FIELD OF THE INVENTION
The invention generally relates to a method for measuring thermal properties of solids and more particularly relates to a method for estimating thermal diffusivity of dielectric solids using CCD camera.

BACKGROUND OF THE INVENTION
Thermal diffusivity is one of the important thermo-physical properties of current interest. Based on the measurement of thermal response, optical techniques can be broadly classified into three groups, firstly thermal response measured inside the sample e.g. thermal lensing; secondly thermal response measured outside the sample e.g. Photo-thermal beam deflection technique, and thirdly thermal response measured at the interface, the only technique used here is the Dew-film boundary translatory motion technique.

The major advantage of the dew-film boundary translatory motion technique is the magnitude of change in refractive index at the interface which is 0.330 for the given thermal input. In comparison to other optical methods, the thermal response is high (four orders of magnitude). The major drawback of said method is that it requires the knowledge of several parameters like percentage of relative humidity, dew-point temperature, step-temperature value, ambient temperature, velocity etc. It requires several measurements, and also the temporal resolution of camera is not adequate as the resolution is limited by number of frames/second.

In this existing technique of dew-film boundary translator motion technique for estimation of thermal diffusivity the position dependent velocity of optical mark is measured at sample-solid. The knowledge of several ambient parameters like percentage of relative humidity of ambient, velocity of optical mark, ambient temperature, dew-point-temperature, and input-temperature are mandatory to estimate thermal diffusivity of solid in this case.

Therefore, in order to eliminate the number of measuring quantities and to improve the spatial and temporal resolution, there exist a need to provide a method for estimating thermal diffusivity without using the traditional methods involving the number of measuring quantities like ambient-humidity, ambient-temperature and excitation/input temperature. The present invention provides one such method that estimates thermal diffusivity of dielectric solids, based on location of optical mark using CCD camera.

OBJECT OF THE INVENTION

The main object of the present invention is to provide a method for estimating the thermal diffusivity of dielectric solid using a ‘single- input-image’ captured by CCD camera.

Another object of the present invention is to provides a novel ‘Thermal activation’ simultaneously in both sample-solid, and reference-solids such that ’the characteristic moving boundary layer‘ is generated ‘within the thermal boundary layer’.

Another object of the present invention is to convert the problem of measurement of thermal diffusivity into measurement of length or distance of thermally activated region. The boundary of thermal activation is exhibited by optical mark.

Another objective of the present invention is to provide an approach for direct measurement of thermal diffusivity with a novel algebraic relationship using modified boundary value problem of heat conduction.

Yet another object of the present invention is to estimate the thermal diffusivity of dielectric solids directly by utilizing a measured spatial data using image processing technique and a given diffusivity of reference solid.

SUMMARY OF THE INVENTION

The present invention relates to a novel approach to measure thermal diffusivity of dielectric solid using a single-image captured by CCD camera.

The main embodiment of the present invention is the method to activate thermally selective behaviour of solid with suitable thermal excitation. Under favourable condition ’the characteristic moving boundary layer‘ is generated inside both reference-solid and sample-solid and within the thermal boundary layer thickness. The location of characteristic moving boundary layer is governed by thermal diffusivity of solid. The said moving boundary layer exhibits a visible optical mark at lateral surfaces of solid.

Another embodiment of the present invention is that by using CCD camera single input image is captured which consist of thermally activated solid-sample and reference solids indicated by optical mark.

Yet another embodiment of the present invention is that image processing technique is utilized to measure the spatial distance with sub-pixel accuracy. Hence thermal diffusivity is direcly measured.

Other objects and advantages of the present invention will become apparent from the following description.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be better understood after reading the following detailed description of the presently preffered aspects with reference to the apended drawings:

Figure 1a) shows the solid at ambient temperature and uniform temperature inside the ambient;

Figure 1b) shows the boundary conditions, and location of thermal layer d(t) without thermal activation;
Figure 2a) shows after thermal activation; at time t1 seconds, within the thermal boundary layer the characteristic moving boundary layer exist at distance ?BC(t1) indicated by optical mark;

Figure 2b) shows after thermal activation; at time t2 seconds both layers are moved and only characteristic boundary layer exhibits optical mark at ?BC(t2).

Figure 3 shows isometric view of 2a) that thermal layer and characteristic boundary layer exist simultaneously and ?BC is the region indicated by optical mark.

Figure 4 shows a Schematic diagram where 4a), & 4b) shows before thermal activation of Reference solid and sample solid respectively at time t=0 second, 4c), & 4d) shows after thermal activation of Reference solid and sample solid respectively at time t=t1 seconds.

Figures 5a), 5b) and 5c) shows Cropped input image, processed-image and Zernike moment image respectively.

Figure 6 shows a graphical plot to indicate location of optical mark in mm at different instant of time for both sample-solid and reference-solid.

Figure 7 represents a graphical plot showing the linear fitting of data represented in Figure 6 for both sample-solid and Reference-solid.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides a novel optical method to measure the thermal diffusivity of dielectric solid using single input image from CCD camera.

