CN106094070A - Measure liquid refractivity and the aplanasia varifocal biliquid stem stem lens of Liquid Diffusion Coefficient - Google Patents

Abstract

Measure liquid refractivity and the aplanasia varifocal biliquid stem stem lens of Liquid Diffusion Coefficient, belong to optical measuring device and method.Present invention wick-containing post lens in the past are as liquid phase diffusion cell and image-forming component, rear wick-containing post lens are as aplanasia element, choose the aplanasia position of the refractive index value scalable biliquid stem stem lens of liquid in rear wick-containing post lens, and in wick-containing, liquid refractivity has wider excursion before ensureing in the range of less spherical aberration.The present invention improves the detection sensitivity of liquid refractivity in front wick-containing, in conjunction with etc. refractive index thin layer Mobile Method or transient state refractive index spatial distribution method, can more accurately and reliably measure the diffusion coefficient of different liquids.

Description

Measure liquid refractivity and the aplanasia varifocal biliquid stem stem of Liquid Diffusion Coefficient Lens

Technical field

The invention belongs to aplanatic optical column lens, the particularly aplanasia of wick-containing varifocal optical column lens.

Background technology

Liquid refractivity and Liquid Diffusion Coefficient are industry research mass transport process, the calculating such as biology, chemical industry, medical science and environmental protection The important foundation data of mass transfer rate and Chemical Engineering Design and exploitation.But both data to be accurately measured need lens combination to obtain Obtaining focus image clearly, the image that preferable aplanatic imaging system can make liquid refractivity is the sharpest, and focal position is clear, surveys It is more accurate to measure.Before proposing the present invention, we to propose the refractive index thin-layer method measurement refractive indexs such as use and liquid phase diffusion are Number (Sun Licun, general cloudling, Meng Weidong etc., Chinese invention patent 201310412166.X [P]), and propose quickly to measure diffusion system Transient state refractive index spatial distribution method (Meng Weidong, general cloudling, Sun Licun etc., the Chinese invention patent 201410440938.5 of number [P]).The former chooses different refractive index thin layers and measures same diffusion system or the diffusion coefficient of different diffusion system, and the latter is only Liquid Diffusion Coefficient can need to be quickly measured with piece image.For these methods, spherical aberration (i.e. longitudinal spherical aberration) remains impact The main cause that Liquid Diffusion Coefficient is accurately measured, correcting spherical aberration then must have refractive index highly sensitive and can eliminate institute Select refractive index thin layer focal point and the lens of the existing spherical aberration of transient state refractive index spatial distribution or system.Spherical aberration corrector method at present Generally by increase lens material refractive index, write music for a song, positive and negative lens combination or use the method such as non-spherical lens, these methods Typically can only there is aplanasia effect on some fixing refractive index point, measure refractive index and diffusion coefficient accordingly, and can not Accurately measure two kinds of data of whole diffusion system continuous distribution.Therefore, the problem of required solution is, one quickly, accurately Measuring liquid refractivity and the wick-containing post lens imaging system of Liquid Diffusion Coefficient, it is not only able to improve selected refractive index thin layer The refractive index sensitivity of focal position, and can eliminate or reduce fluid to be measured ball in the range of wider variations in refractive index Difference.

Summary of the invention

It is contemplated that based on above-mentioned wick-containing post lens method, it is provided that a kind of measurement liquid refractivity and Liquid Diffusion Coefficient Aplanasia varifocal biliquid stem stem lens, by the refractive index of liquid in wick-containing after regulation biliquid stem stem lens, improve refraction Rate sensitivity, eliminates or reduces spherical aberration, and can eliminate or reduce fluid to be measured spherical aberration in the range of wider variations in refractive index, Obtain image clearly.

The present invention is accomplished by:

This aplanasia varifocal biliquid stem stem lens are made up of, wherein front wick-containing post lens and rear wick-containing post lens:

Front wick-containing post lens are liquid phase diffusion cell and image-forming component, and rear wick-containing post lens are aplanasia element, rear wick-containing post Lens are n ' liquid built with refractive index, and this n ' liquid can reduce the spherical aberration of front wick-containing post lens and ensure liquid in front wick-containing Refractive index n has wider excursion.

Further, described aplanasia varifocal biliquid stem stem lens are by front wick-containing post lens and the 3 of rear wick-containing post lens The connection of sheet lens gluing is constituted, and wherein, front wick-containing post lens are made up of the 1st, 2 symmetrical sphere post lens, this sphere Injecting refractive index in post lens is that the liquid of n is as imaging original paper, it is also possible to load two kinds of liquid as liquid phase diffusion cell；Rear liquid Stem stem lens are by the 3rd lens plano-convex post lens and hollow spacing d of the 2nd, 3 two panels lens₅, and spacing d₅Built with refractive index N ' liquid is formed, for aplanasia element；

If the image distance of the 6 of 3 lens surface imagings is respectively S '₁、S’₂、S’₃、S’₄、S’₅、S’₆, the most described biliquid stem stem Gauss imaging method focal length between each lens thickness and the spacing of lens is:

f_Gauss(n)=s'₆(n,n′)+d₃+d₄+d₅+d₆,

F in formula_Gauss(n) and s'₆Relation between (n, n ') represents by following recurrence relation:

${s_6}^{\′}(n,n^{\′})=\frac{{s_5}^{\′}-d_6}{n_0},{s_5}^{\′}=\frac{n_0{R}_5({s_4}^{\′}-d_5)}{n^{\′}{R}_5+(n_0-n^{\′})({s_4}^{\′}-d_5)},$

${s_4}^{\′}=\frac{n^{\′}{R}_4({s_3}^{\′}-d_4)}{n_0{R}_4-(n^{\′}-n_0)({s_3}^{\′}-d_4)},{s_3}^{\′}=\frac{n_0{R}_3({s_2}^{\′}-d_2-d_3)}{{\mathrm{nR}}_3-(n_0-n)({s_2}^{\′}-d_2-d_3)},$

${s_2}^{\′}=\frac{{\mathrm{nR}}_2({s_1}^{\′}-d_1)}{n_0{R}_2+(n-n_0)({s_1}^{\′}-d_1)},{s_1}^{\′}=\frac{n_0{R}_1}{n_0-1}.$

Further, the radius of curvature of 3 lens of described aplanasia varifocal biliquid stem stem lens is respectively as follows: R₁=R₄ =45.0mm, R₂=R₃=27.9mm, R₅=21.5mm, lens thickness and spacing are respectively d₁=d₄=4.0mm, d₂=d₃= 3.0mm、d₅=1.0mm, d₆=12.0mm, d₇=8.3mm, d₈=3.7mm, light line width 2h=20.0mm, lens half-breadth height h₁ =12.6mm, h₂=17.0mm, length L=50.0mm of lens, material is refractive index n₀The K9 glass of=1.5163.

Further, described aplanasia varifocal biliquid stem stem lens are: the liquid refractivity n ' in rear wick-containing post lens Numerical value is 1.3950～1.4250, and in current wick-containing, liquid refractivity n is changed by one thousandth in the range of 1.3280～1.4310 During change, the spherical aberration of the focal length of its correspondence is less.

Preferably, described aplanasia varifocal biliquid stem stem lens are: the liquid refractivity n ' in rear wick-containing post lens Numerical value is 1.4010～1.4050, and in current wick-containing, liquid refractivity n is changed by one thousandth in the range of 1.3280～1.4310 During change, the spherical aberration of the focal length of its correspondence is the least.

The purposes of described aplanasia varifocal biliquid stem stem lens.

(1) focal length of biliquid stem stem lens of the present invention and wick-containing index of refraction relationship

Such as Fig. 1, the biliquid core cylindrical lens that 36 curved surface gluings of the present invention are got up.Wherein, R₁、R₂、R₃、R₄、R₅Respectively Representing the radius of curvature of five curved surfaces, the 6th face is plane.n₀Representing the glass refraction of biliquid stem stem lens, n ' is biliquid The refractive index of the filled liquid of rear wick-containing of stem stem lens, the refractive index of the filled liquid of front wick-containing that n is biliquid stem stem lens, d₁、 d₄、d₆It is the thickness of first, second, third lens glass, d₂、d₃It is the distance of first, second lens distance center O, d₅ Being the distance between second and the 3rd lens, 2h is the width of incident illumination.

1, when injecting the liquid that refractive index is n in the front wick-containing of biliquid stem stem lens of the present invention, with Gauss imaging method meter Calculate focal distance f_GaussWith the relation of liquid refractivity n in front wick-containing.

The object distance of 6 surface imagings is expressed as S₁、S₂、S₃、S₄、S₅、S₆, the image distance of imaging is expressed as S '₁、S’₂、 S’₃、S’₄、S’₅、S’₆, then focal distance f_GaussIt is represented by (1) formula with the relation of liquid refractivity n in front wick-containing:

f_Gauss(n)=s'₆(n,n′)+d₃+d₄+d₅+d₆ (1)

(derivation and recurrence relation are shown in detailed description of the invention before Section 2 liquid refractivity and biliquid stem stem in wick-containing Relation between the focal length of lens, the 2.1st trifle Gauss imaging method).

2, when injecting the liquid that refractive index is n in the front wick-containing of biliquid stem stem lens of the present invention, with geometry imaging method meter Calculate focal distance f_GeometryThe relation of liquid refractivity n in front wick-containing with biliquid stem stem lens

When incident illumination incides biliquid stem stem lens with the directional light of width 2h, with the side by face refractive index law imaging Method calculates focal distance f_GeometryIt is represented by (2) formula with front wick-containing refractive index n relation:

(derivation see in detailed description of the invention before Section 2 in wick-containing liquid refractivity and the biliquid stem stem focal length of lens it Between relation, the 2.2nd trifle geometry imaging method).

(2) a in formula₆、b₆For distance optical axis h height light to after biliquid stem stem lens after by face dioptric imaging With the intersection point of the 6th optical flat, k₁₁Represent light slope of emergent ray after the 6th optical flat.

