Caustic wavefront encoded imaging for snapshot three-dimensional fluorescence microscopy

doi:10.21203/rs.3.rs-3703898/v1

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Caustic wavefront encoded imaging for snapshot three-dimensional fluorescence microscopy

https://doi.org/10.21203/rs.3.rs-3703898/v1

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High-resolution, three-dimensional fluorescence microscopy is widely used in biology and neuroscience. The challenges of conventional three-dimensional fluorescence microscopy which relies on scanning the focal spot across the object include limited imaging cycles due to photobleaching of the fluorophores, ambiguous spatiotemporal information in dynamic samples due to long scanning times, and mechanical perturbation during the scanning process. In this paper, we report a snapshot three-dimensional fluorescence microscopy method (CausWEI) where three-dimensional sample information is encoded in a single wide-field image by engineering a high-contrast, laterally invariant point-spread function composed of caustics generated via the interaction of a uniform, thick glass sample holder and a high-numerical aperture objective. The three-dimensional information is computationally reconstructed from the caustic pattern recorded at the camera plane. The method can be implemented with a wide-field fluorescence microscope, without any internal modification in the microscope optics. We qualitatively and quantitatively evaluate CausWEI’s capabilities and limitations with reference fluorescent beads, neural cells on three-dimensional scaffolds, and spinal cord tissue sections. CausWEI microscopy is of importance when fluorescently labelled features are located in a depth range significantly larger than the depth-of-field of the objective lens.

Physical sciences/Optics and photonics/Optical techniques/Microscopy/Wide-field fluorescence microscopy

Physical sciences/Optics and photonics/Optical techniques/Imaging and sensing

Fluorescence microscopy allows sensitive detection and tracking of gene expression, protein expression and dynamics of molecular interactions [1–3]. Although, fluorescent molecules may be stable and can be stored for months, photobleaching limits the number of imaging cycles. Wide-field microscopy [4–5], laser-scanning confocal microscopy [6], spinning- disk confocal microscopy [7] and light-sheet microscopy[8–10] are the prevalent methods of fluorescence microscopy. Although, these methods capture the image information from one focal plane at a time, all the fluorescent probes encountered in the excitation beam path are simultaneously excited to some degree, resulting in wasted photons and the risk of photobleaching. Light-sheet microscopy alleviates the photobleaching problem by selectively exciting a plane of fluorescence molecules from a direction that is orthogonal (or in some cases at a tilt) to the optical axis. However, there is a tradeoff between the light sheet thickness and the usable field-of-view [8]. In all these methods, 3D images are obtained either by point-scanning or by combining the focal stack of 2D images that are acquired after the sequential refocusing. The scanning process is time consuming and may yield ambiguous spatiotemporal information in dynamic samples. Moreover, the movement of the microscope stage or objective during refocusing can mechanically perturb the sample, for example when an immersion objective is used.

To overcome these limitations, several techniques which capture the 3D image data simultaneously by mapping axial information onto a single lateral plane have been proposed. These include multifocal imaging [11–12], light-field microscopy [13–15], and wavefront encoding [16–23]. In each of these methods, a traditional fluorescence microscope is modified either by adding a diffractive optical element at the Fourier plane [11–12], a microlens array at the image plane [13–15], or a phase mask at the Fourier plane [17–18], respectively. The ability to acquire depth-resolved image data in a wide-field fluorescence microscope is especially important in bioimaging applications, such as cortex-wide imaging systems, where the curvature of the cortical surface results in out-of-focus blur in the periphery of the field-of-view [24].

