干涉图处理的关键技术
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Advanced Materials Research Vols. 301-303 (2011) pp 1719-1723 Online available since 2011/Jul/27 at © (2011) Trans Tech Publications, Switzerland doi:10.4028//AMR.301-303.1719
Abstract. Interferogram processing is one of main techniques in optical interferometry metrology. Modern interferometry for thin-film thickness has the advantages of noncontact and high accuracy, etc. Interferogram processing is important Step of interferometry. This article is the sum-up about the key technology of interferogram processing in interferometry, it reduce key technology of interferogram processing to three steps: removing the noise, edge detection, region spreading and phase unwrapping. Interferogram processing can be realized by using software developed by the key technologies. Then getting surface of the measured material object, thus the measured material object is measured automatically. In this paper, the thin-film thickness is determined by the key technologies, setting the results of this method against results from ZYGO, the PV error and RMS maximum error are 0.0364λ and 0.002λ respectively. Although single interferogram was processed in this study, a phase distribution with high accuracy was achieved. Introduction Interferometry is one of the best methods in the international[1-5]. It realizes accurate and automatic measurement since the 1980s. To get the interferogram with information of measured material object base on the principle of interferometry[6]. The researchers can get frequency spectrum distribution of interferogram through the image preprocessing and 2D-FFT. Researchers can get the positive first grade frequency spectrum by appropriate filter, and move it to center of frequency spectrum image. Wave surface of measured material object could be restored by 2D-IFFT and phase unwrapping after the steps. This article introduces the key technologies in image processing of interferogram from edge detection, region spreading and phase unwrapping. Interferogram preprocessing Interferogram preprocessing divided mainly into two parts: edge detection and region spreading. Edge detection. Edge detection divided into two parts: edge of substratum and measured material object, edge of flight of steps. The edge region can not be restored with ordinary wave surface, because this must unwrap the region alone. For this reason, researchers must get edge position before unwrapping phase. The general edge detection operator include Robert, Sorbet, Prewitt and Laplacian operator and so on. Robert, Sorbet and Prewitt operator belongs to first order differential operator. The operators are simple, but they have low antinoise. Laplacian operator have two drawbacks: first, it is not easy to save edge directional information, second, it have low antinoise. Gaussian Laplacian operator is based on Laplacian operator, it has both higher precision and signal to noise ratio advantage. Gaussian Laplacian operator( h(r ) is second derivatives of r ) can be represented by Eq. 1: ∇ h(r ) = −[
2
r2 −σ 2
−
r2 2σ 2
σ4
]e
(1)
This formula is the Gaussian form of Laplacian operator, figure 1 is the 5 × 5 template of approximate ∇ 2 h .
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, . (ID: 221.11.46.229-15/08/11,09:48:11)
1720
Advanced Measurement and Test
0 0 -1 0 0
0 -1 -2 -1 0
-1 -2 16 -2 -1
0 -1 -2 -1 0
0 0 -1 0 0
Fig.1 The Gaussian form of Laplacian operator template Region spreading. Region spreading is the key step of interferogram preprocessing. Fourier transforms for interferogram processing must be FFT, because the unsettled data block must be rectangle. But the effective region of common interferogram is round, so the effective region of interferogram must be spread as rectangle. 2D-DFT iteration method[7] is an efficient region spreading method. In the first place, researchers can get new interferogram with obscure spreading fringe by 2D-FFT, extract of the positive and negative first grade frequency spectrum and 2D-IFFT. Secondly, corresponding region of new interferogram should be replaced by gas sooner or the effective region of primary interferogram. Spreading interferogram can be got by repeat the first and second step N times. Third, Final spreading interferogram can be obtained by the transformation of intensity levels. To process concrete interferogram by 2D-DFT iteration method, Fig. 2 is the results of data processing. The method can avoid producing interference fringe.
sujunhong@, b155216513@, c53751807@, d1049652540@
Keywords: Interferogram, Interferometry, Phase unwrapping, Region spreading.
(a) (b) (c) Fig.ram; (b)The result of N times iteration; (c) Final spreading interferogram by 2D-DFT iteration method. Phase unwrapping During the interferogram processing, phase unwrapping[8-11] is the key of FFT transformation technology, phase-shifting technology, space projection technology, etc, and those interferogram processing technology[1] will involve the computation of the arctan function. Owing to the process of phase unwrapping involve the computation of the arctan function, the phase value is wrapped in [-π,π]. In order to get factual phase distribution, we need further processing for the wrapped phases. If the border of the wrapped wave surface is regular form, and the wrapped wave surface has no noise in ideal status, we could unwrap the phase in fringe scanning method. Interferogram will form ineffectual regions by shape defects of measured object and some devices in optical structure or some random elements, etc. The ineffectual regions have an effect on edge form of valid data and make edge form show irregularity. In this case, traditional method will become helpless. In this article, algorism of diamond phase unwrapping is used to unwrap this type of interferogram. Because the algorism don’t depend on the edge form of interferogram, it can round ineffectual regions automatically.
