CN103196066B - Narrow-beam LED lamp optical system and designing method thereof - Google Patents

Abstract

The invention discloses narrow-beam LED lamp optical system and a designing method thereof. A freeform curved lens and a freeform curved reflector cup are utilized to realize regionalized complementary control of light emitted by a COB (chip on board) type LED, the freeform curved lens is used for controlling small-angle light emitted by the COB type LED, and the freeform curved reflector cup is used for controlling large-angle light emitted by the COB type LED. Respective advantages of the lens and the reflector cup are combined to overcome the defect that not all light rays can be utilized by only utilizing the reflector cup or the lens. A Fresnel lens is adopted to collect small-angle light rays to enable an optical system to be light, thin and small, the thickness of the center of the lens is reduced, and light efficiency is improved. Meanwhile, a step-shaped microstructure lens is used on the inner side of the lens to enable the same optical system to be applicable to COB light sources in different sizes.

Description

Arrow beam of light LED lamp optical system and method for designing thereof

Technical field

The present invention relates to LED lamp optical system, relate in particular to a kind of secondary optical system for multi-chip integrated form high-capacity LED (COB type LED), and realize a kind of method for designing of the narrow smooth outgoing effect of low-angle, belong to nonimaging optics technical field.

Background technology

LED light source itself is an approximate Lambertian source, be difficult to meet the demand of various lighting uses, therefore must, according to different application scenarios, design different optical systems for LED light source, the light that LED light source is sent carries out shaping, carries out the quadratic distribution of light energy.

Along with the development of direct chip encapsulation (COB) technology on circuit board, the feature such as the even and volume of its high power density, colourity is little, is more and more applied in commercial lighting COB type LED light source.The more single LEDs light source of COB type LED light source area is much larger, during by tens of LEDs integrated chip encapsulation, light source area can reach 10mm*10mm to 25mm*25mm, the advantage of this light source is to greatly reduce the quantity of LED light source, reduce light fixture area, reduce light fixture cost, lower color tolerance official post application luminaire has good colour consistency.

But, but comparatively difficult towards the secondary optical design of COB type light source.The method for designing of most patent is the design based on approximate spot light all, and COB type LED belongs to expansion light source, and spot light method for designing is no longer applicable to COB type LED.

The optical system adopting mostly at present is reflector, but it controls the limited in one's ability of light, cannot well control for low-angle light, want to reach the accurately light distribution effect of illumination of low-angle, often need larger volume, and easily produce veiling glare, make the relative light utilization efficiency of receiving plane functional area lower.

Towards the small-sized TIR(total internal reflection of single LEDs) lens can complete preferably arrow beam of light light distribution requirements, but in the time that it is applied to COB type LED light source, goes out light effect and can produce serious distortion.Adjusting direction with its optical axis is angled with interior light and ordinary lens can only send LED light source conventionally,, also there is the lower problem of relative light utilization efficiency of receiving plane functional area in the light of uncontrollable wide-angle.

Therefore, how solving the problem of COB type LED light source luminous intensity distribution difficulty, realize accurately function and the method for designing thereof of illumination of arrow beam of light, is LED lighting technical field, in particular for commercial lighting field problem demanding prompt solution.

Summary of the invention

The object of the present invention is to provide a kind of light energy for COB type LED light source to carry out arrow beam of light LED lamp optical system and the method for designing thereof of reasonable distribution.

The technical problem to be solved in the present invention is, for the efficiency of light energy utilization that how to improve LED light fixture, a kind of light distributing system taking COB type LED as light source is provided, realizes low-angle accent light, and realize the higher luminosity uniformity in field of illumination and the effect of uniformity of chromaticity.Mainly solve the shortcomings and deficiencies of original conventional reflector formula or lens type optical system.

Technical scheme of the present invention is as follows:

A kind of arrow beam of light LED lamp optical system, comprises COB type LED light source, free-form surface lens and free form surface reflector; The light that described free-form surface lens and free form surface reflector send COB type LED light source carries out compartmentalization control; Wherein, the low-angle light that free-form surface lens control COB type LED light source sends, the light of the wide-angle that free form surface reflector control COB type LED light source sends.

