Optically transmissive element generation for variable function optical system
View Patent ↗An example is a method by a processor(s). First and second boundary thickness variations (T A , T B ) of first and second boundary elements (A, B) are obtained. The A, B are configured to obtain first and second boundary conditions of a variable function optical system. First and second functional thickness variations (T F1 , T F2 ) of first and second optically transmissive elements of the variable function optical system are determined. Determining the T F1 includes a first sum of a first term and a second term, and determining the T F2 includes a second sum of a third term and a fourth term. The first and third terms each are based on an integration of the T A , T B . The second and fourth terms each are based on an average thickness variation of the T A , T B . A design file is generated including digital representations of the optically transmissive elements based on the T F1 , T F2 .
1 . A method comprising:
obtaining, by one or more processors, a first boundary thickness variation of a first boundary element and a second boundary thickness variation of a second boundary element, the first boundary element being configured to obtain a first boundary condition of a variable function optical system, the second boundary element being configured to obtain a second boundary condition of the variable function optical system;
determining, by the one or more processors, a first functional thickness variation of a first optically transmissive element of the variable function optical system and a second functional thickness variation of a second optically transmissive element of the variable function optical system, wherein determining the first functional thickness variation includes a first sum of a first term and a second term, and determining the second functional thickness variation includes a second sum of a third term and a fourth term, each term of the first term and the third term being based on an integration of the first boundary thickness variation and the second boundary thickness variation, each term of the second term and the fourth term being based on an average thickness variation of the first boundary thickness variation and the second boundary thickness variation; and
generating, by the one or more processors, a non-transitory design file that enables manufacturing the first and second optically transmissive elements, the design file comprising a first digital representation of the first optically transmissive element based on the first functional thickness variation and comprising a second digital representation of the second optically transmissive element based on the second functional thickness variation.
2 . The method of claim 1 further comprising:
obtaining, by the one or more processors, a lateral shift range of the first optically transmissive element and the second optically transmissive element of the variable function optical system, wherein each term of the first term and the third term is further based on the lateral shift range.
3 . The method of claim 1 , wherein obtaining the first boundary thickness variation and the second boundary thickness variation includes receiving, by the one or more processors, the first boundary thickness variation and the second boundary thickness variation.
4 . The method of claim 1 , wherein obtaining the first boundary thickness variation and the second boundary thickness variation includes:
receiving, by the one or more processors, a first thickness of the first boundary element and a second thickness of the second boundary element;
calculating, by the one or more processors, the first boundary thickness variation based on the first thickness; and
calculating, by the one or more processors, the second boundary thickness variation based on the second thickness.
5 . The method of claim 1 , wherein obtaining the first boundary thickness variation and the second boundary thickness variation includes:
receiving, by the one or more processors, the first boundary condition of the first boundary element and the second boundary condition of the second boundary element;
determining, by the one or more processors, a first thickness of the first boundary element based on the first boundary condition;
determining, by the one or more processors, a second thickness of the second boundary element based on the second boundary condition;
calculating, by the one or more processors, the first boundary thickness variation based on the first thickness; and
calculating, by the one or more processors, the second boundary thickness variation based on the second thickness.
6 . The method of claim 1 , wherein:
the first boundary thickness variation is represented by T A (x,y);
the second boundary thickness variation is represented by T B (x,y);
a maximum lateral shift of each of the first optically transmissive element and the second optically transmissive element is represented by an absolute value of a max wherein each of the first optically transmissive element and the second optically transmissive element is configured to be translated in the variable function optical system by a lateral shift range 2a max ;
the first term is equal to
1
2
a
max
∫
T
A
(
x
,
y
)
-
T
B
(
x
,
y
)
2
dx
;
the second term is equal to
T
A
(
x
,
y
)
+
T
B
(
x
,
y
)
4
;
the third term is equal to
-
1
2
a
max
∫
T
A
(
x
,
y
)
-
T
B
(
x
,
y
)
2
dx
;
and
the fourth term is equal to
T
A
(
x
,
y
)
+
T
B
(
x
,
y
)
4
.
