Counter‐Propagating Evanescent Illumination Super‐Resolution Chip

Super‐resolution chip (SRC) made of fluorescent polymer film and polygon film waveguide can realize subdiffraction imaging. However, the propagation losses of evanescent waves impose a serious restriction on imaging performance. Meanwhile, the required redundant raw images hinder the imaging speed. Multiple‐azimuths evanescent illumination at the same time can efficiently increase the illumination intensity and uniformity, and reduce the number of required raw images. But, the experimental realization is impeded by the complex spatial frequency mixing problem. Herein, an SRC microscopy method with counter‐propagating evanescent illumination is demonstrated, which circumvents the influence of complex spatial frequency mixing, and efficiently enhances the reconstructed results. Meanwhile, the proposed method reduces the number of required raw images by half and saves the image acquisition time, which benefits the imaging speed enhancement of the SRC microscopy system and promotes its future practical application.


Introduction
Super-resolution microscopy techniques circumvent the diffraction limit, which restricts the best resolving capability of optical microscopy to about 200 nm laterally, enabling the visualization of subcellular organization to nanometer scales.For instance, fluorescence-based super-resolution techniques such as stimulated emission depletion microscopy, [1,2] stochastic optical reconstruction microscopy, [3,4] and structured illumination microscopy (SIM) [5][6][7] have led to various breakthrough discoveries in the life sciences with tens of nanometers spatial resolution.However, the dependence on special fluorescent labeling limits the application of these techniques in fluorescent-probe-limited samples like integrated chip defect inspection.
Meanwhile, various label-free spatial frequency shift (SFS)-enabled superresolution imaging techniques are promoted to extend the collectable spatial frequency region of the system.For instance, SIM [5][6][7][8][9][10] and Fourier ptychographic microscopy (FPM) [11][12][13][14][15] are two typical SFS techniques.In SIM, the sample is illuminated by a well-defined structured pattern of light.Because of the interactions between the illumination grid and the sample, high spatial-frequency information of the sample is encoded in the form of Moiré fringes.In FPM, large-angle tilt illumination with different incident angles is applied to downshift the uncollectable frequency information of the sample.However, limited by the fineness of illumination patterns in conventional SIM, the resolution enhancement is up to 2 times better than that of the wide-field microscope.While in FPM, because of the reliance on low magnification objective lens and oblique illumination, the maximum resolution cannot break the diffraction limit of conventional wide-field microscope (≈200 nm).[18][19][20][21][22][23][24][25][26][27] With the introduction of high-refractive-index materials or metamaterials, evanescent wave illumination with large wave-vectors is generated, enabling deep SFS to achieve much higher resolution than conventional SIM and FPM.But up to now, to remap a wide spatial frequency spectrum of subwavelength structures, evanescent illumination with different wave vectors from various azimuths is applied step by step. [20,21]he whole imaging speed of the system is limited by the required redundant raw images.Meanwhile, the intensity of light propagated within the film waveguide decays with the propagation distance rapidly, leading to inhomogeneous distribution of illumination light.As a result, the acquired far-field image of the sample usually cannot carry the whole subwavelength details, which ultimately degrades the reconstructed results.
To address these challenges, multiple azimuths evanescent illumination at the same time is a possible solution.
However, the complex spatial frequency mixing problem impedes the experimental realization of frequency spectrum remapping.In this work, a novel waveguide chip-based superresolution imaging method with counter-propagating evanescent illumination is proposed, which overcomes the redundant raw images and low illumination uniformity restrictions in current evanescent wave-based SFS-enabled microscopy.Specially, our mathematic analysis and simulation results show that the proposed method circumvents the influence of spatial frequency mixing.In experiments, through the combination of fluorescent polymer films (9,9`-dioctylfluorene-alt-benzothiadiazole (F8BT)) with deposited polygon planar waveguides array, a superresolution chip (SRC) with multiple working regions is fabricated.By symmetrically exciting the F8BT films around the polygon planar waveguides, evanescent illumination with multiple wavelengths is generated and propagates oppositely to the working region within the SRC.Then, the counterpropagating evanescent waves interact with the sample placed on the surface of the working region.Far field images of the sample illuminated at different wavelengths are selected using corresponding narrow band-pass filters.The conventional bright field illumination image of the sample is used to offer the lowfrequency information, while images of the sample under counter-propagating evanescent illumination are used to provide different high-frequency components.An iterative algorithm is used to remap a wide spatial frequency spectrum of the sample.By manipulating the illumination azimuths and wavelengths, a wide spatial frequency spectrum in Fourier space is recovered.And a high-fidelity image without blurring can be reconstructed.The experimental results show that our proposed method can effectively reduce the required number of raw images by half and save the image acquisition time.Meanwhile, the proposed method can efficiently improve the illumination uniformity and signal-to-noise ratio (SNR) of the reconstructed results.

