CN102878528A - Deformed ellipsoidal condenser - Google Patents

Abstract

The present invention relates to a kind of ellipsoid of deformation face condenser, face type equation is as follows:

Wherein t=- (1-e2), e is elliptical eccentricity, r is the radius of curvature of the paraxial apex of ellipsoid, a, b, c and d are the deformation coefficient of ellipsoid, two-term coefficient a should meet 1≤a≤1.5, four term coefficient b, which should meet 0 ＜ b≤1, six term coefficient c, should meet 0 c≤1 ＜, and reinforcement power term coefficient d range is 0≤d≤2. The present invention can be by changing the light going direction after condenser reflects, and then change the spot energy distribution on the second focal plane, increase the distribution of intermediate energy, the intensity of energy is greatly reduced, thus substantially improves the uniformity of hot spot on the second focal plane.

Description

The ellipsoid of deformation face condenser

Technical field

The present invention relates to a kind of ellipsoid condenser, particularly a kind ofly can improve the inhomogeneity ellipsoid of deformation face condenser of the second focal plane hot spot.

Background technology

The ellipsoid condenser is widely used in uniform illumination system, the Down lamp of using such as household, car light, stage shot-light etc., (take the high pressure xenon short-act lamp as light source) also usually uses the ellipsoid condenser in to the high solar simulation system of output facula irradiation uniformity requirement.The beam dump that the ellipsoid condenser can send the ideal point light source that is positioned at the first focus converges to the second focus place of ellipsoid, yet actual light source all has certain size and volume, thereby what obtain at the second focal plane is a hot spot, this hot spot is the very low Gaussian distribution of the high edge energy of intermediate energy, the hot spot of this distribution is totally unfavorable to the uniformity of optical system output facula, and the hot spot uniformity of therefore managing to improve on ellipsoid the second focal plane is to improve the importance of whole optical system output irradiation surface uniformity.In most cases can adopt the second focal plane out of focus for the hot spot uniformity that improves the second focal plane, just need this moment the special focus adjusting mechanism of design or the mode of taking to adjust pad to realize, its method complexity and assembly difficulty are larger, and also once the someone proposes at ellipsoid equation y ²=ax+bx ²Other power items of middle adding x make equation become the equation of higher degree: y ²=ax+bx ^3/2+ cx ²+ dx ^5/2+ ... form, but the feasible operability of the method principle is very poor, be difficult to determine item number and the coefficient of the equation of higher degree.

Summary of the invention

The technical problem to be solved in the present invention provides the ellipsoid of deformation face condenser of the hot spot good uniformity on a kind of the second focal plane.

In order to solve the problems of the technologies described above, ellipsoid of deformation face condenser ellipsoid face type equation of the present invention is as follows:

$x=\frac{a}{2r}{y}^2-\frac{b}{8r^3}{\mathrm{ty}}^4+\frac{c}{{16r}^5}{t}^2{y}^6+...+\frac{d}{n!}\left[\underset{i=0}{\overset{i=n-1}{\mathrm{\Π}}}(\frac{1}{2}-i)\right]\frac{1}{r^{2n-1}}{t}^{n-1}{y}^{2n}---\left(1\right)$

T=-(1-e wherein ²), e is oval eccentricity, r is the radius of curvature at place, the paraxial summit of ellipsoid, a, b, c and d are the deformation coefficient of ellipsoid, quadratic term coefficient a should satisfy 1≤a≤1.5, four item coefficient b should satisfy 0＜b≤1, six time item coefficient c and should satisfy 0＜c≤1, and its reinforcement power item coefficient d scope is 0≤d≤2.

The face type equation that the ellipsoid of deformation face condenser that the present invention proposes adopts no longer is general ellipsoid equation but a high order aspheric surface equation, this equation is by obtaining after the ellipsoid equation Taylor expansion, this equation can make raising of ellipsoid curve part or reduces by revising deformation coefficient, and adjustment ellipsoid slope of a curve, thereby change the light going direction after the reflection of process ellipsoid condenser, and then change the spot energy distribution on the second focal plane.The present invention can make the distribution of intermediate energy increase, and the intensity of energy significantly reduces, thereby has greatly improved the uniformity of hot spot on the second focal plane.

Formula (1) obtains formula (2) after omitting the high-order amount.