7 . The method of claim 1 , wherein the first functional thickness variation further includes a third sum of the first sum and a first tilt term, and the second functional thickness variation includes a fourth sum of the second sum and a second tilt term.
8 . The method of claim 1 , wherein determining the first functional thickness variation and the second functional thickness variation includes:
calculating the average thickness variation of the first boundary thickness variation and the second boundary thickness variation;
calculating a first extracted thickness variation and a second extracted thickness variation comprising extracting the average thickness variation from the first boundary thickness variation and the second boundary thickness variation, respectively;
calculating a first transformed thickness variation and a second transformed thickness variation comprising integrating the first extracted thickness variation or the second extracted thickness variation, the first transformed thickness variation being the first term, the second transformed thickness variation being the second term; and
calculating the first functional thickness variation and the second functional thickness variation, the third term being half of the average thickness variation, the fourth term being half of the average thickness variation.
9 . The method of claim 1 further comprising:
manufacturing the first optically transmissive element based on the first digital representation of the design file; and
manufacturing the second optically transmissive element based on the second digital representation of the design file.
10 . The method of claim 9 further comprising:
operating the variable function optical system comprising the first optically transmissive element and the second optically transmissive element, wherein:
when light is transmitted through the first optically transmissive element and the second optically transmissive element, and when the first optically transmissive element and the second optically transmissive element are positioned at respective opposing positive maximum lateral shifts, the light has a boundary condition corresponding to the first boundary condition; and
when light is transmitted through the first optically transmissive element and the second optically transmissive element, and when the first optically transmissive element and the second optically transmissive element are positioned at respective opposing negative maximum lateral shifts, the light has a boundary condition corresponding to the second boundary condition.
11 . A system comprising:
a memory storing instructions; and
one or more processors, coupled with the memory and to execute the instructions, the instructions when executed cause the one or more processors to:
obtain a first boundary thickness variation of a first boundary element and a second boundary thickness variation of a second boundary element, the first boundary element being configured to obtain a first boundary condition of a variable function optical system, the second boundary element being configured to obtain a second boundary condition of the variable function optical system;
determine a first functional thickness variation of a first optically transmissive element of the variable function optical system and a second functional thickness variation of a second optically transmissive element of the variable function optical system, wherein determining the first functional thickness variation includes a first sum of a first term and a second term, and determining the second functional thickness variation includes a second sum of a third term and a fourth term, each term of the first term and the third term being based on an integration of the first boundary thickness variation and the second boundary thickness variation, each term of the second term and the fourth term being based on an average thickness variation of the first boundary thickness variation and the second boundary thickness variation; and
generate a non-transitory design file that enables manufacturing the first and second optically transmissive elements, the design file comprising a first digital representation of the first optically transmissive element based on the first functional thickness variation and comprising a second digital representation of the second optically transmissive element based on the second functional thickness variation.
12 . The system of claim 11 , wherein the instructions when executed further cause the one or more processors to:
obtain a lateral shift range of the first optically transmissive element and the second optically transmissive element of the variable function optical system, wherein each term of the first term and the third term is further based on the lateral shift range.
13 . The system of claim 11 , wherein the instructions when executed causing the one or more processors to obtain the first boundary thickness variation and the second boundary thickness variation further cause the one or more processors to:
receive the first boundary thickness variation and the second boundary thickness variation.
14 . The system of claim 11 , wherein the instructions when executed causing the one or more processors to obtain the first boundary thickness variation and the second boundary thickness variation further cause the one or more processors to:
receive a first thickness of the first boundary element and a second thickness of the second boundary element;
calculate the first boundary thickness variation based on the first thickness; and
calculate the second boundary thickness variation based on the second thickness.
15 . The system of claim 11 , wherein the instructions when executed causing the one or more processors to obtain the first boundary thickness variation and the second boundary thickness variation further cause the one or more processors to:
receive the first boundary condition of the first boundary element and the second boundary condition of the second boundary element;
determine a first thickness of the first boundary element based on the first boundary condition;
determine a second thickness of the second boundary element based on the second boundary condition;
calculate the first boundary thickness variation based on the first thickness; and
calculate the second boundary thickness variation based on the second thickness.
