Measuring film thickness with Dual-laser imaging method

Abstract

In order to realize the online thickness measurement of thin films, an automatic film thickness measuring system was established, and its optical design, mechanical structure design, as well as the analysis and evaluation of the optical aberration based on the software of ZEMAX were researched. Project two laser beams vertically onto the same position of the film respectively from upper and lower side there will be two round spots on the film surfaces, image the two spots onto the image detector the film thickness can be got according to the relationship between the measured film thickness and the orthocenters of the upper and lower imaging spots. During the calibrating experiment, a nonlinear correction method was proposed. Experimental results indicated that the measurement precision is±1 μm. After a period time of three months online working, the system was proven to have the characteristics of good stabilization, high precision and convenient maintenance.

Keywords

Film measuring laser triangulation measurement thickness measurement optical imaging measurement

1 Introduction

Thickness detecting of the lithium cell membranes has drawn much attention due to the uniformity of the membrane thickness influences the performance of the lithium cell significantly [1]. Meanwhile, the online thickness measuring technique is conductive to the improving of the manufacturing efficiency and the production automation degree while reducing the human resource cost and raw material waste.

There are mechanical methods, radial methods and optical methods to get the thin film thickness. The mechanical methods mainly include micrometer caliper method and probe method. The accuracy of the micrometer caliper is merely 0.01 mm, its measuring accuracy is significantly influenced by the human factors, which limit its industrial application. The accuracy of the probe method can reach nanoscale which makes it one of the most precise gauging ways. Thickness information is got by gliding the probe over the film surfaces, however, it will leave scratches if the film is made of soft material. The radial methods are often used in steel plant for the online thickness gauging, its precision is about 0.2% of the film thickness, but it costs much to reduce the radiation hazard. There are various optical methods for the thin film thickness measurement such as the multiple-beam interferometry method [2], the spectral reflectance method [3], the phase-shift interferometry method [4], and the Ellipsometry method, etc [5]. Most of these methods have complicated optical systems which render the users difficult to maintain the stability of the apparatuses.

Laser triangulation is a method with simple structure and high accuracy that can be applied in off-line thickness measurement [6, 7] or distance measurement [8]. Differential laser triangulation [9] can be used for online thickness measurement which is composed of two laser triangulation measurement systems that are placed up and down symmetrically (as shown in Fig. 1). In dynamic measuring process, the distance information’s from the gauging arms to the film surfaces are achieved by the two laser sensors, the film thickness can be get: h = H-H₁-H₂ (1). There exist problems that the synchronism of the two image detectors is inevitable and a small deformation of the U shape gauging arm will misplace the two measuring systems apparently, which will cause the measuring error while the measured is dithering in the online measuring process. To solve these two problems, a modified measurement model called dual laser imaging method was proposed (as illustrated in Fig. 2). There is only one image detector is this measuring model, it eliminates the measuring error induced by the asynchronism of the two image detectors and decreased the measuring error caused by the deformation of the U shape gauging arm as well. It can be seen as well that the angle between the incident light and the reflection light become larger comparing to the dual laser triangulation method, hence, the resolution of the system was increased [10]. In summary, the new measuring model not only has simple mechanical structure and good stability but also has high precision.

Fig.1

Schematic of differential laser triangulation.

Fig.2

Schematic of Dual-laser imaging.

2 Working principle and the characteristic

As revealed in Fig. 2, each of the two lasers projects a convergent beam vertically onto the film which was requested to be placed in the view of the image detector, part of the diffuse reflection lights are focused on the image detector by the lens group, the imaging information was transmitted to the image processor, the film thickness can be acquired according to the relationship between the orthocenter coordinates of the imaging spots and the film thickness.

The locations of the components are also shown in Fig. 2. The lasers were installed symmetrically in the front end of the U shape gauging arms, and the axes of the upper and lower laser beams need to be concentric through monitoring the direction of the laser devices, because the deviation of the axes will bring measurement error. The optical axis of the lens group must be perpendicular with the photo surface of the image detector. The diagram was designed to have two vertical symmetric layout photic holes, which insures the vertical intensity of the imaging spots and cut down the impact of the environmental stray light. These design models improve the imaging quality of the optical system as the film thickness is related to the vertical shape and size of the two imaging spots. The system has the following advantages: it is convenient to install and maintain for its simple mechanical structure, and the defocus and dispersion of the imaging spots were decreased to the largest extent as the object distance is constant, what’s more, the accuracy and resolution of the system was significantly improved as a result of adopting the 4f optical designing principle.