(2) spherical aberration of biliquid stem stem lens of the present invention and front wick-containing liquid refractivity relation

The crossover optical axis of different height of incidence h (u) has deviation in various degree in diverse location, relative paraxial picture point, This deviation is referred to as axial spherical aberration.Axial spherical aberration picture point in Gauss image planes is not the most a point, but a disc of confusion, more The radius of speckle is referred to as hang down axle spherical aberration or longitudinal spherical aberration.

The focal length that the Gauss imaging genealogy of law uses paraxial ray to try to achieve is f_Gauss, the geometry imaging genealogy of law uses non-paraxial light Rim ray and optical axes crosspoint are f_Geometry, f_GaussWith f_GeometryDifference be spherical lateral aberration δ L '_{Spherical lateral aberration}=| f_Geometry-f_Gauss|。

If the light that tgU ' is h height to after biliquid stem stem lens after by face dioptric imaging hexahedro emergent ray Convergent angle tangent value, can be obtained longitudinal spherical aberration by geometrical relationship and be represented by:

Δy′_{Longitudinal spherical aberration}=δ L ' tgU '=-k₁₁|f_Geometry-f_Gauss| (3)。

(3) the refractive index sensitivity of biliquid stem stem lens of the present invention and liquid refractivity relation in front wick-containing

Liquid refractivity in the front wick-containing of biliquid stem stem lens is changed the focal length knots modification referred to as folding that one thousandth produces Penetrate the sensitivity of rate, it may be assumed that

Δf_Sensitivity=| f_Gauss-f_High′_This| (4)。

(1) biliquid stem stem lens aplanasia effect of the present invention

1, aplanasia Contrast on effect when wick-containing injects different refractivity liquid after biliquid stem stem lens of the present invention

As it is shown in figure 1, biliquid stem stem lens the 1st, 2 two panels lens glue of the present invention the most i.e. to constitute symmetrical wick-containing post saturating Mirror.When loading different refractivity n ' liquid in rear wick-containing (the 1st row of table 1), the often row of the liquid refractivity n in front wick-containing increases One thousandth (the 1st row of table 1), the spherical aberration change of the two correspondence is as shown in table 1.Fig. 3 is the spherical aberration change song corresponding with table 1 Line.

The situation of change of liquid refractivity in the spherical aberration wick-containing subsequently of table 1 biliquid of the present invention stem stem lens

As shown in table 1 spherical aberration changes, compared with other n', when in wick-containing after the present invention, liquid refractivity is n'= 1.4010,1.4030 time, y longitudinal spherical aberration is less.As Fig. 4,5, along with the adjustment of liquid refractivity n ' in rear wick-containing, biliquid stem stem In lens, aplanatic position changes therewith.Such as Fig. 5, when in rear wick-containing liquid refractivity be n'=1.4010,1.4030 time ball Difference sum is less, for 3.383mm, 3.368mm.

2, biliquid stem stem lens of the present invention and symmetrical wick-containing post lens aplanasia Contrast on effect

Such as Fig. 1, according to above (1), (2), (3) formula and experimental result, obtain with liquid refractivity n change in front wick-containing Simple symmetrical wick-containing post lens (the most front wick-containing post lens) and add rear wick-containing post lens (this with liquid refractivity n ' Bright biliquid stem stem lens) focal length, spherical aberration, the two contrast as shown in table 2:

The simple symmetrical wick-containing post lens of table 2 and biliquid stem stem lens spherical aberration of the present invention and sensitive analysis

Front wick-containing post lens Δ f_SensitivityFocal length changes corresponding with the biliquid stem stem focal length of lens of the present invention change, i.e. the former liquid 1.3280～1.4310 excursions of body refractive index n change, by one thousandth (the 1st row), the Δ f caused_SensitivityFocal length variations 0.742mm～0.248mm (the 4th row), corresponding to the focal length Δ f of the latter_SensitivityKnots modification 1.806mm～0.390mm (the 8th row), The focal length knots modification of biliquid stem stem lens of the present invention is the focal length knots modification about 2 times of front wick-containing post lens.

Liquid refractivity n ' numerical value in rear wick-containing post lens is 1.3950～1.4250, liquid refractivity in its front wick-containing N is changed by one thousandth in the range of 1.3280～1.4310, and the focal length knots modification of its correspondence is 1.806mm～0.390mm, and It it is aplanatic focal length 105.250 μm.

When the liquid refractivity n ' numerical value in rear wick-containing post lens is 1.4010, corresponding to liquid in front wick-containing post lens 1.3280～1.4310 excursions (the 1st row) of refractive index n, the focal distance f of the liquid refractivity in wick-containing post lens thereafter_Gauss It is changed to 168.710mm～82.860mm (the 6th row).

