基于涡旋滤波的图像边缘增强研究进展
|
摘要
作为图像处理的一个重要手段,边缘增强技术对振幅型和相位型物体成像有着重要的作用。而基于径向希尔伯特变换的涡旋滤波技术因其能够实现各向同性边缘增强倍受关注,但传统的涡旋滤波由于中心奇点和锐利边缘引起的衍射会造成背景噪声的加剧和对比度的降低。近年来众多课题组针对涡旋滤波旁瓣抑制提出了种类各异的新型涡旋滤波器,此外基于涡旋滤波的各向同性和各向异性边缘增强技术也得到了迅速发展。文中扼要地总结了近年来几种抑制涡旋旁瓣的方法,包括拉盖尔高斯振幅调制、贝塞尔振幅调制、艾里振幅调制,并从标量涡旋滤波和矢量涡旋滤波两个方面分别综述了各向同性和各向异性边缘增强的实现方法与研究进展。
As an important means of image processing, the edge enhancement techniques play an important role in amplitude-contrast and phase-contrast objects imaging. The vortex filtering techniques based on radial Hilbert transform have attracted much attention because it can achieve isotropic edge enhancement. However, the classical vortex filtering causes background noise and contrast reduction due to diffraction caused by central singularities and sharp edges. In recent years, many research groups have proposed new types of vortex filters for vortex filtering side lobe suppression. In addition, the isotropic and anisotropic edge enhancement techniques based on vortex filtering have also developed rapidly. In this paper, several methods for suppressing vortex side lobes were summarized in recent years, including Laguerre Gaussian amplitude modulation, Bessel-like amplitude modulation, and Airy amplitude modulation. What′ s more, from two aspects: scalar vortex filtering and vector vortex filtering, the isotropic and anisotropic edge enhancement methods and progress were reviewed.
As an important means of image processing, the edge enhancement techniques play an important role in amplitude-contrast and phase-contrast objects imaging. The vortex filtering techniques based on radial Hilbert transform have attracted much attention because it can achieve isotropic edge enhancement. However, the classical vortex filtering causes background noise and contrast reduction due to diffraction caused by central singularities and sharp edges. In recent years, many research groups have proposed new types of vortex filters for vortex filtering side lobe suppression. In addition, the isotropic and anisotropic edge enhancement techniques based on vortex filtering have also developed rapidly. In this paper, several methods for suppressing vortex side lobes were summarized in recent years, including Laguerre Gaussian amplitude modulation, Bessel-like amplitude modulation, and Airy amplitude modulation. What′ s more, from two aspects: scalar vortex filtering and vector vortex filtering, the isotropic and anisotropic edge enhancement methods and progress were reviewed.
引文
[1]JoséA Ferrari,Flores J L,César D Perciante,et al.Edge enhancement and image equalization by unsharp masking using self-adaptive photochromic filters[J].Applied Optics,2009,48(19):3570-3579.
[2]Mazzaferri J,Ledesma S.Rotation invariant real-time optical edge detector[J].Optics Communications,2007,272(2):367-376.
[3]César D Perciante,JoséA Ferrari.Visualization of twodimensional phase gradients by subtraction of a reference periodic pattern[J].Applied Optics,2000,39(13):2081-2083.
[4]Meihua X.Image enhancement based on edge-directed diffusion[J].Acta Photonica Sinica,2005,34(9):274-277.
[5]Xue J,Jie L,Liu Z.An enhancement algorithm for low quality fingerprint image based on edge filter and Gabor filter[C]//SPIE,2009,7383:848-849.
[6]Jiang X.Research on the key technique of image preprocessing in the fingerprint identification[C]//Software Engineering WCSE WRI World Congress on,2009,2:391-394.
[7]Foo G,Palacios D M,Swartzlander G A.Optical vortex coronagraph[J].Optics Letters,2005,30(24):3308-3310.
[8]Mawet D,Serabyn E,Wallace J K,et al.Improved high contrast imaging with on-axis telescopes using a,multi-stage vortex coronagraph[J].Optics Letters,2011,36(8):1506-1508.
