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. 2026 Apr 29;16:19872. doi: 10.1038/s41598-026-48574-4

Fast 3D dynamic visualization of porcine spermatozoa by using high-resolution wavefront coding light sheet microscopy and machine learning

Jacob Licea-Rodriguez 1,2,✉, Gustavo Castro-Olvera 2, Omar Palillero-Sandoval 1, Martin Eriksen 3,4, Gonzalo Merino 4,5, Roberto A Beltran-Vargas 1, Israel Rocha-Mendoza 6, Omar E Olarte 7, Pablo Loza-Alvarez 2,✉
PMCID: PMC13314992  PMID: 42056271

Abstract

We present a wavefront coding (WFC) based decoupled illumination-detection light sheet fluorescence microscopy (DID-LSFM) system that integrates machine learning for high-speed volumetric imaging. This approach enables high-speed volumetric imaging of three-dimensional (3D) sperm flagellar dynamics at up to 80 volumes/s, more than twice the typical volumetric video rate. The speed is enabled by wavefront-coded DID-LSFM and extended depth-of-field imaging, whereas the image quality is significantly enhanced by applying machine learning-based denoising prior to deconvolution. By incorporating a cubic phase mask for WFC, we extend the depth of field (DoF) of a high numerical aperture (NA = 1.0) collection objective from 2.6 up to 40 µm, more than an order of magnitude increase. Image sharpness and contrast are restored through digital deconvolution using measured and simulated point spread functions (PSFs). Because deconvolution is highly noise-sensitive, we incorporate a self-supervised machine learning-based denoising algorithm (Noise2Void) applied to the raw sperm images prior to deconvolution. The PSFs of the generated cubic phase masks were denoised using a classical non-local means filter implemented in scikit-image, followed by median background subtraction. This approach was selected as a conservative and deterministic method that reduces noise while preserving the characteristic PSF structure required for reliable deconvolution. This denoising step significantly enhances the reconstruction fidelity and stability. We conduct a comparative analysis of images restored using both measured and simulated PSFs and provide a quantitative assessment of the resolution achieved using the cubic phase mask. Fast, high-contrast volumetric sperm imaging is essential for assessing fertility and reproductive health. The proposed method provides an approach to visualize the 3D sperm flagellar dynamics, information that is not include in Computer-Assisted Sperm Analysis (CASA). The proposed imaging system combined with CASA could have the potential to provide an advanced platform for quantitative reproductive studies.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-48574-4.

Introduction

Structural details and motility of spermatozoa are crucial indicators of sperm health and viability. Motility is also important from the perspectives of fundamental biology and, more generally, for understanding reproductive health disorders1,2. Spermatozoa exhibit several motility modes and swimming patterns during their natural 3D locomotion, and imaging flagellar dynamics is particularly informative for assessing sperm health. However, due to the flagellum’s small diameter (< 1 µm) and its rapid oscillating motion, visualizing it with sufficient time and spatial resolution remains challenging. Addressing this challenge requires a fast volumetric and high-resolution imaging technique. Optical and holographic techniques such as optical coherence tomography3, computational and digital holographic microscopy combined with interpolation methods4,5 have been used to track 3D spermatozoa locomotion, but these techniques generally sacrifice spatial resolution for volumetric capability.

Other methods for fast volumetric imaging have been developed, such as light-field microscopy (LFM), in which the entire volume is captured in a single snapshot6–12. Although these approaches substantially increase acquisition speed, they often compromise imaging depth or spatial resolution. LFM also suffers from low contrast due to background signals generated by its wide-field illumination. Even though the contrast reduction can be mitigated by combining LFM with selective plane illumination microscopy or structured light illumination13,14, limitations in the resolution and imaging depth can still persist. Li et al.15 recently proposed an alternative single-shot 3D imaging approach that combines point spread function (PSF) engineering with neural network reconstruction to encode volumetric information into a single 2D image. The authors conducted simulations in a 10 × magnification wide-field microscope showing that a V-shaped PSF offers good 3D resolution (< 2.5 µm lateral and ∼15 µm axial) over an extended depth of field (DoF) of about 350 µm. However, this method has not yet been validated in biological experiments. Other related techniques such as Fourier light-field microscopy (FLFM), capture the 4D light field in the Fourier domain, reducing artifacts and computational cost while extending depth coverage16,17. More recently, high-speed 4D fluorescence light-field tomography (ReFLeCT) has enabled snapshot volumetric imaging of whole organisms at up to 120 volumes/s, albeit at the cost of reduced 3D spatial resolution (up to 15–20 µm)18. While these approaches represent advances in volumetric wide-field imaging, they still lack the intrinsic optical sectioning required for high-contrast biological imaging, relying instead on computational post-processing to approximate optical sectioning.

In contrast to the LFM approach, light sheet fluorescence microscopy (LSFM) offers true optical sectioning and reduced out-of-focus background. LSFM has been widely used to study fast 3D biological dynamics, particularly in neuroscience and developmental biology19–22. Typically, 3D imaging is performed by physically translating the sample across the light sheet or by implementing a precise synchronization between the illumination and detection arms23–27. To overcome mechanical or synchronization constraints, some strategies have been proposed for fast volumetric imaging without translational motion of either the sample or collection objective, such as the use of electrically tunable lens28,29 or a tunable acoustic gradient lens30. Furthermore, for rapid 3D imaging of large volumes it has been combined the capability of light-field imaging to simultaneously capture volumetric images and the capability of light-sheet excitation to optically section the sample volume, this technique is the so called light-sheet light-field microscopy (LSLFM). In LSLFM a limited axial volume of the sample is excited with a scanned light-sheet while the images are acquired with light-field microscopy. Commonly, these hybrid systems use passive optical elements such as microlens array where no complex dynamic calibration is needed and may be adjusted to specific imaging needs However, in some cases either temporal31 or spatial32 resolution could be sacrificed.

