U.S. patent application number 13/661469 was filed with the patent office on 2013-03-21 for shape measurement of specular reflective surface.
The applicant listed for this patent is Sergey Potapenko. Invention is credited to Sergey Potapenko.
Application Number | 20130070087 13/661469 |
Document ID | / |
Family ID | 42620776 |
Filed Date | 2013-03-21 |
United States Patent
Application |
20130070087 |
Kind Code |
A1 |
Potapenko; Sergey |
March 21, 2013 |
SHAPE MEASUREMENT OF SPECULAR REFLECTIVE SURFACE
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.
Inventors: |
Potapenko; Sergey; (Painted
Post, NY) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Potapenko; Sergey |
Painted Post |
NY |
US |
|
|
Family ID: |
42620776 |
Appl. No.: |
13/661469 |
Filed: |
October 26, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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12391585 |
Feb 24, 2009 |
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13661469 |
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Current U.S.
Class: |
348/135 |
Current CPC
Class: |
C03B 17/064 20130101;
H04N 7/18 20130101; G01B 11/2513 20130101 |
Class at
Publication: |
348/135 |
International
Class: |
H04N 7/18 20060101
H04N007/18 |
Claims
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 ) ; ##EQU00020## 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, .alpha.=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 ; ##EQU00021## where (x.sub.p,z.sub.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 ) ;
##EQU00022## 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 = { - .differential. z
.differential. x , - .differential. z .differential. y , 1 } 1 + (
.differential. z .differential. x ) 2 + ( .differential. z
.differential. y ) 2 ; ##EQU00023## wherein z(x,y) is the surface
profile and .differential. z .differential. x ##EQU00024## and
.differential. z .differential. y ##EQU00025## 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 ) ; ##EQU00026## 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, .alpha.=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 ; ##EQU00027## wherein (x.sub.p,z.sub.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 ) ; ##EQU00028##
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 = { - .differential. z .differential.
x , - .differential. z .differential. y , 1 } 1 + ( .differential.
z .differential. x ) 2 + ( .differential. z .differential. y ) 2 ;
##EQU00029## wherein z is the surface profile and .differential. z
.differential. x ##EQU00030## and .differential. z .differential. y
##EQU00031## are the partial derivatives of the surface profile.
Description
FIELD
[0001] The invention relates generally to optical methods and
apparatus for measuring shapes of objects. More specifically, the
invention relates to a method and an apparatus for measuring a
shape of an object having a specular reflective surface.
BACKGROUND
[0002] Fusion draw process is used to make a sheet of material from
molten material such as molten glass (Dockerty U.S. Pat. No.
3,338,696 and Dockerty U.S. Pat. No. 3,682,609). Typically, the
fusion draw process involves delivering molten material into a
trough and overflowing the molten material down the sides of the
trough in a controlled manner. The separate streams of material
flowing down the sides of the trough merge at the root of the
trough into a single stream of material, which is drawn into a
continuous sheet of material. The continuous sheet of material is
separated into discrete pieces at the bottom of the fusion draw
machine. A key advantage of this process is that the surfaces of
the sheet of material do not come in contact with the sides of the
trough or other forming equipment and therefore are pristine.
Another benefit of the process is that the sheet of material is
very flat and has a uniform thickness (Dockerty U.S. Pat. No.
3,682,609).
[0003] Large sheets of glass produced by fusion draw process are a
key component in making large flat panel displays. Alternatively,
they can be diced to make other devices such as active electronic
devices, photovoltaic devices, and biological arrays. However, as
the demand for larger large-sized sheet increases, so does the
difficulty in forming and handling of these sheets. For example,
sheet scoring and separation processes at the bottom of the fusion
draw machine contribute significantly to the sheet motion in the
forming zone of the fusion draw machine. Sheet motion in the
forming zone can negatively impact the level of stress and stress
variation within the sheet, possibly leading to distortion in the
final product. The larger the sheet being handled, the more
significant the effect of sheet motion can be on the stress level
and variation with the sheet.
[0004] Corning Incorporated, the assignee of the present invention,
has developed various techniques for minimizing sheet motion at the
bottom of the draw. One such technique involves scoring the glass
sheet by laser, thereby avoiding physical contact with the glass
sheet that can result in sheet motion (Abramov et al. U.S. patent
application Ser. No. 12/008,949). Another technique involves use of
a conformable nosing device to engage a glass sheet while the glass
sheet is being scored, thereby reducing motion of the glass sheet
during scoring (Chalk et al. U.S. Patent Publication 2008/0276646).