[9]Eschbach R.Error-diffusion algorithm with edge enhancement[J].Journal of the Optical Society of America A,1991,8(12):1844-1850.
[10]Chung K L,Pei S C,Pan Y L,et al.A gradient-based adaptive error diffusion method with edge enhancement[J].Expert Systems with Applications,2011,38(3):1591-1601.
[11]Lai J Z C,Chen C C.Algorithms of halftoning color images with edge enhancement[J].Journal of Visual Communication and Image Representation,2003,14(4):389-404.
[12]Rose R A S,Govindaraju S.Hardware based algorithm for chaotic and edge enhanced error diffusion[J].IEEE Transactions on Consumer Electronics,2010,56(3):1755-1762.
[13]Feinberg J.Real-time edge enhancement using the photorefractive effect[J].Optics Letters,1980,5(8):330.
[14]Jose A Ferrari,Jorge L Flores,Gaston A Ayubi,et al.Orientation-selective edge enhancement of phase objects[J].Optics Communications,2019,434:44-48.
[15]Shishido A.Optical image processing by means of photosensitive nonlinear liquid crystal film:edge enhancement and image addition subtraction[J].Optics Letters,2001,26(15):1140.
[16]Chaira T.A rank ordered filter for medical image edge enhancement and detection using intuitionistic fuzzy set[J].Applied Soft Computing,2012,12(4):1259-1266.
[17]Lohmann A W,Mendlovic D,Zalevsky Z.Fractional Hilbert transform[J].Optics Letters,1996,21(4):281.
[18]Davis J A,Mcnamara D E,Cottrell D M.Analysis of the fractional Hilbert transform[J].Applied Optics,1998,37(29):6911-6913.
[19]Lohmann A W,E Tepichín,J G Ramírez.Optical implementation of the fractional Hubert transform for twodimensional objects[J].Applied Optics,1997,36(26):6620-6626.
[20]Davis J A,Mcnamara D E,Cottrell D M,et al.Image processing with the radial Hilbert transform:theory and experiments[J].Optics Letters,2000,25(2):99-101.
[21]Crabtree K,Davis J A,Moreno I.Optical processing with vortex-producing lenses[J].Applied Optics,2004,43(6):1360-1367.
[22]Swartzlander G A.Peering into darkness with a vortex spatial filter[J].Optics Letters,2001,26(8):497-499.
[23]Maurer C,Jesacher A,Fürhaper S,et al.Upgrading a microscope with a spiral phase plate[J].Journal of Microscopy,2008,230(1):9.
[24]Severin Fürhapter,Jesacher A,Bernet S,et al.Spiral phase contrast imaging in microscopy[J].Optics Express,2005,13(3):689-694.
[25]Bernet S,Jesacher A,Severin Fürhapter,et al.Quantitative imaging of complex samples by spiral phase contrast microscopy[J].Optics Express,2006,14(9):3792-3805.
[26]Kotlyar V V,Kovalev A A,Soifer V A,et al.Sidelobe contrast reduction for optical vortex beams using a helical axicon[J].Optics Letters,2007,32(8):921-923.
[27]Kotlyar V V,Kovalev A A,Skidanov R V,et al.Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate[J].Journal of the Optical Society of America A,2007,24(7):1955-1964.
[28]Lin J,Yuan X C,Tao S H,et al.Variable-radius focused optical vortex with suppressed sidelobes.[J].Optics Letters,2006,31(11):1600-1602.
[29]Nándor Bokor,Iketaki Y.Laguerre-Gaussian radial Hilbert transform for edge-enhancement Fourier transform X-ray microscopy[J].Optics Express,2009,17(7):5533-5539.
[30]Qiu X,Li F,Zhang W,et al.Spiral phase contrast imaging in nonlinear optics:Seeing phase objects using invisible illumination[J].Optica,2018,5(2):208.
[31]Shibiao W,Jing B,Siwei Z,et al.Image edge-enhancement in optical microscopy with a phase mismatched spiral phase plate[J].Chinese Optics Letters,2011,9(3):29-32.