Wherein a kind of structure is: at the bottom of described free-form surface lens is arranged on the inner cup of free form surface reflector and be connected with free form surface reflector, within described COB type LED light source is arranged on the space surrounding with the inner chamber of free-form surface lens at the bottom of the inner cup of free form surface reflector.

What described COB type LED light source sent 0 spends to the light of α degree and sees through free-form surface lens top, is evenly distributed in β degree; The α degree that described COB type LED light source sends sees through free-form surface lens sidewall to the light of 90 degree, through free form surface reflector internal surface reflection, is distributed in field of illumination.

Described free-form surface lens comprises lens top, lens sidewall and lens bottom; Described lens top is made up of inner surface and outer surface; Described lens outer surface of cupular part is epirelief or recessed free form surface.Described lens outer surface of cupular part is made Fresnel Lenses.

The inner surface of described free form surface reflector is coating processing.The inner surface of described free form surface reflector is scale and shell structure, and described scale and shell height is not higher than 0.05mm.

The present invention also provides a kind of method for designing of arrow beam of light LED lamp optical system claimed in claim 1, taking light source place plane as x axle, perpendicular bisector is that y axle is set up coordinate system, taking light source center as initial point, if expansion light source radius is R, generate lens free form surface and reflector free form surface;

The step that generates lens free form surface is as follows:

1) establishing H is LED light source left hand edge R _llight and the intersection point of y axle, coordinate is (0, H);

2) according to dimension of light source D(D=2R), get the some X on refracted ray for the first time ₀as the starting point of lens outer surface curve, and make X ₀the normal at some place straight up;

3) according to optical extend conservation formula

$2n\×D=\underset{-\mathrm{\β}}{\overset{\mathrm{\β}}{\∫}}\mathrm{Ld\β}$

Obtain projection width L; Wherein, D is light source diameter, and β is emergent ray and y axle clamp angle, the refractive index that n is optical material;

4) straight line a is R _lemergent ray, gets with the straight line b of its distance L as light source edge R _remergent ray, on straight line b, get a Y ₀;

5) according to law of refraction vector form

Obtain Y ₀put to obtain normal direction wherein with be respectively outgoing and incident ray unit vector, for interface normal unit vector;

6) according to X ₀, Y ₀coordinate and their normal direction with full curve of interpolation, makes it to pass through X ₀and Y ₀, meet normal direction at these 2 simultaneously with can draft thus a full curve X ₀y ₀as calculating virgin curve;

7) by initial curve X ₀y ₀divide n segment, obtain the n+1 point on curve, be respectively X ₀～X _n, the some Y of corresponding unknown curve ₀～Y _n;

8) get X ₀nearlyer 1 X ₁, emergent ray is straight line c, using the straight line d that is L apart from straight line c as R _ranother after lens reflection light; Calculate straight line d and Y ₀point the intersection point Y of tangent line ₁, calculate Y according to law of refraction vector form ₁put to obtain normal direction; Equally according to X ₁, Y ₁coordinate and their normal direction, interpolation cubic curve;

9) get X ₁nearlyer 1 X ₂, the like calculating, use synchronous many Surface Method to calculate remaining point, until the scope of α is at 40 °～45 °, finally obtain lens cross section curve;

The step that generates reflector free form surface is as follows:

1) determine initial segment A ₁b ₁, from starting to consider with the maximum light in y axle clamp angle, the starting point on the corresponding screen of this cluster light is r ₁, initial incident ray R _la ₁arrive r through reflection ₁; According to rim ray theory, R _ra certain the light sending incides initial curve terminal B ₁also can be reflected to r ₁, curved section A ₁b ₁with R _rand r ₁it is the part curve of two focus ellipses; Angle θ _r, angle θ ₁be respectively emergent ray A _nr _n, B _nr _nangle with optical axis y;

2) establishing light-source brightness is B, and send with y axle clamp angle compared with little and direct irradiation on screen and the illumination producing can be by

$E\left(r\right)=\∫B\·\cos \mathrm{\θ}\·\mathrm{d\θ}=\mathrm{B\Ω}$ Obtain.

