Taking the minimum value of the set range;

by the formula

Calculating the refractive index of the wavelength corresponding to the residual 2 monochromatic light, calculating the error between the refractive index of the wavelength corresponding to the actually measured residual 2 monochromatic light and the calculated refractive index of the wavelength corresponding to the residual 2 monochromatic light, and if the error is greater than the set threshold, adjusting the coefficient X₁、X₂And X₃Until the error is less than the set threshold.

Optionally, the wavelength term power series is set in the following range: x is more than or equal to 0.1₁≤3，3.1≤X₂≤8，0.1≤X₃≤5。

In another aspect, a method for calibrating the refractive index of a planar medium with equal thickness is provided, which comprises the following steps:

providing a calibration device, wherein the calibration device comprises a spectrum confocal sensor, a spectrometer and a distance adjusting mechanism, wherein the spectrum confocal sensor comprises a white light point light source, a semi-transparent semi-reflecting mirror and a dispersion objective lens; the semi-transparent and semi-reflective mirror (X) and the dispersive objective lens are sequentially arranged between the white light point light source and the measured medium along an optical axis, the semi-transparent and semi-reflective mirror (X) is close to the white light point light source, and the dispersive objective lens is close to the side of the measured medium;

the distance adjusting mechanism drives the spectrum confocal sensor and the measured medium to be close to or far away from each other so that the distance between the dispersion objective lens and the measured medium changes 5 times along the optical axis;

the spectrometer is arranged opposite to the reflecting surface of the semi-permeable and semi-reflective mirror and is used for detecting the wavelength of monochromatic light which is focused and reflected on a measured medium;

detecting according to a spectrum confocal principle to obtain the refractive indexes of 6 monochromatic light wavelengths, sequencing the 6 monochromatic light wavelengths according to the wavelength, calculating a refractive index curve of a detected medium (13) by taking the refractive indexes of 4 monochromatic light wavelengths with the wavelengths in the middle position, and correcting a refractive index formula by using the refractive indexes of the remaining 2 monochromatic light wavelengths;

and when the error between the residual 2 wavelength refractive indexes in the corrected refractive index curve and the actually measured residual 2 wavelength refractive indexes is smaller than a set threshold value, the calibration is considered to be successful.

Optionally, the set threshold is 0.003% -0.005%.

Optionally, defining:

the thickness of the plane uniform-thickness medium is H;

；

(ii) a The refractive index of the measured medium at the wavelength λ

Is derived from the following formula:

，

wherein the content of the first and second substances,

and

Optionally, defining:

When the distance between the dispersion objective lens and the measured medium is changed for the fourth time, the wavelength of the upper monochromatic light is lambda₉Wavelength of the lower monochromatic light is λ₁₀

And has the following components:

，

by the formula

One of the above technical solutions has the following advantages or beneficial effects: the accuracy of the predicted refractive index curve can be improved by correcting the wavelength term coefficient in the ACF formula, so that the accurate refractive index formula of the measured sample is obtained, and the accurate refractive index curve of the sample is obtained at the same time.

Another technical scheme in the above technical scheme has the following advantages or beneficial effects: the refractive index measurement under 6 different wavelengths can be quickly realized by changing the distance between the dispersion objective lens and the measured medium for 5 times along the optical axis, the refractive index curve of the measured medium can be accurately calculated only according to the middle 4 wavelengths in the 6 different wavelengths obtained by detection, and the calculated refractive index curve can be corrected by utilizing 2 wavelengths at the edge so as to further improve the precision of the refractive index curve.

Drawings

In order to more clearly illustrate the technical solution of the embodiments of the present invention, the drawings of the embodiments will be briefly described below, and it is apparent that the drawings in the following description relate only to some embodiments of the present invention and are not limiting thereof, wherein:

FIG. 1 is a front view of a device for calibrating the refractive index of a planar medium with equal thickness according to an embodiment of the present invention;

FIG. 2 is a schematic diagram and an optical path structure of a device for calibrating a refractive index of a planar medium with equal thickness according to an embodiment of the present invention;

fig. 3 is a schematic diagram illustrating a principle of chromatic dispersion of a spectral confocal sensor in a calibration apparatus for refractive index of a planar uniform-thickness medium according to an embodiment of the present invention;

fig. 4 is a schematic diagram illustrating a principle that a spectral confocal sensor in a calibration apparatus for refractive index of a planar uniform-thickness medium measures the refractive index of the medium at a current wavelength according to an embodiment of the present invention;

FIG. 5 is a schematic diagram illustrating the variation of the focal length of the objective lens L from 350 to 1100 nm;

FIG. 6 is a point diagram of focal positions of a dispersive objective lens in a device for calibrating refractive index of a planar uniform-thickness medium according to an embodiment of the present invention at different wavelengths;

FIG. 7 is a comparison of the curve calculated by ACF formula using four wavelengths of 500, 600, 700, 800nm with the collected data;

FIG. 8 is a comparison of the curve calculated by ACF formula using four wavelengths of 500, 600, 700, 800nm with the collected data;

FIG. 9 is a flowchart illustrating a method for calibrating a refractive index of a planar uniform-thickness medium according to an embodiment of the present invention;

FIG. 10 is a graph illustrating the error of the refractive index profile of the SF66 glass material calculated by the calibrated equation;

fig. 11 shows the error of the refractive index curve of the SF66 glass material calculated by the formula after calibration.

Detailed Description

The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.

In the drawings, the shape and size may be exaggerated for clarity, and the same reference numerals will be used throughout the drawings to designate the same or similar components.

Unless defined otherwise, technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs. The use of "first," "second," and similar terms in the description and claims of the present application do not denote any order, quantity, or importance, but rather the terms are used to distinguish one element from another. Also, the use of the terms "a," "an," or "the" and similar referents do not denote a limitation of quantity, but rather denote the presence of at least one. The word "comprise" or "comprises", and the like, means that the element or item listed before "comprises" or "comprising" covers the element or item listed after "comprising" or "comprises" and its equivalents, and does not exclude other elements or items. "upper", "lower", "left", "right", and the like are used merely to indicate relative positional relationships, and when the absolute position of the object being described is changed, the relative positional relationships may also be changed accordingly.

In the following description, terms such as center, thickness, height, length, front, back, rear, left, right, top, bottom, upper, lower, etc., are defined with respect to the configurations shown in the respective drawings, and in particular, "height" corresponds to a dimension from top to bottom, "width" corresponds to a dimension from left to right, "depth" corresponds to a dimension from front to rear, which are relative concepts, and thus may be varied accordingly depending on the position in which it is used, and thus these or other orientations should not be construed as limiting terms.

Terms concerning attachments, coupling and the like (e.g., "connected" and "attached") refer to a relationship wherein structures are secured or attached, either directly or indirectly, to one another through intervening structures, as well as both movable or rigid attachments or relationships, unless expressly described otherwise.

Example one

Referring to fig. 1 to 4, fig. 1 is a front view of a device 1 for calibrating a refractive index of a planar medium with a uniform thickness according to an embodiment of the present invention. In order to obtain a more accurate refractive index formula of a material and measure a more accurate refractive index of the material, the calibration device 1 provided in this embodiment includes a spectrum confocal sensor 11 and a spectrometer 14, and is characterized by further including a distance adjusting mechanism, wherein the spectrum confocal sensor 11 includes a white light point light source S, a semi-transparent semi-reflective mirror X and a dispersive objective lens L; the semi-transparent semi-reflecting mirror X and the dispersive objective lens L are sequentially arranged between the white light point light source S and the measured medium 13 along an optical axis, the semi-transparent semi-reflecting mirror X is close to the white light point light source S, and the dispersive objective lens L is close to the measured medium 13 side; the distance adjusting mechanism drives the spectrum confocal sensor 11 and the measured medium 13 to be close to or far away from each other so that the distance between the dispersive objective lens L and the measured medium 13 changes 5 times along the optical axis; the spectrometer 14 is opposite to the reflecting surface of the semi-transparent and semi-reflective mirror X and is used for detecting the wavelength of the monochromatic light focused and reflected on the measured medium 13; detecting the refractive index of 6 monochromatic light wavelengths according to a spectrum confocal principle, sequencing the 6 monochromatic light wavelengths according to the wavelength, calculating a refractive index curve of the detected medium 13 by taking the refractive indexes of 4 monochromatic light wavelengths with the wavelengths in the middle position, and correcting a refractive index formula by using the refractive indexes of the remaining 2 monochromatic light wavelengths; and when the error between the residual 2 wavelength refractive indexes in the corrected refractive index curve and the actually measured residual 2 wavelength refractive indexes is smaller than a set threshold value, the calibration is considered to be successful.

Further, the set threshold is 0.003% -0.005%. In this embodiment, the set threshold is 0.005%, i.e. the refractive index error is less than 0.005%, and the calibration is considered to be successful, and the actual refractive index curve and the predicted refractive index curve are almost coincident.

In the present embodiment, the measured medium 13 is placed on the platform 12 below the dispersive objective lens L, and the distance between the dispersive objective lens L and the measured medium 13 can be adjusted by lifting the platform 12 or the spectral confocal sensor 11. Referring to fig. 2, fig. 2 shows a light path schematic diagram of a spectral confocal sensor 11, which is an optical system that produces an image S' of a point source S on the surface of a medium, the backscattered light being collected by the same optical system that is imaged at a pinhole S ″.

The pinhole S ″ is placed in front of the photodetector 14 so that light of a specific wavelength reflected back from the surface of the medium can pass through and light of wavelengths at other positions is blocked, and therefore it is also referred to as a "spatial filter". The spectral confocal sensor is characterized by a special signal-to-noise ratio. According to the principle of spectral confocal, the optical system is a dispersive lens and the photodetector 14 is a spectrometer. The spectrometer signal exhibits a spectral peak corresponding to the spectral redistribution of the collected light. The spectral peak on the spectrometer changes as the medium is displaced within the measurement range. In this embodiment, the measured medium 13 has the characteristic of equal thickness, and may be a glass material, a crystal material, a transparent film material, a liquid crystal material, a transparent liquid material, or a transparent plastic material.

Referring again to fig. 2, define:

the thickness of the plane uniform-thickness medium is H;

the plurality of monochromatic lights decomposed by the dispersion objective lens L are composed of at least one monochromatic light subset, and each monochromatic light subset comprises an upper monochromatic light and a lower monochromatic light; the upper monochromatic light in each monochromatic photon set is focused on the upper surface of the measured medium 13, and the lower monochromatic light in each monochromatic photon set is focused on the lower surface of the measured medium 13;

；

(ii) a The refractive index of the measured medium 13 at the wavelength λ

Is derived from the following formula:

，

wherein the content of the first and second substances,

and

is a known parameter of the dispersive objective lens L in the spectroscopic confocal sensor 11.

