Research Paper:
Phase Retrieval Algorithm for Surface Topography Measurement Using Multi-Wavelength Scattering Spectroscopy
Satoshi Itakura, Tsutomu Uenohara, Yasuhiro Mizutani, and Yasuhiro Takaya
Department of Mechanical Engineering, Graduate School of Engineering, Osaka University
2-1 Yamadaoka, Suita, Osaka 565-0871, Japan
Corresponding author
We are currently developing a high-precision and wide-range in-process surface topography measurement system using the laser inverse scattering method. In the laser inverse scattering method, a monochromatic plane wave is illuminated perpendicular to the target surface and the surface topography is measured by retrieving the phase distribution of the reflected light. However, the dynamic range of this method is limited to the sub-micrometer range because of phase wrapping during phase retrieval. In this paper, we propose a laser inverse scattering method using a multi-wavelength light source based on the fact that the phase of light is inversely proportional to the wavelength with the propagation distance as a coefficient. We also constructed a surface profilometer based on the proposed method and measured the profile of a single rectangular groove with a width of 50 µm and a depth of 2 µm. The dimensions of the measured profiles agree well with the nominal dimensions of the rectangular groove.
- [1] Y. Wang, Q. Zhao, Y. Shang, P. Lv, B. Guo, and L. Zhao, “Ultraprecision Machining of Fresnel Microstructure on Die Steel Using Single Crystal Diamond Tool,” J. of Materials Processing Technology, Vol.211, No.12, pp. 2152-2159, 2011. https://doi.org/10.1016/j.jmatprotec.2011.07.018
- [2] M. Davies, B. Dutterer, T. Suleski, J. Silny, and E. Kim, “Diamond Machining of Diffraction Gratings for Imaging Spectrometers,” Precision Engineering, Vol.36, No.2, pp. 334-338, 2012. https://doi.org/10.1016/j.precisioneng.2011.09.006
- [3] A. Partanen, J. Väyrynen, S. Hassinen, H. Tuovinen, J. Mutanen, T. Itkonen, P. Silfsten, P. Pääkkönen, M. Kuittinen, K. Mönkkönen, and T. Venäläinen, “Fabrication of Terahertz Wire-Grid Polarizers,” Appl. Opt., Vol.51, No.35, pp. 8360-8365, 2012. https://doi.org/10.1364/AO.51.008360
- [4] Y. Takaya, “In-Process and On-Machine Measurement of Machining Accuracy for Process and Product Quality Management: A Review,” Int. J. Automation Technol., Vol.8, No.1, pp. 4-19, 2014. https://doi.org/10.20965/ijat.2014.p0004
- [5] W. Gao, H. Haitjema, F. Fang, R. Leach, C. Cheung, E. Savio, and J. Linares, “On-Machine and in-Process Surface Metrology for Precision Manufacturing,” CIRP Annals, Vol.68, Issue 2, pp. 843-866, 2019. https://doi.org/10.1016/j.cirp.2019.05.005
- [6] L. C. Chen and X. L. Nguyen, “Dynamic 3D Surface Profilometry Using a Novel Colour Pattern Encoded with a Multiple Triangular Model,” Measurement Science and Technology, Vol.21, No.5, 054009, 2010. https://doi.org/10.1088/0957-0233/21/5/054009
- [7] K. Takashi, U. Megumi, and M. Kaoru, “No-Scanning 3D Measurement Method Using Ultrafast Dimensional Conversion with a Chirped Optical Frequency Comb,” Scientific Reports, Vol.7, No.1, 3670, 2017. https://doi.org/10.1038/s41598-017-03953-w