Method and Algorithm
For a waveguide chip-based super-resolution imaging system under evanescent illumination, evanescent waves traveling along different azimuths are introduced to interact with the sample.Different high spatial frequency components of the sample are downshifted to the detectable region, and recorded by the far-field detector.Such a process can be described as follows: here F 0 ð kÞ represents then shifted high-frequency components of the sample; keva: means the SFS vector introduced by evanescent illumination; TFð kÞ is the transfer function of the system, which is a low-pass filter function with a cutoff frequency determined by the objective lens and illumination wavelength; and F eva: ð kÞ represents the detected spatial frequency spectrum before the camera plane.As described by the above mathematical expression, keva determines the largest detectable spatial frequency information of the sample and ultimately determines the best achievable system resolution.
In a typical waveguide chip-based SFS-enabled super-resolution imaging system under evanescent illumination, materials with high refractive index, like titanium dioxide and aluminum oxide, are used to fabricate the film waveguide, the penetration depth of evanescent waves at the visible band is usually limited to less than 150 nm.For pathological samples placed in the water, given their refractive index is 1.38-1.45,and the illumination wavelength is 532 nm, then the phase change is less than 0.2 rad.While for etched patterns on a ≈100 nm thick titanium dioxide film with 70 nm depth, the effective refractive index is ≈1.9, and the phase change is ≈0.74 rad.Such sample distributions can well meet the requirements of a weak phase object approximation model (usually less than 1 rad).Thereby, the shifted high-frequency components F 0 ð k À keva: Þ of the sample can be expressed as: Under partial coherent evanescent illumination, the intensity spectrum I eva: ð kÞ acquired by far-field detector can be represented as the convolution of the spectrum distribution of F eva: ð kÞ and its complex conjugate.Here, both of the amplitude (absorption) distribution (ℱ À1 ½Að kÞ) and phase distribution ðℱ À1 ½∅ð kÞ) of the sample can be considered as real functions.ℱ À1 represents inverse Fourier transform.Thereby, here is the convolution operators.S eva: ð kÞ is defined as the selfconvolution term of amplitude and the self-convolution term of phase.Under weak phase approximation, the self-convolution term of phase can be omitted.Mð kÞ is defined as the crossconvolution terms of the absorption and phase: From Equation ( 5), under counter-propagating evanescent illumination with SFS vectors of keva: and À keva: respectively, the imaginary part Mð kÞ will be offset by each other.Then, the far-field detected intensity satisfies the following relations: Consequently, with weak phase object approximation, image of the sample under counter-propagating evanescent illumination can be used to offer both subaperture spectrums without information demultiplexing, which circumvents the spatial frequency mixing problem and can reduce the number of required raw images by half.
As demonstrated in Figure 1a, to realize counter-propagating evanescent illumination, ≈70 nm thick F8BT film with wide band fluorescence emission (from 480 to 700 nm) is spin-coated on the surface of a 1 mm thick, 1.5 cm Â 1.5 cm glass slide to fabricate the SRC.Then, using laser-direct-writing method, F8BT film within a polygon area is etched off.Finally, a ≈100 nm thick titanium dioxide (TiO 2 ) film is deposited on the surface of the etched area by electron-beam (E-beam) evaporation.In experiments, samples are placed on the surface of the polygonal region.By symmetrically exciting the F8BT films around the polygon film waveguide, counter-propagating evanescent waves from the opposite directions will be generated and traveled toward the working region, and interact with the samples simultaneously.Then scattered light from the sample will be collected by an objective lens and imaged by a far-field detector.As demonstrated in Figure 1b, the acquired image is then used to update both subaperture spectrums, which are centralsymmetrically distributed in the Fourier domain.By changing the excited locations along the polygon waveguide, high spatial frequency components along different azimuths are extracted to update the recovered spatial frequency spectrum.Meanwhile, by inserting different narrow band pass filters before the detector, the magnitude of keva: can be manipulated, and high spatial frequency component of the sample over a wide band is remapped.Because of the introduction of narrow band pass filters, high-frequency components carried by images under counter-propagating evanescent illumination are filtered by coherent transfer function.In this work, image of the sample under conventional bright field illumination is used to offer low-frequency spectrum, thus, optical transfer function, which can generate 2Â bandwidth of coherent diffraction limit, is used to select the low-frequency information.
After the acquisition of all raw images, a designed reconstruction algorithm is applied to remap the frequency spectrum in Fourier space.As shown in Figure 2, at the beginning of the reconstruction process, image of the sample under conventional bright field illumination is used to offer an initial guess of the frequency spectrum.Then, during each iteration, Fourier transformed amplitude of subaperture spectrum corresponding to low spatial frequency information is updated with the image of the sample under conventional illumination.And, each image of the sample under counter-propagating evanescent illumination is used to update both subapertures, that are central-symmetrically located in Fourier domain.Here, locations of the subapertures in Fourier space are determined by corresponding SFS vectors keva: and À keva: .Meanwhile, to extend the frequency spectrum accessible from the sample and ensure the overlapping of different subapertures, images of the sample under evanescent illumination at different wavelengths are acquired to offer different high-frequency components.After several times iterations, a well-converged solution is acquired in Fourier space, and a super-resolution image with subwavelength details can be reconstructed over a wide field of view (FoV).
As demonstrated in Figure 2, in simulation, an ideal object-ZJU eagle logo pattern is reconstructed using our proposed method.Numerical aperture (NA) of the collecting objective lens is 0.85.Image of the sample under conventional bright field illumination at 532 nm offers the low spatial frequency information, and images of the sample under counter-propagating evanescent illumination at 532 and 632.8 nm provide corresponding high spatial frequency components.The number of counterpropagating evanescent illumination azimuths is 10.After about 20 times iterations, a well-converged solution is acquired.Then using inverse Fourier transformation, a super-resolution image of the sample is recovered with the converged solution.These conditions are also used for subsequent simulations and experiments presented.