Here, we propose Caustic Wavefront Encoded Imaging (CausWEI), a novel approach to single-shot 3D imaging that does not require any modification of a fluorescent microscope but instead uses spherical aberration generated by the interaction of the sample holder and a conventional (high numerical aperture) objective. CausWEI utilizes point-spread functions (PSFs) that are caustics: First order spherical aberration causes the ray angles to deviate from an ideal focus and this family of rays can be bounded by an envelope that is tangent to each ray which is the observed ring caustic. Similar to other wavefront encoding schemes, this strong spherical aberration dominates the other aberration terms, such as defocus over an extended depth of field [25–29]. In this way, we can preserve the high-contrast of the PSF across long axial distances – facilitating computational recovery of individual features. Unlike previous work on wavefront encoding schemes [16–23], there is no need to include an additional phase mask (or spatial light modulator) in the microscope and the resulting defocus PSF is a caustic that preserves a sharp ring-shape over long defocus distances. This caustic PSF can be described analytically across the entire field-of-view while performing computational reconstructions.

With CausWEI, we demonstrate snapshot 3D reconstructions of fluorescent features in rat astrocyte samples grown on a curved scaffold made of electrospun fibers. The electrospun fibers mimic the size scale and architecture of the natural extracellular matrix. The curvature is introduced to replicate the challenging imaging condition faced in-situ in live rat brain imaging due to the curvature of the cortical surface [24].

Caustic pattern as fluorescence 3D image encoder

Figure 1a shows the illustration of the optical setup used for data acquisition in the proposed method. It is based on utilizing high spatial-frequency preserving, laterally (x-y)-invariant but depth (z)-variant caustics as the optical image encoder. The method preserves the high contrast optical signals from fluorescent sources located over a large depth range. For instance, Fig. 1b shows that the caustic signal remains above the noise floor for up to a defocus depth > 175 µm, while imaging with a 0.5 numerical aperture (NA) objective lens. While the preserved contrast presents an opportunity to perform extended depth-of-field microscopy, the caustic’s z-variant nature allows precise depth-encoding of these sources (in a single 2D wide-field image). The axial resolution and depth-localization accuracy of this computational microscopy method depends upon the NA of the objective lens. For instance, for a 0.5 NA objective, this caustic ring’s radius grows by 200 nm when the depth is shifted by 0.5 µm (Fig. 1c). The resulting accuracy with which the location can be resolved in z is 0.5 µm.

Microscope objectives are designed to minimize aberrations, and hence in the above experiments we employ a 1.1 mm thick parallel glass plate covering the sample to introduce spherical aberration and generate the caustic patterns in the defocus volume. When this glass plate is inserted between the sample and the objective lens, in an epifluorescence microscope, as shown in Fig. 1a, the rays incident at larger angles suffer larger displacements, as compared to rays incident at smaller angles and this phenomenon introduces the spherical aberration in the optical wave-field. The combination of spherical aberration and defocus results in a rotationally symmetric caustic pattern. The effect of the glass plate on the optical-field is negligible for low NA objective lenses and caustics becomes noticeable only above the NA around 0.40 (see Supplementary Figure S1).

When compared to the disc (Gaussian) defocus PSF observed in conventional imaging – without the glass plate - where there is minimal spherical aberration at the sample, CausWEI images exhibit a strong and clear retention of high spatial frequencies (see Supplementary Figure S2). Since the point spread function is a sharp circle, different depths can be digitally reconstructed by deconvolution with an analytically defined circular PSF of appropriate radii. Figure 1e-g and 2 shows the single-shot capture of objects located at various different defocus depths and their corresponding reconstructions.

Quantitative assessment of single-shot 3D reconstruction of fluorescent beads dispersed in PDMS

