Multi-moded high-index contrast optical waveguide for super-contrast high-resolution label-free microscopy

3.1 Near-field information to far-field

If an ideal waveguide without any sample is imaged, no light will reach the camera plane. However, any perturbation in the refractive index at the core-cladding interface can scatter photons into the camera [28]. The physical mechanism behind the conversion of nonpropagating evanescent waves into propagating waves may be understood from the following simplified illustration [31, 33]. A two-dimensional sample is illuminated by an incident field E x , y , z . Let us represent the two-dimensional Fourier transform of this field by E ̃ α , ß ; z where α, ß and γ are spatial frequencies with respect to x, y and z axis respectively, i.e., propagation vector k ⃗ = α x ̂ + ß y ̂ + γ z ̂ . The magnitude of the wave vector of a waveguide mode is 2 π λ vac n eff , where n _eff is the effective mode index. The evanescent wave vector corresponds to the largest spatial frequency components of the field. This field interacts with a thin sample placed at z = 0. The sample may be represented by a transmission function T(x, y). Invoking the Born approximation, just after the thin sample the field becomes [31]

By the property of Fourier transform, Eq. (1) may be represented alternatively as the convolution of the two signals in the spatial frequency domain as

But the illuminating field may be represented via the sifting property of the delta function as follows

Combining Eqs. (2) and (3) the spatial frequencies of the sample represented by T ̂ α , ß gets convolved with the spatial frequencies of the incident field. Or in other words, if a mode of an evanescent field is represented by δ α eva , ß eva , then the electric field just after the thin sample contains the shifted object spectrum T ̂ α − α eva , ß − ß eva , where α _eva and ß _eva are the spatial frequencies of the evanescent wave illuminating the sample. This is illustrated in Figure 1(b). If the shifted version of the function falls within the passband of the microscope, those high spatial frequencies of the object will reach the camera plane. Thus, sub-diffraction limit sized features are captured using cELS due to the high n _eff of the waveguide core that is typically not accessible with conventional objective based illumination schemes or index-matched waveguide geometries.

3.2 Waveguide as a partially coherent light source

In conventional bright field imaging, the incident light E i r , t and the light scattered off the sample E s r , t reach the camera. The total complex scalar field at the camera plane is E T r , t = E i r , t + E s r , t . For weakly scattering specimens, the only modulation in the total field will be in its phase. But the intensity registered by the camera, I r , t , will have no phase information and hence poor contrast, where represents time averaging. But while imaging using waveguides, only scattered light off the sample gets detected, i.e., E T r , t = E s r , t . Therefore, the point will be visible with enhanced contrast as a bright spot on a dark background.

Consider two-point scatterers represented by j = 1, 2. The incident field induces Rayleigh dipoles [34] which radiate into the far-field. Let the field emitted by each emitter at the camera plane be given by E j r , t = E 0 r exp i φ j r , t − i ω t . Here we assume that the scatterers are identical, i.e., the radiated fields have the same amplitude. The total field intensity averaged over the integration time of the camera is then represented as [35]

where

First, let us consider the situation of coherent illumination. Although the phases φ 1 r , t and φ 2 r , t are a function of time, the phase difference χ r , t is time-invariant and can be simply represented as χ r . The cosine term in Eq. (4A) becomes time invariant and therefore, the interference phenomenon is observed. On the contrary, in the case of incoherent illumination as in fluorescence imaging, the phase difference χ r , t is not time-invariant and the cosine term is a function of temporal variations. Since the phase fluctuations occur on a time scale much smaller than the integration time of the camera, the time-averaged cosine term tends to zero and therefore no interference is observed.

However, multi-moded illumination patterns inside the photonic waveguides presents a very interesting case. Let the electric fields emitted from the scatterers due to a particular mode “m” be represented as E j , m ( r , t ) = E 0 , m ( r ) exp i φ j , m r , t − i ω m t , where the subscript m denotes the mode. Correspondingly, the subscript m may be introduced in I _m ( r , t) and χ m r as well. Since the modes are coherent individually and with respect to each other, the time term in the function χ m r , t is absent. At any given point in time t, due to galvo scanning, the mode combinations will be different. Representing the complex mode coefficients at a given time t as a _m (t), the average intensity within a camera integration time due to all the mode combinations is given as