Simulation and Experiment
In simulation, to quantificationally analyze weak phase influence on the reconstructed results, a ground truth complex object is built from the amplitude image in Figure 3a and the phase image in Figure 3b.Here, we set the phase change ranging from 0 to 0.6 rad. Figure 3c,d demonstrates the remapped frequency spectrum and intensity image of the amplitude distribution in Figure 3a using our proposed method.For comparison, Figure 3e,f shows the recovered frequency spectrum and intensity result of the built complex object using our proposed method.Obviously, the reconstructed frequency spectrums and intensity images of the amplitude distribution with and without phase change share the same distributions.As shown in Figure 3e, two centrosymmetric subapertures in Fourier domain are extracted separately.Figure 3g,h shows the corresponding simulated far-field images.Figure 3i illustrates image of the built complex object under counter-propagating evanescent illuminations, which is created by superimposing the intensity image in Figure 3g,h.As demonstrated in Figure 3g-i, almost no visible intensity change caused by the phase distribution is presented, which is consistent with the derivation of Equation ( 6) and (7).Thus, under weak phase condition, the captured images of the sample under counter-propagating evanescent illumination can be used to simultaneously offer the two subaperture spectrums.
For waveguide chip-based SFS-enabled super-resolution imaging, the quality of film waveguide plays a key role in determining imaging performance, including system resolution, FoV, etc.In our experiments, ≈100 nm thick titanium dioxide film waveguide is deposited using E-beam evaporation to form a planar waveguide.The surface roughness of the film waveguide is characterized using atomic force microscopy (AFM).As demonstrated in Figure 4a,b, though the film surface is smooth, there are still some imperfect defects in several nanometers.When light propagates within the film waveguide, interactions between light with these defects will lead to the propagation loss.Meanwhile, scattering loss of evanescent waves stemming from samples is also analyzed in simulation using finite-difference time-domain (FDTD) method.As shown in Figure 4c, a 2 um long, 180 nm wide, and 60 nm tall ridge is placed on the surface of a 150 nm thick titanium dioxide film.When evanescent light propagates within the waveguide, light transmissivity before and after the ridge is about 92.44% and 76.95%, respectively.Thereby, for a randomly distributed complex sample, scattering loss from the sample will cause serious inhomogeneous illumination.
As demonstrated in Figure 5a,b, two different normalized light distributions are created to mimic the intensity distribution of evanescent waves propagated along the azimuths of 180°and 0°with a random propagation loss, respectively.Figure 5d,e demonstrates the corresponding intensity distribution along the red dot lines in Figure 5a,b.Under omnidirectional evanescent illumination with light intensity distributions depicted in Figure 5a, b, far-field image of the complex object in Figure 3 is acquired, as shown in Figure 5g,h, respectively.Obviously, image intensity in the rectangular red boxes is very weak.For comparison, in Figure 5c, light intensity distribution under counter-propagating evanescent illumination is created by superimposing the   intensity images in Figure 5a,b.As demonstrated in Figure 5f, light distribution in Figure 5c is more uniform than that in Figure 5a,b.Thus, the acquired far-field image in Figure 5i can better demonstrate all details of the object.
As demonstrated in Figure 6, in experiments, the emission light from a 405 nm CW laser is collimated by a 20X/0.4NAobjective lens and split into two centrosymmetric excitation beams.Then, the two beams are focused by a 100X, 0.85NA objective lens and central-symmetrically distributed on the surface of the SRC, and F8BT film around the focused spots is excited.The emission light from the polymer film located in the opposite sides couples into the polygon waveguide, to generate counter-propagating evanescent illumination with multiple wave vector components.After interaction with samples placed on the surface of the working region, the counter-propagating evanescent waves are scattered into far field and collected by the objective lens.Our