[32]Sharma M,Joseph J,Senthilkumaran P.Selective edge enhancement using shifted anisotropic vortex filter[J].Journal of Optics,2013,42(1):1-7.
[33]Sharma M K,Joseph J,Senthilkumaran P.Effect of aberrations in vortex spatial filtering[J].Optics&Lasers in Engineering,2012,50(11):1501-1507.
[34]Jesacher A,Fürhapter S,Bernet S,et al.Shadow effects in spiral phase contrast microscopy[J].Physical Review Letters,2005,94(23):233902.
[35]Teich M,Mattern M,Sturm J,et al.Spiral phase mask shadow-imaging for 3D-measurement of flow fields[J].Optics Express,2016,24(24):27371-27381.
[36]Gozali R,Nguyen T A,Bendau E,et al.Compact OAMmicroscope for edge enhancement of biomedical and object samples[J].Review of Scientific Instruments,2017,88(9):093701.
[37]Ram B S B,Senthilkumaran P,Sharma A.Polarizationbased spatial filtering for directional and nondirectional edge enhancement using an S-waveplate[J].Applied Optics,2017,56:3171-3178.
[38]Davis J A,Mcnamara D E,Cottrell D M,et al.Image processing with the radial Hilbert transform:theory and experiments.[J].Optics Letters,2000,25(2):99-101.
[39]Guo C S,Liu X,He J L,et al.Optimal annulus structures of optical vortices[J].Optics Express,2004,12(19):4625-4634.
[40]Guo C S,Liu X,Ren X Y,et al.Optimal annular computer-generated holograms for the generation of optical vortices[J].Journal of the Optical Society of America A,2005,22(2):385.
[41]Guo C S,Han Y J,Xu J B,et al.Radial Hilbert transform with Laguerre-Gaussian spatial filters[J].Optics Letters,2006,31(10):1394-1396.
[42]Chen J,Yuan X C,Zhao X,et al.Generalized approach to modifying optical vortices with suppressed sidelobes using Bessel-like functions[J].Optics Letters,2009,34(21):3289-3291.
[43]Wei S B,Zhu S W,Yuan X C.Image edge enhancement in optical microscopy with a Bessel-like amplitude modulated spiral phase filter[J].Journal of Optics,2011,13(10):219-224.
[44]Zhou Y,Feng S,Nie S,et al.Image edge enhancement using airy spiral phase filter.[J].Optics Express,2016,24(22):25258.
[45]Situ G,Pedrini G,Osten W.Spiral phase filtering and orientation-selective edge detection/enhancemen[J].Journal of the Optical Society of America A,2009,26(8):1788.
[46]Joshi M,Shakher C,Singh K.Image encryption and decryption using fractional Fourier transform and radial Hilbert transform[J].Optics and Lasers in Engineering,2008,46(7):522-526.
[47]Zhou Y,Feng S,Nie S,et al.Anisotropic edge enhancement with spiral zone plate under femtosecond laser illumination[J].Applied Optics,2017,56(10):2641.
[48]Wang J,Zhang W,Qi Q,et al.Gradual edge enhancement in spiral phase contrast imaging with fractional vortex filters[J].Scientific Reports,2015,5:15826.
[49]Sharma M K,Joseph J,Senthilkumaran P.Selective edge enhancement using anisotropic vortex filter[J].Applied Optics,2011,50(27):5279-5286.
[50]Sharma M K,Joseph J,Senthilkumaran P.Directional edge enhancement using superposed vortex filter[J].Optics&Laser Technology,2014,57:230-235.
[51]Li X,Cao Y,Gu M.Superresolution-focal-volume induced30 Tbytes/disk capacity by focusing a radially polarized beam[J].Optics Letters,2011,36(13):2510-2512.
[52]Yu W,Ji Z,Dong D,et al.Super-resolution deep imaging with hollow Bessel beam STED microscopy[J].Laser&Photonics Reviews,2016,10(1):147-152.
[53]Xu-Zhen G,Yue P,Meng-Dan Z,et al.Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model[J].Optics Express,2018,26(2):1597-1614.
