Introduction

Fluorescence imaging techniques have dramatically changed biology and medicine. Recently, it was proved beyond a doubt that, fluorescence imaging techniques are capable of going beyond the classical resolution limit1, thereby revealing molecular dynamics with nanoscale resolution. Broadly, these super-resolution techniques may be categorized based on either point spread function (PSF) engineering or photophysical properties of the molecule. Techniques using PSF engineering include, 4PI2,3, stimulated emission depletion (STED) microscopy4,5, aperture engineering/multiple excitation spot optical (MESO) microscopy6,7, spatially structured light illumination8, non-linear patterned excitation microscopy9 and standing-wave total internal reflection fluorescence (TIRF) microscopy10 in addition to others11,12. Photophysical property-based super-resolution techniques include photo-activation localization microscopy (PALM)13, stochastic optical reconstruction microscopy (STORM)14, fPALM15, ground-state depletion (GSDIM) microscopy16 and IML-SPIM17. Other techniques that do not belong to these categories are evanescent field-based techniques such as, TIRF18,19 and HILO20. Notably, 3D image reconstruction in conjunction with these super-resolution techniques produce images of the highest quality5,21,22,23. PSF engineering utilizes optical techniques, such as, interference and spatial filtering to shrink the system PSF, whereas localization techniques use photophysical phenomena, such as, photoactivation and depletion, to achieve super-resolution. The down side of these photophysical techniques is the sacrifice of temporal resolution to gain spatial resolution because these techniques collect thousands of frames to construct a single super-resolution image. Nevertheless, the contribution of some of the super-resolution techniques are noteworthy and considered to be a tool for future development. The contributions include, resolving lateral elements of the synaptonemal complex and the detection of chromosomes as twisted strings24. Localization-based microscopy has revealed the clustering nature of chemotaxis receptors in the E. Coli cell membrane, which supports the fact that stochastic self-assembly is the cause behind periodic distribution of the receptors25. The study of vesicle dynamics reveals the release of lipid probes (from granules) into the membrane without fusing thereby revealing a new mechanism26,27. Multicolor TIRF microscopy is extremely useful for observing cellular dynamics near the cell membrane28. Diffraction-unlimited optical data storage has been achieved with polychromic GFP using STED imaging29. A variant of STED i.e., iso-STED, was able to resolve and study the distribution of mitochondrial proteins30. It was observed that, nuclear pore complexes are adjoined in peripheral and lamin heterochromatin using structured illumination microscopy31. There are many more studies revealing the benefits of super-resolution microscopy ranging from biology to optics. Unfortunately, the super-resolution capabilities are limited to a depth of < 150 microns, which is largely attributed to scattering in complex biological specimens.

Most of these techniques have impressive super-resolution capabilities but are limited in terms of depth imaging and suffer from poor axial resolution. Another limitation is the point-by-point-based slow scanning employed in most of the existing fluorescence imaging systems. A Bessel beam-based illumination scheme has shown promise for monitoring and imaging large specimens32. Because a pencil-like region is illuminated, the specimen is well-protected from photobleaching in comparison to confocal microscopy which illuminates the layers above and below the optical plane. We plan to lift some of these restrictions using spatial filtering techniques by employing a Bessel-like diffraction-less beam for excitation in-conjugation with theta-based orthogonal detection scheme33,34. A Bessel-like excitation beam is produced by placing a binary mask at the back-aperture of the excitation objective. The generation of a Bessel-like beam using an aperture engineering technique has been reported in the literature35,36,37. Notably, the proposed aperture engineering technique substantially reduces the ringing effect, thereby enabling fine sampling of the specimen. Reducing the ringing effect in a Bessel-like beam minimizes the background fluorescence, thereby improving the signal-to-background ratio. Such an imaging technique allows continuous scanning of specimens along the z-axis at variable depths. This technique substantially simplifies the imaging system and eliminates the need for a specialized illumination technique such as structured illumination. The advantage of the proposed technique is its simplicity and adaptability to existing imaging techniques. Specifically, this technique is well-suited for tracking functional nano-particles at greater penetration depths, enabling better understanding of complex biological processes deep inside large specimens such as, tissue, membrane and even live embryos.

