메뉴 건너뛰기




Volumn 18, Issue 8, 2001, Pages 1862-1870

Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform

Author keywords

[No Author keywords available]

Indexed keywords

FOURIER OPTICS; HARMONIC ANALYSIS; IMAGE RECONSTRUCTION; LIGHT PROPAGATION; PATTERN RECOGNITION;

EID: 0000713775     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.18.001862     Document Type: Article
Times cited : (440)

References (60)
  • 1
    • 0000293183 scopus 로고
    • Theory of communications
    • D. Gabor, “Theory of communications,” J. Inst. Electr. Eng. 93, 429-457 (1947).
    • (1947) J. Inst. Electr. Eng , vol.93 , pp. 429-457
    • Gabor, D.1
  • 2
    • 0005496480 scopus 로고
    • Observation of phase objects by optically processed Hilbert transform
    • S. Lowenthal and Y. Belvaux, “Observation of phase objects by optically processed Hilbert transform,” Appl. Phys. Lett. 11, 49-51 (1967).
    • (1967) Appl. Phys. Lett , vol.11 , pp. 49-51
    • Lowenthal, S.1    Belvaux, Y.2
  • 3
    • 0015125592 scopus 로고
    • An extension to the Hilbert transform product theorem
    • H. Stark, “An extension to the Hilbert transform product theorem,” Proc. IEEE 59, 1359-1360 (1971).
    • (1971) Proc. IEEE , vol.59 , pp. 1359-1360
    • Stark, H.1
  • 4
    • 0015681467 scopus 로고
    • Isotropic Hilbert spatial filtering
    • J. K. T. Eu and A. W. Lohmann, “Isotropic Hilbert spatial filtering,” Opt. Commun. 9, 257-262 (1973).
    • (1973) Opt. Commun , vol.9 , pp. 257-262
    • Eu, J.K.T.1    Lohmann, A.W.2
  • 5
    • 0038719565 scopus 로고
    • Isotropic Hilbert transform by anisotropic spatial filtering
    • J. Ojeda-Castanada and E. Jara, “Isotropic Hilbert transform by anisotropic spatial filtering,” Appl. Opt. 25, 4035-4038 (1986).
    • (1986) Appl. Opt , vol.25 , pp. 4035-4038
    • Ojeda-Castanada, J.1    Jara, E.2
  • 6
    • 0038043053 scopus 로고
    • Hilbert transform pairs mechanisms
    • (ARVO
    • E. Peli, “Hilbert transform pairs mechanisms,” Invest. Oph-thalmol. Visual Sci. 30 (ARVO Suppl.), 110 (1989).
    • (1989) Invest. Oph-Thalmol. Visual Sci , vol.30 , pp. 110
    • Peli, E.1
  • 7
    • 0010024813 scopus 로고    scopus 로고
    • Optical implementation of the fractional Hilbert transform for two-dimensional objects
    • A. W. Lohmann, E. Tepichin, and J. G. Ramirez, “Optical implementation of the fractional Hilbert transform for two-dimensional objects,” Appl. Opt. 36, 6620-6626 (1997).
    • (1997) Appl. Opt , vol.36 , pp. 6620-6626
    • Lohmann, A.W.1    Tepichin, E.2    Ramirez, J.G.3
  • 8
    • 0025403946 scopus 로고
    • The use of a two-dimensional Hilbert transform for Wigner analysis of 2-dimensional real signals
    • Y. M. Zhu, F. Peyrin, and R. Goutte, “The use of a two-dimensional Hilbert transform for Wigner analysis of 2-dimensional real signals,” Signal Process. 19, 205-220 (1990).
    • (1990) Signal Process , vol.19 , pp. 205-220
    • Zhu, Y.M.1    Peyrin, F.2    Goutte, R.3
  • 11
    • 85010100309 scopus 로고    scopus 로고
    • presented at the 8th International Conference on Computer Analysis of Images and Patterns, Ljubljana, Slovenia, September 1 -3
    • T. Billow and G. Sommer, “A novel approach to the 2D analytic signal,” presented at the 8th International Conference on Computer Analysis of Images and Patterns, Ljubljana, Slovenia, September 1 -3, 1999.