The dispersion objective lens L in the spectrum confocal sensor is a core optical component, an important index in the dispersion objective lens is the dispersion degree, namely the distance of focuses with different wavelengths, the usable wavelength of the dispersion objective lens designed in the embodiment is 350-1100 nm, the dispersion range distance of the conventional dispersion objective lens is small, and the dispersion distance of a 350-1000 nm wave band in the dispersion objective lens L designed in the embodiment is about 100 mm. FIG. 5 shows the focal length variation from 350-1100 nm of the dispersive objective lens L designed in this embodiment, in which the focal length at the leftmost end is 350nm and the focal length at the rightmost end is 1100 nm. Specific parameters of the dispersive objective lens are given in table 1, and the relation data of the wavelength of the dispersive objective lens L and the rear intercept position are given in table 2:

TABLE 1 Dispersion Objective lens parameters

Radius of	Thickness of	Material
			-447.5490655	15	SF5
1018.981527	15
			-362.2092075	20	LASFN31
-163.217273	1.500246975
			381.2234648	20	LASFN31
-361.9773786	2
			186.9408128	20	SF5
-1148.928833	12	LASFN31
			315.0239796	14.99996772
79.14349559	16	SF5
			69.61822764	303.3756885

TABLE 2 wavelength and back intercept position of dispersive objective (back intercept refers to the distance from the last surface of the lens to the focal point)

Wavelength (nm)	350	400	500	600	700	800	900	1000	1100
										Rear intercept (mm)	207.641	230	257.581	273.511	283.685	290.719	295.919	300	303.376

Referring to fig. 6, a point diagram of the focal position of the dispersive objective lens at different wavelengths is shown, and it can be seen that each wavelength point diagram of the dispersive objective lens L in this embodiment at a wavelength band of 350 to 1100nm is within a diffraction limit, and the image quality is good, so that the detection requirement of this embodiment can be satisfied.

Further, defining:

when the distance between the dispersion objective lens (L) and the measured medium (13) is not changed, the wavelength of the upper monochromatic light is lambda₁Wavelength of the lower monochromatic light is λ₂；

When the distance between the dispersion objective lens (L) and the measured medium (13) is changed for the first time, the wavelength of the upper monochromatic light is lambda₃Wavelength of the lower monochromatic light is λ₄；

When the distance between the dispersion objective lens (L) and the measured medium (13) changes for the second time, the wavelength of the upper monochromatic light is lambda₅Wavelength of the lower monochromatic light is λ₆；

When the distance between the dispersion objective lens (L) and the measured medium (13) changes for the third time, the wavelength of the upper monochromatic light is lambda₇Wavelength of the lower monochromatic light is λ₈；

When the distance between the dispersion objective lens (L) and the measured medium (13) is changed for the fourth time, the wavelength of the upper monochromatic light is lambda₉Wavelength of the lower monochromatic light is λ₁₀

When the distance between the dispersion objective lens (L) and the measured medium (13) changes for the fifth time, the wavelength of the upper monochromatic light is lambda₁₁Wavelength of the lower monochromatic light is λ₁₂(ii) a Then the incident angle of each monochromatic light can be obtained

And has the following components:

，

Formula medium waveThe range of the long term power series is determined by using the wavelength corresponding to the 4 monochromatic lights with the wavelength in the middle region according to the refractive index

Calculating the refractive index curve of the measured medium 13, wherein the wavelength term is power series X₁、X₂And X₃Taking the minimum value of the set range;

by the formula

In this example, the wavelength term power series is set to a range of: x is more than or equal to 0.1₁≤3，3.1≤X₂≤8，0.1≤X₃≤5。

Further, the dispersive objective lens is a lens with large dispersion and large NA, and the focal positions and corresponding angles of different wavelengths are different, but the objective lens can be expressed by an ACF formula. The formula of the angle and the wavelength of the dispersive objective lens is given as follows:

（1）

in the present embodiment, there is defined:

A_θ=7.527112332；

B_θ=295192.053；

C_θ=3121436248142；

D_θ=-0.0001857713779；

substituting into equation (1) yields:

，

fig. 7 is a comparison between an angle-wavelength curve calculated by an ACF formula using four wavelength angle data of 500 nm, 600nm, 700nm, and 800nm and acquired data, where the curve is calculated according to the above formula, and the circle is data acquired by a spectral confocal system, it can be seen that actual data is highly consistent with calculated values, and further, a corresponding relationship between an exit angle of any edge light and a wavelength can be calculated according to formula (1).

The same reasoning gives the formula of the back intercept and the wavelength:

，

in this example, the following are given:

A_l=301.5655938；

B_l=-12595691.497；

C_l=-29136610073690；

D_l=0.010931337642；

further, it is found that:

（2），

referring to fig. 8, the back intercept-wavelength curve calculated by the ACF formula (3) using the back intercept data of four wavelengths of 500, 600, 700nm, and 800nm in this embodiment is compared with the acquired data, the curve is calculated according to the above formula, and the circle is the data acquired by measurement, so that the calculated value and the acquired value are better matched. Thus, the back intercept at any wavelength and the interval between any two wavelengths can be calculated according to the formula (2)

。

When the thickness H of the slab-like medium is known, it can be calculated according to the formula:

（3），

the refractive index of 6 wavelengths is obtained by calculation

。

FIG. 9 shows a procedure for calibrating the refractive index of a planar uniform-thickness medium.

In the present embodiment, 520nm, 600nm, 680nm and 760nm (i.e., respectively, in this order) are further used

、

) The refractive index curve is obtained by solving the ACF formula (4),

（4）

the refractive index measurements at 400nm and 1100nm (i.e. in turn, respectively) were then used

And

) Comparing with the refractive indexes of 400nm and 1100nm calculated by the ACF formula (4), when the errors of 400nm and 1100nm are less than 0.005% (other error ranges can be set, and the coefficient ranges are different according to different ranges), outputting the corresponding coefficient ACF formula, drawing the corresponding refractive index curve according to the coefficient of the ACF formula, and inputting and outputting the coefficient and the error of each wavelength term into the table. In this example, the refractive index formula of 400nm and 1100nm calibration is used (the range of calibration wavelength determines the range of the refractive index curve to be calculated accurately), wherein the range of the 350-400 nm band dispersion lens is 22mm (400 nm is at the lower surface), so the thickness of the flat plate material should be within 30mm (when the refractive index of the material is 400nm, the minimum refractive index is 1.4). FIGS. 10 to 11 showRespectively give out X₁=2.1，X₂=6.4，X₃=3.2；X₁=2.5，X₂=7.8，X₃SF66 glass material refractive index profile error calculated with ACF at = 0.3. Table 3 gives the coefficients and nominal wavelength error of the ACF equation for SF66 refractive index:

TABLE 3 coefficients and nominal wavelength error for ACF equation conforming to SF66 refractive index

X₁	X₂	X₃	400nm error (%)	1100nm error (%)
					2.1	6.4	3.1	0.001773	-0.00432
2.1	6.4	3.2	0.002217	-0.00358
					2.1	6.4	3.3	0.002654	-0.00281
2.1	6.4	3.4	0.003085	-0.00202
					2.1	6.4	3.5	0.003508	-0.0012
2.1	6.4	3.6	0.003925	-0.00037
					2.1	6.4	3.7	0.004335	0.000487
2.2	6.7	1.6	0.002396	-0.00496
					2.2	6.7	1.7	0.003526	-0.00403
2.2	6.7	1.8	0.004637	-0.00308
					2.2	6.8	1.8	-0.0029	-0.00428
2.2	6.8	1.9	-0.00182	-0.00333
					2.2	6.8	2	-0.00075	-0.00236
2.2	6.8	2.1	0.000296	-0.00135
					2.2	6.8	2.2	0.001327	-0.00032
2.2	6.8	2.3	0.002342	0.000732
					2.2	6.8	2.4	0.003341	0.001816
2.2	6.8	2.5	0.004324	0.002929
					2.2	6.9	2.5	-0.00345	0.001527
2.2	6.9	2.6	-0.00249	0.002636
					2.2	6.9	2.7	-0.00155	0.003775
2.2	6.9	2.8	-0.00062	0.004944
					2.3	7	0.9	0.003563	-0.00411
2.3	7.1	0.9	-0.00318	-0.00488
					2.3	7.1	1	-0.0011	-0.00372
2.3	7.1	1.1	0.000951	-0.00253
					2.3	7.1	1.2	0.002965	-0.00132
2.3	7.1	1.3	0.004946	-6.6E-05
					2.3	7.2	1.2	-0.00388	-0.00212
2.3	7.2	1.3	-0.00188	-0.00089
					2.3	7.2	1.4	7.93E-05	0.000378
2.3	7.2	1.5	0.002011	0.001677
					2.3	7.2	1.6	0.003911	0.003009
2.3	7.3	1.6	-0.00303	0.002152
					2.3	7.3	1.7	-0.00114	0.003501
2.3	7.3	1.8	0.00071	0.004886
					2.4	7.3	0.4	0.003498	-0.00396
2.4	7.4	0.4	-0.00265	-0.00451
					2.4	7.4	0.5	0.000715	-0.0031
2.4	7.4	0.6	0.004027	-0.00166
					2.4	7.5	0.6	-0.00216	-0.00222
2.4	7.5	0.7	0.00115	-0.00075
					2.4	7.5	0.8	0.004402	0.000759
2.4	7.6	0.8	-0.00182	0.000197
					2.4	7.6	0.9	0.001431	0.001734
2.4	7.6	1	0.004625	0.00331
					2.4	7.7	0.9	-0.00487	0.001174
2.4	7.7	1	-0.00163	0.002742
					2.4	7.7	1.1	0.001561	0.004351
2.4	7.8	1.1	-0.00478	0.003784
					2.5	7.8	0.3	0.004714	-0.00035
2.5	7.9	0.3	-0.00096	-0.00075
					2.5	7.9	0.4	0.004008	0.001014
2.5	8	0.4	-0.0017	0.000618
					2.5	8	0.5	0.003286	0.002425

When X is present₁，X₂And X₃Taking the above coefficients, the refractive index profile of SF66 has errors of less than 0.005% at both 400 and 1100 nm. The error of the refractive index curve is usually solved by a large error in the wavelength at both ends, so that the whole refractive index curve is very accurate in the case of a small error of 400nm and 1100nm in the present example.

