Investigation of cross-polarized heterodyne technique for measuring refractive index and thickness of glass panels

Optics Communications 283 (2010) 3310–3314

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Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m

Investigation of cross-polarized heterodyne technique for measuring refractive index and thickness of glass panels Long Gao ⁎, Chunhui Wang, Yanchao Li, Haifang Cong, Yang Qu National Key Laboratory of Tunable Laser Technology, Harbin Institute of Technology, Harbin 150001, China

a r t i c l e

i n f o

Article history: Received 16 October 2009 Received in revised form 3 April 2010 Accepted 6 April 2010 Keywords: Cross-polarized Heterodyne detection Zeeman effect Dual-balanced detection

a b s t r a c t A new mathematical model of cross-polarized heterodyning is proposed for measuring glass panels. An optical system is presented for obtaining relative thickness variation and difference distribution of refractive indices simultaneously, and the dual-balanced coherent demodulation technique is used. The experiment results show that the transmittance of light beam can be less than 0.5% when the vibration amplitude of the glass panels is equal to 5 mm. It takes about 200 s to scan the whole glass sample with size of 1430 × 1360 mm2. The resolution of the thickness variation is 0.3 μm, and the lateral sampling resolution is 1 mm. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Glass substrate is an extremely important component of the liquid crystal display (LCD) where quality significantly depends on it. In recent years, the tenth generation of the glass substrate with the size of 2880 × 3130 mm2, whose thickness is between 0.3 mm and 0.7 mm, is developed in western countries; whereas the fifth generation of the glass substrate with the size of 1430 × 1360 mm2, whose thickness is between 0.5 mm and 0.7 mm, is developing in China. As the glass substrate of the thin film transistor (TFT) LCD, there are three requirements to be met for the glass substrate: first, it should not contain arsenic, antimony, barium or halides; second, the thinner the thickness of the glass substrate, the less variation of the thickness; last, the glass substrate should have good heat-resistant quality. Therefore, the qualified product can be chosen by measuring the thickness variation and the difference distribution of refractive indices. Obviously, it is most important to measure these two parameters simultaneously in manufacturing the glass panels. Traditionally thickness and difference distribution of refractive indices were measured separately, using different techniques; while thickness can be measured by a variety of well-elaborated methods such as heterodyne ellipsometry [1,2], optical triangulation and interferometry [3], ultrasound [4], etc. Measurement of difference distribution of refractive indices remained a challenging task through the past decades. To the best of

⁎ Corresponding author. E-mail address: [email protected] (L. Gao). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.04.014

our knowledge, the first attempt to design a reliable technique for the measurement of difference distribution of refractive indices was done by Chen [5]. Further development of modulation of the polarization state of the light beam was then extended by Serreze and Goldner [6,7]. These methods cost much time to measure difference distribution of refractive indices. Another method based on heterodyning technique was first proposed by Tsukiji [8]. In recent years, this technique has been developed [9–12] and commercialized in the market from CORING Inc and IRICO group. There is also the cross-polarized technique, which has many advantages, such as easy operation, high stability, good resolution and accuracy. SunghoonCho uses the cross-polarized heterodyne technique to scan the sample with horizontal and vertical lights side by side [13], but in this reference, firstly, there is no discussion about the difference distribution of refractive indices problem, secondly, the horizontal and vertical lights are scanned side by side on the surface of the sample, so the lateral sampling resolution is not high. The goal of our research is to develop a new optical system for measuring both thickness variation and difference distribution of refractive indices of the glass panel simultaneously based on cross-polarized heterodyne technique. In the present article we introduce the mathematical model of crosspolarized heterodyning for measuring glass panels firstly and present the optical system for measuring relative thickness variation and refractive indices distribution simultaneously. A heterodyne I/Q-interferometer scheme which can map the phase and the amplitude change simultaneously is also given. I/Qdemodulation is a well known technology in rf-communications and we apply this technique for demodulating the heterodyne beat signal [14–15]. Finally, the experimental results and discussions are presented.

