CN100495113C - Design method of three-dimensional optical lens and lens - Google Patents

Abstract

The 3D optical lens design method comprises: based on law of conservation of energy, dividing out some sub-areas as the light source energy equal to illuminant plane energy; selecting one point any of the point in one emergence line and corresponding equal-energy illuminant plane points as the initial point for target lens; iterative solving coordinate and normal vector for every discrete point to determine the lens surface. Compared with prior art, this invention is convenient and high efficient, and can save energy for wide application.

Description

A kind of method for designing of three-dimensional optical lens and lens

Technical field

A kind of method for designing of three-dimensional optical lens and lens relate to three-dimensional given Illumination Distribution optical design technical field in the nonimaging optics.

Technical background:

The lens of traditional image optics design have rotational symmetry usually, are used for the point of object plane is looked like above the plane through being imaged onto behind the lens.What the lens design of traditional optical was paid attention to more is the preservation of picture information in imaging process, and the light ray energy transfer efficiency then is placed on less important position, and therefore the common transfer efficiency of lens that designs is lower.

Nonimaging optics is to have grown up gradually abroad since the seventies in last century, specializes in a new optical branching of the power transfer problem of light.The collection that nonimaging optics is mainly studied sun power at first utilizes problem, light coupled problem just, how the incident ray of a big input aperture is collected, transmit a little output aperture fully, thereby the convenient utilization of raising energy density has produced a cover gradually in research process is used to control the theory of light ray energy transmission as " marginal ray theory " (Ries, H and Rabl, A " Edge-ray principle of nonimaging optics; " J.Opt.Soc.Am.43 712-715), (the H.Ries that " cuts out theory ", J.A.Muschaweck, " Tailoring freeform optical lenses for illuminations; " Novel Optical Systems Designand Optimization IV, Proc.SPIE, vol 4442, pp.43-50, (2001)) (Andreas Timinger a, Julius Muschaweck a, HaraldRiesa, " Designing Tailored Free-Form Surfaces for General Illumination; " Proc.SPIE, vol 5186, pp.128-132, (2003)) and " symmetrical analysis theory " (Ries, H Shatz, N, Bortz, J and Spirkl, W " Performance limitations ofrotationally symmetric nonimaging devices " J.O pt.Soc.AmA vol 14,10,2855-2862,1997).Another direction of nonimaging optics development is illuminator of design, can use a given light source to form given Illumination Distribution, just given Illumination Distribution problem on a target screen.

The problem that nonimaging optics faces in the space of different dimensions has different difficulty.The nonimaging optics of two-dimensional space is mainly studied to be had necessarily symmetricly, as rotates the symmetry and the optical system of translation symmetry.Though symmetry has been carried out certain simplification to the nonimaging optics problem, made things convenient for and found the solution, but symmetry itself will restrict the further raising of transfer efficiency, therefore for the basic energy transmission efficiency problem that solves, the difficulty that present nonimaging optics mainly faces is how will find the solution the space to be extended to field of three dimension, and design does not have symmetric optical system.This has been proposed a lot of advanced persons' theory and algorithm abroad:

Aspect the light coupled problem, the method that can design the three dimensions optical system at present theoretically has Bo Yinting to draw together arrow (J.C.Minano " design of three-dimensional nonimaging concentrator with inhomogeneous media " J.opt.Soc.AmA (3) pp.1345-1353,1986), streamline method (R.Winston, W.T.Welford " Geometrical vector flux and some newnonimaging concentrators ", J.opt.Soc.Am 69 (4), pp.532-536,1979) and Lorentz method of geometry (Guti é rrez, M., Minano, J.C., Vega, C.and Ben í tez, P. " Application of Lorentz Geometry to Nonimaging optics:New 3D idealconcentrators ", J.opt.Soc.Am 13, pp.532-540,1996), these methods have proved that theoretically free three-dimensional optical system can the realization theory transfer efficiency, yet because the method for design is very complicated, and the dielectric material that needs graded index can not be used for designing practical optical system.SMS multilist face method for designing simultaneously is the method that is used for designing the practical optics system (P.Ben í tez, the J.C.Mi of up-to-date proposition

Iano, et al, " Simultaneous multiple surface optical design method in three dimensions ", Opt.Eng, 43 (7) 1489-1502, (2004)), owing to adopted the distinctive design theory of nonimaging optics in the design--" marginal ray " theory, realized having the three-dimensional surface optical system of uniform dielectric material, yet the SMS method for designing wants to be generalized to given Illumination Distribution problem, still require that given Illumination Distribution is transformed into optical wave-front earlier and adopt method to design then, therefore must find the solution several second nonlinears and cover special ampere equations with the light coupling;

Aspect given illumination problem, mainly contain two research directions at present: utilize the variational integral optimization method, the geometric approximation method is found the solution method (the L.Caffarelli and V.Oliker that second order nonlinear is covered special ampere equation, " Weak solutions of one inverseproblem in geometric optics " Preprint, 1994.) (S.Kochengin and V.Oliker, " Determination of reflector surfacesfrom near-field scattering data II.Numerical solution; " Numerishe Mathematik 79 (4), pp.553-568,1998.) (LCaffarelli, S.Kochengin, and V.Oliker, " On thenurnerical solution of the problem of reflector design with givenfar-field scattering data; " Contemporary Mathematics 226, pp.13-32,1999.) and the cut-out method (as preceding) of free three-dimensional surface.Adopt geometric approximation and this method of variational integral mainly to be used in the given Illumination Distribution problem of having only a reflecting surface of finding the solution.Utilize the method for geometric approximation the problem of finding the solution a reflective surface can be transformed into the problem of finding the solution a series of reflective surface, ask the method for the limit finally to obtain a convergent reflective surface to these a series of reflective surfaces then, yet can not guarantee the smooth degree of reflective surface, be called weak approximate solution; Adopt the method for variational integral the problem of finding the solution reflective surface can be changed into the problem that variation is asked extreme value, therefore be convenient to adopt the method for optimization to find the solution, more than all exist convergent to separate on two kinds of theoretical methods, but because solution procedure complexity, increase along with solving precision, calculated amount rapidly increases, and efficiency of algorithm is low; The method that free three-dimensional surface is cut out makes up the mathematical model of refractive surface on principle, target is to adopt refractive surface to realize given Illumination Distribution, final mathematical model still is summed up as finds the solution the special ampere of SEVERAL NONLINEAR second order illiteracy equation, and because in solution procedure, adopt the continuous method of curved surface Gaussian curvature to guarantee the local slickness of curved surface, can in small angle range, obtain more satisfactory Illumination Distribution, along with the increase of angle, can not guarantee the existence of refractive surface.

Summary of the invention

The invention solves need be according to concrete Illumination Distribution in the actual illumination field, and the problem of design optical system has proposed a kind of method for designing of three-dimensional optical lens and the lens that design according to this method.

