If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continu...If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.展开更多
Coherent diffraction imaging(CDI)enables diffraction-limited high-resolution imaging without using high-quality lenses.It will be desirable to combine it with multiple spectral light sources to achieve chemically reso...Coherent diffraction imaging(CDI)enables diffraction-limited high-resolution imaging without using high-quality lenses.It will be desirable to combine it with multiple spectral light sources to achieve chemically resolved imaging capability.Here,we demonstrate a single-frame multiwavelength CDI approach that can provide complex transmittance images of a sample at multiple wavelengths.The superior performance of our method in terms of rapid convergence and improved image quality over current methods has been validated through high-harmonic extreme ultraviolet experiments.The feasibility of our method for single-frame chemical imaging is also demonstrated by the simulation.This work can pave the way for implementing in situ chemical imaging with tabletop high-harmonic generation extreme ultraviolet sources.展开更多
基金This research is partially supported by NIH,No.R15EB024283.
文摘If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.
基金supported by the National Natural Science Foundation of China(No.12074167)the Shenzhen ScienceandTechnologyInnovationProgram(No.JCYJ20241202125334045)。
文摘Coherent diffraction imaging(CDI)enables diffraction-limited high-resolution imaging without using high-quality lenses.It will be desirable to combine it with multiple spectral light sources to achieve chemically resolved imaging capability.Here,we demonstrate a single-frame multiwavelength CDI approach that can provide complex transmittance images of a sample at multiple wavelengths.The superior performance of our method in terms of rapid convergence and improved image quality over current methods has been validated through high-harmonic extreme ultraviolet experiments.The feasibility of our method for single-frame chemical imaging is also demonstrated by the simulation.This work can pave the way for implementing in situ chemical imaging with tabletop high-harmonic generation extreme ultraviolet sources.