where α m t represents the phase of a _m (t). The presence of a time-varying cosine term cos α m t which changes continuously with the galvo scan position implies that the average intensity shown in Eq. (5) is no longer coherent. However, it is also not strictly incoherent because the galvo scan times are comparable to the camera exposure time. To ensure that there is no strict correlation between the images acquired across different frames we set the galvo scan rate to a prime number. In essence, we realize a partially coherent illumination case per frame. Equation (5) may be understood as many speckle patterns getting added at the camera plane. As per the central limit theorem, the contrast of these speckles scales as 1 / N when added on an intensity basis, where N is the number of independent speckle patterns added [36]. This is illustrated schematically in Figure 1(c). In the experiments described here, the galvo oscillation rate is set at a prime number of 1013 Hz. The logic behind choosing a prime number can be understood as follows. During oscillation at each position of the galvo, a set of modes are excited in the waveguide that get coherently scattered off the sample onto the camera. Within one exposure time of the camera, the galvo would have oscillated (0.030 s × 1013 Hz ≈ 31) times and excited the modes. Due to a prime number setting, it will ensure that 31 distinct set of mode patterns or speckle patterns get averaged within the integration time of the camera. This condition will help suppress the speckle noise according to the Central Limit Theorem. Thus, the issue of coherent noise is mitigated via the usage of a multi-moded waveguide and galvo scanning, demonstrating a multi-moded waveguide as a partially coherent light source that enables high-contrast imaging.

3.3 Coherent scattering of modes enable super-contrast label-free imaging

Consider two particles “1” and “2” placed on top of the waveguide surface as shown in Figure 2(a). The input coherent laser light excites a few modes of the waveguide. These modes are described mathematically as given by Eq. (S3) in the supplementary material. So, any mode “m” may be decomposed into a pair of plane waves propagating at angles ±θ _m with respect to the propagation direction, z-axis. For brevity only two such modes are shown in green and red in Figure 2. The tails of these modes extend into the cladding and polarize the particles “1” and “2”. The particles then radiate into the far-field as described earlier. As per the first order Born approximation, the incident and scattered waves can be assumed to have the same phase [34]. Therefore, the phase difference between the scattered waves off the two particles will be dependent only on the positions of these particles on the waveguide. Therefore, the imaging process may be described as follows.

Figure 2:

Theory of cELS image formation.

(a) A rectangular waveguide with transverse widths “a” and “b” units guiding power via fundamental and higher-order modes is shown. The two modes m1 and m2 are shown in green and red color respectively in the side view diagram. The modes are decomposed into a pair of plane waves propagating at discrete angles with respect to the optical axis along z. The evanescent tails of these guided modes polarize particles 1 and 2 placed on the surface and scatter into the far-field. (b–e) Experimental demonstration of the theory of image formation using a multi-moded waveguide. The images are of 100 nm gold nanoparticles imaged using a 10X/0.25 NA MO. The multi moded speckle pattern causes variations in the intensity of the coherently scattered light. Scale bar 2 μm.

Two particles separated by one Rayleigh distance = 0.61λ/NA, are located on a rectangular waveguide with transverse widths “a” and “b” units as shown in Figure 2. For λ = 660 nm and NA = 1.2., the two particles can then be assumed to be located at points with coordinates (0, b/2, 0) and (0.508a, b/2, 0). In the case of incoherent imaging, i.e., if particles “1” and “2” are fluorescent beads, they will be just resolved in an ideal microscope as per Rayleigh’s resolution criteria. However, the coherent scattering off the particles by the multi-moded waveguide chip presents the following interesting scenarios in contrast the incoherent fluorescent imaging. This is listed below.

1. The two particles are illuminated by the same mode. For example, consider illumination with TE₁₁ mode (m = 1, n = 1) which is described in Eq. (S3) of the supplementary text. Substituting the above-mentioned particle’s location into Eq. (S3), the phase difference between the coherently scattered light reaching the detector will be approximately 1.6 radians. Due to interference between these coherently scattered fields as described by Eq. (4A), the particles will no longer be resolved as per Rayleigh’s criteria. This contrasts with these two particles getting resolved as in the case of incoherent imaging.

2. The two particles are illuminated by say TE₁₁ (m = 1, n = 1) and TE₂₁ (m = 2, n = 1) mode. Substituting the abovementioned particle locations into Eq. (S3), the phase difference between the fields is seen to be π radians. As a result, the particles get resolved in label-free mode as per Rayleigh’s criteria.