Another technique involves separation of the glass sheet without
bending the glass sheet (Kemmerer et al. U.S. Patent Publication US
2007/0039990). These techniques require real-time information about
the displacement and shape of the glass sheet. Such information at
different elevations of the FDM may also be useful in fine-tuning
and optimizing the draw process.
[0005] Smooth glass sheets have surfaces that behave as specular
reflective surfaces for visible light. Shape measurement of
specular reflective surfaces by optical means is fundamentally
different from shape measurement of diffuse reflective surfaces by
optical means. A diffuse reflective surface can be considered as a
collection of secondary point light sources. Thus, the shape of a
diffuse reflective surface may be estimated by locating the
position of these sources. A specular reflective surface, on the
other hand, cannot be observed directly. Only reflection from the
specular reflective surface is visible. The problem of measuring
the shape of a specular reflective surface has been studied in, for
example, Savarese et al., "Local shape from mirror reflections,"
International Journal of Computer Vision, 64(1), 31-67 (2005);
Haeusler, et al U.S. Patent Publication 2005/0238237; Knauer et
al., "Phase measuring deflectometry: a new approach to measure
specular free-form surfaces." In Optical Metrology in Production
Engineering. Proceedings of SPIE v. 5457 (2004): 366-376; Kochengin
et al, "Determination of reflector surfaces from near field
scattering data." Inverse Problems v. 13 (1997): 363-373, and
Winkelbach, et al "Shape from single stripe pattern illumination."
Ed. Luc Van Gool. In Pattern Recognition. Lecture Notes in Computer
Science v. 2449 (Springer, 2002), 240-247. These references did not
study the problem of measuring the shape of a large-sized glass
sheet, such as useful in the flat panel display industry.
[0006] Techniques for measuring shapes of specular reflective
surfaces have the same difficulty to overcome: slope-position
uncertainty. The slope-position uncertainty problem can be
illustrated with reference to FIG. 1 (Haeusler et al. U.S. Patent
Publication 2005/0238237). In FIG. 1, a camera K.sub.1 captures a
reflection of a pattern 2 via a specular surface 3. Line 5a
represents a beam coming from point 7 on a screen 1, where pattern
2 is produced, and incident on point 6 on the specular surface 3.
Line 5b represents a beam reflected from point 6 on the specular
surface 3 and incident on point 9 in the image plane 8 of the
camera K.sub.1. The positions of screen 1 and camera K.sub.1 are
known. The positions of point 7 and point 9 are also known.
However, this information is not sufficient to allow the position
of point 6, having surface normal 11, to be determined with
certainty for two reasons: (i) the specular surface 3 is invisible
and (ii) other points along the line of sight 5b, e.g., point 6a
having suitable surface normal 11a, would also image point 7 to
point 9. Without knowing the position of reflection points on the
specular surface, it is not possible to uniquely determine the
shape of the specular surface.
[0007] Haeusler et al. U.S. Patent Publication 2005/0238237 and
Knauer et al. "Phase measuring deflectometry: a new approach to
measure specular free-form surfaces." In Optical Metrology in
Production Engineering. Proceedings of SPIE v. 5457 (2004):
366-376, use stereo-deflectometry to resolve ambiguities in
position of the reflection point. The method generally involves
capturing multiple reflected images of a sinusoidal pattern from
different lines of sight and looking for points in the measuring
space at which potential surface normals have the least deviation
from one another. Kochengin, et al "Determination of reflector
surfaces from near field scattering data."Inverse Problems v. 13
(1997): 363-373, takes a different approach including measuring the
shape of the reflecting surface R from near-field scattering data
measured on an object T. The setup is such that rays reflected off
the reflecting surface R are incident on the object T. The position
of object T is known, Kochengin, et al. "Determination of reflector
surfaces from near field scattering data." Inverse Problems v. 13
(1997): 363-373 and shows that if the position and intensity of
source O are also known, the reflector can be determined by solving
an inverse problem. Savarese et al., "Local shape from mirror
reflections," International Journal of Computer Vision, 64(1),
31-67 (2005) propose schemes for measuring local geometric
information of a mirror surface around a reflection point r by
analyzing the deformation produced upon a planar pattern of
intersecting lines through specular reflection on the mirror
surface at the point r.