3 Analysis of the optical system

The optical imaging path of the system is shown in Fig. 3, from which we can figure out that the focal length F′ of the lens group is constant, so does the image distance between the lens group and the image detector, besides, the refractive index n′ equals to n as the optical system is placed in the same medium. Thus, the modulus of the two focal length of the system is equivalent while the mark is opposite: $F^{'} = - F$ (1)

Fig.3

Schematic diagram of optical imaging system.

The conjugate object distance can be deduced out by Gauss formulas $1 / L^{'} - 1 / L = 1 / F^{'}$ (2)

Take the Newton formulas: ${XX}^{'} = {FF}^{'}$ (3)

As the Fig. 3 shows: $L = F + X$ (4) $L^{'} = F^{'} + X^{'}$ (5)

Combine Equations (2–6) result that: $- X = - F = X^{'} = F^{'} = - L / 2 = L^{'} / 2$ (6)

The paraxial magnification of the optical system can be obtained: $β = - Y^{'} / Y = - 1$ (7)

This optical system is exactly a 4f optical model as what Equation 7 has revealed. Since the size of the CCD (Charge Coupled Device) target surface is just 1/4 inches, its view field is rather small, the optical system is approximately a linear model which repro ratio is 1:1 while ignoring the shape distortion of the CCD target. Respectively, the pictures of imaging light path, spot diagram, aberration curves as well as the wavefront aberration curves.

The measuring accuracy of the optical system is significantly impacted by the quality of the imaging spots. The sophistication of the designing optical system is the paramount factor that influencing the shape of the spots, then comes with the position and diameter of the diaphragm, also, the assembly quality as well as the locating accuracy of the components takes an unignorable role, and it is essential to guarantee the surface forming and smoothness of the lens. Beyond these factors, the coaxalities of the two lasers together with the lens group in the tube also affect the measurement accuracy partially. It has been proven that the surface topology affects the performance of the laser triangulation sensor as well [11].

The spot diagram reveled the density of the light spots based on the geometric optical imaging theory, it is a very effective method to evaluate the imaging quality of an optical system. Usually, a dispersion spot is an area that contains more than 30% of the light-spots or rays, and the reciprocal of the diameter of the dispersion spot is the so called optical resolution. If a dispersion spot consists of too little light-spots, the system resolution can not reach sub-pixel, while the sensitivity of the system will be greatly decreased if the dispersion spot contain too many light-spots. When the dispersion spot is compose of approximately 3∼5 light-spots, the system has both a sub-pixel resolution and a high measuring accuracy. It can find that the imaging spot met the requirements of RMS <3 μm and GEO <7 μm, the dimension of the imaging spot is small enough to fulfill the precisely industrial measurement. And revealed that the aberration and the wave aberration of the optical system obey the Rayleigh criterion as the maximal aberration scale is±10 MICRONS and the maximal wave aberration scale is 0.1 WAVES, it indicated that the aberration and the wave aberration satisfied the requirement of the optical system.

It has been expounded previously that the measuring accuracy is influenced by the diameter of the aperture and the coaxality of the lens group. The larger the aperture the bigger the imaging spot will be and the lower accuracy the measurement system will has. Reversely, too minor aperture will result in no images. Hence, the diameter of the aperture in this optical system is a merit value. Figure 4(a) shown the imaging spots with the diaphragm removed from the optical system, the longitudinal size of the two imaging spots are so long that it will result in considerable instablity in finding the vertical barycenter of the two spots. If the lens group were misaligned, the imaging spots will be wedge-shaped as revealed in Fig. 4(b). The ideal imaging spots has a horizontal distribution shape with a tiny longitudinal size just as Fig. 4(c) shown, because the two spots both have a pediocratic vertical orthocenter.

Fig.4

The image in the field of view.

4 System calibration and nonlinear correction

The spots spacing on the imaging plane is considerate to be linear relationship with the thickness of the measurand according to the geometrical optics [12]. However, it is rather difficult to guarantee the surface accuracy and roughness of the lens in the grinding process, the defect of the lens geometry can cause irregular transmission of the light, and the nonuniformity of the optical materials will result in the difference of the refractive index in different part of the lens, the locating accuracy of the components can hardly meet the requirements of the optical system, what’s more, the drifting of the laser is inevitable as the unstable luminous of the light-emitting junction, in addition, there exist nonuniformity among the CCD pixels, thus, nonlinearity effect will come out during the measurement process, that is the fluctuation of the spots spacing while placing the measurand in different sites within the range, the system as shown in Figs. 5 and 6.