Angle A ₁r ₁b ₁size by r ₁illumination determine; Emergent ray A ₁r ₁angle theta with y axle _rby A ₁coordinate determine, r ₁the energy that the illumination receiving can deduct reflector reflection by the energy of light source direct irradiation obtains,

E _r=E-BΩ=B(sinθ _r-sinθ ₁)

Obtain emergent ray B ₁r ₁angle theta with y axle ₁and obtain B ₁the coordinate of point, initial curve A ₁b ₁equation can be determined;

3) from R _lpoint sends the light slightly little with y axle clamp angle, incides curve A ₁b ₁on A ₂point can be obtained A from curvilinear equation ₂coordinate with and normal vector can obtain its reflection ray by reflection law, establishing the point that reflection ray incides on screen is r ₂, emergent ray A ₂r ₂angle theta with y axle _rcan determine; Obtain emergent ray B by Flux conservation ₂r ₂angle theta with y axle ₁, determine r ₂light receives the light on another one border of cone, itself and B ₁the tangent line of point meets at B ₂, as new curve point;

4) light source is from edge R _rthe light R sending _rb ₂reflection ray through reflection is B ₂r ₂, according to reflection law, B ₂coordinate and normal vector also can determine; Reflector A ₁b ₂profile can determine, then consider by R _rthe light less with y axle clamp angle that point sends, repeats above step, and outline line will constantly be expanded, until reach desired border.

Useful technique effect of the present invention is:

The present invention, in conjunction with the advantage separately of lens and reflector, has overcome the shortcoming that cannot utilize merely all light with reflector or lens.Use Fresnel Lenses that low-angle light is converged, make that optical system reaches gently, the effect of Bao He little, reduce lens center thickness, raising optical efficiency.Stepped Lenticular lens applies to lens medial surface, realizes same set of optical system and be applicable to the COB type light source of different size size.

The additional advantage of the present invention will provide in the description of detailed description of the invention part below, and part will become obviously from the following description, or recognize by practice of the present invention.

Brief description of the drawings

Fig. 1 is the structural representation of optical system of the present invention.

Fig. 2 is the generative process figure of lens free form surface.

Fig. 3 is the generative process figure of reflector free form surface.

Detailed description of the invention

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described further.

As shown in Figure 1, optical system of the present invention is made up of COB type LED light source 1, free-form surface lens 2, free form surface reflector 3 three parts.The light that free-form surface lens 2 and free form surface reflector 3 send COB type LED light source 1 carries out compartmentalization control.

In the embodiment shown in fig. 1, at the bottom of free-form surface lens 2 is arranged on the inner cup of free form surface reflector 3 and be connected with free form surface reflector 3.Within COB type LED light source 1 is arranged on the space surrounding with the inner chamber of free-form surface lens 2 at the bottom of the inner cup of free form surface reflector 3.

Wherein, COB type LED light source 1 adopts commercially available high-power type (10W～60W) light source, and light-emitting area is larger, and the range of choice of light-emitting area diameter is 10mm～25mm.

The function of free-form surface lens 2 is: the light of the 0 degree-α degree (α gets 45 degree conventionally) that COB type LED light source 1 is sent is evenly distributed in β degree, according to corresponding COB type LED light source 1 light-emitting zone diameter D, jointing edge ray theory, designs the free-form surface lens 2 of Sizes.

Free-form surface lens 2 comprises three parts, lens top, lens sidewall and lens bottom.

Lens top is made up of inside and outside two free form surfaces.Lens top inner surface can be sphere, fovea superior or lower protruding free form surface, and lens outer surface of cupular part can be epirelief or recessed free form surface.

Lens outer surface of cupular part can be made Fresnel Lenses, reduces lens thickness, when improving irradiation area central light strength, has saved material.

Lens madial wall can be plain cylindrical form inner cavity surface, can be also stepped cylindrical cavity face, and lens lateral wall is sphere or free form surface.

Lens bottom circular diameter size is adjustable, according to COB type LED light source 1 light-emitting zone diameter D size, selects plain cylindrical form inner chamber or stepped cylindrical cavity.