SUMMARY
Technical Problem
[0008] A practical method and apparatus for unambiguously measuring
shapes of specular reflective surfaces, particularly large-sized
glass sheets, under online or offline conditions is desired.
Solution to Technical Problem
[0009] In a first aspect, a method of measuring a shape of a
specular reflective surface is provided. The method comprises
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. The method includes
recording an image of the reflection at an imaging plane. The
method further includes determining positions of a plurality of
points on the specular reflective surface relative to the imaging
plane. The method includes determining a first relation between
feature positions on the image of the reflection and feature
positions on the pattern. The method also includes 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.
[0010] In a first variation of the first aspect, producing the
reflection comprises illuminating the pattern.
[0011] In a first sub-variation of the first variation, producing
the reflection comprises illuminating the pattern by continuous
light.
[0012] In a second sub-variation of the first variation, producing
the reflection comprises illuminating the pattern by flash
light.
[0013] In a second variation of the first aspect, producing the
reflection comprises selecting a planar geometric pattern, e.g.,
checkerboard, stripes, dots, circles, or crosses, as the pattern
displayed on the surface of the target.
[0014] In a third variation of the first aspect, the method further
comprises focusing the image of the reflection on the target
plane.
[0015] In a sub-variation of the immediate above, 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.
[0016] In a fourth variation of the first aspect, determining
positions of the plurality of points on the specular reflective
surface comprises measuring the positions of the points relative to
the measurement plane.
[0017] In a sub-variation of the immediate above, 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. In one
variation, the line is located at or near the edge of the specular
reflective surface that is closest to the imaging plane.
[0018] In a sub-variation of the immediate above, measuring the
positions of the points comprises measuring the position of the
points with a linear array of displacement sensors disposed
adjacent to the specular reflective surface.
[0019] In a sub-variation of the immediate above, measuring the
positions of the points comprises measuring without changing
relative positions of the target plane, the measurement plane, and
the imaging plane.
[0020] In a fifth variation of the first aspect, determining
positions of the plurality of points on the specular reflective
surface relative to the imaging plane comprises selecting the
plurality of points on the measurement plane and extracting
positions of the plurality of points from a known position of the
measurement plane relative to the imaging plane.
[0021] In a sixth variation of the first aspect, 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 ) ; ##EQU00001##
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,
.alpha.=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 ; ##EQU00002##
wherein (x.sub.p,z.sub.p) is a location of a center of projection
of the reflection onto the imaging plane.
[0022] In a seventh variation of the first aspect, the second
relation has the form:
I ( t ) = R - t - 2 N ( N ( R - t ) ) ( R - t ) ( R - t )
##EQU00003##
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 = { - .differential. z .differential. x , - .differential. z
.differential. y , 1 } 1 + ( .differential. z .differential. x ) 2
+ ( .differential. z .differential. y ) 2 ; ##EQU00004##
wherein z(x,y) is the surface profile and
.differential. z .differential. x ##EQU00005##
and
.differential. z .differential. y ##EQU00006##
are the partial derivatives of the surface profile.
[0023] In an eighth variation of the first aspect, 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.
[0024] In a sub-variation of the immediate above, 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.
[0025] In a sub-variation of the immediate above, the method
further comprises combining the shapes of the sub-areas of the
specular reflective surface to obtain the shape of the specular
reflective surface.
[0026] In a second aspect, an apparatus for measuring a shape of a
specular reflective surface is provided. The apparatus includes a
target having a surface on which a pattern is displayed and a
camera having a recording media for recording an image of a
reflection of the pattern from the specular reflective surface. The
apparatus includes 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.
[0027] In a first variation of the second aspect, the apparatus
further includes a linear array of displacement sensors for
measuring positions of a plurality of points on the specular
reflective surface relative to a reference plane.
[0028] In a second variation of the second aspect, 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.
[0029] In a third variation of the second aspect, 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 ) ; ##EQU00007##
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,
.alpha.=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 ; ##EQU00008##
wherein (x.sub.p,z.sub.p) is a location of a center of projection
of the reflection onto the recording media.