Now as the galvo oscillates to vary the illumination patterns in the waveguide, the complex mode coefficient a _m (t) changes with time, hence, both the amplitude and phase of the scattered light change. An image stack so acquired over time exhibits fluctuations in intensity. This is shown via the experimental results in Figure 2(b). As a result, image contrast can be enhanced by performing the average or standard deviation of such an image stack.

Naturally, the feasibility of employing intensity-fluctuation based algorithms to such an image stack exhibiting fluctuations in intensity is worth analyzing. These fluctuation-based algorithms are typically used in fluorescence microscopy to circumvent the diffraction limit. However, applying these fluorescence-based algorithms in the partial coherent imaging regime as in cELS presents some caveats [37]. In fluorescence microscopy, the fluorescent molecules which are typically a few nanometers in size emit independently and portray a linear mapping between the fluorophore concentration and image plane. But the partial coherent imaging nature of cELS implies that the sample plane concentration and image plane intensity obey a nonlinear relationship due to the interference term described in Eq. (5). This can lead to artificial sharpening and false localizations by the algorithm and hence, lead to artifacts in the reconstructed image. E.g., consider the scenario presented in case 1 above, where the particles are no longer resolvable as per Rayleigh’s criteria. The algorithm may then localize to the point of maximum intensity which lies in between the two particles, thus leading to a false localization. However, if the particles are resolvable as per the scenario presented in case 2 above, the algorithm can artificially sharpen the image and lead to a seemingly improved contrast and resolution. The nonlinear sharpening effect can also lead to masking of regions with lower scattering intensity.

4.1 Weakly scattering specimens

Firstly, 60 nm polystyrene nanobeads are imaged to compare the performance of TIRF and cELS. Figure 3(a) shows the images of 60 nm polystyrene beads acquired in cELS and TIRF mode and the two images are in good agreement. The signal to background ratio (SBR) is higher for the cELS image. The Fourier transform of the TIRF image shows that higher spatial frequencies get attenuated faster which is the case for incoherent imaging. On the other hand, cELS is a partially coherent imaging technique and therefore, the contrast does not drop significantly even for the higher spatial frequencies which is expected for coherent imaging. Thus, cELS supports superior contrast imaging of nano-sized structures that have predominantly high spatial frequencies. The difference in the Fourier spectrum between the coherent and incoherent imaging is further discussed in Supplementary material section S2 .

Figure 3:

Experimental results of weakly scattering specimens.

(a) cELS and TIRF images of 60 nm polystyrene beads. The signal to background ratio (SBR) is given in the table and the Fourier transform of the beads imaged using cELS and TIRF is given alongside. Scale bar 2 μm in the image plane (x–y plane) and 5 μm⁻¹ in the spatial frequency plane (α–ß plane). The colorbar shows the intensity variation along the dotted lines in the Fourier plane. (b) Liposomes of <125 nm in size imaged using epi-illumination laser mode, (c) TIRF mode, (d) Dynamic Speckle Illumination mode and (e) cELS are compared. The colorbar shows the pixel values of the images. The corresponding SBR is given in the table below. Scale bar 2 μm. (f) cELS and TIRF images of <225 nm sized extracellular vesicles (EVs). The TIRF image shows photo-bleaching with time whereas cELS allows long-term imaging of the EVs. A larger field-of-view image of EVs is provided in Supplementary article, Figure S7. The colorbar shows the pixel values of the images. Scale bar 2 μm.

Next, we opted for samples that are both weakly scattering and are nanoscale in size, liposomes. The index contrast of liposomes with its surrounding is only about 0.04 [38] and the size of the liposomes used here is about 125 nm. This constitutes a weakly scattering specimen and hence, to detect these structures they are typically prepared including fluorescent molecules for fluorescence imaging. Due to their limited size, the fluorescence signal emitted by the structures is usually weak. But due to the use of high-index contrast waveguide material with a thin waveguide geometry (150 nm thick), the evanescent field intensity at the waveguide surface is high and decays rapidly, aiding in generating label-free images of such weakly scattering specimens with higher signal to background noise as opposed to TIRF. cELS image also shows the presence of a larger number of particles whereas the TIRF image of the same region of interest showed a fewer number of particles, see also Figure S6 of supplementary material. This could be attributed to bleaching out of the fluorescence or due to a very weak fluorescence signal. A similar behavior is also noted in Ref. [25].