16 . The system of claim 11 , wherein:
the first boundary thickness variation is represented by T A (x,y);
the second boundary thickness variation is represented by T B (x,y);
a maximum lateral shift of each of the first optically transmissive element and the second optically transmissive element is represented by an absolute value of a max wherein each of the first optically transmissive element and the second optically transmissive element is configured to be translated in the variable function optical system by a lateral shift range 2a max ;
the first term is equal to
1
2
a
max
∫
T
A
(
x
,
y
)
-
T
B
(
x
,
y
)
2
dx
;
the second term is equal to
T
A
(
x
,
y
)
+
T
B
(
x
,
y
)
4
;
the third term is equal to
-
1
2
a
max
∫
T
A
(
x
,
y
)
-
T
B
(
x
,
y
)
2
dx
;
and
the fourth term is equal to
T
A
(
x
,
y
)
+
T
B
(
x
,
y
)
4
.
17 . The system of claim 11 , wherein the first functional thickness variation further includes a third sum of the first sum and a first tilt term, and the second functional thickness variation includes a fourth sum of the second sum and a second tilt term.
18 . The system of claim 11 , wherein the instructions when executed causing the one or more processors to determine the first functional thickness variation and the second functional thickness variation further cause the one or more processors to:
calculate the average thickness variation of the first boundary thickness variation and the second boundary thickness variation;
calculate a first extracted thickness variation and a second extracted thickness variation comprising extracting the average thickness variation from the first boundary thickness variation and the second boundary thickness variation, respectively;
calculate a first transformed thickness variation and a second transformed thickness variation comprising integrating the first extracted thickness variation or the second extracted thickness variation, the first transformed thickness variation being the first term, the second transformed thickness variation being the second term; and
calculate the first functional thickness variation and the second functional thickness variation, the third term being half of the average thickness variation, the fourth term being half of the average thickness variation.
19 . A method comprising:
obtaining, by one or more computer systems, a first boundary thickness variation T A (x,y) of a first boundary element and a second boundary thickness variation T B (x,y) of a second boundary element, the first boundary element being configured to obtain a first boundary condition of a variable function optical system, the second boundary element being configured to obtain a second boundary condition of the variable function optical system;
obtaining, by the one or more computer systems, a maximum lateral shift, represented by an absolute value of a max of each of a first optically transmissive element and a second optically transmissive element of the variable function optical system, wherein each of the first optically transmissive element and the second optically transmissive element is configured to be translated in the variable function optical system by a lateral shift range 2a max ;
determining, by the one or more computer systems, a first functional thickness variation T F 1 (x,y) of the first optically transmissive element and a second functional thickness variation T F 2 (x,y) of the second optically transmissive element, wherein:
T F 1 (x,y) is calculated to include
1
2
a
max
∫
T
A
(
x
,
y
)
-
T
B
(
x
,
y
)
2
dx
+
T
A
(
x
,
y
)
+
T
B
(
x
,
y
)
4
;
and
T F 2 (x,y) is calculated to include
-
1
2
a
max
∫
T
A
(
x
,
y
)
-
T
B
(
x
,
y
)
2
dx
+
T
A
(
x
,
y
)
+
T
B
(
x
,
y
)
4
;
and
generating, by the one or more computer systems, a design file comprising a first digital representation of the first optically transmissive element based on the first functional thickness variation T F 1 (x,y) and comprising a second digital representation of the second optically transmissive element based on the second functional thickness variation T F 2 (x,y).
20 . The method of claim 19 further comprising determining a tilt term D x , wherein:
T
F
1
(
x
,
y
)
=
1
2
a
max
∫
T
A
(
x
,
y
)
-
T
B
(
x
,
y
)
2
dx
+
T
A
(
x
,
y
)
+
T
B
(
x
,
y
)
4
+
D
x
;
and
T
F
2
(
x
,
y
)
=
-
1
2
a
max
∫
T
A
(
x
,
y
)
-
T
B
(
x
,
y
)
2
dx
+
T
A
(
x
,
y
)
+
T
B
(
x
,
y
)
4
-
D
x
.