Imaging deep inside thick biological tissue is severely hampered by photon scattering, which results in intensity modulations and phase mis-matches. Most fluorescence imaging techniques use a Gaussian beam for illumination. The Gaussian illumination technique is well-established and useful for shallow imaging (less than 150 microns), but fails to produce quality images at larger depths (few hundreds of microns). Two-photon excitation has been specifically introduced to overcome the above drawbacks. However, the output fluorescence is severely compromised as a result of the small absorption cross-section, thereby limiting its use for fluorescence imaging38. This calls for a beam that maintains its shape and size at larger penetration depths. Such a diffraction-less beam is known as a Bessel beam. It is the self-reconstruction property of the Bessel beam that maintains the profile of the beam in thick scattering specimens39.

Results

In this paper, we demonstrate the generation of a Bessel-like beam and show that it can reach deep inside the sample. Another aspect of the generated Bessel-like beam is the reduction of ringing effects that enhance background fluorescence. By using an orthogonal detection system, we demonstrate the scanning capability of the imaging system with a considerable reduction in the background fluorescence. This study shows an elongated Bessel-like beam and larger penetration depths.

System PSF and its characterization

Studies were carried out to characterize the PSF of the imaging system. The excitation and emission wavelengths were chosen as 532 nm and 560 nm respectively. The schematic diagram of the proposed imaging system is shown in figure 1. The imaging system consists of two arms: the excitation arm is basically an aperture-engineered objective lens. The spatial filter belongs to the family of binary filter that allows light from the peripheral regions of the spatial filter. Spatial filtering followed by focusing using an objective lens results in a Bessel-like penetrating beam whose dimension (along the optical axis) can be tuned (by the stop angle θ1 or equivalently by the radius r of the spatial filter) to generate a uniform field strength throughout the depth-of-focus. This technique simultaneously excites a pencil-like region encompassing all of the specimen layers and the detection system is placed orthogonal to the optical z-axis, thereby enabling quick scanning and high axial resolution. In this configuration, the axial resolution is essentially the lateral resolution of detection objective. The detection objective (O2) can be rapidly scanned (along the optical z-axis) to obtain structural information throughout the specimen layers (see figure 1).

Figure 1
figure 1

Schematic diagram of the proposed imaging system, in which a Bessel-like beam illuminates the sample with theta-detection at 90°.

Spatial filtering using a binary optical mask behind the illumination objective results in the generation of a Bessel-like beam. Position 1 and position 2 of the detection arm represents two different scanning positions along the optical z- axis for depth imaging.

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The system PSF at an excitation (αexc) and detection (αdet) semi-aperture angle of 60° is shown in figure 2. The lateral XY-plane shows the ringing effects associated with Bessel beams. This effect disappears in the system PSF (XY-plane), thereby producing an ellipse-like lateral PSF. The z–profile of the Bessel-like beam (see, YZ and XZ planes) is shown in figure 2. Excitation PSF multiplied by the detection PSF results in a high resolution spot along the optical z-axis. The FWHM of the PSF along the z-axis is approximately 300 nm below the classical diffraction limit. This is impressive considering poor axial resolution of the existing fluorescence imaging system.

Figure 2
figure 2

The excitation, detection and system PSF at an excitation and detection aperture angle of αill = 60° and αdet = 60°, respectively.

Linearly polarized light of wavelength 532 nm is employed for excitation and the fluorescence is observed at a wavelength of 560 nm. The resulting axial and lateral beam profile for the generated Bessel-like beam (central lobe) along with the side rings is clearly visible. The system PSF are obtained by multiplying the excitation and detection PSFs. Scale bar = 1 µm.