A useful strategy for achieving fast volumetric imaging in LSFM, while keeping the sample and the objective stationary, is to extend the DoF of the collection objective. In this configuration, the light sheet can be rapidly scanned axially through the sample volume within the extended DoF, and the imaging speed becomes limited only by the camera’s readout rate. It should be noted, that at the highest imaging speed, where short exposure times are required, the acquired images exhibit a reduced signal-to-noise ratio.

Several methods have been implemented to extend the DoF of collection objectives for fast 3D imaging. Tomer et al.33 implemented a spherical-aberration-assisted extended depth-of-field (SPED) system, in which the collection objective’s PSF is elongated by induced spherical aberrations, thereby increasing the DoF. The authors achieve to extend the DoF of two different objectives with low numerical apertures (4 × /0.28 NA and 10 × /0.25 NA) up to 200 µm, and demonstrated SPED light sheet capability by performing 12 volumes/second (0.9 mm × 0.4 mm × 0.2 mm, 40 z slices) imaging of an entire larval zebrafish brain. Another approach relies on using wavefront coding (WFC), which if implemented in LSFM, is referred to as decoupled illumination-detection (DID) LSFM34–37. In this technique, a cubic phase mask (CPM) is added at the microscope’s exit pupil imaging path, generating an elongated axial PSF while preserving the numerical aperture (NA) of the collection objective36,37. This enables the use of high NA’s objectives (NA ≥ 1) to extend their limited DoF that typically is less than 3 µm which are used for high resolution volumetric imaging. Furthermore, the DID approach offers flexibility, as the CPM and thus the DoF can be fully customized for the task, sample, or experiment requirements. Because the CPM introduces phase modulations, the acquired images are distorted and should be restored by using a digital deconvolution method based on the measured PSF. Importantly, this deconvolution procedure can, in principle, yield aberration-free image reconstructions.

In parallel, machine learning has recently been applied in biological imaging to suppress instrumental noise and enhance biomedical images quality. The denoising and image restoration fields have advanced significantly with the adoption of deep learning and convolutional neural networks (CNN). In a typical supervised setting, the training set consists of pairs of noisy and noiseless images used to train a deep neural network. However, obtaining a noiseless image or this pair is impractical in experimental conditions. As an alternative, the Noise2Noise38 requires only pairs of noisy images corresponding to the same underlying scene. While for static or slow-moving scenes, this method is not applicable to high-speed volumetric imaging such as ours. More recent self-supervised methods can perform denoising without any noiseless reference image. For example, in the Noise2Void algorithm39, the network learns to predict masked pixels in the input image, effectively modelling the underlying spatial structure of the data. Several subsequent works and related algorithms further improved upon this approach (e.g.40,41).

In this work, we present the use of DID-LSFM under high NA conditions combined with machine-learning-based denoising, specifically using the Noise2Void algorithm. This approach enables visualization of the 3D dynamics of sperm flagellar motion at an imaging speed up to 80 volumes/s, more than twice volumetric video rate. In our previous work, we demonstrated the LSFM incorporating a WFC mask for high-speed volumetric imaging of in vivo dynamics and 3D particle tracking, using a low numerical aperture (NA = 0.5) collection objective (CO) and achieving up to 73 volumes/s36. In the present study, we employ a 20×, high NA = 1 water immersion objective and extend the DoF from 2.6 up to 40 µm, an increase of more than one order of magnitude. We also present a quantitative analysis of the resolution enhancement achieved with the cubic phase mask.

Materials and methods

Experimental setup

Wavefront coding

The cubic phase mask (CPM) introduced in the imaging system to extend the DoF is described by the following phase function36:

graphic file with name d33e467.gif 1

where Inline graphic are the normalized spatial frequency coordinates confined within the unitary circle (Inline graphic), and α denotes the amplitude of the phase modulation.

To implement the CPM using an adaptive optics (AO) system with a deformable mirror (DM), it is convenient to express the CPM phase function (Eq. 1) as a Zernike expansion:

graphic file with name d33e485.gif 2

where the terms Inline graphic, Inline graphic and Inline graphic represents the tip-tilt, coma and trefoil aberrations, respectively.

A phase mask shape associated with this Zernike polynomial superposition is shown in Fig. 1 The phase profile is normalized and considers a 15 mm aperture, corresponding to the physical aperture of the deformable mirror used in our experiments. The use of the Zernike polynomial representation facilitates the design, manipulation, and measurement of the CPM, as discussed in the Results section.

Fig. 1.

Fig. 1

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Normalized cubic phase mask considering an aperture of 15 mm diameter.

The CPM was generated according to the methodology reported in36. Briefly, CPM was generated on the DM using a closed-loop system with a wavefront sensor (WFS), iteratively correcting the mirror shape until the error between the target and measured wavefront was about 30 nm RMS (Root Mean Square). The final mirror shapes of the CPM, and including the flat reference phase mask (FPM), were digitally stored.

