CN103912809A - Turn-back type LED lighting optical system - Google Patents

Abstract

The invention relates to the technical field of collimating optical system of LED lighting, in particular to a turn-back type LED lighting optical system. The turn-back type LED lighting optical system comprises a free curved-surface lens and a free curved-surface reflector. The free curved-surface lens and the free curved-surface reflector are coaxial with the spacing ranging from 0.01m to 0.1m; the free curved-surface lens comprises a first curved surface, a second curved surface, a third curved surface, a fifth curved surface and a fourth curved surface, the first curved surface, the second curved surface and the fifth curved surface are rotationally symmetrical free curved surfaces, the third curved surface is a rotational paired paraboloid, and a focal point of the paraboloid is a virtual light point of reflected ray of the second curved surface, and the fourth curved surface is a cylindrical surface and used for connecting the third curved surface and the fifth curved surface. The free curved-surface reflector is composed of three curved surfaces. By the arrangement, optional viewing angles can be lit, and lighting effect of the optical system cannot be lowered due to total reflection.

Description

Zigzag type LED lamp optical system

Technical field

The collimating optical system technical field that the present invention relates to LED illumination, is specifically related to a kind of Zigzag type LED lamp optical system.

Technical background

LED is as a kind of new type light source, and due to its high light efficiency, the life-span is long, nonhazardous etc., and advantage makes it the perfect replacer who becomes traditional light source such as incandescent lamp, fluorescent lamp.But because the light distribution of LED is that circular lambert's type distributes, if directly apply to illumination, can in target face, form very inhomogeneous Illumination Distribution, cannot meet the requirement of various illumination occasions to light fixture optical property.In order to make LED better be applied to lighting field, need designs secondary optics system to redistribute the light distribution of LED, it can be formed evenly or other specific Illumination Distribution in target face.

In order to realize the set Illumination Distribution of LED light fixture in target face, the design LED free-form surface lens that adopt reach this object more at present.A kind of lens of the LED of control light beam are disclosed in Chinese invention patent description CN101144863B.These lens utilize free form surface beam projecting face accurately to control the distribution of outgoing beam energy space, can realize the light spot shape and the Illumination Distribution that meet different illumination needs.A kind of arrow beam of light LED lamp optical system is disclosed in Chinese utility model patent description CN20320202741U.This optical system utilizes Fresnel Lenses to assemble low-angle light; Adopting fully reflecting surface to realize set illumination to the light of wide-angle.Thereby realize the low-angle high light efficiency illumination of LED.Except lens, the optical system of reflection-type is also used in the middle of LED illumination.A kind of free-form surface LED optical system based on high diffuse reflectance has been proposed in Chinese invention patent application description CN103234173A.This optical system utilizes free form surface reflecting surface to realize redistributing LED light.

Although the set illumination that LED secondary lens can realize target face, but also there is following problem: (1) exists total reflection phenomenon while propagation from optically denser medium to optically thinner medium due to light, therefore when illumination field of view angle is approximately greater than 60 while spending, because making the light efficiency of lens, the existence of total reflection phenomenon constantly declines along with the increase of the angle of visual field; (2) according to the definition of brightness, the less brightness of the size of light source is higher, and now people just feels to get over " dazzling ".Because the luminous size of LED is minimum, be generally 1mm × 1mm, there is more serious " dazzling " phenomenon in the LED optical system of transmission-type therefore.Compare LED secondary lens, the reflective LED secondary optical system angle of visual field is unrestricted, there is no " dazzling " phenomenon, but in actual use, the devices such as LED chip, fin, pcb board are installed due to needs, therefore there is occlusion issue, can cause and can not all utilize light or the part light that LED sends can not be through the shaping direct irradiation of optical system to target face.

Summary of the invention

The object of the invention is for general illumination occasions such as room lightings, design the LED secondary optical system of the Zigzag type of a kind of realize target region Uniform Illumination, not there is not " dazzling " phenomenon in this optical system, have higher light efficiency simultaneously.