[0030] In a fourth variation of the second aspect, 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 ) ;
##EQU00009##
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 = { - .differential. z .differential. x , - .differential. z
.differential. y , 1 } 1 + ( .differential. z .differential. x ) 2
+ ( .differential. z .differential. y ) 2 ; ##EQU00010##
wherein z(x,y) is the surface profile and
.differential. z .differential. x ##EQU00011##
and
.differential. z .differential. y ##EQU00012##
are the partial derivatives of the surface profile.
[0031] In a fifth variation of the second aspect of the invention,
the apparatus further comprises a light source for illuminating the
surface of the target.
[0032] Other features of the invention will be apparent from the
description of embodiments and the claims.
Advantageous Effects
[0033] The invention in one or more aspects, and variations
thereof, may provide one or more of the following advantages.
[0034] First, the invention unambiguously resolves the
slope-position uncertainty problem associated with measuring the
shape of a specular reflective surface.
[0035] Second, the invention can be used to recover the shape of a
sheet having specular reflective surfaces in any orientation of the
sheet.
[0036] Third, shape measurement of a specular reflective surface
using the invention is robust and practical. The shape of the
specular reflective surface can be determined from a single
reflection image and positions of points on the specular reflective
surface relative to an imaging plane. The positional data may be
known, for example, if the points are selected on a line at or near
the edge of the specular reflective surface and the distance
between the edge and the imaging plane is known or can be
determined. Alternatively, the positional data can be obtained with
a linear array of displacement sensors, which would make the system
less expensive compared to surface measurements based on
two-dimensional array of displacement sensors.
[0037] Fourth, shape measurement of a specular reflective surface
using the invention is as fast as the reflection image and the
sensor data acquisition time. This time can be in a range of tens
of milliseconds with a continuous light source or even tens of
microseconds with a flash light to display the pattern on the
target.
[0038] Fifth, the invention allows grazing viewing angles to be
used to increase the sensitivity to surface waviness with the wave
vectors along the viewing direction. Grazing viewing angles can be
used because the displacement sensors, which provide initial
condition, maintain the sensitivity for the perpendicular
waviness.
[0039] Sixth, the invention allows grazing viewing angles to be
used to make the apparatus compact. Compactness becomes more
important for larger sheet sizes.
[0040] Other advantages of the invention will be apparent from the
description of embodiments and claims.
BRIEF DESCRIPTION OF DRAWINGS
[0041] FIG. 1 is a diagrammatic illustration for explaining the
slope-position uncertainty.
[0042] FIG. 2 is a flowchart illustrating a method of measuring a
shape of a specular reflective surface.
[0043] FIG. 3A is a measurement setup for carrying out the method
illustrated in FIG. 2.
[0044] FIG. 3B is a diagram of a checkerboard pattern.
[0045] FIG. 3C is a diagram of a striped pattern.
[0046] FIG. 3D shows a reflection image of a checkerboard pattern
produced from a specular reflective surface.
[0047] FIG. 4 is a geometric representation of a shape recovery
method in three-dimensional space.
[0048] FIG. 5 is a geometric representation of a shape recovery
method in one-dimension.
[0049] FIG. 6 is a setup for measuring a shape profile at the edge
of a specular reflective surface.
[0050] FIG. 7A shows a reflection of a striped pattern produced
from a specular reflective surface.
[0051] FIG. 7B is a plot of a shape of a glass sheet measured using
the method outlined in FIG. 2.
[0052] FIG. 7C is a plot of a shape of a glass sheet measured by
scanning the glass sheet with a displacement sensor.
[0053] FIGS. 8 and 9 are shapes of glass sheets measured using the
method outlined in FIG. 2.
[0054] FIG. 10 depicts a glass sheet manufacturing process with
online sheet shape measurement.
DESCRIPTION OF EMBODIMENTS
[0055] FIG. 2 is an overview of a method of measuring a shape of a
specular reflective surface. The measurement area is prepared
(100). This includes positioning a specular reflective surface at a
measurement plane, positioning a target at a target plane, and
positioning a recording media at an imaging plane. A pattern on the
target is reflected from the specular reflective surface (102). The
recording media records an image of the reflection (reflection
image) (104). Points are selected on the specular reflective
surface and positions of the points relative to the measurement
plane are measured (106). The reflection image obtained in 104 and
the pattern are analyzed to obtain a mapping relation that relates
feature positions on the reflection image to feature positions on
the pattern (108). The shape of the specular reflective surface is
determined by solving a geometric relation that relates the shape
of the specular reflective surface to the mapping relation (110).