The function of free form surface reflector 3 is: control the high angle scattered light that COB type LED light source 1 sends, be that α degree sees through free-form surface lens 2 sides to the light of 90 degree, pass through again free form surface reflector 3 inner reflections, according to illumination distances, the emergent ray of wide-angle is controlled in required big or small field of illumination.

The inner surface of free form surface reflector 3 is coating processing, realizes minute surface transmitting, for solving glare problem, micro-structural (as scale and shell structure) is acted on to reflector inner side, and scale and shell height is not higher than 0.05mm.

Keynote idea of the present invention is the light subregion design that COB type LED light source 1 is sent, and low-angle light is controlled by free-form surface lens 2, and the light of wide-angle is controlled by free form surface reflector 3.Embodiment in Fig. 1 is a kind of feasible configurations of the present invention, but the invention is not restricted to said structure.

Free-form surface lens 2 can be controlled the low-angle light that departs from optical axis preferably, but in the time that the angle of incident ray is greater than critical angle, will produce full transmitting, and this limitation reduces free-form surface lens 2 optical efficiencies; On the contrary, free form surface reflector 3 can be controlled the high angle scattered light that departs from optical axis preferably, but cannot accurately control low-angle light.

Free-form surface lens 2 is thought sources of the present invention with the characteristic of free form surface reflector 3 complementations.The illuminator that the present invention proposes can be applied to multiple LED light fixture, as LED projecting lamp, LED bulkhead lamp capable, LED Down lamp etc.

In said lighting system, realize the LED illumination of arrow beam of light, be to the lens outer surface of cupular part of free-form surface lens 2, and the curve of free form surface reflector 3 reasonably designs.Provide the lens outer surface of cupular part of free-form surface lens 2 below, and a kind of method for designing of free form surface reflector 3 (or generation method).The design of all the other lens top inner surface such as free-form surface lens 2, lens sidewall and lens bottom can be followed prior art.

The generation method of lens free form surface is as follows:

As shown in Figure 2, taking light source place plane as x axle, perpendicular bisector is that y axle is set up coordinate system, taking light source center as initial point.If expansion light source radius is R, face 1 and face 2 are respectively the surfaces externally and internally at lens top, determine that free form surface step is as follows:

1) establishing H is LED light source left hand edge R _llight and y axle intersection point, coordinate is (0, H).

2) according to dimension of light source D(D=2R), suitably get certain 1 X on refracted ray for the first time ₀as the starting point of lens outer surface curve, and make X ₀the normal at some place straight up.

3) according to optical extend conservation formula

$2n\×D=\underset{-\mathrm{\β}}{\overset{\mathrm{\β}}{\∫}}\mathrm{Ld\β}$

Obtain projection width L.

Wherein, D is light source diameter, and β is emergent ray and y axle clamp angle, the refractive index that n is optical material.

4) straight line a is R _lemergent ray, gets with the straight line b of its distance L as light source edge R _remergent ray, on straight line b, suitably get 1 Y ₀.

5) according to law of refraction vector form

Can obtain Y ₀put to obtain normal direction

Wherein with be respectively outgoing and incident ray unit vector, for interface normal unit vector.

6) according to X ₀, Y ₀coordinate and their normal direction with full curve of interpolation (conventionally getting cubic curve), makes it to pass through X ₀and Y ₀, meet normal direction at these 2 simultaneously with can draft thus a full curve X ₀y ₀as calculating virgin curve.

7) initial curve is divided to n segment, obtained the n+1 point on curve, be respectively X ₀～X _n, the some Y of corresponding unknown curve ₀～Y _n.

8) get X ₀nearlyer 1 X ₁, emergent ray is straight line c, using the straight line d that is L apart from straight line c as R _ranother after lens reflection light.Calculate straight line d and Y ₀point the intersection point of tangent line (is Y ₁), calculate Y according to law of refraction vector form ₁put to obtain normal direction.Equally according to X ₁, Y ₁coordinate and their normal direction, interpolation cubic curve.