Mask design was performed using proprietary software HASOv3™ software. Fluorescent quantum dots sparsely embedded in agar were used as point-like emitters (see Section Sample preparation) to perform the wavefront measurements required to determine and set the appropriate DM shape. To select a single quantum dot, the sample was translated through the light sheet (using the flat reference phase mask) until an individual emitter was positioned at the center of the field of view.

Optical setup

The general optical layout of the DID-LSFM system is shown in Fig. 2. The setup was adapted in the Light Sheet Fluorescence Single-Molecule Microscopy (LSFSMM) platform42, which is implemented in an inverted configuration. For clarity, Fig. 2 presents the DID-LSFM configuration in a planar-orthogonal representation similar to that of a conventional LSFM system, although in practice the implementation follows the inverted geometry (see Fig. 1 of reference42).

Fig. 2.

Fig. 2

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(a) General scheme of the DID-LSFM system. In the scheme: EO: excitation objective; CO: collection objective; BF: bandpass filter, TL: tube lens, L: lens; DM: deformable mirror; FM: flip mirror; WFS: wavefront sensor.

Briefly, the excitation sources used were two diode lasers at 488 nm (Cobolt 06-MLD) and 561 nm (Cobolt 06-DPL) with 60 mW and 50 mW output power, respectively. The light beam was expanded and collimated by a telescope to fill the back aperture excitation objective, EO (10×, NA = 0.3, WD = 3.5 mm, Nikon CFI Plan Fluorite). The light sheet is generated in the xy-plane by a cylindrical lens (not shown) and projected on the sample by the EO. The measured light sheet thickness at its waist was about 2 µm and a height of about 1.2 mm (enough to cover the whole imaging area). A galvanometric mirror (GVS002) placed in a conjugate plane with the back focal plane of the EO (not shown) was used to scan the light sheet axially (in the Inline graphic direction) across the whole sample volume. To scan the light sheet axially, the galvanometric mirror is driven by a sawtooth voltage signal. A step-function trigger signal controls the camera data acquisition, ensuring that each image is captured only when de galvanometric mirror is stationary. The voltage signal was generated using an NI USB-6353 data acquisition and generation device (National Instruments Corp., Austin, TX, USA). The z-scanning signal was implemented in discrete steps, with one step per image. At each z position, a trigger pulse is issued after the galvanometric mirror reaches the programmed value and an image is captured. The exposure time was set slightly shorter than the step interval to ensure stable imaging conditions.

The sample was mounted in a fluorinated ethylene propylene (FEP) tube, sealed at both ends with plugs and suspended within a Petri dish. The Petri dish was filled with water until both objectives were fully submerged and placed in a chamber maintained at 37 °C. The chamber is mechanically connected to a motorized linear XYZ. The FEP tube, having a refractive index closely matched to that of water, was effectively transparent for imaging. A detailed description of the optical excitation arm and sample mounting scheme of the LSFSMM platform is provided in Fig. 1 of Ref.42. In the detection path, the fluorescent signal is collected by a 20 × water immersion collection objective (Olympus XLUMPLFLN Objective, 1.0 NA, 2.0 mm WD). The collected light passed through a filter (Semrock, 647 LP longpass or Edmund, 592 nm/43 nm bandpass) and a 200 mm tube lens, TL (TTL200-A, Thorlabs). An additional lens L1 (AC508-150-A-ML) projects the Fourier plane onto the deformable mirror DM (Mirao52e™, Imagine Optic) which encodes the wavefront. Subsequently, lens L2 (AC508-200-A-ML) projects the encoded image onto the sCMOS camera (OrcaFlash4 v.3, Hamamatsu). This configuration provided a total magnification of 22.2 × (20 × Olympus objective coupled to 200 mm tube lens). Considering the effective area of the sCMOS camera sensor (13.312 mm × 13.312 mm) and its pixel array (2048 × 2048), the resulting effective imaging area is approximately 600 µm × 600 µm, with an effective pixel size of 292.9 nm. Additionally, a Shack-Hartmann wavefront sensor WFS (HASO v3™, Imagine Optic) is positioned in a plane conjugate with the DM by using the optical system composed of lenses L2 and L3 (AC254-050-A-ML). Finally, a mirror mounted on a flip mount (FM) directs the fluorescence signal to either the WFS or the sCMOS camera as required.

Computational image restoration

Deconvolution

WFC-based systems introduce controlled phase modulation to generate an extended point spread function (PSF) with a smoothly decaying modulation transfer function (MTF), thereby increasing depth of field while preserving spatial information over an extended axial range. Consequently, the selection of an appropriate deconvolution strategy is critical for reconstruction stability and image fidelity.

In this work, Wiener filtering was selected as the reconstruction method because it provides a regularized inverse solution that incorporates both the optical transfer function and noise statistics. Under additive noise assumptions, it yields a closed-form frequency-domain estimator that minimizes mean-square error while attenuating noise-dominated frequencies, stabilizing inversion in WFC systems under moderate SNR conditions34,43,44.

In contrast, Richardson–Lucy (RL) deconvolution is iterative and highly sensitive to noise amplification and often requiring early stopping or additional regularization to prevent divergence45,46. By comparison, Wiener filtering provides explicit spectral regularization, computational efficiency via a single FFT operation, and stable edge-preserving reconstructions, though performance depends on accurate PSF and noise estimation.

