Research on spatial frequency shift super-resolution imaging based on evanescent wave illumination

Abstract

In spite of the success of fluorescence microscopes (such as STED, STORM and PALM) 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 applied. However, limited by the theory itself or engineering practice, the resolution of these approaches is hard to break through 50 nm, which restricts their application in many fields.
Enlightened by synthetic aperture technique, researchers 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 as its resolution limit could be broken through continually. Currently, due to the restriction of the refractive index of optical materials, the wavelength of illumination evanescent wave is hard to be shorten when 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 of imaging resolution in different directions, as only in the direction along the wave vector of illumination evanescent wave, the image has the highest resolution; while in the direction perpendicular to it, the image has the lowest resolution, as same as that obtained by far-field illumination.
In order to solve the above thorny questions, a new model for evanescent wave generation has been proposed, which could generate omnidirectional evanescent wave with arbitrary wavelength based the phase modulation of nano-structure, and solve the both problem in imaging system at the same time. To verify the possibility of 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 its interaction with the nano-structures at imaging target, with could be simulated with FDTD algorithm; the propagation of light field from near-field to far-field, from the sample surface to the focal plane of objective lens, which could be calculated with angular spectrum theory; the propagation of light field from the focal place to the image plane, which could be calculated with Chirp-Z transform.
With this complete simulation model, we compared the resolution of microscopy illuminated by evanescent wave and propagating wave, firstly. The results verified the super-resolution imaging ability of evanescent wave illumination, and also demonstrated the influence of refractive index of prism, as higher refractive index makes shorter wavelength of evanescent wave and higher resolution of spatial frequency shift imaging system. Secondly, we demonstrated the resolution difference at a series directions with a three-bar imaging target rotated to different directions. The result shows that the highest imaging resolution occurs at the direction of illumination evanescent wave vector, and the lowest resolution appears at the direction perpendicular to the wave vector. At last, we simulated the evanescent wave generated by nano-strcuture and demonstrated its properties of wavelength and vector direction. When applied to near-field illumination super-resolution imaging, the omnidirectional evanescent wave solved the both problems existing in the model of total internal reflection at prism surface.
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. Our research opened up a new perspective of spatial frequency shift super-resolution imaging, and established a theoretical foundation for its application.