9) get X ₁nearlyer 1 X ₂, the like calculating, can computer iterations calculate, use synchronous many Surface Method to calculate remaining point, until the scope of α is 40 °～45 ° (angle can be finely tuned according to actual conditions), finally obtain lens cross section curve.

In the situation that calculating permission, it is more that the quantity of putting on initial curve is selected, and model accuracy is higher.

Through the high angle scattered light of lens side outgoing by reflector control.

The generation method of reflector free form surface is as follows: as shown in Figure 3,

1) first determine one section of initial segment A ₁b ₁(wherein A ₁coordinate be to determine at the very start according to concrete application), from starting to consider with the maximum light in y axle clamp angle.Starting point on the corresponding screen of this cluster light is r ₁, initial incident ray R _la ₁arrive r through reflection ₁.Can be according to rim ray theory, R _ra certain the light sending incides initial curve terminal B ₁also can be reflected to r ₁, curved section A ₁b ₁with R _rand r ₁it is the part curve of two focus ellipses.Angle θ _r, angle θ ₁be respectively emergent ray A _nr _n, B _nr _nangle with optical axis y.

2) establishing light-source brightness is B, and send with y axle clamp angle compared with little and direct irradiation on screen and the illumination producing can be by

$E\left(r\right)=\∫B\·\cos \mathrm{\θ}\·\mathrm{d\θ}=\mathrm{B\Ω}$ Obtain.

Angle A ₁r ₁b ₁size by r ₁illumination determine.Emergent ray A ₁r ₁angle theta with y axle _rcan be by A ₁coordinate determine, r ₁the energy that the illumination receiving can deduct reflector reflection by the energy of light source direct irradiation obtains,

E _r=E-BΩ=B(sinθ _r-sinθ ₁)

Can try to achieve emergent ray B ₁r ₁angle theta with y axle ₁, and can obtain B ₁the coordinate of point, initial curve A ₁b ₁equation can be determined.

3) from R _lpoint sends the light slightly little with y axle clamp angle, incides curve A ₁b ₁on A ₂point can be obtained A from curvilinear equation ₂coordinate with and normal vector can obtain its reflection ray by reflection law, establishing the point that reflection ray incides on screen is r ₂, emergent ray A ₂r ₂angle theta with y axle _rcan determine.Can try to achieve emergent ray B by Flux conservation ₂r ₂angle theta with y axle ₁, can determine r ₂light receives the light on another one border of cone, itself and B ₁the tangent line of point meets at B ₂, can be used as new curve point.

4) light source is from edge R _rthe light R sending _rb ₂reflection ray through reflection is B ₂r ₂, according to reflection law, B ₂coordinate and normal vector also can determine.Reflector A ₁b ₂profile can determine, then consider by R _rthe light less with y axle clamp angle that point sends, repeats above step, and outline line will constantly be expanded, until reach desired border.

This method for designing can be set according to light source size the coordinate of rim ray point, and shadow surface how far is determined the size of field of illumination according to demand, and can perfectly overlap with the smaller angle light of lens control.Determine because the curvilinear equation of reflector has each pip, range changing is adjustable, can better receive light to the light of wide-angle outgoing.

Detailed description of the invention:

Provide a specific embodiment of above-mentioned method for designing below.

1) determine the size (the desirable 10mm～25mm of D) of dimension of light source parameter D, determine the size (20mm<H<30mm) of lens height H, determine the size (40 ° of < α <45 °) of light splitting angle [alpha], determine the size (4 ° of < β <9 °) of rising angle β.

2) expand two conservation formulas according to optics calculate projection width L.

3) on face 2, get 1 X ₀as the starting point of lens outer surface curve, and make X ₀the normal at some place straight up, emergent ray angle is β, determines Y according to the size of distance L and β ₀point position.According to law of refraction vector form obtain Y ₀point normal direction

4) draft a full curve X ₀y ₀as calculating virgin curve, curve is divided to n segment, obtain obtaining n+1 point on curve, be respectively X ₀～X _n, the some Y of corresponding unknown curve ₀～Y _n.

