메뉴 건너뛰기




Volumn 15, Issue 6, 2007, Pages 3053-3066

Approximations for the arctangent function in efficient fringe pattern analysis

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; FUNCTION EVALUATION; POLYNOMIALS;

EID: 33947418475     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.15.003053     Document Type: Article
Times cited : (10)

References (35)
  • 1
    • 0019927495 scopus 로고
    • Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry
    • M. Takeda, H. Ina, and S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72, 156-160 (1982).
    • (1982) J. Opt. Soc. Am , vol.72 , pp. 156-160
    • Takeda, M.1    Ina, H.2    Kobayashi, S.3
  • 2
    • 0020919219 scopus 로고
    • Fourier transform profilometry for the automatic measurement of 3-D object shapes
    • M. Takeda and K. Mutoh, "Fourier transform profilometry for the automatic measurement of 3-D object shapes." Appl. Opt. 22, 3977-3982 (1983).
    • (1983) Appl. Opt , vol.22 , pp. 3977-3982
    • Takeda, M.1    Mutoh, K.2
  • 3
    • 0037057812 scopus 로고    scopus 로고
    • Technique for phase measurement and surface reconstruction by use of colored structured light
    • O. A. Skydan, M. J. Lalor, and D. R. Burton, "Technique for phase measurement and surface reconstruction by use of colored structured light," Appl. Opt. 41, 6104-6117 (2002).
    • (2002) Appl. Opt , vol.41 , pp. 6104-6117
    • Skydan, O.A.1    Lalor, M.J.2    Burton, D.R.3
  • 4
    • 0041698080 scopus 로고    scopus 로고
    • New method for measuring dynamic response of small components by fringe projection
    • C. J. Tay, C. Quan, H. M. Shang, T. Wu, and S. Wang, "New method for measuring dynamic response of small components by fringe projection," Opt. Eng. 42, 1715-1720 (2003).
    • (2003) Opt. Eng , vol.42 , pp. 1715-1720
    • Tay, C.J.1    Quan, C.2    Shang, H.M.3    Wu, T.4    Wang, S.5
  • 5
    • 21244477526 scopus 로고    scopus 로고
    • High-speed optical measurement for the drumhead vibration
    • Q. Zhang and X. Su, "High-speed optical measurement for the drumhead vibration," Opt. Express 13, 3110-3116 (2005), http://www. opticsinfobase.org/abstract.cfm?URI=oe-13-8-3110.
    • (2005) Opt. Express , vol.13 , pp. 3110-3116
    • Zhang, Q.1    Su, X.2
  • 6
    • 33747584417 scopus 로고    scopus 로고
    • Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination
    • Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, "Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination," Opt. Eng. 44, 113601, (2005).
    • (2005) Opt. Eng , vol.44 , pp. 113601
    • Zhang, Q.1    Su, X.2    Cao, Y.3    Li, Y.4    Xiang, L.5    Chen, W.6
  • 7
    • 0001492036 scopus 로고    scopus 로고
    • Frequency-multiplex Fourier-transform profilometry: A single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations
    • M. Takeda, Q. Gu, M. Kinoshita, H. Takai, and Y. Takahashi, "Frequency-multiplex Fourier-transform profilometry: a single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations," App. Opt. 36, 5347-5354 (1997).
    • (1997) App. Opt , vol.36 , pp. 5347-5354
    • Takeda, M.1    Gu, Q.2    Kinoshita, M.3    Takai, H.4    Takahashi, Y.5
  • 8
    • 33749411074 scopus 로고    scopus 로고
    • Calibration-based two-frequency projected fringe profilometry: A robust, accurate, and single-shot measurement for objects with large depth discontinuities
    • W-H. Su and H. Liu, "Calibration-based two-frequency projected fringe profilometry: a robust, accurate, and single-shot measurement for objects with large depth discontinuities," Opt. Express 14, 9178-9187 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-20-9178.