The method that the present invention proposes is characterised in that, this method is according to law of conservation of energy, in computing machine, with the energy of light source and the energy binned on illumination plane is some zonules of energy correspondent equal, then at an emergent ray and optional between the point on the illumination plane of energy correspondent equal with it a bit as initial point of lens surface to be found the solution, energy binned result in conjunction with light source and illumination plane, utilization iterates coordinate and the normal vector that the method for finding the solution solves all discrete points of lens surface, thereby has determined a lens surface.This method contains the following steps of moving in computing machine:

1) initialization:

For the light direction of light source set up a coordinate system (u, v), for the point on the illumination plane set up a coordinate system (x, y);

An initial light (u on the given light source light direction ₀, v ₀), an initial point (x on the given illumination plane ₀, y ₀);

The number m+1 of discrete point in the energy corresponding relation is walked crosswise in number n+1 of discrete point in given vertical energy corresponding relation, and wherein n and m are natural number;

Step delta u between the given source light ₀Δ u _n, Δ v _oΔ v _m

The refractive index n of given lens material ₁Refractive index n with air ₂

2) light source and illumination plane are carried out the correspondence division of energy:

2.1) set up with the light direction of light source and a vertical corresponding relation of the point on the illumination plane:

2.1.1) calculating source light (u ₀, v ₀), at Δ u ₀The energy size that has in the scope:

$E\left({\mathrm{\Δu}}_0\right){|}_{u=u_0}={\∫}_{u=u_0}I(u,v)\left|J(u,v)\right|\mathrm{dv}\·{\mathrm{\Δu}}_0,$ Wherein

(u v) is that light source is at (u, the v) light on the direction

It is powerful little, U, v) | for adopt (u, v) coordinate system need be scaled dudv the Jacobian of unit area; 2.1.2) calculate the point (x on the illumination plane ₀, y ₀) corresponding step delta x ₀:

${\mathrm{\Δx}}_0=E\left({\mathrm{\Δu}}_0\right){|}_{u=u_0}/{\∫}_{x=x_0}L(x,y)\left|J(x,y)\right|\mathrm{dy},$ Wherein L (x, y) be illustrated on the illumination plane (x, the y) brightness value at some place,

(x, y) | for adopt (x, y) coordinate system need be scaled dxdy the Jacobian of unit area;

2.1.3) make u ₁=u ₀+ Δ u ₀, x ₁=x ₀+ Δ x ₀Thereby, the light that obtains that pointolite sends and the energy corresponding relation of a point on the illumination plane: (u ₁, v ₀) corresponding to (x ₁, y ₀);

2.1.3) utilize step 2.1.1) and in formula compute ray (u ₁, v ₀) at Δ u ₁The energy size that has in the scope:

$E\left({\mathrm{\Δu}}_1\right){|}_{u=u_1}={\∫}_{u=u_1}I(u,v)\left|J(u,v)\right|\mathrm{dv}\·{\mathrm{\Δu}}_1;$

2.1.4) utilize step 2.1.2) and in formula calculate point (x on the illumination plane ₁, y ₀) corresponding step delta x ₁:

${\mathrm{\Δx}}_1=E\left({\mathrm{\Δu}}_1\right){|}_{u=u_1}/{\∫}_{x=x_1}L(x,y)\left|J(x,y)\right|\mathrm{dy};$

2.1.5) make u ₂=u ₁+ Δ u ₁, x ₂=x ₁+ Δ x ₁, utilize step 2.1.1) and step 2.1.2) in formula, obtain another light that pointolite sends and the energy corresponding relation of another point on the illumination plane: (u ₂, v ₀) corresponding to (x ₂, y ₀);

2.1.6) repeating step 2.1.1)～2.1.5), iterate a vertical corresponding relation of energy of the some formation that calculates on source light and the illumination plane $U_{v_0}=h\left(X_{y_0}\right)$ And Δ X, wherein:

$U_{v_0}=\{(u_0,v_0),(u_1,v_0),......(u_n,v_0)\}$

$X_{y_0}=\{(x_0,y_0),(x_1,y_0),......(x_n,y_0)\}$

ΔX＝{Δx ₀，Δx ₁，......Δx _n}；

2.2) to set up with the point on above-mentioned vertical corresponding relation be n+1 the light of initial point and the horizontal corresponding relation of energy of the point on the illumination plane:

2.2.1) from above-mentioned vertical corresponding relation $U_{v_0}=h\left(X_{y_0}\right)$ In get initial point (u ₀, v ₀) and initial step length Δ v ₀, compute ray (u ₀, v ₀) at (Δ u ₀, Δ v ₀) the energy size that has in the scope:

$E({\mathrm{\Δu}}_0,{\mathrm{\Δv}}_0){|}_{(u=u_0,v=v_0)}=I(u_0,v_0)\left|J(u_0,v_0)\right|{\mathrm{\Δu}}_0{\mathrm{\Δv}}_0;$

2.2.2) calculate the initial point (x on the illumination plane ₀, y ₀) corresponding step delta y ₀:

${\mathrm{\Δy}}_0=\frac{E({\mathrm{\Δu}}_0,{\mathrm{\Δv}}_0){|}_{(u=u_0,v=v_0)}}{L(x_0,y_0)\left|J(x_0,y_0)\right|{\mathrm{\Δx}}_0};$

2.2.3) make v ₁=v ₀+ Δ v ₀, y ₁=y ₀+ Δ y ₀Obtain the energy corresponding relation of a point on light of pointolite and the illumination plane: (u ₀, v ₁) corresponding to (x ₀, y ₁);

2.2.4) according to step 2.2.1) and formula compute ray (u ₀, v ₁) at (Δ u ₀, Δ v ₁) the energy size that has in the scope:

$E({\mathrm{\Δu}}_0,{\mathrm{\Δv}}_1){|}_{(u=u_0,v=v_1)}=I(u_0,v_1)\left|J(u_0,v_1)\right|{\mathrm{\Δu}}_0{\mathrm{\Δv}}_1;$

2.2.5) according to step 2.2.2) and formula calculate (x on the illumination plane ₀, y ₁) corresponding step delta y ₁:

${\mathrm{\Δy}}_1=\frac{E({\mathrm{\Δu}}_0,{\mathrm{\Δv}}_1){|}_{(u=u_0,v=v_1)}}{L(x_0,y_1)\left|J(x_0,y_1)\right|{\mathrm{\Δx}}_0};$

2.2.6) make v ₂=v ₁+ Δ v ₀, y ₂=y ₁+ Δ y ₁Obtain another light of pointolite and the energy corresponding relation of another point on the illumination plane: (u ₀, v ₂) corresponding to (x ₀, y ₂);

2.2.7) recycling step 2.2.1) and 2.2.2) in formula, iterate a horizontal corresponding relation of energy of the point that calculates on pointolite emergent ray and the illumination plane $V_{u_0}=Y_{x_0},$ Wherein $V_{u_0}=\{(u_0,v_0),(u_0,v_1),......(u_0,v_m)\},$ $Y_{x_0}=\{(x_0,y_0),(x_0,y_1),......(x_0,y_m)\};$

2.2.8) repeating step 2.2.1～2.2.7), calculating with the n+1 on vertical corresponding relation point is n+1 the horizontal corresponding relation of energy of initial point, wherein finding the solution of each bar horizontal curve adopted Δ X={ Δ x ₀, Δ x ₁... Δ x _nIn a corresponding step-length as the step-length of discrete point on the x direction

