US2013070087A1PendingUtilityA1
Shape measurement of specular reflective surface
Est. expiryFeb 24, 2029(~2.6 yrs left)· nominal 20-yr term from priority
Inventors:Sergey Potapenko
H04N 7/18C03B 17/064G01B 11/30G01B 11/2513G01N 21/86G01B 11/25
39
PatentIndex Score
0
Cited by
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References
0
Claims
Abstract
A method of measuring a shape of a specular reflective surface is provided. A pattern displayed on a surface of a target positioned at a target plane is produced from a specular reflective surface positioned at a measurement plane. An image of the reflection is recorded at an imaging plane. Positions of a plurality of points on the specular reflective surface relative to the imaging plane are determined. A first relation between feature positions on the image of the reflection and feature positions on the pattern is determined. The shape of the specular reflective surface is determined from a second relation involving a surface profile of the specular reflective surface and the first relation using the positions of the plurality of points as an initial condition.
Claims
exact text as granted — not AI-modifiedWhat is claimed is:
1 . A method of measuring a shape of a specular reflective surface, the method comprising:
producing a reflection of a pattern displayed on a surface of a target positioned at a target plane from a specular reflective surface positioned at a measurement plane; recording an image of the reflection at an imaging plane; determining positions of a plurality of points on the specular reflective surface relative to the imaging plane; determining a first relation between feature positions on the image of the reflection and feature positions on the pattern; and determining the shape of the specular reflective surface from a second relation involving a surface profile of the specular reflective surface and the first relation using the positions of the plurality of points as an initial condition.
2 . The method of claim 1 , wherein producing the reflection comprises illuminating the pattern.
3 . The method of claim 1 , wherein producing the reflection comprises selecting a planar geometric pattern as the pattern on the surface of the target.
4 . The method of claim 1 , further comprising focusing the image of the reflection on the target plane.
5 . The method of claim 4 , wherein focusing the image of the reflection on the target plane comprises using a lens to focus the imaging plane on a reflection of the target plane into the measurement plane.
6 . The method of claim 1 , wherein determining positions of the plurality of points on the specular reflective surface comprises measuring the positions of the points relative to the measurement plane.
7 . The method of claim 6 , wherein determining positions of the plurality of points on the specular reflective surface further comprises selecting the plurality of points along a line at or near an edge of the specular reflective surface.
8 . The method of claim 7 , wherein measuring the positions of the points comprises measuring with a linear array of displacement sensors disposed adjacent to the specular reflective surface.
9 . The method of claim 8 , wherein measuring the positions of the points comprises measuring without changing relative positions of the target plane, the measurement plane, and the imaging plane.
10 . The method of claim 1 , wherein the second relation in one dimension has the form:
z
x
=
ux
-
t
(
u
)
+
z
1
+
u
2
(
t
(
u
)
-
z
)
2
+
x
2
+
x
+
u
(
t
(
u
)
-
z
)
;
wherein z is the surface profile in a direction perpendicular to the measurement plane, dz/dx is the derivative of the surface profile, x is a direction parallel to the measurement plane, α=ArcTan(u) is the angle between a vector in the direction of the reflected light and the measurement plane, t(u) is the first relation and
u
=
z
p
-
z
x
p
-
x
;
where (x p ,z p ) is a location of a center of projection of the reflection onto the imaging plane.
11 . The method of claim 1 , wherein the second relation has the form:
I
(
t
)
=
R
-
t
-
2
N
(
N
·
(
R
-
t
)
)
(
R
-
t
)
·
(
R
-
t
)
;
wherein I(t) is the first relation, R is a point on the specular reflection surface, and N is a normal vector to the specular reflection surface;
wherein
N
=
{
-
∂
z
∂
x
,
-
∂
z
∂
y
,
1
}
1
+
(
∂
z
∂
x
)
2
+
(
∂
z
∂
y
)
2
;
wherein z(x,y) is the surface profile and
∂
z
∂
x
and
∂
z
∂
y
are the partial derivatives of the surface profile.
12 . The method of claim 1 , wherein determining the first relation comprises identifying a plurality of sub-areas on the image of the reflection and a plurality of corresponding sub-areas on the pattern and determining a first sub-relation between feature positions on each of the sub-areas on the image of the reflection and feature positions on each of the corresponding sub-areas on the pattern.
13 . The method of claim 12 , wherein determining the shape of the specular reflective surface from the second relation comprises determining the shapes of sub-areas of the specular reflective surface from the second relation and the first sub-relations using the positions of the plurality of points as an initial condition.
14 . The method of claim 13 , further comprising combining the shapes of the sub-areas of the specular reflective surface to obtain the shape of the specular reflective surface.
15 . An apparatus for measuring a shape of a specular reflective surface, comprising:
a target having a surface on which a pattern is displayed; a camera having a recording media for recording an image of a reflection of the pattern produced from the specular reflective surface; a data analyzer configured to determine the shape of the specular reflective surface from a first relation between feature positions on the image of the reflection and feature positions on the pattern and a second relation involving a surface profile of the specular reflective surface and the first relation.
16 . The apparatus of claim 15 , further comprising a light source for illuminating the surface of the target.
17 . The apparatus of claim 15 , further comprising a linear array of displacement sensors for measuring positions of a plurality of points on the specular reflective surface relative to a reference plane.
18 . The apparatus of claim 15 , wherein the data analyzer is further configured to receive as input an initial condition comprising measured or known positions of a plurality of points on the specular reflective surface relative to a reference plane and to use the initial condition in determining the shape of the specular reflective surface.
19 . The apparatus of claim 15 , wherein the data analyzer is configured to resolve the second relation having in one dimension the form:
z
x
=
ux
-
t
(
u
)
+
z
1
+
u
2
(
t
(
u
)
-
z
)
2
+
x
2
+
x
+
u
(
t
(
u
)
-
z
)
;
wherein z is the surface profile in a direction perpendicular to the measurement plane, dz/dx is the derivative of the surface profile, x is a direction parallel to the measurement plane, α=ArcTan(u) is the angle between a vector in the direction of the reflected light and the measurement plane, t(u) is the first relation, and
u
=
z
p
-
z
x
p
-
x
;
wherein (x p ,z p ) is a location of a center of projection of the reflection onto the recording media.
20 . The apparatus of claim 15 , wherein the data analyzer is configured to resolve the second relation having the form:
I
(
t
)
=
R
-
t
-
2
N
(
N
·
(
R
-
t
)
)
(
R
-
t
)
·
(
R
-
t
)
;
wherein t is first relation, R is a point on the specular reflection surface, and N is a normal vector to the specular reflection surface;
wherein
N
=
{
-
∂
z
∂
x
,
-
∂
z
∂
y
,
1
}
1
+
(
∂
z
∂
x
)
2
+
(
∂
z
∂
y
)
2
;
wherein z is the surface profile and
∂
z
∂
x
and
∂
z
∂
y
are the partial derivatives of the surface profile.Join the waitlist — get patent alerts
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