previous work has shown that light scattered from the sample is predominantly polarized along the direction vertical to evanescence illumination direction. [17]hereby, a rotatable polarizer is inserted in front of the camera, to restrain the influence of light polarized along other azimuths.Meanwhile, through the combination of a dichroic mirror with two narrow band pass filters at 532 AE 2 nm (full width at half maximum (FWHM) = 10 AE 2 nm) and 632.8 AE 2 nm (FWHM = 10 AE 2 nm), images of the sample under counter-propagating evanescent illumination at different wavelengths can be simultaneously acquired.Precise manipulation of excitation conditions and propagation directions of the SRC are key factors to the success of the method.By rotating the mask and polarizer, images of the sample under counterpropagating evanescent illumination along different azimuths are captured.Meanwhile, conventional bright field illumination is used to transmit the low-frequency information for imaging.
As demonstrated in Figure 8a, the pattern of a Chinese character for "light" is etched on the surface of the working region using focused ion beam etching technique.Center-to-center distance between the two parallel grooves is ≈168 nm (88 nm linewidth and 80 nm gap width), and the depth is ≈70 nm.Since the feature sizes of the sample are much smaller than the diffraction limit, as depicted in Figure 8b, images of the sample under conventional bright field illumination cannot offer subdiffraction details.  c).g,h) Simulated far-field images of the complex object in Figure 3 under omnidirectional evanescent illumination along the azimuths of 180°and 0°, respectively.i) Simulated far-field images of the complex object in Figure 3 under counter-propagating evanescent illumination.Scale bar is 500 nm.
By central-symmetrically excited the F8BT film around the working region, as shown in Figure 7a-t, far-field images of the character under counter-propagating evanescent illumination along different azimuths are captured subsequently.In Figure 7, the arrows depict the propagation direction of evanescent waves.Figure 7a-j shows the images of the pattern under counterpropagating evanescent illumination at 532 nm, while Figure 7k-t demonstrates the images of the pattern under counter-propagating evanescent illumination at 632.8 nm.Useful subwavelength details along corresponding azimuths are captured separately.Compared with images of the pattern under omnidirectional evanescent illumination in Figure 7u-x, images of the sample under counter-propagating evanescent illumination in Figure 7c,m carry more details, which will finally benefit our reconstructed results.Even so, it should be noted that counter-propagation illumination can only alleviate the inhomogeneity of evanescent illumination distribution, FoV of the SRC is still limited by the gradually decaying nature of evanescent waves.The useful FoV of the SRC is determined by the overlapping region of evanescent waves illumination propagating along different azimuths.Since side length of the polygon film waveguide is about 20 μm, the useful FoV of the SRC is about 400 μm 2 .To achieve high-throughput imaging, by fabricating  working region array on a chip, multiple FoVs can be excited simultaneously.
In this work, to reconstruct a 2D pattern of the etched character, counter-propagating evanescent illumination along 10 azimuths is applied to acquire the raw intensity images in sequence.Compared with our previous work, [20] using this new method, the number of required raw images is effectively reduced by more than half.Meanwhile, the image acquisition time is saved.After acquisition, subfrequency components carried in the raw images are shifted back to their correct positions in Fourier space.Here, the shift distance is determined by the illumination SFS vectors, which are acquired using the FDTD method.As demonstrated in Figure 8d, after ≈20 times iterations, a well-reconstructed result is recovered using our reconstruction algorithm.Compared to the reconstructed result under omnidirectional evanescent illumination in Figure 8c, reconstructed image in Figure 8d offers much more subdiffraction details and demonstrates higher SNR. Figure 8e shows the intensity profiles along the red dashed lines indicated in Figure 8a,c,d, good agreement between the reconstructed results and SEM image is demonstrated.