$V_{u_0}=g\left(Y_{x_0}\right),$ $V_{u0}=\{(u_0,v_0),(u_0,v_1),......(u_0,v_m)\},$ $Y_{x_0}=\{(x_0,y_0),(x_0,y_1),......(x_0,y_m)\}$

$V_{u_1}=g\left(Y_{x_1}\right),$ $V_{u_1}=\{(u_1,v_0),(u_1,v_1),......(u_1,v_m)\},$ $Y_{x_1}=\{(x_1,y_0),(x_1,y_1),......(x_1,y_m)\}$

$V_{u_n}=g\left(Y_{x_n}\right),$ $V_{u_n}=\{(u_n,v_0),(u_n,v_1),......(u_1,v_m)\},$ $Y_{x_n}=\{(x_n,y_0),(x_n,y_1),......(x_n,y_m)\};$

3) iterating of lens surface data point found the solution:

3.1) the determining of a vertical curve of lens surface:

3.1.1) according to vertical corresponding relation on light source and illumination plane $U_{v_0}=h\left(X_{y_0}\right),$ On light source, select an initial light Corresponding to an initial position P on the illumination plane ₀₀(x ₀, y ₀);

3.1.2) initial point S of selection on the travel path of initial light ₀₀Starting point as optical surface;

3.1.3) utilize initial point S ₀₀With the correspondence position P on the illumination plane ₀₀Obtain at a S ₀₀The direction vector of the emergent ray at place ${\stackrel{\→}{O}}_{00}=\stackrel{\→}{S_{00}{P}_{00}},$ Obtain at S according to refraction law ₀₀The normal vector that the some surface should have

${\stackrel{\→}{N}}_{00}=n_1*{\stackrel{\→}{I}}_{00}-n_2*{\stackrel{\→}{O}}_{00};$

Or obtain at S according to reflection law ₀₀The normal vector that the some surface should have

${\stackrel{\→}{N}}_{00}={\stackrel{\→}{I}}_{00}-{\stackrel{\→}{O}}_{00};$

3.1.4) on light source, select the second emergent ray according to vertical corresponding relation on light source and illumination plane

Corresponding illumination plane P ₁₀(x ₁, y ₀) point, according to S ₀₀The normal vector on some surface

Obtain S ₀₀The section T of point ₀₀

3.1.5) obtain light

Through propagating and S ₀₀The section T of point ₀₀Position of intersecting point S ₁₀

3.1.6) in conjunction with the corresponding point P on illumination plane ₁₀, obtain a S ₁₀The direction vector of emergent ray ${\stackrel{\→}{O}}_{10}=\stackrel{\→}{S_{10}{P}_{10}},$ Obtain at S according to refraction law ₁₀The normal vector that the some surface should have

${\stackrel{\→}{N}}_{10}=n_1*{\stackrel{\→}{I}}_{10}-n_2*{\stackrel{\→}{O}}_{10};$

Or obtain at S according to reflection law ₀₀The normal vector that the some surface should have

:

${\stackrel{\→}{N}}_{10}={\stackrel{\→}{I}}_{10}-{\stackrel{\→}{O}}_{10};$

3.1.7) on light source, continue to select emergent ray according to vertical corresponding relation on light source and illumination plane, according to step 3.1.2)～3.1.6) go on foot, obtain the discrete data point S on vertical curve of lens surface ₀₀, S ₁₀S _N0, and the normal vector of the emergent ray of every bit correspondence

Promptly determined a vertical curve of lens surface;

3.2) with the finding the solution of the discrete point on vertical curve of lens surface as the n+1 bar horizontal curve of initial point:

3.2.1) get an initial point S from vertical curve on said lens surface ₀₀,, select S according to the horizontal corresponding relation of the energy on light source and illumination plane as the initial point of a horizontal curve ₀₀The incident ray that point is contiguous

Some P0 on the corresponding illumination plane ₁(x ₀, y ₁);

3.2.2) obtain light Through propagating and S ₀₀The section T of point ₀₀Position of intersecting point S ₀₁

3.2.3) this is corresponding to the some P on the illumination plane ₀₁(x ₀, y ₁), thereby obtain S ₀₁The direction vector of the emergent ray of some light ${\stackrel{\→}{O}}_{01}=\stackrel{\→}{S_{01}{P}_{01}},$ Obtain at S according to refraction law ₀₁The normal vector that the some surface should have

${\stackrel{\→}{N}}_{01}=n_1*{\stackrel{\→}{I}}_{01}-n_2*{\stackrel{\→}{O}}_{01};$

Or obtain at S according to reflection law ₀₁The normal vector that the some surface should have

${\stackrel{\→}{N}}_{01}={\stackrel{\→}{I}}_{01}-{\stackrel{\→}{O}}_{01};$

3.2.4) on light source, continue to select successively contiguous emergent ray according to the horizontal corresponding relation on light source and illumination plane

According to step 3.2.1)～3.2.4), obtain with the some S on the vertical curve of lens surface ₀₀Be the discrete data point S on the horizontal curve of initial point ₀₀, S ₀₁S _0m, and the normal vector of every bit correspondence

${\stackrel{\→}{N}}_{00},{\stackrel{\→}{N}}_{01}\·\·\·\·\·\·{\stackrel{\→}{N}}_{0m};$

3.2.5) continue to select successively initial point S ₁₀S _N0,, find the solution and obtain with on the vertical curve on the lens all with discrete point S according to step 3.2.1～3.2.4) ₀₀S _N0Be the normal vector that the discrete point on the n+1 bar horizontal curve of initial point and this point have, then all data points of lens surface and normal vector thereof are found the solution and are finished, and have promptly determined the surface of lens.

In above-mentioned initialization, described coordinate system (u, v) and coordinate system (x y) adopts same initial point.(u v) can adopt spherical coordinates or polar coordinates to coordinate system.Initial light on the light direction of described light source

Select the light at edge or the light at center, the initial point (x on the illumination plane ₀, y ₀) be the point (x of the marginal position corresponding with described initial light ₀, y ₀) or the point of center.

In the travel path of light, when having given surface,

Step 3.1.2) changes into: after preliminary ray trace is crossed given surface, on travel path, select an initial point S ₀₀Starting point as optical surface;

Step 3.1.5) changes into: obtain light

After trace is crossed given surface, through propagating and S ₀₀The section T of point ₀₀Position of intersecting point S ₁₀Step 3.2.2) changes into: obtain light

After trace is crossed given surface, through propagating and S ₀₀The section T of point ₀₀Position of intersecting point S ₀₁

The method for designing of the present invention and lens that design is characterized in that having the peanut shell mould outside surface of medial recess.

The method for designing of the present invention and lens that design is characterized in that having the spherical outer surface of three above ribs.

Evidence can make full use of the energy of light source, thereby save the energy according to the needs design three-dimensional lens of Illumination Distribution according to method for designing of the present invention, has broad application prospects.