For achieving the above object, the Zigzag type LED lamp optical system that the present invention is designed, comprises free-form surface lens and free-form surface reflector, and described free-form surface lens and free-form surface reflector are coaxial, and spacing is 0.01m-0.1m;

Described free-form surface lens comprises first surface, is Rotational Symmetry free form surface, for the light refraction that LED is sent, make refraction after light ray parallel in z axle; The second curved surface, is Rotational Symmetry free form surface, for the light refraction that LED is sent, makes the light after refraction become the light sending with spot light on x axle and overlap; The 3rd curved surface, for rotation is to parabola, paraboloidal focus is the virtual optical source point of the second curved surface refracted ray, by the extremely direction parallel with z axle of light reflection through after the second curved surface refraction; The 5th curved surface, for Rotational Symmetry free form surface, for controlling the light through being parallel to z axle after first surface, the second curved surface and the 3rd curved surface, the light that makes this bundle be parallel to z axle is forming uniform Illumination Distribution on any disk vertical with z axle after the 5th curved surface in space; And the 4th curved surface, be the face of cylinder, for connecting the 3rd curved surface and the 5th curved surface;

Described free-form surface reflector, is made up of three curved surfaces, and wherein first surface is free form surface, direction and the energy of the light beam that control the second free-form surface lens sends, and the second curved surface and the 3rd curved surface are respectively the first pedestal and second pedestal of reflector.

Further, the coordinate of putting on described first surface and the second curved surface is calculated by following formula: set the initial point of the first free form surface, obtain its outline line by following formula iteration:

$\left\{\begin{array}{c}{x}_i=\frac{z_{i-1}+x_{i-1}k}{\cot {\mathrm{\θ}}_i+k}\\ z_i=x_i\cot {\mathrm{\θ}}_i\end{array}\right.---\left(1\right)$

Wherein (x _i, z _i) be the coordinate of the calculative point of current iteration, (x _i-1, z _i-1) be more front coordinate, (N _x, N _z) be more front normal vector coordinate.Obtain can obtaining the first free form surface with z axle position symmetry axis rotating 360 degrees after contour curve.

Again further, x, the y axial coordinate on described the 5th curved surface, put are identical with corresponding points on first surface, the second curved surface and the 3rd curved surface, the angular region of light source is divided into M × N part, luminous flux in every part is identical, calculate x, the y axial coordinate of the 5th corresponding curved surface, outgoing hot spot is formed to equally distributed disk simultaneously and be divided into M × N the unit that area is equal, and calculate x, the y axial coordinate of these cell nodes, the initial point of selected curved surface, solves by the method for iteration the z axial coordinate of putting on initial skeleton curve and is:

$z_{1,i}=\frac{-(x_{1,i}-x_{1,i-1})N_{1x}-(y_{1,i}-y_{1,i-1})N_{1y}}{N_{1z}}+z_{1,i-1}---\left(2\right)$

Wherein (x _{1, i}, y _{1, i}, z _{1, i}) be the coordinate of the calculative point of current iteration, (x _{1, i-1}, y _{1, i-1}, z _{1, i-1}) be upper coordinate, (N _1x, N _1y, N _1z) be the coordinate of upper normal vector.Obtaining obtaining next skeleton curve by (2) formula iteration after initial skeleton curve, after obtaining all skeleton curves, obtain the 5th curved surface thereby obtain all subsurfaces by the mode of setting-out.

Again further, the free form surface of described free-form surface reflector is made up of certain multiple subsurface, between two adjacent subsurfaces, is connected by the plane that is parallel to z axle, and target face is divided, and the node coordinate of division is (T _x, T _y, T _z), the initial point of selected curved surface, solves by the method for iteration the z axial coordinate of putting on initial skeleton curve and is:

$\left\{\begin{array}{c}{x}_{2,i}=\mathrm{lx}(z_{2,i}-z_{1,i})+x_{1,i}\\ y_{2,i}=\mathrm{ly}(z_{2,i}-z_{1,i})+y_{1,i}\\ z_{2,i}=\frac{((\mathrm{lx}\×z_{1,i}-x_{1,i}+x_{2,i-1})N_{2,x}+(\mathrm{ly}\×z_{1,i}-y_{1,i}+y_{2,i-1})N_{2,y}+z_{2,i-1}{N}_{2,z})}{\mathrm{lx}\×N_{2,x}+\mathrm{ly}\×N_{2,y}+N_{2,z}}\end{array}\right.---\left(3\right)$