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Depth scanning

Fast scanning at a depth of hundreds of microns is essential for obtaining vital information about a specimen. In this paper, we propose Bessel beam-based depth imaging to gain depth information. Figure 3 shows the system PSF at various stages of the z-scanning process starting from z = 0 to z = 1.92 µm. Specifically, the system PSFs are shown for Δz = 0 nm, 510 nm and 1.47 µm. The PSF retains its shape and size throughout the scanning process along the optical axis, but this may not be true with a real sample which is non-isotropic and causes prominent scattering. Nevertheless, this shape retention is beneficial for depth imaging applications. Because of the non-diffracting nature of Bessel-like beams, the technique may also perform well in scattering samples. However, emitted photons may undergo significant scattering as they travel through the specimen along the orthogonal direction to reach the detector. Overall, the proposed system benefits as far as high resolution depth imaging is concerned and provides the flexibility to scan the desired specimen layer. Next, we show the effect of the filter characteristics on the system PSF. Figure 4 shows the excitation PSF for varying filter stop angles. The PSF scales with the stop angle (θ1), as the transmission window Δθ = (α − θ1) is varied from 5° to 20°. The corresponding FWHM along the optical axis are FWHMz = 1.56 µm (for Δθ = 20°), FWHMz = 2.94 µm (for Δθ = 10°) and FWHMz ≫ 3.84 µm (for Δθ = 5°). Additionally, the FWHMz becomes hundreds of microns for Δθ < 5°. Ideally, the system PSF resembles widefield PSF for small stop angles (i.e., large Δθ), resembling full aperture uniform illumination. This scaling makes the system flexible for many biological applications that demand PSF of specific dimensions in real time, especially when imaging large biological samples such as an embryo. Finally, the polarization-dependence of the excitation PSF is analyzed. Figure 5 shows, respectively the contour plots of the excitation PSF for both x-polarized and randomly polarized light illumination. For randomly polarized light, a uniform decrease is observed in the field strength as the distance form the geometrical focus i.e, (x, y, z) = (0, 0, 0) increases along the transverse plane. This uniform decrease is completely different from that of linearly polarized light illumination, which shows elliptical field structures as the distance from the focus increases along the y-axis. The field strength does not decrease significantly along the y-axis, even as far as 1.92 µm from the geometrical focus.

Figure 3
figure 3

The PSFs obtained by performing z-scans along the optical axis.

The detection objective is scanned along the optical axis to obtain data at varying sample depths: Δz = 0, Δz = 510 nm and Δz = 1470 nm. In this figure, Δz represents the shift from the origin as depicted schematically in Figure 1. At varying depths, the system PSF preserves its shape and size. The effects of prominent side rings are clearly minimal. Scale bar = 1 µm.

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Figure 4
figure 4

PSF resizing by varying the transmission angle Δθ = α − θ1, where the stop angle θ1 is determined by the spatial filter.

The excitation PSF axially elongates with decrease in Δθ and ranges from 1.56 µm to > 3.84 µm. For large Δθ, the excitation PSF resembles the PSF obtained using plane wave illumination. The intensities are normalized for each image. Scale bar = 1 µm.

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Figure 5
figure 5

Polarization effect on the excitation PSF: (a) Linearly-polarized light illumination (polarized along x-axis) and (b) Randomly polarized light illumination.

The contour plots clearly show an isotropic field distribution for randomly polarized light, whereas the field has anisotropy along the y-axis.

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Experimental results

Following the computational study, we constructed an optical system to generate a Bessel-like beam for exciting the fluorescent gel sample. The self-reconstruction property of Bessel-like beams facilitate navigations through thick and turbid media. The interference of the diffracted beam emerging from the engineered aperture mask results in the formation of Bessel-like beam. Aperture engineering has been quite successful for producing Bessel beams of desired dimension. Altering the filter parameters (aperture width 2r or equivalently, stop angle θ1) of the spatial filter mask varies the size in a simple way37. This adaptability is the advantage over axicon-based Bessel beam generation, where there is no tunability in the axial dimension of the Bessel beam.

The schematic diagram for obtaining the Bessel beam-based high resolution imaging is shown in figure 1. The input Gaussian beam is appropriately expanded to fill the back-aperture of the objective lens and subsequently subjected to the binary spatial filter before entering the illumination objective lens O1. The diffracted waves undergo constructive interference along the optical axis, thereby forming a penetrative diffraction-less Bessel-like beam. The XY, XZ and YZ planes of the Bessel beam are shown in figure 6. The measurements were taken by translating the camera that was placed directly in the beam path. The Bessel beam extends over a length of approximately 750 µm (FWHMz) with a lateral (y) dimension FWHMy of approximately, 50 µm. These dimensions proves that, the generated Bessel-like beam is uniform over a fairly large axial distance, which is beneficial for precise microscopy imaging and spectroscopy deep inside the specimen. Moreover, the extent of the reported beam is larger than that earlier reported in the literature32. The advantages of using the proposed spatial filter instead of axicons are the easy tunability of the Bessel beam, the depth imaging capability and the low-cost37.