    • (1999) A Novel Approach to the 2D Analytic Signal
    • Billow, T.1    Sommer, G.2
  • 13
    • 0030469636 scopus 로고    scopus 로고
    • Analytic signals for multivariate data
    • M. Craig, “Analytic signals for multivariate data,” Math. Geol. 28, 315-329 (1996).
    • (1996) Math. Geol , vol.28 , pp. 315-329
    • Craig, M.1
  • 14
    • 0002510023 scopus 로고
    • The role of analyticity in image recovery
    • H.Stark, ed. (Academic, Orlando, Fla
    • M. A. Fiddy, “The role of analyticity in image recovery,” in Image Recovery: Theory and Application, H.Stark, ed. (Academic, Orlando, Fla., 1987).
    • (1987) Image Recovery: Theory and Application
    • Fiddy, M.A.1
  • 15
    • 84975571733 scopus 로고
    • Phase retrieval stagnation problems and solution
    • J. R. Fienup and C. C. Wackerman, “Phase retrieval stagnation problems and solution,” J. Opt. Soc. Am. A 3, 1897-1907 (1986).
    • (1986) J. Opt. Soc. Am. A , vol.3 , pp. 1897-1907
    • Fienup, J.R.1    Wackerman, C.C.2
  • 16
    • 0037705212 scopus 로고
    • Generalisations to higher dimensions of the Cauchy integral formula
    • D. G. Fulton and G. Y. Rainich, “Generalisations to higher dimensions of the Cauchy integral formula,” Am. J. Math. 54, 235-241 (1932).
    • (1932) Am. J. Math , vol.54 , pp. 235-241
    • Fulton, D.G.1    Rainich, G.Y.2
  • 17
    • 0033935157 scopus 로고    scopus 로고
    • Using the Hilbert transform for 3D visualisation of differential interference contrast microscope images
    • M. R. Arnison, C. J. Cogswell, N. I. Smith, P. W. Fekete, and K. G. Larkin, “Using the Hilbert transform for 3D visualisation of differential interference contrast microscope images,” J. Microsc. 199, 79-84 (2000).
    • (2000) J. Microsc , vol.199 , pp. 79-84
    • Arnison, M.R.1    Cogswell, C.J.2    Smith, N.I.3    Fekete, P.W.4    Larkin, K.G.5
  • 18
    • 0000054238 scopus 로고    scopus 로고
    • Efficient nonlinear algorithm for envelope detection in white light interferometry
    • K. G. Larkin, “Efficient nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Soc. Am. A 13, 832-843 (1996).
    • (1996) J. Opt. Soc. Am. A , vol.13 , pp. 832-843
    • Larkin, K.G.1
  • 19
    • 34250971770 scopus 로고
    • Sur les fonctions conjugues
    • M. Riesz, “Sur les fonctions conjugues,” Math. Z. 27, 218-244 (1927).
    • (1927) Math. Z , vol.27 , pp. 218-244
    • Riesz, M.1
  • 20
    • 0038381301 scopus 로고
    • Equazioni integrali contenenti il valor prin- cipale di un integrale doppio
    • F. G. Tricomi, “Equazioni integrali contenenti il valor prin- cipale di un integrale doppio,” Math. Z. 27, 87-133 (1928).
    • (1928) Math. Z , vol.27 , pp. 87-133
    • Tricomi, F.G.1
  • 21
    • 84893997275 scopus 로고
    • Sur une classe generale d’equations a integrales principales
    • G. Giraud, “Sur une classe generale d’equations a integrales principales,” C. R. Acad. Sci. 202, 2124-2126 (1936).
