Research on spatial frequency shift super-resolution imaging based on evanescent wave illumination
Authors: Ling Jin-Zhong , Guo Jin-Kun , Wang Yu-Cheng , Liu Xin , Wang Xiao-Rui ,   School of Optoelectronic Engineering, Xidian University, Xi’an 710071, China,   State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China
Published: September 2023

<sec>In spite of the success of fluorescence microscopes (such as stimulated emission depletion microscopy, stochastic optical reconstruction microscopy and photoactivated localization microscopy) in biomedical field, which have realized nanometer scale imaging resolution and promoted the great development of bio-medicine, the super-resolution imaging method for non-fluorescent sample is still scarce, and the resolution still has a big gap to nanometer scale. Among existing methods, structured illumination microscopy, PSF engineering, super-oscillatory lens and microsphere assisted nanoscopy are more mature and widely used. However, limited by the theory itself or engineering practice, the resolutions of these methods are hard to exceed 50 nm, which limits their applications in many fields. Enlightened by synthetic aperture technique, researchers have proposed spatial frequency shift super-resolution microscopy through shifting and combining the spatial frequency spectrum of imaging target, which is a promising super-resolution imaging scheme, for its resolution limit can be broken through continually. Currently, owing to the limitation of the refractive index of optical material, the wavelength of illumination evanescent wave is hard to shorten when this wave is generated at prism surface via total internal reflection, which determines the highest resolution of this spatial frequency shift super-resolution imaging system. Another deficiency of this scheme is the difference in imaging resolution among different directions, for the image has the highest resolution only in the direction along the wave vector of illumination evanescent wave; while, the image has the lowest resolution in the direction perpendicular to the wave vector, which is the same as that obtained by far-field illumination.</sec><sec>In order to solve the above thorny questions, a new model of generating the evanescent wave is proposed, which can generates an omnidirectional evanescent wave with arbitrary wavelength based on the phase modulation of nano-structure, and solve the both problem in imaging system at the same time. To verify the our scheme, we set up a complete simulation model for spatial frequency shift imaging scheme, which includes three parts: the generation of evanescent wave and the interaction of the evanescent wave with the nano-structures at imaging target, which can be simulated with FDTD algorithm; the propagation of light field from near-field to far-field region, from the sample surface to the focal plane of objective lens, which can be calculated with angular spectrum theory; the propagation of light field from the focal place to the image plane, which can be worked out with Chirp-Z transform.</sec><sec>Firstly, with this complete simulation model, we compare the resolution of microscopy illuminated by evanescent wave with that by propagating wave. The experimental results verify the super-resolution imaging ability of evanescent wave illumination and the influence of prism refractive index. The higher the refractive index, the shorter the wavelength of evanescent wave is and the higher the resolution of spatial frequency shift imaging system. Secondly, we demonstrate the resolution difference in a series of directions with a three-bar imaging target rotated to different directions. The result shows that the highest imaging resolution occurs in the direction of illumination evanescent wave vector, and the lowest resolution appears in the direction perpendicular to the wave vector. Finally, we simulate the evanescent wave generated by nano-strcuture and demonstrate its properties of wavelength and vector direction. When applied to near-field illumination super-resolution imaging, the omnidirectional evanescent wave solves the both problems in the model of total internal reflection from the prism surface.</sec><sec>Therefore, the advantages of our scheme are higher imaging resolution and faster imaging speed, no need for multi-direction and multiple imaging, and also image post-processing. In this study, a new spatial frequency shift super-resolution imaging method is proposed, which lays a theoretical foundation for its applications.</sec>