By table 2 and Fig. 4 it can be seen that maximum spherical aberration y of symmetrical wick-containing post lens and biliquid stem stem lens of the present invention_{Longitudinal spherical aberration} All it is rendered as parabolic curve.The former, by write music for a song and positive and negative lens combination lens combination can be made to have very at some refractive index point Good aplanasia effect, arrives the liquid in n=1.3610 (ethanol) ranges of indices of refraction as injected n=1.3330 (water) in front wick-containing During body, aplanasia effect is more apparent, and especially when n=1.3370, aplanasia effect is best.But with n=1.3370 for top, along n =1.3280 to n=1.4310 refractive index two ends change greatly.Thus, this aplanatic method is difficult to select as desired The multiple spot aplanasia effect of selecting property, it is also difficult to have preferable aplanasia effect in a wider ranges of indices of refraction.The latter, at n= 1.3280 arrive in n=1.4310 ranges of indices of refraction, maximum spherical aberration y_{Longitudinal spherical aberration}=105.250 μm, and with liquid refractivity in front wick-containing The change of change spherical aberration very slow, during n=1.3280, its spherical aberration is about the former 0.15 times, and during n=1.4310, its spherical aberration is big About only the former 1/4, therefore, has steady, good aplanasia effect (such as figure in the range of wider variations in refractive index 4)。

3, biliquid stem stem lens of the present invention and the refractive index Sensitivity comparison of simple symmetrical wick-containing post lens

The raising of refractive index sensitivity can measure liquid refractivity and Liquid Diffusion Coefficient more accurately.By table 1 and Fig. 5 During it can be seen that inject n=1.3330 (water), the refractive index sensitivity Δ f of wick-containing before biliquid stem stem lens of the present invention_Sensitivity= 1.620mm, and symmetrical wick-containing post lens are Δ f_Sensitivity=0.693mm, the sensitivity of biliquid stem stem lens of the present invention is symmetrical liquid 2.34 times of stem stem lens sensitivity.

The method proposed before this with us, such as " expands by the instantaneous refractive index spatial distribution measuring liquid phase of wick-containing post lens The method dissipating coefficient " etc. wick-containing post lens method compare, the present invention has a following good effect:

Biliquid stem stem lens of the present invention can change lens combination aplanasia by liquid refractivity in wick-containing after changing Focal position.Meanwhile, this lens combination is in the range of a less spherical aberration, it is ensured that in front wick-containing, liquid refractivity has Wider excursion.Utilize these lens adjustable feature of aplanatic focal position, the refractive index thin-layer method such as can use to measure Same diffusion system variable concentrations diffusion coefficient, it is also possible to measure the diffusion coefficient of different diffusion system.Simultaneously available less Spherical aberration in the range of, it is ensured that in front wick-containing, liquid refractivity has the feature of wider excursion, quick according to Transient Method Measure Liquid Diffusion Coefficient.

Biliquid stem stem lens of the present invention can change lens combination aplanasia by liquid refractivity in wick-containing after changing Focal position.Meanwhile, the present invention have aplanasia position according to adjustable, the higher refractive index sensitivity of experiment demand and Before changing in relative broad range, in wick-containing, during liquid refractivity, its spherical aberration is less, change stable feature.

Biliquid stem stem lens of the present invention obtain aplanatic diffusion image, improve measurement refractive index less than percentage One of two kinds of liquid between the precision of diffusion coefficient, preferably solve with etc. refractive index thin-layer method measure same and expand Image focal point position is caused to be not easy to sentence due to image spherical aberration during the diffusion coefficient of prose style free from parallelism system variable concentrations or different diffusion system Disconnected and the measurement that causes and calculate error, and preferably solve and measure liquid phase diffusion system with transient state refractive index spatial distribution method Can not accurately measure, owing to lens exist spherical aberration, measurement and the calculating error that picture traverse is caused during number.Therefore, the present invention is double Liquid Diffusion Coefficient can more accurately be measured by wick-containing post lens, meets scientific research, the experiment demand to Liquid Diffusion Coefficient further.

Additionally, the aplanatic varifocal biliquid stem stem lens combination of biliquid stem stem lens of the present invention can be widely used in Aplanatic focal position need to choose according to actual demand or need in the range of less spherical aberration before liquid refracting in wick-containing Rate has in the system of wider excursion.

Accompanying drawing explanation

Fig. 1 is the aplanatic varifocal biliquid stem stem lens devices structural representation of the present invention.In figure, aplanatic variable Burnt biliquid stem stem lens combination is made up of symmetric lens, 1 specific folding between planoconvex lens and lens 2 meniscate meniscuss Penetrate the liquid composition of rate, be three hexahedro formula biliquid stem stem lens.

Fig. 2 is the aplanatic varifocal biliquid stem stem lens devices pictorial diagram of the present invention.In figure, the 3 hexahedro aplanasias of chip The radius of curvature of lens is respectively R₁、R₂、R₃、R₄、R₅, lens thickness and spacing are respectively d₁、d₂、d₃、d₄、d₅、d₆, O is lens The center of system, O₁、O₂、O₃、O₄、O₅It is respectively the center of circle of first to the 5th curved surface.

Fig. 3 is that after aplanatic varifocal biliquid stem stem lens change in wick-containing during liquid refractivity, spherical aberration is with front wick-containing Interior liquid refractivity change curve.Wherein, ◆ when representing wick-containing refractive index n'=1.3950 after biliquid stem stem lens, spherical aberration is with front The change curve of liquid refractivity in wick-containing；When * representing wick-containing refractive index n'=1.4010 after biliquid stem stem lens, spherical aberration is with front The change curve of liquid refractivity in wick-containing；▲ when representing wick-containing refractive index n'=1.4030 after biliquid stem stem lens spherical aberration with front The change curve of liquid refractivity in wick-containing；× when representing wick-containing refractive index n'=1.4050 after biliquid stem stem lens spherical aberration with front The change curve of liquid refractivity in wick-containing；When ■ represents wick-containing refractive index n'=1.4080 after biliquid stem stem lens, spherical aberration is with front The change curve of liquid refractivity in wick-containing；● when representing wick-containing refractive index n'=1.4150 after biliquid stem stem lens, spherical aberration is with front The change curve of liquid refractivity in wick-containing；Spherical aberration spherical aberration during wick-containing refractive index n'=1.4250 after+expression biliquid stem stem lens With the change curve of liquid refractivity in front wick-containing.