Wherein (x _{2, i}, y _{2, i}, z _{2, i}) be the coordinate of the calculative point of current iteration, (x _{2, i-1}, y _{2, i-1}, z _{2, i-1}) be more front coordinate, (N _2x, N _2y, N _2z) be more front normal vector coordinate, (x _{1, i}, y _{1, i}, z _{1, i}) be the coordinate of corresponding points on free-form surface lens the 5th free form surface.The expression formula of lx and ly is:

$\left\{\begin{array}{c}\mathrm{lx}=\frac{T_{x,i}-x_{1,i}}{T_{z,i}-z_{1,i}}\\ \mathrm{ly}=\frac{T_{y,i}-y_{1,i}}{T_{z,i}-z_{1,i}}\end{array}\right.---\left(4\right)$

Obtaining obtaining next skeleton curve by (2) formula iteration after initial skeleton curve, re-construct initial skeleton curve at the section start of each subsurface, after obtaining all skeleton curves, obtain all subsurfaces by the mode of setting-out, obtain the free form surface of free-form surface reflector.

Design LED secondary optical system of the present invention, has good light control ability, can in target face, realize needed Illumination Distribution.Owing to adopting the design of Zigzag type, be equivalent to expand the area of light source, reduce the brightness value of light source, therefore do not have the phenomenon of " dazzling ".Because reflecting surface does not exist total reflection phenomenon, therefore can realize the illumination of any angle of visual field, and can not reduce because of total reflection the light efficiency of optical system.Owing to adopting free-form surface lens to collect and shaping the light of LED, solve in the optical system that only has reflecting surface and existed and block or the uncontrollable problem of a part of light simultaneously.

Brief description of the drawings

Fig. 1 is the side view of one embodiment of the invention;

The side view of free-form surface lens in Fig. 2 Fig. 1 (1);

The cutaway view of Fig. 3 Fig. 2;

Fig. 4 is the side view of free-form surface reflector in Fig. 1 (2);

Fig. 5 is the cutaway view of Fig. 4;

Fig. 6 is the grid corresponding relation using while calculating the upper coordinate of free-form surface reflector (2);

Fig. 7 is that the present embodiment obtains Illumination Distribution simulation result in target face in optical design software; Free-form surface lens (1) and free-form surface reflector (2)

In figure, 1-free-form surface lens, 11-first surface; 12-the second curved surface; 13-the 3rd curved surface; 14-the 4th curved surface; 15-the 5th curved surface; 2-free-form surface reflector; 21-free form surface; 22-the first pedestal; 23-the second pedestal.

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail:

Zigzag type LED lamp optical system comprises free-form surface lens 1 and free-form surface reflector 2, and free-form surface lens 1 and free-form surface reflector 2 are coaxial, and spacing is 0.01m-0.1m; Free-form surface lens 1 comprises first surface 11, is Rotational Symmetry free form surface, for the light refraction that LED is sent, make refraction after light ray parallel in z axle; The second curved surface 12, is Rotational Symmetry free form surface, for the light refraction that LED is sent, makes the light after refraction become the light sending with spot light on x axle and overlap; The 3rd curved surface 13, for rotation is to parabola, paraboloidal focus is the virtual optical source point of the second curved surface refracted ray, by the extremely direction parallel with z axle of the light reflection after reflecting through the second curved surface 12; The 5th curved surface 15, for Rotational Symmetry free form surface, for controlling the light through being parallel to z axle after first surface 11, the second curved surface 12 and the 3rd curved surface 13, the light that makes this bundle be parallel to z axle is forming uniform Illumination Distribution on any disk vertical with z axle after the 5th curved surface 15 in space; And the 4th curved surface 14, be the face of cylinder, for connecting the 3rd curved surface 13 and the 5th curved surface 15; Free-form surface reflector 2, is made up of three curved surfaces, and wherein first surface is free form surface 21, direction and the energy of the light beam that control the second free-form surface lens 2 sends, and the second curved surface and the 3rd curved surface are respectively the first pedestal 22 and second pedestal 23 of reflector.