Figure 6
figure 6

Experimentally obtained illumination PSF along the XY, XZ and YZ planes showing the extended depth-of-field.

A camera was placed directly in the beam path near the focal plane of the illumination objective and several images of its transverse profile were captured by repeatedly translating the camera through a known distance to obtain a 3D image. These orthogonal views are obtained from the 3D data. The Bessel beam spatially extends approximately 750 µm along the optical axis. Intensity plots are shown along the x, y and z axes for detailed visualization of the field structure at and near the focal plane. The field is uniformly stretched along the optical z-axis showing the extended depth of the Bessel beam.

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The detection arm consists of a separate objective for collecting the fluorescence emanating from the fluorescent gel-matrix sample (see, sample preparation section for the preparation details of the sample). The detection arm is placed at an orthogonal angle offering high numerical aperture (NA) at long working distance apart from achieving maximum elimination of incident light. After emerging from the back of objective lens O2, the parallel rays are then filtered using a long-pass filter (with a cut-off wavelength of 550 nm) to remove the stray light and are finally focused on to the CCD camera. It may be reminded that, the system PSF is the product of excitation PSF and the detection PSF. In this system, the excitation PSF is the diffractionless Bessel-like beam penetrating through all of the specimen layers and the detection PSF is a dot-like structure (formed by the objective lens O2) which is placed orthogonal to the excitation objective (see, figure 1 and figure 2). The schematic diagram (see, figure 7A) shows the translation of detection PSF along the Bessel beam, thereby scanning the specimen along the length of the excitation PSF. The corresponding contour plots of the system PSF at varying depths of the fluorescent gel matrix are shown in figure 7B. The system PSF is obtained at a depth ranging from 50 µm to almost 1 mm. This range demonstrates the incredible penetrating property of the excitation PSF. Moreover, the system PSF preserves its shape to a depth of 650 µm. The axial length (measured as the FWHM along the optical axis) and lateral (along transverse y-axis) extent of the Bessel-like beam are approximately 300 µm and 25 µm, respectively. The length of the Bessel beam can be varied by changing the diameter 2r of the spatial filter which is equivalent to changing the stop angle (θ1). The adaptable length of Bessel-like beam which depends on the spatial filter radius (shown in figure 1) provides the tunability required for various applications in bioimaging.

Figure 7
figure 7

(A) Cartoon showing the system PSF as it enters the fluorescent gel sample at varying z-depths along with the theta-detection geometry, (B) The experimentally obtained contour plots of the PSF at varying depth (ranging from 50 µm to 1.25 mm) of the fluorescent gel sample.

The depth information is indicated on each image and denotes the distance of the right-most corner of each image from the coverslip. The depth penetration capability of the Bessel beam is quite evident.

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We imaged coated CaCO3 particle clusters with dimensions of 3 – 10 µm in a gel matrix. In the present experimental setup, we have used both 10X, NA = 0.3 and 20X, NA = 0.4 objectives. Specifically, the imaging of CaCO3 particles in the gel-matrix were carried out using 20X detection objective. The images were acquired at varying depths, from which only 2 images at a depths of 108 µm and 358 µm (shown by red circles) are shown in figure 8. The zoomed image of coated CaC03-cluster is also shown for visualizing the structures. The image quality is impressive at a depth of 358 µm considering the fact that the gel matrix is highly scattering. The internal structure of the CaCO3 cluster is clearly visible even at a depth of 350 µm and thus demonstrates in-depth high resolution imaging in a scattering medium (gel-matrix). This enhanced depth is a result of the self-reconstruction property of the Bessel beam39. Traces of the larger cluster are also visible in the image at position 1 (green circle) which are caused by the stray light and the large field-of-view of the detection objective.