Fig.5

Diagram of the measurement position.

Fig.6

Dual-laser imaging thickness gauge.

In order to reduce the nonlinear effect, a nonlinear correction method was proposed that is to get the fitted curves between each laser spot along with the measurand location on the image detector coordinate respectively, then the thickness was considerate to be relevant with the vertical ordinates of the two spots instead of the spots spacing.

Placing a measurand within the gagebeam, the upper and lower surface can be seen as two planes which height are h₁ and h₂, and the vertical orthocenter ordinates of the two imaging spots seen as y₁ and y₂ (as shown in Fig. 7). Use third order function to get the fitted equation. The correlation between the height of the upper surface of the measurand h₁ and the vertical ordinate of the imaging spot y₁ is set as: $h_{1} = a_{0} + a_{1} y_{1} + a_{2} y_{1}^{2} + a_{3} y_{1}^{3}$ (8)

Fig.7

Schematic diagram of imaging.

Similarly, the correlation between the height of the lower surface of the measurand h₂ and the vertical ordinate of the imaging spot y₂ is: $h_{2} = b_{0} + b_{1} y_{2} + b_{2} y_{2}^{2} + b_{3} y_{2}^{3}$ (9)

Thus, the thickness of the measurand can be got: $H = h_{2} - h_{1}$ (10)

Unite Equations (9–11), the film thickness can be expressed as:

$\begin{matrix} H & = & (b_{0} - a_{0}) + b_{1} y_{2} - a_{1} y_{1} + b_{2} y_{2}^{2} \\ - a_{2} y_{1}^{2} + b_{3} y_{2}^{3} - a_{3} y_{1}^{3} \end{matrix}$ (11)

Since there are Equation 7 unknown parameters on the right side of the equation, if we calibrating the system using i groups of standard thickness measurand di in j different positions can we get i × j groups of equations:

${\begin{matrix} H_{11} = (b_{0} - a_{0}) + b_{1} y_{2 (11)} - a_{1} y_{1 (11)} + b_{2} y_{2 (11)}^{2} - a_{2} y_{1 (11)}^{2} + b_{3} y_{2 (11)}^{3} - a_{3} y_{1 (11)}^{3} \\ H_{12} = (b_{0} - a_{0}) + b_{1} y_{2 (12)} - a_{1} y_{1 (12)} + b_{2} y_{2 (12)}^{2} - a_{2} y_{1 (12)}^{2} + b_{3} y_{2 (12)}^{3} - a_{3} y_{1 (12)}^{3} \\ \cdot \cdot \cdot \\ H_{21} = (b_{0} - a_{0}) + b_{1} y_{2 (21)} - a_{1} y_{1 (21)} + b_{2} y_{2 (21)}^{2} - a_{2} y_{1 (21)}^{2} + b_{3} y_{2 (21)}^{3} - a_{3} y_{1 (21)}^{3} \\ H_{22} = (b_{0} - a_{0}) + b_{1} y_{2 (22)} - a_{1} y_{1 (22)} + b_{2} y_{2 (22)}^{2} - a_{2} y_{1 (22)}^{2} + b_{3} y_{2 (22)}^{3} - a_{3} y_{1 (22)}^{3} \\ \cdot \cdot \cdot \\ H_{ij} = (b_{0} - a_{0}) + b_{1} y_{2 (ij)} - a_{1} y_{1 (ij)} + b_{2} y_{2 (ij)}^{2} - a_{2} y_{1 (ij)}^{2} + b_{3} y_{2 (ij)}^{3} - a_{3} y_{1 (ij)}^{3} \end{matrix}$ (12)

Transformed Equation 13 into matrix form can we get:

$[\begin{matrix} 1 y_{2 (11)} y_{1 (11)} y_{2 (11)}^{2} y_{1 (11)}^{2} y_{2 (11)}^{3} y_{1 (11)}^{3} \\ 1 y_{2 (12)} y_{1 (12)} y_{2 (12)}^{2} y_{1 (12)}^{2} y_{2 (12)}^{3} y_{1 (12)}^{3} \\ \cdot \cdot \cdot \\ 1 y_{2 (21)} y_{1 (21)} y_{2 (21)}^{2} y_{1 (21)}^{2} y_{2 (21)}^{3} y_{1 (21)}^{3} \\ 1 y_{2 (22)} y_{1 (22)} y_{2 (22)}^{2} y_{1 (22)}^{2} y_{2 (22)}^{3} y_{1 (22)}^{3} \\ \cdot \cdot \cdot \\ 1 y_{2 (ij)} y_{1 (ij)} y_{2 (ij)}^{2} y_{1 (ij)}^{2} y_{2 (ij)}^{3} y_{1 (ij)}^{3} \end{matrix}] [\begin{matrix} (b_{0} - a_{0}) \\ b_{1} \\ a_{1} \\ b_{2} \\ a_{2} \\ b_{3} \\ a_{3} \end{matrix}] = [\begin{matrix} H_{11} \\ H_{12} \\ \cdot \cdot \cdot \\ H_{21} \\ H_{22} \\ \cdot \cdot \cdot \\ H_{ij} \end{matrix}]$ (13)

