Axial Super-resolution Evanescent Wave Tomography
Sarang Pendharker,1 Swapnali Shende,2 Ward Newman,1, 3 Stephen Ogg,4 Neda Nazemifard,2 and Zubin Jacob1, 3
1Department of Electrical and Computer Engineering,University of Alberta, Edmonton, Alberta T6G 1H9, Canada
2Department of Chemical and Materials Engineering,University of Alberta, Edmonton, Alberta T6G 1H9, Canada
3Birck Nanotechnology Center, School of Electrical and Computer Engineering,Purdue University, West Lafayette, IN 47906, USA4Department of Medical Microbiology & Immunology,
University of Alberta, Edmonton, Alberta T6G 2E1, Canada
Optical tomographic reconstruction of a 3D nanoscale specimen is hindered by the axial diffrac-tion limit, which is 2-3 times worse than the focal plane resolution. We propose and experimentallydemonstrate an axial super-resolution evanescent wave tomography (AxSET) method that enablesthe use of regular evanescent wave microscopes like Total Internal Reflection Fluorescence Micro-scope (TIRF) beyond surface imaging, and achieve tomographic reconstruction with axial super-resolution. Our proposed method based on Fourier reconstruction achieves axial super-resolution byextracting information from multiple sets of three-dimensional fluorescence images when the sampleis illuminated by an evanescent wave. We propose a procedure to extract super-resolution featuresfrom the incremental penetration of an evanescent wave and support our theory by 1D (along theoptical axis) and 3D simulations. We validate our claims by experimentally demonstrating tomo-graphic reconstruction of microtubules in HeLa cells with an axial resolution of 130 nm. Ourmethod does not require any additional optical components or sample preparation. The proposedmethod can be combined with focal plane super-resolution techniques like STORM and can also beadapted for THz and microwave near-field tomography.
Optical tomography is a major tool in three-dimensional visualization of sub-micrometer scale spec-imens in biology, material sciences and nano-fabricationtechnology . Tomographic reconstruction is doneby optical sectioning of the object in the focal planefollowed by 3D stitching of the acquired z-stack of fo-cal plane images. Resolution of the 3D tomographic re-construction of an object is therefore governed by thefocal plane resolution and the axial resolution of theunderlying optical image acquisition. A wide range ofwell advanced fluorescence based super-resolution mi-croscopy techniques have been reported and are currentlyin practice . Super-resolution in the focal plane canbe achieved by localization techniques like StimulatedEmission Depletion (STED) , Stochastic Optical Re-construction Microscopy (STORM) , Photo-ActivatedLocalization Microscopy (PALM) , or by patterned il-lumination techniques like Structured Illumination Mi-croscopy (SIM) , Plasmonic Structured IlluminationMicroscopy (PSIM)  etc. Even though many focal-plane super-resolution techniques are available, accurate3D tomographic reconstruction still remains a challengedue to the ellipsoidal shape of the Point Spread Func-tion (PSF), which makes resolution in axial direction 2-3times worse .
The 4PI  and I5M microscope  have increasedthe resolution in the axial direction with an almost spher-ical PSF. More recently a triple-view capture and fu-sion approach  has been reported to improve vol-umetric resolution by a factor of two. However, these
techniques require imaging and illuminating the same fo-cal plane from both sides of the sample and depend onextensive optical components and precise optical phasematching. 3D STED  and 3D STORM [2, 3] for three-dimensional localization have also been reported. Axialsuper-resolution can also be achieved by placing a re-flective mirror behind the sample to squeeze the PSFin the axial direction by interference from the reflectedSTED beam [14, 15]. However, STORM and STED im-pose constraints on properties of the fluorescent probes,limiting their applicability to image photo-switchable flu-orophores and samples with a sharp emission spectrum,respectively. Evanescent wave illumination techniqueslike Total internal Reflection Fluorescence (TIRF) mi-croscopy [16, 17], Plasmon enhanced TIRF , variable-angle TIRF  and pseudo-TIRF  provide super-resolution along the optical axis with very high signal-to-noise ratio (SNR) without imposing constraints on thefluorescence properties of the sample. However, the ca-pabilities of the evanescent wave techniques were so farlimited to near-surface imaging, thus making them unfitfor direct 3D tomography. 3D geometric estimation froma large number of TIRF surface images captured at dif-ferent incident angles has been recently reported [21, 22].These methods require solving inverse estimation prob-lems and prior knowledge of the sample features. Morerecently, a simpler protocol of sequential imaging andphotobleaching with multiangle TIRF to localize fluores-cence emission to a region within the PSF of the objectivewas reported to achieve axial super-resolution .