Fig. 4 is symmetrical wick-containing post lens and aplanatic varifocal biliquid stem stem lens spherical aberration and refractive index Sensitivity comparison Analysis chart.Wherein, × and * represent that in the front wick-containing of symmetrical wick-containing post lens and biliquid stem stem lens, liquid refractivity exists respectively Spherical aberration curve time between 1.3280 1.4310.● and ▲ represent symmetrical posts lens and the front wick-containing of biliquid stem stem lens respectively Refractive index change of sensitivity curve when the refractive index of middle liquid is between 1.3280 1.4310.

Fig. 5 be aplanatic varifocal biliquid stem stem lens rear wick-containing in liquid refractivity be respectively as follows:

When n'=1.3950,1.4010,1.4030,1.4050,1.4080,1.4150,1.4250, the interior liquid of front wick-containing Every millesimal variations in refractive index corresponding spherical aberration sum from n=1.3280 to n=1.4310.

In rear wick-containing liquid refractivity be n'=1.4030,1.4050 time spherical aberration sum less, for 3.383mm, 3.368mm。

Fig. 6 is height for several through aplanatic varifocal biliquid stem stem lens first, second curved surface of the light of h What ray tracing image.

Fig. 7 is height for several through aplanatic varifocal biliquid stem stem lens the three, the 4th curved surface of one article of light of h What ray tracing image.

Fig. 8 is height for several through aplanatic varifocal biliquid stem stem lens the five, the 6th curved surface of one article of light of h What ray tracing image.

Further illustrating the present invention below in conjunction with detailed description of the invention, the example in detailed description of the invention includes but is not intended to Protection scope of the present invention.

Detailed description of the invention

§ 1 lens devices of the present invention

Apparatus of the present invention are as it is shown in figure 1,3 hexahedro formula aplanasias of aplanatic varifocal biliquid stem stem lens of design are saturating The radius of curvature of mirror is respectively R₁=R₄=45.0mm, R₂=R₃=27.9mm, R₅=21.5mm, thickness and spacing d₁=d₄= 4.0mm、d₂=d₃=3.0mm, d₅=1.0mm, d₆=12.0mm, d₇=8.3mm, d₈=3.7mm, highly 2h=20.0mm, thoroughly Length L=50.0mm of mirror, material is K9 glass, refractive index n₀=1.5163, before biliquid stem stem lens, wick-containing is both as liquid phase Diffusion cell is again as image-forming component, and rear wick-containing is used for improving refractive index sensitivity and reducing spherical aberration.

Relation between liquid refractivity and the biliquid stem stem focal length of lens in wick-containing before § 2

2.1 Gauss imaging methods

In order to try to achieve the focal distance f of biliquid stem stem lens (1) formula with Gauss imaging method_GaussWith the radius of curvature in six faces of lens, Relation between liquid refractivity in wick-containing front and back:

f_Gauss(n)=s'₆(n,n′)+d₃+d₄+d₅+d₆

If the object distance of 6 surface imagings is respectively S₁、S₂、S₃、S₄、S₅、S₆, the image distance of imaging is respectively S '₁、S’₂、S’₃、S ’₄、S’₅、S’₆, then:

First curved surface S₁、S’₁It is represented by:

$S_1=-\mathrm{\∞},{s_1}^{\′}=\frac{n_0{R}_1}{n_0-1}.$

Second curved surface S₂、S’₂It is represented by:

$S_2={S_1}^{\′}-d_1,{s_2}^{\′}=\frac{{\mathrm{nR}}_2({s_1}^{\′}-d_1)}{n_0{R}_2+(n-n_0)({s_1}^{\′}-d_1)}.$

3rd curved surface S₃、S’₃It is represented by:

$S_3={S_2}^{\′}-d_2-d_3,{s_3}^{\′}=\frac{n_0{R}_3({s_2}^{\′}-d_2-d_3)}{{\mathrm{nR}}_3-(n_0-n)({s_2}^{\′}-d_2-d_3)}.$

4th curved surface S₄、S’₄It is represented by:

$S_4={S_3}^{\′}-d_4,{s_4}^{\′}=\frac{n^{\′}{R}_4({s_3}^{\′}-d_4)}{n_0{R}_4-(n^{\′}-n_0)({s_3}^{\′}-d_4)}.$

5th curved surface S₅、S’₅It is represented by:

$S_5={S_4}^{\′}-d_5,{s_5}^{\′}=\frac{n_0{R}_5({s_4}^{\′}-d_5)}{n^{\′}{R}_5+(n_0-n^{\′})({s_4}^{\′}-d_5)}.$