    • (1936) C. R. Acad. Sci , vol.202 , pp. 2124-2126
    • Giraud, G.1
  • 22
    • 0038719566 scopus 로고
    • Singular integral equations
    • (in Russian)
    • S. G. Mikhlin, “Singular integral equations,” Usp. Mat. Nauk 3, 29-112 (1948) (in Russian).
    • (1948) Usp. Mat. Nauk , vol.3 , pp. 29-112
    • Mikhlin, S.G.1
  • 24
    • 34250593672 scopus 로고
    • On the existence of certain singular integrals
    • A. P. Calderon and A. Zygmund, “On the existence of certain singular integrals,” Acta Math. 88, 85-139 (1952).
    • (1952) Acta Math , vol.88 , pp. 85-139
    • Calderon, A.P.1    Zygmund, A.2
  • 25
    • 12144256861 scopus 로고
    • On singular integrals
    • A. Zygmund, “On singular integrals,” Rend. Mat. 16, 468-505 (1957).
    • (1957) Rend. Mat , vol.16 , pp. 468-505
    • Zygmund, A.1
  • 27
    • 0031986769 scopus 로고    scopus 로고
    • Harmonic analysis of the Calderon-Zygmund school, 1970-1993
    • A. Carbery, “Harmonic analysis of the Calderon-Zygmund school, 1970-1993,” Bull. London Math. Soc. 30, 11-23 (1998).
    • (1998) Bull. London Math. Soc , vol.30 , pp. 11-23
    • Carbery, A.1
  • 28
    • 85071192393 scopus 로고
    • The analytic signal of two-dimensional magnetic bodies with polygonal cross-section: Its properties and use for automated anomaly interpretation
    • M. N. Nabighian, “The analytic signal of two-dimensional magnetic bodies with polygonal cross-section: Its properties and use for automated anomaly interpretation,” Geophysics 37, 507-517 (1972).
    • (1972) Geophysics , vol.37 , pp. 507-517
    • Nabighian, M.N.1
  • 29
    • 0021642517 scopus 로고
    • Toward a three-dimensional automatic interpretation of potential field data via generalized Hilbert transform: Fundamental relations
    • M. N. Nabighian, “Toward a three-dimensional automatic interpretation of potential field data via generalized Hilbert transform: Fundamental relations,” Geophysics 49, 780-786 (1984).
    • (1984) Geophysics , vol.49 , pp. 780-786
    • Nabighian, M.N.1
  • 30
    • 0024072525 scopus 로고
    • Application of 2-D Hilbert transform in geophysical imaging with potential field data
    • W. M. Moon, A. Ushah, V. Singh, and B. Bruce, “Application of 2-D Hilbert transform in geophysical imaging with potential field data,” IEEE Trans. Geosci. Remote Sens. 26, 502-510 (1988).
    • (1988) IEEE Trans. Geosci. Remote Sens , vol.26 , pp. 502-510
    • Moon, W.M.1    Ushah, A.2    Singh, V.3    Bruce, B.4
  • 31
    • 0029730827 scopus 로고    scopus 로고
    • Theory of 2-D complex seismic trace analysis
    • A. E. Barnes, “Theory of 2-D complex seismic trace analysis,” Geophysics 61, 264-272 (1996).
    • (1996) Geophysics , vol.61 , pp. 264-272
    • Barnes, A.E.1
  • 32
    • 0038719567 scopus 로고
    • Surface extraction from 3D images via local energy and ridge tracing
    • Australian Pattern Recognition Society, Brisbane, Australia
    • C. Pudney and M. Robbins, “Surface extraction from 3D images via local energy and ridge tracing,” in Digital Image Computing: Techniques and Analysis (Australian Pattern Recognition Society, Brisbane, Australia, 1995), pp. 240- 245.
    • (1995) Digital Image Computing: Techniques and Analysis
    • Pudney, C.1    Robbins, M.2
  • 33
    • 0024294846 scopus 로고
    • Feature detection in human vision: A phase-dependent energy model
    • M. C. Morrone and D. C. Burr, “Feature detection in human vision: A phase-dependent energy model,” Proc. R. Soc. London Ser. B 235, 221-245 (1988).