In Figure 3(b)–(e), we compare the images of liposomes acquired using different light sources and in different modes. Here, both laser and pseudo-thermal light sources (PTS) are used in epi-illumination mode, and TIRF and cELS in the near-field illumination mode via a photonic-chip. A PTS is generated by passing a laser through a rotating diffuser to reduce the coherent noise [36] and such an illumination method is termed dynamic speckle illumination (DSI). As anticipated, the laser in the epi-fluorescence mode generates coherent noise that hinders label-free imaging of weakly scattering nano-object, Figure 3(b). The coherent noise, however, can be reduced using DSI. Even after addressing the coherent noise issue, the epi-configuration illumination mode generates a background signal comparable to that of the weakly scattered light from the object, consequently reducing the contrast of the images. In TIRF, fluorescence tagging, and near-field excitation helps reduce out-of-focus light to improve the image contrast. However, this method still suffers from photo-bleaching, labeling nonuniformity and background fluorescence signal arising from unspecific labeling that are inherent to fluorescence-based approaches. Contrary to all these approaches, cELS generates superior contrast imaging of liposomes in label-free mode, which is devoid of bleaching issues as well, as shown next.

Figure 3(f) shows the time-lapse imaging of another weakly scattering object, <225 nm extra-cellular vesicles (EVs). Photo-bleaching is a well-known problem in fluorescence microscopy and the bleaching of the fluorescence signal from EVs is depicted in the TIRF images. The fluorescent molecules bleach out over time in TIRF mode whereas cELS continued to generate high-contrast images of EVs even after photo-bleaching of its fluorescence. This demonstrates the time-lapse label-free imaging capability of cELS that would find application for imaging nano-sized biological structures like liposomes or EVs where the fluorescence signal will be limited. Also, cELS can be combined with image segmentation algorithms for estimating nano-particle density for different scattering intensities, as shown in Supplementary Figure S7.

Next, we demonstrate the competitive edge of cELS over incoherent epi-illumination methods. The decoupled illumination/detection paths of cELS configuration allow the use of a low magnification objective lens. This supports imaging of large areas without sacrificing the optical sectioning supported by the evanescent field. In Figure 4, 100 nm polystyrene beads are imaged in cELS and epi-illumination mode with both DSI and white light (WL) sources using a low magnification 20×/0.45N.A objective lens. The isolated nano-beads are not visible with DSI and WL. Only aggregated 100 nm beads are barely visible with DSI and white light sources. On the contrary, cELS provide high-contrast images even with 20×/0.45N.A. objective lens, thus enabling superior contrast imaging over large FoV. This is attributed to a multitude of factors like decoupled illumination/detection in dark-field mode, coherent scattering of multiple modes and use of high-index contrast waveguide material. The high effective index of the guided modes (n _eff = 1.75) scatters the dominant high spatial frequency components of the nano-sized samples. On the other hand, in epi-illumination mode, the illumination and detection schemes are coupled and both the light sources, i.e., spatially incoherent light (partially incoherent) for DSI and temporally incoherent light for WL fail to generate sufficient contrast. See Supplementary Figure S8 for scalable field of view imaging of 100 nm polystyrene beads in cELS mode using 25×/0.85NA and 60×/1.2NA MOs.

Figure 4:

100 nm polystyrene beads imaged using 20×/0.45NA with white light (WL), dynamic speckle illumination (DSI) and cELS.

(a, e, i) 100 nm beads imaged using WL, DSI and cELS respectively. Scale bar 50 μm. A few regions of interest, ROI 1–3, with aggregated and sparse beads are chosen within the FoV enclosed by red, green and blue boxes which are blown up and displayed. (b, c, d) WL images of 100 nm beads, (f, g, h) 100 nm beads imaged in DSI mode and (j, k, l) 100 nm beads imaged using cELS. Scale bar 20 μm in the blown-up regions.