Figure 8
figure 8

Images of clusters of fluorescent polymer coated CaCO3 particles (size 3 – 10 µm) inside a tissue-like gel matrix at depths of 108 µm and 358 µm from the sample boundary.

The location of this sample boundary is indicated by the red line and both positions 1 and 2 are located with respect to this line. A few out-of-focus clusters can be observed in position 1, one of these is encircled in blue. This same location is brought to focus by adjusting the detection arm along the optical axis (x-axis, see Figure 1.) and captured in position 2. A section in which a few coated CaCO3 particles are clustured has been magnified. The scale bar (in white) represents 55 µm.

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Imaging cells deep inside a tissue-like scattering specimen is of potential interest for understanding complex biological phenomenon. In the present study, yeast cells were imaged in a tissue-like scattering gel-matrix. This type of specimen is important for assessing imaging capabilities in a scattering specimen while isolating other effects such as, auto-fluorescence and photobleaching. The yeast cells were coated with three-layers of fluorescently-tagged polymers. The coating process and sample preparation are described in Supplementary 1. Figure 9 shows the cell images at varying depths, Δz = 296 µm (A), Δz = 478 µm (B) and Δz = 616 µm (C) (shown by the white arrow in figure 9). Similar to CaCO3 imaging (in figure 8), traces of cells from other layers are also visible. Again, these traces are caused by stray light and the large field-of-view of the detection objective (O2). Practically, the working distance for large NA objective (NA > 0.4), is usually very small (approximately few millimeters). Therefore, the optical alignment and data collection in the orthogonal detection configuration become very difficult. Moreover, the full-width half-maxima (FWHM) is calculated for several yeast samples at varying depths as shown in figure 9. The intensity plots are shown in figure 9 (D,E,F) and the corresponding FWHM is found to be 2.04 µm, 2.36 µm and 2.12 µm at depths of Δz = 296 µm, 478 µm and 616 µm respectively. These findings reveal that, the the FWHM is approximately preserved throughout the sample depth of 616 µm, thereby demonstrating the diffractionless property of the Bessel beam.

Figure 9
figure 9

Fluorescent polymer (PAH conjugated with NHS-Rhodamine dye) coated Yeast cells are uniformly distributed throughout the tissue-like gel sample.

Several images were captured by translating the detection arm by 50 µm; three of these images are shown here, each highlighting a prominent cluster of Yeast cells. These clusters were observed at depths of 296 µm (A), 478 µm (B) and 616 µm (C) from the coverslip. The inset shows a zoomed portion of a few clustered Yeast cells. (D), (E) and (F) are the intensity plots along the white line passing through the clusters in these inset figures of (A), (B) and (C). The FWHM values (obtained by averaging the Y and Z profile) are indicated in each intensity plot. It is evident that, the FWHM does not appreciably increase at greater penetration depths thereby supporting the fact that resolution deep inside the specimen is restored. The scale bar (in white) represents 25 µm.

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Finally, we performed depth-imaging studies with a state-of-art laser scanning confocal microscope (Zeiss, LSM 700) for comparison with the proposed technique. We used a confocal pinhole of 46.5 µm for obtaining the sectional images at varying specimen depths. The specimen comprised of fluorescently-coated Yeast cells encaged in a gel-matrix. Figure 10(a,b,c) shows the XY-, YZ- and ZX- sections of the specimen along with a cartoon (figure 10d) describing the imaging parameters (such as, the position of the coverslip and the coordinates of the sample plane). From the YZ-plane (figure 10b), it is clear that the penetration depth of the confocal system is approximately 227 µm. A penetration depth of about 200 µm for a confocal system was recently reported in the literature40. Figures 10e and 10f show the magnified image (obtained using a PLAN Neofluor 20X/0.4 NA objective lens) of the specimen at a depth of 16 µm for direct comparison with the images at a depth of 227 µm (see, inset of figure 10a). To further demonstrate the system resolution, FWHM was obtained at varying depths. At depths of 16 µm and 227 µm, the FWHM is found to be 2.29 µm and 3.15 µm respectively (see, figure 10g and 10h). The broadening of the FWHM is clearly evident, revealing the deteriorating resolution of the confocal system at greater depths. In contrast, the proposed Bessel beam-based imaging system retains the FWHM of the system PSF at much greater depths (see, figure 9). This gives an approximate estimate of the resolution of the proposed imaging system and its comparison with the confocal system. Similar images were also obtained for another specimen (fluorescent polymer-coated CaCO3 particles embedded in the gel-matrix) as shown in the supplementary material (see, supplementary 1, figure 4).