    • (1988) Proc. R. Soc. London Ser. B , vol.235 , pp. 221-245
    • Morrone, M.C.1    Burr, D.C.2
  • 34
    • 84975604875 scopus 로고
    • Contrast in complex images
    • E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032-2040 (1990).
    • (1990) J. Opt. Soc. Am. A , vol.7 , pp. 2032-2040
    • Peli, E.1
  • 35
    • 0030260162 scopus 로고    scopus 로고
    • Scale-space properties of quadratic feature detectors
    • P. Kube and P. Perona, “Scale-space properties of quadratic feature detectors,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 987-999 (1996).
    • (1996) IEEE Trans. Pattern Anal. Mach. Intell , vol.18 , pp. 987-999
    • Kube, P.1    Perona, P.2
  • 37
    • 0032628036 scopus 로고    scopus 로고
    • Die Hilberttransformation und ihre Verallgemeinerung in Optik und Bildeverarbei- tung
    • R. Muller and J. Marquard, “Die Hilberttransformation und ihre Verallgemeinerung in Optik und Bildeverarbei- tung,” Optik (Stuttgart) 110, 99-109 (1999).
    • (1999) Optik (Stuttgart) , vol.110 , pp. 99-109
    • Muller, R.1    Marquard, J.2
  • 38
    • 0001806403 scopus 로고    scopus 로고
    • Image processing with the radial Hilbert transform: Theory and experiments
    • J. A. Davis, D. E. McNamara, D. Cottrel, and J. Campos, “Image processing with the radial Hilbert transform: Theory and experiments,” Opt. Lett. 25, 99-101 (2000).
    • (2000) Opt. Lett , vol.25 , pp. 99-101
    • Davis, J.A.1    McNamara, D.E.2    Cottrel, D.3    Campos, J.4
  • 40
    • 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
  • 41
    • 84873559847 scopus 로고
    • Interferogram analysis using an accurate fully automatic algorithm
    • K. A. Nugent, “Interferogram analysis using an accurate fully automatic algorithm,” Appl. Opt. 24, 3101-3105 (1985).
    • (1985) Appl. Opt , vol.24 , pp. 3101-3105
    • Nugent, K.A.1
  • 42
    • 0000682663 scopus 로고
    • Fringe-pattern analysis using a 2-D Fourier transform
    • D. J. Bone, H.-A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653-1660 (1986).
    • (1986) Appl. Opt , vol.25 , pp. 1653-1660
    • Bone, D.J.1    Bachor, H.-A.2    Sandeman, R.J.3
  • 43
    • 85010106038 scopus 로고    scopus 로고
    • Principles and Methods (Akademie, Berlin
    • T. Kreis, Holographic Interferometry. Principles and Methods (Akademie, Berlin, 1996), Vol. 1.
    • (1996) Holographic Interferometry , vol.1
    • Kreis, T.1
  • 46
    • 0022012336 scopus 로고
    • Fraunhofer diffraction from a circular annular aperture with helical phase factor
    • W. J. Condell, “Fraunhofer diffraction from a circular annular aperture with helical phase factor,” J. Opt. Soc. Am. A 2, 206-208 (1985).
    • (1985) J. Opt. Soc. Am. A , vol.2 , pp. 206-208
    • Condell, W.J.1
  • 50
    • 5444236478 scopus 로고    scopus 로고
    • The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis
    • N. E. Huang, Z. Shen, S. Long, M. C. Wu et al., “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis,” Proc. R. Soc. London Ser. A 454, 903-995 (1998).
