US 12,196,540 B2 · Method for measuring the diameter of filament diffraction fringes by calculating the frequency domain

Abstract

A method for measuring the diameter of filament diffraction fringes by frequency domain calculation comprising: building a set of diffraction optical path measurement system and capturing diffraction fringe images; determining the starting point of the imaging range; Simulating the electromagnetic field propagation process in Fraunhofer diffraction, and determining the optimal fringe range considering the noise caused by the difference in CCD sensitivity; Finally calculating the filament diameter by Fourier transform for different lengths of fringe. The final value of the calculated filament diameter is obtained by fitting an envelope to the variation of the diameter. The invention is simple in calculation and has little dependence on the experimental device, which means the superiority of using the frequency domain for parameter measurement, and the measurement accuracy is in the sub-nanometer level. In addition, the invention proves the feasibility of extracting the fringe period information in the frequency domain.

A method for measuring a diameter of filament diffraction fringes by calculating the frequency domain, comprising:

building an optical path system required for a diffraction measurement, said building comprising:
using a Fraunhofer diffraction device to emit a laser that passes through two mirrors and an optical power attenuator, the laser being vertically incident on a filament to be measured to generate diffraction fringes, the diffraction fringes being converged by a convex lens to a charge coupled device (CCD) at a focal point of the CCD to obtain a diffraction fringe image, where the CCD is connected to a computer to capture the diffraction fringes by programs wherein a center of the two mirrors, a center of the optical power attenuator, a center of the filament, and a center of the convex lens lie on a same optical axis, while the CCD is deviated from the optical axis to avoid damage to the CCD due to excessive light converging energy;
deriving a calculation and an error of a diffractive filament diameter, said deriving comprising:
theoretically analyzing an error in said diffraction, wherein the filament is irradiated uniformly by a plane wave and a field source distribution at the filament is E(Y′, 0)=A0, where Y′≤±b/2, and b is a diameter of the filament, and Y′ is a distance at the filament in a direction perpendicular to a direction of light, and wherein when a Fraunhofer diffraction approximation condition is satisfied, an expression of the electric field of a light intensity distribution on an observation screen is:
E
⁡
(
Y
,
f
)
=
exp
[
i
⁢
k
⁢
f
]
i
⁢
k
⁢
f
⁢
exp
[
i
⁢
k
2
⁢
f
⁢
(
Y
2
)
]
⁢
∫
∫
plane
⁢
E
⁡
(
Y
′
,
0
)
⁢
exp
[
-
ikY
′
⁢
sin
⁢
θ
Y
]
⁢
d
2
⁢
Y
′
,
(
1
)
wherein, θY is an angle between a direction of a wave vector and a Y direction, k is a wave vector of the laser, Y′ is the distance in the direction of the filament diameter, and f is a focal length of the convex lens, and an intensity distribution of a light field is expressed as:
I
=
E
⁢
E
*
≈
A
0
2
λ
⁢
f
⁢
sin
⁢
c
⁡
(
b
⁢
sin
⁢
θ
Y
/
λ
)
2
,
(
2
)
If Y/f<<1, sin θY≈sin(arctan(Y/f))≈Y/f, then formula (2) is:
I
≈
A
0
2
λ
⁢
f
⁢
sin
⁢
c
⁡
(
bY
/
λ
⁢
f
)
2
.
(
3
)
wherein Y=y−y0(y=y′d), d is a pixel size of the CCD, and Y is a number of pixels along a y axis on the imaging plane, y′ is the pixel point distance of the diffraction fringe on the CCD, and y is a distance along the y axis, and y0 is a center position coordinate of the zero-order fringe;
formula (4) is obtained by a fast Fourier transform of formula (3):
F
⁢
{
I
}
=
1
b
2
⁢
i
⁢
e
-
ivy
0
⁢
f
⁢
λ
(
(
b
-
fv
⁢
λ
)
⁢
(
Γ
[
-
1
,
i
⁡
(
-
b
+
fv
⁢
λ
)
⁢
(
y
max
-
y
0
)
f
⁢
λ
]
-
Γ
[
-
1
,
i
(
b
f
⁢
λ
-
v
)
⁢
y
0
]
+
Log
[
y
max
-
y
0
]
-
Log
[
i
⁡
(
-
b
+
fv
⁢
λ
)
⁢
(
y
max
-
y
0
)
f
⁢
λ
]
-
Log
[
-
y
0
]
+
Log
[
i
(
b
f
⁢
λ
-
v
)
⁢
y
0
]
)
-
2
⁢
f
⁢
λ
⁢
v
⁡
(
Log
[
-
y
0
]
-
Γ
[
-
1
,
iv
⁡
(
y
max
+
y
0
)
]
+
Γ
[
-
1
,
-
iv
⁢
y
0
]
-
Log
[
y
max
-
y
0
]
-
Log
[
-
iv
⁢
y
0
]
⁢
Log
[
iv
⁡
(
y
max
-
y
0
)
]
)
-
(
b
+
f
⁢
λ
⁢
v
)
⁢
(
Γ
[
-
1
,
i
⁡
(
b
+
fv
⁢
λ
)
⁢
(
y
max
-
y
0
)
f
⁢
λ
]
-
Γ
[
-
1
,
-
i
⁡
(
-
b
+
fv
⁢
λ
)
⁢
y
0
f
⁢
λ
]
+
Log
[
y
max
-
y
0
]
-
Log
[
i