Figure 10
figure 10

The gel-matrix containing yeast cells (coated with multiple layers of polymer [PAH] conjugated with fluorescent dye [NHS-Rhodamin] and PSS), is imaged by using a confocal microscopy.

Several XY images were acquired to form a 3D stack. The farthest observable yeast cell cluster was observed at a distance of Δz = 227 µm from the sample boundary. (a) XY-plane of the 3D stack at a depth of Δz = 227 µm. The insert shows the zoomed portion of the Yeast cell cluster. (b) and (c) are the corresponding YZ and XZ planes, respectively, that are obtained from the 3D stack. (d) A schematic diagram depicting the location of the planes within the specimen and its distance from the coverslip. (e) For comparison, XY plane similar to (a) is also shown at a closer depth of 16 µm. (f) Magnified view of a small Yeast cluster taken from the highlighted portion of (e). (g) and (h) are the intensity plots along the white lines in the inset figures of (a) and (f), respectively, for comparison at two varying depths. The broadening of the FWHM at a penetration depth of 227 µm is evident, indicating the deteriorating system resolution. Scale bars are inserted in the respective images.

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Discussions

The aperture engineering technique offers an efficient way of generating a Bessel-like beam and the ability to reach a depth of hundreds of microns. The diffraction-less property of the Bessel-beam makes it a natural choice for imaging scattering specimens which are otherwise inaccessible by other means of microscopy imaging techniques such as, widefield, CLSM, 4PI, structured illumination microscopy and others. Notably, the experimental results show substantial minimization of the concentric ring effect, thereby facilitating a fine scanning ability without causing undue background fluorescence.

Confocal laser scanning microscopy (CLSM), Structural illumination microscopy (SIM) and other scanning-based fluorescence imaging techniques have advanced the fields of biophysics, biophotonics and nanoscale imaging. However, the inability to improve the penetration depth has limited the use of these techniques in thick scattering samples such as tissue. The PSF of these imaging systems broadens at large depths in the sample, results in phase-mismatch and gives rise to poor-resolution. These effects rules out the very concept of high-resolution noise-free imaging. Widefield and CLSM imaging suffer from autofluorescence and off-layer (top and bottom of focal plane) excitation. With the improved depth penetration of Bessel-like beam, the illumination can be limited to just a pencil-like region of the specimen, thereby preventing premature photobleaching of the neighboring regions. Additionally, we observed a substantial reduction of the ringing effect surrounding the central pencil-like beam, which further reduce undue photobleaching and off-focus fluorescence. This illumination scheme coupled with orthogonal detection demonstrates the capability for selective imaging from a specific plane deep inside the specimen. In such a configuration, the lateral resolution of the illumination arm determines the axial resolution of the overall imaging system, which is beneficial for deep selective plane imaging. It is difficult to go down to a resolution of few hundreds of nanometers because of the small working distance of high NA detection objective. Nevertheless, this configuration enables the study of thick scattering biological specimens at large penetration depths.

The ability to look deeper inside a biological specimen has profound implications in biological systems. This ability is prohibited by the poor transmission of light through the specimen which comprises several interfaces and scattering centers. To increase penetration, one has to employ a beam that does not undergo significant diffraction. Specifically, the Gaussian beam is known to have significant diffraction. Bessel beams show much promise which is mainly because they are diffractionless and can self-reconstruct. When obstructed, the scattered field interferes with the unscattered field, resulting in constructive interference along the direction of beam propagation (which is same as the optical axis). Mathematically, the complex amplitude of the Bessel-like beam can be modeled as, , for which the intensity distribution is, , where, ; kx, ky, & kz are the components of the wave-vector. The presence of a Bessel function in the intensity expression accounts for the side rings which decrease as increases and most importantly the intensity is independent of the propagation direction z, thus there is no spread of intensity. Therefore, the Bessel beam can propagate deep inside the scattering sample. In contrast, the intensity of the Gaussian beams is given by, ; and has a z-dependence. Therefore the intensity spreads strongly at interfaces (refractive index mis-matches) in the biological specimen.

