Method of measuring offset of optical axis
A method of measuring an offset of an optical axis of an imaging system is implemented by a computing device. The imaging system captures a reference central marker and two reference outer markers on a surface to obtain a captured central marker and two captured outer markers on an image. The imaging system is rotated by a target angle such that the captured central marker is located at a center point of the image. The method includes: obtaining an input of an FOV of the imaging system, and a pair of distances from the reference central marker to each of the reference outer markers, or to each of the captured outer markers; based on the FOV and the pair of distances, obtaining a value of the target angle; and obtaining the offset based on the value of the target angle and an EFL of the imaging system.
1 . A method of measuring an offset of an optical axis of an imaging system, being implemented by a computing device, the imaging system including a lens and an image sensor, and being configured to capture a reference central marker and two reference outer markers that are on two opposite sides of the reference central marker, where the reference central marker and the two reference outer markers are all on a capturing surface, the imaging system being disposed such that, when capturing the reference central marker and the two reference outer markers to obtain a captured central marker and two captured outer markers on an image, an entrance pupil of the lens is intersected by a normal line that passes through the reference central marker and that is perpendicular to the capturing surface, the imaging system to be rotated by an undetermined target angle (α) about an axis that passes through a position of the entrance pupil such that the captured central marker is located at a center point of the image, the method comprising:
obtaining an input of a field of view (FOV) of the imaging system, and one of a first pair of distances (L 1 , L 2 ) and a second pair of distances (L 1 ′, L 2 ′), where the first pair of distances (L 1 , L 2 ) refers to two distances from the reference central marker to each of the two reference outer markers, and where the second pair of distances (L 1 ′, L 2 ′) refers to two distances from the captured central marker to each of the two captured outer markers on the image;
based on the field of view (FOV) of the imaging system, and one of the first pair of distances (L 1 , L 2 ) and the second pair of distances (L 1 ′, L 2 ′), obtaining a value of the undetermined target angle (α); and
obtaining the offset of the optical axis of the imaging system based on the value of the undetermined target angle (α) and an effective focal length (EFL) of the imaging system.
2 . The method as claimed in claim 1 , wherein the value of the undetermined target angle (α) is obtained based on the FOV of the imaging system and the first pair of distances (L 1 , L 2 ) using an equation as follows:
α
=
tan
-
1
[
D
2
+
L
2
2
D
2
+
L
1
2
-
1
D
2
+
L
2
2
D
2
+
L
1
2
+
1
·
cot
FOV
2
]
.
3 . The method as claimed in claim 2 , wherein the two reference outer markers are disposed such that the two captured outer markers are respectively located at two opposite edges of the image, and the value of the undetermined target angle (α) is obtained based on the FOV of the imaging system and the first pair of distances (L 1 , L 2 ).
4 . The method as claimed in claim 3 , further comprising:
controlling the imaging system to rotate by a first angle about the axis that passes through the entrance pupil, such that the captured central marker is located at one of the two opposite edges of the image;
controlling the imaging system to rotate by a second angle about the axis that passes through the entrance pupil, such that the captured central marker is located at another one of the two opposite edges of the image; and
obtaining the FOV of the imaging system, which is equal to the second angle.
5 . The method as claimed in claim 1 , wherein the value of the undetermined target angle (α) is obtained based on the FOV of the imaging system and the second pair of distances (L 1 ′, L 2 ′) using an equation as follows:
α
=
tan
-
1
[
D
2
+
L
2
′
2
D
2
+
L
1
′
2
-
1
D
2
+
L
2
′
2
D
2
+
L
1
′
2
+
1
·
cot
FOV
2
]
.
6 . The method as claimed in claim 1 , wherein the two reference outer markers are disposed such that the two distances from the reference central marker to each of the two reference outer markers are identical, and the value of the undetermined target angle (α) is obtained based on the FOV of the imaging system and the second pair of distances (L 1 ′, L 2 ′).
7 . The method as claimed in claim 6 , further comprising:
controlling the imaging system to rotate by a first angle about the axis that passes through the entrance pupil, such that the captured central marker is located at one of the two opposite edges of the image;
controlling the imaging system to rotate by a second angle about the axis that passes through the entrance pupil, such that the captured central marker is located at another one of the two opposite edges of the image; and
obtaining the FOV of the imaging system, which is equal to the second angle.
8 . The method as claimed in claim 1 , wherein the offset of the optical axis is obtained based on the value of the undetermined target angle (α) and the EFL using an equation as follows:
offset
=
EFL
·
α
.
9 . The method as claimed in claim 1 , further comprising:
determining whether the offset lies within a predetermined range; and
in response to determining that the offset does not lie within the predetermined range, outputting a warning message.
10 . A computing device configured to implement a method of measuring an offset of an optical axis of an imaging system as claimed in claim 1 .
11 . The computing device as claimed in claim 10 , wherein the value of the undetermined target angle (α) is obtained based on the FOV of the imaging system and the first pair of distances (L 1 , L 2 ) using an equation as follows:
α
=
tan
-
1
[
D
2
+
L
2
2
D
2
+
L
1
2
-
1
D
2
+
L
2
2
D
2
+
L
1
2
+
1
·
cot
FOV
2
]
.
12 . The computing device as claimed in claim 11 , wherein the two reference outer markers are disposed such that the two captured outer markers are respectively located at two opposite edges of the image, and the value of the undetermined target angle (α) is obtained based on the FOV of the imaging system and the first pair of distances (L 1 , L 2 ).
13 . The computing device as claimed in claim 12 , further configured to:
control the imaging system to rotate by a first angle about the axis that passes through the entrance pupil, such that the captured central marker is located at one of the two opposite edges of the image;
control the imaging system to rotate by a second angle about the axis that passes through the entrance pupil, such that the captured central marker is located at another one of the two opposite edges of the image; and
obtain the FOV of the imaging system, which is equal to the second angle.
14 . The computing device as claimed in claim 10 , wherein the value of the undetermined target angle (α) is obtained based on the FOV of the imaging system and the second pair of distances (L 1 ′, La′) using an equation as follows:
α
=
tan
-
1
[
D
2
+
L
2
′
2
D
2
+
L
1
′
2
-
1
D
2
+
L
2
′
2
D
2
+
L
1
′
2
+
1
·
cot
FOV
2
]
.
15 . The computing device as claimed in claim 10 , wherein the two reference outer markers are disposed such that the two distances from the reference central marker to each of the two reference outer markers are identical, and the value of the undetermined target angle (α) is obtained based on the FOV of the imaging system and the second pair of distances (L 1 ′, L 2 ′).
16 . The computing device as claimed in claim 15 , further configured to:
control the imaging system to rotate by a first angle about the axis that passes through the entrance pupil, such that the captured central marker is located at one of the two opposite edges of the image;
control the imaging system to rotate by a second angle about the axis that passes through the entrance pupil, such that the captured central marker is located at another one of the two opposite edges of the image; and
obtain the FOV of the imaging system, which is equal to the second angle.
17 . The computing device as claimed in claim 10 , wherein the offset of the optical axis is obtained based on the value of the undetermined target angle (α) and the EFL using an equation as follows:
offset
=
EFL
·
α
.
18 . The computing device as claimed in claim 10 , further configured to:
determine whether the offset lies within a predetermined range; and
in response to determining that the offset does not lie within the predetermined range, output a warning message.