The resolution supported by cELS is λ _vac/(n _eff + N.A.). While for other methods that use the same MO for illumination and collection, the resolution supported is given by λ _vac/2N.A. As n _eff is independent of the imaging objective lens, even with a lower N.A. MO, cELS enables high-contrast and higher resolution imaging. To validate this point experimentally, a comparison between dark-field (DF) microscopy and cELS is demonstrated in Figure 5. For this experiment, 100 nm gold nanoparticles (GNP) are imaged in cELS mode using a 10X/0.25 NA MO and in DF mode using a 10X/0.30 NA MO. In cELS, the camera acquisition time is set at 1 ms and an image stack of 100 images is acquired. Three different regions of interest in the acquired image stack are shown in Figure 5(a1)–(a3). The same regions of interest are also imaged using DF microscopy. The exposure time of the DF microscope is set at 100 ms for a fair comparison between the two techniques and the images are given in Figure 5(b1)–(b3). Comparing Figure 5(a1) and (b1), the beads contained within the red box are resolvable as two distinct beads in cELS method, as shown by the line plot in Figure 5(c). A similar improvement in performance of cELS over DF is visible in the green boxes shown in Figure 5(a2) and (b2). The corresponding Fourier spectrum of the images is also provided alongside each of the images. The difference in the spectrum is attributed to cELS being a partially coherent imaging technique while DF microscopy uses an incoherent white light source for imaging. Also, due to the use of coherent laser and high effective index of the guided modes, the scattering signal in cELS images is almost two orders of magnitude higher than the corresponding DF images.

Figure 5:

Comparison of 100 nm gold nanoparticles (GNP) imaged using cELS and dark-field (DF) microscopy.

(a1)–(a3) Averaged image (x–y plane) of 100 nm GNP of three different regions of interest imaged in cELS mode and acquired using a 10X/0.25 NA MO. Their corresponding Fourier spectrum (α–ß plane) is shown alongside. (b1)–(b3) 100 nm beads imaged (x–y plane) using a DF microscope with 10×/0.3 NA and their corresponding Fourier spectrum (α–ß plane) is shown. The colorbars indicate the pixel values in the real image (x–y plane). In the Fourier images (α–ß plane) the colorbars indicate logarithm of the pixel values along the black dotted line. (c) Line plots of the cELS and DF images are shown. The line plots given by the red and green lines correspond to the boxes in (a1)–(a2) and are for the cELS images. The red and green dotted lines correspond to the dotted boxes in (b1)–(b2) and are for the DF images. To match the magnification between cELS and DF microscope, cELS images are bilinearly interpolated and displayed here. All the Fourier images are displayed on log scale for a better visualization. Scale bar 2 μm in real space and 500 mm⁻¹ in Fourier space.

4.2 cELS for imaging cells

Here the compatibility of cELS for bioimaging is demonstrated and compared with fluorescence imaging. Figure 6 compares cELS and TIRF images of a fixed HeLa cell. cELS imaging was performed at 660 nm excitation and detection. For TIRF imaging, the actin filaments were labeled at 532 nm excitation and the Stoke shifted signal was detected using a 595/40 nm band-pass filter. Three different boxes in red, yellow, and green are blown-up and shown alongside for both cELS and TIRF. The yellow box contains the nucleus of the cell. Typically, the nucleus of the cell accommodates many fluorophores. As a result, the fluorescence intensity even in TIRF mode will be high. This can obscure some of the features as opposed to cELS. cELS image shows more features as the nucleus is situated slightly above the cell membrane and hence the evanescent field scattering will be less. Next for regions outside the nucleus, the TIRF image exhibited a reduced contrast for the filament like structures which could be attributed to weak fluorescence intensity, nonuniform, and unspecific labeling. Being a label-free method would enable cELS to perform long duration live cell imaging without worrying about photo-bleaching. In Figure S9 of the supplementary material, epifluorescence, TIRF and cELS images of the same region of interest presented here are given. The dynamics of a living HeLa cell acquired in cELS mode is provided as a supplementary movie.

Figure 6:

Comparison between cELS and TIRF images of Hela cells, scale bar 25 μm. Three different regions of interest enclosed by red, yellow, and green boxes are blown-up and provided alongside. The yellow box shows the nucleus region of the cell whereas the red and green boxes are the filaments, scale bar 8 μm. The color bars given alongside the magnified regions indicate the pixel values.