The coefficient matrix on the left side of the matrix Equation (14) delegates the vertical ordinates of the two imaging spots in different groups, and the matrix on the right side represent the actual thicknesses. In actual measurement, measurement thickness of the measurand can be acquired through substituting the orthocenter ordinates of the two imaging spots into the calibrated equation.

Nine pieces of standard films consist of four pieces of feelers and five pieces of gauge blocks were selected to calibrate the measurement system. The thickness values were modified by the vertical metroscope which accuracy is 0.1 μm. Thicknesses of the feelers are 0.1045 mm, 0.3099 mm, 0.5161 mm, 0.7588 mm and gauge blocks thicknesses are 1.0003 mm, 1.5002 mm, 2.0001 mm, 2.5004 mm and 3.0003 mm. Each of the films been measured one time in the five positions shown in Fig. 7, then, get the coefficients of (b₀ - a₀), b₁, b₂, b₃, a₁, a₂, a₃ through solving the matrix Equation 14.

Speckle noise is an inevitable limitation to the laser triangulation thickness measurement method [8]. During the calibration process, the measurand was slight dithering manually to reduce the error induced by the speckle noise. The coefficients we get are as follows: (b₀ - a₀) = -3.0502 × 10^-1, b₁ = 3.4119 × 10^-3, a₁ = -3.0936 × 10^-3, b₂ = -8.7206 × 10^-8, a₂ = -5.7691 × 10^-8, b₃ = 7.5271 × 10^-12, a₃ = 1.0002 × 10^-12.

To verify the performance of this nonlinear correction method, a contrast experiment was conducted. The imaging spots ordinates were got from the calibrating data in the preceding experiment, and this guarantees the consistency of the contrast experiment. The fitted equation using the least-square method is as follows: $H = 2.713 \times 10^{- 9} h^{2} + 0.0033 h - 0.1084$ (14)

The value H in Equation 15 delegates the film thickness and the variable h represents the spots spacing. The measuring data and error analysis after and before nonlinear correction are shown in Tables 1 and 2 respectively.

Table 1

Measuring data and error analysis after nonlinear correction

No.	Actual Thickness h (mm)	Measuring Thickness H (mm)					Maximum Deviation Δh (mm)	Maximum Relative Error s (%)
		No. 1 Position	No. 2 Position	No. 3 Position	No. 4 Position	No.5 Position
1	0.1045	0.1043	0.1045	0.1046	0.1045	0.1053	0.0008	0.7656
2	0.3099	0.3100	0.3104	0.3099	0.3010	0.3099	0.0005	0.1613
3	0.5161	0.5153	0.5158	0.5157	0.5165	0.5170	0.0009	0.1744
4	0.7588	0.7591	0.7595	0.7591	0.7583	0.7580	0.0007	0.0923
5	1.0003	1.0008	0.9994	1.0003	1.0007	1.0006	0.0005	0.0500
6	1.5002	1.5005	1.4995	1.4996	1.5004	1.5009	0.0007	0.0467
7	2.0001	1.9993	2.0002	2.0009	2.0004	1.9994	–0.0008	0.0400
8	2.5001	2.4992	2.4998	2.5004	2.5002	2.4992	0.0003	0.0120
9	3.0003	3.0000	2.9999	3.0003	3.0005	2.9995	0.0002	0.0067