[54]Pan Y,Li Y N,Ren Z C,et al.Parabolic-symmetry vector optical fields and their tightly focusing properties[J].Physical Review A,2014,89(3):035801.
[55]Pan Y,Li Y,Li S M,et al.Vector optical fields with bipolar symmetry of linear polarization[J].Optics Letters,2013,38(18):3700-3703.
[56]Lerman G M,Levy U.Tight focusing of spatially variant vector optical fields with elliptical symmetry of linear polarization[J].Optics Letters,2007,32(15):2194-2196.
[57]Lerman G M,Stern L,Levy U.Generation and tight focusing of hybridly polarized vector beams[J].Optics Express,2010,18(26):27650-27657.
[58]Pan Y,Gao X Z,Cai M Q,et al.Fractal vector optical fields[J].Optics Letters,2016,41:3161-3164.
[59]Han L,Liu S,Li P,et al.Managing focal fields of vector beams with multiple polarization singularities[J].Applied Optics,2016,55(32):9049-9053.
[60]Pan Y,Li Y N,Ren Z C,et al.Parabolic-symmetry vector optical fields and their tightly focusing properties[J].Physical Review A,2014,89(3):035801.
[61]Pan Y,Li Y N,Li S M,et al.Elliptic-symmetry vector optical fields[J].Optics Express,2014,22(16):19302-19313.
[62]Pan Y,Li Y,Li S M,et al.Vector optical fields with bipolar symmetry of linear polarization[J].Optics Letters,2013,38(18):3700-3703.
[63]Gao X Z,Pan Y,Cai M Q,et al.Hyperbolic-symmetry vector fields[J].Optics Express,2015,23(25):32238-32252.
[64]Chen H,Zheng Z,Zhang B F,et al.Polarization structuring of focused field through polarization-only modulation of incident beam[J].Optics Letters,2010,35(16):2825-2827.
[65]Chen Z,Zeng T,Ding J.Reverse engineering approach to focus shaping[J].Optics Letters,2016,41(9):1929-1932.
[66]Lerman G M,Levy U.Tight focusing of spatially variant vector optical fields with elliptical symmetry of linear polarization[J].Optics Letters,2007,32(15):2194-2196.
[67]Lerman G M,Lilach Y,Levy U.Demonstration of spatially inhomogeneous vector beams with elliptical symmetry[J].Optics Letters,2009,34(11):1669-1671.
[68]Kozawa Y,Sato S.Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams[J].Optics Express,2010,18(10):10828-10833.
[69]Kawauchi H,Yonezawa K,Kozawa Y,et al.Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam[J].Optics Letters,2007,32(13):1839-1841.
[70]Zhan Q.Trapping metallic Rayleigh particles with radial polarization[J].Optics Express,2004,12(15):3377-3382.
[71]Wang X L,Chen J,Li Y N,et al.Optical orbital angular momentum from the curl ofpolarization[J].Physical Review Letters,2010,105(25):253602.
[72]Xu D,Gu B,Rui G,et al.Generation of arbitrary vector fields based on a pair of orthogonal elliptically polarized base vectors[J].Optics Express,2016,24(4):4177-4186.
[73]Wang X L,Li Y,Chen J,et al.A new type of vector fields with hybrid states of polarization[J].Optics Express,2010,18(10):10786-10795.
[74]Li L,Chang C,Yuan X,et al.Generation of optical vortex array along arbitrary curvilinear arrangement[J].Optics Express,2018,26(8):9798.
[75]Li L,Chang C,Yuan C,et al.High efficiency generation of tunable ellipse perfect vector beams[J].Photonics Research,2018,6(12):1116-1123.
[76]Li Delin,Feng Shaotong,Nie Shouping,et al.Generation of arbitrary perfect Poincarébeams[J].Journal of Applied Physics,2019,125:073105.
[77]Gu Fengyan,Lin L,Chang Chenliang,et al.Generation offractional ellipse perfect vector beams[J].Optics Communications,2019,443:44-47.
[78]Li Delin,Chang Chenliang,Nie Shouping,et al.Generation of elliptic perfect optical vortex and elliptic perfect vector beam by modulating the dynamic and geometric phase[J].Applied Physics Letters,2018,113:121101.