The shape of the specular reflective surface is determined such
that the geometric relation is true for the points whose positions
were measured in 106. In 108, a plurality of sub-areas may be
identified on the reflection image and a plurality of corresponding
sub-areas may be identified on the pattern. Then, the mapping
relation may be determined for each corresponding sub-areas of the
reflection image and pattern. As an example, three sub-areas RM1,
RM2, and RM3 may be identified on the reflection image, and three
corresponding sub-areas PM1, PM2, and PM3 may be identified on the
pattern. A total of three mapping relations would be determined for
the following combinations of sub-areas: RM1 and PM1; RM2 and PM2;
and RM3 and PM3. In 110, the shape of each sub-area of the specular
reflective surface may be determined using the geometric relation,
the mapping relation associated with each sub-area (as determined
in 108), and the initial condition obtained in 106. The shapes of
the sub-areas may be combined to obtain the shape or full surface
profile of the specular reflective surface.
[0056] FIG. 3A is an illustration of a measurement area prepared as
indicated at 100 of FIG. 2. In FIG. 3A, a sheet of material 120,
whose shape is to be measured, is positioned at a measurement plane
122. The measurement plane 122 is an imaginary plane that is
coincident with the ideal plane of the sheet of material 120. The
ideal plane of the sheet of material 120 is the plane of the sheet
of material assuming that the sheet of material is perfectly flat.
The sheet of material 120 has specular reflective surfaces 124,
126. The specular reflective surface to be measured is indicated at
124. In one example, the sheet of material 120 is a sheet of
glass-based material having smooth surfaces that behave as specular
reflective surfaces. The sheet of material 120 may be arranged in
any suitable manner, e.g., vertical, horizontal, or inclined
position. For example, the sheet of material 120 may be supported
on a horizontal table surface, supported on an inclined surface,
supported at the bottom or top edge, or hung by the top edge. In
the example illustrated in FIG. 3, the sheet of material 120 is
hung in a vertical position, with opposing vertical edges 128, 130
disposed in grooves 132, 134 in fixtures 136, 138, respectively. In
a fusion draw process, the fixtures 136, 138 may be sets of paired
rollers arranged to guide the sheet of glass 120 along the fusion
draw machine. As previously mentioned, alternative arrangements may
include placing the sheet of material 120 on a horizontal or
inclined surface.
[0057] FIG. 3A shows a target 140 having a surface 144 positioned
at a target plane 142. The surface 144 of the target 140 includes a
pattern displayed thereon that will be reflected off the specular
reflective surface 124 of the sheet of material 120. In one
example, the pattern on the surface 144 includes planar features.
In one example, the planar features include geometric shapes, such
as a checkerboard pattern 145 shown in FIG. 3B or a striped pattern
147 shown in FIG. 3C. Other examples of geometric shapes include,
but are not limited to, circles, dots, and crosses. In general, any
pattern features that can be assigned location coordinates and used
in determining feature locations in an image analysis may be used.
In alternate examples, the pattern may be continuous fringes, e.g.,
sinusoidal fringes. Referring to FIG. 3A, the pattern may be
displayed on the surface 144 of the target 140 using any suitable
method. For example, the target 140 may be made of an opaque
material and the surface 144 may be illuminated from the front to
form the pattern, or the target 140 may be made out of translucent
material and the surface 144 may be illuminated from the back to
form the pattern. The pattern also may be a computer-generated
pattern displayed on a screen, e.g. by an LCD monitor, or projected
on a screen. The illumination light source (identified for
illustration purposes as 143) may be a continuous light or a flash
light. In the latter case, the measurement can be done while the
sheet 120 is moving, e.g. for online measurements. Light travels
from the target surface 144 to the specular reflective surface 124
of the sheet of material 120 as indicated by line 146 and is
reflected from the specular reflective surface 124 along the line
150. If the sheet 120 is transparent, part of the light will pass
through the sheet 120. Part of the light passed through the sheet
120 will be reflected by back surface 126. In this case, the sheet
120 should be thin enough so the light reflected from two (or more)
surfaces will not deviate from each other to the extent that the
analysis of the reflection image is impossible
[0058] FIG. 3A shows a recording media 152 of a camera 153
positioned at an imaging plane 154 to record a reflection from the
specular reflective surface 124. Any suitable camera 153, such as a
CCD camera or video camera with sufficient pixel resolution to
achieve the desired accuracy, may be used. The recording media 152
may include one or more imaging sensors. The imaging plane 154 is
substantially perpendicular (e.g., 90.degree..+-.5.degree.) to the
measurement plane 122. In some examples, the target plane 142 is
substantially perpendicular (e.g., 90.degree..+-.5.degree.) to the
measurement plane 122. In this position, the optical axis 156 of
the recording media 152 is substantially perpendicular (e.g.,
90.degree..+-.5.degree.) to the target plane 142. A lens 158, e.g.,
a shift lens, is used to focus the image of the reflection produced
by the specular reflective surface 124 onto the imaging plane 154.
