Optical: systems and elements – Lens – Selective wavelength transmitting or blocking
Reexamination Certificate
1999-07-20
2001-06-26
Epps, Georgia (Department: 2873)
Optical: systems and elements
Lens
Selective wavelength transmitting or blocking
C359S742000, C362S338000, C428S195100
Reexamination Certificate
active
06252724
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Technical Field
The invention relates to a method for producing a Fresnel lens on a catadioptric basis having a staged entrance surface, reflecting surfaces and an at least partially curved exit surface. The invention also relates to a Fresnel lens.
2. Prior Art
U.S. Pat. No. 5,404,869 discloses a Fresnel lens by means of which the light beams from a punctiform light source are rendered parallel by suitable beam guidance. The particular advantage of the lens consists in the low overall height, the large diameter and the short distance between the lens and light source. This is rendered possible by a staged design of the Fresnel lens. In a central region, the lens has a curved entrance surface and a likewise curved exit surface, compare FIG. 23 of the document. Concentric stages, for example 11 stages, are arranged outside the middle region. Each stage can be regarded as a prismatic element (or annular prism) and has an entrance surface (top side), a reflecting surface (underside) and an exit surface. The top side and underside are plane in each case, while the exit surface is curved in each case.
The light beams must be guided exactly in order to achieve an optimum light yield. In a corresponding manner, the geometry of the individual stages is to be calculated exactly. If the optimum shape of the individual stages and of the middle region are known, machine tools can be programmed to produce a corresponding Fresnel lens or a mould therefor. Because of the rotationally symmetrical construction of the Fresnel lens, the determination of the data of a radial cross section, specifically from the middle of the lens up to the outer edge (or vice versa), suffices for a unique description of the shape.
BRIEF SUMMARY OF THE INVENTION
In accordance with the method according to the invention, the shape of the Fresnel lens is determined as follows:
a) a radial cross section (
14
) is determined in a stagewise fashion, specifically firstly for an arbitrary first stage (stage 1), then for the stages adjacent thereto, and thereafter successively for all further adjacent stages until the cross sections of the individual stages have all been determined,
b) starting from
predetermined angles &agr;
A
i
of top sides of the stages relative to a central axis (x-axis) of the lens,
the coordinates (x
A
1
, Y
A
1
) of a corner point A
1
of the first stage referred to the location (0,0) of a punctiform light source (
11
),
the angular ranges in which the individual stages (i) receive light,
a coordinate flx
1
of an outermost point (flx
1
, fly
1
) of the section of the exit surface (
13
) which belongs to the first stage (i=1),
and an angle &dgr;
1
of a reflecting surface of the first stage,
c) firstly the coordinates fly
1
of the outermost point (flx
1
, fly
1
), the eikonal and the further coordinates (flx
1
, fly
1
) of the exit surface (
13
) are determined for the first stage, specifically for a number of light beams corresponding to the desired accuracy,
d) on the basis of the data determined for the first stage, the data of a second stage, then of a third stage, etc. are determined for all the stages as a whole,
e) finally, for a middle region (middle part
15
) of the lens (
10
) having no reflecting surfaces the data of a curved entrance surface (inner surface
28
) are determined taking account of the eikonal condition and with the exit surface (
13
) prescribed, and
f) the complete outer shape of the lens (
10
) is determined by rotation of the radial cross section (
14
) about a central axis (x-axis).
The mode of procedure described permits a rapid determination of the complete outer shape of the Fresnel lens for different initial data and different applications.
It is advantageous to employ the following boundary conditions as a basis:
the punctiform light source is at the zero point of an (xy) coordinate system,
the middle part of the lens has an aspherical entrance surface and a plane exit surface,
the top sides of all the stages run parallel to the x-direction,
the corner point (point of intersection of the top side and underside) of the outermost stage (1
st
stage) lies on the y-axis, and
every stage receives light from a 5° angular range.
Particularly advantageous is a mode of procedure in which an angle between the reflecting surface and entrance surface in each stage is selected such that a beam section iii of the outer edge beam a forms with the entrance surface in this region an angle which is as small as possible. Dark zones after the exit of the light from the lens are largely avoided in this way.
The variables &dgr;, flx
1
, fly
1
act reciprocally for determining the data of the first stage. Either &dgr;
1
and flx
1
, or else flx
1
and fly
1
, are prescribed, and the respective other value is determined. If &dgr;
1
and flx
1
are prescribed, fly
1
is yielded by the intersection of the beam reflected at the reflecting surface as a section of the inner edge beam b of the first stage with the plane defined by flx
1
. The term “inner” edge beam relates to the arrangement before the beams enter the lens. The edge beams closest to the central axis of the lens are denoted as inner edge beams, and the edge beams respectively closest to the circumference of the lens are denoted as outer edge beams. The edge beams cross one another inside the lens, with the result that the inner edge beam b of the first, outer stage on the exit side marks the outermost edge.
It is possible to proceed from estimated or empirical values when establishing the variables flx
1
and fly
1
. In any case, flx
1
is to be substantially larger than the x-coordinate for the corner point of the first stage, and fly
1
is equally to be substantially larger than the y-coordinate of the corner point of the first stage. In this case, flx
1
largely establishes the thickness of the lens, while fly
1
relates to the diameter of the lens.
It is important for the eikonal condition to be satisfied inside every stage. That is to say, the sums of the optical path lengths of the beams correspond inside every stage. It is known that the optical path length of a light beam is yielded by the geometrical path length multiplied by the refractive index. Normally, the result is three different zones with different optical path lengths, specifically the entrance side (air), the lens material and exit side (air). The geometrical path length terminates at a reference plane which can be assumed to be somewhere behind the exit side of the lens, and which naturally runs perpendicular to the central axis of the lens or to the optical axis. The beam guidance is calculated in this case such that the individual light beams strike parallel to one another and perpendicular to the reference plane. Such a lens produces a maximum degree of light yield in conjunction with uniform distribution of the light. Expansion of the light beam or focusing of the latter is also conceivable. The reference plane must then be assumed to be a surface which is concave or convex, as seen from the light source.
A special feature is examination of t he data of the second stage after establishing the first stage. For this purpose, two iteration steps are conducted in a nested fashion. Firstly, an estimated value is assumed for the x-coordinate of the corner point A
2
of the second stage, specifically x
A
2
. Since the angular ranges in which the stages receive light are known, as are the angles &agr;
A
i
of the top sides of the stages i, the y-coordinates of the corner point A
2
, and thus the point (x
A
2
, y
A
2
) can be calculated. Hereafter, the angle &dgr;
2
of the reflecting surface of the second stage is determined iteratively until a beam section y
iii
for an inner edge beam b of the second stage lies on the point with the coordinates (flx
2
, fly
2
), (flx
2
, fly
2
) corresponding to the closest coordinates (flx
1
, fly
1
) of the first stage, to the edge beam a there. Finally, the angle between the inner edge beam b of the second stage and the outer edge beam a of the first stage is checked before exit fro
aqua signal Aktiengesellschaft Spezialleuchfabrik
Epps Georgia
Technoprop Colton LLC
Thompson Tim
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