Method of forming a freeform surface shaped element for an illumination system

Patent metadata

Field	Value
Publication number	US-9818223-B2
Application number	US-201514709861-A
Country	US
Kind code	B2
Filing date	May 12, 2015
Priority date	Jun 13, 2014
Publication date	Nov 14, 2017
Grant date	Nov 14, 2017

Abstract

A construction method of freeform surface shape based on XY-polynomial obtains a plurality of data points of a freeform surface according to an object point and an imaging point in a three-dimensional Cartesian coordinates system Oxyz. Each of the plurality of data points comprises a coordinate value Q i and a normal vector N i . A first sum of squares e 1 (P) of coordinate differences in z direction between the coordinate value Q i and the freeform surface is applied, and by a second sum of squares e 2 (P) between the normal vector N i of the data points and a normal vector n i of the freeform surface, a modulus of vector differences is acquired. An evaluation function ƒ(p)=e 1 (P)+we 2 (P) is proposed and a plurality of freeform surface shapes obtained by selecting and applying different weightings. A final freeform surface shape Ω opt is chosen from the plurality of freeform surface shapes.

First claim

What is claimed is:

1. A method of forming a freeform surface shaped element for an illumination system comprising:
step (S1), obtaining a plurality of data points of a freeform surface according to an object point and an imaging point corresponding to the object point, in a three-dimensional Cartesian coordinate system Oxyz, wherein each of the plurality of data points comprises a coordinate value Q i =(x i , y i , z i )(i=1, 2, . . . , n) and a normal vector N i =(u i , v i , −1)(i=1, 2, . . . , n), the object point is imaged at the imaging point through the freeform surface, and the freeform surface is expressed as

z
=

f
⁡

(

x
,

y
;
P

)

=

∑

i
,

j
=
0

⁢

⁢

P

i
,
j

⁢

x
i

⁢

y
j

;

step (S2), acquiring a first sum of squares e 1 (P), of coordinate differences in z direction between the coordinate value Q i =(x i , y i , z i )(i=1, 2, . . . , n) and the freeform surface, wherein the first sum of squares e 1 (P) is expressed in terms of a first equation:

e
1

⁡

(
P
)

=

∑

i
=
1

n

⁢

⁢

[

z
i

-

f
⁡

(

x
i

,

y
i

;
P

)

]

2

=

(

Z
-

A
1

⁢
P

)

T

⁢

(

Z
-

A
1

⁢
P

)

,

⁢
wherein

Z
=

[

z
1

z
2

…

z
n

]

T

,

⁢

A
1

=

[

1

x
1

y
1

x
1
2

x
1

⁢

y
1

y

Assignees

• Univ Tsinghua
• Hon Hai Prec Ind Co Ltd

Inventors

• Zhu Jun
• Wu xiao-fei
• Hou Wei
• Yang Tong
• Jin Guo-Fan
• Fan Shou-Shan

Classifications

• G06F17/10

  Complex mathematical operations {(function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544)} · CPC title

• G06T17/30 Primary

  Polynomial surface description · CPC title