Description of drawings:

Fig. 1 is the synoptic diagram to vertical division of energy of light source and field of illumination energy;

Fig. 2 is the horizontal division synoptic diagram to the energy of energy of light source and field of illumination;

Fig. 3 is according to vertically dividing the synoptic diagram that obtains the vertical curve data point of immersion lens;

Fig. 4 is according to laterally dividing the synoptic diagram that obtains immersion lens horizontal curve data point;

Fig. 5 is a horizontal curve that generates lens surface according to the data point on the horizontal curve of lens;

Fig. 6 becomes an optical surface with a series of horizontal curve matches;

Fig. 7 is when having two given refraction spheres, the synoptic diagram of lens surface data;

Fig. 8 is according to Chinese road illumination standards, to the energy binned synoptic diagram of field of illumination and Lambertian source;

Fig. 9 is the immersion lens that the division methods according to Fig. 8 obtains;

Figure 10 is that the chip that the division methods according to Fig. 8 obtains has the once lens of encapsulation;

Figure 11 is the energy binned method to regular hexagon illumination zone and Lambertian source;

Figure 12 is the immersion lens according to the division methods design of Figure 11;

Figure 13 is arranging of one 5 * 5 lens arra;

Figure 14 is the process flow diagram of this method.

Embodiment:

The present invention is based on energy conservation theory, the energy of the light direction of pointolite and the energy on illumination plane are cut apart earlier, carry out the energy of the two corresponding one by one with the form of some discrete points, then according to this corresponding relation, folded band solves coordinate and the light direction corresponding to the optical system surface discrete data point between two energy corresponding relations, thereby has determined the shape of lens surface.

The energy unit division methods, at first be used in and form in the given light distribution, see (W.A.Parkyn, " adopt the method design illuminating lens of exterior differentiation geometry ", Proc.SPIE, vol 3482, pp.191-193 (1998) .), in the method that the present invention proposes, the energy unit division methods is further promoted becomes point-to-point mapping relations, and can be used for forming given Illumination Distribution.This energy binned method is applicable to the relative and smaller situation of optical system of dimension of light source.Since in the process of dividing, two separated processing of variable, and therefore this method also can be thought the method that variable separates.

Suppose to send from light source, the light in our limit of consideration all incides on the plane of given illumination, can obtain according to law of conservation of energy:

${\∫\∫}_{\mathrm{\Ω}}I\left(\stackrel{\→}{L}\right)\mathrm{d\Ω}={\∫\∫}_{D}L\left(\stackrel{\→}{p}\right)\mathrm{ds}---\left(1\right)$

In formula (1)

The direction of expression light, the light intensity angle of pointolite is distributed in

Direction is

Some position on the expression objective plane,

The given illumination of some position is The solid angle scope that the Ω representative emits beam from light source, the range of exposures of D representative on objective plane.

A mapping on reflecting surface in the optical system or refractive surface are actually and realize from the light source to the irradiated plane $\mathrm{\γ}:\stackrel{\→}{l}\→\stackrel{\→}{p},$ If mapping γ continuously differentiable, above-mentioned integral equation can be converted into the differential equation: the physical meaning of γ is exactly $\mathrm{\γ}:\stackrel{\→}{l}\→\stackrel{\→}{p}$

$L\left(\stackrel{\→}{p}\right)=I\left(\stackrel{\→}{l}\right)/\left|J\left(\mathrm{\γ}\left(\stackrel{\→}{l}\right)\right)\right|---\left(2\right)$

Wherein The size of the Jacobian that the mapping γ of expression definition has.

Utilize the method for energy binned to find the solution a mapping from the light source to the objective plane now, according to energy conservation formula (1), to the light source light direction adopt (u, v) coordinate system is described, to the position on illumination plane adopt (x, y) coordinate system is described and can obtains:

I(u，v)|J(u，v)|dudv＝L(x，y)|J(x，y)|dxdy (3)

Wherein be that (u, v) (u, v) coordinate system need be scaled dudv the Jacobian of unit area to J in employing

| J (x, y) | (x, y) coordinate system need be scaled dxdy the Jacobian of unit area in order to adopt

With the energy of light source along the u line (along the v line also can) be divided into a series of energy area simultaneously with corresponding objective plane energy along the x line (along the y line also can) be divided into a series of energy areas, can obtain:

(∫I(u，v)|J(u，v)|dv)du＝(∫L(x，y)|J(x，y)|dy)dx (4)

Equation (4) is an One first-order ordinary differential equation f (u) du=g (x) dx, just can adopt the method for numerical evaluation to iterate after the given starting condition and find the solution.Find the solution out the vertical corresponding relation U=h (X) that obtains energy, identical method can draw horizontal corresponding relation V=m (Y).

To can obtain in equation (4) the substitution equation (3):

$I(u,v)\left|J(u,v)\right|\mathrm{du}=L(x,y)\left|J(x,y)\right|\frac{\∫I(u,v)\left|J(u,v)\right|\mathrm{du}}{\∫L(x,y)\left|J(x,y)\right|\mathrm{dx}}\mathrm{dx}---\left(5\right)$

The mapping relations of the point-to-point that is actually equation (a 3) requirement of satisfying to have Jacobian that from equation (4) and (5), obtains.In the definition of this mapping, key is that (u is v) with the variable (x that represents the illumination position to the variable that is used to represent radiation direction, y) divide other correspondence, in division, can adopt different orthogonal curvilinears to cut apart, as polar curve or rectangular coordinate curve.After the division by above-mentioned energy, just set up grid lattice point one-to-one relationship from light source to the illumination plane.Light from light source sends through behind the optical surface, just is projected onto corresponding correspondence position on the illumination plane.

Based on above principle, the method of the present invention's design is moved in computing machine, this method at first utilizes the pass of energy conservation to tie up to definite vertical curve that is made of some discrete points on the pointolite light direction, on the illumination plane, also determine a vertical curve that constitutes by the discrete point that equates accordingly, form vertical corresponding relation of energy, be starting point with the discrete point on vertical curve then, adopting uses the same method constitutes some horizontal curves that are made of some discrete points, form the horizontal corresponding relation of energy, thereby light source light direction and illumination plane are divided into the corresponding face of energy that several discrete points are formed; Get the starting point that a point calculates as lens (optical system) surface then from two between the face from two energy correspondences, adopt folded band method, calculate the coordinate and the light direction of all discrete points of lens surface, thereby determined a lens surface.Concrete steps are seen summary of the invention.

In above-mentioned steps, (u is v) with (x y) preferably adopts same initial point to coordinate system, so that subsequent calculations, as the coordinate of pointolite light direction, (u can be spherical coordinates or polar coordinates etc. v), and rectangular coordinate be generally adopted on the illumination plane to coordinate system.

The selection of initial point is a very important design parameter, the position of having only rational selection initial point, as the boundary value of the u parameter of light source and the boundary value of illumination plane x parameter or the central value of u parameter and the central value of illumination plane x parameter are carried out correspondence, just may obtain rational corresponding relation.In step, initial step length given depends on the density that light source is divided, and divides closely more, and the approximate solution that obtains is accurate more, also can select an initial step delta x earlier, calculates corresponding Δ u.

Initial step length Δ u ₀Δ u _n, Δ v ₀Δ v _nDetermine relevantly with number n+1, the m+1 of discrete point, the shape in the illumination zone that the deviser can be as required and the size of size and lens surface are determined the number and the initial step length of discrete point, discrete point is many more, step-length is then more little, otherwise big more.