On first surface 11 and the second curved surface 12, the coordinate of point is calculated by following formula: set the initial point of the first free form surface, obtain its outline line by following formula iteration:

$\left\{\begin{array}{c}{x}_i=\frac{z_{i-1}+x_{i-1}k}{\cot {\mathrm{\θ}}_i+k}\\ z_i=x_i\cot {\mathrm{\θ}}_i\end{array}\right.---\left(5\right)$

Wherein (x _i, z _i) be the coordinate of the calculative point of current iteration, (x _i-1, z _i-1) be more front coordinate, (N _x, N _z) be more front normal vector coordinate.Obtain can obtaining the first free form surface with z axle position symmetry axis rotating 360 degrees after contour curve.

On the 5th curved surface 15, x, the y axial coordinate of point are identical with corresponding points on first surface 11, the second curved surface 12 and the 3rd curved surface 13, the angular region of light source is divided into M × N part, luminous flux in every part is identical, calculate x, the y axial coordinate of the 5th corresponding curved surface 15, outgoing hot spot is formed to equally distributed disk simultaneously and be divided into M × N the unit that area is equal, and calculate x, the y axial coordinate of these cell nodes, the initial point of selected curved surface, solves by the method for iteration the z axial coordinate of putting on initial skeleton curve and is:

$z_{1,i}=\frac{-(x_{1,i}-x_{1,i-1})N_{1x}-(y_{1,i}-y_{1,i-1})N_{1y}}{N_{1z}}+z_{1,i-1}---\left(6\right)$

Wherein (x _{1, i}, y _{1, i}, z _{1, i}) be the coordinate of the calculative point of current iteration, (x _{1, i-1}, y _{1, i-1}, z _{1, i-1}) be upper coordinate, (N _1x, N _1y, N _1z) be the coordinate of upper normal vector.Obtaining obtaining next skeleton curve by (2) formula iteration after initial skeleton curve, after obtaining all skeleton curves, obtain the 5th curved surface 15 thereby obtain all subsurfaces by the mode of setting-out.

The free form surface 21 of free-form surface reflector 2 is made up of certain multiple subsurface, between two adjacent subsurfaces, is connected by the plane that is parallel to z axle, and target face is divided, and the node coordinate of division is (T _x, T _y, T _z), the initial point of selected curved surface, solves by the method for iteration the z axial coordinate of putting on initial skeleton curve and is:

$\left\{\begin{array}{c}{x}_{2,i}=\mathrm{lx}(z_{2,i}-z_{1,i})+x_{1,i}\\ y_{2,i}=\mathrm{ly}(z_{2,i}-z_{1,i})+y_{1,i}\\ z_{2,i}=\frac{((\mathrm{lx}\×z_{1,i}-x_{1,i}+x_{2,i-1})N_{2,x}+(\mathrm{ly}\×z_{1,i}-y_{1,i}+y_{2,i-1})N_{2,y}+z_{2,i-1}{N}_{2,z})}{\mathrm{lx}\×N_{2,x}+\mathrm{ly}\×N_{2,y}+N_{2,z}}\end{array}\right.---\left(7\right)$

Wherein (x _{2, i}, y _{2, i}, z _{2, i}) be the coordinate of the calculative point of current iteration, (x _{2, i-1}, y _{2, i-1}, z _{2, i-1}) be more front coordinate, (N _2x, N _2y, N _2z) be more front normal vector coordinate, (x _{1, i}, y _{1, i}, z _{1, i}) be the coordinate of corresponding points on free-form surface lens the 5th free form surface.The expression formula of lx and ly is:

$\left\{\begin{array}{c}\mathrm{lx}=\frac{T_{x,i}-x_{1,i}}{T_{z,i}-z_{1,i}}\\ \mathrm{ly}=\frac{T_{y,i}-y_{1,i}}{T_{z,i}-z_{1,i}}\end{array}\right.---\left(8\right)$

Obtaining obtaining next skeleton curve by (2) formula iteration after initial skeleton curve, re-construct initial skeleton curve at the section start of each subsurface, after obtaining all skeleton curves, obtain all subsurfaces by the mode of setting-out, obtain the free form surface 21 of free-form surface reflector 2.

Be the structural representation of a specific embodiment of the present invention as shown in Figure 1, wherein LED is positioned at the origin of coordinates, and this optical system comprises two parts, free-form surface lens 1 and free-form surface reflector 2.