[79]Liu Yuanyuan,Liu Zhenxing,Zhou Junxiao,et al.Measurements of Pancharatnam-Berry phase in mode transformations on hybrid-order Poincarésphere[J].Optics Letters,2017,42(17):3447-3450.
[80]Luo H,Zhou J,Wen S,et al.Higher-order laser mode converters with dielectric metasurfaces[J].Optics Letters,2015,40(23):5506-5509.
[81]Milione G,Evans S,Nolan D A,et al.Higher order Pancharatnam-Berry phase and the angular momentum of light[J].Physical Review Letters,2012,108(19):190401.
[82]Han Y J,Guo C S,Rong Z Y,et al.Radial Hilbert transform with the spatially variable half-wave plate[J].Optics Letters,2013,38(23):5169-5171.
[83]Bhargava Ram B S.Paramasivam Senthil-kumaran.Edge enhancement by negative Poincare-Hopf index filters[J].Optics Letters,2018,43(8):1830-1833.
[84]Zhang B,Chen Z,Sun H,et al.Vectorial optical vortex filtering for edge enhancement[J].Journal of Optics,2016,18(3):035703.
[85]Li Delin,Feng Shaotong,Nie Shouping,et al.Scalar and vectorial vortex filtering based on geometric phase modulation with a Q-plate[J].Journal of Optics,2019,21(6):065702.
[2]Mazzaferri J,Ledesma S.Rotation invariant real-time optical edge detector[J].Optics Communications,2007,272(2):367-376.
[3]César D Perciante,JoséA Ferrari.Visualization of twodimensional phase gradients by subtraction of a reference periodic pattern[J].Applied Optics,2000,39(13):2081-2083.
[4]Meihua X.Image enhancement based on edge-directed diffusion[J].Acta Photonica Sinica,2005,34(9):274-277.
[5]Xue J,Jie L,Liu Z.An enhancement algorithm for low quality fingerprint image based on edge filter and Gabor filter[C]//SPIE,2009,7383:848-849.
[6]Jiang X.Research on the key technique of image preprocessing in the fingerprint identification[C]//Software Engineering WCSE WRI World Congress on,2009,2:391-394.
[7]Foo G,Palacios D M,Swartzlander G A.Optical vortex coronagraph[J].Optics Letters,2005,30(24):3308-3310.
[8]Mawet D,Serabyn E,Wallace J K,et al.Improved high contrast imaging with on-axis telescopes using a,multi-stage vortex coronagraph[J].Optics Letters,2011,36(8):1506-1508.
[9]Eschbach R.Error-diffusion algorithm with edge enhancement[J].Journal of the Optical Society of America A,1991,8(12):1844-1850.
[10]Chung K L,Pei S C,Pan Y L,et al.A gradient-based adaptive error diffusion method with edge enhancement[J].Expert Systems with Applications,2011,38(3):1591-1601.
[11]Lai J Z C,Chen C C.Algorithms of halftoning color images with edge enhancement[J].Journal of Visual Communication and Image Representation,2003,14(4):389-404.
[12]Rose R A S,Govindaraju S.Hardware based algorithm for chaotic and edge enhanced error diffusion[J].IEEE Transactions on Consumer Electronics,2010,56(3):1755-1762.
[13]Feinberg J.Real-time edge enhancement using the photorefractive effect[J].Optics Letters,1980,5(8):330.
[14]Jose A Ferrari,Jorge L Flores,Gaston A Ayubi,et al.Orientation-selective edge enhancement of phase objects[J].Optics Communications,2019,434:44-48.
[15]Shishido A.Optical image processing by means of photosensitive nonlinear liquid crystal film:edge enhancement and image addition subtraction[J].Optics Letters,2001,26(15):1140.
[16]Chaira T.A rank ordered filter for medical image edge enhancement and detection using intuitionistic fuzzy set[J].Applied Soft Computing,2012,12(4):1259-1266.
[17]Lohmann A W,Mendlovic D,Zalevsky Z.Fractional Hilbert transform[J].Optics Letters,1996,21(4):281.