In other examples, the target plane 142 is not perpendicular or
substantially perpendicular to the measurement plane 122, and the
lens 158 is used shifted and titled as necessary to focus the
imaging plane 154 on the reflection of the target plane 142 into
the measurement plane 124.
[0059] As explained with reference to FIG. 2, the pattern on the
target surface 144 is reflected off the specular reflective surface
124 and recorded by the recording media 152. A data analyzer 167
includes machine-readable instructions that receives the reflection
image and pattern as input and analyzes the reflection image and
pattern to obtain a mapping relation between the pattern and
reflection image. The data analyzer 167 may receive a
representation or image of the pattern. The instructions of the
data analyzer 167 may be executed on a general-purpose CPU 160
having appropriate hardware. A data analyzer 169 includes
machine-readable instructions that receives the mapping relation as
input and determines the shape of the specular reflective surface
124 using the mapping relation and a geometric relation, as will be
explained below. The data analyzer 169 also receives positional
data from a displacement sensor array 162 as input. The positional
data is used as initial condition when resolving the geometric
relation. If the position of the sheet 120 along a line preferably
closest to the camera is known, e.g. the sheet edge is arranged
with respect to a fixture 138 whose position is determined during
the measurement setup and does not change, the displacement sensors
are not needed. In this case the data analyzer 169 will use the
data on the fixture location. The instructions of the data analyzer
169 may be executed on the CPU 160 or on a separate CPU (not
shown). Execution of the instructions of the analyzers 167, 169 may
be achieved through the use of one or more program storage devices
readable by the CPU(s) 160 and encoding one or more programs of
instructions executable by the computer for performing the
operations described herein. The program storage device may take
the form of, for example, one or more floppy disks; a CD ROM or
other optical disk; a magnetic tape; a read-only memory chip (ROM);
and other forms of the kind well-known in the art or subsequently
developed. The program of instructions may be "object code," i.e.,
in binary form that is executable more-or-less directly by the
computer; in "source code" that requires compilation or
interpretation before execution; or in some intermediate form such
as partially compiled code. The precise forms of the program
storage device and of the encoding of instructions are immaterial
here. The data analyzers 167, 169 may be sub-components of a single
data analyzer or may be separate data analyzers.
[0060] FIG. 3D shows an example of a reflection image 161 acquired
through reflection of a checkerboard pattern 163 off a specular
glass surface 165. The reflection image 161 is distorted in
comparison to the checkerboard pattern 163 by the shape of the
glass 165. The data analyzer (161 in FIG. 3A) may contain a
procedure for determining the mapping relation between features in
the pattern 163 and features in the reflection image 161. Mapping
involves marking features in the pattern 163 and identifying the
position of the marked features in the reflection image 161. In the
checkerboard pattern 163, a feature may be a grid point or a line.
The positions of the features in the pattern and the corresponding
features in the reflection image in a global coordinate system can
be determined if (i) the locations of the target surface (144 in
FIG. 3A) and the recording media (152 in FIG. 3A) in the global
coordinate system are known and (ii) the feature locations with
respect to the target and the image of the feature with respect to
the recording media are known. The locations of the features in the
target pattern are determined from the image analysis. The
locations of other components (target, measurement plane, lens,
imaging plane and displacement sensors) may be obtained by direct
measurement or by analyzing location of known objects in the image
other than target reflection features, e.g. fiducials on the target
and in the measurement plane.