Initial light And initial point (x ₀, y ₀) selection, consider to select the point of edge or center from the angle being convenient to calculate.

In the folded band of lens surface data point is found the solution, initial light

Selection not necessarily

Can be in the energy corresponding relation more arbitrarily, but, select for the ease of calculating

Proper as initial light.After obtaining a vertical curve, should be starting point with the point on this vertical curve, find the solution a series of horizontal curves, can be from S ₀₀, S ₁₀S _N0The middle selection found the solution more arbitrarily, as long as all horizontal curves that are starting point with these points are found the solution out, not necessarily finds the solution by order.

At step 3.1.3), 3.1.6), 3.2.3) in, adopting refraction law is light directly shines the illumination plane through optical element situation, adopting reflection law is that light shines reflecting surface earlier, reflexes to the situation on illumination plane then.

In some designs of using this method, some light source that adopts need once encapsulate, be that the light that light source sends need pass some given surfaces, as led light source is actual use in for the light extraction efficiency that improves LED and easy to use, need in advance led chip once to be encapsulated, as adopt the packaged type of globe lens, simultaneously in order to cooperate the once encapsulation of light source, the groove that a sphere is also arranged at the lower surface of lens, therefore the optical system of design need be considered some given surfaces of existence, as sphere or plane.In order to realize the mapping one by one on above-mentioned light source and illumination plane, the ray tracing that needs earlier light source to be sent is crossed these given surfaces.For known optical surface, it is n that light has refractive index from a side of this optical surface ₁Medium in incide opposite side to have refractive index be n ₂Medium in, can be easy to obtain the position of intersecting point P on light and known optical surface, thereby obtain normal direction in P point position, can utilize refraction law to obtain emergent ray direction after light leaves given optical surface then.

When having given optical surface, initiation parameter also should comprise: the position of given optical surface and normal vector, the reflectivity of given optical material and refractive index.The light that light source sends needs trace to cross a series of given optical surfaces, obtains emergent ray at last, utilizes emergent ray to determine the lens surface data point.Therefore only 3.1.2 that need be in step 3), 3.1.5), the 3.1.7) process of preceding adding trace light.Given optical surface is s ₁S _k, the incident ray that light source sends is

, the other and a series of optical surfaces of people intersect at ins ₁Ins _t, finally obtain emergent ray

The method on the given surface of ray tracing is into 3.1.7) process of preceding adding trace light.Given optical surface is s ₁S _k, the incident ray that light source sends is Ripe respectively prior art can be with reference to (R.Courant, LBers, J.J.Stoker " Modern Geometrical Optics (Modern Geometry optics) ", Interscience Publishers, Inc, New York) document.

When having given optical surface, the division methods of energy is with not have the situation of given optical surface be the same because energy binned definite be the corresponding relation on light source and illumination plane, and the effect of optical system is exactly to realize this corresponding relation.

According to above-mentioned method for designing, obtained the discrete data point of lens surface, comprise the coordinate of each point and at the normal vector of this point.The quadrature parameter that divide to adopt at light source (u, (x, (p, q), serve as reasons and have the first identical footmark i, i.e. (S y) in fact also to have induced the parametric representation of a nature at optical surface v) to divide the quadrature parameter that adopts with the illumination plane by i bar p line _I1, S _I2S _In), the curve that constitutes of data point, the horizontal curve of p line direction and curved surface is consistent; J bar q line is served as reasons and is had the second identical footmark j, i.e. (S _1j, S _2jS _Nj), the curve that constitutes of data point, vertical curve of q line direction and curved surface is consistent.Cross each data point and have along the p line direction of crossing this point, and the tangent line vertical with normal direction

According to NURBS (non-uniform rational b spline curve) theory, can be according to point coordinate on every horizontal curve and tangential direction, the horizontal curve of obtaining these points of smooth mistake and having given tangential direction.Can generate the point on two horizontal curves of a mistake between two horizontal curves that face mutually, and have with these aspects on a little patch of given normal direction.These little patchs are coupled together, just constituted the full surface of lens.

Be described in detail below in conjunction with accompanying drawing:

Fig. 1. (a) expression adopts a series of vertical u-curves (120) that the energy of light source is partitioned into different energy block (130) to vertical piecemeal of light source (110) energy, 110 expression pointolites.(b) expression is to vertical energy piecemeal in corresponding illumination zone, adopt a series of horizontal x (140) curve that the energy in illumination zone is partitioned into different energy block (150), on illumination zone and light source, contain identical energy size in the energy piecemeal (130) of correspondence and (150).

Fig. 2. (a) be illustrated on the basis of piecemeal, to the horizontal division of the energy of light source.Adopt a series of vertical V curve (210) that the energy of light source is divided into different junior unit (220).(b) be illustrated on the basis of piecemeal, the horizontal division of the energy in illumination zone.Adopt a series of vertical y curve (230) that the energy of light source is divided into different junior unit (240).On illumination zone and light source, contain identical energy size in the energy unit lattice of correspondence.

Fig. 3 represents the vertical division according to light source and illumination plane, utilize equation (4), obtain a vertical curve of optical surface, (a) the discrete point on the vertical curve on 380, the 390 expression optical lens surfaces of the point among the figure, generate according to following method, describe in conjunction with Fig. 3 (b):

1) goes up initial light of selection according to vertical corresponding relation on light source and illumination plane at light source (300)

(310), corresponding to an initial position P on the illumination plane ₁₁(380), on the travel path of initial light, select an initial point S ₁₁(311) as the starting point of optical surface;

2) utilize initial point S ₁₁(311) and the correspondence position P on the illumination plane ₁₁(380) just can obtain the direction vector of emergent ray

${\stackrel{\→}{O}}_{10}=\stackrel{\→}{S_{11}{P}_{11}};$

3) obtain the direction of the normal vector that should have according to refraction law (6) on this some surface

4) at S ₁₁The section T of point ₁₁(340) on, according to the 2nd contiguous incident ray

Obtain and T ₁₁(340) point of intersection S ₁₂(351) position is in conjunction with the corresponding point P on illumination plane ₁₂(390);

5) according to refraction law (6), obtain at S ₁₂The direction of the normal vector of point

6) obtain a discrete data point on the vertical curve of lens surface according to the above-mentioned method of iterating.

When the grid that is used to divide light source and illumination plane is enough thin, can be similar to and thinks that the position of a back point is positioned on the section of previous point and does not change the C1 slickness of curve.

Fig. 4 represents the horizontal partition V according to light source and illumination plane _u=g (Y _x), utilize data point on the vertical curve of optics as initial point, obtain the horizontal curve of the lens surface shown in Fig. 4 (a), in conjunction with Fig. 4 (b), Fig. 4 (c):

1) chooses 1 S from vertical curve ₁₁(311) as the initial point of a horizontal curve;

2) incident ray

(410) and S ₁₁(311) section (340) S that intersects at a point ₂₁(411), it is P corresponding to the point on the illumination plane ₂₁(420), thus the exit direction of obtaining light be

3) obtain the surface at S according to refraction law ₂₁(440) normal vector that has;

4) with vertical curve on discrete point to find the solution mode identical, iterate the discrete point on the horizontal curve that solves optical surface.