$x=\frac{a}{2r}{y}^2-\frac{b}{8r^3}{\mathrm{ty}}^4+\frac{c}{{16r}^5}{t}^2{t}^6---\left(2\right)$

Because the high-order amount is less for the face type impact of ellipsoid of deformation face, affect not quite for technique effect of the present invention after omitting the high-order amount, therefore the present invention proposes three deformation coefficients namely: quadratic term deformation coefficient a, four item deformation coefficient b and six item deformation coefficient c, only need travel through the scope of these three deformation coefficients during design, just can realize the inhomogeneity optimization of ellipsoid the second focal plane, and be easy to realize the processing of ellipsoid of deformation face face type.

Description of drawings

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

Fig. 1 is light source for adopting 3kW high pressure xenon short-act lamp, and the ellipsoid condenser is the Optical system model of energy harvester.

Fig. 2 is ellipsoid of deformation face condenser of the present invention and standard spheroid face condenser face type comparison diagram.I is the standard spheroid face among the figure, and II is the ellipsoid of deformation face.

The ellipsoid condenser was along with the variation reflection ray of angular aperture and the ordinate value change curve of the second focal plane intersection point when Fig. 3 was xenon arc height h=2.5.

Fig. 4 is the hot spot (1/4 circle spot) that the light of xenon arc height h=2.5 forms at ellipsoid condenser the second focal plane.

The ellipsoid condenser was along with the variation reflection ray of angular aperture and the ordinate value change curve of the second focal plane intersection point when Fig. 5 was different h value.

Hot spot when Fig. 6 is different h value on ellipsoid condenser the second focal plane.

Fig. 7 is ellipsoid of deformation face condenser and the standard spheroid face condenser face type comparison diagram of the embodiment of the invention 1.I is the standard spheroid face among the figure, and II is the ellipsoid of deformation face.

Fig. 8 is that the ellipsoid of deformation face condenser of the embodiment of the invention 1 is along with the variation reflection ray of angular aperture and the ordinate value change curve of the second focal plane intersection point.

Fig. 9 is the hot spot on ellipsoid of deformation face condenser second focal plane of the embodiment of the invention 1.

Figure 10 is ellipsoid of deformation face condenser and the standard spheroid face condenser face type comparison diagram of the embodiment of the invention 2.I is the standard spheroid face among the figure, and II is the ellipsoid of deformation face.

Figure 11 is that the ellipsoid of deformation face condenser of the embodiment of the invention 2 is along with the variation reflection ray of angular aperture and the ordinate value change curve of the second focal plane intersection point.

Figure 12 is the hot spot on ellipsoid of deformation face condenser second focal plane of the embodiment of the invention 2.

Figure 13 is ellipsoid of deformation face condenser and the standard spheroid face condenser face type comparison diagram of the embodiment of the invention 3.I is the standard spheroid face among the figure, and II is the ellipsoid of deformation face.

Figure 14 is that the ellipsoid of deformation face condenser of the embodiment of the invention 3 is along with the variation reflection ray of angular aperture and the ordinate value change curve of the second focal plane intersection point.

Figure 15 is the hot spot on ellipsoid of deformation face condenser second focal plane of the embodiment of the invention 3.

Figure 16 is ellipsoid of deformation face condenser and the standard spheroid face condenser face type comparison diagram of the embodiment of the invention 4.I is the standard spheroid face among the figure, and II is the ellipsoid of deformation face.

Figure 17 is that the ellipsoid of deformation face condenser of the embodiment of the invention 4 is along with the variation reflection ray of angular aperture and the ordinate value change curve of the second focal plane intersection point.

Figure 18 is the hot spot on ellipsoid of deformation face condenser second focal plane of the embodiment of the invention 4.

Figure 19 is ellipsoid of deformation face condenser and the standard spheroid face condenser face type comparison diagram of the embodiment of the invention 5.I is the standard spheroid face among the figure, and II is the ellipsoid of deformation face.

Figure 20 is that the ellipsoid of deformation face condenser of the embodiment of the invention 5 is along with the variation reflection ray of angular aperture and the ordinate value change curve of the second focal plane intersection point.

Figure 21 is the hot spot on ellipsoid of deformation face condenser second focal plane of the embodiment of the invention 5.

Figure 22 is ellipsoid of deformation face condenser and the standard spheroid face condenser face type comparison diagram of the embodiment of the invention 6.I is the standard spheroid face among the figure, and II is the ellipsoid of deformation face.

Figure 23 is that the ellipsoid of deformation face condenser of the embodiment of the invention 6 is along with the variation reflection ray of angular aperture and the ordinate value change curve of the second focal plane intersection point.