Table 4 gives the coefficients and nominal wavelength error for an ACF equation that corresponds to the refractive index of N-LASF 9:

TABLE 4 coefficients and nominal wavelength error for ACF equation conforming to refractive index of N-LASF9

X₁	X₂	X₃	400nm error (%)	1100nm error (%)
					1.8	4.9	3.4	0.002502	-0.00434
1.8	4.9	3.5	0.002806	-0.00353
					1.9	5.2	3	0.002051	-0.00222
1.9	5.2	3.1	0.002522	-0.00124
					1.9	5.2	3.2	0.002984	-0.00024
1.9	5.2	3.3	0.00344	0.00079
					1.9	5.2	3.4	0.003888	0.001848
1.9	5.2	3.5	0.004329	0.002935
					1.9	5.3	3	-0.00191	-0.00376
1.9	5.3	3.1	-0.00145	-0.00282
					1.9	5.3	3.2	-0.001	-0.00186
1.9	5.3	3.3	-0.00055	-0.00087
					1.9	5.3	3.4	-0.00012	0.000145
1.9	5.3	3.5	0.000317	0.001188
					1.9	5.4	3.3	-0.00463	-0.0025
1.9	5.4	3.4	-0.0042	-0.00153
					1.9	5.4	3.5	-0.00378	-0.00053
2	5.6	3	0.00301	0.003587
					2	5.6	3.1	0.003678	0.004844
2	5.7	3	-0.00054	0.002428
					2	5.7	3.1	0.000123	0.003659
2	5.7	3.2	0.000779	0.004922
					2	5.8	3	-0.00417	0.001291
2	5.8	3.1	-0.00351	0.002494
					2	5.8	3.2	-0.00285	0.00373
2	5.8	3.3	-0.00221	0.005

Table 5 gives the coefficients and nominal wavelength error for an ACF equation that corresponds to the index of refraction of H-K9L:

TABLE 5 coefficients and nominal wavelength error for ACF equation conforming to refractive index H-K9L