4.3 Sample illumination via four-arm crossing waveguide and application of fluorescence-based intensity-fluctuation algorithm to cELS

A multi-moded straight waveguide supports modes predominantly along a straight line. For the waveguide geometry shown in Figure S3 of the supplementary section, the angle the modes described by Eq. (S3) of the supplementary material make with respect to the optic axis (z-axis) is given by θ = cos⁻¹ ß/kn ₁ [39]. The difference in θ between the first mode ß = 1.75 and say the twentieth mode ß = 1.76 is only about 5 degrees. This fact of limited angular diversity between the modes can also be understood from Figure S2 in supplementary section. It is known that the period of interference fringes is inversely proportional to the angle between the modes. The argument of the cosine function in Eq. (5) depends on the angle between the two interfering beams. Since the angle between the modes is small, the Fourier peaks of the cosine function are also located close to the origin, which is what is seen experimentally as shown in Figure S2. As a result, the enhancement in resolution is not isotropic. To mitigate this issue, a four-arm crossing waveguide is proposed, shown in Figure 7(a). The imaging region is highlighted by the green dotted lines in Figure 7(a) where several modes from the four-arms interfere. By illuminating the sample from several azimuthal orientations, the illumination frequencies become isotropic [27, 40], [41], [42]. This concept is illustrated experimentally in Figure 7(a) where 100 nm polystyrene beads are imaged using straight and four-arm junction waveguide. The images acquired using straight waveguides show the presence of coherent noise, predominantly along the direction of propagation of light. This is mitigated when illuminating the sample from all azimuthal directions as shown by the images of 100 nm polystyrene beads acquired using a four-arm crossing waveguide. Using a four-arm crossing waveguide, though we have more illumination frequencies illuminating the sample as shown in Figure S2 of the supplementary text, it is still not isotropic. Resolution enhancement will be predominantly along the direction of propagation of the light. To achieve isotropic resolution enhancement, the photonic-chip geometry used for structured illumination microscopy as in Ref. [30] needs to be adopted for cELS.

Figure 7:

cELS on four arm junction waveguide and application of intensity fluctuation algorithm to cELS images.

(a) Four arm junction waveguide used for the experiments. 100 nm polystyrene beads imaged in cELS mode using a four-arm crossing waveguide is given, scale bar 10 μm. The green dotted box in the waveguide shows the imaging region. The use of a four-arm crossing waveguide mitigates the coherent scattering noise as shown by the images of 100 nm polystyrene beads imaged using straight and four crossing waveguides. Scale bar 5 μm. (b) Three different regions of interest of 100 nm polystyrene beads imaged in cELS mode. (c) The corresponding MUSICAL reconstruction is shown. A stack of 100 images is given as input for MUSICAL. Three separate regions of interest in yellow, orange, and blue boxes in cELS and the corresponding MUSICAL reconstructions are shown side by side. The line profiles of the regions are given as well. Scale bar 500 nm.

Next, we investigate the effect of MUltiple SIgnal Classification ALgorithm (MUSICAL) on the cELS data stack. MUSICAL helps extract sub-diffraction limit sized features from diffraction-limited image stacks like other intensity-fluctuation based fluorescence algorithms like SOFI (Super-resolution Optical Fluctuation Imaging) [43], SRRF (Super-Resolution Radial Fluctuations) [44], ESI (Entropy based Super-resolution Imaging) [45], 3B (Bayesian analysis of Blinking and Bleaching) [46], SACD (Super-resolution with Auto-Correlation two-step Deconvolution) [47]. Via singular value decomposition, MUSICAL decomposes the diffraction-limited image stack into spatial patterns in the shape of eigen-vectors and eigen values. Then based on the user input, the algorithm splits the eigen-vectors into two disjoint subsets – signal and noise to compute the final MUSICAL image which contains sub-diffraction limit sized features. For a more detailed analysis on MUSICAL, the readers may refer to [28].

The average diffraction-limited image of 100 nm polystyrene beads acquired in cELS mode is shown in Figure 7(a). Three different regions of interest from this diffraction-limited image are blown up and shown in Figure 7(b). The corresponding MUSICAL reconstructions are shown alongside. MUSICAL helps resolve beads better than the cELS image as explained earlier. However, caution must be exercised as artifacts could be introduced due to false localizations and artificial sharpening. The corresponding line profiles, green for cELS and red for MUSICAL on cELS, help illustrate the concepts explained.