Conclusion and Discussions
In summary, we have demonstrated a novel SRC-based SFS-enabled microscopy method using counter-propagating evanescent illumination, which circumvents the influence of spatial frequency mixing problem.Through the combination of a widefield SRC with centrosymmetric excitation manipulation, evanescent illumination from opposite azimuths is simultaneously applied to interact with the sample to acquire far-field images.With sequential excitation of fluorescent polymer films located at different sides of a polygon waveguide, far-field images of the sample under counter-propagating evanescent illumination along different azimuths are acquired.Meanwhile, by inserting corresponding narrow band pass filters, far-field images of the sample under counter-propagating evanescent illumination at different wavelengths are selected, permitting sampling of different parts of the spatial frequency spectrum of the sample.Then, using a designed reconstruction algorithm, spatial frequency information carried by images under conventional bright field illumination and counter-propagating evanescent illumination are extracted and remapped in Fourier space.After several times iterations, super-resolution images of 2D samples are recovered.We demonstrated the methods on subdiffraction-sized features of different patterns in simulations and experiments.Our experimental reconstruction result matches well with the SEM image.
In traditional waveguide chip-based SFS-enabled superresolution imaging, both the propagation loss induced by film surface roughness and scattering loss stemming from the sample reduce the evanescent illumination homogeneity, which ultimately degrade the reconstructed results.In contrast, the introduction of counter-propagating evanescent illumination effectively enhances the intensity and uniformity of evanescent illumination, more comprehensive subdiffraction details of the sample can be captured by the far-field detector.Thus, the recovered subaperture spectrums from the raw images are more precise, which finally contribute to the reconstructed results.Meanwhile, our proposed method in this work reduces the number of required raw images by half, and saves the image acquisition time, which will ultimately enhance the imaging speed of the SRC microscopy system.Here, limited by the penetration depth of evanescent waves, the phase change induced by evanescent illumination is pretty weak along the axial direction, high-resolution phase retrieval is challenging for our proposed method.But, as long as the intensity of scattering light from the transparent biosamples is strong enough for far-field detection, the intensity distribution of the sample can be well reconstructed.Besides, though the influence of phase mixing can be omitted under multiple-azimuths evanescent illumination, the influence of amplitude mixing still exists, making it hard to realize information demultiplexing.Since light scattered from the sample is predominantly polarized along the direction vertical to evanescence illumination direction, [17] in the future, by applying perpendicular counter-propagation illumination with polarization selectivity, imaging speed of the SRC can be further improved.