5) get X ₀nearlyer 1 X ₁, emergent ray angle is β, determines Y according to the size of L and β ₁point position.Calculate Y according to law of refraction vector form equally ₁point normal direction, interpolation curve.

6) get more closely, the like calculating, can computer iterations calculate, use synchronous many Surface Method to calculate remaining point, until α=45 ° finally obtain lens cross section curve.

7) discrete point calculating is imported in mechanical modeling software (as: Rhinoceros, UG etc.), connect into a free curve, symmetrical rotary obtains lens physical model.

8) for saving material, improve central light strength, do not change lens top curvature, lens outer surface of cupular part is adopted to Fresnel Lenses.

9) determine irradiation distance S=1.2m, according to the size of β, determine the illumination zone radius r in target face _maxsize, r _max=S × tan β.

10) determine one section of initial segment A ₁b ₁, initial incident ray R _la ₁arrive r through reflection ₁, according to rim ray theory, R _ra certain the light sending incides initial curve B ₁also can be reflected to r ₁.

11) establishing light-source brightness is B, on screen and produce illumination be calculated as follows:

$E\left(r\right)=\&Integral;B\&CenterDot;\cos \mathrm{\&theta;}\&CenterDot;\mathrm{d\&theta;}=\mathrm{B\&Omega;}$

R ₁the energy that the illumination receiving can deduct reflector reflection through the energy irradiating after lens by light source obtains,

E _r=E-BΩ=B(sinθ _r-sinθ ₁)

Can obtain angle θ ₁and B ₁the coordinate of point, determines curvilinear equation A ₁b ₁.

12) from R _lpoint sends the light slightly little with y axle clamp angle, incides curve A ₁b ₁on A ₂point, by curvilinear equation A ₁b ₁obtain A ₂coordinate with and normal vector obtain its reflection ray by reflection law, the point on corresponding screen is r ₂, determine A ₂r ₂angle theta with y axle _rsize.Can obtain θ by Flux conservation ₁, can determine r ₂light receives the light on another one border of cone, itself and B ₁the tangent line of point meets at B ₂, as new curve point.

13) from light source edge R _rthe light R sending _rb ₂reflection ray through reflection is B ₂r ₂, according to reflection law, B ₂coordinate and normal vector also can determine.Reflector A ₁b ₂profile can determine, then consider by R _rthe light less with y axle clamp angle that point sends, repeats above step, and outline line will constantly be expanded, and stops until being reduced to 45 degree with y axle clamp angle, obtains final reflector curve.

14) the reflector curve symmetric rotation calculating is obtained to reflector physical model.

15) light effect for improving, in the situation that not changing reflector curvature, by scale and shell structure function in reflector medial surface.

16) lens model and reflector models coupling, obtains final LED lamp optical system, as shown in Figure 1.

17) the COB type LED light source of employing diameter 15mm, uses the LED light distributing system obtaining, and finally at illumination distances S=1.2m place, forms the uniform light spots of 30cm～40cm left and right.Half light intensity bright dipping full-shape is 16 degree, and central light strength reaches 7500cd/klm.

Above-described is only the preferred embodiment of the present invention, the invention is not restricted to above embodiment.Be appreciated that the oher improvements and changes that those skilled in the art directly derive or associate without departing from the basic idea of the present invention, within all should thinking and being included in protection scope of the present invention.

Claims (1)

1. the method for designing of an arrow beam of light LED lamp optical system, it is characterized in that: taking light source place plane as x axle, perpendicular bisector is that y axle is set up coordinate system, taking light source center as initial point, if expansion light source radius is R, generate lens free form surface and reflector free form surface;

The step that generates lens free form surface is as follows:

1) establishing H is LED light source left hand edge R _llight and the intersection point of y axle, coordinate is (0, H);

2), according to dimension of light source D (D=2R), get the some X on refracted ray for the first time ₀as the starting point of lens outer surface curve, and make X ₀the normal at some place straight up;

3) according to optical extend conservation formula

$2n\&times;D=\underset{-\mathrm{\&beta;}}{\overset{\mathrm{\&beta;}}{\&Integral;}}\mathrm{Ld\&beta;}$