Figure 24 is the hot spot on ellipsoid of deformation face condenser second focal plane of the embodiment of the invention 6.

Figure 25 is ellipsoid of deformation face condenser and the standard spheroid face condenser face type comparison diagram of the embodiment of the invention 7.I is the standard spheroid face among the figure, and II is the ellipsoid of deformation face.

Figure 26 is that the ellipsoid of deformation face condenser of the embodiment of the invention 7 is along with the variation reflection ray of angular aperture and the ordinate value change curve of the second focal plane intersection point.

Figure 27 is the hot spot on ellipsoid of deformation face condenser second focal plane of the embodiment of the invention 7.

The specific embodiment

Ellipsoid condenser Optical system

As shown in Figure 1, be light source for adopting 3kW high pressure xenon short-act lamp, the ellipsoid condenser is the Optical system model of energy harvester.

The ellipsoid equation is:

y ²=2rx-(1-e ²)x ²

Wherein r is the radius of curvature at place, the paraxial summit of ellipsoid, and e is oval eccentricity, and r and the satisfied following formula of e.

$r=\frac{2f1f2}{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002065787500022.png,HDA00002065787500082.png"\; state="\{\{state\}\}">f</figure-callout>}2+\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002065787500022.png,HDA00002065787500082.png"\; state="\{\{state\}\}">f</figure-callout>}1}$

$e=\frac{f2-f1}{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002065787500022.png,HDA00002065787500082.png"\; state="\{\{state\}\}">f</figure-callout>}2+\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002065787500022.png,HDA00002065787500082.png"\; state="\{\{state\}\}">f</figure-callout>}1}$

In the formula:

The first focal length of f1---ellipsoid;

The second focal length of f2---ellipsoid;

Make f1=57.35 for ease of analysis, f2=1319.05, the xenon arc height h=2.5 of xenon lamp.F1 and F2 are the first focus and second focus of ellipsoid among Fig. 1, u0 and um be on the axle luminous point to the initial aperture angle of ellipsoid condenser and final angular aperture, uh0 and uhm are that the outer luminous point of axle is to initial aperture angle and the final angular aperture of ellipsoid condenser, uh is that the outer luminous point of axle is to the point (x on the ellipsoid condenser, y) angular aperture, a, b, c are the three beams light that the outer luminous point of axle sends.

If the point that the light that the outer luminous point (f1, h) of axle sends arrives on the ellipsoid is (x ₀, y ₀), when angular aperture uh gives regularly, can obtain (x according to following formula ₀, y ₀).

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA00002065787500022.png,HDA00002065787500082.png"\; state="\{\{state\}\}">y</figure-callout>}}^2=2\mathrm{Rx}-(1-e^2)x^2\\ y-h=\tan (\mathrm{\&pi;}-\mathrm{uh})(x-f1)\end{array}\right.$

Then the incident ray equation is:

$y-h=\frac{y_0-h}{x_0-f1}(x-f1)$

Normal equation is

$y-y_0=-\frac{1}{\mathrm{dy}/\mathrm{dx}{|}_{\underset{y=y_0}{x=x_0}}}(x-x_0)$

According to reflection law, angle of reflection equates that with the angle of incidence angle can calculate the slope of reflection ray, the result is as follows.

$k=\frac{(t^2-{t_0}^2)(h-y_0)+{2y}_{0}t(f1-x_0)}{({y_0}^2-t^2)(f1-x_0)+{2y}_{0}t(h-y_0)}$

Wherein:

t=r-(1-e ²)x ₀

The equation of reflection ray is:

y-y ₀=k(x-x ₀)

When x=f2, then can calculate the xenon arc height is h, and angular aperture is that the light of uh is through the radius of the round spot that forms at the second focal plane after the ellipsoid reflection and the y value of correspondence.

The value of ordinate is as shown in table 1 on the second focal plane in the time of uh=30 °～130 °, and what Fig. 3 showed is along with the variation reflection ray of angular aperture and the ordinate value of the second focal plane intersection point.What Fig. 4 showed is the shape (1/4 circle spot) of hot spot on the second focal plane.