Figure 1 .
Figure 1.a) Schematic diagram of counter-propagating evanescent illumination process.F8BT film around the polygon waveguide is central-symmetrically excited, then the emission fluorescent light couples into the waveguide and oppositely propagates toward the sample placed in the center of the working region.b) Schematic of reconstruction method.k cov . is the cut-off wavenumber of the microscope system under conventional bright field illumination.k eva.1 and k eva.2 are wave vectors for evanescent field illumination at wavelengths of λ 1 and λ 2 , respectively.

Figure 2 .
Figure 2. The flowchart of the iteration reconstruction of our proposed method.The lower left inset figures demonstrate the far-field images of the object under omnidirectional evanescent illumination from 90°and 270°at the wavelength of 532 nm.

Figure 3 .
Figure 3. Analysis of the influence of weak phase distribution on the reconstructed results.a,b) Ground-truth amplitude and phase images for simulation.c,d) Reconstructed frequency spectrum and intensity image of the amplitude distribution in (a).e,f ) Reconstructed frequency spectrum and intensity image of the built complex object.g,h) Far-field images of the built complex object corresponding to subaperture 1 and subaperture 2 in (e).i) Far-field image of the built object under counter-propagating evanescent illumination.Scale bar is 500 nm.

Figure 4 .
Figure 4. a,b) AFM images of the surface of deposited titanium dioxide film.Scale bar is 500 nm.c) Cross-section view of the scattering process induced by a ridge on the surface of a titanium dioxide film.T1 is light transmissivity before the ridge, and T2 is light transmissivity after the ridge.

Figure 5 .
Figure 5. a-c) Created evanescent light distribution propagated along the azimuths of 180°, 0°, and both.d-f ) Normalized intensity profiles along red dashed lines in a-c).g,h) Simulated far-field images of the complex object in Figure3under omnidirectional evanescent illumination along the azimuths of 180°and 0°, respectively.i) Simulated far-field images of the complex object in Figure3under counter-propagating evanescent illumination.Scale bar is 500 nm.

Figure 6 .
Figure 6.Schematic setup of the SRC microscopy system under counterpropagating evanescent illumination.

Figure 7 .
Figure7.a-j) Far-field images of the etched pattern in Figure8aunder counter-propagating evanescent illumination along the green arrows at wavelength of 532 nm.k-t) Far-field images of the etched pattern under counter-propagating evanescent illumination along the red arrows at wavelength of 632.8 nm.u,v) Far-field images of the etched pattern under omnidirectional evanescent illumination along the green arrows at wavelength of 532 nm.w,x) Far-field images of the etched pattern under omnidirectional evanescent illumination along the red arrows at wavelength of 632.8 nm.Scale bar is 500 nm.

Figure 8 .
Figure 8.Comparison of the reconstructed result under counter-propagating evanescent illumination with scanning electron microscopy (SEM) image and traditional reconstructed result under omnidirectional evanescent illumination.a) SEM image of the etched pattern on the surface of the SRC.b) Image of the etched pattern under conventional bright field illumination.c,d) Reconstructed image of the etched pattern under omnidirectional evanescent illumination and counter-propagating evanescent illumination respectively.Scale bar is 500 nm.e) Normalized intensity profiles along the red dashed lines in a,c,d).