    • (2006) Opt. Express , vol.14 , pp. 9178-9187
    • Su, W.-H.1    Liu, H.2
  • 9
    • 0009288777 scopus 로고    scopus 로고
    • Accelerating fast Fourier transform and filtering operations in Fourier fringe analysis for accurate measurement of three-dimensional surfaces
    • M. A. Herráez, D. R. Burton, and M. J. Lalor, "Accelerating fast Fourier transform and filtering operations in Fourier fringe analysis for accurate measurement of three-dimensional surfaces," Opt. Lasers Eng. 31, 135-145 (1999).
    • (1999) Opt. Lasers Eng , vol.31 , pp. 135-145
    • Herráez, M.A.1    Burton, D.R.2    Lalor, M.J.3
  • 10
    • 0015373101 scopus 로고
    • Direct Phase Detecting System
    • Y. Ichioka and M. Inuiya, "Direct Phase Detecting System," Appl. Opt. 11, 1507-1514 (1972).
    • (1972) Appl. Opt , vol.11 , pp. 1507-1514
    • Ichioka, Y.1    Inuiya, M.2
  • 11
    • 0021463845 scopus 로고
    • Interferometric phase measurement using spatial synchronous detection
    • K. H. Womack, "Interferometric phase measurement using spatial synchronous detection," Opt. Eng. 23, 391-395 (1984).
    • (1984) Opt. Eng , vol.23 , pp. 391-395
    • Womack, K.H.1
  • 12
    • 84957704716 scopus 로고
    • Fast profilometer for the automatic measurement of 3-D object shapes
    • S. Tang and Y. Y. Hung, "Fast profilometer for the automatic measurement of 3-D object shapes," Appl. Opt. 29, 3012-3018 (1990).
    • (1990) Appl. Opt , vol.29 , pp. 3012-3018
    • Tang, S.1    Hung, Y.Y.2
  • 13
    • 0020749979 scopus 로고
    • Real-time fringe-pattern analysis
    • L. Mertz, "Real-time fringe-pattern analysis," Appl. Opt. 22, 1535-1539 (1983).
    • (1983) Appl. Opt , vol.22 , pp. 1535-1539
    • Mertz, L.1
  • 14
    • 0020940715 scopus 로고
    • Two-dimensional fringe-pattern analysis
    • W. W. Macy, "Two-dimensional fringe-pattern analysis," Appl. Opt. 22, 3898-3901 (1983).
    • (1983) Appl. Opt , vol.22 , pp. 3898-3901
    • Macy, W.W.1
  • 16
    • 0029478555 scopus 로고
    • Spatial phase stepping method of fringe-pattern analysis
    • P. H. Chan and P. J. Bryanston-Cross, "Spatial phase stepping method of fringe-pattern analysis," Opt. Lasers Eng. 23, 343-354 (1995).
    • (1995) Opt. Lasers Eng , vol.23 , pp. 343-354
    • Chan, P.H.1    Bryanston-Cross, P.J.2
  • 17
    • 0000529187 scopus 로고    scopus 로고
    • High precision two-dimensional spatial fringe analysis method
    • Y. Arai, S. Yokozeki, K. Shiraki, and T. Yamada, "High precision two-dimensional spatial fringe analysis method," J. Mod. Opt. 44, 739-751(1997).
    • (1997) J. Mod. Opt , vol.44 , pp. 739-751
    • Arai, Y.1    Yokozeki, S.2    Shiraki, K.3    Yamada, T.4
  • 18
    • 0000625580 scopus 로고    scopus 로고
    • Video-rate fringe analyzer based on phaseshifting electronic moiré patterns
    • J. Kato, I. Yamaguchi, T. Nakamura, and S. Kuwashima, "Video-rate fringe analyzer based on phaseshifting electronic moiré patterns," Appl. Opt. 36, 8403-8412 (1997).