The imaging technique has demonstrated quality imaging of both functionalized nanoparticles and polymercoated yeast in a thick gel matrix. PSF distortion is inevitable at large penetration depths especially in a scattering sample. This technique demonstrates that Bessel beam-based excitation extends the imaging limit to almost 650 µm. In contrast, Gaussian beam-based excitation techniques are limited to ≈ 200 microns. Moreover, in an ideal isotropic medium, the computational study revealed that the PSF retains its shape at greater penetration depths. We have already witnessed in our gel-matrix sample that this does not hold true for z > 650 µm. In the computational study, scattering effects were not incorporated, which is a result of the difficulty in modeling the scattering process in a complex biological environment. The PSF undergoes substantial distortion at greater penetration depths in a realistic sample, such as the tissue-like gel-matrix sample. Therefore, we conclude that reliable imaging is possible for z ≤ 650 µm. Within this range, the recorded images (see, figures 8 and 9) show the capability for high quality imaging. In the future, this technique will attract applications in particle tracking deep inside tissue and optical injection in addition to fluorescence imaging applications.

Methods

Excitation and detection scheme

The flexibility for obtaining information from any desired layer of the specimen is of paramount importance in fluorescence imaging. Assuming linearly polarized light illumination and spatial filtering techniques, the resulting electric field at the geometrical focus is given by41,42,

where, the modified diffraction integrals over the aperture angle are, , and . u, v and φ are the longitudinal coordinate, transverse coordinates and azimuthal angle respectively42. The function, M(*) = H[θ − θ1] − H[θ − α] represents the spatial filter and H[a − b] = {0, a ≤ b; 1, a > b} is the Heaviside step function. θ1 is the parameter controlling the transmission characteristics of the filter through the outermost annulus defined by Δθ = α − θ1 (see figure 1).

We employ confocal theta detection scheme, where the detection is performed in the orthogonal plane, as shown in figure 1. The transformation matrix representing the orthogonal plane is given by, . This detection scheme has the advantage of high resolution at long working distances. Since, the emission process is isotropic and the fluorescent light is randomly polarized, the detection PSF is given by,

where the integration on the aperture-free detection objective is carried over the detection aperture angle αdet. Overall, system PSF of the proposed imaging system is given by,

For the computational study, the excitation wavelength was chosen as 532 nm, for which the fluorescence emission was collected at 560 nm. We have chosen to work at a sampling rate (well above the Nyquist sampling rate) of 30 nm along the entire x, y, & z axes. For the simulation, the number of pixels chosen along the lateral x, y axes were 128 × 128 and 128 of these planes were considered along z-axis. This gave a lateral (xy) and axial (z) range of about 3.84 × 3.84 µm2 and 3.84 µm respectively. The integration over the modified diffraction integrals, , and was performed over the transmission angle (Δθ). The detection PSF is similar to the excitation PSF except for the scaling introduced by the Stokes-shifted emission wavelength of 560 nm. The detection scheme consists of scanning along the z-axis to successively collect light from different layers of the 3D specimen.

Generation and characterization of a bessel-like beam

To generate a Bessel beam, we used aperture engineering techniques. A special optical binary mask was employed that allows the light to pass through the outermost annular region (see, Supplementary 2). This structured light is then allowed to pass through the back-aperture of the objective lens. The spatial filter has a radius of 12 mm and is tailored in the workshop to fine tune the edges. The back-aperture of the objective lens (Olympus, UPlanFLN 10X/0.3NA) is approximately 15 mm and the light is transmitted through the outermost window of 12 – 15 mm. The characteristics of the spatial filter mask are detailed in Supplementary 2. Upon excitation and with the consequent focusing by the excitation objective, the light from the periphery undergoes constructive interference at the core along with low intensity rings due to further interferences.

