Lommel beams have been potential candidates for optical communication and optical manipulation,due to their adjustable symmetry of transverse intensity distribution and continuously variable orbital angular momentum.H...Lommel beams have been potential candidates for optical communication and optical manipulation,due to their adjustable symmetry of transverse intensity distribution and continuously variable orbital angular momentum.However,the wavefront of the Lommel beam is scrambled when it transmits through highly scattering media.Here,we explore the construction of Lommel beams through highly scattering media with a transmission matrix-based point spread function engineering method.Experimentally,various Lommel beams with different parameters were generated through a ZnO scattering layer by use of a digital micromirror device.The construction of Lommel beams under high scattering is expected to benefit the optical applications behind highly scattering media.展开更多
The imaging interferometer(IIM)aboard the Chang’E-1 lunar orbiter is the first multispectral imaging spectrometer for Chinese lunar missions.Before science applications(e.g.,FeO and TiO2mapping)of the IIM raw data,th...The imaging interferometer(IIM)aboard the Chang’E-1 lunar orbiter is the first multispectral imaging spectrometer for Chinese lunar missions.Before science applications(e.g.,FeO and TiO2mapping)of the IIM raw data,the radiance variation due to changes in illumination and viewing geometry has to be removed from the radiometrically calibrated IIM Level 2A images.To achieve this,we fit the IIM Level 2A radiance data with a Lommel-Seeliger photometric model consisting of an exponential term and a fourth order polynomial in the phase function,without distinguishing between lunar maria and highlands.The exponential and the fourth order polynomial parameters are derived separately by fitting to two datasets divided at a solar phase angle threshold,avoiding a decrease in the phase function close to zero phase angle.Different phase angle thresholds result in coincident fitting curves between 20°and 75°,while large discrepancies occur at other phase angles.Then the derived photometric model is used to normalize the IIM Level 2A data to radiance values at an incidence and phase angle of 30°and emission angle of 0°.Our photometric model is validated by comparing two photometrically normalized IIM radiance spectra covering the same areas,showing a relative deviation consistent with the IIM preflight calibration.展开更多
In analogy to the role of Lommel polynomials ?in relation to Bessel functions Jv(z) the theory of Associated Hermite polynomials in the scaled form ?with parmeter v to Parabolic Cylinder functions Dv(z) is developed. ...In analogy to the role of Lommel polynomials ?in relation to Bessel functions Jv(z) the theory of Associated Hermite polynomials in the scaled form ?with parmeter v to Parabolic Cylinder functions Dv(z) is developed. The group-theoretical background with the 3-parameter group of motions M(2) in the plane for Bessel functions and of the Heisenberg-Weyl group W(2) for Parabolic Cylinder functions is discussed and compared with formulae, in particular, for the lowering and raising operators and the eigenvalue equations. Recurrence relations for the Associated Hermite polynomials and for their derivative and the differential equation for them are derived in detail. Explicit expressions for the Associated Hermite polynomials with involved Jacobi polynomials at argument zero are given and by means of them the Parabolic Cylinder functions are represented by two such basic functions.展开更多
基金supported by the National Key Research and Development Program of China(No.2019YFA0705000)the National Natural Science Foundation of China(NSFC)(Nos.12004219,12192254,91750201,and 11974218)+1 种基金the Innovation Group of Jinan(No.2018GXRC010)the Local Science and Technology Development Project of the Central Government(No.YDZX20203700001766)。
文摘Lommel beams have been potential candidates for optical communication and optical manipulation,due to their adjustable symmetry of transverse intensity distribution and continuously variable orbital angular momentum.However,the wavefront of the Lommel beam is scrambled when it transmits through highly scattering media.Here,we explore the construction of Lommel beams through highly scattering media with a transmission matrix-based point spread function engineering method.Experimentally,various Lommel beams with different parameters were generated through a ZnO scattering layer by use of a digital micromirror device.The construction of Lommel beams under high scattering is expected to benefit the optical applications behind highly scattering media.
基金supported by the National Natural Science Foundation of China(11003012,41373068)the Natural Science Foundation of Shandong Province(ZR2011AQ001)+1 种基金Joint Funds of the National Natural Science Foundation of China and the Chinese Academy of Sciences(U1231103)Independent Innovation Foundation of Shandong University(2013ZRQP004)
文摘The imaging interferometer(IIM)aboard the Chang’E-1 lunar orbiter is the first multispectral imaging spectrometer for Chinese lunar missions.Before science applications(e.g.,FeO and TiO2mapping)of the IIM raw data,the radiance variation due to changes in illumination and viewing geometry has to be removed from the radiometrically calibrated IIM Level 2A images.To achieve this,we fit the IIM Level 2A radiance data with a Lommel-Seeliger photometric model consisting of an exponential term and a fourth order polynomial in the phase function,without distinguishing between lunar maria and highlands.The exponential and the fourth order polynomial parameters are derived separately by fitting to two datasets divided at a solar phase angle threshold,avoiding a decrease in the phase function close to zero phase angle.Different phase angle thresholds result in coincident fitting curves between 20°and 75°,while large discrepancies occur at other phase angles.Then the derived photometric model is used to normalize the IIM Level 2A data to radiance values at an incidence and phase angle of 30°and emission angle of 0°.Our photometric model is validated by comparing two photometrically normalized IIM radiance spectra covering the same areas,showing a relative deviation consistent with the IIM preflight calibration.
文摘In analogy to the role of Lommel polynomials ?in relation to Bessel functions Jv(z) the theory of Associated Hermite polynomials in the scaled form ?with parmeter v to Parabolic Cylinder functions Dv(z) is developed. The group-theoretical background with the 3-parameter group of motions M(2) in the plane for Bessel functions and of the Heisenberg-Weyl group W(2) for Parabolic Cylinder functions is discussed and compared with formulae, in particular, for the lowering and raising operators and the eigenvalue equations. Recurrence relations for the Associated Hermite polynomials and for their derivative and the differential equation for them are derived in detail. Explicit expressions for the Associated Hermite polynomials with involved Jacobi polynomials at argument zero are given and by means of them the Parabolic Cylinder functions are represented by two such basic functions.
