Data processing: measuring – calibrating – or testing – Measurement system – Dimensional determination
Reexamination Certificate
2000-04-27
2002-07-16
Hilten, John S. (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system
Dimensional determination
C702S159000
Reexamination Certificate
active
06421629
ABSTRACT:
FIELD OF THE INVENTION
This invention relates generally to a three-dimensional shape measurement technique, and more particularly, to a method and apparatus for measuring a three-dimensional shape based on phase shifting method and to a computer program product for use with a three-dimensional shape measurement apparatus.
BACKGROUND OF THE INVENTION
Up to now, a variety of techniques for measuring a three-dimensional shape of an object have been proposed. A grating pattern projection method, introducing a striped scanning, as one of such techniques, is first explained based on reference (1) entitled: “Grating Projection System for Profiling with the Aid of Fringe Scanning Method ” Journal of Precision Engineering (JSPE), vol. 55, No. 10, pp. 1817-1822, 1989.
FIG. 11
shows schematic diagram of a three-dimensional shape measurement device disclosed in the reference (1). Referring to
FIG. 11
, a light pattern having a sinusoidal luminance pattern is projected from a light source
101
on an object
100
through a sinusoidal grating
102
having a gray scale values printed thereon sinusoidally. A point
104
on the object
100
is scanned by a camera
103
which outputs an image data. If a coordinate value of the point
104
on an image taken by the camera
103
are denoted x and a luminance value on the coordinate x is denoted I(x), the luminance value I(x) is given by a following equation (1)
I
(
x
)=
a
0
(
x
)+
A
(
x
)cos(&phgr;+&agr;(
x
)) (1)
where a
0
(x) is a bias component and &phgr;, &agr;(x) denote the phase.
The image is captured by the camera
103
, each time after shifting the grating
102
, by a length equal to 1/N of the wavelength of a printed sinusoidal pattern N times, along an axis u, with the object
100
remaining stationary.
The image appears as if the sinusoidal light pattern projected on the object
100
is proceeding 2&pgr;/N radian each time. Assuming that the phase &phgr; is shifted from 0 radian up to 2(N−1)&pgr;/N radian where N is a positive integer, with an increment of 2&pgr;/N radian each time, the luminance value I
k
(x) at a point x obtained for the kth shifting (0≦k≦N) is given by a following equation (2)
I
k
(
x
)
=
a
0
(
x
)
+
A
(
x
)
cos
(
2
π
k
N
+
α
(
x
)
)
(
2
)
The phase &agr;(x) is a phase value at a point x in an image photographed for k=0. The point
104
is present on a half line originating from the coordinate x on the camera screen to pass through a lens center. The Point
104
as viewed from the light source
101
is present on a plane of the sinusoidal grating
102
determined by a straight line with the phase &agr;(x) and the light source
101
. Therefore, if a point of intersection between the straight line and the plane is found, it may be seen that the three-dimensional coordinate value of the point of intersection is that of the point
104
.
By introducing two new coefficients &agr;
1
(x) and B
1
(x), shown by a following equation (3), the above equation (2) can be rewritten to a following equation (4):
a
1
(
x
)
=
A
(
x
)
cos
α
(
x
)
b
1
(
x
)
=
-
A
(
x
)
sin
α
(
x
)
(
3
)
I
k
(
x
)
=
a
0
(
x
)
+
a
1
(
x
)
cos
2
π
k
N
+
b
1
(
x
)
sin
2
π
k
N
(
4
)
a
1
(x) and b
1
(x) may be found by a following equation (5), using luminance values I
0
(x), . . . I
N−1
(x) at the point x obtained on Nth image-capture operations, whilst the phase &agr;(x) may be found by a following equation (6)
a
1
(
x
)
=
1
N
∑
k
=
0
N
-
1
I
k
cos
(
2
π
k
N
)
b
1
(
x
)
=
1
N
∑
k
=
0
N
-
1
I
k
sin
(
2
π
k
N
)
(
5
)
α
(
x
)
=
tan
-
1
-
b
1
(
x
)
a
1
(
x
)
(
6
)
The phase value of the object
100
on the image data is obtained by executing the above-described phase calculations for each pixel on the image taken by the camera
103
.
Meanwhile, &agr;(x) obtained from the above equation (6) is unexceptionally wrapped (folded) between −&pgr; and &pgr;, as may be seen from a fact that calculation is made using an arctangent function tan
−1
( ). The result is that the phase &agr;(x) as found exhibits indefiniteness corresponding to an integer number times 2&pgr;, such that, in this state, a three-dimensional shape of the object
100
cannot be found.
By projecting a sinusoidal pattern composed of a period on the entire object
100
, the Phase &agr;(x) can be uniquely determined. Since a narrow phase value from −&pgr; to &pgr; is allocated at this time to the entire object
100
, a high measurement accuracy cannot be realized.
For this reason, a method is adopted to improve a measurement accuracy at the cost of phase uniqueness in which a domain of an initial phase is enlarged and a sinusoidal pattern of plural periods is projected on the object
100
.
FIG. 12
shows a Phase image
105
which is an example of the phase as found in each pixel within an image date captured by the camera
103
. In
FIG. 12
, a phase taking a value from −&pgr; to &pgr; is allocated to black to white.
If, for example, a plane is measured, as shown in
FIG. 12
, there is obtained non-continuous phase, so that it is necessary to determine a relative phase value within an image by suitable techniques to convert non-continuous phases into continuous values. Also, since an absolute phase value cannot be directly obtained, the absolute phase needs to be determined by some means or other.
One of conventional phase connection technique for converting the Phase wrapped to between −&pgr; and &pgr; into a continuous phase is described in, for example, reference (2) of T. R. Judge and P. J. Bryanston—Cross, entitled “A review of Phase Unwrapping Techniques in Fringe Analysis”, Optics and Lasers in Engineering, Vol. 21, pp. 199-239, 1994. The phase fringe counting/scanning approach technique, which is the simplest one of the phase connection methods, is hereinafter explained based on the description on pp. 211-212 of the reference (2).
This technique is constituted by following steps:
(1) Noise is removed by applying a filter having a spatial spreading or an low-pass filter (LPF) exploiting Fast Fourier Transform (FFT) to an input image. From the noise-eliminated image, the phase is calculated using e.g., the equation (6).
(2) A threshold value processing is executed for phase difference between neighbouring pixels to find a non-continuous phase boundary (changes in value from &pgr; to −&pgr;).
(3) The image is scanned from row to row in a horizontal direction, and 2&pgr; is added or subtracted each time a non-continuous phase boundary is traversed to find a continuous phase value between neighboring pixels.
(4) Phase values, continuous from row to row are compared in a vertical direction, and further converted to phase values which are continuous throughout the entire image.
In general, the phase connection method, inclusive of the above-described technique, suffers a drawback that satisfactory results cannot be obtained unless the supposition holds that a surface of the object
100
is sufficiently smooth, no significant changes in values are contained in the measured phase values, and that noise is only small. For this reason, the phase connection processing can pose a significant problem in automatic measurement.
The phase connection processing simply converts the phase value, wrapped from −&pgr; to &pgr;, so that the phase value will be continuous in its entirety, without obtaining the phase value as the absolute value. Therefore, there is left indefiniteness equal to &pgr; multiplied by an integer number in the phase value.
In the above reference (1) entitled “Method for Projecting Grating Pattern Introducing Stripe
Hilten John S.
Washburn Douglas N
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