To characterize the beam, we placed a CCD camera (Jenoptik MFcool) directly at the geometrical focus of the illumination objective lens. The camera was then translated along the optical z—axis to collect the images of the XY-profile of the Bessel-like beam. The translation was achieved using a micro-meter translator at an interval of 10 µm within a range of 1 mm. The images were then stacked together to obtain the 3D view of the field distribution as shown in figure 6.

We employed theta detection in which the light was collected 90° to the optical axis. The detection objective (Olympus, UPlanFLN 10X/0.3NA or Olympus UMPlan FL 20X/0.4NA) collected and collimated the light. This was followed by an iris that is introduced to reduce spherical aberration. The fluorescence light was then allowed to pass through a biconvex lens (focal length 150 mm) that focuses it on the CCD camera. The data were collection from different z-layers of the specimen by translating the detection objective with incremental steps of 50 µm. To enable sharp focusing of the detection objective, the translator on which the sample was mounted was adjusted along the z-axis accordingly.

The sample chamber was mounted on a holder that was placed on two orthogonally oriented micrometer translation stages (Holmarc ,TS – 50 – Mu10 – 01, India). This arrangement allows the sample to be displaced with respect to the illuminating beam both axially (z-axis) and along the transverse x-axis with a resolution of 10 µm. We used cover-glass to build a sample chamber which ensured that we have a perfect parallel plane facing the illumination beam and the detection objective. Having an irregular surface facing the detection objective increases spherical aberration and as a result produces image distortion.

Sample preparation.

Materials

Poly(styrenesulfonate sodium salt) (PSS; MW = 70,000), poly(allylamine hydrochloride) (PAH; MW = 15,000), Ammonium bicarbonate(NH4HCO3), calcium nitrate(Ca(NO3)2), Sodium chloride (NaCl) and dimethyl sulfoxide (DMSO) were obtained from Sigma- Aldrich. The fluorescent dye NHS-Rhodamine (MW: 528, Ex/Em wavelength: 552/575) and fluorescent dye removal columns were purchased from Thermo Scientific. Agar powder was acquired from Sd Fine Chemicals. An optical filter with a cutoff at 550 nm was purchased from Thorlabs for filtering the incident light.

System PSF characterization

To characterize the Bessel beam, we prepared a fluorescent gel sample. 100 mg of Agar powder was dissolved in 20 ml of distilled water and kept at 100°C for 10–15 min. The liquid gel was then allowed to cool down to 40°C. Then, 500 µlit of molten agar gel was added to 100 µlit of NHS-Rhodamine dye with constant stirring. This mixure was then poured into a detachable cubical chamber and allowed to solidify. Special care was taken to ensure that smooth surfaces faced the excitation light as well as the detection camera to reduce undue lensing effect. Once solidified, the fluorescent-gel sample was ready for the PSF characterization of the imaging system.

Preparation of the PAH-NHS Rhocamine Conjugate

The labeling procedure43,44 consisted of mixing a PAH solution (1 mg/ml) prepared in double-distilled water, with the dye dissolved in DMSO (10 mM), in a 1 : 15 (w : w) ratio. The mixture was then placed in the incubator. Darkness was maintained overnight with continuous gentle stirring to avoiding photobleaching. Subsequently, the resulting PAH-NHS Rhodamine was purified using fluorescent dye removal columns.

Coated Yeast Cell and CaCO3 Suspended Gel Samples

To prepare the gel sample, 100 mg of Agar powder was dissolved in 20 ml distilled water and heated at 100°C for 10 minutes. The melted agar gel was then cooled to 40°C. 500 µlit of melted agar gel is added to 100 µlit of coated CaCO3 crystals with intense stirring. This was then shaped as a cube. The preparation of coated CaCO3 is described in Supplementary 1. Special care was taken to obtain a smooth surface that included the surface facing the excitation Bessel-like beam and the adjacent side facing the detection objective.

A similar technique was employed for preparing the Cell-suspended gel sample. Care was taken to cool the melted agar gel to 37°C. Then, 500µlit of the gel solution was added to the coated yeast cells and mixed well by pipetting. The resulting mixture was then allowed to solidify in a cubical detachable container.