Analysis apparatus, analysis method, and interference measurement system
An analysis apparatus includes an acquisition part that acquires a plurality of interference images of the object to be measured from the interference measurement apparatus, a calculation part that calculates a sine wave component and a cosine wave component of an interference signal for each pixel in the plurality of interference images, respectively, an error detection part that detects an error between a first Lissajous figure constructed on the basis of the sine wave component and the cosine wave component for each pixel and an ideal second Lissajous figure, a correction part that corrects the sine wave component and the cosine wave component for each pixel on the basis of the error, and a geometry calculation part that calculates surface geometry of the object to be measured on the basis of the corrected sine wave component and cosine wave component.
1. An interference measurement system comprising an interference measurement apparatus and an analysis apparatus, wherein:
the interference measurement apparatus includes:
a light source part that irradiates a surface of an object to be measured with a laser light;
a reference surface that is movably provided on an optical axis of the laser light;
an image capturing part that captures an interference image of reference light reflected at the reference surface and measurement light reflected at the surface of the object to be measured, and wherein
the analysis apparatus includes:
an acquisition part that acquires a plurality of the interference images based on a plurality of optical path lengths between the reference surface and the surface of the object to be measured from the interference measurement apparatus;
a calculation part that calculates a sine wave component and a cosine wave component of an interference signal for each pixel in the plurality of the interference images, respectively;
an error detection part that detects an error between a first Lissajous figure constructed on the basis of the sine wave component and the cosine wave component for each pixel and an ideal second Lissajous figure;
a correction part that corrects the sine wave component and the cosine wave component for each pixel on the basis of the error; and
a geometry calculation part that calculates surface geometry of the object to be measured on the basis of the corrected sine wave component and cosine wave component.
2. The interference measurement system according to claim 1 , wherein
the error detection part uses a circle having a predetermined radius as the second Lissajous figure, and
the correction part corrects the first Lissajous figure to approach the second Lissajous figure by correcting center coordinates and an ellipticity of the first Lissajous figure based on the sine wave component and the cosine wave component for each pixel.
3. The interference measurement system according to claim 1 , wherein
the error detection part extracts information of the first Lissajous figure having an elliptical shape from the sine wave component and the cosine wave component of an interference signal for each pixel in the plurality of the interference images.
4. The interference measurement system according to claim 1 , wherein
the calculation part calculates the sine wave component as I sin (x n , y m ) and the cosine wave component as I cos (x n , y m ), according to the following equation,
I
s
i
n
(
x
n
,
y
m
)
=
∑
i
=
1
K
I
i
(
x
n
,
y
m
)
sin
δ
i
γ
(
x
n
,
y
m
)
[
Equation
1
]
I
c
o
s
(
x
n
,
y
m
)
=
∑
i
=
1
K
I
i
(
x
n
,
y
m
)
cos
δ
i
γ
(
x
n
,
y
m
)
γ
(
x
n
,
y
m
)
=
∑
i
=
1
K
I
i
(
x
n
,
y
m
)
where I i (x n , y m ) shows image data of N×M pixels of K interference images, where i=1, 2, 3, . . . , K, n=1, 2, 3, . . . , N, and m=1, 2, 3, . . . , M, and δ i is a phase shift amount corresponding to an optical path length between the reference surface and the surface of the object to be measured when i-th interference image is generated.
5. The interference measurement system according to claim 4 , wherein
the error detection part extracts information of the first Lissajous figure having an elliptical shape including the center coordinates (u 0 , v 0 ), a major axis a x , a minor axis a y , and an angle θ of an axis of the ellipse from the first Lissajous figure, in which u=I cos (x n , y m ) and v=I sin (x n , y m ) are plotted with the horizontal axis as a u-axis and the vertical axis as a v-axis, and
the correction part corrects the sine wave component and the cosine wave component using the following equation such that the first Lissajous figure approaches the second Lissajous figure whose center coordinates are the origin
I sin ′( x n ,y m )= I sin ( x n ,y m )− v 0
I cos ′( x n ,y m )= I cos ( x n ,y m )− u 0 [Equation 2].
6. The interference measurement system according to claim 5 , wherein
the correction part rotates a Lissajous figure, which consists of the sine wave component and the cosine wave component after the correction of the center coordinates, by −θ according to the following equation and then further corrects the Lissajous figure to make the length of the major axis coincides with the length of the minor axis, such that the first Lissajous figure approaches the second Lissajous figure
[
I
sin
″
(
x
n
,
y
m
)
I
cos
″
(
x
n
,
y
m
)
]
=
R
(
θ
)
[
a
y
/
a
x
1
]
R
(
-
θ
)
[
I
sin
′
(
x
n
,
y
m
)
I
cos
′
(
x
n
,
y
m
)
]
.
[
Equation
3
]
7. The interference measurement system according to claim 6 , wherein
the geometry calculation part calculates, by using the sine wave component and the cosine wave component corrected by the correction part, a phase difference φ nm from a reference height at a position (x n , y m ) on the surface of the object to be measured corresponding to a pixel (x n , y m ) of the interference image, according to the following equation,
φ
n
,
m
=
tan
-
1
-
I
sin
″
(
x
n
,
y
m
)
I
cos
″
(
x
n
,
y
m
)
[
Equation
4
]
and calculates, by using the phase difference φ nm , the height h nm at the position (x n , y m ) on the surface of the object to be measured, according to the following equation,
h
n
,
m
=
λ
4
π
φ
n
,
m
[
Equation
5
]
where λ is a wavelength of the laser light.
8. An interference measurement method for measuring a shape of an object to be measured, which is executed by a computer, comprising the steps of:
irradiating the surface of the object to be measured with laser light;
capturing an interference image of reference light reflected at a reference surface that is movably provided on an optical axis of the laser light and measurement light reflected at the surface of the object to be measured;
acquiring a plurality of the interference images based on a plurality of optical path lengths between the reference surface and the surface of the object to be measured from the interference measurement apparatus;
calculating a sine wave component and a cosine wave component of an interference signal for each pixel in the plurality of the interference images, respectively;
detecting an error between a first Lissajous figure constructed on the basis of the sine wave component and the cosine wave component for each pixel and an ideal second Lissajous figure;
correcting the sine wave component and the cosine wave component for each pixel on the basis of the error; and
calculating surface geometry of the object to be measured on the basis of the corrected sine wave component and cosine wave component.