[0061] FIG. 4 shows the specular reflective surface 124, the target
surface 144, and the recording media 152 relative to a spatial
coordinate system XYZ. R is the position vector of a point 157 on
the specular reflective surface 124. N is a normal vector to the
specular reflective surface 124 at point R. T is a vector from the
surface point 157 on the specular reflective surface 124 to a point
159 on the target surface 144. T* is a vector in the direction of
the reflected light, from the surface point 157 to a point 171 on
the recording media 152. Vector T* has the following
expression:
T*=-T+2N(NT) (1)
I is the unit vector in the direction of the reflected light and is
given by:
I = T * T * ( 2 ) ##EQU00013##
From equations (1) and (2), the relationship between the normal
vector N and the unit vector I is given by:
I = - T + 2 N ( N T ) T ( 3 ) ##EQU00014##
[0062] If t=T-R is the position vector of point 159 on the target
surface 144, then equation (3) can be written in terms of position
vector t as follows:
I ( t ) = R - t - 2 N ( N ( R - t ) ) ( R - t ) ( R - t ) where ( 4
) N = { - .differential. z .differential. x , - .differential. z
.differential. y , 1 } 1 + ( .differential. z .differential. x ) 2
+ ( .differential. z .differential. y ) 2 ( 5 ) ##EQU00015##
[0063] In equation (4), I(t) represents the mapping relation
between the pattern and the image of the reflection (reflection
image) of the pattern. In equation (5), z(x,y) is the surface
profile and
.differential. x .differential. z ##EQU00016##
and
.differential. z .differential. y ##EQU00017##
are the partial derivatives of the surface profile. From equations
(4) and (5), if I(t) is known and R={x,y,z(x,y)}, the surface
profile z(x,y) can be determined.
[0064] Using I(u(t))={Cos .alpha., 0, Sin .alpha.}, u=Tan .alpha.,
the surface profile for the one-dimensional case is given by:
z x = ux - t ( u ) + z 1 + u 2 ( t ( u ) - z ) 2 + x 2 + x + u ( t
( u ) - z ) ( 6 ) ##EQU00018##
In equation (6), t(u) is the function known from the image
analysis, where u should be substituted with
u = z p - z x p - x . ( 7 ) ##EQU00019##
In equation (6), z(x) is the surface profile along one dimension,
dz/dx is the derivative of the surface profile, x is a direction
parallel to the measurement plane, .alpha.=ArcTan(u) is the angle
between the vector in the direction of the reflected light and the
measurement plane, and t(u) is the mapping relation between the
pattern and an image of the pattern captured from the specular
reflective surface. Equation (6), being exact in one dimensional
case, is also applicable as an approximation in two dimensional
cases for small viewing angles .alpha., e.g., less than 30.degree..
FIG. 5 is a geometrical representation of the shape recovery for
the one-dimensional case. In FIG. 5, the target is placed at x=0,
the projective point is at {x.sub.p,z.sub.p}, and the recording
media is at x=x.sub.s. The lens is shifted along z with respect to
the center of the recording media and focused on the target plane.
Angle .alpha. is the angle between the tangent to the surface at
x=x.sub.m and the horizontal axis, .alpha..sub.t is the angle of
the incident ray from point t, and .alpha..sub.s is the angle of
the reflected ray.
[0065] For the integration of the differential equation shown in
equation (6), an initial condition is needed. The initial condition
may be a shape profile measured on the specular reflective surface
(124 in FIG. 3A). In the method described in FIG. 2, this initial
condition is obtained at 106. In one example, the shape profile at
an edge of the specular reflective surface (124 in FIG. 3A), e.g.,
edge 130 in FIG. 2, is used as the initial condition. Referring to
FIG. 6, the shape profile at the edge of the specular reflective
surface 124 relative to the measurement plane 122 may be obtained
using a linear array 162 of displacement sensors 164 arranged along
the edge 130 of the specular reflective surface 124. A single
displacement sensor 164 may also be used to obtain the shape
profile, but this would require translating the single displacement
sensor 164 along the edge of the specular reflective surface 124.