In this paper we propose an axial super-resolutionevanescent wave tomography (AxSET) method basedon Total Internal reflection Fluorescence (TIRF) mi-croscopy. We extract features with super-resolution from
FIG. 1. Schematic of a TIRF microscope. Penetration depthof an evanescent wave can be controlled by the incident angle of the illuminating beam. As the incident angle is increased,the illumination depth decreases. When illumination depth ofthe sample increments in discrete steps, the information cap-tured within the PSF of the objective lens also increments insteps, and the incremental information corresponds to super-resolution features.
multiple sets of diffraction limited 3D images, whereeach set of 3D image is acquired at different illumina-tion depths of the TIR evanescent wave. The proposedmethod does not require explicit knowledge of illumina-tion depth or the PSF, nor does it rely on photobleachingof the sample. The method is tolerant to local variationsin refractive index of the sample and angular bandwidthof the incident beam. We present the theoretical basisof our algorithm and show that it enables 3D tomogra-phy without additional optical components and samplepreparation. We support our claims with 1D and 3DFourier optics simulations and show that our algorithmcan discern and reconstruct objects which otherwise ap-pear coalesced with a conventional microscope. We ex-perimentally validate our method by imaging and demon-strating super-resolution reconstruction of microtubulesin HeLa cells. We demonstrate tomographic reconstruc-tion with an axial resolution of 130nm (in contrast to>450 nm limit of the microscope). Although, the maingoal of this paper is to increase the resolution in the ax-ial direction, our method can be combined with otherfocal-plane super-resolution techniques like STORM andPSIM to achieve 3D super-resolution.
The resolution limit arising from the ellipsoidal shapeof the PSF of an optical microscope is r /(2n sin)in the focal plane, and z /(n sin2 ) along the op-tical axis . Here is the wavelength of light in freespace, n is the refractive index of the medium, and is the aperture angle of the lens. The axial resolution,which is worse by a factor greater than two as comparedto the focal-plane resolution, is significantly enhanced ifinstead of a propagating wave, the fluorescence in thesample is excited by an evanescent wave generated by to-tal internal reflection at the interface of cover-slip and thesample, as shown in Fig. 1. The attenuation coefficientof an evanescent wave (EW) in the sample is given by = (2/)(n21 sin
2 n22)(1/2), where n1 is the refractiveindex of the cover-slip and n2 is the refractive index of thesample. is the angle between the incident light and nor-
Axial Super-resolution EW Tomography (AxSET)
FIG. 2. Fourier reconstruction with confocal and TIRF im-age. fobj and Fobj is the object in spatial domain and Fourierdomain respectively. In conventional microscopy the objectis passed through the Optical Transfer Function (OTF). Theband-limited optical transfer function of the microscope in-troduces diffraction limit, and the resultant captured imagefconventional is diffraction limited as shown in blue curves inleft panel. The same object when imaged by TIRF is firstilluminated with evanescent wave and the differentially illu-minated object is then imaged by conventional system to getsuper-resolution fTIRF . Fourier reconstruction is then per-formed on Fconventional and FTIRF to extract and reconstructthe object with super-resolution.
mal to the interface. When the incident angle of light ()is above the critical angle c = sin
1(n2/n1), the wave isevanescent in the sample, with a theoretical upper limitto the attenuation being max = (2/)(n
Since the attenuation of the wave can be controlled be-tween 0 and max by the incident angle , it is possibleto allow illumination of a desired thickness and acquire az-stack of the focal-plane images over the desired thick-ness, as depicted in Fig. 1. The 3D image thus obtainedwill have high SNR, but since the image is captured viaa conventional optical microscope, the resolution of eachfocal plane image will be diffraction limited, and will begoverned by an ellipsoidal PSF. Thus tomography withoptical sectioning is diffraction li