We first establish the depth-range and accuracy of depth-localisation of this imaging method with 10 µm fluorescent beads dispersed in ~ 1 mm thick PDMS (Polydimethylsiloxane). Figure 1e shows a single-shot wide-field 2D image with optical signal from beads located at various depths. From this measurement, a reconstruction of 3D volume with 100 depth slices was obtained, out of which 4 slices have been shown in Fig. 1g. Supplementary Video 1 shows the visualization of full 3D reconstructed volume. This result experimentally demonstrates that our method enables a scan-free imaging of objects located as deep as 175 µm defocus depth. To demonstrate the accuracy of depth-localization, we experimentally measure the change in the radius of the circle PSF with respect to a change in the depth of the source (calibration bead here). To achieve this, we estimate a value of the circle radius which produces the best focus in the reconstructed image. With a 0.5 µm change in depth, this estimated PSF grows by a radius of 200 nm. Both the depth-range and depth-localization values were specific for the 0.5 NA objective and will change with the NA of the objective. A lateral resolution of < 3 µm was experimentally measured, for an objective lens of 0.5 NA. Supplementary Figure S3 shows experimental data with 10 µm beads and ~ 3 µm nuclei. Confocal microscopy, to capture a 3D sample located across a 115 µm depth range in a clear background, would require scanning in both lateral and depth directions. To capture the same data volume at the same lateral resolution as CausWEI captured in one shot, a confocal microscope has to sequentially scan 7.3 x 10⁶ voxels (lateral field-of-view x depth slices = 206 x 154 x 230 samples). Single-shot capture allows a data compression by a factor of the number of reconstructed depth slices, for example 230x in this example. Although our lateral resolution may be lower than the theoretical diffraction limit for a given objective lens, the depth localization accuracy is comparable to the theoretical axial resolution of confocal microscopy with the same NA objective.

To demonstrate the 3D imaging of extended objects, we consider an aggregate of fluorescent beads of size distribution 9.8 ± 0.5 µm in a PDMS medium. Figure 2a shows a caustic pattern image from this 3D object captured in one of the defocus planes. A reconstruction of 20 different slices was obtained and has been shown in Supplementary Video File 2. 5 out of these 20 slices showing the digital refocusing of different beads located at different depths are shown in Fig. 2b. The average diameter of the beads in this reconstructed aggregate is estimated to be 9.4 ± 0.5 µm, this includes measurements from 5 different depths.

Experiments on multicolor fluorescence microscopy of astrocytes on curved fiber scaffold: We apply CausWEI to single-shot 3D reconstructions of rat astrocytes grown on a curved scaffold made of electrospun fibers. The cells’ nuclei and cytoskeleton were fluorescently labelled with DAPI (4′,6-diamidino-2-phenylindole) and GFAP (Glial fibrillary acidic protein) respectively. In the in-situ microscopy of cells within tissues, it is seldom possible that all the fluorescent molecules in the field-of-view are located within the depth-of-field of a high NA objective. The electrospun fiber scaffold mimics the size scale and architecture of the natural extracellular matrix that is present in tissues. In-addition, the curvature of the scaffold replicates the natural tissue curvature, a challenging imaging condition encountered in the cortex-wide imaging of rat brain. For imaging of non-fluorescent electrospun fibers, we used scanning electron microscopy (Fig. 3a). For comparison and obtaining baseline for fluorescently labelled cells, we scanned this scaffold sample with a conventional wide-field fluorescence microscopy. The fluorescent markers in the field-of-view shown in the Fig. 3 are located in a depth range of 30 µm and hence this imaging experiment required 30 depth scans at a depth step-size of 1µm. Three of these depth-scans corresponding to nuclei and cytoskeleton markers are shown in Fig. 3. The focused regions are marked with a red arrow. Next, we captured the 3D information from the same sample and field-of-view in a single snapshot as caustic pattern with CausWEI method as shown in Figs. 3c and 3g. A reconstruction of 24 different depth-slices from this caustic snapshot was obtained and the reconstructions are shown in Supplementary Video Files 3 and 4. 3 out of these 24 depth slices of fluorescently labeled astrocyte nuclei and cytoskeleton are shown in Fig. 3.

In summary, we report a computational microscopy method, CausWEI, which maps the fluorescent sources located across a large depth range in a single snapshot with micron-order depth accuracy. The caustic pattern obtained by the interaction of spherical aberration and defocus aberration is introduced by the sample holder without loss of contrast and higher spatial frequencies over a significant defocus range. The optimization based computational reconstruction with total-variation regularized maximum-likelihood as loss function— enables the estimation a 3D volume from the captured caustic pattern. The method’s lateral and axial resolution, as well as depth range, which is captured in a single caustic pattern can be optimized by using objective lens of suitable NA. The method can be implemented with a conventional wide-field microscope and is particularly useful for data compressibility, high-speed, scan-free spatio-temporal microscopic imaging.