Go out a horizontal curve with each dot generation on vertical curve, the discrete point of these a series of horizontal curves has covered the surface of optical lens, can see Fig. 4 (c) with generating optical surface.

Fig. 5 represents data point and the normal on the horizontal curve, has obtained smooth horizontal curve (510), and horizontal curve has the tangential direction of appointment at every bit.

Fig. 6 represents that the adjacent discrete point on two adjacent horizontal curves (510) forms a little patch (610), and being connected by the patch that faces mutually then becomes a complete lens surface (620).

Fig. 7 obtains the surface design of energy distribution when being illustrated in given two ball surfaces:

1) ray tracing is crossed two given spherical surfaces (700), obtains emergent ray

(710);

2) at light

(710) choose 1 S on ₁₁(711) as the initial point of design, the requirement of shining upon according to energy obtains at S ₁₁The normal direction (720) of point;

3) light

(730) trace is crossed behind two given spherical surfaces and is crossed S ₁₁The section of point intersects at S ₁₂(731), according to the requirement of energy mapping, obtain at S ₁₂The normal direction (740) of point;

4) iterate the discrete data point and the discrete normal vector of a vertical curve obtaining the optical lens surface;

5) utilize point above vertical curve as the initial parameter of horizontal curve, obtain the discrete data point on a series of horizontal curves on surface.

An important application of this method is according to Chinese road lighting requirement, and the lens of Illumination Distribution are satisfied in design.In a specific embodiment of this method, the light source of employing is a large power white light LED, and the light intensity of light source has lambert's shape and distributes.According to the street lighting standard-required, the distance of light source from the road surface is 9m, and illumination zone is to be the interior road surface of 10m * 40m rectangular extent at center with the light source, forms uniform Illumination Distribution.

Among Fig. 8 (a), the illumination plane is divided into N by first alongst (810) ₁Piece is divided into N then in Width (820) is gone up each piece ₂Individual energy unit; Only consider the bright of a part among Fig. 8 (b)

Type energy of light source, light source are at first by the corresponding N that is divided into of the vertical curve of cluster (830) ₁Part energy block, each piece has identical energy size with energy block on the corresponding illumination plane, and the span of the longitude angle u of consideration (840) is (90 ⁰, 90 ⁰) totally 180 ⁰Light source is cut into slices perpendicular to the horizontal curve (850) of the vertical curve of this bunch with another bunch, energy of light source further is divided into N ₂Part little energy unit, each energy unit has identical energy size with energy unit corresponding on the illumination plane, considers to such an extent that the span (860) of angle of latitude v is (80 ⁰, 80 ⁰) totally 160 ⁰

Fig. 9 (a) is that (910) are the upper surfaces of lens according to the folded front view of being with the immersion lens that calculates of this method, and (920) are the support cylinders of lens; Fig. 9 (b) is the vertical view of the lens that obtain, and a led chip (930) has been enclosed in together by the lower surface of epoxy resin and lens.The light that chip sends is directly incident on the surface of lens.This structure has low-loss characteristics because of the refractive surface that has seldom.

Figure 10 (a) is the lens side view that has once encapsulation that obtains according to this method, (1010) be the upper surface of lens, led chip once is encapsulated in the dome-type lenslet (1030), also design a hemisphere surface (1020) in the bottom of lens accordingly the guiding of the light of chip is entered in the big lens, lead-in wire (1040) can be drawn from the slit of lens bottom surface and substrate (1050) simultaneously.Figure 10 (b) is the vertical view of the lens that obtain.Therefore this structure has characteristics easy for installation because chip separates with lens.This lens surface is the peanut shell external form, and there are the transverse axis and the longitudinal axis in the middle part of this external form, and this shape is symmetrical fully with respect to the transverse axis and the longitudinal axis.

Another specific embodiment is to form a just hexagonal Illumination Distribution design, because the illumination that hexangle type distributes is spliced easily, can be used for general illuminations such as some Landscape Lightings and road lighting easily and use.In this specific embodiment, the height of design is 5m, and the positive capable circumradius of hexagon is 7m.

Figure 11 (a) is the energy binned to the illumination plane, adopts polar method at first along radially (1110) light source to be divided into N ₁Energy block further is divided into N with each energy block in the direction (1120) along polar angle ₂Energy unit, thus N obtained ₁* N ₂Net point; (b) figure is the division methods to energy of light source, at first along the direction (1130) of longitude the energy of lambert's type light source is divided into corresponding N ₁Energy block, each piece has identical energy size with energy block on the corresponding illumination plane, and the longitude angle span (1140) of consideration is (90 ⁰, 90 ⁰) totally 180 ⁰Direction (1150) along latitude further is divided into N accordingly with the energy of each piecemeal and then ₂Little energy unit, each energy unit has identical energy size with energy unit corresponding on the illumination plane, and angle of latitude span (1160) is (80 ⁰, 80 ⁰) totally 160 ⁰Thereby, also obtained N ₁* N ₂Corresponding net point.

Figure 12 (a) is the shape of the lens front view that obtains of folded band computing method according to the present invention, consider orthohexagonal symmetry, be positioned at directly over the center of regular polygon with light source, sixth part of lens upper surface is as (1220), chip (1210) and lens become one by epoxy encapsulation, and (b) figure is the vertical view that obtains lens.Lens shape among the figure is the sphere that six limits are arranged, and with respect to the illumination plane, these six ribs are symmetrical.According to the design on illumination plane, the shape of lens also can be the spherical form of triangular, four ribs or more ribs.

The total light flux of common single led chip is limited, can not reach relevant illumination requirement value, can a plurality of chips and lens be lined up array according to concrete needs, finish given illumination requirement jointly, because each lens all forms one with the proportional Illumination Distribution of given illumination in whole illumination zone, therefore the array of arranging is very convenient, specifically needs the just lens of adjustment and the number of chip.

Figure 13 is the array of one 5 * 5 lens, and the lens of employing (1310) are the street lamp lens models according to national lighting standard design.

Generally speaking, the key based on the three-dimensional optical surface design of variables separation principle is:

1) adopt the method for variables separation to determine horizontal and vertical energy corresponding relation;

2) utilize horizontal and vertical energy corresponding relation to obtain the data point of lens surface

Figure 14 is based on the basic flow sheet of the three-dimensional given Illumination Distribution design of variables separation division methods: mainly comprise given initial input parameter, find the solution the mapping corresponding relation, vertically the finding the solution of curve, horizontal curve finds the solution and these parts of generation of last optical surface.Because finding the solution vertical curve only needs vertical corresponding relation, finding the solution horizontal curve only needs horizontal corresponding relation, so the step among the figure also can change 1,2,4,3,5,6 into, does not influence Design for optical system.

Lens according to method for designing design of the present invention can have non-rotating symmetric shape, can form given Illumination Distribution design on an objective plane, make full use of the energy of light source, thereby save the energy.According to the design concept requirement, on behalf of the led light source of future development trend, the size of light source will become a kind of suitable illumination Design light source much smaller than the size of optical system.Another advantage is that each optical system can form one with the proportional Illumination Distribution of given illumination in whole field of illumination, therefore can be according to the concrete illumination requirement and the luminous flux level of light source, light source and lens are lined up array, form a given Illumination Distribution jointly.The present invention compares with existing lighting engineering, has characteristics efficient, energy-conservation and flexible and convenient to use, and in various illumination occasions, as road lighting, Landscape Lighting and display backlight source lighting etc. all have broad application prospects.