    • (1998) Proc. R. Soc. London Ser. A , vol.454 , pp. 903-995
    • Huang, N.E.1    Shen, Z.2    Long, S.3    Wu, M.C.4
  • 51
    • 84938437548 scopus 로고
    • On the quadrature approximation to the Hil-bert transform of modulated signals
    • A. H. Nuttall, “On the quadrature approximation to the Hil-bert transform of modulated signals,” Proc. IEEE 54, 1458-1459 (1966).
    • (1966) Proc. IEEE , vol.54 , pp. 1458-1459
    • Nuttall, A.H.1
  • 52
    • 0028530354 scopus 로고
    • Andresen, “Fringe-orientation maps and fringe skeleton extraction by the two-dimensional derivative-sign binary-fringe method,”Appl
    • Q. Yu and K. Andresen, “Fringe-orientation maps and fringe skeleton extraction by the two-dimensional derivative-sign binary-fringe method,”Appl. Opt. 33, 6873-6878 (1994).
    • (1994) Opt , vol.33 , pp. 6873-6878
    • Yu, Q.1
  • 53
    • 0029278560 scopus 로고
    • Demodulation, predictive coding, and spatial vision
    • J. G. Daugman and C. J. Downing, “Demodulation, predictive coding, and spatial vision,” J. Opt. Soc. Am. A 12, 641-660 (1995).
    • (1995) J. Opt. Soc. Am. A , vol.12 , pp. 641-660
    • Daugman, J.G.1    Downing, C.J.2
  • 54
    • 85076354073 scopus 로고
    • Propagation of errors in different phase-shifting algorithms: A special property of the arctangent function
    • G. M. Brown, O. Y. Kwon, M. Kujawinska, and G. T. Reid, eds., Proc. SPIE 1755
    • K. G. Larkin and B. F. Oreb, “Propagation of errors in different phase-shifting algorithms: A special property of the arctangent function,” in Interferometry: Techniques and Analysis, G. M. Brown, O. Y. Kwon, M. Kujawinska, and G. T. Reid, eds., Proc. SPIE 1755, 219-227 (1992).
    • (1992) Interferometry: Techniques and Analysis , pp. 219-227
    • Larkin, K.G.1    Oreb, B.F.2
  • 56
    • 0000818955 scopus 로고    scopus 로고
    • Fourier spectrum of radially periodic images
    • I. Amidror, “Fourier spectrum of radially periodic images,” J. Opt. Soc. Am. A 14, 816-826 (1997).
    • (1997) J. Opt. Soc. Am. A , vol.14 , pp. 816-826
    • Amidror, I.1
  • 58
    • 0033349541 scopus 로고    scopus 로고
    • On an ambiguity in the definition of the amplitude and phase of a signal
    • L. Cohen, P. Loughlin, and D. Vakman, “On an ambiguity in the definition of the amplitude and phase of a signal,” Signal Process. 79, 301-307 (1999).
    • (1999) Signal Process , vol.79 , pp. 301-307
    • Cohen, L.1    Loughlin, P.2    Vakman, D.3
  • 59
    • 84937425491 scopus 로고    scopus 로고
    • The multidimensional isotro-pic generalization of quadrature filters in geometric algebra
    • Springer-Verlag, Heidelberg
    • M. Felsberg and G. Sommer, “The multidimensional isotro-pic generalization of quadrature filters in geometric algebra,” in Algebraic Frames for the Perception-Action Cycle, AFPAC 2000 (Springer-Verlag, Heidelberg, 2000), pp. 175-185.
    • (2000) Algebraic Frames for the Perception-Action Cycle, AFPAC 2000 , pp. 175-185
    • Felsberg, M.1    Sommer, G.2
  • 60
    • 21144474403 scopus 로고
    • Doran, “Imaginary numbers are not real-the geometric algebra of spacetime
    • S. Gull, A. Lasenby, and C. Doran, “Imaginary numbers are not real-the geometric algebra of spacetime,” Found. Phys. 23, 1175-1201 (1993).
    • (1993) Found. Phys , vol.23 , pp. 1175-1201
    • Gull, S.1    Lasenby, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.