Table 1 is along with the ordinate value on variation second focal plane of angular aperture

uh	30	40	50	60	70	80	90	100	110	120	130
												y	-46.10	-38.56	-30.11	-21.42	-13.15	-5.86	0	4.17	6.59	7.38	6.85

The above-mentioned table 1 that provides, Fig. 3 and Fig. 4 obtain during luminous point h=2.5 outside axle, and when considering actual conditions, the outer luminous point of axle is a series of luminous points of 0～2.5.Along with the ordinate value variation diagram on variation second focal plane of angular aperture, Fig. 6 provided the shape of hot spot on the second focal plane when Fig. 5 provided different h value.

Can see from Fig. 5 and Fig. 6, along with reducing gradually of h value, the overlapping region of hot spot also reduces gradually on the second focal plane, in the scope less than Φ 20, concentrated a large amount of energy, and be the overlapping of small part in Φ 20 scopes with UV light, the hot spot of a kind of Gaussian distribution that Here it is, this Energy distribution have also obtained checking in the development process of solar simulator.

Can see also that from Fig. 5 the y value integral body of reflection ray on the second focal plane is less than normal when the final angular aperture, therefore the emergent pupil face type partly of ellipsoid need to be done slightly and be raised, the face type of the ellipsoid that the initial aperture angle is corresponding reduces slightly simultaneously, thereby the distribution of y value on the second focal plane is enlarged, spot energy distribution on the second focal plane can change at this moment, the uniformity of hot spot is improved, and the face type equation that the ellipsoid of deformation face condenser that the present invention proposes adopts just can make ellipsoid face type make local lifting or reduction.

Ellipsoid of deformation face condenser Optical system

It is as follows that ellipsoid equation Taylor expansion is obtained equation:

$x=\frac{1}{2r}{y}^2-\frac{1}{8r^3}{\mathrm{ty}}^4+\frac{1}{{16r}^5}{t}^2{y}^6+...+\frac{1}{n!}\left[\underset{i=0}{\overset{i=n-1}{\mathrm{\&Pi;}}}(\frac{1}{2}-i)\right]\frac{1}{r^{2n-1}}{t}^{n-1}{y}^{2n}$

In the formula:

T=-(1-e ²), e is oval eccentricity, r is the radius of curvature at place, the paraxial summit of ellipsoid.

Here it is as follows to introduce new equation (being ellipsoid of deformation face equation of the present invention):

$x=\frac{a}{2r}{y}^2-\frac{b}{{8r}^3}{\mathrm{ty}}^4+\frac{c}{{16r}^5}{t}^2{y}^6+...+\frac{d}{n!}\left[\underset{i=0}{\overset{i=n-1}{\mathrm{\&Pi;}}}(\frac{1}{2}-i)\right]\frac{1}{r^{2n-1}}{t}^{n-1}{y}^{2n}---\left(1\right)$

In the formula: t=-(1-e ²), e is oval eccentricity, r is the radius of curvature at place, the paraxial summit of ellipsoid, and a, b, c and d are the deformation coefficient of ellipsoid.Quadratic term coefficient a should satisfy 1≤a≤1.5, four time item coefficient b and should satisfy 0＜b≤1, six time item coefficient c and should satisfy 0＜c≤1, and its reinforcement power item coefficient d scope is 0≤d≤2.As shown in Figure 2, the xoy coordinate system is take the summit o of ellipsoid of deformation face as the origin of coordinates; Y is the ordinate of any point on the ellipsoid of deformation face, and x is abscissa corresponding to this point on the ellipsoid of deformation face.

Because the high-order amount is less for the face type impact of ellipsoid of deformation face, affect not quite for technique effect of the present invention after omitting the high-order amount, therefore the present invention only designs and has proposed three deformation coefficients namely: quadratic term deformation coefficient a, four item deformation coefficient b and six item deformation coefficient c, only need travel through the scope of these three deformation coefficients during design, just can realize the inhomogeneity optimization of ellipsoid the second focal plane, and be easy to realize the processing of ellipsoid of deformation face face type.

The equation that omits the high-order amount and only use first three items to obtain is as follows:

$x=\frac{a}{2r}{y}^2-\frac{b}{8r^3}{\mathrm{ty}}^4+\frac{c}{{16r}^5}{t}^2{y}^6---\left(2\right)$

A wherein, b, c are called the deformation coefficient of ellipsoid.

Constant and improve the uniformity of hot spot distribution on the second focal plane for the basic side type that guarantees ellipsoid of deformation face and standard spheroid face, analyzing deformation coefficient a, b, c determines afterwards that on the impact of ellipsoid of deformation face face type quadratic term coefficient a should satisfy 1≤a≤1.5, four item coefficient b should satisfy 0＜b≤1, six time item coefficient c and should satisfy 0＜c≤1.