If the position of the edge of the specular reflective surface 124
relative to the measurement plane is known, the position of the
edge of the specular reflective surface 124 relative to the imaging
plane can be determined. Positions of the measurement plane 122,
recording media (152 in FIG. 3A), and the lens 158 can be obtained
by direct measurements. A reference sheet may also be used to find
the position of the edge of the specular reflective surface 124
relative to the imaging plane.
EXAMPLES
[0066] The examples below demonstrate the validity of the method
described above in measuring shapes of specular reflective
surfaces.
Example 1
[0067] FIG. 7B shows shape measurement of a glass sheet on a
horizontal platform using the method described above with reference
to FIGS. 2-6. The shape of the glass sheet was induced by placing a
plate under the glass. The glass edge facing the target was
touching the table, which was used as the initial condition for the
differential condition. The target had a striped pattern. FIG. 7A
shows the reflection image 170 acquired from the striped pattern
172. The reflection image 170 was used in obtaining the mapping
relation, as described above. For comparison purposes, the profile
of the glass was also measured by an optical displacement sensor
mounted on the a rail. The result is shown in FIG. 7C. As can be
observed visually, there is agreement between the profiles shown in
FIGS. 7B and 7C.
Example 2
[0068] FIGS. 8 and 9 show shapes of two different glass sheets
recovered by the method described above at different orientations
of the glass sheets on the measurement table. An array of
displacement sensors along the right edge of the glass was used to
obtain the initial condition for the integration of the
differential equation. Four measurements of the same glass sheet at
different orientations are shown in FIG. 8. Similarly, four
measurements of the same glass sheet at different orientations are
shown in FIG. 9. FIGS. 8 and 9 show that the method described above
is not dependent on the orientation of the glass sheet.
[0069] In the description of FIG. 2 above, it was mentioned that at
108, the reflection image may be sub-divided into sub-areas and the
mapping relation may be determined for each sub-area. There are two
ways of interpreting this process. A single large reflection image
may be captured with a single camera and then sub-divided into
sub-areas. With a single camera the target size needs to be larger
than the portion of the specular reflective surface whose shape is
to be recovered in at least one dimension. An alternative is to use
multiple cameras to generate multiple reflection images, where each
reflection image captured by each camera corresponds to a sub-area
of the specular reflective surface. With multiple cameras, the
target size does not need to be larger than the measurement area of
the specular reflective surface. As an example, two cameras may be
used. The cameras may be stacked vertically or horizontally. If the
viewing direction of the second camera is perpendicular to the
viewing direction of the first camera, then only one displacement
sensor at a single point (as opposed to a linear array of
displacement sensors) would be needed to resolve the shaping
relation. Using this single point as an initial condition, a
profile along a line parallel to the viewing direction of the
second camera can be recovered. This profile in combination with
the analysis of the image acquired by the first camera can then be
used to recover the shape of the rest of the specular reflective
surface.
INDUSTRIAL APPLICABILITY
[0070] The apparatus and method described above can be applied to
measurement of specular reflective surfaces. A practical
application of the apparatus and method described above is in
measurement of large-sized glass sheets useful in manufacture of
flat panel displays. Measurements may be made using the apparatus
and method described above under online conditions (i.e., while the
glass sheet is being formed) or offline conditions (i.e., after
forming the glass sheet). Offline measurements are illustrated in
Examples 1 and 2 above.
[0071] FIG. 10 illustrates a fusion draw process incorporating the
apparatus and method described above under online conditions. In
the example illustrated in FIG. 10, molten glass 230 flows into a
fusion pipe 232 and overflows down the sides of the fusion pipe 232
to form a sheet-like flow 234, which is received in a channel 236.
The channel 236 is defined by a pair of elongated guide members 238
arranged in parallel. The channel 236 may be vertical or may have
other orientations, for example, horizontal or inclined. Rollers
240 arranged along the guide members 238 grip the side edges of the
sheet-like flow 234 and draw the sheet-like flow 234 into a glass
sheet 242. The fusion pipe 232, guide members 238, rollers 240, and
channel 236 may be a part of a fusion draw machine. Target 140
having the pattern-bearing target surface 144, camera 153 having
recording media 152, lens 158 for focusing functions, and linear
array 162 of displacement sensors, as described above, may be
provided at the bottom of the channel 236 to provide information
about the shape of the glass sheet 242. Such information may be
used in a no-bend separation, for example, or to optimize the
fusion draw process, or for quality control.
* * * * *