6th curved surface S₆、S’₆It is represented by:

$S_6={S_5}^{\′}-d_6,{s_6}^{\′}(n,n^{\′})=\frac{{s_5}^{\′}-d_6}{n_0}.$

2.2 geometry imaging methods

In order to determine in (2) formula biliquid stem stem focal length of lens f in geometry imaging method_GeometryWith the radius of curvature in six faces of lens, Relation between liquid refractivity in wick-containing front and back.The focal length of biliquid stem stem lens and the relation of liquid refractivity n in front wick-containing Can be expressed as:

First curved planar reformation:

The parameter of the physical quantity related in derivation represents respectively: h is that incident ray half-breadth is high, R₁It it is first face curvature Radius, 1,1 ' for light through first curved surface angle of incidence and refraction angle, n₀For glass refraction, k₁It is first curved surface Normal, k₂It is the slope of first face refraction light, d₁Thickness, d for lens₂For second distance of curved surface center O point of lens Distance, x₁It is the central coordinate of circle of first curved surface, a₁、b₁Transverse and longitudinal coordinate for light and the intersection point of first curved surface.Such as Fig. 6 institute Showing, geometrical relationship and derivation are as follows:

$sin1=\frac{h}{R_1},tan1=\frac{sin1}{\sqrt{1-{\sin }^{2}1}},\frac{sin1}{sin{1}^{\′}}=\frac{n_0}{1}\⇒sin{1}^{\′}=\frac{sin1}{n_0},$

k₁=-tan1, x₁=R₁-d₁-d₂,

b₁=h,

$tan{1}^{\′}=\frac{k_2-k_1}{1+k_1{k}_2}\⇒k_2=\frac{k_1+tan{1}^{\′}}{1-k_{1}tan{1}^{\′}}.$

Second curved planar reformation:

The parameter of the physical quantity related in derivation represents respectively: R₂Being the second curvature radius, 2,2 ' is light warp Angle of incidence and refraction angle when crossing second curved surface, n is front wick-containing refractive index, k₃It is second normal to a surface, k₄It is second song The slope of face refraction light, x₂It is the central coordinate of circle of second curved surface, a₂、b₂For light and the transverse and longitudinal of the intersection point of second curved surface Coordinate, as shown in Figure 6, geometrical relationship and derivation are as follows: x₂=R₂-d₂,

$\left\{\begin{array}{c}y-b_1=k_2(x-a_1)\\ {\left(x-x_2\right)}^2+y^2=R_2^2\end{array}\right.\⇒$

$\left\{\begin{array}{c}{a}_2=\frac{(2x_2+2a_1{k}_2^2-2k_2{b}_1)-\sqrt{\begin{array}{c}{(2x_2+2a_1{k}_2^2-2k_2{b}_1)}^2-\\ 4(1+k_2^2)(x_2^2+k_2^2{a}_1^2+b_1^2-2a_1{b}_1{k}_2-R_2^2)\end{array}}}{2(1+k_2^2)},\\ b_2=b_1+k_2(a_2-a_1)\end{array}\right.$

$k_3=\frac{b_2-0}{a_2-x_2},tan2=\frac{k_2-k_3}{1+k_2{k}_3},sin2=\frac{tan2}{\sqrt{1+{\tan }^{2}2}},$

$\frac{sin2}{sin{2}^{\′}}=\frac{n}{n_0}\⇒sin{2}^{\′}=\frac{n_0}{n}sin2,tan{2}^{\′}=\frac{sin{2}^{\′}}{\sqrt{1-{\sin }^2{2}^{\′}}},$

$tan{2}^{\′}=\left|\frac{k_3-k_4}{1+k_3{k}_4}\right|\⇒tan{2}^{\′}=\frac{k_4-k_3}{1+k_3{k}_4}\⇒k_4=\frac{k_3+tan{2}^{\′}}{1-k_{3}tan{2}^{\′}}.$

3rd curved planar reformation:

The parameter of the physical quantity related in derivation represents respectively: R₃Being the 3rd surface curvature, 3,3 ' is light warp Cross angle of incidence and refraction angle, the k of the 3rd curved surface₅It is the 3rd normal to a surface, k₆It is the oblique of the 3rd curved refractive light Rate, d₃For the distance of O point distance the 3rd curved surface of lens, x₃It is the central coordinate of circle of the 3rd curved surface, a₃、b₃For light and the 3rd The transverse and longitudinal coordinate of the intersection point of individual curved surface.As it is shown in fig. 7, geometrical relationship and derivation are as follows:

x₃=-(R₃-d₃),

$\left\{\begin{array}{c}y-b_2=k_4(x-a_2)\\ {\left(x-x_3\right)}^2+y^2=R_3^2\end{array}\right.\⇒$

$\left\{\begin{array}{c}{a}_3=\frac{(2x_3+2a_2{k}_4^2-2k_4{b}_2)+\sqrt{\begin{array}{c}{(2x_3+2a_2{k}_4^2-2k_4{b}_2)}^2-\\ 4(1+k_4^2)(x_3^2+k_4^2{a}_2^2+b_2^2-2a_2{b}_2{k}_4-R_3^2)\end{array}}}{2(1+k_4^2)},\\ b_3=b_2+k_4(a_3-a_2)\end{array}\right.$