Claims (7)

1, a kind of method for designing of two-dimension optical lens is characterized in that, this method contains the following steps of moving in computing machine:

1) initialization:

For the light direction of light source set up a coordinate system (u, v), for the point on the illumination plane set up a coordinate system (x, y);

An initial light (u on the given light source light direction ₀, v ₀), an initial point (x on the given illumination plane ₀, y ₀);

The number m+1 of discrete point in the energy corresponding relation is walked crosswise in number n+1 of discrete point in given vertical energy corresponding relation,

Wherein n and m are natural number;

Step delta u between the given source light ₀Δ u _n, Δ v _oΔ v _m

The refractive index n of given lens material ₁Refractive index n with air ₂

2) light source and illumination plane are carried out the correspondence division of energy:

2.1) set up with the light direction of light source and a vertical corresponding relation of the point on the illumination plane:

2.1.1) calculating source light (u ₀, v ₀), at Δ u ₀The energy size that has in the scope:

$E\left({\mathrm{\Δu}}_0\right){|}_{u=u_0}={\∫}_{u=u_0}I(u,v)\left|J(u,v)\right|\mathrm{dv}\·{\mathrm{\Δu}}_0,$ Wherein 1 (u v) is a light source (u, the v) light intensity magnitude on the direction,

For adopt (u, v) coordinate system need be scaled dudv the Jacobian of unit area;

2.1.2) calculate the point (x on the illumination plane ₀, y ₀) corresponding step delta x ₀:

${\mathrm{\Δx}}_0=E\left({\mathrm{\Δu}}_0\right){|}_{u=u_0}/{\∫}_{x=x_0}L(x,y)\left|J(u,v)\right|\mathrm{dy},$ Wherein L (x, y) be illustrated on the illumination plane (x, the y) brightness value at some place, For adopt (x, y) coordinate system need be scaled dxdy the Jacobian of unit area;

2.1.3) make u ₁=u ₀+ Δ u ₀, x ₁=x ₀+ Δ x ₀Thereby, the light that obtains that pointolite sends and the energy corresponding relation of a point on the illumination plane: (u ₁, v ₀) corresponding to (x ₁, y ₀);

2.1.3) utilize step 2.1.1) and in formula compute ray (u ₁, v ₀) at Δ u ₁The energy size that has in the scope:

$E\left({\mathrm{\Δu}}_1\right){|}_{u=u_1}={\∫}_{u=u_1}I(u,v)\left|J(u,v)\right|\mathrm{dv}\·{\mathrm{\Δu}}_1;$

2.14) utilize step 2.1.2) and in formula calculate point (x on the illumination plane ₁, y ₀) corresponding step delta x ₁:

${\mathrm{\Δx}}_1=E\left({\mathrm{\Δu}}_1\right){|}_{u=u_1}/{\∫}_{x=x_1}L(x,y)\left|J(u,v)\right|\mathrm{dy};$

2.1.5) make u ₂=u ₁+ Δ u ₁, x ₂=x ₁+ Δ x ₁, utilize step 2.1.1) and step 2.1.2) in formula, obtain another light that pointolite sends and the energy corresponding relation of another point on the illumination plane: (u ₂, v ₀) corresponding to (x ₂, y ₀);

2.1.6) repeating step 2.1.1)～2.1.5), iterate a vertical corresponding relation of energy of the some formation that calculates on source light and the illumination plane $U_{v_0}=h\left(X_{y_0}\right)$ And Δ X, wherein:

$U_{v_0}=\{(u_0,v_0),(u_1,v_0),......(u_n,v_0)\}$

$X_{y_0}=\{(x_0,y_0),(x_1,y_0),......(x_n,y_0)\}$

Δ X={ Δ x ₀, Δ x ₁... Δ x _n;

2.2) to set up with the point on above-mentioned vertical corresponding relation be n+1 the light of initial point and the horizontal corresponding relation of energy of the point on the illumination plane:

2.2.1) from above-mentioned vertical corresponding relation $U_{v_0}=h\left(X_{y_0}\right)$ In get initial point (u ₀, v ₀) and initial step length Δ v ₀, compute ray (u ₀, v ₀) at (Δ u ₀, Δ v ₀) the energy size that has in the scope:

$E({\mathrm{\Δu}}_0,{\mathrm{\Δv}}_0){|}_{(u=u_0,v=v_0)}=I(u_0,v_0)\left|J(u_0,v_0)\right|{\mathrm{\Δu}}_0{\mathrm{\Δv}}_0;$

2.2.2) calculate the initial point (x on the illumination plane ₀, y ₀) corresponding step delta y ₀:

${\mathrm{\Δy}}_0=\frac{E({\mathrm{\Δu}}_0,{\mathrm{\Δv}}_0){|}_{(u=u_0,v=v_0)}}{L(x_0,y_0)\left|J(x_0,y_0)\right|{\mathrm{\Δx}}_0};$

2.2.3) make v ₁=v ₀+ Δ v ₀, y ₁=y ₀+ Δ y ₀Obtain the energy corresponding relation of a point on light of pointolite and the illumination plane:

(u ₀, v ₁) corresponding to (x ₀, y ₁);

2.2.4) according to step 2.2.1) and formula compute ray (u ₀, v ₁) at (Δ u ₀, Δ v ₁) the energy size that has in the scope:

$E({\mathrm{\Δu}}_0,{\mathrm{\Δv}}_1){|}_{(u=u_0,v=v_1)}=I(u_0,v_1)\left|J(u_0,v_1)\right|{\mathrm{\Δu}}_0{\mathrm{\Δv}}_1;$

2.2.5) according to step 2.2.2) and formula calculate (x on the illumination plane ₀, y ₁) corresponding step delta y ₁:

${\mathrm{\Δy}}_1=\frac{E({\mathrm{\Δu}}_0,{\mathrm{\Δv}}_1){|}_{(u=u_0,v=v_1)}}{L(x_0,y_1)\left|J(x_0,y_1)\right|{\mathrm{\Δx}}_0};$

2.2.6) make v ₂=v ₁+ Δ v ₀, y ₂=y ₁+ Δ y ₁Obtain another light of pointolite and the energy corresponding relation of another point on the illumination plane: (u ₀, v ₂) corresponding to (x ₀, y ₂);

2.2.7) recycling step 2.2.1) and 2.2.2) in formula, iterate a horizontal corresponding relation of energy of the point that calculates on pointolite emergent ray and the illumination plane $V_{u_0}=Y_{x_0},$ Wherein $V_{u_0}=\{(u_0,v_0),(u_0,v_1),......(u_0,v_m)\},$ $Y_{x_0}=\{(x_0,y_0),(x_0,y_1),......(x_0,y_m)\};$

2.2.8) repeating step 2.2.1～2.2.7), calculating with the n+1 on vertical corresponding relation point is n+1 the horizontal corresponding relation of energy of initial point, wherein finding the solution of each bar horizontal curve adopted Δ X={ Δ x ₀, Δ x ₁... Δ x _nIn a corresponding step-length as the step-length of discrete point on the x direction