Table 2

Measuring data and error analysis before nonlinear correction

No.	Actual Thickness h′ (mm)	Measuring Thickness H (mm)					Maximum Deviation Δh (mm)	Maximum Relative Error s (%)
		No. 1 Position	No. 2 Position	No. 3 Position	No. 4 Position	No.5 Position
1	0.1045	0.1211	0.0912	0.0935	0.1082	0.1243	0.0198	18.9164
2	0.3099	0.3079	0.2949	0.2916	0.3083	0.3348	0.0249	8.0475
3	0.5161	0.5118	0.4986	0.4997	0.5218	0.5592	0.0431	8.3420
4	0.7588	0.7565	0.7432	0.7346	0.7549	0.7881	0.0293	3.8860
5	1.0003	0.9961	0.9580	0.9838	1.0031	1.0150	0.0120	1.1959
6	1.5002	1.4916	1.4831	1.4887	1.5110	1.5389	0.0387	2.5809
7	2.0001	1.9957	1.9831	1.9849	2.0102	2.0395	0.0394	0.0002
8	2.5001	2.4938	2.4874	2.4908	2.5022	2.5239	0.0238	0.9507
9	3.0003	2.9931	2.9900	2.9912	3.0024	3.0182	0.0179	0.5971

Table 1 revealed that maximum deviation after nonlinear correction is 0.0009 mm which is less than 1 μm, and the max relative error is 0.1744%. The maximum deviation before nonlinear correction was shown in Table 2 which is 0.0394 mm, the max relative error is 18.9164%. The Variance in Table 1 is smaller in contrast to that in Table 2 as well. Notice that the explicit formula for the relative error is S = (H - h)/h× 100 %. The measurement thickness was proven to be more stable and more accurate after nonlinear comparing Tables 1 with 2. Then, a conclusion can be drawn that the nonlinear correction method fits the measuring system well and the measuring accuracy of this system after nonlinear correction is±1 μm.

5 Conclusion

In summary, a way called dual-laser imaging method was proposed to implement the industrial thickness gauge requirement of high accuracy, fast speed and online measurement. Its optical structure, mechanical structure and measurement principle were described. The analysis and evaluation about the image abbreviation of the optical system were discussed, and the influencing of the aperture on the optical system was studied. A nonlinear correction method was proposed to reduce the nonlinear effect of the optical system. A contrast experiment was conducted to evaluate the performance of the nonlinear correction method. The calibrating experiment was conducted to verify the system accuracy. It has been proven by experiment that the system measuring accuracy can reach±1 μm.

Footnotes

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant no. 61505169), and also was supported by Key projects in Sichuan province department of education (No. 15zd1114), and the natural science foundation of Southwest University of science and technology (No. 14zx7160), and was supported by the Key Project of Fundamental Co-construction of Sichuan Province in China (No. 13zxzk06).973 of Ministry of Science and technology of China (Grant no. 2013CB035405).

References

Y.P.

, Zhang

H.P.

and Wu

, Polymer Lithium Ion Batteries, Beijing: Chemical Industry Press, 2007, pp. 1–16.

Abdelsalam

D.G.

, Baek

B.J.

, Abdel-Aziz

, Chegal

and Kim

, Highly accurate film thickness measurement based on automatic fringe analysis, Optik123 (2012), 1444–1449.

Jiči

, Petr

and Milena

, Simple method for determination of the thickness of a nonabsorbing thin film using spectral reflectance measurement, Appl Opt48(S0003-6935) (2009), 985–989.

Köysal

, Önal

and Özder

, Thickness measurement of dielectric films by wavelength scanning method, Opt Commun205 (2002), 1–6.

Azzam

R.M.A.

, Ellipsometry: A sophisticated tool for optical metrology, Proceedings of SPIE, Optical (2000), 184–196.

Peterson

J.P.

and Peterson

R.B.

, Laser triangulation for liquid film thickness measurements through multiple interfaces, Appl Opt45 (2006), 4916–4926.

Amann

M.C.

, Bosch

, Lescure

, Myllyla

and Rioux

, Laser ranging: A critical review of usual techniques for distance measurement, Opt Eng40 (2001), 10–19.

Dorsch

R.G.

, Hausler

and Herrmann

J.M.

, Laser triangulation: Fundamental uncertainty in distance measurement, Appl Opt33 (1994), 1306–1314.

Hattuniemi

A.M.

and Mäkyen

A.J.

, Thickness measurement of thin wood material by differential laser triangulation method, Advan Laser Technol7022:70220R (2008), 1–8.

10.

Vukašinović

, Bračun

and Možina

, The influence of incident, object color and distance on CNC laser scanning, Int J Adv Manuf Technol50 (2010), 265–274.

11.

Vukašinović

, Korošec

and Duhovink

, The influence of surface topology on the accuracy of laser triangulation scanning results, Journal of Mechanical Engineering56 (2010), 23–30.

12.

D.Y.

and Tan

H.Y.

, Engineering Optics, 2rd ed., Beijing, 2009, pp. 15–33.