L. Gao et al. / Optics Communications 283 (2010) 3310–3314

2. Experiment The schematic of optical arrangement is shown in Fig. 1. A dual-frequency, dual-polarization, stabilized, Zeeman laser is used as a light source of the scanning interferometer. The operational wavelength is 632.8 nm. Frequency difference between the two linearly cross-polarized waves is 2.34 MHz. Output light from the laser enters into a quarter-wave plate, and the purpose of this element is to compensate for residual ellipticity of one of the two linearly polarized laser components. The transmitted beam from the quarter-wave plate is split by a beam splitter (BS) into two paths. Two polarization modes in the reflected beam from BS are mixed by the use of an analyzing polarizer oriented at 45° to the polarization modes and a high speed photodiode, PD1. AC component of the beat signal from PD1 is used as the local oscillator signal (LO) in the RF mixing. As shown in Fig. 1, the transmitted beam from BS is used as the probe beam signal (PB) of the scanning heterodyne interferometry. The PB probe is focused on the sample by using a lens system, which decreases the diameter of incident beam into 1 mm. The diameter of transmitted beam from sample is increased to 6 mm by using the same lens system. When the two polarization modes are transmitting in the sample, these two polarization modes are orthogonal all the time, but their phases are also changed by the sample. Finally, these two polarization modes are mixed by the use of an analyzer oriented at 45° to the polarization mode and a high speed photodiode, PD2. Therefore, the information about thickness variation and difference distribution of refractive indices is contained in the photocurrent. Let us consider now the case of the physical procedure between the two polarization mode beam and the sample as shown in Fig. 2. The field expressions of the two polarization modes are E1ei(ω1t + φ01) and E2ei(ω2t + φ02), where E1 and E2, ω1 and ω2, φ01 and φ02, stand for amplitude, angular frequency, and initial phase of the two beams, respectively. As we know, glass is an isotropic media and, therefore, principal axes of stress tensor and ellipsoid of wave directions coincide. Also, directions of linearly polarized wave vectors which can propagate in the media without changes in polarization are always orthogonal. Therefore, independent of orientation of stress ellipsoid in the given point of glass sample we can consider two orthogonal directions along which refractive indices are n1 and n2. In Fig. 2, the photocurrent is proportional to 2

i = jA1 + A2 j ;

ð1Þ

Fig. 1. Schematic of experimental arrangement (BS: beam splitter, L: lens, A: analyzer, PD: detector, C: capacitance, DS: demodulation system, WP: wave plate).

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where A1 and A2 denote projections of the complex amplitude components along the directions of the waves E1 and E2 on the direction of the analyzer: A1 = E1 exp½iðω1 t + φ01 Þ ⋅½cosα ⋅ cos θ ⋅ exp ðikn1 lÞ− sin α ⋅ sin θ ⋅ exp ðikn2 lÞ

ð2Þ A2 = E2 exp½iðω2 t + φ02 Þ ⋅½cosα ⋅ sin θ ⋅ exp ðikn1 lÞ + sin α ⋅ cos θ ⋅ exp ðikn2 lÞ

ð3Þ where, k = 2π / λ is the wave number, and l is the thickness of a glass panel. α is the angular between analyzer axis and direction of n1, θ is the angular between E1 and direction of n1. For making good use of the heterodyne detection principle, expressions of A1 and A2 are transformed by the mathematical transformation operation, respectively: A1 = E1 r1 exp ½iðω1 t + θ1 Þ

ð4Þ

A2 = E2 r2 exp ½iðω2 t + θ2 Þ

ð5Þ

where 2

2

2

2

2

2

r1 = cos α cos θ + sin α sin sin θ−2 cos α sin α cos θ sin θ cos ðΔφÞ

ð6Þ −1

θ1 = tan




 cosα cosθ sin ðΔφÞ− sin α sin θ sin ðΔφÞ cos α cos θ cos ðΔφÞ− sin α sin θ cos ðΔφÞ

Δφ = kðn1 −n2 Þl:

ð7Þ ð8Þ

In a similar way, we can get the expressions of r2 and θ2, and substituting Eqs. (4) and (5) into Eq. (1), we then obtain the photocurrent: h i 2 2 2 2 i = η ⋅ E1 r1 + E2 r2 + 2E1 E2 r1 r2 cosðΔωt + θ1 −θ2 + φ01 −φ02 Þ ð9Þ Δφ ⋅ sin2α tgðθ1 −θ2 Þ≈ sinð2α + 2θÞ

ð10Þ

where η and Δω = ω1 − ω2 are the responsivity of the photodetector and frequency difference between A1 and A2, respectively. As can be seen from Eq. (7), the first and the second items stand for the direct photocurrent. The direct photocurrent variations of the heterodyne scheme provide information about thickness variations. Due to interference the intensity of a laser beam transmitted through a

Fig. 2. Schematic of heterodyne detection.

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L. Gao et al. / Optics Communications 283 (2010) 3310–3314

The phase modulation induced by the surface structure can be obtained by θ1 −θ2 = tan

−1


 iQ : iI

ð17Þ

Then we combine Eqs. (17) and (10) to get the parameter Δφ. Meanwhile using the radio-frequency component to get parameter l, finally, the difference distribution of refractive index is obtained. This part is the mathematical modeling for measuring the thickness and difference distribution of refractive indices based on cross-polarized heterodyne technique. 3. Measurement results and discussions

Fig. 3. Intermediate signal of cross-polarized heterodyne.

glass panel depends on the panel's thickness. Transmittance at normal incidence is equal to [16] 16n2  T=  4 4 ð1 + nÞ + ðn−1Þ −2ðn−1Þ2⋅ðn + 1Þ2⋅ cosð2ψÞ

ð11Þ

where n is the refraction index of a glass, here n is equal to 1.5028, and Ψ = 2π · l · n / λ. According to the measurement system, another transmittance coefficient is expressed as:

T=

E12 r12 + E22 r22 : E12 + E22

ð12Þ

Thus the intensity of a transmitted beam and consequently the direct current component of a photocurrent will exhibit variations, according to the panel thickness l. This procedure is corresponding to the number 2 part in Fig. 1. The third item of the right part of Eq. (9) is the radio-frequency signal, which contains information about frequency difference and phase related with difference distribution of refractive index. In order to obtain information about phase difference, let us review Fig. 1 once again, the LO signal, the AC component of the output signal from PD1 is given by iLO = η ⋅E1⋅E2 cos ðΔωt + φ01 −φ02 Þ;

ð13Þ

In the optical system, a dual-frequency, dual-polarization, stabilized, Zeeman laser is used as a light source of the scanning interferometer. The operational wavelength is 632.8 nm. Frequency difference between the two linearly cross-polarized waves is 2.34 MHz. The diameter of incident beam is 6 mm. The intermediate frequency signal of the measurement beam is depicted in Fig. 3. For the sake of analyzing relationship between relative thickness variation and light transmittance coefficient, and to make sure if the transmittance coefficient of the beam can be distinguished when the resolution of thickness variation is met, we measured the intensity of the beam which was transmitted from the glass panels. As described in Fig. 4, the black dots stand for separate intensity for the different thickness of the panels. After curve fitting, the fitting value, measurement value and theory value are well matched. The light transmittance has 15% variance when the thickness variation is approximately 0.3 µm. The thickness of glass substrate for liquid crystal display is always between 0.3 mm and 0.7 mm, while dimension of length and width is much larger than that of thickness. Therefore, there must be subtle mechanical vibration, whose amplitude is supposed to be 5 mm, and the expression of transmittance in Eq. (11) is changed complicatedly and not given here. Similarly, the relationship between transmittance and relative vibration variance is showed in Fig. 5. We can see that the variation of light intensity is less than 0.3% when the amplitude of vibration is 5 mm, so this error caused by vibration during measurement can be neglected. The measurement time is one of the most important parameters to evaluate the measurement system. Generally speaking, speed of measurements is limited basically by the time constant of the lock-in amplifier. The high-frequency lock-in amplifier model SR844 of the Stanford Corporation measures the amplitude and phase of the input

and the AC component of the PB beam from D2 can be written as, ibeat = η ⋅E1⋅E2⋅r1⋅r2 ⋅ cos ðΔωt + θ1 −θ2 + φ01 −φ02 Þ:

ð14Þ

The beat signal and LO signal are mixed at a commercial broad band I/Q-demodulator, which consists of two mixers. Both the beat signal and LO signal are divided into two signals and drive the corresponding ports of the two mixers, for which the LO signal phase of one of the two mixers is shifted by 90°. After low-pass filtering, the output intermediate frequency (IF) signal from each mixer can be written as, 2 2

iI = η ⋅E1 E2 r1 r2 cos ðθ1 −θ2 Þ 2 2

iQ = η ⋅E1 E2 r1 r2 sin ðθ1 −θ2 Þ:

ð15Þ

ð16Þ

Fig. 4. Relation between transmittance and relative variation thickness.

L. Gao et al. / Optics Communications 283 (2010) 3310–3314

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Fig. 5. Relation between transmittance and vibration and relative variation thickness.

signal. In order to preserve high enough signal-to-noise ratio, we chose the time constant that equals to 100 μs. With this value one line scan, containing (1430 × 1360) pixels in the sample, could be performed in 200 s. Fig. 6 shows the final result about the thickness variation with lateral scanning. Typical maps are shown in Fig. 6. In Fig. 7(a), the interference pattern of each fringe corresponds to 0.2 μm thickness variation. Thus, total thickness variation in this sample with size 150 × 300 mm2 is of about 4.8 μm. In Fig. 7(b), the difference distribution of refractive indices map shows the homogeneity state, and the red circles correspond to some stains, which can be considered as an inspection criterion. 4. Conclusion An optical system based on the cross-polarized heterodyne technique, which can measure the thickness variation and difference refractive indices of the glass panels, is introduced in this paper. It is the first investigation that illustrates the mathematical modeling of the two orthogonal polarized beams transmitting in the glass panels using the heterodyne detection principle. Parameters about phase retardation and thickness variation are switched into radio-frequency signal. This method not only takes advantage of the coherent

Fig. 7. Measurement results. (a) Map of the relative thickness variation. (b) Map of the refractive indices distribution. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

detection technique, but also enhances the measurement system accuracy. It is a great optical measurement system, which has a He–Ne laser with operational wavelength of 632.8 nm, the lateral sampling resolution is 1 mm, the thickness variation is 0.3 μm, the size of the glass panels is 1430 × 1360 mm2, and it costs about 200 s to complete a measurement process. This measurement system has the advantage of real time inspection and the possibility of simultaneous measurement of thickness and refractive spatial variations. It is believed that this technique could be regarded as an important tool to measure the glass panels of the thin film transistor (TFT) LCD. Acknowledgements The authors gratefully acknowledge financial support from the National Natural Science Foundation of China, Grant No. 60577032. They would also like to extend their gratitude to Professor Wang Chun-Hui of Harbin Institute of Technology for the revised manuscript. References [1] [2] [3] [4]

Fig. 6. Relative thickness variation for different lengths.

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