$k_5=\frac{b_3-0}{a_3-x_3},tan3=\frac{k_5-k_4}{1+k_4{k}_5},sin3=\frac{tan3}{\sqrt{1+{\tan }^{2}3}},$

$\frac{sin3}{sin{3}^{\′}}=\frac{n_0}{n}\⇒sin{3}^{\′}=\frac{n}{n_0}sin3,tan{3}^{\′}=\frac{sin{3}^{\′}}{\sqrt{1-{\sin }^2{3}^{\′}}},$

$tan{3}^{\′}=\left|\frac{k_5-k_6}{1+k_5{k}_6}\right|\⇒tan{3}^{\′}=\frac{k_5-k_6}{1+k_5{k}_6}\⇒k_6=\frac{k_5-tan{3}^{\′}}{1+k_{5}tan{3}^{\′}}.$

4th curved planar reformation:

The parameter of the physical quantity related in derivation represents respectively: R₄For fourth face radius of curvature, 4,4 ' pass through for light The angle of incidence in the 4th face and refraction angle, n ' is liquid refractivity, k in rear wick-containing₇It is the 4th normal to a surface, k₈It is the 4th The slope of individual face refraction light, d₄For the thickness of lens, x₄It is the central coordinate of circle of the 4th curved surface, a₄、b₄For light and the 4th The transverse and longitudinal coordinate of the intersection point of curved surface.As it is shown in fig. 7, geometrical relationship and derivation are as follows:

$x_4=-(R_4-d_3-d_4),$

$\left\{\begin{array}{c}y-b_3=k_6(x-a_3)\\ {\left(x-x_4\right)}^2+y^2=R_4^2\end{array}\right.\⇒$

$\left\{\begin{array}{c}{a}_4=\frac{(2x_4+2a_3{k}_6^2-2k_6{b}_3)+\sqrt{\begin{array}{c}{(2x_4+2a_3{k}_6^2-2k_6{b}_3)}^2-\\ 4(1+k_6^2)(x_4^2+k_6^2{a}_3^2+b_3^2-2a_3{b}_3{k}_6-R_4^2)\end{array}}}{2(1+k_6^2)},\\ b_4=b_3+k_6(a_4-a_3)\end{array}\right.$

$k_7=\frac{b_4-0}{a_4-x_4},tan4=\frac{k_7-k_6}{1+k_6{k}_7},sin4=\frac{tan4}{\sqrt{1+{\tan }^{2}4}},$

$\frac{sin4}{sin{4}^{\′}}=\frac{n^{\′}}{n_0}\⇒sin{4}^{\′}=\frac{n_{0}sin4}{n^{\′}},tan{4}^{\′}=\frac{sin{4}^{\′}}{\sqrt{1-{\sin }^2{4}^{\′}}},$

$tan{4}^{\′}=\left|\frac{k_8-k_7}{1+k_7{k}_8}\right|\⇒tan{4}^{\′}=\frac{k_7-k_8}{1+k_7{k}_8}\⇒k_8=\frac{k_7-tan{4}^{\′}}{1+k_{7}tan{4}^{\′}}.$

5th curved planar reformation:

The parameter of the physical quantity related in derivation represents respectively: R₅Being the 5th curvature radius, 5,5 ' pass through for light The angle of incidence of the 5th curved surface and refraction angle, k₉For light through the 5th normal to a surface, k₁₀Reflect through the 5th face for light The slope of light, x₅It is the central coordinate of circle of the 5th curved surface, d₅For the distance between symmetrical wick-containing post lens and convex plano lens, a₅、b₅ For light and the transverse and longitudinal coordinate of the intersection point of the 5th curved surface, n ' is rear wick-containing refractive index.As shown in Figure 8, geometrical relationship and derivation Process is as follows:

x₅=R₅+d₃+d₄+d₅,

$\left\{\begin{array}{c}y-b_4=k_8(x-a_4)\\ {\left(x-x_5\right)}^2+y^2=R_5^2\end{array}\right.\⇒$

$\left\{\begin{array}{c}{a}_5=\frac{(2x_5+2a_4{k}_8^2-2k_8{b}_4)+\sqrt{\begin{array}{c}{(2x_5+2a_4{k}_8^2-2k_8{b}_4)}^2-\\ 4(1+k_8^2)(x_5^2+k_8^2{a}_4^2+b_4^2-2a_4{b}_4{k}_8-R_5^2)\end{array}}}{2(1+k_8^2)},\\ b_5=b_4+k_8(a_5-a_4)\end{array}\right.$

$k_9=\frac{b_5-0}{a_5-x_5},tan5=\left|\frac{k_8-k_9}{1+k_8{k}_9}\right|\⇒tan5=\frac{k_9-k_8}{1+k_8{k}_9},$

$sin5=\frac{tan5}{\sqrt{1+{\tan }^{2}5}},\frac{sin5}{sin{5}^{\′}}=\frac{n_0}{n^{\′}}\⇒sin{5}^{\′}=\frac{n^{\′}sin5}{n_0},$