The present invention, explore the thermally-selective behaviour of solids, which is exhibited by suitable thermal excitation resulting from step-temperature excitation via Surface-cooling. Thermally-activated solid produces a visible optical mark at lateral surfaces of the both sample-solids, and reference-solids. An Optical mark (at the interface between solid and ambient) is defined as the distance from the origin beyond which the refractive index at the interface is unaffected. The moving boundary of an optical mark indicates a unique temperature and a unique non-dimensional temperature irrespective of solid.

In the present invention, the method is realised using the apparatus, which include solid-sample under test, reference solid-sample, cooler with power supply, CCD camera, and a computer with a module. When the solids are subjected to step-temperature excitation via cooling and after some time elapses, the position of dew-film at the lateral surface of the solids which is depend on thermal diffusivity of solid is captured by CCD camera.

Further, in the present invention a module is provided in-which thermally selective behaviour of solid is activated with suitable thermal excitation. Under favourable condition the optical mark is visible and indicates the boundary of characterisitic moving boundary layer. The location of characteristic moving boundary layer is governed by thermal diffusivity of solid. The said moving boundary layer exhibits a visible optical mark at lateral surfaces of solid. Further, the said module directly relates the optical mark of solids, with its diffusivities.

The modified boundary value problem of heat conduction is special type of thermal boundary value problem in which the moving boundary-temperature, and the non-dimensional temperature are indicated by optical mark.

Another embodiment of the present invention is that by using CCD camera, the location of optical mark for both solids are captured in a single frame and using image processing technique, the location of optical mark in both solids are measured in pixel level based on Principle component analysis. A Zernike moment is utilized to improve spatial-resolution of optical mark and obtain sub-pixel resolution with fourth decimal place. Thermal diffusivity of solid under test is computed for the given thermal diffusivity of reference-solid, and the measured optical mark of both solids by the said image processing method.

The present method eliminates the need for measurement of ambient-related physical quantities like relative ambient humidity, velocity of optical mark, dew-point temperature, ambient temperature and also excitation/input-temperature to estimate the thermal diffusivity of dielectric solids. By obtaining the position of an optical mark in sample-solid with respect to the data of reference solid, thermal diffusivity of sample-solid is directly computed.

In the aforesaid module, consider a semi-infinite solid 0=x<8 surrounded by its ambient as shown in Fig 1(a) and Fig1(b) and refered to as 1, Solid is initially at an ambient temperature Ti indicated as 2 in both Fig 1(a) and Fig 1(b). For time t>0 the surface at x=0 is kept at constant temperature T0 indicated as 3 in both Fig 1(a) and Fig 1(b). Also for time t>0 there will be no heat flux q in x=?(t). For all practical purposes the region x=?(t) is at the initial temperature Ti. The boundary-value problem of heat conduction is given as:

(?^2 T(x,t))/(?x^2 )= 1/a (?T(x,t))/?t in 0=x<8 , t>0 ----(1)

T(x,t)= T_0 at x=0 , t>0 ---(2)

T(x,t)= T_i in 0=x<8 , t=0 ---(3)

q(x,t)= 0 in x=?(t) , t>0 ----(4)

[024] The solution of the problem is obtained by the differential equation of heat conduction using the integral method given by [1]

(T(x,t)-T_i)/(T_0- T_i ) = [1 - x/d ]3 ---(5)
From equation (4) it is known that beyond thermal layer ? shown as region 4 in Fig 1b) no heat flow ocurs hence initial temperature remain the same. The temperature at thermal boundary layer is 1% that of initial temperature. The relationship between thermal layer and thermal diffusivity of material is given by equation [1].

d= v24at ---(6)

and the corresponding temperature distribution is given by

(T(x,t)-T_i)/(T_0- T_i ) = [1 - x/v24at ]3 0=x=? ----(7)
[026] One- dimensional heat flow is established by subjecting solid to suitable surface temperature T0 by cooling at x=0; indicated with the reference numeral 3 in Fig 2(a), a solid exhibit thermally selective behaviour i.e., ‘within thermal layer ? indicated in region 4’ a characteristic moving boundary layer ?BC is created indicated as region 5 (in Fig 2(a) and Fig 2(b) . The position of moving thermal layer and characteristic moving boundary layer ?BC at different instant of time t1 and time t2 seconds are shown in figure 2(a) and Figure 2(b) respectively. 3D Isometric view of Fig 2(a) is shown in Fig 3, and in Fig 3, the reference numerals 1, 2, 3, 4, and 5 indicates Ambient, initial temperature Ti of Solid, Step-temperature T0 at x=0, thermal boundary layer and Optical mark respectively.

[027] The thermally selective behaviour of solid is independent of solid and is utilized to separate a unique isothermal surface (lies between T0 and Ti) from the temperature profile in both sample-solid, and reference-solids. Under identical experimental condition at optical mark LHS of equation (7) is numerically same for both the solids, however, its locations are governed by diffusivity of solids. The time dependent position of the said boundary is shown in figure 2(a) and 2(b). The characteristic boundary is named as Dew-film boundary and its thickness from the origin is named as optical mark. Assume temperature Tdp at which the thermally selective behaviour is activated, and assume its magnitude is equal to some temperature closer to dew-point temperature of ambient.