Fig. 2 and Fig. 3 are side-looking and the cutaway views of free-form surface lens 1 in Fig. 1.Wherein first surface 11, the second curved surface 12 and the 3rd curved surface 13 are planes of incidence of LED light, and object is that the spherical wave collimation that LED is sent is the plane wave vertical with z axle.

First surface 11 is by the light refraction from LED to parallel with z axle, and this curved surface is rotational symmetric, only need calculate a contour curve while therefore calculating, then revolves to turn around around z axle to obtain the face type of first surface 11.While calculating contour curve, first determine the coordinate figure of initial point, initial point is the intersection point of curved surface and z axle, calculates the coordinate figure of putting on contour curve by the mode of iteration.Make current known point (x _i-1, z _i-1) normal vector be N=(N _x, N _z), under the contour curve that calculate, any corresponding incident ray and the angle of z axle are θ _i, lower any coordinate figure (x _i, z _i) be:

$\left\{\begin{array}{c}{x}_i=\frac{z_{i-1}+x_{i-1}k}{\cot {\mathrm{\θ}}_i+k}\\ z_i=x_i\cot {\mathrm{\θ}}_i\end{array}\right.---\left(9\right)$

Wherein k=N _x/ N _z.In this implements, the z coordinate figure of the initial point of first surface 11 is 5mm, and the corresponding LED light of curved edges and z axle clamp angle are 30 °.

The object of the second curved surface 12 be make the reverse extending line of light that LED the sends emergent ray after this curved surface refraction meet at x axle a bit, thereby can obtain a virtual optical source point.The initial point of S12 is the marginal point of S11, uses equally (1) when calculating.

The focus of the 3rd curved surface 13 is the virtual optical source point that the second curved surface 12 is created, and utilizes total reflection principle, by the light reflection from the second curved surface 12 to z axle parallel direction.

The energy by the plane wave through after first surface 11, the second curved surface 12 and the 3rd curved surface 13 of the 5th curved surface 15 is redistributed, and makes certain center in space form and be uniformly distributed on z axle and on the disk vertical with z axle.On the 4th curved surface 14, the coordinate account form of point is for utilizing the conservation of energy, incident wavefront and target circle plane are divided into the grid that energy is equal, determine the corresponding relation between mesh point according to space topological, recycling (1) formula can be calculated the coordinate of point on the 5th curved surface 15.Because the 5th curved surface 15 is rotational symmetric, therefore only need to calculate contour curve can obtain curved surface face type.In this enforcement, this disk is positioned at z=80mm place, and radius is 20mm, and the initial point of free form surface S15 is (0,0,21.36).

The 4th curved surface 14 is the face of cylinder, for connecting the 3rd curved surface 13 and the 5th curved surface 15.

After calculating all curved surfaces of free-form surface lens 1, height is 24.27mm, and wide is 32.44mm.The space height of first surface 11,12 formation of the second curved surface is 5mm, and wide is 4.9mm, for placing LED light source.

Fig. 4 and Fig. 5 are side-looking and the cutaway views of free-form surface reflector 2 in Fig. 1.Reflector in this enforcement is made up of first surface 11, the second curved surface 12 and the 3rd curved surface 13.

The first pedestal 22 and the second pedestal 23 are the pedestal of free-form surface reflector 2, can have any shape in actual use, and in this enforcement, column type pedestal of these two Surface formings.

The object of free form surface 21 is the beam reflection from free-form surface lens 1 to be formed to uniform illuminance to target face and in target face.In this enforcement, target setting face is that the length of side is 8m × 6m and the rectangle vertical with y axle, and target face central point is positioned on y axle and apart from LED light source 2.5m.Adopt the conservation of energy and Snell's law to calculate the coordinate of putting on free form surface.First the target circle plane of according to the conservation of energy, design being set when the 5th curved surface 15 and illumination target face are divided into grid that energy is equal as shown in Figure 6, and due to symmetry, the grid that has only provided first quartile is here divided corresponding relation.After obtaining this corresponding relation, according to Snell's law, setting initial point is the central point of the target circle plane of setting while designing the 5th curved surface 15, adopts the mode of iteration to obtain the coordinate of point on free form surface 21.For the error that reduces to produce in iterative process, adopt the mode of patch to construct free form surface 21, between each patch, use the face of cylinder to connect.