X₁	X₂	X₃	400nm error (%)	1100nm error (%)
					1	3	2.9	-0.00456	-0.0043
1	3	3	-0.00435	-0.00354
					1	3	3.1	-0.00414	-0.00276
1	3	3.2	-0.00393	-0.00196
					1	3	3.3	-0.00373	-0.00114
1	3	3.4	-0.00353	-0.00029
					1	3	3.5	-0.00333	0.000576
1.1	3	2.6	-0.00414	-0.00491
					1.1	3	2.7	-0.00389	-0.00413
1.1	3	2.8	-0.00364	-0.00333
					1.1	3	2.9	-0.00339	-0.0025
1.1	3	3	-0.00315	-0.00166
					1.1	3	3.1	-0.00292	-0.00079
1.1	3	3.2	-0.00268	0.000103
					1.1	3	3.3	-0.00245	0.001018
1.1	3	3.4	-0.00222	0.001957
					1.1	3	3.5	-0.002	0.00292
1.1	3.1	2.9	-0.00487	-0.00401
					1.1	3.1	3	-0.00464	-0.0032
1.1	3.1	3.1	-0.00441	-0.00238
					1.1	3.1	3.2	-0.00418	-0.00153
1.1	3.1	3.3	-0.00396	-0.00066
					1.1	3.1	3.4	-0.00374	0.000232
1.1	3.1	3.5	-0.00352	0.001148
					1.2	3	2.5	-0.00334	-0.00423
1.2	3	2.6	-0.00305	-0.00339
					1.2	3	2.7	-0.00276	-0.00253
1.2	3	2.8	-0.00248	-0.00165
					1.2	3	2.9	-0.00221	-0.00074
1.2	3	3	-0.00194	0.000189
					1.2	3	3.1	-0.00167	0.001143
1.2	3	3.2	-0.00141	0.002122
					1.2	3	3.3	-0.00115	0.003127
1.2	3	3.4	-0.0009	0.004158
					1.2	3.1	2.6	-0.00437	-0.00462
1.2	3.1	2.7	-0.00409	-0.0038
					1.2	3.1	2.8	-0.00381	-0.00295
1.2	3.1	2.9	-0.00354	-0.00208
					1.2	3.1	3	-0.00328	-0.00118
1.2	3.1	3.1	-0.00302	-0.00026
					1.2	3.1	3.2	-0.00276	0.000677
1.2	3.1	3.3	-0.00251	0.001644
					1.2	3.1	3.4	-0.00226	0.002636
1.2	3.1	3.5	-0.00201	0.003655
					1.2	3.2	2.9	-0.0049	-0.00339
1.2	3.2	3	-0.00464	-0.00253
					1.2	3.2	3.1	-0.00439	-0.00165
1.2	3.2	3.2	-0.00414	-0.00074
					1.2	3.2	3.3	-0.00389	0.000189
1.2	3.2	3.4	-0.00364	0.001143
					1.2	3.2	3.5	-0.0034	0.002122
1.2	3.3	3.5	-0.00482	0.000619
					1.3	3	2.3	-0.00291	-0.00456
1.3	3	2.4	-0.00258	-0.0037
					1.3	3	2.5	-0.00225	-0.00281
1.3	3	2.6	-0.00193	-0.0019
					1.3	3	2.7	-0.00161	-0.00096
1.3	3	2.8	-0.0013	2.25E-07
					1.3	3	2.9	-0.001	0.000986
1.3	3	3	-0.0007	0.001997
					1.3	3	3.1	-0.0004	0.003034
1.3	3	3.2	-0.00011	0.004099
					1.3	3.1	2.4	-0.00375	-0.00473
1.3	3.1	2.5	-0.00343	-0.00387
					1.3	3.1	2.6	-0.00311	-0.00298
1.3	3.1	2.7	-0.0028	-0.00207
					1.3	3.1	2.8	-0.00249	-0.00114
1.3	3.1	2.9	-0.00219	-0.00018
					1.3	3.1	3	-0.00189	0.000798
1.3	3.1	3.1	-0.0016	0.001806
					1.3	3.1	3.2	-0.00131	0.00284
1.3	3.1	3.3	-0.00103	0.003902
					1.3	3.1	3.4	-0.00075	0.004992
1.3	3.2	2.5	-0.00463	-0.00491
					1.3	3.2	2.6	-0.00432	-0.00405
1.3	3.2	2.7	-0.00401	-0.00316
					1.3	3.2	2.8	-0.0037	-0.00226
1.3	3.2	2.9	-0.00341	-0.00133
					1.3	3.2	3	-0.00311	-0.00038
1.3	3.2	3.1	-0.00282	0.000601
					1.3	3.2	3.2	-0.00254	0.001605
1.3	3.2	3.3	-0.00225	0.002636
					1.3	3.2	3.4	-0.00198	0.003694
1.3	3.2	3.5	-0.00171	0.00478
					1.3	3.3	2.8	-0.00494	-0.00336
1.3	3.3	2.9	-0.00465	-0.00246
					1.3	3.3	3	-0.00435	-0.00153
1.3	3.3	3.1	-0.00407	-0.00058
					1.3	3.3	3.2	-0.00378	0.000393
1.3	3.3	3.3	-0.00351	0.001393
					1.3	3.3	3.4	-0.00323	0.00242
1.3	3.3	3.5	-0.00297	0.003474
					1.3	3.4	3.3	-0.00479	0.000174
1.3	3.4	3.4	-0.00451	0.00117
					1.3	3.4	3.5	-0.00425	0.002193
1.4	3	2.2	-0.00224	-0.00422
					1.4	3	2.3	-0.00187	-0.00331
1.4	3	2.4	-0.0015	-0.00238
					1.4	3	2.5	-0.00114	-0.00142
1.4	3	2.6	-0.00079	-0.00043
					1.4	3	2.7	-0.00044	0.000576
1.4	3	2.8	-0.0001	0.001612
					1.4	3	2.9	0.000235	0.002676
1.4	3	3	0.000566	0.003767
					1.4	3	3.1	0.000892	0.004887
1.4	3.1	2.3	-0.00291	-0.00419
					1.4	3.1	2.4	-0.00255	-0.00328
1.4	3.1	2.5	-0.00219	-0.00234
					1.4	3.1	2.6	-0.00183	-0.00137
1.4	3.1	2.7	-0.00149	-0.00038
					1.4	3.1	2.8	-0.00115	0.000629
1.4	3.1	2.9	-0.00081	0.00167
					1.4	3.1	3	-0.00048	0.002738
1.4	3.1	3.1	-0.00016	0.003834
					1.4	3.1	3.2	0.000164	0.004959
1.4	3.2	2.4	-0.00361	-0.00416
					1.4	3.2	2.5	-0.00325	-0.00324
1.4	3.2	2.6	-0.0029	-0.00229
					1.4	3.2	2.7	-0.00255	-0.00133
1.4	3.2	2.8	-0.00221	-0.00033
					1.4	3.2	2.9	-0.00188	0.000683
1.4	3.2	3	-0.00155	0.001728
					1.4	3.2	3.1	-0.00122	0.002801
1.4	3.2	3.2	-0.0009	0.003902
					1.4	3.3	2.5	-0.00434	-0.00412
1.4	3.3	2.6	-0.00399	-0.0032
					1.4	3.3	2.7	-0.00364	-0.00225
1.4	3.3	2.8	-0.0033	-0.00128
					1.4	3.3	2.9	-0.00297	-0.00028
1.4	3.3	3	-0.00264	0.000738
					1.4	3.3	3.1	-0.00231	0.001787
1.4	3.3	3.2	-0.002	0.002865
					1.4	3.3	3.3	-0.00168	0.003971
1.4	3.4	2.7	-0.00475	-0.00316
					1.4	3.4	2.8	-0.00441	-0.00221
1.4	3.4	2.9	-0.00408	-0.00123
					1.4	3.4	3	-0.00375	-0.00023
1.4	3.4	3.1	-0.00343	0.000793
					1.4	3.4	3.2	-0.00311	0.001847
1.4	3.4	3.3	-0.0028	0.002929
					1.4	3.4	3.4	-0.00249	0.00404
1.4	3.5	3	-0.00488	-0.00119
					1.4	3.5	3.1	-0.00456	-0.00018
1.4	3.5	3.2	-0.00424	0.000849
					1.4	3.5	3.3	-0.00393	0.001908
1.4	3.5	3.4	-0.00362	0.002995
					1.4	3.5	3.5	-0.00332	0.004111
1.4	3.6	3.4	-0.00478	0.001968
					1.4	3.6	3.5	-0.00448	0.00306
1.5	3	2	-0.00205	-0.00495
					1.5	3	2.1	-0.00163	-0.00402
1.5	3	2.2	-0.00121	-0.00307
					1.5	3	2.3	-0.00081	-0.00209
1.5	3	2.4	-0.00041	-0.00109
					1.5	3	2.5	-1.6E-05	-5.7E-05
1.5	3	2.6	0.00037	0.000998
					1.5	3	2.7	0.00075	0.002081
1.5	3	2.8	0.001124	0.003191
					1.5	3	2.9	0.001492	0.004331
1.5	3.1	2.1	-0.00254	-0.00474
					1.5	3.1	2.2	-0.00212	-0.0038
1.5	3.1	2.3	-0.00172	-0.00284
					1.5	3.1	2.4	-0.00131	-0.00185
1.5	3.1	2.5	-0.00092	-0.00084
					1.5	3.1	2.6	-0.00053	0.000202
1.5	3.1	2.7	-0.00015	0.001269
					1.5	3.1	2.8	0.000226	0.002363
1.5	3.1	2.9	0.000595	0.003485
					1.5	3.1	3	0.000958	0.004638
1.5	3.2	2.2	-0.00305	-0.00452
					1.5	3.2	2.3	-0.00264	-0.00357
1.5	3.2	2.4	-0.00224	-0.0026
					1.5	3.2	2.5	-0.00184	-0.0016
1.5	3.2	2.6	-0.00145	-0.00058
					1.5	3.2	2.7	-0.00107	0.000472
1.5	3.2	2.8	-0.00069	0.00155
					1.5	3.2	2.9	-0.00032	0.002656
1.5	3.2	3	4.49E-05	0.003791
					1.5	3.2	3.1	0.000404	0.004956
1.5	3.3	2.3	-0.00359	-0.00429
					1.5	3.3	2.4	-0.00318	-0.00333
1.5	3.3	2.5	-0.00278	-0.00235
					1.5	3.3	2.6	-0.00239	-0.00134
1.5	3.3	2.7	-0.00201	-0.00031
					1.5	3.3	2.8	-0.00163	0.000753
1.5	3.3	2.9	-0.00125	0.001842
					1.5	3.3	3	-0.00089	0.00296
1.5	3.3	3.1	-0.00053	0.004108
					1.5	3.4	2.3	-0.00455	-0.005
1.5	3.4	2.4	-0.00414	-0.00406
					1.5	3.4	2.5	-0.00374	-0.00309
1.5	3.4	2.6	-0.00335	-0.00209
					1.5	3.4	2.7	-0.00296	-0.00108
1.5	3.4	2.8	-0.00258	-3E-05
					1.5	3.4	2.9	-0.00221	0.001044
1.5	3.4	3	-0.00184	0.002145
					1.5	3.4	3.1	-0.00148	0.003276
1.5	3.4	3.2	-0.00112	0.004437
					1.5	3.5	2.5	-0.00472	-0.00381
1.5	3.5	2.6	-0.00433	-0.00283
					1.5	3.5	2.7	-0.00394	-0.00183
1.5	3.5	2.8	-0.00355	-0.0008
					1.5	3.5	2.9	-0.00318	0.00026
1.5	3.5	3	-0.00281	0.001346
					1.5	3.5	3.1	-0.00244	0.00246
1.5	3.5	3.2	-0.00208	0.003603
					1.5	3.5	3.3	-0.00173	0.004778
1.5	3.6	2.7	-0.00493	-0.00256
					1.5	3.6	2.8	-0.00455	-0.00155
1.5	3.6	2.9	-0.00417	-0.00051
					1.5	3.6	3	-0.0038	0.000561
1.5	3.6	3.1	-0.00343	0.001659
					1.5	3.6	3.2	-0.00307	0.002786
1.5	3.6	3.3	-0.00272	0.003943
					1.5	3.7	3	-0.00481	-0.00021
1.5	3.7	3.1	-0.00444	0.000873
					1.5	3.7	3.2	-0.00408	0.001983
1.5	3.7	3.3	-0.00372	0.003123
					1.5	3.7	3.4	-0.00337	0.004294
1.5	3.8	3.3	-0.00475	0.002319
					1.5	3.8	3.4	-0.00439	0.003472
1.5	3.8	3.5	-0.00405	0.004657
					1.6	3	2	-0.00107	-0.00393
1.6	3	2.1	-0.00062	-0.00294
					1.6	3	2.2	-0.00017	-0.00193
1.6	3	2.3	0.000272	-0.00089
					1.6	3	2.4	0.000706	0.000181
1.6	3	2.5	0.001133	0.001276
					1.6	3	2.6	0.001553	0.002401
1.6	3	2.7	0.001966	0.003554
					1.6	3	2.8	0.002373	0.004738
1.6	3.1	2	-0.00186	-0.00453
					1.6	3.1	2.1	-0.0014	-0.00355
1.6	3.1	2.2	-0.00094	-0.00254
					1.6	3.1	2.3	-0.0005	-0.00151
1.6	3.1	2.4	-6E-05	-0.00045
					1.6	3.1	2.5	0.000371	0.000632
1.6	3.1	2.6	0.000796	0.001745
					1.6	3.1	2.7	0.001213	0.002888
1.6	3.1	2.8	0.001623	0.004061
					1.6	3.2	2.1	-0.00219	-0.00414
1.6	3.2	2.2	-0.00174	-0.00315
					1.6	3.2	2.3	-0.00128	-0.00212
1.6	3.2	2.4	-0.00084	-0.00108
