Method for producing a fresnel lens on a catadioptric basis, and a fresnel lens produced using this method

• US 6,252,724 B1
• Filed: 07/20/1999
• Issued: 06/26/2001
• Est. Priority Date: 07/31/1998
• Status: Expired due to Fees

• Current Assignee: Aqua Signal AG Spezialleuchtenfabrik
• Original Assignee: Aqua Signal AG Spezialleuchtenfabrik
• Inventors: Scheer, Ulla
• Primary Examiner(s): Epps, Georgia
• Assistant Examiner(s): THOMPSON, TIMOTHY J
• Application Number:
  US09/357,472
• Time in Patent Office: 707 Days
• Field of Search: 359/742, 359/743, 362/338, 362/334, 362/337, 428/195, 264/1.32
• US Class Current: 359/723
• CPC Class Codes: G02B 17/006 Systems in which light light is reflected on a plurality of parallel surfaces, e.g. louvre mirrors, total internal reflection [TIR] lenses Fresnel mirrors G02B5/09, Fresnel lenses G02B3/08
• CPC Class Codes: G02B 19/0028 refractive and reflective surfaces, e.g. non-imaging catadioptric systems
• CPC Class Codes: G02B 19/0061 the light source comprising a LED semiconductor devices with at least one potential-jump barrier or surface barrier specially adapted for light emission H01L33/00
• CPC Class Codes: G02B 3/08 with discontinuous faces, e.g. Fresnel lens diffractive Fresnel lenses G02B5/1876
• CPC Class Codes: Y10T 428/24802 Discontinuous or differential coating, impregnation or bond [e.g., artwork, printing, retouched photograph, etc.]

Abstract

The invention relates to a method for producing a Fresnel lens having a staged entrance surface, reflecting surfaces and an exit surface. The entrance surface is subdivided into outer concentric stages and a central part. The central part is aspherically curved on an entrance side and plane on an exit side by satisfying the eikonal condition. Every stage has a top side, underside and outer side, top sides and undersides being of plane design, and the outer sides having curvatures appropriate for satisfying the eikonal condition.

Claims

1. Method for producing a Fresnel lens on a catadioptric basis having a staged entrance surface (12), reflecting surfaces and an at least partially curved exit surface (13), the shape of the Fresnel lens (10) being 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 α

_Ai of top sides of the stages relative to a central axis (x-axis) of the lens,

the coordinates (x_A1, y_A1) of a corner point A₁ 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 flx₁ of an outermost point (flx₁, fly₁) of the section of the exit surface (13) which belongs to the first stage (i=1),

and an angle δ

₁ of reflecting surface of the first stage,

c) firstly the coordinates fly₁ of the outermost point (flx₁, fly₁), the eikonal and the further coordinates (flx₁, fly₁) 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).

2. Method according to claim 1, characterized in that the radial cross section is determined in a stagewise fashion, specifically starting with the outermost stage 1 and stage by stage inwardly progressively.

3. Method according to claim 1, characterized in that the following conditions are prescribed:

the angles α

_Ai of the top sides (22) of all the stages (i) relative to the central axis (x-axis) are equal to 0,

the top sides (22) and reflecting surfaces (undersides 24) are plane.

4. Method according to claim 1, characterized in that the angle δ

₁ of the reflecting surface (underside 24) relative to the central axis (x-axis) is determined iteratively, specifically by variation until a beam section y_iii for an inner edge beam b lies on the point with the coordinates (flx₁, fly₁).

5. Method according to claim 4, characterized in that upon transition from a first stage to the adjacent (inner) second stage an estimated value of the x-coordinate of the corner point A₂ of the second stage, specifically x_A2, is initially assumed, in that the y-coordinate of the corner point A₂, and thus the first point (x_A2, y_A2), are calculated on the basis of the predetermined angular ranges in which the stages receive light, and on the basis of the predetermined angle α

_Ai of the top sides of the stages i,

in that the angle δ

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 (flx₂, fly₂), it being intended that this point (flx₂, fly₂) should correspond to the adjacent coordinates (flx₁, fly₁) of the first stage,

in that 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 from the lens and minimized by variation of x_A2 and the subsequent iteration of δ

₂,

and in that the further points (flx₂, fly₂) of the second stage are then determined taking account of the eikonal condition.

6. Method according to claim 1, characterized in that the angle δ

₁ of the reflecting surface of the first stage is selected—

given a right angle between the outer edge beam a and entrance surface (12)—

to be greater than 45°

, but as close as possible to 45°

.

7. Method according to claim 1, characterized in that 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.

8. Method according to claim 1, characterized in that the middle region (middle part 15) of the lens (10) has a plane exit surface (13).

9. Method according to claim 1, characterized in that the middle region (middle part 15) of the lens (10) has an exit surface (13) which is convexly curved in continuation of the individual stages.

13. Fresnel lens produced using a method according to claim 1.

10. Method for producing a Fresnel lens on a catadioptric basis having a staged entrance surface (12), reflecting surfaces and an at least partially curved exit surface (13), the shape of the Fresnel lens (10) being 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 α

_Ai of top sides of the stages relative to a central axis (x-axis) of the lens,

the coordinates (x_A1, y_A1) of a corner point A₁ 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,

and coordinates of an outermost point (flx₁, fly₁) of the section of the exit surface (13) which belongs to the first stage (i=1),

c) firstly the angle δ

₁ of a reflecting surface of the first stage, the eikonal and the further coordinates (flx₁, fly₁) 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).

12. Lens according to claim 10, characterized in that the top sides of the stages run parallel to a central axis (x-axis) of the lens (10).

11. Fresnel lens having a staged entrance surface (12), reflecting surfaces and an exit surface (13), the following conditions being fulfilled:

a) the entrance surface (12) is subdivided into outer concentric stages and a middle part (15),

b) the middle part (15) is aspherically curved on an entrance side and plane on an exit side, the curvature on the entrance side being such that—

given mutually parallel beams on the exit side and a punctiform light source on the entrance side—

the eikonal condition is fulfilled inside each stage,

c) each stage has a top side, underside and outer side, the top side being the entrance side, the underside reflecting totally and the outer side being the exit surface,

d) the outer sides of the stages merge into one another with the formation of the common exit surface (13) of the lens (10), the plane exit side of the middle part (15) being part of the common exit surface (13),

e) top sides and undersides are plane, and

f) the outer sides of the stages are curved, the curves being such that the eikonal condition is fulfilled inside every stage.