In order to construct free form surface 21, target face is done to the division shown in Fig. 6, the node coordinate of division is (T _x, T _y, T _z).The initial point of selected curved surface, solves by the method for iteration the z axial coordinate of putting on initial skeleton curve and is:

$\left\{\begin{array}{c}{x}_{2,i}=\mathrm{lx}(z_{2,i}-z_{1,i})+x_{1,i}\\ y_{2,i}=\mathrm{ly}(z_{2,i}-z_{1,i})+y_{1,i}\\ z_{2,i}=\frac{((\mathrm{lx}\×z_{1,i}-x_{1,i}+x_{2,i-1})N_{2,x}+(\mathrm{ly}\×z_{1,i}-y_{1,i}+y_{2,i-1})N_{2,y}+z_{2,i-1}{N}_{2,z})}{\mathrm{lx}\×N_{2,x}+\mathrm{ly}\×N_{2,y}+N_{2,z}}\end{array}\right.---\left(10\right)$

Wherein (x _{2, i}, y _{2, i}, z _{2, i}) be the coordinate of the calculative point of current iteration, (x _{2, i-1}, y _{2, i-1}, z _{2, i-1}) be more front coordinate, (N _2x, N _2y, N _2z) be more front normal vector coordinate, (x _{1, i}, y _{1, i}, z _{1, i}) be the coordinate of corresponding points on free form surface 21.The expression formula of lx and ly is:

$\left\{\begin{array}{c}\mathrm{lx}=\frac{T_{x,i}-x_{1,i}}{T_{z,i}-z_{1,i}}\\ \mathrm{ly}=\frac{T_{y,i}-y_{1,i}}{T_{z,i}-z_{1,i}}\end{array}\right.---\left(11\right)$

Obtaining obtaining next skeleton curve by (2) formula iteration after initial skeleton curve.Re-construct initial skeleton curve at the section start of each subsurface.After obtaining all skeleton curves, obtain free form surface 21 thereby obtain all subsurfaces by the mode of setting-out.

Fig. 7 is lens Illumination Distribution result in target face in optical simulation software of this enforcement, obtain by 1,000,000 light of trace, wherein left side is the Illumination Distribution in target face, in figure, gray value size is directly proportional to brightness value, and right side is the Illumination Distribution on two centre coordinate axles in target face.Wherein the optical efficiency of optical system is 80%.In target face, the illumination uniformity on long limit and minor face is 75% and 70% simultaneously, good uniformity.

Claims (4)

1. a Zigzag type LED lamp optical system, is characterized in that: comprise free-form surface lens (1) and free-form surface reflector (2), described free-form surface lens (1) and free-form surface reflector (2) are coaxial, and spacing is 0.01m-0.1m;

Described free-form surface lens (1) comprises first surface (11), is Rotational Symmetry free form surface, for the light refraction that LED is sent, make refraction after light ray parallel in z axle; The second curved surface (12), is Rotational Symmetry free form surface, for the light refraction that LED is sent, makes the light after refraction become the light sending with spot light on x axle and overlap; The 3rd curved surface (13), for rotation is to parabola, paraboloidal focus is the virtual optical source point of the second curved surface refracted ray, will be through the light reflection after the second curved surface (12) refraction to the direction parallel with z axle; The 5th curved surface (15), for Rotational Symmetry free form surface, be used for controlling the light that is parallel to afterwards z axle through first surface (11), the second curved surface (12) and the 3rd curved surface (13), the light that makes this bundle be parallel to z axle is forming uniform Illumination Distribution on any disk vertical with z axle after the 5th curved surface (15) in space; And the 4th curved surface (14), be the face of cylinder, for connecting the 3rd curved surface (13) and the 5th curved surface (15);

Described free-form surface reflector (2), formed by three curved surfaces, wherein first surface is free form surface (21), direction and the energy of controlling the light beam that the second free-form surface lens (2) sends, the second curved surface and the 3rd curved surface are respectively the first pedestal (22) and second pedestal (23) of reflector.