In WFC, the acquired images are restored using a digital deconvolution algorithm. In this work, we use the image formation theory of a wavefront coding system to develop an inverse filter based on the Wiener filter47–49, taking into account experimental conditions such as the measured PSFs and encoded images. This approach enables estimation of the object function from the recorded data. The image formation process can be described by the convolution expression

graphic file with name d33e606.gif 3

where Inline graphic is the recorded image, Inline graphic to the object, and Inline graphic is the point spread function (PSF); Inline graphic denote the spatial variables, and ⋆ represents the convolution process. In the Fourier domain, this relationship becomes as follows:

graphic file with name d33e628.gif 4

where Inline graphic, Inline graphic and Inline graphic are the Fourier transforms for the image, object, and PSF, respectively; Inline graphic denotes the spatial frequency variables. The object can then be estimated using the Wiener filter, expressed as:

graphic file with name d33e650.gif 5

where Inline graphic corresponds to the ratio of the power spectral densities of the image and the noise and Inline graphic is the complex conjugate of the optical transfer function (OTF).

In our experiments, this Wiener filtering process was applied to each acquired image to suppress noise and enhance signal quality in the restored images.

Machine learning-based denoising algorithm description

To denoise the raw sperm images prior to deconvolution, we used the Noise2Void algorithm. The method employs a blind-spot neural network based on a U-Net architecture to transform noising input images to denoised outputs50. Our implementation was based on a public implementation51 in PyTorch52. The core network architecture, number of layers, and data augmentation strategy were kept identical to those described in the original Noise2Void publication39 components, while the training pipeline was implemented independently for our experimental datasets, following the original Noise2Void methodology without algorithmic modifications.

The network was trained using approximately 12,000 raw fluorescence images acquired with the DID-LSFM system under the same imaging conditions as the reported experiments. These images correspond to individual frames extracted from multiple volumetric acquisitions prior to deconvolution. Because Noise2Void is a self-supervised blind-spot denoising method that learns pixel statistics by masking input pixels rather than using clean images, the same dataset was used both for network training and subsequent denoising. In this framework, the prediction target for each pixel is excluded from the network input during training, preventing the network from learning an identity mapping and avoiding information leakage.

For the blind-spot network, 10% of pixels were randomly masked and predicted during training. Each image was independently normalized by subtracting the median pixel value and dividing by the standard deviation. An additional 9.8% Gaussian noise was added to images during training to improve robustness. The network was trained using the Adam optimizer with a fixed learning rate of Inline graphic and a batch size of 853. Training converged within approximately 30 epochs on a single NVIDIA RTX 2080 Ti GPU.

After convergence, the model weights were saved and a single trained network was subsequently applied to denoise all raw experimental datasets in this study. Visual inspection and quantitative evaluation confirmed that the denoising process effectively reduced noise without altering signal intensity or structural features.

For denoising the experimentally measured CPM PSF, a different strategy was adopted. While preliminary tests employed the Noise2Void framework for CPM PSF processing, we observed that blind-spot neural networks could introduce subtle modifications to the CPM PSF structure, potentially biasing the subsequent deconvolution. To preserve the intrinsic optical response, the CPM PSF was therefore denoised using classical non-local means filtering as implemented in scikit-image54. The noise level was estimated using estimate_sigma, and denoising was performed with denoise non local means using a fixed parameter σ = 5. After denoising, the background was removed by subtracting the median pixel intensity to correct for constant detector offsets and residual background signal. This conservative processing pipeline ensured effective noise suppression while maintaining the spatial fidelity of the CPM PSF, which is critical for reliable deconvolution.

Sample preparation

Fluorescent quantum dots

A sample containing fluorescent quantum dots (Qdot 655, Thermo Fisher) was used for the experimental characterization of the phase masks. In this case, the 488 nm diode laser and 647 LP long pass filter were used. A 1:103 dilution was prepared in ultrapure water (Mili-Q) in an 1.5 ml Eppendorf conical tube and vortexed for 30 s. Then, 1 µl of the solution was added to 1 ml of 1% low-melting-point agarose in another 1.5 ml Eppendorf conical tube, which was also vortex for 30 s. The bead-agarose solution was introduced into a FEP tube. One end of the FEP tube was sealed, and the other end was connected to a glass capillary tube. The sample was incubated at 4 °C for 10 min to allow for solidification and stabilization. After incubation, the glass capillary tube was mounted on the LSFM capillary sample holder, attached to a linear translation xyz motorized stage and a rotation stage. The capillary tube with the FEP tube plugged up is placed into a custom-made chamber filled with Mili-Q water. The central region of the FEP tube containing the sample was positioned in front of the water-immersion collection objective for imaging.

Porcine sperm

For spermatozoa visualization, commercially available porcine sperm from the DUROC UPB line acquired from Semen Cardona, S L., Spain (https://semencardona.com) was used in this study. This supplier routinely distributes semen doses to farms for artificial insemination and breeding purposes. A dose of 85 ml was purchased and used exclusively for the experiments. No animals were housed, handled, bred, sedated, or euthanized. Therefore, the study does not fall within the scope of the ARRIVE guidelines, as it involved no in vivo experiments or interventions on live vertebrate animals. All sperm samples were stored and handled according to the supplier’s guidelines.