					1.6	3.2	2.5	-0.00041	-3.9E-07
1.6	3.2	2.6	2.27E-05	0.001103
					1.6	3.2	2.7	0.000444	0.002235
1.6	3.2	2.8	0.000859	0.003396
					1.6	3.2	2.9	0.001267	0.004588
1.6	3.3	2.1	-0.003	-0.00472
					1.6	3.3	2.2	-0.00254	-0.00374
1.6	3.3	2.3	-0.00209	-0.00272
					1.6	3.3	2.4	-0.00164	-0.00169
1.6	3.3	2.5	-0.0012	-0.00062
					1.6	3.3	2.6	-0.00077	0.000472
1.6	3.3	2.7	-0.00034	0.001594
					1.6	3.3	2.8	7.9E-05	0.002744
1.6	3.3	2.9	0.000491	0.003925
					1.6	3.4	2.2	-0.00336	-0.00431
1.6	3.4	2.3	-0.0029	-0.00331
					1.6	3.4	2.4	-0.00245	-0.00228
1.6	3.4	2.5	-0.00201	-0.00123
					1.6	3.4	2.6	-0.00157	-0.00015
1.6	3.4	2.7	-0.00114	0.000965
					1.6	3.4	2.8	-0.00072	0.002105
1.6	3.4	2.9	-0.0003	0.003275
					1.6	3.4	3	0.000109	0.004476
1.6	3.5	2.2	-0.0042	-0.00488
					1.6	3.5	2.3	-0.00374	-0.00389
1.6	3.5	2.4	-0.00328	-0.00287
					1.6	3.5	2.5	-0.00283	-0.00183
1.6	3.5	2.6	-0.00239	-0.00075
					1.6	3.5	2.7	-0.00196	0.000348
1.6	3.5	2.8	-0.00153	0.001477
					1.6	3.5	2.9	-0.00111	0.002637
1.6	3.5	3	-0.00069	0.003827
					1.6	3.6	2.3	-0.00459	-0.00446
1.6	3.6	2.4	-0.00413	-0.00345
					1.6	3.6	2.5	-0.00367	-0.00241
1.6	3.6	2.6	-0.00323	-0.00135
					1.6	3.6	2.7	-0.00279	-0.00026
1.6	3.6	2.8	-0.00236	0.000862
					1.6	3.6	2.9	-0.00193	0.002011
1.6	3.6	3	-0.00151	0.00319
					1.6	3.6	3.1	-0.0011	0.0044
1.6	3.7	2.4	-0.00499	-0.00401
					1.6	3.7	2.5	-0.00453	-0.00298
1.6	3.7	2.6	-0.00408	-0.00193
					1.6	3.7	2.7	-0.00364	-0.00085
1.6	3.7	2.8	-0.0032	0.000258
					1.6	3.7	2.9	-0.00277	0.001396
1.6	3.7	3	-0.00235	0.002565
					1.6	3.7	3.1	-0.00193	0.003764
1.6	3.7	3.2	-0.00152	0.004996
					1.6	3.8	2.6	-0.00495	-0.0025
1.6	3.8	2.7	-0.00451	-0.00143
					1.6	3.8	2.8	-0.00406	-0.00033
1.6	3.8	2.9	-0.00363	0.000794
					1.6	3.8	3	-0.0032	0.001952
1.6	3.8	3.1	-0.00278	0.00314
					1.6	3.8	3.2	-0.00237	0.004361
1.6	3.9	2.8	-0.00494	-0.00092
					1.6	3.9	2.9	-0.0045	0.000202
1.6	3.9	3	-0.00407	0.00135
					1.6	3.9	3.1	-0.00365	0.002528
1.6	3.9	3.2	-0.00323	0.003738
					1.6	3.9	3.3	-0.00282	0.00498
1.6	4	3	-0.00496	0.000759
					1.6	4	3.1	-0.00453	0.001927
1.6	4	3.2	-0.00411	0.003126
					1.6	4	3.3	-0.00369	0.004358
1.6	4.1	3.3	-0.00458	0.003747
					1.7	3	2	-8.3E-05	-0.00294
1.7	3	2.1	0.00041	-0.00189
					1.7	3	2.2	0.000896	-0.00082
1.7	3	2.3	0.001373	0.000287
					1.7	3	2.4	0.001843	0.00142
1.7	3	2.5	0.002305	0.002582
					1.7	3	2.6	0.002759	0.003775
1.7	3	2.7	0.003206	0.004998
					1.7	3.1	2	-0.00074	-0.00343
1.7	3.1	2.1	-0.00024	-0.00238
					1.7	3.1	2.2	0.000257	-0.00131
1.7	3.1	2.3	0.000742	-0.00021
					1.7	3.1	2.4	0.001219	0.000914
1.7	3.1	2.5	0.001687	0.00207
					1.7	3.1	2.6	0.002148	0.003257
1.7	3.1	2.7	0.002602	0.004474
					1.7	3.2	2	-0.0014	-0.0039
1.7	3.2	2.1	-0.00089	-0.00287
					1.7	3.2	2.2	-0.00039	-0.0018
1.7	3.2	2.3	9.8E-05	-0.00071
					1.7	3.2	2.4	0.000582	0.000417
1.7	3.2	2.5	0.001058	0.001568
					1.7	3.2	2.6	0.001525	0.002749
1.7	3.2	2.7	0.001986	0.003961
					1.7	3.3	2	-0.00208	-0.00437
1.7	3.3	2.1	-0.00157	-0.00334
					1.7	3.3	2.2	-0.00106	-0.00228
1.7	3.3	2.3	-0.00056	-0.00119
					1.7	3.3	2.4	-6.8E-05	-7E-05
1.7	3.3	2.5	0.000415	0.001075
					1.7	3.3	2.6	0.00089	0.002251
1.7	3.3	2.7	0.001357	0.003457
					1.7	3.3	2.8	0.001817	0.004695
1.7	3.4	2	-0.00278	-0.00483
					1.7	3.4	2.1	-0.00225	-0.0038
1.7	3.4	2.2	-0.00174	-0.00274
					1.7	3.4	2.3	-0.00123	-0.00166
1.7	3.4	2.4	-0.00073	-0.00055
					1.7	3.4	2.5	-0.00024	0.000592
1.7	3.4	2.6	0.000242	0.001762
					1.7	3.4	2.7	0.000716	0.002963
1.7	3.4	2.8	0.001183	0.004195
					1.7	3.5	2.1	-0.00295	-0.00425
1.7	3.5	2.2	-0.00243	-0.0032
					1.7	3.5	2.3	-0.00191	-0.00212
1.7	3.5	2.4	-0.00141	-0.00102
					1.7	3.5	2.5	-0.00091	0.000118
1.7	3.5	2.6	-0.00042	0.001283
					1.7	3.5	2.7	6.22E-05	0.002479
1.7	3.5	2.8	0.000536	0.003705
					1.7	3.5	2.9	0.001002	0.004964
1.7	3.6	2.1	-0.00366	-0.0047
					1.7	3.6	2.2	-0.00313	-0.00365
1.7	3.6	2.3	-0.00261	-0.00258
					1.7	3.6	2.4	-0.0021	-0.00148
1.7	3.6	2.5	-0.00159	-0.00035
					1.7	3.6	2.6	-0.00109	0.000813
1.7	3.6	2.7	-0.00061	0.002003
					1.7	3.6	2.8	-0.00012	0.003224
1.7	3.6	2.9	0.000349	0.004478
					1.7	3.7	2.2	-0.00385	-0.00409
1.7	3.7	2.3	-0.00332	-0.00302
					1.7	3.7	2.4	-0.0028	-0.00193
1.7	3.7	2.5	-0.00229	-0.0008
					1.7	3.7	2.6	-0.00178	0.000352
1.7	3.7	2.7	-0.00129	0.001536
					1.7	3.7	2.8	-0.0008	0.002752
1.7	3.7	2.9	-0.00032	0.004001
					1.7	3.8	2.2	-0.00459	-0.00453
1.7	3.8	2.3	-0.00405	-0.00346
					1.7	3.8	2.4	-0.00352	-0.00237
1.7	3.8	2.5	-0.003	-0.00125
					1.7	3.8	2.6	-0.00248	-0.0001
1.7	3.8	2.7	-0.00198	0.001079
					1.7	3.8	2.8	-0.00148	0.002289
1.7	3.8	2.9	-0.001	0.003532
					1.7	3.8	3	-0.00052	0.004808
1.7	3.9	2.3	-0.00479	-0.00389
					1.7	3.9	2.4	-0.00425	-0.0028
1.7	3.9	2.5	-0.00372	-0.00169
					1.7	3.9	2.6	-0.0032	-0.00055
1.7	3.9	2.7	-0.00269	0.00063
					1.7	3.9	2.8	-0.00219	0.001835
1.7	3.9	2.9	-0.00169	0.003072
					1.7	3.9	3	-0.0012	0.004343
1.7	4	2.4	-0.005	-0.00323
					1.7	4	2.5	-0.00446	-0.00212
1.7	4	2.6	-0.00393	-0.00098
					1.7	4	2.7	-0.00341	0.000189
1.7	4	2.8	-0.0029	0.001389
					1.7	4	2.9	-0.0024	0.002621
1.7	4	3	-0.0019	0.003886
					1.7	4.1	2.6	-0.00468	-0.00141
1.7	4.1	2.7	-0.00415	-0.00024
					1.7	4.1	2.8	-0.00363	0.000952
1.7	4.1	2.9	-0.00312	0.002179
					1.7	4.1	3	-0.00262	0.003438
1.7	4.1	3.1	-0.00212	0.004732
					1.7	4.2	2.7	-0.0049	-0.00067
1.7	4.2	2.8	-0.00438	0.000522
					1.7	4.2	2.9	-0.00386	0.001744
1.7	4.2	3	-0.00335	0.002999
					1.7	4.2	3.1	-0.00284	0.004287
1.7	4.3	2.9	-0.00461	0.001318
					1.7	4.3	3	-0.00409	0.002567
1.7	4.3	3.1	-0.00358	0.00385
					1.7	4.4	3	-0.00485	0.002143
1.7	4.4	3.1	-0.00433	0.003421
					1.7	4.4	3.2	-0.00382	0.004733
1.7	4.5	3.2	-0.00458	0.004307
					1.8	3	2	0.000927	-0.00197
1.8	3	2.1	0.001459	-0.00086
					1.8	3	2.2	0.001982	0.000273
1.8	3	2.3	0.002496	0.001439
					1.8	3	2.4	0.003001	0.002635
1.8	3	2.5	0.003499	0.003861
					1.8	3.1	2	0.000408	-0.00235
1.8	3.1	2.1	0.000949	-0.00124
					1.8	3.1	2.2	0.001482	-0.00011
1.8	3.1	2.3	0.002006	0.001058
					1.8	3.1	2.4	0.002522	0.002253
1.8	3.1	2.5	0.003028	0.003479
					1.8	3.1	2.6	0.003527	0.004737
1.8	3.2	2	-0.00012	-0.00272
					1.8	3.2	2.1	0.00043	-0.00162
1.8	3.2	2.2	0.000973	-0.00048
					1.8	3.2	2.3	0.001507	0.000684
1.8	3.2	2.4	0.002032	0.001879
					1.8	3.2	2.5	0.002549	0.003104
1.8	3.2	2.6	0.003057	0.004362
					1.8	3.3	2	-0.00066	-0.00309
1.8	3.3	2.1	-0.0001	-0.00198
					1.8	3.3	2.2	0.000453	-0.00085
1.8	3.3	2.3	0.000998	0.000318
					1.8	3.3	2.4	0.001533	0.001512
1.8	3.3	2.5	0.00206	0.002737
					1.8	3.3	2.6	0.002577	0.003993
1.8	3.4	2	-0.00121	-0.00344
					1.8	3.4	2.1	-0.00064	-0.00234
1.8	3.4	2.2	-7.7E-05	-0.0012
					1.8	3.4	2.3	0.000478	-4.1E-05
1.8	3.4	2.4	0.001024	0.001152
					1.8	3.4	2.5	0.001561	0.002376
1.8	3.4	2.6	0.002088	0.003632
					1.8	3.4	2.7	0.002608	0.004921
1.8	3.5	2	-0.00178	-0.00379
					1.8	3.5	2.1	-0.00119	-0.00269
1.8	3.5	2.2	-0.00062	-0.00156
					1.8	3.5	2.3	-5.2E-05	-0.00039
1.8	3.5	2.4	0.000504	0.000799
					1.8	3.5	2.5	0.001051	0.002022
1.8	3.5	2.6	0.00159	0.003277
					1.8	3.5	2.7	0.002119	0.004566
1.8	3.6	2	-0.00235	-0.00414
					1.8	3.6	2.1	-0.00176	-0.00303
1.8	3.6	2.2	-0.00117	-0.0019
					1.8	3.6	2.3	-0.00059	-0.00074
1.8	3.6	2.4	-2.6E-05	0.000452
					1.8	3.6	2.5	0.000532	0.001675
1.8	3.6	2.6	0.001081	0.00293
					1.8	3.6	2.7	0.00162	0.004217
1.8	3.7	2	-0.00294	-0.00447
					1.8	3.7	2.1	-0.00233	-0.00337
1.8	3.7	2.2	-0.00173	-0.00224
					1.8	3.7	2.3	-0.00114	-0.00108
1.8	3.7	2.4	-0.00057	0.000112
					1.8	3.7	2.5	2.15E-06	0.001334
1.8	3.7	2.6	0.000561	0.002588
					1.8	3.7	2.7	0.001111	0.003875
1.8	3.8	2	-0.00353	-0.0048
					1.8	3.8	2.1	-0.00291	-0.0037
1.8	3.8	2.2	-0.00231	-0.00257
					1.8	3.8	2.3	-0.00171	-0.00141
1.8	3.8	2.4	-0.00112	-0.00022