Embodiment 1

Get a=1, b=0.05, c=0.05, the ellipsoid of deformation of this moment looks like shown in Figure 7, in this moment different h value situations along with the variation of y value on variation second focal plane of angular aperture as shown in Figure 8, Fig. 9 is the light spot shape on the second focal plane.

Embodiment 2

Get a=1.5, b=0.05, c=0.05, the ellipsoid of deformation of this moment looks like shown in Figure 10, in this moment different h value situations along with the variation of y value on variation second focal plane of angular aperture as shown in figure 11, Figure 12 is hot spot distribution situation on the second focal plane.

Embodiment 3

Get a=1.5, b=1, c=1, the ellipsoid of deformation of this moment looks like shown in Figure 13, in this moment different h value situations along with the variation of y value on variation second focal plane of angular aperture as shown in figure 14, Figure 15 is hot spot distribution shape on the second focal plane.

Embodiment 4

Get a=1, b=1, c=1, the ellipsoid of deformation of this moment looks like shown in Figure 16, in this moment different h value situations along with the variation of y value on variation second focal plane of angular aperture as shown in figure 17, Figure 18 is hot spot distribution shape on the second focal plane.

Embodiment 5

Get a=1.25, b=0.5, c=0.5, the ellipsoid of deformation of this moment looks like shown in Figure 19, in this moment different h value situations along with the variation of y value on variation second focal plane of angular aperture as shown in figure 20, Figure 21 is the hot spot distribution shape on the second focal plane at this moment.

Embodiment 6

Get a=1.1, b=0.5, c=0.5, the ellipsoid of deformation of this moment looks like shown in Figure 22, in this moment different h value situations along with the variation of y value on variation second focal plane of angular aperture as shown in figure 23, Figure 24 is hot spot distribution shape on the second focal plane at this moment.

Embodiment 7

Get a=1.08, b=0.4, c=0.45, the ellipsoid of deformation of this moment looks like shown in Figure 25, in this moment different h value situations along with the variation of y value on variation second focal plane of angular aperture as shown in figure 26, Figure 27 is hot spot distribution shape on the second focal plane at this moment.

From above seven examples as seen, when deformation coefficient satisfies: 1≤a≤1.5,0＜b≤1,0＜c≤1 o'clock, ellipsoid of deformation face and standard spheroid face have a little variation, but can both improve the hot spot uniformity on ellipsoid the second focal plane, as seen two examples have reduction slightly during in the low stage and slightly lifting are arranged during in high-stage when ellipsoid of deformation face and standard spheroid face from behind, y value no longer concentrates on zero neighbouring and be to be distributed in certain scope on this moment the second focal plane during the low stage, the high-stage distribution has than the standard spheroid face dwindles, thereby the energy gradient of hot spot on the second focal plane is slowed down, can obtain more uniformly hot spot on the second focal plane.

It all is 0 example that above-described embodiment has only provided its reinforcement power item coefficient d, but the invention is not restricted to above-described embodiment, adopts ellipsoid of deformation face that formula (1) forms in every case all within protection domain of the present invention.

Claims (4)

1. ellipsoid of deformation face condenser is characterized in that face type equation is as follows: $x=\frac{a}{2r}{y}^2-\frac{b}{8r^3}{\mathrm{ty}}^4+\frac{c}{16r^5}{t}^2{y}^6+...+\frac{d}{n!}\left[\underset{i=0}{\overset{i=n-1}{\mathrm{\&Pi;}}}(\frac{1}{2}-i)\right]\frac{1}{r^{2n-1}}{t}^{n-1}{y}^{2n}---\left(1\right)$

T=-(1-e wherein ²), e is oval eccentricity, r is the radius of curvature at place, the paraxial summit of ellipsoid, a, b, c and d are the deformation coefficient of ellipsoid, quadratic term coefficient a should satisfy 1≤a≤1.5, four item coefficient b should satisfy 0＜b≤1, six time item coefficient c and should satisfy 0＜c≤1, and its reinforcement power item coefficient d scope is 0≤d≤2.

2. ellipsoid of deformation face condenser according to claim 1 is characterized in that high power item coefficient d=0.

3. ellipsoid of deformation face condenser according to claim 2 is characterized in that a=1.1, b=0.5, c=0.5.

4. ellipsoid of deformation face condenser according to claim 2 is characterized in that a=1.08, b=0.4, c=0.45.

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