    • (1997) Appl. Opt , vol.36 , pp. 8403-8412
    • Kato, J.1    Yamaguchi, I.2    Nakamura, T.3    Kuwashima, S.4
  • 19
    • 0002020248 scopus 로고
    • Spatial phase measurement methods
    • D. W. Robinson and G. Reid, eds, IOP, Bristol, UK
    • M. Kujawinska, "Spatial phase measurement methods," in Interferogram Analysis: Digital Fringe Pattern Measurement, D. W. Robinson and G. Reid, eds. (IOP, Bristol, UK, 1993), pp. 141-193.
    • (1993) Interferogram Analysis: Digital Fringe Pattern Measurement , pp. 141-193
    • Kujawinska, M.1
  • 20
    • 0032224126 scopus 로고    scopus 로고
    • Real-time phase distribution analysis of fringe pattern
    • P.K. Rastogi, and F. Gyímesi eds, Proc. SPIE
    • Y. Morimoto and M. Fujigaki. "Real-time phase distribution analysis of fringe pattern," in International Conference on Applied Optical Metrology, P.K. Rastogi, and F. Gyímesi eds., Proc. SPIE, 3407, 34-39 (1998).
    • (1998) International Conference on Applied Optical Metrology , vol.3407 , pp. 34-39
    • Morimoto, Y.1    Fujigaki, M.2
  • 21
    • 33645730228 scopus 로고    scopus 로고
    • A single-shot pixellated phase-shifting interferometer utilizing a liquid-crystal spatial light modulator
    • K. L. Baker and E. A. Stappaerts, "A single-shot pixellated phase-shifting interferometer utilizing a liquid-crystal spatial light modulator," Opt. Lett. 31, 733-735 (2006).
    • (2006) Opt. Lett , vol.31 , pp. 733-735
    • Baker, K.L.1    Stappaerts, E.A.2
  • 22
    • 0032628769 scopus 로고    scopus 로고
    • Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring
    • P. S. Huang, Q. Hu, and F-P. Chiang, "Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring," Opt. Eng. 38, 1065-1071 (1999).
    • (1999) Opt. Eng , vol.38 , pp. 1065-1071
    • Huang, P.S.1    Hu, Q.2    Chiang, F.-P.3
  • 23
    • 0344291114 scopus 로고    scopus 로고
    • Composite structured light pattern for three-dimensional video
    • C. Guan, L. G. Hassebrook, and D. L. Lau "Composite structured light pattern for three-dimensional video," Opt. Express 11, 406-417 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-5-406.
    • (2003) Opt. Express , vol.11 , pp. 406-417
    • Guan, C.1    Hassebrook, L.G.2    Lau, D.L.3
  • 24
    • 0032597649 scopus 로고    scopus 로고
    • High-speed surface profilometer based on a spatial light modulator and pipeline image processor
    • C. R. Coggrave and J. M. Huntley, "High-speed surface profilometer based on a spatial light modulator and pipeline image processor," Opt. Eng. 38, 1573-1581 (1999).
    • (1999) Opt. Eng , vol.38 , pp. 1573-1581
    • Coggrave, C.R.1    Huntley, J.M.2
  • 25
    • 0037251204 scopus 로고    scopus 로고
    • High-speed 3-D shape measurement based on digital fringe projection
    • P. S. Huang, C. P. Zhang, and F. P. Chiang, "High-speed 3-D shape measurement based on digital fringe projection," Opt. Eng. 42, 163-168 (2003).
    • (2003) Opt. Eng , vol.42 , pp. 163-168
    • Huang, P.S.1    Zhang, C.P.2    Chiang, F.P.3
  • 26
    • 33645501774 scopus 로고    scopus 로고
    • High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method
    • S. Zhang and S-T. Yau, "High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method," Opt. Express 14, 2644-2649 (2006), http://www.opticsinfobase.org/abstract.cfm? URI=oe-14-7-2644.