After thermal activation in both solids, at time t1 second, dew-film boundary layer occurs in both samples at different locations as shown in Figure 4c & 4d. Consider at optical mark, apply in equation (5), then, T represents Tdp, and x represents ?BC.

Additional boundary conditions are provided and as follows,

T(x,t)= Tdp at x= ?BC , t>0 ----(8)

Ti < Tdp < T0 ----(9)

Substitute equation (8) in equation (5), then

For reference sample,

(T_(dp(x,t)) -T_i)/(T_0- T_i ) = [1 - ?_BC1/(d_1 (t_1)) ]3 --(10)

For sample under test,

(T_(dp(x,t)) -T_i)/(T_0- T_i ) = [1 - ?_BC2/(d_2 (t_1)) ]3 ---(11)

Neglecting thermal contact resistance, In Eq (10) and Eq (11) left hand sides represents a unique, and identical Non-dimensional temperature, equate (10) and (11); apply Eq (6) and simplify we get,

?_BC1/v(24a_1 t_1 ) = ?_BC2/v(24a_2 t_1 ) ----- (12)

Rearrange the above algebraic equation, thermal diffusivity of sample under test is given by

a_2 = a_1 ( ?_BC1/?_BC2 )2 ---(13)

Where, a1 is thermal diffusivity of reference sample. ?BC1 and ?BC2 are optical mark at reference and sample solid respectively.

Conduct the experiment, to capture the ?BC1 and ?BC2 which can be seen with the naked eye and capture the image using CCD camera. For the given thermal diffusivity of reference-sample a1, thermal diffusivity of sample under test a2 is computed.

Using a user interface, accurate measurement of the position of optical mark ?BC1, and ?BC2 is obtained using Principle component analysis (PCA) and Zernike moment. First, PCA is utilized to locate the boundary of ?BC1 and ?BC2 from the input image with the resolution of pixels. For more accurate measurement of position of optical mark subpixel method is utilized based on Zernike moment. Fig 5a), 5b) and 5c) consist of a pair of images wherein left-one is image of reference solid & right-one is the image of sample under test after t1 seconds. The procedure to obtain thermal diffusivity is given below:

1. Conduct experiment to obtain an Input image with Optical marks ?BC1, and ?BC2.
2. Read the images using appropriate tool (e.g. Matlab).
3. Convert them into gray scale.
4. Crop according to area of interest (as shown in figure 5a)).
5. Apply Principle Component Analysis.
6. Reconstruct image using Optimum principal components.
7. Find pixel level edge location of boundary for both samples using gradient operator like Prewitt. Fix proper threshold value for finding the appropriate boundary (as shown in Figure 5b)).
8. Find Optical mark of both samples using subpixel edge detection method (as shown in Figure 5c)).
9. Using equation (13) to calculate Thermal diffusivity of unknown Solid.

Further, Figure 6 as depicted in the drawings shows a graphical representation of location of optical mark in mm against time window for both Reference-solid and sample-solids.

Figure 7 as depicted in the drawings represents a Linear fitting of data mentioned in Figure 6 of the drawings.

In present invention, the measurement of thermal diffusivity is stable for the time window of 65 seconds to 135 seconds for a Relative Humidity present in the range of 55% to 65%. The time window can be altered by changing boundary conditions like ambient temperature Ti, percentage of Relative Humidity, and Step-Cooling temperature T0.

Although the embodiments herein are described with various specific embodiments, it will be obvious for a person skilled in the art to practice the invention with modifications. However, all such modifications are deemed to be within the scope of the invention.

Claim:
1. An optical method for estimating thermal diffusivity of dielectric solid, wherein the method comprising:

selecting a sample solid and a reference solid;
subjecting the said solids to Thermally activation by step-temperature excitation via cooling;
obtaining visible optical mark at lateral surfaces in said solids indicating the boundary of characteristic moving boundary layer which is governed by thermal diffusivity of solid;
capturing the said thermal diffusivity of solid by CCD camera; and
computing the thermal diffusivity of sample solid using diffusivity of reference solid and the measured optical mark of both solids.

2. The method as claimed in claim 1, wherein the CCD camera captures a single input image.

3. The method as claimed in claim 2, wherein in the said input image the location of optical mark for both solids are captured in a single frame and using image processing technique.

4. The method as claimed in claim 2 and 3, wherein the location of optical mark in both solids are measured in sub-pixel level.

5. The method as claimed in claim 1, wherein measurement of thermal diffusivity is stable for time window of 65 seconds to 135 seconds for a Relative Humidity in the range of 55% to 65%.

6. The method as claimed in claims 1 and 5, wherein the time window is altered by changing boundary conditions like ambient temperature Ti, percentage of Relative Humidity, and Step-Cooling temperature T0.