					1.8	3.8	2.5	-0.00054	0.001
1.8	3.8	2.6	3.14E-05	0.002254
					1.8	3.8	2.7	0.000592	0.00354
1.8	3.8	2.8	0.001143	0.00486
					1.8	3.9	2.1	-0.00351	-0.00403
1.8	3.9	2.2	-0.00289	-0.0029
					1.8	3.9	2.3	-0.00228	-0.00174
1.8	3.9	2.4	-0.00168	-0.00055
					1.8	3.9	2.5	-0.00109	0.000673
1.8	3.9	2.6	-0.00051	0.001925
					1.8	3.9	2.7	6.21E-05	0.003211
1.8	3.9	2.8	0.000624	0.00453
					1.8	4	2.1	-0.00412	-0.00435
1.8	4	2.2	-0.00349	-0.00322
					1.8	4	2.3	-0.00287	-0.00206
1.8	4	2.4	-0.00226	-0.00087
					1.8	4	2.5	-0.00165	0.000351
1.8	4	2.6	-0.00106	0.001603
					1.8	4	2.7	-0.00048	0.002888
1.8	4	2.8	9.45E-05	0.004206
					1.8	4.1	2.1	-0.00474	-0.00466
1.8	4.1	2.2	-0.0041	-0.00353
					1.8	4.1	2.3	-0.00347	-0.00237
1.8	4.1	2.4	-0.00284	-0.00118
					1.8	4.1	2.5	-0.00223	3.52E-05
1.8	4.1	2.6	-0.00162	0.001286
					1.8	4.1	2.7	-0.00103	0.002571
1.8	4.1	2.8	-0.00045	0.003889
					1.8	4.2	2.2	-0.00472	-0.00384
1.8	4.2	2.3	-0.00408	-0.00268
					1.8	4.2	2.4	-0.00344	-0.00149
1.8	4.2	2.5	-0.00281	-0.00027
					1.8	4.2	2.6	-0.0022	0.000976
1.8	4.2	2.7	-0.00159	0.002259
					1.8	4.2	2.8	-0.001	0.003577
1.8	4.2	2.9	-0.00041	0.004929
					1.8	4.3	2.3	-0.0047	-0.00298
1.8	4.3	2.4	-0.00405	-0.0018
					1.8	4.3	2.5	-0.00341	-0.00058
1.8	4.3	2.6	-0.00278	0.000671
					1.8	4.3	2.7	-0.00217	0.001954
1.8	4.3	2.8	-0.00156	0.003271
					1.8	4.3	2.9	-0.00096	0.004622
1.8	4.4	2.4	-0.00467	-0.00209
					1.8	4.4	2.5	-0.00402	-0.00088
1.8	4.4	2.6	-0.00338	0.000372
					1.8	4.4	2.7	-0.00275	0.001654
1.8	4.4	2.8	-0.00214	0.00297
					1.8	4.4	2.9	-0.00153	0.004321
1.8	4.5	2.5	-0.00465	-0.00117
					1.8	4.5	2.6	-0.00399	7.87E-05
1.8	4.5	2.7	-0.00335	0.00136
					1.8	4.5	2.8	-0.00272	0.002676
1.8	4.5	2.9	-0.0021	0.004026
					1.8	4.6	2.6	-0.00462	-0.00021
1.8	4.6	2.7	-0.00396	0.001071
					1.8	4.6	2.8	-0.00332	0.002386
1.8	4.6	2.9	-0.00269	0.003736
					1.8	4.7	2.7	-0.00459	0.000788
1.8	4.7	2.8	-0.00393	0.002102
					1.8	4.7	2.9	-0.00329	0.003451
1.8	4.7	3	-0.00265	0.004836
					1.8	4.8	2.8	-0.00456	0.001823
1.8	4.8	2.9	-0.0039	0.003171
					1.8	4.8	3	-0.00325	0.004556
1.8	4.9	2.9	-0.00452	0.002897
					1.8	4.9	3	-0.00386	0.004281
1.8	5	3	-0.00449	0.00401
					1.9	3	2	0.001957	-0.00102
1.9	3	2.1	0.002527	0.000144
					1.9	3	2.2	0.003088	0.00134
1.9	3	2.3	0.00364	0.002566
					1.9	3	2.4	0.004182	0.003824
1.9	3.1	2	0.001573	-0.0013
					1.9	3.1	2.1	0.002157	-0.00013
1.9	3.1	2.2	0.00273	0.001073
					1.9	3.1	2.3	0.003295	0.002303
1.9	3.1	2.4	0.003849	0.003565
					1.9	3.1	2.5	0.004395	0.004859
1.9	3.2	2	0.001182	-0.00156
					1.9	3.2	2.1	0.001779	-0.00039
1.9	3.2	2.2	0.002366	0.000811
					1.9	3.2	2.3	0.002943	0.002045
1.9	3.2	2.4	0.00351	0.003311
					1.9	3.2	2.5	0.004069	0.004609
1.9	3.3	2	0.000783	-0.00183
					1.9	3.3	2.1	0.001394	-0.00065
1.9	3.3	2.2	0.001994	0.000555
					1.9	3.3	2.3	0.002584	0.001792
1.9	3.3	2.4	0.003165	0.003061
					1.9	3.3	2.5	0.003736	0.004364
1.9	3.4	2	0.000376	-0.00209
					1.9	3.4	2.1	0.001001	-0.00091
1.9	3.4	2.2	0.001614	0.000303
					1.9	3.4	2.3	0.002218	0.001544
1.9	3.4	2.4	0.002812	0.002817
					1.9	3.4	2.5	0.003396	0.004123
1.9	3.5	2	-3.9E-05	-0.00234
					1.9	3.5	2.1	0.000599	-0.00116
1.9	3.5	2.2	0.001227	5.63E-05
					1.9	3.5	2.3	0.001845	0.001301
1.9	3.5	2.4	0.002452	0.002577
					1.9	3.5	2.5	0.003049	0.003887
1.9	3.6	2	-0.00046	-0.00259
					1.9	3.6	2.1	0.00019	-0.0014
1.9	3.6	2.2	0.000832	-0.00019
					1.9	3.6	2.3	0.001464	0.001062
1.9	3.6	2.4	0.002085	0.002342
					1.9	3.6	2.5	0.002696	0.003655
1.9	3.7	2	-0.00089	-0.00283
					1.9	3.7	2.1	-0.00023	-0.00164
1.9	3.7	2.2	0.00043	-0.00042
					1.9	3.7	2.3	0.001075	0.000828
1.9	3.7	2.4	0.00171	0.002111
					1.9	3.7	2.5	0.002335	0.003428
1.9	3.7	2.6	0.002949	0.004779
					1.9	3.8	2	-0.00134	-0.00307
1.9	3.8	2.1	-0.00065	-0.00188
					1.9	3.8	2.2	1.86E-05	-0.00066
1.9	3.8	2.3	0.000679	0.000598
					1.9	3.8	2.4	0.001328	0.001885
1.9	3.8	2.5	0.001967	0.003205
					1.9	3.8	2.6	0.002595	0.00456
1.9	3.9	2	-0.00179	-0.0033
					1.9	3.9	2.1	-0.00109	-0.00211
1.9	3.9	2.2	-0.0004	-0.00088
					1.9	3.9	2.3	0.000274	0.000372
1.9	3.9	2.4	0.000938	0.001663
					1.9	3.9	2.5	0.001592	0.002986
1.9	3.9	2.6	0.002234	0.004345
					1.9	4	2	-0.00224	-0.00354
1.9	4	2.1	-0.00153	-0.00234
					1.9	4	2.2	-0.00083	-0.00111
1.9	4	2.3	-0.00014	0.000151
					1.9	4	2.4	0.000541	0.001445
1.9	4	2.5	0.001208	0.002772
					1.9	4	2.6	0.001865	0.004133
1.9	4.1	2	-0.00271	-0.00376
					1.9	4.1	2.1	-0.00198	-0.00256
1.9	4.1	2.2	-0.00127	-0.00133
					1.9	4.1	2.3	-0.00056	-6.6E-05
1.9	4.1	2.4	0.000135	0.001231
					1.9	4.1	2.5	0.000817	0.002561
1.9	4.1	2.6	0.001489	0.003926
					1.9	4.2	2	-0.00319	-0.00398
1.9	4.2	2.1	-0.00244	-0.00278
					1.9	4.2	2.2	-0.00171	-0.00155
1.9	4.2	2.3	-0.00099	-0.00028
					1.9	4.2	2.4	-0.00028	0.001021
1.9	4.2	2.5	0.000418	0.002354
					1.9	4.2	2.6	0.001105	0.003723
1.9	4.3	2	-0.00368	-0.0042
					1.9	4.3	2.1	-0.00292	-0.00299
1.9	4.3	2.2	-0.00217	-0.00176
					1.9	4.3	2.3	-0.00143	-0.00049
1.9	4.3	2.4	-0.0007	0.000815
					1.9	4.3	2.5	1.12E-05	0.002151
1.9	4.3	2.6	0.000713	0.003523
					1.9	4.3	2.7	0.001404	0.004931
1.9	4.4	2	-0.00418	-0.00441
					1.9	4.4	2.1	-0.0034	-0.0032
1.9	4.4	2.2	-0.00263	-0.00196
					1.9	4.4	2.3	-0.00188	-0.00069
1.9	4.4	2.4	-0.00113	0.000613
					1.9	4.4	2.5	-0.0004	0.001952
1.9	4.4	2.6	0.000313	0.003327
					1.9	4.4	2.7	0.001019	0.004738
1.9	4.5	2	-0.00468	-0.00462
					1.9	4.5	2.1	-0.00389	-0.00341
1.9	4.5	2.2	-0.0031	-0.00217
					1.9	4.5	2.3	-0.00233	-0.00089
1.9	4.5	2.4	-0.00157	0.000414
					1.9	4.5	2.5	-0.00083	0.001757
1.9	4.5	2.6	-9.5E-05	0.003135
					1.9	4.5	2.7	0.000627	0.004549
1.9	4.6	2.1	-0.00439	-0.00361
					1.9	4.6	2.2	-0.00359	-0.00237
1.9	4.6	2.3	-0.0028	-0.00109
					1.9	4.6	2.4	-0.00202	0.000219
1.9	4.6	2.5	-0.00126	0.001565
					1.9	4.6	2.6	-0.00051	0.002946
1.9	4.6	2.7	0.000226	0.004364
					1.9	4.7	2.1	-0.0049	-0.00381
1.9	4.7	2.2	-0.00408	-0.00257
					1.9	4.7	2.3	-0.00327	-0.00129
1.9	4.7	2.4	-0.00248	2.82E-05
					1.9	4.7	2.5	-0.0017	0.001377
1.9	4.7	2.6	-0.00094	0.002761
					1.9	4.7	2.7	-0.00018	0.004181
1.9	4.8	2.2	-0.00458	-0.00276
					1.9	4.8	2.3	-0.00376	-0.00148
1.9	4.8	2.4	-0.00295	-0.00016
					1.9	4.8	2.5	-0.00215	0.001192
1.9	4.8	2.6	-0.00137	0.002579
					1.9	4.8	2.7	-0.0006	0.004002
1.9	4.9	2.3	-0.00426	-0.00166
					1.9	4.9	2.4	-0.00343	-0.00034
1.9	4.9	2.5	-0.00261	0.00101
					1.9	4.9	2.6	-0.00181	0.0024
1.9	4.9	2.7	-0.00103	0.003827
					1.9	5	2.3	-0.00476	-0.00185
1.9	5	2.4	-0.00392	-0.00052
					1.9	5	2.5	-0.00308	0.000832
1.9	5	2.6	-0.00227	0.002224
					1.9	5	2.7	-0.00146	0.003654
1.9	5.1	2.4	-0.00441	-0.0007
					1.9	5.1	2.5	-0.00356	0.000657
1.9	5.1	2.6	-0.00273	0.002052
					1.9	5.1	2.7	-0.0019	0.003485
1.9	5.1	2.8	-0.0011	0.004955
					1.9	5.2	2.4	-0.00492	-0.00088
1.9	5.2	2.5	-0.00405	0.000485
					1.9	5.2	2.6	-0.0032	0.001883
1.9	5.2	2.7	-0.00236	0.003318
					1.9	5.2	2.8	-0.00153	0.004792
1.9	5.3	2.5	-0.00455	0.000316
					1.9	5.3	2.6	-0.00368	0.001717
1.9	5.3	2.7	-0.00282	0.003155
					1.9	5.3	2.8	-0.00198	0.004631
1.9	5.4	2.6	-0.00417	0.001554
					1.9	5.4	2.7	-0.00329	0.002994
1.9	5.4	2.8	-0.00243	0.004473
					1.9	5.5	2.6	-0.00467	0.001394
1.9	5.5	2.7	-0.00378	0.002837
					1.9	5.5	2.8	-0.00289	0.004318
1.9	5.6	2.7	-0.00427	0.002682
					1.9	5.6	2.8	-0.00337	0.004166
1.9	5.7	2.7	-0.00477	0.00253
					1.9	5.7	2.8	-0.00385	0.004017
1.9	5.8	2.8	-0.00434	0.00387
					1.9	5.9	2.8	-0.00485	0.003726
2	3	2	0.003007	-9E-05
					2	3	2.1	0.003616	0.001132
2	3	2.2	0.004216	0.002385
					2	3	2.3	0.004805	0.003671
2	3.1	2	0.002762	-0.00026
					2	3.1	2.1	0.003387	0.000968
2	3.1	2.2	0.004003	0.002229
					2	3.1	2.3	0.004608	0.003523
2	3.2	2	0.002512	-0.00043
					2	3.2	2.1	0.003154	0.000808
2	3.2	2.2	0.003785	0.002077
					2	3.2	2.3	0.004406	0.003378