1 ml of porcine sperm was mixed with a dilution of octadecyl rhodamine BR18 on PBS. The octadecyl rhodamine’s maximum excitation and emission wavelengths are 556 and 578 nm, respectively. In this case, the 561 nm diode laser and 592/43 nm bandpass filter were used. The final dye concentration into the vial was 1:106. The vial was centrifuged at 1000 rcf for 5 min at 37 °C, and the pellet was re-suspended in 1 ml filtered porcine sperm solution (using a filter pore size 0.45 µm). Immediately after, a micropipette tip was loaded with the sperm sample and inserted into a FEP tube, which was connected to a glass capillary tube. The glass capillary tube was mounted on the DID- LSFM capillary sample holder attached to a linear translation xyz motorized stage. The assembly was placed into a custom-made chamber filled with Mili-Q water. The central region of the FEP tube containing the sperm sample was positioned in front of the water-immersion collection objective for imaging.

Results and discussion

Phase mask optimization and characterization

Phase masks, including the flat reference phase mask (FPM) and the cubic phase mask (CPM), were generated on the DM using predesigned phase targets implemented through an adaptive optics iterative closed-loop procedure based on the corresponding Zernike expansion36. Although this method allows the generation of phase masks with a 30 nm RMS error, we found that in most cases the accuracy of the wavefront representation was not optimal. This was evident from direct inspection of the PSF, where residual astigmatism persisted even after several rounds of fine alignment. To address this, we found that optimal CPMs required removal of the tip and tilt Zernike components, Inline graphic and Inline graphic from the cubic phase function. These components use most of the available stroke, and produce stress on the DM surface, yet do not change any relevant imaging property. Although this correction reduced most of the aberrations, we performed a final round of open-loop optimization based on direct observation of the PSF in real time to eliminate any remaining defects55. Because the CPM could be monitored in real time, the final phase-modulation amplitude Inline graphic was determined using the coefficients of the four remaining Zernike polynomials in Eq. (2).

Figure 3a shows the PSF at zero defocus for a CPM with Inline graphic = 17.5 π obtained after fine alignment and mask optimization. Despite intensive optimization some defects remain visible at the frequency lobes of the PSF. In contrast, Fig. 3b displays an equivalent optimized CPM with the applied tip and tilt components removed. Here the PSF lobe structure is reproduced with high fidelity and contrast.

Fig. 3.

Fig. 3

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Optimization and characterization of the PSF. In (a) and (b), PSF of the CPM (Inline graphic = 17.5π, NA = 1) with and without tip and tilt Zernike components, respectively. The inset of (b) shows the corresponding deconvolved CPM PSF. In c) and d), experimental and simulated x–z profiles of the PSF for the CPM, respectively, in a 70 µm axial range around the CO focus. Dotted-lines in (c) indicate the limits of the estimated DoF of 40 µm. (e) Lateral (x–y) and (f) axial (x, z) PSF of the FPM used as reference. The measured lateral width (lateral resolution) and the DoF (axial resolution) of the FPM mask are 0.4 µm and 2.6 µm, respectively. In (c) and (d), the scale bar applies only to horizontal dimension; the full vertical extent of the images is 70 µm.

The imaging characteristics of WFC systems are governed primarily by the phase modulation amplitude, Inline graphic, which determines not only the achievable DoF, but also the reduction in the spatial frequency cut-off toward the edges of the DoF. The maximum DoF achievable in a WFC imaging system was found to be bounded by a defocus of Inline graphic56; however, in our case, a more realistic defocus interval of Inline graphic was found to preserve the high spatial resolution. Within this defocus range, the imaging planes with the worst frequency cut-off, of a half the frequency cut-off of the standard incoherent imaging system, are located at the extremes of the DoF. Therefore, by using Inline graphic = 17.5 π, a region of approximately Inline graphic µm around the focus position is available for DID-LSFM imaging, as indicated by the dotted lines in Fig. 3c.

To experimentally measure the axial PSF response of our microscope we recorded volumetric images over 70 µm axial range using the DID-LSFM approach, imaging a single fluorescent point source (quantum dot) displaced along the optical axis in 1 µm steps. Figure 3c shows the xz-view of the PSF axial stack obtained for the optimized CPM. As expected for WFC, the PSF shows the characteristic curved trajectory in the axial direction and intensity oscillations in the transversal direction. Owing to the optimization process, the PSF is axially symmetric around the center of the DoF, and its intensity oscillations of the PSF are preserved within the DoF. As the absolute value of the defocus increases from the center of the DoF, the PSF expands, and the high-frequency oscillations gradually diminish, leading to a reduction in optical resolution. Figure 3d presents the simulated axial PSF of the proposed WFC system, which closely resembles the main experimental features such as: overall size, curvature, axial symmetry, and frequency of the oscillations. Figure 3e and f show the lateral (xy-view) and axial (xz-view) PSFs with the flat phase mask (FPM) used as reference. The measured lateral width (lateral resolution) and the DoF (axial resolution) for the FPM mask were 0.4 µm and 2.6 µm, respectively. In contrast, using the CPM mask, the DoF is extended up to 40 µm, i.e., more than one order of magnitude improvement.