[18]Davis J A,Mcnamara D E,Cottrell D M.Analysis of the fractional Hilbert transform[J].Applied Optics,1998,37(29):6911-6913.
[19]Lohmann A W,E Tepichín,J G Ramírez.Optical implementation of the fractional Hubert transform for twodimensional objects[J].Applied Optics,1997,36(26):6620-6626.
[20]Davis J A,Mcnamara D E,Cottrell D M,et al.Image processing with the radial Hilbert transform:theory and experiments[J].Optics Letters,2000,25(2):99-101.
[21]Crabtree K,Davis J A,Moreno I.Optical processing with vortex-producing lenses[J].Applied Optics,2004,43(6):1360-1367.
[22]Swartzlander G A.Peering into darkness with a vortex spatial filter[J].Optics Letters,2001,26(8):497-499.
[23]Maurer C,Jesacher A,Fürhaper S,et al.Upgrading a microscope with a spiral phase plate[J].Journal of Microscopy,2008,230(1):9.
[24]Severin Fürhapter,Jesacher A,Bernet S,et al.Spiral phase contrast imaging in microscopy[J].Optics Express,2005,13(3):689-694.
[25]Bernet S,Jesacher A,Severin Fürhapter,et al.Quantitative imaging of complex samples by spiral phase contrast microscopy[J].Optics Express,2006,14(9):3792-3805.
[26]Kotlyar V V,Kovalev A A,Soifer V A,et al.Sidelobe contrast reduction for optical vortex beams using a helical axicon[J].Optics Letters,2007,32(8):921-923.
[27]Kotlyar V V,Kovalev A A,Skidanov R V,et al.Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate[J].Journal of the Optical Society of America A,2007,24(7):1955-1964.
[28]Lin J,Yuan X C,Tao S H,et al.Variable-radius focused optical vortex with suppressed sidelobes.[J].Optics Letters,2006,31(11):1600-1602.
[29]Nándor Bokor,Iketaki Y.Laguerre-Gaussian radial Hilbert transform for edge-enhancement Fourier transform X-ray microscopy[J].Optics Express,2009,17(7):5533-5539.
[30]Qiu X,Li F,Zhang W,et al.Spiral phase contrast imaging in nonlinear optics:Seeing phase objects using invisible illumination[J].Optica,2018,5(2):208.
[31]Shibiao W,Jing B,Siwei Z,et al.Image edge-enhancement in optical microscopy with a phase mismatched spiral phase plate[J].Chinese Optics Letters,2011,9(3):29-32.
[32]Sharma M,Joseph J,Senthilkumaran P.Selective edge enhancement using shifted anisotropic vortex filter[J].Journal of Optics,2013,42(1):1-7.
[33]Sharma M K,Joseph J,Senthilkumaran P.Effect of aberrations in vortex spatial filtering[J].Optics&Lasers in Engineering,2012,50(11):1501-1507.
[34]Jesacher A,Fürhapter S,Bernet S,et al.Shadow effects in spiral phase contrast microscopy[J].Physical Review Letters,2005,94(23):233902.
[35]Teich M,Mattern M,Sturm J,et al.Spiral phase mask shadow-imaging for 3D-measurement of flow fields[J].Optics Express,2016,24(24):27371-27381.
[36]Gozali R,Nguyen T A,Bendau E,et al.Compact OAMmicroscope for edge enhancement of biomedical and object samples[J].Review of Scientific Instruments,2017,88(9):093701.
[37]Ram B S B,Senthilkumaran P,Sharma A.Polarizationbased spatial filtering for directional and nondirectional edge enhancement using an S-waveplate[J].Applied Optics,2017,56:3171-3178.
[38]Davis J A,Mcnamara D E,Cottrell D M,et al.Image processing with the radial Hilbert transform:theory and experiments.[J].Optics Letters,2000,25(2):99-101.
[39]Guo C S,Liu X,He J L,et al.Optimal annulus structures of optical vortices[J].Optics Express,2004,12(19):4625-4634.