$tan{5}^{\′}=\frac{sin{5}^{\′}}{\sqrt{1-{\sin }^2{5}^{\′}}},$

$tan{5}^{\′}=\left|\frac{k_9-k_{10}}{1+k_9{k}_{10}}\right|\⇒tan{5}^{\′}=\frac{k_9-k_{10}}{1+k_9{k}_{10}}\⇒k_{10}=\frac{k_9-tan{5}^{\′}}{1+k_{9}tan{5}^{\′}}.$

6th curved planar reformation:

The parameter of the physical quantity related in derivation represents respectively: 6,6 ' for light through the angle of incidence of the 6th curved surface and Refraction angle, k₁₁Reflect the slope of light, x through the 6th curved surface for light₆It is that the 6th curved surface emergent ray is handed over primary optical axis The coordinate of point, d₆For the thickness of convex plano lens, a₆、b₆For light and the transverse and longitudinal coordinate of the intersection point of the 6th curved surface.As shown in Figure 8, Geometrical relationship and derivation are as follows:

a₆=d₃+d₄+d₅+d₆, y-b₅=k₁₀(x-a₅), b₆=b₅+k₁₀(a₆-a₅),

Tan6=-k₁₀,

k₁₁=-tan6 ', y-b₆=k₁₁(x-a₆),

Work as y₆When=0,

Claims (8)

1. measure liquid refractivity and the aplanasia varifocal biliquid stem stem lens of Liquid Diffusion Coefficient, it is characterized in that: this biliquid Stem stem lens are made up of, wherein front wick-containing post lens and rear wick-containing post lens:

Front wick-containing post lens are liquid phase diffusion cell and image-forming component, and rear wick-containing post lens are aplanasia element, rear wick-containing post lens Built with refractive index it isn' liquid, this liquid can reduce the spherical aberration of front wick-containing post lens and ensure before liquid refracting in wick-containing RatenThere is wider excursion.

Aplanasia the most according to claim 1 varifocal biliquid stem stem lens, is characterized in that:

These biliquid stem stem lens are made up of 3 lens gluings connections of front wick-containing post lens and rear wick-containing post lens, wherein, front Wick-containing post lens are made up of the 1st, 2 symmetrical sphere post lens, inject refractive index and be in these sphere post lensnLiquid make For imaging original paper, it is also possible to load two kinds of liquid as liquid phase diffusion cell；Rear wick-containing post lens are by the 3rd lens plano-convex post lens Hollow spacing with the 2nd, 3 two panels lensd ₅, and spacingd ₅Formed built with refractive index liquid, for aplanasia element；

If the image distance of the 6 of 3 lens surface imagings is respectivelyS’ ₁、S’ ₂、S’ ₃、S’ ₄、S’ ₅、S’ ₆, the most described biliquid stem stem lens Each lens thickness and spacing between Gauss imaging method focal length be:

,

In formula and between relation represent by following recurrence relation:

。

Aplanasia the most according to claim 1 and 2 varifocal biliquid stem stem lens, is characterized in that: described biliquid stem stem is saturating The radius of curvature of 3 lens of mirror is respectively as follows:R ₁= R ₄=45.0mm、R ₂=R ₃=27.9mm、R ₅=21.5mm, lens thickness and spacing It is respectivelyd ₁=d ₄=4.0mm、d ₂=d ₃=3.0mm、d ₅=1.0mm、d ₆=12.0mm,d ₇=8.3mm、d ₈=3.7mm, light line width 2h= 20.0mm, lens half-breadth is highh ₁=12.6mm、h ₂=17.0mm, the length of lensL=50.0mm, material is refractive indexn ₀=1.5163 'sK9 glass.

Aplanasia the most according to claim 1 and 2 varifocal biliquid stem stem lens, is characterized in that: in rear wick-containing post lens Liquid refracting rate score be 1.3950～1.4250, liquid refractivity in current wick-containingnIn the range of 1.3280～1.4310 When changing by one thousandth, the spherical aberration of the focal length of its correspondence is less.

Aplanasia the most according to claim 3 varifocal biliquid stem stem lens, is characterized in that: the liquid in rear wick-containing post lens Body refractive index value is 1.3950～1.4250, liquid refractivity in current wick-containingnBy thousand in the range of 1.3280～1.4310 During/mono-change, the spherical aberration of the focal length of its correspondence is less.

Aplanasia the most according to claim 1 and 2 varifocal biliquid stem stem lens, is characterized in that: preferably, rear wick-containing post Liquid refracting rate score in lens is 1.4010～1.4050, liquid refractivity in current wick-containingn1.3280～1.4310 In the range of by one thousandth change time, the spherical aberration of the focal length of its correspondence is the least.

Aplanasia the most according to claim 3 varifocal biliquid stem stem lens, is characterized in that: preferably, rear wick-containing post is saturating Liquid refracting rate score in mirror is 1.4010～1.4050, liquid refractivity in current wick-containingnAt 1.3280～1.4310 models When changing by one thousandth in enclosing, the spherical aberration of the focal length of its correspondence is the least.

8. the purposes of the aplanasia varifocal biliquid stem stem lens as described in claim 1～7.