⁡
(
b
+
fv
⁢
λ
)
⁢
(
y
max
-
y
0
)
f
⁢
λ
]
-
Log
[
-
y
0
]
+
Log
[
-
i
⁡
(
b
+
fv
⁢
λ
)
⁢
y
0
f
⁢
λ
]
)
)
(
4
)
wherein v is a spatial frequency extreme point, ymax is a maximum fringe value, and formula (5) is obtained by calculating an extreme value of formula (3):
b−fλv=0 (5);
performing a Fourier transform on the diffraction fringes of the filament, and the extreme value point (v) in the frequency domain is extracted to solve the diameter of the filament;
and
shearing, scaling and splicing the diffraction fringes;
performing an algorithmic processing, comprising:
capturing filament diffraction fringe images with the CCD;
cutting, filtering and preprocessing the filament diffraction fringe images:
extracting one-dimensional diffraction fringes from the filament diffraction fringe images, and extracting a size range of local diffraction fringes;
forming pseudo-fringes by compressing and splicing the local diffraction fringes;
obtaining frequency domain information of the diffraction fringes by performing a Fourier transform on the pseudo-fringes;
calculating the diameter of the filament, and obtaining a change curve of the diameter of the filament by continuously extending the diffraction fringes;
and
extracting an upper interval limit and a lower interval limit of the filament diameter, and solving a diameter convergence value of the filament;
and
measuring the filament diffraction, comprising:
determining the size range of local diffraction fringes;
directly reducing a proportion of the local diffraction fringes causes the light intensity of the pseudo-fringes deviating from a light intensity of the diffraction fringes;
a light intensity extreme value ratio of the diffraction fringes satisfies formula (8):
I
n
+
1
I
n
=
(
1
-
1
n
-
k
+
3
2
)
2
,
(
8
)
wherein In is an extreme value of a light intensity of nth order fringes, and a kth bright fringe is a central bright fringe of the image;
and
obtaining diffraction fringes by simulating light field propagation using COMSOL, wherein some of the diffraction fringes are used as a basis for repeated splicing, and the central bright fringe and 1st-3rd order bright fringes are not selected, and simulated fringes in different ranges are analyzed to obtain an optimal fringe range A<y<B, a scale factor of the simulated fringes is defined as y/λb, and an optimal value range is:
C<y/λb<D, where A is a position of the two fringes at a fourth level of the diffraction stripe, and B is a position of the bright stripe at an eleventh level, C is denoted as equal to A/λb, and D is denoted as equal to B/λb;
and
calculating the filament diameter, said calculating comprising:
using Butterworth low-pass filtering to process noise to obtain a smooth fringe curve, wherein the diameter of the filament to be measured is x, the focal length of the lens is f, a minimum pixel point of the CCD is d, and a size of a local fringe image is l;
excluding the bright fringes in the center and the bright fringes of the 1st-3rd order;
splicing cropped pseudo fringes to the last bright fringes of a segment;
and
then repeating said using, said excluding and said splicing of the cropped pseudo fringes,
wherein a diameter of the filament gradually converges to an interval;
a peak point and a valley point in the smooth fringe curve are extracted, and the peak point and the valley point are fitted respectively to obtain the convergence interval of the diameter;
a fitting equation is as follows:
Z
=
k
(
1
y
-
y
*
)
+
C
(
9
)
wherein, k, y*, C are constants of the fitting equation, and y is the lengths of the fringes, and
wherein a positive error peak fitting and a negative error peak fitting curve are obtained by fitting, and the diameter of the filament is calculated as {tilde over (b)}=Cup+Cdown, to obtain a relationship between the diameter of the filament and a length of the fringe wherein Cup is the positive error peak fitting curve and Cdown is the negative error peak fitting curve.

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Method for measuring the diameter of filament diffraction fringes by calculating the frequency domain

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Method for measuring the diameter of filament diffraction fringes by calculating the frequency domain

Life of this patent

Abstract

Claims1