- [8] A. Taguchi, T. Miyoshi, Y. Takaya, and S. Takahashi, “Optical 3D Profilometer for In-Process Measurement of Microsurface Based on Phase Retrieval Technique,” Precision Engineering, Vol.28, Issue 2, pp. 152-163, 2004. https://doi.org/10.1016/j.precisioneng.2003.07.002
- [9] R. M. Goldstein, H. A. Zebker, and C. L.Werner, “Satellite Radar Interferometry: Two-Dimensional Phase Unwrapping,” Radio Science, Vol.23, Issue 4, pp.713-720, 1988. https://doi.org/10.1029/RS023i004p00713
- [10] D. C. Ghiglia and L. A. Romero, “Robust Two-Dimensional Weighted and Unweighted Phase Unwrapping That Uses Fast Transforms and Iterative Methods,” J. Opt. Soc. Am. A, Vol.11, No.1, pp. 107-117, Jan 1994. https://doi.org/10.1364/JOSAA.11.000107
- [11] W. Xu and I. Cumming, “A Region-Growing Algorithm for InSAR Phase Unwrapping,” IEEE Trans. on Geoscience and Remote Sensing, Vol.37, No.1, pp. 124-134, 1999. https://doi.org/10.1109/36.739143
- [12] M. Servin, J. L. Marroquin, D. Malacara, and F. J. Cuevas, “Phase Unwrapping with a Regularized Phase-Tracking System,” Appl. Opt., Vol.37, Issue 10, pp. 1917-1923, 1998. https://doi.org/10.1364/AO.37.001917
- [13] Y.-Y. Cheng and J. C. Wyant, “Two-Wavelength Phase Shifting Interferometry,” Appl. Opt., Vol.23, Issue 24, pp. 4539-4543, 1984. https://doi.org/10.1364/AO.23.004539
- [14] K. Creath, Y.-Y. Cheng, and J. Wyant, “Contouring Aspheric Surfaces Using Twowavelength Phase-shifting Interferometry,” J. Opt. Soc. Am. A, Vol.32, Issue 12, pp.1455-1464, 1985. https://doi.org/10.1080/713821689
- [15] P. K. Upputuri, N. K. Mohan Sr., and M. P. Kothiyal Sr., “Measurement of Discontinuous Surfaces Using Multiple-Wavelength Interferometry,” Optical Engineering, Vol.48, No.7, 073603, 2009. https://doi.org/10.1117/1.3159867
- [16] M. Born and E. Wolf, “Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light: 6th (corrected) edition,” Cambridge University Press, 1997.
- [17] R. W. Gerchberg, “A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures,” Optik, Vol.35, Issue 2, pp. 237-246, 1972. https://api.semanticscholar.org/CorpusID:55691159
- [18] J. R. Fienup, “Phase Retrieval Algorithms: a Comparison,” Appl. Opt., Vol.21, No.15, pp. 2758-2769, 1982. https://doi.org/10.1364/AO.21.002758
- [19] D. R. Luke, J. V. Burke, and R. G. Lyon, “Optical Wavefront Reconstruction: Theory and Numerical Methods,” SIAM Review, Vol.44, No.2, pp. 169-224, 2002. https://doi.org/10.1137/S003614450139075
- [20] J. H. Seldin and J. R. Fienup, “Numerical Investigation of the Uniqueness of Phase Retrieval,” J. Opt. Soc. Am. A, Vol.7, No.3, pp. 412-427, 1990. https://doi.org/10.1364/JOSAA.7.000412
- [21] L. Gao, R. T. Kester, and T. S. Tkaczyk, “Compact Image Slicing Spectrometer (ISS) for Hyperspectral Fluorescence Microscopy,” Opt. Express, Vol.17, No.15, pp. 12293-12308, 2009. https://doi.org/10.1364/OE.17.012293
- [22] L. Gao, N. Bedard, N. Hagen, R. T. Kester, and T. S. Tkaczyk, “Depth-Resolved Image Mapping Spectrometer (IMS) with Structured Illumination,” Opt. Express, Vol.19, No.18, pp. 17439-17452, 2011. https://doi.org/10.1364/OE.19.017439
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.