2. Zigzag type LED lamp optical system according to claim 1, it is characterized in that: the coordinate of the upper point of described first surface (11) and the second curved surface (12) is calculated by following formula: set the initial point of the first free form surface, obtain its outline line by following formula iteration:

$\left\{\begin{array}{c}{x}_i=\frac{z_{i-1}+x_{i-1}k}{\cot {\mathrm{\θ}}_i+k}\\ z_i=x_i\cot {\mathrm{\θ}}_i\end{array}\right.---\left(1\right)$

Wherein (x _i, z _i) be the coordinate of the calculative point of current iteration, (x _i-1, z _i-1) be more front coordinate, (N _x, N _z) be more front normal vector coordinate.Obtain can obtaining the first free form surface with z axle position symmetry axis rotating 360 degrees after contour curve.

3. Zigzag type LED lamp optical system according to claim 1, it is characterized in that: the x of the upper point of described the 5th curved surface (15), y axial coordinate and first surface (11), the second curved surface (12) is identical with the upper corresponding points of the 3rd curved surface (13), the angular region of light source is divided into M × N part, luminous flux in every part is identical, calculate the x of the 5th corresponding curved surface (15), y axial coordinate, outgoing hot spot is formed to equally distributed disk simultaneously and be divided into M × N the unit that area is equal, and calculate the x of these cell nodes, y axial coordinate, the initial point of selected curved surface, solving by the method for iteration the z axial coordinate of putting on initial skeleton curve is:

$z_{1,i}=\frac{-(x_{1,i}-x_{1,i-1})N_{1x}-(y_{1,i}-y_{1,i-1})N_{1y}}{N_{1z}}+z_{1,i-1}---\left(2\right)$

Wherein (x _{1, i}, y _{1, i}, z _{1, i}) be the coordinate of the calculative point of current iteration, (x _{1, i-1}, y _{1, i-1}, z _{1, i-1}) be upper coordinate, (N _1x, N _1y, N _1z) be the coordinate of upper normal vector.Obtaining obtaining next skeleton curve by (2) formula iteration after initial skeleton curve, after obtaining all skeleton curves, obtain the 5th curved surface (15) thereby obtain all subsurfaces by the mode of setting-out.

4. Zigzag type LED lamp optical system according to claim 1, it is characterized in that: the free form surface (21) of described free-form surface reflector (2) is made up of certain multiple subsurface, between two adjacent subsurfaces, connected by the plane that is parallel to z axle, target face is divided, and the node coordinate of division is (T _x, T _y, T _z), the initial point of selected curved surface, solves by the method for iteration the z axial coordinate of putting on initial skeleton curve and is:

$\left\{\begin{array}{c}{x}_{2,i}=\mathrm{lx}(z_{2,i}-z_{1,i})+x_{1,i}\\ y_{2,i}=\mathrm{ly}(z_{2,i}-z_{1,i})+y_{1,i}\\ z_{2,i}=\frac{((\mathrm{lx}\×z_{1,i}-x_{1,i}+x_{2,i-1})N_{2,x}+(\mathrm{ly}\×z_{1,i}-y_{1,i}+y_{2,i-1})N_{2,y}+z_{2,i-1}{N}_{2,z})}{\mathrm{lx}\×N_{2,x}+\mathrm{ly}\×N_{2,y}+N_{2,z}}\end{array}\right.---\left(3\right)$

Wherein (x _{2, i}, y _{2, i}, z _{2, i}) be the coordinate of the calculative point of current iteration, (x _{2, i-1}, y _{2, i-1}, z _{2, i-1}) be more front coordinate, (N _2x, N _2y, N _2z) be more front normal vector coordinate, (x _{1, i}, y _{1, i}, z _{1, i}) be the coordinate of corresponding points on free-form surface lens the 5th free form surface.The expression formula of lx and ly is:

$\left\{\begin{array}{c}\mathrm{lx}=\frac{T_{x,i}-x_{1,i}}{T_{z,i}-z_{1,i}}\\ \mathrm{ly}=\frac{T_{y,i}-y_{1,i}}{T_{z,i}-z_{1,i}}\end{array}\right.---\left(4\right)$

Obtaining obtaining next skeleton curve by (2) formula iteration after initial skeleton curve, re-construct initial skeleton curve at the section start of each subsurface, after obtaining all skeleton curves, obtain all subsurfaces by the mode of setting-out, obtain the free form surface (21) of free-form surface reflector (2).