One of the limitations of CausWEI is the distortion of the caustic PSF resulting from multiple scattering. The contrast and the shape of caustic pattern will vary for the fluorescent sources embedded deeper in an inhomogeneous medium such as thick tissue samples. The shape of this caustic pattern cannot be assumed to be constant within a given field-of-view for such different thick tissue samples. As a result, the accuracy of the reconstruction will also reduce with respect to the depth of the fluorescent marker in such tissue samples. To study this limitation, we tested CausWEI with 50 µm thick rat spinal cord tissue sections. The tissue sample was 3D scanned in a wide-field microscope at a step-size of 1 µm, 4 depths are shown in Fig. 4a. The scan-free imaging of the same 3D tissue sample was also performed with CausWEI, 3D reconstruction of 48 depth slices are shown in Fig. 4c and Supplementary Video File 5. In both methods, the imaging was limited only to ~ 20 µm depth range.

In the future, CausWEI can be applied to tracking and measuring the dynamics of fluorescently labeled proteins within a single cell and for inter-cell communications. In conventional fluorescence microscopy, high resolution tracking of such molecular dynamics is restricted within the depth of focus, unless the microscope tracks, scans and follows the direction of the labelled molecule’s 3D movements. With CausWEI, we can implement a scan-free tracking of such molecules with the caustic patterns captured in a fixed defocus plane. While we have chosen to use simple computational reconstruction in this first demonstration of CausWEI, it is straightforward to apply deep neural networks trained on datasets composed of focus and CausWEI caustic image pairs as reconstruction method, to further improve the accuracy of the reconstructed shapes.

Optical imaging experiments in CausWEI: Fig. 1a shows illustration of a wide-field epifluorescence microscope used for the data acquisition in this paper. A ~ 1.1 mm thick parallel glass plate (sample holder) was introduced between the sample and the objective lens, as a source of spherical aberration in the microscope. For capturing ground truth images free of any aberration, only a coverslip of thickness ~ 150 µm was present between the sample and objective lens. The lateral scanning of the samples was controlled by a motorized stage. While capturing the baseline wide-field images, the sample was axially scanned with the motorized movement of objective at a step-size of 0.5 µm. For CausWEI implementation, the sample was defocused at an arbitrary defocus depth of more than 50 µm.

For obtaining the axial images of conventional defocus and caustic pattern shown in Fig. 1b and 1c, a smear of 10 µm fluorescent beads on a glass slide was prepared. In both cases, the sample and defocus planes were scanned axially to obtain a given 3D volume image. 2D slice of this 3D defocus signal image, sliced through the centre of a 10 µm bead is shown in the Fig. 1b and 1c. For 3D imaging experiments with beads, shown in Figs. 1 and 2, 10 µm beads were dispersed in a PDMS (Polydimethylsiloxane) solution and solidified.

Sample preparation: ~2µm polycaprolactone (PCL) electrospun scaffold sheet was prepared using 14% PCL in 2,2,2-Trifluoroethanol, with the following conditions: +6/-3 kV tip/collector voltages, 0.5 mL/h polymer solution flow rate, 22G needle size, 11.5 cm collection distance and 1200 rpm rotation speed. Thereafter, the fiber sheet periphery was fixed by a 30 µm thickness polyethylene terephthalate frame. The whole scaffold was then mounted with ~ 0.13–0.16 mm cover glasses. The astrocytes were isolated from P0 rat brain following the protocol as mentioned in our previous study [30]. The spinal cord samples were cross-sectioned from 4–6 weeks aged rat spinal cord with cryosection method [30]. Rabbit anti-GFAP (anti-Glial fibrillary acidic protein, Agilent, #Z0334, 1:1000), 555 Alexa Fluor Goat anti-Rabbit (# A-21428 invitrogen 1:1000) and DAPI (4′,6-diamidino-2-phenylindole) were used for cell staining.