[40]Guo C S,Liu X,Ren X Y,et al.Optimal annular computer-generated holograms for the generation of optical vortices[J].Journal of the Optical Society of America A,2005,22(2):385.
[41]Guo C S,Han Y J,Xu J B,et al.Radial Hilbert transform with Laguerre-Gaussian spatial filters[J].Optics Letters,2006,31(10):1394-1396.
[42]Chen J,Yuan X C,Zhao X,et al.Generalized approach to modifying optical vortices with suppressed sidelobes using Bessel-like functions[J].Optics Letters,2009,34(21):3289-3291.
[43]Wei S B,Zhu S W,Yuan X C.Image edge enhancement in optical microscopy with a Bessel-like amplitude modulated spiral phase filter[J].Journal of Optics,2011,13(10):219-224.
[44]Zhou Y,Feng S,Nie S,et al.Image edge enhancement using airy spiral phase filter.[J].Optics Express,2016,24(22):25258.
[45]Situ G,Pedrini G,Osten W.Spiral phase filtering and orientation-selective edge detection/enhancemen[J].Journal of the Optical Society of America A,2009,26(8):1788.
[46]Joshi M,Shakher C,Singh K.Image encryption and decryption using fractional Fourier transform and radial Hilbert transform[J].Optics and Lasers in Engineering,2008,46(7):522-526.
[47]Zhou Y,Feng S,Nie S,et al.Anisotropic edge enhancement with spiral zone plate under femtosecond laser illumination[J].Applied Optics,2017,56(10):2641.
[48]Wang J,Zhang W,Qi Q,et al.Gradual edge enhancement in spiral phase contrast imaging with fractional vortex filters[J].Scientific Reports,2015,5:15826.
[49]Sharma M K,Joseph J,Senthilkumaran P.Selective edge enhancement using anisotropic vortex filter[J].Applied Optics,2011,50(27):5279-5286.
[50]Sharma M K,Joseph J,Senthilkumaran P.Directional edge enhancement using superposed vortex filter[J].Optics&Laser Technology,2014,57:230-235.
[51]Li X,Cao Y,Gu M.Superresolution-focal-volume induced30 Tbytes/disk capacity by focusing a radially polarized beam[J].Optics Letters,2011,36(13):2510-2512.
[52]Yu W,Ji Z,Dong D,et al.Super-resolution deep imaging with hollow Bessel beam STED microscopy[J].Laser&Photonics Reviews,2016,10(1):147-152.
[53]Xu-Zhen G,Yue P,Meng-Dan Z,et al.Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model[J].Optics Express,2018,26(2):1597-1614.
[54]Pan Y,Li Y N,Ren Z C,et al.Parabolic-symmetry vector optical fields and their tightly focusing properties[J].Physical Review A,2014,89(3):035801.
[55]Pan Y,Li Y,Li S M,et al.Vector optical fields with bipolar symmetry of linear polarization[J].Optics Letters,2013,38(18):3700-3703.
[56]Lerman G M,Levy U.Tight focusing of spatially variant vector optical fields with elliptical symmetry of linear polarization[J].Optics Letters,2007,32(15):2194-2196.
[57]Lerman G M,Stern L,Levy U.Generation and tight focusing of hybridly polarized vector beams[J].Optics Express,2010,18(26):27650-27657.
[58]Pan Y,Gao X Z,Cai M Q,et al.Fractal vector optical fields[J].Optics Letters,2016,41:3161-3164.
[59]Han L,Liu S,Li P,et al.Managing focal fields of vector beams with multiple polarization singularities[J].Applied Optics,2016,55(32):9049-9053.
[60]Pan Y,Li Y N,Ren Z C,et al.Parabolic-symmetry vector optical fields and their tightly focusing properties[J].Physical Review A,2014,89(3):035801.
[61]Pan Y,Li Y N,Li S M,et al.Elliptic-symmetry vector optical fields[J].Optics Express,2014,22(16):19302-19313.
[62]Pan Y,Li Y,Li S M,et al.Vector optical fields with bipolar symmetry of linear polarization[J].Optics Letters,2013,38(18):3700-3703.