2	3.3	2	0.002257	-0.00059
					2	3.3	2.1	0.002916	0.00065
2	3.3	2.2	0.003564	0.001927
					2	3.3	2.3	0.004201	0.003236
2	3.3	2.4	0.004828	0.00458
					2	3.4	2	0.001998	-0.00076
2	3.4	2.1	0.002673	0.000496
					2	3.4	2.2	0.003338	0.00178
2	3.4	2.3	0.003991	0.003097
					2	3.4	2.4	0.004634	0.004448
2	3.5	2	0.001733	-0.00091
					2	3.5	2.1	0.002426	0.000344
2	3.5	2.2	0.003107	0.001636
					2	3.5	2.3	0.003778	0.00296
2	3.5	2.4	0.004437	0.004319
					2	3.6	2	0.001462	-0.00107
2	3.6	2.1	0.002173	0.000196
					2	3.6	2.2	0.002872	0.001494
2	3.6	2.3	0.00356	0.002826
					2	3.6	2.4	0.004236	0.004193
2	3.7	2	0.001186	-0.00122
					2	3.7	2.1	0.001915	5.02E-05
2	3.7	2.2	0.002632	0.001356
					2	3.7	2.3	0.003337	0.002695
2	3.7	2.4	0.00403	0.004069
					2	3.8	2	0.000905	-0.00137
2	3.8	2.1	0.001652	-9.3E-05
					2	3.8	2.2	0.002387	0.00122
2	3.8	2.3	0.00311	0.002566
					2	3.8	2.4	0.003821	0.003947
2	3.9	2	0.000618	-0.00152
					2	3.9	2.1	0.001384	-0.00023
2	3.9	2.2	0.002137	0.001086
					2	3.9	2.3	0.002878	0.002439
2	3.9	2.4	0.003607	0.003828
					2	4	2	0.000325	-0.00166
2	4	2.1	0.00111	-0.00037
					2	4	2.2	0.001883	0.000955
2	4	2.3	0.002642	0.002315
					2	4	2.4	0.003389	0.003711
2	4.1	2	2.62E-05	-0.0018
					2	4.1	2.1	0.000831	-0.00051
2	4.1	2.2	0.001623	0.000827
					2	4.1	2.3	0.002401	0.002193
2	4.1	2.4	0.003167	0.003596
					2	4.2	2	-0.00028	-0.00194
2	4.2	2.1	0.000546	-0.00064
					2	4.2	2.2	0.001357	0.0007
2	4.2	2.3	0.002155	0.002074
					2	4.2	2.4	0.00294	0.003483
2	4.2	2.5	0.003712	0.004929
					2	4.3	2	-0.00059	-0.00208
2	4.3	2.1	0.000255	-0.00077
					2	4.3	2.2	0.001086	0.000577
2	4.3	2.3	0.001904	0.001956
					2	4.3	2.4	0.002708	0.003372
2	4.3	2.5	0.003499	0.004825
					2	4.4	2	-0.00091	-0.00221
2	4.4	2.1	-4.2E-05	-0.0009
					2	4.4	2.2	0.00081	0.000455
2	4.4	2.3	0.001648	0.001841
					2	4.4	2.4	0.002472	0.003264
2	4.4	2.5	0.003282	0.004723
					2	4.5	2	-0.00123	-0.00234
2	4.5	2.1	-0.00034	-0.00102
					2	4.5	2.2	0.000528	0.000336
2	4.5	2.3	0.001386	0.001728
					2	4.5	2.4	0.00223	0.003157
2	4.5	2.5	0.003061	0.004623
					2	4.6	2	-0.00156	-0.00247
2	4.6	2.1	-0.00065	-0.00114
					2	4.6	2.2	0.00024	0.000219
2	4.6	2.3	0.001119	0.001617
					2	4.6	2.4	0.001984	0.003052
2	4.6	2.5	0.002835	0.004525
					2	4.7	2	-0.0019	-0.0026
2	4.7	2.1	-0.00097	-0.00126
					2	4.7	2.2	-5.4E-05	0.000104
2	4.7	2.3	0.000847	0.001509
					2	4.7	2.4	0.001733	0.00295
2	4.7	2.5	0.002604	0.004429
					2	4.8	2	-0.00224	-0.00272
2	4.8	2.1	-0.00129	-0.00138
					2	4.8	2.2	-0.00035	-8.4E-06
2	4.8	2.3	0.000569	0.001402
					2	4.8	2.4	0.001476	0.002849
2	4.8	2.5	0.002369	0.004334
					2	4.9	2	-0.0026	-0.00284
2	4.9	2.1	-0.00162	-0.0015
					2	4.9	2.2	-0.00066	-0.00012
2	4.9	2.3	0.000285	0.001297
					2	4.9	2.4	0.001214	0.00275
2	4.9	2.5	0.002129	0.004241
					2	5	2	-0.00295	-0.00296
2	5	2.1	-0.00196	-0.00161
					2	5	2.2	-0.00097	-0.00023
2	5	2.3	-4.6E-06	0.001194
					2	5	2.4	0.000947	0.002653
2	5	2.5	0.001883	0.00415
					2	5.1	2	-0.00332	-0.00308
2	5.1	2.1	-0.0023	-0.00172
					2	5.1	2.2	-0.00129	-0.00033
2	5.1	2.3	-0.0003	0.001093
					2	5.1	2.4	0.000674	0.002557
2	5.1	2.5	0.001633	0.00406
					2	5.2	2	-0.0037	-0.0032
2	5.2	2.1	-0.00265	-0.00183
					2	5.2	2.2	-0.00162	-0.00044
2	5.2	2.3	-0.0006	0.000993
					2	5.2	2.4	0.000396	0.002464
2	5.2	2.5	0.001377	0.003973
					2	5.3	2	-0.00408	-0.00331
2	5.3	2.1	-0.003	-0.00194
					2	5.3	2.2	-0.00195	-0.00054
2	5.3	2.3	-0.00091	0.000896
					2	5.3	2.4	0.000111	0.002371
2	5.3	2.5	0.001116	0.003886
					2	5.4	2	-0.00447	-0.00342
2	5.4	2.1	-0.00337	-0.00205
					2	5.4	2.2	-0.00229	-0.00064
2	5.4	2.3	-0.00123	0.0008
					2	5.4	2.4	-0.00018	0.002281
2	5.4	2.5	0.00085	0.003801
					2	5.5	2	-0.00487	-0.00353
2	5.5	2.1	-0.00374	-0.00215
					2	5.5	2.2	-0.00263	-0.00074
2	5.5	2.3	-0.00155	0.000706
					2	5.5	2.4	-0.00048	0.002192
2	5.5	2.5	0.000578	0.003718
					2	5.6	2.1	-0.00412	-0.00226
2	5.6	2.2	-0.00299	-0.00084
					2	5.6	2.3	-0.00187	0.000614
2	5.6	2.4	-0.00078	0.002105
					2	5.6	2.5	0.0003	0.003636
2	5.7	2.1	-0.00451	-0.00236
					2	5.7	2.2	-0.00335	-0.00094
2	5.7	2.3	-0.00221	0.000523
					2	5.7	2.4	-0.00109	0.00202
2	5.7	2.5	1.61E-05	0.003556
					2	5.8	2.1	-0.0049	-0.00245
2	5.8	2.2	-0.00372	-0.00103
					2	5.8	2.3	-0.00255	0.000434
2	5.8	2.4	-0.0014	0.001936
					2	5.8	2.5	-0.00027	0.003477
2	5.9	2.2	-0.0041	-0.00112
					2	5.9	2.3	-0.0029	0.000346
2	5.9	2.4	-0.00173	0.001853
					2	5.9	2.5	-0.00057	0.003399
2	5.9	2.6	0.000568	0.004987
					2	6	2.2	-0.00448	-0.00121
2	6	2.3	-0.00326	0.00026
					2	6	2.4	-0.00205	0.001772
2	6	2.5	-0.00087	0.003323
					2	6	2.6	0.000293	0.004916
2.1	3	2	0.004076	0.000823
					2.1	3	2.1	0.004726	0.0021
2.1	3.1	2	0.003973	0.000752
					2.1	3.1	2.1	0.004642	0.002041
2.1	3.2	2	0.003867	0.000682
					2.1	3.2	2.1	0.004556	0.001982
2.1	3.3	2	0.00376	0.000614
					2.1	3.3	2.1	0.004468	0.001925
2.1	3.4	2	0.00365	0.000547
					2.1	3.4	2.1	0.004378	0.00187
2.1	3.5	2	0.003538	0.000481
					2.1	3.5	2.1	0.004287	0.001815
2.1	3.6	2	0.003424	0.000417
					2.1	3.6	2.1	0.004193	0.001761
2.1	3.6	2.2	0.004951	0.00314
					2.1	3.7	2	0.003307	0.000354
2.1	3.7	2.1	0.004098	0.001708
					2.1	3.7	2.2	0.004877	0.003098
2.1	3.8	2	0.003188	0.000292
					2.1	3.8	2.1	0.004001	0.001657
2.1	3.8	2.2	0.004801	0.003057
					2.1	3.9	2	0.003067	0.000231
2.1	3.9	2.1	0.003902	0.001606
					2.1	3.9	2.2	0.004724	0.003017
2.1	4	2	0.002943	0.000171
					2.1	4	2.1	0.003801	0.001556
2.1	4	2.2	0.004645	0.002977
					2.1	4.1	2	0.002817	0.000113
2.1	4.1	2.1	0.003698	0.001507
					2.1	4.1	2.2	0.004565	0.002938
2.1	4.2	2	0.002688	5.52E-05
					2.1	4.2	2.1	0.003593	0.001459
2.1	4.2	2.2	0.004483	0.0029
					2.1	4.3	2	0.002556	-1.2E-06
2.1	4.3	2.1	0.003486	0.001412
					2.1	4.3	2.2	0.0044	0.002863
2.1	4.4	2	0.002422	-5.6E-05
					2.1	4.4	2.1	0.003376	0.001366
2.1	4.4	2.2	0.004315	0.002826
					2.1	4.5	2	0.002285	-0.00011
2.1	4.5	2.1	0.003264	0.001321
					2.1	4.5	2.2	0.004228	0.00279
2.1	4.6	2	0.002145	-0.00016
					2.1	4.6	2.1	0.00315	0.001276
2.1	4.6	2.2	0.004139	0.002754
					2.1	4.7	2	0.002003	-0.00022
2.1	4.7	2.1	0.003034	0.001233
					2.1	4.7	2.2	0.004048	0.00272
2.1	4.8	2	0.001857	-0.00027
					2.1	4.8	2.1	0.002915	0.00119
2.1	4.8	2.2	0.003956	0.002686
					2.1	4.8	2.3	0.00498	0.00422
2.1	4.9	2	0.001709	-0.00032
					2.1	4.9	2.1	0.002794	0.001148
2.1	4.9	2.2	0.003861	0.002652
					2.1	4.9	2.3	0.004912	0.004196
2.1	5	2	0.001557	-0.00037
					2.1	5	2.1	0.00267	0.001107
2.1	5	2.2	0.003765	0.002619
					2.1	5	2.3	0.004842	0.004172
2.1	5.1	2	0.001402	-0.00042
					2.1	5.1	2.1	0.002544	0.001066
2.1	5.1	2.2	0.003667	0.002587
					2.1	5.1	2.3	0.004772	0.004148
2.1	5.2	2	0.001244	-0.00046
					2.1	5.2	2.1	0.002415	0.001026
2.1	5.2	2.2	0.003566	0.002555
					2.1	5.2	2.3	0.004699	0.004125
2.1	5.3	2	0.001083	-0.00051
					2.1	5.3	2.1	0.002283	0.000987
2.1	5.3	2.2	0.003464	0.002524
					2.1	5.3	2.3	0.004626	0.004102
2.1	5.4	2	0.000918	-0.00056
					2.1	5.4	2.1	0.002149	0.000949
2.1	5.4	2.2	0.003359	0.002494
					2.1	5.4	2.3	0.00455	0.004079
2.1	5.5	2	0.00075	-0.0006
					2.1	5.5	2.1	0.002011	0.000911
2.1	5.5	2.2	0.003252	0.002464
					2.1	5.5	2.3	0.004473	0.004057
2.1	5.6	2	0.000578	-0.00065
					2.1	5.6	2.1	0.001871	0.000874
2.1	5.6	2.2	0.003143	0.002434
					2.1	5.6	2.3	0.004395	0.004036
2.1	5.7	2	0.000403	-0.00069
					2.1	5.7	2.1	0.001728	0.000838
2.1	5.7	2.2	0.003032	0.002405
					2.1	5.7	2.3	0.004315	0.004014
2.1	5.8	2	0.000224	-0.00073
					2.1	5.8	2.1	0.001582	0.000802
2.1	5.8	2.2	0.002918	0.002377
					2.1	5.8	2.3	0.004233	0.003993
2.1	5.9	2	4.11E-05	-0.00077
					2.1	5.9	2.1	0.001433	0.000767
2.1	5.9	2.2	0.002802	0.002349
					2.1	5.9	2.3	0.004149	0.003973
2.1	6	2	-0.00015	-0.00082
					2.1	6	2.1	0.001281	0.000733
2.1	6	2.2	0.002684	0.002322
					2.1	6	2.3	0.004064	0.003953

