Thickness measurement method, thickness measurement device, defect detection method, and defect detection device
Method for measuring a depth of a defect inside an inspection object is provided. The method comprises steps of: generating thermal image data corresponding to a temperature of a surface of the inspection object by photographing a heated surface of the inspection object at a predetermined time interval by a photographing device; obtaining a temperature curve showing a temporal change in temperature of the surface of the inspection object based on the thermal image data; fitting a theoretical equation obtained from a heat conduction equation including a parameter related to the depth of the defect of the inspection object to the temperature curve to obtain a theoretical curve showing a temporal change in temperature of the surface of the inspection object; and obtaining the depth of the defect of the inspection object based on a value of the parameter in the theoretical equation corresponding to the theoretical curve.
1. A thickness measurement method for measuring a thickness of a measurement object, comprising the steps of:
heating a surface of the measurement object by a heating device;
generating thermal image data corresponding to a temperature of the surface of the measurement object by photographing the heated surface of the measurement object at a predetermined time interval by a photographing device;
obtaining a temperature curve showing a temporal change in temperature of the surface of the measurement object based on the thermal image data generated by the photographing device;
fitting a theoretical equation derived from a heat conduction equation and including a parameter which is an unknown quantity to the temperature curve to obtain a value of the parameter; and
obtaining the thickness of the measurement object from the obtained value of the parameter,
wherein the parameter is one related to the thickness of the measurement object; and
the theoretical equation is represented by Eq. (1)
[
Math
1
]
T
(
L
,
t
)
=
a
(
bt
+
1
3
+
2
π
2
∑
n
=
1
∞
-
1
n
2
e
-
bn
2
π
2
t
)
(
1
)
where T(L,t) is the temperature [K] of the surface of the measurement object; L is the thickness [m] of the measurement object; t is time [s]; and a and b are the respective parameters, and wherein
the two parameters a and b are represented by Eqs. (2) and (3), respectively,
[
Math
2
]
a
=
F
0
L
k
(
2
)
b
=
α
L
2
(
3
)
where F 0 is a heat flux [W/m 2 ]; ρ is a density [kg/m 3 ] of the measurement object; c is a specific heat [J/(kg·K)] of the measurement object; ρc is a volumetric specific heat [J/(m 3 ·K)] of the measurement object; k is a heat conductivity [W/(m·K)] of the measurement object; and α=k/ρc is a thermal diffusivity [m 2 /s] of the measurement object.
2. The thickness measurement method according to claim 1 , wherein
the heating device starts heating the surface of the measurement object in a step-like manner, and wherein
simultaneously with the start of heating of the measurement object, the photographing device starts photographing the surface of the measurement object to start generation of the thermal image data.
3. The thickness measurement method according to claim 1 , wherein
the theoretical equation is an equation based on a step response.
4. The thickness measurement method according to claim 3 , wherein
the theoretical equation includes at least two independent parameters.
5. The thickness measurement method according to claim 1 , wherein
the theoretical curve is obtained by using a nonlinear least-squares method to perform the fitting such that a residual is minimized.
6. The thickness measurement method according to claim 1 , wherein
the theoretical equation includes a heat transfer coefficient related to heat transfer that is movement of heat from the surface of the measurement object to a fluid in contact with the surface.