To probe that the effective resolution is not substantially compromised after the deconvolution, the optimized CPM PSF shown in Fig. 3b was deconvolved. The resulting PSF image is presented as an inset in Fig. 3b. The measured full width at half maximum (FWHM) is 0.48 µm, whereas the width obtained using the reference flat phase mask was 0.40 µm (Fig. 3e). These values are closely other, indicating that after deconvolution, the resolution is slightly reduced. Besides, as discussed previously, at the edges of the DOF the resolution will decline and the PSF will have a FWHM of approximately 1 µm.

To further analyze the imaging properties of our optical system, we converted the PSF into the modulated transfer function (MTF)47. In our case, the MTF enables the assessment of the resolution and contrast achieved when changing from a standard imaging system to the proposed DID-LSFM system. In this case, we reduced the NA of our system from 1 to 0.8 and generated another optimized CPM with Inline graphic = 16.8π. Under this configuration, the effective axial range available for DID-LSFM increased to approximately Inline graphic µm, providing a more suitable DoF for the intended application. Figure 4 shows the MTFs of the system with and without the CPM, obtained at the center of the DoF by averaging the measured PSFs to enhance the SNR. Figure 4a,b show the 2D MTF for the system without CPM, corresponding to a flat (zero phase function) phase mask with 25 nm RMS surface error, and the optimized CPM, respectively. The MTF support in both cases extends beyond 2000 mm−1, although for CPM this maximum extension is mainly confined around the axes Inline graphic. This indicates that, in principle, there is no intrinsic loss in resolution due to the CPM, at least at the center of the DoF.

Fig. 4.

Fig. 4

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MTF Characterization. In (a) and (b), two-dimensional MTFs of the system without a CPM (flat wavefront, 25 nm RMS) and with an optimized CPM Inline graphic = 16.8π), respectively. Color bars units are decibels (dB). (c) Comparison of the MTF profiles for the DID-LSFM system using a flat phase mask and the CPM numerically calculated (CPM Theo), obtained experimentally (CPM Exp) and obtained experimentally with the denoising applied (CPM Exp denoise). In (a) and (b), the tick mark spacing along the axes is 500 mm-1.

Nevertheless, fast volumetric imaging techniques, including DID-LSFM, are sensitive to low SNR conditions36. To evaluate the performance of the CPM under such conditions, we calculated the MTF without PSF averaging, thereby preserving the effect of noise. Instead of showing the 2D MTF image, we computed an average MTF for each configuration. For the FPM, the MTF was obtained by performing a radial average over the first quadrant, whereas for the CPMs, the average was taken over a region of 12 pixels wide around the Inline graphic axis. Figure 4c shows the resulting MTF profiles of the CPM, including a version obtained from a denoised PSF using the machine learning approach. For comparison, the MTFs for the experimental flat phase mask and the theoretically calculated CPM are also included. Although the theoretical MTF extends beyond the maximum frequency displayed in the plot, the MTF of the flat mask defines a hard limit for achievable resolution at approximately 1300 mm−1 (attenuation ~ 12 dB). The experimental CPM MTFs show higher attenuations at higher spatial frequencies: about 20 dB near the cutoff for the unprocessed PSF and about 25 dB for the denoised PSF.

The results of this section point to the fact that in our system there is a trade-off between the available volume depth and transversal resolution. This trade-off is not unique to our DID-LSFM but it is inherent in WFC systems and other Extended-DoF imaging methods34,36,56. Although the resolution decline is unavoidable given the designed DoF, in this work we have implemented several measures to control further sources of image degradation. First, the DID- LSFM approach uses an efficient light sheet fluorescence excitation and a highly sensitive sCMOS camera for fluorescence detection, which helps to avoid information losses and artifacts generated at very low SNR scenarios. Second, we have proposed a new and optimized method for CPM mask generation; i.e. tilt removal and open-loop correction, which is one step ahead of previous DID-LSFM implementation in terms of getting closer to expected theoretical performance. Finally, we implemented a state-of-the art machine-learning-based denoising algorithm to mitigate the degrading effects of the noise on the image restoration step, as described in Section “Computational image restoration”.

Free swimming porcine sperm imaging

We used the experimental DID-DSLM system to image freely moving porcine spermatozoa at imaging speeds of 40 and 80 volumes/s. To fully use the extended DoF (40 µm) achieved with the CPM, each volume was defined to contain 10 planes separated by 4 µm for 40 volumes/s, and 5 planes separated by 8 µm for 80 volumes/s. That is, the light sheet was scanned in the axial direction (Inline graphic axis) across the whole sample volume at each corresponding z-plane step (i.e. 4 µm step size for 40 volumes/s and 8 µm step size for 80 volumes/s). Each volume was reconstructed by collecting 2D images at the different light sheet positions within the sample. In both cases, the sCMOS camera was set to operate at 512 × 512 pixels and the maximum frame rate of 400 fps (frames per second), resulting in an exposure time of 2.5 ms per image. With this settings, the signal-to-noise ratio remains still detectable for imaging.

Figure 5 presents the results corresponding to 40 volumes/s. In the first column of Fig. 5a, the experimental raw and experimental raw denoised images (this last one obtained using the machine learning-based denoising algorithm described in Section “Machine learning-based denoising algorithm description”) of a single volume of porcine spermatozoa moving in the aqueous buffer medium are shown. The corresponding deconvolved images for the different configurations are also shown in Fig. 5a. During the deconvolution, only spatial frequencies below the incoherent frequency-limit of the MTF were retained (see Fig. 4c). Frequencies above this limit were discarded to avoid introducing artifacts in the reconstructed images. As aforementioned, in this case each volumetric dataset consisted of 10 planes separated by 4 µm, covering a total depth of 40 µm which lies within the range of the extended DoF achieved with the CPM.

