US 12,607,459 B2 · Real-time three-dimensional shape measurement system and shape measurement method using diagonal line pattern irradiation method

In a deflectometry applied to real-time three dimensional shape measurement of freeform surfaces, a system for real-time acquisition of a three dimensional phase using a diagonal fringe pattern, the system comprising:

a pattern generation portion that generates a single-direction pattern in the diagonal direction and project the generated pattern onto a measurement object;
a detector that obtains an image of a deformed pattern reflected from the measurement object;
and
a phase acquisition portion that partially differentiates and integrates a phase of the diagonal fringe pattern in the x axis direction and y axis direction respectively, to obtain an x axis direction phase component and a y direction phase component,
wherein:
a single-direction pattern in the diagonal direction generated from the pattern generation portion is represented by the following equation 1:
I
s
(
x
s
,
y
s
)
=
(
G
2
)
⁢
{
1
+
cos
⁡
(
2
⁢
π
⁢
f
x
⁢
x
s
+
2
⁢
π
⁢
f
x
⁢
y
s
)
}
,
[
Equation
⁢
1
]
wherein
G is an arbitrary constant value representing a background light and a modulation amplitude, fx and fy represent carrier frequency components in the x axis and y axis directions, and (xs, ys) represents a position of a screen pixel;
a pattern obtained through the detector is represented by the following equation 2:
I
d
(
x
,
y
)
=
A
⁡
(
x
,
y
)
+
B
⁡
(
x
,
y
)
⁢
cos
⁢
{
2
⁢
π
⁢
f
x
⁢
x
+
2
⁢
π
⁢
f
y
⁢
y
+
φ
x
(
x
,
y
)
+
φ
y
(
x
,
y
)
}
,
[
Equation
⁢
2
]
wherein
(x,y) is a camera pixel position, A (x,y) and B (x,y) represent a background light component and a modulation amplitude, and φx and φy represent an x direction phase component and a y direction phase component of the measured object;
the diagonal pattern phase is calculated by normalizing a first-order derivation component and a second-order derivation component, wherein the first-order derivation component is divided by the second-order derivation component in equation 2;
the first-order derivation component,
I
dx
′
+
I
dy
′
is calculated from the following equation 3:
I
dx
′
=
-
2
⁢
π
⁢
f
x
⁢
B
⁢
sin
⁢
{
φ
}
,
I
dy
′
=
-
2
⁢
π
⁢
f
y
⁢
B
⁢
sin
⁢
{
φ
}
[
Equation
⁢
3
]
the second-order derivation component,
I
dx
*
+
I
dy
*
is calculated from the following equation 4:
I
dx
″
=
-
4
⁢
π
2
⁢
f
x
2
⁢
B
⁢
cos
⁢
{
φ
}
,
I
dy
″
=
-
4
⁢
π
2
⁢
f
y
2
⁢
B
⁢
cos
⁢
{
φ
}
;
[
Equation
⁢
4
]
the diagonal pattern phase is represented by the following equation 5:
φ
=
arctan
⁡
(

I
dx
′
+
I
dy
′


I
dx
″
+
I
dy
″

)
;
[
Equation
⁢
5
]
the phase acquisition portion restores the diagonal pattern phase of equation 5 through a phase unwrapping algorithm, and then partially differentiates the restored phase, represented by the following equation 7:
φ
x
′
=
2
⁢
π
⁢
f
x
+
ϕ
x
′
,
φ
y
′
=
2
⁢
π
⁢
f
y
+
ϕ
y
′
;
[
Equation
⁢
7
]
the equation 7 is integrated to separate and calculate an x axis direction phase component and a y axis direction phase component of the following equation 8:
φ
x
=
∫
φ
x
′
⁢
dx
=
2
⁢
π
⁢
f
x
⁢
x
+
φ
x
φ
y
=
∫
φ
y
′
⁢
dy
=
2
⁢
π
⁢
f
y
⁢
y
+
φ
y
.
[
Equation
⁢
8
]

351 more elements

In a deflectometry applied to real-time three dimensional shape measurement of freeform surfaces, a method for real-time acquisition of a three dimensional phase using a diagonal fringe pattern, the method comprising steps of:

S1:
a pattern generation portion generates a single direction pattern in the diagonal direction and projects the generated pattern onto a measurement object;
S2:
a detector obtains an image of a deformed pattern reflected from the measurement object;
S3:
a phase acquisition portion normalizes a first-order derivation component and a second-order derivation component for the diagonal fringe pattern, wherein the first-order derivation component is divided by the second-order derivation component, to calculate a diagonal pattern phase;
S4:
the phase acquisition portion performs a partial derivation in the x direction and a partial derivation in the y direction for the diagonal pattern;
and
S5:
the phase acquisition portion integrates partial derivations respectively, to obtain an x axis direction phase component and a y axis direction phase component,
wherein:
the single-direction pattern in the diagonal direction generated from the pattern generation portion is represented by the following equation 1:
I
s
(
x
s
,
y
s
)
=
(
G
2
)
⁢
{
1
+
cos
⁡
(
2
⁢
π
⁢
f
x
⁢
x
s
+
2
⁢
π
⁢
f
x
⁢
y
s
)
}
,
[
Equation
⁢
1
]
wherein
G is an arbitrary constant value representing a background light and a modulation amplitude, fx and fy represent carrier frequency components in the x axis and y axis directions, and (xs, ys) represents a position of a screen pixel;
a pattern obtained through the detector is represented by the following equation 2:
I
d
(
x
,
y
)
=
A
⁡
(
x
,
y
)
+
B
⁡
(
x
,
y
)
⁢
cos
⁢
{
2
⁢
π
⁢
f
x
⁢
x
+
2
⁢
π
⁢
f
y
⁢
y
+
φ
x
(
x
,
y
)
+
φ
y
(
x
,
y
)
}
,
[
Equation
⁢
2
]
wherein
(x,y) is a camera pixel position, A(x,y) and B(x,y) represent a background light component and a modulation amplitude, and φx and φy represent an x direction phase component and a y direction phase component of the measured object;
the diagonal pattern phase is calculated by normalizing the first-order derivation component and the second-order derivation component, wherein the first-order derivation component is divided by the second-order derivation component in equation 2;
the first-order derivation component,
I
dx
′
+
I
dy
′
is calculated from the following equation 3:
I
dx
′
=
-
2
⁢
π
⁢
f
x
⁢
B
⁢
sin
⁢
{
φ
}
,
I
dy
′
=
-
2
⁢
π
⁢
f
y
⁢
B
⁢
sin
⁢
{
φ
}
[
Equation
⁢
3
]
the second-order derivation component,
I
dx
″
+
I
dy
″
is calculated from the following equation 4:
I
dx
″
=
-
4
⁢
π
2
⁢
f
x
2
⁢
B
⁢
cos
⁢
{
φ
}
,
I
dy
″
=
-
4
⁢
π
2
⁢
f
y
2
⁢
B
⁢
cos
⁢
{
φ
}
;
[
Equation
⁢
4
]
the diagonal pattern phase is represented by the following equation 5:
φ
=
arctan
⁡
(

I
dx
′
+
I
dy
′


I
dx
″
+
I
dy
″

)
;
[
Equation
⁢
5
]
the phase acquisition portion restores the diagonal pattern phase of equation 5 through a phase unwrapping algorithm, and then partially differentiates the restored phase, represented by the following equation 7:
φ
x
′
=
2
⁢
π
⁢
f
x
+
φ
x
′
,
φ
y
′
=
2
⁢
π
⁢
f
y
+
φ
y
′
;
[
Equation
⁢
7
]
the equation 7 is integrated to separate and calculate an x axis direction phase component and a y axis direction phase component of the following equation 8:
φ
x
=
∫
φ
x
′
⁢
dx
=
2
⁢
π
⁢
f
x
⁢
x
+
φ
x
φ
y
=
∫
φ
y
′
⁢
dy
=
2
⁢
π
⁢
f
y
⁢
y
+
φ
y
.
[
Equation
⁢
8
]

358 more elements

In a method for real-time three dimensional shape measurement of free surfaces, a method for real-time measurement method of a three dimensional phase using a diagonal fringe pattern, the method comprising steps of:

S1:
a pattern generation portion generates a single-direction pattern in the diagonal direction and projects the generated pattern onto a measurement object;
S2:
a detector obtains an image of a deformed pattern reflected form the measurement object;
S3:
a phase acquisition portion calculates a diagonal pattern phase by normalizing a first-order derivation component and a second-order derivation component for the diagonal fringe pattern, wherein the first-order derivation component is divided by the second-order derivation component;
S4:
the diagonal pattern phase is restored through a phase unwrapping algorithm;
S5:
the phase acquisition portion a partial derivation in the x direction and a partial derivation in the y direction for the diagonal pattern;
S6:
the phase acquisition portion integrates partial derivations respectively, to obtain an x axis direction phase component and a y axis direction phase component;
S7:
a gradient computing portion computes an X direction gradient component from an x axis direction phase component obtained from the phase acquisition system and computes a Y direction gradient component from a y axis direction phase component obtained from the phase acquisition system;
and
S8:
an analysis unit analyzes a three dimensional shape of the measurement object based on the X direction gradient component and the Y direction gradient component,
wherein:
the single-direction pattern in the diagonal direction generated from the pattern generation portion is represented by the following equation 1:
I
s
(
x
s
,
y
s
)
=
(
G
2
)
⁢
{
1
+
cos
⁡
(
2
⁢
π
⁢
f
x
⁢
x
s
+
2
⁢
π
⁢
f
y
⁢
y
s
)
}
,
[
Equation
⁢
1
]
wherein
G is an arbitrary constant value representing a background light and a modulation amplitude, fx and fy represent carrier frequency components in the x axis and y axis directions, and (xs, ys) represents a position of a screen pixel;
a pattern obtained through the detector is represented by the following equation 2:
I
d
(
x
,
y
)
=
A
⁡
(
x
,
y
)
+
B
⁡
(
x
,
y
)
⁢
cos
⁢
{
2
⁢
π
⁢
f
x
⁢
x
+
2
⁢
π
⁢
f
y
⁢
y
+
φ
x
(
x
,
y
)
+
φ
y
(
x
,
y
)
}
,
[
Equation
⁢
2
]
wherein
(x,y) is a camera pixel position, A(x,y) and B(x,y) represent a background light component and a modulation amplitude, and φx and φy represent an x direction phase component and a y direction phase component of the measured object;
the diagonal pattern phase is calculated by normalizing the first-order derivation component and the second-order derivation component, wherein the first-order derivation component is divided by the second-order derivation component in equation 2;
the first-order derivation component,
I
dx
′
+
I
dy
′
is calculated from the following the first-order derivation component, equation 3:
I
dx
′
=
-
2
⁢
π
⁢
f
x
⁢
B
⁢
sin
⁢
{
φ
}
,
I
dy
′
=
-
2
⁢
π
⁢
f
y
⁢
B
⁢
sin
⁢
{
φ
}
[
Equation
⁢
3
]
the second-order derivation component,
I
dx
″
+
I
dy
″
is calculated from the following equation 4:
I
dx
″
=
-
4
⁢
π
2
⁢
f
x
2
⁢
B
⁢
cos
⁢
{
φ
}
,
I
dy
′
=
-
4
⁢
π
2
⁢
f
y
2
⁢
B
⁢
cos
⁢
{
φ
}
;
[
Equation
⁢
4
]
the diagonal pattern phase id represented by the following equation 5:
φ
=
arctan
⁡
(

I
dx
′
+
I
dy
′


I
dx
″
+
I
dy
″

)
;
[
Equation
⁢
5
]
the phase acquisition portion restores the diagonal pattern phase of equation 5 through a phase unwrapping algorithm, and then partially differentiates the restored phase, represented by the following equation 7:
φ
x
′
=
2
⁢
π
⁢
f
x
+
φ
x
′
,
φ
y
′
=
2
⁢
π
⁢
f
y
+
φ
y
′
;
[
Equation
⁢
7
]
the equation 7 is integrated to separate and calculate an x axis direction phase component and a y axis direction phase component of the following equation 8:
φ
x
=
∫
φ
x
′
⁢
dx
=
2
⁢
π
⁢
f
x
⁢
x
+
φ
x
φ
y
=
∫
φ
y
′
⁢
dy
=
2
⁢
π
⁢
f
y
⁢
y
+
φ
y
.
[
Equation
⁢
8
]

364 more elements

Real-time three-dimensional shape measurement system and shape measurement method using diagonal line pattern irradiation method

Life of this patent

Real-time three-dimensional shape measurement system and shape measurement method using diagonal line pattern irradiation method

Life of this patent

Abstract

Claims7