$V_{u_0}=g\left(Y_{x_0}\right),$ Vu ₀＝{(u ₀，v ₀)，(u ₀，v ₁)，......(u ₀，v _m)}， $Y_{x_0}=\{(x_0,y_0),(x_0,y_1),......(x_0,y_m)\}$

$V_{u_1}=g\left(Y_{x_1}\right),$ $V_{u_1}=\{(u_1,v_0),(u_1,v_1),......(u_1,v_m)\},$ $Y_{x_1}=\{(x_1,y_0),(x_1,y_1),......(x_1,y_m)\}$

$V_{u_n}=g\left(Y_{x_n}\right),$ $V_{u_n}=\{(u_n,v_0),(u_n,v_1),......(u_n,v_m)\},$ $Y_{x_n}=\{(x_n,y_0),(x_n,y_1),......(x_n,y_m)\};$

3) iterating of lens surface data point found the solution:

3.1) the determining of a vertical curve of lens surface:

3.1.1) according to vertical corresponding relation on light source and illumination plane $U_{v_0}=h\left(X_{y_0}\right)$ , on light source, select an initial light

, corresponding to an initial position P on the illumination plane ₀₀(x ₀, y ₀);

3.1.2) initial point S of selection on the travel path of initial light ₀₀Starting point as optical surface;

3.1.3) utilize initial point S ₀₀With the correspondence position P on the illumination plane ₀₀Obtain at a S ₀₀The direction vector of the emergent ray at place ${\stackrel{\→}{O}}_{00}=\stackrel{\→}{S_{00}{P}_{00}},$ Obtain at S according to refraction law ₀₀The normal vector that the some surface should have

${\stackrel{\→}{N}}_{00}=n_1*{\stackrel{\→}{I}}_{00}-n_2*{\stackrel{\→}{O}}_{00};$

Or obtain at S according to reflection law ₀₀The normal vector that the some surface should have

:

${\stackrel{\→}{N}}_{00}={\stackrel{\→}{I}}_{00}-{\stackrel{\→}{O}}_{00};$

3.1.4) on light source, select the second emergent ray according to vertical corresponding relation on light source and illumination plane Corresponding illumination plane P ₁₀(x ₁, y ₀) point, according to S ₀₀The normal vector on some surface

, obtain S ₀₀The section T of point ₀₀

3.1.5) obtain light

Through propagating and S ₀₀The section T of point ₀₀Position of intersecting point S ₁₀

3.1.6) in conjunction with the corresponding point P on illumination plane ₁₀, obtain a S ₁₀The direction vector of emergent ray ${\stackrel{\→}{O}}_{10}=\stackrel{\→}{S_{10}{P}_{10}}$ , obtain at S according to refraction law ₁₀The normal vector that the some surface should have

${\stackrel{\→}{N}}_{10}=n_1*{\stackrel{\→}{I}}_{10}-n_2*{\stackrel{\→}{O}}_{10};$

Or obtain at S according to reflection law ₀₀The normal vector that the some surface should have

${\stackrel{\→}{N}}_{10}={\stackrel{\→}{I}}_{10}-{\stackrel{\→}{O}}_{10};$

3.1.7) on light source, continue to select emergent ray according to vertical corresponding relation on light source and illumination plane, according to step 3.1.2)～3.1.6) go on foot, obtain the discrete data point S on vertical curve of lens surface ₀₀, S ₁₀S _N0, and the normal vector of the emergent ray of every bit correspondence , promptly determined a vertical curve of lens surface;

3.2) with the finding the solution of the discrete point on vertical curve of lens surface as the n+1 bar horizontal curve of initial point:

3.2.1) get an initial point S from vertical curve on said lens surface ₀₀,, select S according to the horizontal corresponding relation of the energy on light source and illumination plane as the initial point of a horizontal curve ₀₀The incident ray that point is contiguous , the some P on the corresponding illumination plane ₀₁(x ₀, y ₁);

3.2.2) obtain light

Through propagating and S ₀₀The section T of point ₀₀Position of intersecting point S ₀₁

3.2.3) this is corresponding to the some P on the illumination plane ₀₁(x ₀, y ₁), thereby obtain S ₀₁The direction vector of the emergent ray of some light ${\stackrel{\→}{O}}_{01}=\stackrel{\→}{S_{01}{P}_{01}},$ Obtain at S according to refraction law ₀₁The normal vector that the some surface should have

${\stackrel{\→}{N}}_{01}=n_1*{\stackrel{\→}{I}}_{01}-n_2*{\stackrel{\→}{O}}_{01};$

Or obtain at S according to reflection law ₀₁The normal vector that the some surface should have

${\stackrel{\→}{N}}_{01}={\stackrel{\→}{I}}_{01}-{\stackrel{\→}{O}}_{01};$

3.2.4) on light source, continue to select successively contiguous emergent ray according to the horizontal corresponding relation on light source and illumination plane

According to step 3.2.1)～3.2.4), obtain with the some S on the vertical curve of lens surface ₀₀Be the discrete data point S on the horizontal curve of initial point ₀₀, S ₀₁S _0m, and the normal vector of every bit correspondence ${\stackrel{\→}{N}}_{01}\·\·\·\·\·\·{\stackrel{\→}{N}}_{0m};$

3.2.5) continue to select successively initial point S ₁₀S _N0,, find the solution and obtain with on the vertical curve on the lens all with discrete point S according to step 3.2.1～3.2.4) ₀₀S _N0Be the normal vector that the discrete point on the n+1 bar horizontal curve of initial point and this point have, then all data points of lens surface and normal vector thereof are found the solution and are finished, and have promptly determined the surface of lens.

2, the method for designing of three-dimensional optical lens as claimed in claim 1 is characterized in that, in the initialization, described coordinate system (u, v) and coordinate system (x y) adopts same initial point.

3, the method for designing of three-dimensional optical lens as claimed in claim 1 is characterized in that, in the initialization, (u v) is spherical coordinates or polar coordinates to described coordinate system.

4, the method for designing of three-dimensional optical lens as claimed in claim 1 is characterized in that, in the initialization, and the initial light (u on the light direction of described light source ₀, v ₀) select the light at edge or the light at center, the initial point (x on the illumination plane ₀, y ₀) be the point (x of the marginal position corresponding with described initial light ₀, y ₀) or the point of center.

5, the method for designing of three-dimensional optical lens as claimed in claim 1 is characterized in that, when having given surface, and step 3.1.2) change into: after preliminary ray trace is crossed given surface, on travel path, select an initial point S ₀₀Starting point as optical surface;

Step 3.1.5) changes into: obtain light

After trace is crossed given surface, through propagating and S ₀₀The section T of point ₀₀Position of intersecting point S10;

Step 3.2.2) changes into: obtain light

After trace is crossed given surface, through propagating and S ₀₀The section T of point ₀₀Position of intersecting point S ₀₁

6, the method for designing according to claim 1 and lens that design is characterized in that having the peanut shell mould outside surface of medial recess.

7, the method for designing according to claim 1 and lens that design is characterized in that having the spherical outer surface of three above ribs.

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