[63]Gao X Z,Pan Y,Cai M Q,et al.Hyperbolic-symmetry vector fields[J].Optics Express,2015,23(25):32238-32252.
[64]Chen H,Zheng Z,Zhang B F,et al.Polarization structuring of focused field through polarization-only modulation of incident beam[J].Optics Letters,2010,35(16):2825-2827.
[65]Chen Z,Zeng T,Ding J.Reverse engineering approach to focus shaping[J].Optics Letters,2016,41(9):1929-1932.
[66]Lerman G M,Levy U.Tight focusing of spatially variant vector optical fields with elliptical symmetry of linear polarization[J].Optics Letters,2007,32(15):2194-2196.
[67]Lerman G M,Lilach Y,Levy U.Demonstration of spatially inhomogeneous vector beams with elliptical symmetry[J].Optics Letters,2009,34(11):1669-1671.
[68]Kozawa Y,Sato S.Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams[J].Optics Express,2010,18(10):10828-10833.
[69]Kawauchi H,Yonezawa K,Kozawa Y,et al.Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam[J].Optics Letters,2007,32(13):1839-1841.
[70]Zhan Q.Trapping metallic Rayleigh particles with radial polarization[J].Optics Express,2004,12(15):3377-3382.
[71]Wang X L,Chen J,Li Y N,et al.Optical orbital angular momentum from the curl ofpolarization[J].Physical Review Letters,2010,105(25):253602.
[72]Xu D,Gu B,Rui G,et al.Generation of arbitrary vector fields based on a pair of orthogonal elliptically polarized base vectors[J].Optics Express,2016,24(4):4177-4186.
[73]Wang X L,Li Y,Chen J,et al.A new type of vector fields with hybrid states of polarization[J].Optics Express,2010,18(10):10786-10795.
[74]Li L,Chang C,Yuan X,et al.Generation of optical vortex array along arbitrary curvilinear arrangement[J].Optics Express,2018,26(8):9798.
[75]Li L,Chang C,Yuan C,et al.High efficiency generation of tunable ellipse perfect vector beams[J].Photonics Research,2018,6(12):1116-1123.
[76]Li Delin,Feng Shaotong,Nie Shouping,et al.Generation of arbitrary perfect Poincarébeams[J].Journal of Applied Physics,2019,125:073105.
[77]Gu Fengyan,Lin L,Chang Chenliang,et al.Generation offractional ellipse perfect vector beams[J].Optics Communications,2019,443:44-47.
[78]Li Delin,Chang Chenliang,Nie Shouping,et al.Generation of elliptic perfect optical vortex and elliptic perfect vector beam by modulating the dynamic and geometric phase[J].Applied Physics Letters,2018,113:121101.
[79]Liu Yuanyuan,Liu Zhenxing,Zhou Junxiao,et al.Measurements of Pancharatnam-Berry phase in mode transformations on hybrid-order Poincarésphere[J].Optics Letters,2017,42(17):3447-3450.
[80]Luo H,Zhou J,Wen S,et al.Higher-order laser mode converters with dielectric metasurfaces[J].Optics Letters,2015,40(23):5506-5509.
[81]Milione G,Evans S,Nolan D A,et al.Higher order Pancharatnam-Berry phase and the angular momentum of light[J].Physical Review Letters,2012,108(19):190401.
[82]Han Y J,Guo C S,Rong Z Y,et al.Radial Hilbert transform with the spatially variable half-wave plate[J].Optics Letters,2013,38(23):5169-5171.
[83]Bhargava Ram B S.Paramasivam Senthil-kumaran.Edge enhancement by negative Poincare-Hopf index filters[J].Optics Letters,2018,43(8):1830-1833.
[84]Zhang B,Chen Z,Sun H,et al.Vectorial optical vortex filtering for edge enhancement[J].Journal of Optics,2016,18(3):035703.
[85]Li Delin,Feng Shaotong,Nie Shouping,et al.Scalar and vectorial vortex filtering based on geometric phase modulation with a Q-plate[J].Journal of Optics,2019,21(6):065702.