Image reconstruction: To digitally refocus a particular depth of a given sample, 2D deconvolution with the Richardson-Lucy (RL) algorithm with total-variation (TV) denoiser as a regularizer was implemented [31–33]. A circle of a given radius was used as the PSF where depth to be refocussed was tuned by changing this circle’s radius. The RL algorithm iteratively minimizes the negative log-likelihood function and the TV regularization is essential for reconstructing the images captured in low signal-to-noise conditions. At every RL iteration, 5 iterations of TV denoiser with weight = 0.05 was applied. Captured caustic defocus image was used as the initial estimate. Similarly, 3D Volume reconstruction was also obtained by minimizing the TV-regularized negative log-likelihood function. The mapping from 3D object volume to 2D measurement plane was obtained by applying 2D convolutions of different depth-slices with their depth-specific kernels, followed by their summation. PSFs for different depths were defined as the circles of varying radius parameter. In 3D case, all constant values equal to 0.5 (arbitrarily chosen) was used as the initial estimate.

Estimation of caustic PSF radii with respect to (w.r.t.) the depth of the sample: Fig. 1d shows the results from the experiments performed to measure the change of the caustic ring PSF radius w.r.t. the depth of the sample. For a given 10 µm bead sample located at a particular depth, bead image was reconstructed from its caustic pattern, using a circle of a given radius as the PSF. The procedure was iteratively performed for different radius parameter values, and the final PSF radius was chosen by selecting the maxima of the Variance of Gradient (VoG), which corresponded to the best focus w.r.t. the radius parameter. The procedure was repeated for all the other depths by shifting the bead sample axially at a step-size of 0.5 µm.

Calculation of contrast: To measure the contrast in the defocus images, the following formula was used:

\(C=\frac{{I}_{max}-{I}_{min}}{{I}_{max}+{I}_{min}}\) , where \({I}_{max}\) and \({I}_{min}\) denote the maximum and minimum intensity values in the image.

To calculate the gain in contrast shown in Fig. 1d, we calculated the ratio of contrast \(C\) in CausWEI and conventional images for a given defocus depth.

Competing interests

The authors declare no competing interests. Figure 1: Imaging setup and experiments with fluorescents beads for characterization of CausWEI. a An illustration of an epifluorescence microscope with a parallel glass plate between sample and objective, used for introducing caustic pattern in defocus planes. b Comparison of conventional defocus and CausWEI ring with a 10 µm fluorescent bead. c Graph showing the growth of CausWEI ring diameter with change in depth at a step-size of 0.5 µm. d Contrast gain, the ratio of contrast in CausWEI and conventional defocus, measured with the dataset shown in Supplementary Figure S2. e A snapshot CausWEI measurement for PDMS with dispersed 10 µm fluorescent beads as a 3D sample. f Ground truth images obtained by scanning the sample with a wide-field microscope, bead in optical focus is marked with an arrow. g 4 depth-slices out of 100 digitally reconstructed from the image shown in e. The red arrows point to in-focus features in each image.

Author contributions

S.K. and R.J.R. conceived the idea. S.K. performed the calibration, imaging experiments and reconstructions. C.H. and V.L. prepared the imaging samples. Z.L. helped with the calibration experiments and optics discussions. S.Y.C. supervised the sample preparation. R.J.R. supervised the imaging and reconstruction experiments. S.K. and R.J.R. wrote the manuscript. All authors contributed to the final manuscript.

Acknowledgements

This research is supported by the National Research Foundation (NRF), Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) program. Critical Analytics for Manufacturing Personalized-Medicine (CAMP) is an interdisciplinary research group (IRG) of the Singapore-MIT Alliance for Research and Technology (SMART) Centre.

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Caustic wavefront encoded imaging for snapshot three-dimensional fluorescence microscopy

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