Key Technologies in Image Processing of Interferogram Junhong Su1,a, Wenbo Wan1,b, Lihong Yang1,c and Junqi Xu1,d
1 a
Xi'an Technological University, Xi'an, Shaanxi Province, China.
Abstract. Interferogram processing is one of main techniques in optical interferometry metrology. Modern interferometry for thin-film thickness has the advantages of noncontact and high accuracy, etc. Interferogram processing is important Step of interferometry. This article is the sum-up about the key technology of interferogram processing in interferometry, it reduce key technology of interferogram processing to three steps: removing the noise, edge detection, region spreading and phase unwrapping. Interferogram processing can be realized by using software developed by the key technologies. Then getting surface of the measured material object, thus the measured material object is measured automatically. In this paper, the thin-film thickness is determined by the key technologies, setting the results of this method against results from ZYGO, the PV error and RMS maximum error are 0.0364λ and 0.002λ respectively. Although single interferogram was processed in this study, a phase distribution with high accuracy was achieved. Introduction Interferometry is one of the best methods in the international[1-5]. It realizes accurate and automatic measurement since the 1980s. To get the interferogram with information of measured material object base on the principle of interferometry[6]. The researchers can get frequency spectrum distribution of interferogram through the image preprocessing and 2D-FFT. Researchers can get the positive first grade frequency spectrum by appropriate filter, and move it to center of frequency spectrum image. Wave surface of measured material object could be restored by 2D-IFFT and phase unwrapping after the steps. This article introduces the key technologies in image processing of interferogram from edge detection, region spreading and phase unwrapping. Interferogram preprocessing Interferogram preprocessing divided mainly into two parts: edge detection and region spreading. Edge detection. Edge detection divided into two parts: edge of substratum and measured material object, edge of flight of steps. The edge region can not be restored with ordinary wave surface, because this must unwrap the region alone. For this reason, researchers must get edge position before unwrapping phase. The general edge detection operator include Robert, Sorbet, Prewitt and Laplacian operator and so on. Robert, Sorbet and Prewitt operator belongs to first order differential operator. The operators are simple, but they have low antinoise. Laplacian operator have two drawbacks: first, it is not easy to save edge directional information, second, it have low antinoise. Gaussian Laplacian operator is based on Laplacian operator, it has both higher precision and signal to noise ratio advantage. Gaussian Laplacian operator( h(r ) is second derivatives of r ) can be represented by Eq. 1: ∇ h(r ) = −[
2
r2 −σ 2
−
r2 2σ 2
σ4
]e
(1)
This formula is the Gaussian form of Laplacian operator, figure 1 is the 5 × 5 template of approximate ∇ 2 h .
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, . (ID: 221.11.46.229-15/08/11,09:48:11)
1720
Advanced Measurement and Test
0 0 -1 0 0
0 -1 -2 -1 0
-1 -2 16 -2 -1
0 -1 -2 -1 0
0 0 -1 0 0
Fig.1 The Gaussian form of Laplacian operator template Region spreading. Region spreading is the key step of interferogram preprocessing. Fourier transforms for interferogram processing must be FFT, because the unsettled data block must be rectangle. But the effective region of common interferogram is round, so the effective region of interferogram must be spread as rectangle. 2D-DFT iteration method[7] is an efficient region spreading method. In the first place, researchers can get new interferogram with obscure spreading fringe by 2D-FFT, extract of the positive and negative first grade frequency spectrum and 2D-IFFT. Secondly, corresponding region of new interferogram should be replaced by gas sooner or the effective region of primary interferogram. Spreading interferogram can be got by repeat the first and second step N times. Third, Final spreading interferogram can be obtained by the transformation of intensity levels. To process concrete interferogram by 2D-DFT iteration method, Fig. 2 is the results of data processing. The method can avoid producing interference fringe.
sujunhong@, b155216513@, c53751807@, d1049652540@
Keywords: Interferogram, Interferometry, Phase unwrapping, Region spreading.
(a) (b) (c) Fig.ram; (b)The result of N times iteration; (c) Final spreading interferogram by 2D-DFT iteration method. Phase unwrapping During the interferogram processing, phase unwrapping[8-11] is the key of FFT transformation technology, phase-shifting technology, space projection technology, etc, and those interferogram processing technology[1] will involve the computation of the arctan function. Owing to the process of phase unwrapping involve the computation of the arctan function, the phase value is wrapped in [-π,π]. In order to get factual phase distribution, we need further processing for the wrapped phases. If the border of the wrapped wave surface is regular form, and the wrapped wave surface has no noise in ideal status, we could unwrap the phase in fringe scanning method. Interferogram will form ineffectual regions by shape defects of measured object and some devices in optical structure or some random elements, etc. The ineffectual regions have an effect on edge form of valid data and make edge form show irregularity. In this case, traditional method will become helpless. In this article, algorism of diamond phase unwrapping is used to unwrap this type of interferogram. Because the algorism don’t depend on the edge form of interferogram, it can round ineffectual regions automatically.
Key Technologies in Image Processing of Interferogram Junhong Su1,a, Wenbo Wan1,b, Lihong Yang1,c and Junqi Xu1,d
1 a
Xi'an Technological University, Xi'an, Shaanxi Province, China.