Fig. 5.

Fig. 5

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Results at an imaging speed of 40 volumes/s. a) In the first column, the experimental raw and experimental denoised images of a single volume of porcine spermatozoa swimming freely in the aqueous buffer medium are shown. The corresponding deconvolved images for the different configurations (labelled as I, II, …, VI) are also shown. The symbol ⨂ indicates the deconvolution operation. b) SNR and c) GCNR metrics measurements computed over 10 volumes. The solid and dashed squares in the image of the configuration I indicate the target and background ROIs used to calculate the SNR and GCNR metrics. Scale bar: 25 µm.

To quantify the quality of the deconvolved images obtained with the different configurations, we evaluated the metrics signal-to-noise ratio (SNR) and generalized contrast-to-noise ratio (GCNR) defined in57. These methods do not require a reference image, unlike conventional approaches. The SNR was computed using Eq. (8) of reference57, Inline graphic, where Inline graphic is the mean signal amplitude within the region of interest (ROI) inside of the target (i.e. the spermatozoa), and Inline graphic is the standard deviation of signal amplitude within the ROI outside the target (background). The GCNR was calculated using Eq. (3) of reference57 given by Inline graphic where Inline graphic is the index of the bin, Inline graphic the number of histogram bins centered at Inline graphic Inline graphic and Inline graphic are the associated histograms of the target and background ROIs, respectively. The mean SNR and GCNR values considering a single spermatozoid over 10 image volumes are presented in Fig. 5b,c, respectively. The SNR values are similar in the configurations labelled as IV, V and VI. However, the GCNR value is higher for configuration V. This means that the contrast is more enhanced when both the experimental raw image and CPM’s PSF are denoised. The ROIs used to measure the SNR and GCNR metrics are indicated in the image of the configuration I (Fig. 5a), with solid and dashed squares indicating the target and background regions, respectively.

Figure 6a shows a single volume image acquired at an imaging speed of 40 volumes/s corresponding to configuration V in Fig. 5. The imaging depth is color-coded, showing spermatozoa at different depths. Representative depth plane views (six of ten planes) are shown in Fig. 6b. A movie of the whole imaging acquisition is provided in Supplementary Video S1.

Fig. 6.

Fig. 6

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(a) Image of a single volume acquired at an imaging speed of 40 volumes/s corresponding to the configuration V of Fig. 4, with color-coded depth. (b) Z-stack images showing some individual depth plane views. A movie of the full volumetric acquisition is provided in Supplementary Video S1. The scale bar in (a) represents 25 µm.

Figure 7 shows the results obtained at an imaging speed of 80 volumes/s. The image volume was adjusted to contain 5 planes resulting in a total depth of 40 µm (8 µm step between planes). The experimental raw and experimental raw denoised images of a single volume are shown in the first column of Fig. 7a. The corresponding deconvolved images for all the configurations are also displayed in Fig. 7a. As in the previous case (40 volumes/s), the mean SNR value averaged over 10 volumes is very similar for the IV, V and VI configurations (see Fig. 7b). However, the GCNR value is slightly higher for configuration V (see Fig. 7c), that is, when both the experimental raw images and CPM’s PSF are denoised. At this higher imaging speed of 80 volumes/s, more than twice the typical volumetric video rate, the three-dimensional back-and-forth flagellar motion of the spermatozoa becomes more apparent (see Supplementary Videos S2 and S3).

Fig. 7.

Fig. 7

Open in a new tab

Results for the imaging speed of 80 volumes/s. (a) In the first column, the experimental raw and experimental raw denoised images of a single volume of porcine’s sperm are presented. The corresponding deconvolved images for the different configurations (labelled I, II, …, VI) are also shown. The symbol ⨂ indicates the deconvolution operation. (b) SNR and (c) GCNR metrics measurements computed over 10 volumes. The target and background ROIs used to calculate the SNR and GCNR metrics are indicated in the image of the configuration I by the solid and dashed squares, respectively. Scale bar: 25 µm.

It is important to note that the samples used for the acquisitions at 40 volumes/s and 80 volumes/s were not the same. Therefore, given the differing sample conditions, a direct comparison of SNR and GCNR metrics between the two datasets (Figs. 5, 7) is not appropriate.

To better visualize the 3D structure of the spermatozoon, Fig. 8a shows an image of a single volume acquired at 80 volumes/s, with color-coded depth. A movie of the volumetric acquisition is provided in Supplementary Video S2. Furthermore, to better illustrate the 3D flagellar dynamics, a 3D-rendering was generated from the deconvolved experimental images corresponding to configuration V of Fig. 7. The resulting 3D-rendering for 80 volumes/s is shown in Supplementary Video S3. Figure 8b shows the 3D trajectories of the sperm head and flagellar tip, tracked over the volume range 180–314. For reference, only selected volume numbers are indicated in Fig. 8b.

Fig. 8.

Fig. 8

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(a) Image of a single volume acquired at an imaging speed of 80 volumes/s, with color-coded depth. A movie of the complete volumetric acquisition is provided in Supplementary Video S2, and the 3D-rendering is shown in Supplementary Video S3. (b) Three-dimensional tracking of the sperm head (solid circles) and flagellar tip (solid triangles) over the volume range of 180 to 314. For reference, only selected volume numbers are indicated. Scale bar: 25 µm.