Obtain projection width L; Wherein, D is light source diameter, and β is emergent ray and y axle clamp angle, the refractive index that n is optical material;

4) straight line a is R _lemergent ray, gets with the straight line b of its distance L as light source edge R _remergent ray, on straight line b, get a Y ₀;

5) according to law of refraction vector form

${[1+n^2-2n(\stackrel{\&RightArrow;}{\mathrm{Out}}\&CenterDot;\stackrel{\&RightArrow;}{\mathrm{In}})]}^{1/2}\&CenterDot;\stackrel{\&RightArrow;}{N}=\stackrel{\&RightArrow;}{\mathrm{Out}}-n\stackrel{\&RightArrow;}{\mathrm{In}}$

Obtain Y ₀put to obtain normal direction wherein with be respectively outgoing and incident ray unit vector, for interface normal unit vector;

6) according to X ₀, Y ₀coordinate and their normal direction with full curve of interpolation, makes it to pass through X ₀and Y ₀, meet normal direction at these 2 simultaneously with can draft thus a full curve X ₀y ₀as calculating virgin curve;

7) by initial curve X ₀y ₀divide n segment, obtain the n+1 point on curve, be respectively X ₀～X _n, the some Y of corresponding unknown curve ₀～Y _n;

8) get X ₀nearlyer 1 X ₁, emergent ray is straight line c, using the straight line d that is L apart from straight line c as R _ranother after lens reflection light; Calculate straight line d and Y ₀point the intersection point Y of tangent line ₁, calculate Y according to law of refraction vector form ₁put to obtain normal direction; Equally according to X ₁, Y ₁coordinate and their normal direction, interpolation cubic curve;

9) get X ₁nearlyer 1 X ₂, the like calculating, use synchronous many Surface Method to calculate remaining point, until the scope of α is at 40 °～45 °, finally obtain lens cross section curve;

The step that generates reflector free form surface is as follows:

1) determine initial segment A ₁b ₁, from starting to consider with the maximum light in y axle clamp angle, the starting point on the corresponding screen of this cluster light is r ₁, initial incident ray R _la ₁arrive r through reflection ₁; According to rim ray theory, R _ra certain the light sending incides initial curve terminal B ₁also can be reflected to r ₁, curved section A ₁b ₁with R _rand r ₁it is the part curve of two focus ellipses; Angle θ _r, angle θ ₁be respectively emergent ray A _nr _n, B _nr _nangle with optical axis y;

2) establishing light-source brightness is B, and send with y axle clamp angle compared with little and direct irradiation on screen and the illumination producing can be by

E (r)=∫ Bcos θ d θ=B Ω obtains;

Angle A ₁r ₁b ₁size by r ₁illumination determine; Emergent ray A ₁r ₁angle theta with y axle _rby A ₁coordinate determine, r ₁the energy that the illumination receiving can deduct reflector reflection by the energy of light source direct irradiation obtains,

E _r＝E-BΩ＝B(sinθ _r-sinθ ₁)

Obtain emergent ray B ₁r ₁angle theta with y axle ₁and obtain B ₁the coordinate of point, initial curve A ₁b ₁equation can be determined;

3) from R _lpoint sends the light slightly little with y axle clamp angle, incides curve A ₁b ₁on A ₂point can be obtained A from curvilinear equation ₂coordinate with and normal vector can obtain its reflection ray by reflection law, establishing the point that reflection ray incides on screen is r ₂, emergent ray A ₂r ₂angle theta with y axle _rcan determine; Obtain emergent ray B by Flux conservation ₂r ₂angle theta with y axle ₁, determine r ₂light receives the light on another one border of cone, itself and B ₁the tangent line of point meets at B ₂, as new curve point;

4) light source is from edge R _rthe light R sending _rb ₂reflection ray through reflection is B ₂r ₂, according to reflection law, B ₂coordinate and normal vector also can determine; Reflector A ₁b ₂profile can determine, then consider by R _rthe light less with y axle clamp angle that point sends, repeats above step, and outline line will constantly be expanded, until reach desired border.