The refractive index curve of the material obtained by using the corresponding ACF at 400-1100 nm is very high, and the coefficients of ACF formulas of different materials are different, according to simulation verification, the set wavelength term range can meet the calibration of the refractive index formula of the different materials, the refractive index formula of the material can be effectively calibrated by using the method, and meanwhile, the accurate refractive index curve is obtained according to the corresponding refractive index formula.

Example two

The second embodiment provides a method for calibrating the refractive index of a planar uniform-thickness medium, which comprises the following steps:

providing a calibration device, wherein the calibration device comprises a spectrum confocal sensor 11, a spectrometer 14 and a distance adjusting mechanism, wherein the spectrum confocal sensor 11 comprises a white light point light source S, a semi-transparent half-reflecting mirror X and a dispersion objective lens L; the semi-transparent semi-reflecting mirror X and the dispersive objective lens L are sequentially arranged between the white light point light source S and the measured medium 13 along an optical axis, the semi-transparent semi-reflecting mirror X is close to the white light point light source S, and the dispersive objective lens L is close to the measured medium 13 side;

the distance adjusting mechanism drives the spectrum confocal sensor 11 and the measured medium 13 to be close to or far away from each other so that the distance between the dispersive objective lens L and the measured medium 13 changes 5 times along the optical axis;

the spectrometer 14 is arranged opposite to the reflecting surface of the semi-permeable and semi-reflective mirror X, and the spectrometer 14 is used for detecting the wavelength of the monochromatic light which is focused and reflected on the measured medium 13;

detecting the refractive index of 6 monochromatic light wavelengths according to a spectrum confocal principle, sequencing the 6 monochromatic light wavelengths according to the wavelength, calculating a refractive index curve of the detected medium 13 by taking the refractive indexes of 4 monochromatic light wavelengths with the wavelengths in the middle position, and correcting a refractive index formula by using the refractive indexes of the remaining 2 monochromatic light wavelengths; and when the error between the residual 2 wavelength refractive indexes in the corrected refractive index curve and the actually measured residual 2 wavelength refractive indexes is smaller than a set threshold value, the calibration is considered to be successful.

Further, the set threshold is 0.003% -0.005%.

Further, defining:

the thickness of the plane uniform-thickness medium is H;

；

(ii) a The refractive index of the measured medium 13 at the wavelength λ

Is derived from the following formula:

，

wherein the content of the first and second substances,

and

Further, defining:

when the distance between the dispersion objective lens L and the measured medium 13 is not changed, the wavelength of the upper monochromatic light is lambda₁Wavelength of the lower monochromatic light is λ₂；

When the distance between the dispersion objective lens L and the measured medium 13 is changed for the first time, the wavelength of the upper monochromatic light is lambda₃Wavelength of the lower monochromatic light is λ₄；

When the distance between the dispersion objective lens L and the measured medium 13 changes for the second time, the wavelength of the upper monochromatic light is lambda₅Wavelength of the lower monochromatic light is λ₆；

When the distance between the dispersion objective lens L and the measured medium 13 changes for the third time, the wavelength of the upper monochromatic light is lambda₇Wavelength of the lower monochromatic light is λ₈；

When the distance between the dispersion objective lens L and the measured medium 13 is changed for the fourth time, the wavelength of the upper monochromatic light is lambda₉Wavelength of the lower monochromatic light is λ₁₀

When the distance between the dispersion objective lens L and the measured medium 13 changes for the fifth time, the wavelength of the upper monochromatic light is lambda₁₁Wavelength of the lower monochromatic light is λ₁₂(ii) a Then the incident angle of each monochromatic light can be obtained

And has the following components:

，

by the formula

Alternatively to this, the first and second parts may,the wavelength power series is set in the following range: x is more than or equal to 0.1₁≤3，3.1≤X₂≤8，0.1≤X₃≤5；

Other functions/steps of the method for calibrating the refractive index of the planar uniform-thickness medium provided in this embodiment correspond to those of the first embodiment, so that reference may be made to the contents of the first embodiment for other functions of this embodiment, and details are not repeated here.

The number of apparatuses and the scale of the process described herein are intended to simplify the description of the present invention. Applications, modifications and variations of the present invention will be apparent to those skilled in the art.

The features of the different implementations described herein may be combined to form other embodiments not specifically set forth above. The components may be omitted from the structures described herein without adversely affecting their operation. Further, various individual components may be combined into one or more individual components to perform the functions described herein.

Furthermore, while embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable in a variety of fields of endeavor to which the invention pertains, and further modifications may readily be made by those skilled in the art, it being understood that the invention is not limited to the details shown and described herein without departing from the general concept defined by the appended claims and their equivalents.

Claims

1. The calibration device for the plane uniform-thickness medium refractive index comprises a spectrum confocal sensor (11), a spectrometer (14) and a distance adjusting mechanism, wherein the spectrum confocal sensor (11) comprises a white light point light source (S), a semi-transparent semi-reflecting mirror (X) and a dispersion objective lens (L); the semi-transparent semi-reflecting mirror (X) and the dispersive objective lens (L) are sequentially arranged between the white light point light source (S) and the measured medium (13) along an optical axis, the semi-transparent semi-reflecting mirror (X) is close to the white light point light source (S), and the dispersive objective lens (L) is close to the side of the measured medium (13); the distance adjusting mechanism drives the spectrum confocal sensor (11) and the measured medium (13) to be close to or far away from each other so that the distance between the dispersion objective lens (L) and the measured medium (13) changes 5 times along the optical axis; the spectrometer (14) is opposite to the reflecting surface of the semi-transparent and semi-reflective mirror (X) and is used for detecting the wavelength of the monochromatic light which is focused and reflected on the medium (13) to be detected; detecting according to a spectrum confocal principle to obtain the refractive indexes of 6 monochromatic light wavelengths, sequencing the 6 monochromatic light wavelengths according to the wavelength, calculating a refractive index curve of a detected medium (13) by taking the refractive indexes of 4 monochromatic light wavelengths with the wavelengths in the middle position, and correcting a refractive index formula by using the refractive indexes of the remaining 2 monochromatic light wavelengths; and when the error between the residual 2 wavelength refractive indexes in the corrected refractive index curve and the actually measured residual 2 wavelength refractive indexes is smaller than a set threshold value, the calibration is considered to be successful.

2. The apparatus for calibrating the refractive index of a planar iso-thick medium according to claim 1, wherein the set threshold is 0.003% to 0.005%.

3. The apparatus for calibrating the refractive index of a planar uniform-thickness medium according to claim 1 or 2, wherein:

the thickness of the plane uniform-thickness medium is H;

the plurality of monochromatic lights decomposed by the dispersion objective lens (L) are composed of at least one monochromatic light subset, and each monochromatic light subset comprises an upper monochromatic light and a lower monochromatic light; the upper monochromatic light in each monochromatic photon set is focused on the upper surface of the measured medium (13), and the lower monochromatic light in each monochromatic photon set is focused on the lower surface of the measured medium (13);

；

(ii) a The refractive index of the measured medium (13) at the wavelength lambda

Is derived from the following formula:

，

wherein the content of the first and second substances,

and

is a known parameter of a dispersive objective lens (L) in a spectral confocal sensor (11).

4. The apparatus for calibrating refractive index of planar uniform thickness medium according to claim 3,

defining:

The distance between the dispersive objective lens (L) and the measured medium (13) is changed for the fourth timeWhen in use, the wavelength of the upper monochromatic light is lambda₉Wavelength of the lower monochromatic light is λ₁₀

And has the following components:

，

by the formula

5. The apparatus for calibrating the refractive index of a planar uniform thickness medium according to claim 4, wherein the wavelength term power series is set in the range of: x is more than or equal to 0.1₁≤3，3.1≤X₂≤8，0.1≤X₃≤5。

6. A method for calibrating the refractive index of a planar medium with equal thickness is characterized by comprising the following steps:

providing a calibration device, wherein the calibration device comprises a spectrum confocal sensor (11), a spectrometer (14) and a distance adjusting mechanism, wherein the spectrum confocal sensor (11) comprises a white light point light source (S), a semi-transparent semi-reflecting mirror (X) and a dispersion objective lens (L); the semi-transparent semi-reflecting mirror (X) and the dispersive objective lens (L) are sequentially arranged between the white light point light source (S) and the measured medium (13) along an optical axis, the semi-transparent semi-reflecting mirror (X) is close to the white light point light source (S), and the dispersive objective lens (L) is close to the side of the measured medium (13);

the distance adjusting mechanism drives the spectrum confocal sensor (11) and the measured medium (13) to be close to or far away from each other so that the distance between the dispersion objective lens (L) and the measured medium (13) changes 5 times along the optical axis;

the spectrometer (14) is arranged opposite to the reflecting surface of the semi-transparent and semi-reflective mirror (X), and the spectrometer (14) is used for detecting the wavelength of monochromatic light which is focused on a medium to be detected (13) and reflected back;

7. The method for calibrating the refractive index of a planar iso-thick medium according to claim 6, wherein the set threshold is 0.003% to 0.005%.

8. The method for calibrating the refractive index of a planar uniform-thickness medium according to claim 6 or 7, wherein:

the thickness of the plane uniform-thickness medium is H;

；

Is derived from the following formula:

，

wherein the content of the first and second substances,

and

is a spectral confocal sensor11) Known parameters of a medium-dispersion objective lens (L).

9. The method for calibrating the refractive index of a planar uniform-thickness medium according to claim 8, wherein:

And has the following components:

，

by the formula

10. The method for calibrating the refractive index of a planar uniform thickness medium according to claim 9, wherein the wavelength term power series is set in the range of: x is more than or equal to 0.1₁≤3，3.1≤X₂≤8，0.1≤X₃≤5。