Finally, we measure the sperm tail beating frequency at imaging speeds of 40 volumes/s (Fig. 9a) and 80 volumes/s (Fig. 9b). The intensity-versus-time traces from the regions indicated by the inset square in Fig. 9a,b are shown in Fig. 9c,d, corresponding to 40 and 80 vol/s, respectively. In both cases, a time interval of 0.5 s was analyzed, yielding beat frequencies of ~ 12 Hz (for 40 volumes/s) and ~ 22 Hz (for 80 volumes/s). The difference between these measured flagellar beat frequencies arises from undersampling in the case of 40 volumes/s, where a high flagellar beat frequency is not resolved; whereas at an acquisition rate of 80 volumes/s, higher-frequency flagellar motion is resolved. However, compared to 40 volumes/s, more amplitude fluctuations are observed at 80 volumes/s, which are characteristic of sampling beat artifacts. Understanding and visualizing sperm three-dimensional swimming dynamics in real time is of great interest in reproductive biology, as it provides information about sperm health and viability58. In this context, our DID-LSFM system represents an alternative approach for high-resolution, fast 3D imaging, with potential applications in the diagnosis male infertility.

Fig. 9.

Fig. 9

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Sperm-beating frequency. Deconvolved images obtained using machine learning denoising at different time intervals for an imaging speed of (a) 40 volumes/s and (b) 80 volumes/s. Intensity profiles from the inset square indicated in (a) and (b), calculated over a 0.5 s time interval, corresponding to (c) 40 volumes/s and (d) 80 volumes/s. Scale bar: 10 µm.

Conclusions

We implemented wavefront coding (WFC) combined with machine learning in a light sheet fluorescence microscope to achieve fast, high-resolution volumetric imaging. The depth of field (DoF) of the high numerical aperture (NA = 1) collection objective was extended from 2.6 up to 40 µm, representing an increase of than one order of magnitude. To maximize the imaging quality of our DID-LSFM we perform phase mask optimization and applied a machine learning-based denoising algorithm prior to the image restoration required by wavefront coding techniques. The system’s capability for fast volumetric imaging was demonstrated by visualizing the 3D dynamics of sperm flagellar motion at an imaging speed up to 80 volumes/s, more than twice the typical volumetric video rate. The image quality was quantitatively assessed using the signal-to-noise ratio (SNR) and the generalized contrast-to-noise ratio (GCNR) metrics, with the best results obtained when both experimental raw image and cubic phase mask PSF were denoised. The ability to image the complete 3D beating dynamics of the spermatozoa with high temporal and spatial resolutions provides a direct indicator of sperm motility and health. The proposed method combined with Computer-Assisted Sperm Analysis (CASA), could have the potential to provide an advanced platform for quantitative reproductive studies. Finally, thecapability of our imaging system may have important implications for fundamental fertility research, reproductive health assessment, and applications in the food and biotechnology industries.

Supplementary Information

Supplementary Video 1. (766.8KB, mp4)
Supplementary Video 2. (1.6MB, mp4)
Supplementary Video 3. (6.3MB, mp4)

Acknowledgements

All authors acknowledge the involved institutions for their support which contributed to the development of this work, specially to the SLN facility that corresponds to a “Grup reconegut” 2021 SGR 01456 Departament de Recerca i Universitats de la Generalitat de Catalunya

Author contributions

J.L-R wrote the original draft manuscript. J.L-R, G.C., and O.E.O conducted the wavefront coding experiments and analysed the results. O.E.O implemented the phase mask optimization. O.P-S performed the deconvolution process. M.E, and G.M implemented the denoising machine learning algorithm. M.E. made the final edits in the manuscript. R.A.B-V conducted the 3D visualization. I.R-M analysed the results and critically reviewed the manuscript. P.L-A supervised all the experiments and provided founds and resources for the experiments. All the authors reviewed and approved the final manuscript.

Funding

This work was partially funded by CONACyT México, now SECIHTI (grants n. 265120 and 155803) and LASERLAB-EUROPE (under grant agreement no. 871124). The project received support from Fundació CELLEX; Fundació Mir-Puig, Generalitat de Catalunya; the CERCA program European Union’s Horizon 2020 research and innovation programme under grant agreement No 871277; Ministerio de Economía y Competitividad—Severo Ochoa programme for Centres of Excellence in R&D (CEX2019-000910-S); and Ministerio de Ciencia e Innovación PID2021-122807OB-C31. It was also partially funded by the Spanish Ministry of Science and Innovation through the project PID2023-152069NA-I00.

Data availability

Data supporting the results presented in this study are available within the paper and its supplementary information files. The datasets generated and analyzed during the current study are available in the figshare repository, [10.6084/m9.figshare.31497040].

Declarations

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Contributor Information

Jacob Licea-Rodriguez, Email: jacob.licea@uaem.mx.

Pablo Loza-Alvarez, Email: pablo.loza@icfo.eu.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Video 1. (766.8KB, mp4)
Supplementary Video 2. (1.6MB, mp4)
Supplementary Video 3. (6.3MB, mp4)

Data Availability Statement

Data supporting the results presented in this study are available within the paper and its supplementary information files. The datasets generated and analyzed during the current study are available in the figshare repository, [10.6084/m9.figshare.31497040].

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