    • (2006) Opt. Express , vol.14 , pp. 2644-2649
    • Zhang, S.1    Yau, S.-T.2
  • 27
    • 33749392707 scopus 로고    scopus 로고
    • GPU-assisted high-resolution, real-time 3-D shape measurement
    • S. Zhang, D. Royer, and S-T Yau, "GPU-assisted high-resolution, real-time 3-D shape measurement," Opt. Express, 14, 9120-9129 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-20-9120.
    • (2006) Opt. Express , vol.14 , pp. 9120-9129
    • Zhang, S.1    Royer, D.2    Yau, S.-T.3
  • 28
    • 0033896788 scopus 로고    scopus 로고
    • Video-rate surface profiling with acousto-optic accordion fringe interferometry
    • M. S. Mermelstein, D. L. Feldhun, and L. G. Shirley, "Video-rate surface profiling with acousto-optic accordion fringe interferometry," Opt. Eng. 39, 106-113 (2000).
    • (2000) Opt. Eng , vol.39 , pp. 106-113
    • Mermelstein, M.S.1    Feldhun, D.L.2    Shirley, L.G.3
  • 29
    • 0042472787 scopus 로고    scopus 로고
    • Shape measurement by use of liquid-crystal display, fringe projection with two-step phase-shifting
    • C. Quan, C. J. Tay, X. Kang, X. Y. He, and H. M. Shang, "Shape measurement by use of liquid-crystal display, fringe projection with two-step phase-shifting," Appl. Opt. 42, 2329-2335 (2003).
    • (2003) Appl. Opt , vol.42 , pp. 2329-2335
    • Quan, C.1    Tay, C.J.2    Kang, X.3    He, X.Y.4    Shang, H.M.5
  • 31
    • 84975609399 scopus 로고
    • Phase shifting interferometry in the presence of vibration: A new algorithm and system
    • P. L. Wizinowich, "Phase shifting interferometry in the presence of vibration: a new algorithm and system," Appl. Opt. 29, 3271-3279 (1990).
    • (1990) Appl. Opt , vol.29 , pp. 3271-3279
    • Wizinowich, P.L.1
  • 32
    • 84975623966 scopus 로고
    • Image processing algorithms for the analysis of phase-shifted speckle interference patterns
    • H. A. Vrooman and A. A. M. Maas, "Image processing algorithms for the analysis of phase-shifted speckle interference patterns," Appl. Opt. 30, 1636-1641 (1991).
    • (1991) Appl. Opt , vol.30 , pp. 1636-1641
    • Vrooman, H.A.1    Maas, A.A.M.2
  • 33
    • 0031385065 scopus 로고    scopus 로고
    • High-speed fringe analysis by using stair-shaped virtual grating demodulation
    • Z. Gao, S. Zhou, and Y. Hu, "High-speed fringe analysis by using stair-shaped virtual grating demodulation," Opt. Lasers Eng. 28, 411-422 (1997).
    • (1997) Opt. Lasers Eng , vol.28 , pp. 411-422
    • Gao, Z.1    Zhou, S.2    Hu, Y.3
  • 34
    • 33645516896 scopus 로고    scopus 로고
    • Fast three-step phase shifting algorithm
    • P. S. Huang and S. Zhang, "Fast three-step phase shifting algorithm," Appl. Opt. 45, 5086-5091 (2006).
    • (2006) Appl. Opt , vol.45 , pp. 5086-5091
    • Huang, P.S.1    Zhang, S.2
  • 35
    • 84944052000 scopus 로고
    • Fast approximation to the arctangent
    • J. Arvo, ed, AP Professional, Boston, USA
    • R. Capelli, "Fast approximation to the arctangent," in Graphics Gems II, J. Arvo, ed. (AP Professional, Boston, USA, 1995), pp.389-391.
    • (1995) Graphics Gems II , pp. 389-391
    • Capelli, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.