Optical coherence tomography (OCT) offers both structural and functional information with no reliance on exogenous labels or dyes, making it a powerful label-free imaging technique in both clinical and research settings^[1]. The success of OCT lies in its ability to accurately reconstruct the high-resolution micron-scale structural distribution of biological tissues^[2,3].

Despite these advancements, OCT still faces limitations, especially in the anisotropic resolution^[4,5]. Typically, the axial resolution of OCT is determined by the coherence length of the light source^[6], which is proportional to the square of the center wavelength (λc) and inversely proportional to the source bandwidth (Δλ) as λc2/Δλ. The lateral resolution is governed by the numerical aperture (NA) of the imaging objective within the sample arm^[6,7]. There is a trade-off between the lateral resolution and the depth of focus^[8–10]. In order to maintain an effective imaging depth of focus, the lateral resolution is typically lower than its axial resolution^[11,12]. This inherent anisotropy in resolution results in a broadening along the lateral dimension in OCT images, leading to the loss of microstructural detail and a reduction in the authenticity of tissue structure representation^[13].

Optical coherence refraction tomography (OCRT) advances conventional OCT by extending axial resolution into the lateral dimensions, thereby achieving isotropic resolution in reconstructed images^[13]. This innovation effectively mitigates the loss of details associated with resolution anisotropy and exhibits considerable promise for diverse biomedical applications. Based on OCRT, several improved approaches have been developed to expand its applications. Zhou et al. initially extended OCRT into spectroscopic OCRT, which corrected low axial resolution using high-resolution lateral information, thereby enabling the feature-specific reconstruction of hemoglobin, chlorophyll, and lipids^[14]. Subsequently, they further advanced OCRT by achieving three-dimensional (3D) extensions, facilitating isotropic 3D reconstruction across various biological tissues^[15]. More recently, Løvmo et al. integrated an ultrasound-induced sample reorientation strategy into OCRT, enabling non-contact manipulation and dynamic adjustment of the sample’s viewing angles^[16]. Additionally, an implicit neural representation-based computational framework for OCRT has been proposed, allowing the accurate reconstruction of optical parameters even when imaging angles are sparse^[17].

While these advancements have broadened the application of isotropic-resolution OCT reconstruction, a fundamental limitation remains largely unaddressed: the isotropic reconstruction enabled by OCRT is intrinsically constrained by the highest resolution present in the input images, whether axial or lateral. Consequently, enhancing the intrinsic resolution of the original data would facilitate even higher-resolution isotropic reconstructions, thereby improving the resolving power of OCRT and enabling more accurate reconstruction of microscopic details. In addition, current OCRT implementations employing conventional OCT imaging modalities fail to suppress conjugate image artifacts. Consequently, the reference surface at zero optical path difference must be positioned at the sample surface during acquisition, limiting the effective imaging range to half of the available depth^[18–20]. This constraint restricts the applicability of OCRT for large-scale biological tissue reconstructions. In response, our team developed the FROCRT technique, which expands the imaging depth of OCRT and facilitates large-scale imaging^[21]. Nonetheless, as previously noted, it also does not enhance image resolution, thereby constraining its utility for high-resolution reconstructions.

Deconvolution techniques grounded in the point spread function (PSF) have been extensively employed to enhance OCT image resolution. In particular, the Richardson–Lucy (RL) deconvolution algorithm and the Wiener filter-based deconvolution method have exhibited notable advantages in achieving super-resolution reconstruction of OCT images^[22–24]. Following these developments, a considerable body of research has introduced a range of effective methodologies aimed at further advancing the super-resolution capabilities of OCT imaging^[25–27]. Without noise, the above methods can recover high-frequency details through sufficient iterations. However, the intrinsic noise in OCT imaging leads to progressive noise amplification during iterations, ultimately causing reconstructions to be dominated by noise artifacts^[28–30]. Additionally, signal preprocessing, including multiple scans and coherent averaging, is usually needed to suppress noise and improve resolution^[31,32]. Since OCRT requires multi-angle imaging, such preprocessing significantly increases acquisition demands. New resolution enhancement approaches suitable for OCRT are urgently needed.

In this work, we propose sparse continuous full-range optical coherence refraction tomography (SC-FROCRT) that builds upon prior developments and simultaneously achieves high resolution, extended field-of-view, and isotropic image reconstruction. Specifically, a new super-resolution model is formulated by incorporating the inherent sparsity and continuity priors of biological samples. It iteratively refines the initially acquired low-resolution OCT images to achieve resolution upgrading. Concurrently, the super-resolution model is integrated into the previously established full-range OCRT framework, culminating in the development of the SC-FROCRT reconstruction method. SC-FROCRT comprises three major functional modules: the conjugate-free module, the sparse continuous super-resolution iterative module (SC module), and the Fourier synthesis isotropic reconstruction module. Specifically, the conjugate-free module generates low-resolution, range-extended images acquired from multiple angles. The SC module conducts super-resolution enhancement based on prior knowledge of sample properties. The Fourier synthesis module synthesizes the multi-angle super-resolved images to achieve isotropic reconstruction. We applied SC-FROCRT to phantom tape, sparse plant, and cleared tissue samples, achieving full-range, isotropic, and high-resolution OCT imaging over a 4mm×4mm field. In cleared leg bones, we clearly distinguished cancellous from cortical bone, previously hard to detect.

An image captured by the imaging system can be considered as the result of a convolution between the sample and the system’s PSF. Traditional deconvolution methods use the PSF of the system to iteratively optimize and reconstruct high-resolution details of the sample’s structure^[23,24]. Although theoretically deconvolution reconstruction offers optimal spatial resolution, the presence of inherent noise in OCT images often makes deconvolution methods unstable^[33,34]. Deconvolution of targets from noisy images frequently leads to ill-posed inverse problems.

The primary objective of the SC module is to decode low-resolution OCT images. Achieving image resolution enhancement requires the extraction of reconstructions from low-resolution images that closely approximate the structural features of the sample. Nonetheless, the imaging capability of any optical system inherently yields only an approximation of the actual sample morphology, with its precision constrained by fundamental biophysical limits^[28,29]. Consequently, the incorporation of prior knowledge as constraints within the super-resolution reconstruction process is essential for mitigating convergence errors and ensuring more accurate image recovery. Therefore, we incorporate the inherent sparsity and continuity of biological samples as constraints, transforming the deconvolution process into an optimization problem to enhance image resolution. The relationship between the structural distribution of the sample, xj, and the low-resolution image captured by the system, fj, is subject to the following constraint: argminxj{12‖fj−(A⊗xj)‖22+αsϕ(xj)+αcψ(xj)},(1)where A represents the system’s PSF, ‖·‖2 denotes the l2 norm, and ϕ(x) and ψ(x) correspond to the sample’s sparsity and continuity priors, respectively. The terms αs and αc determine the weights of these priors. Notably, the subscript j in xj refers to the jth low-resolution image captured by the conjugate-free module across multiple imaging angles.

The concept of sparsity in OCT samples within an image is illustrated in Fig. 1(a). In a sparse image, significant grayscale variations exist between the central point and adjacent regions, resulting in visually distinct boundaries. This collection of clear boundaries forms a high-resolution OCT image. In contrast, the traditional low-resolution OCT image, with lower spatial resolution and signal-to-noise ratio (SNR), reduces image sparsity. Thus, in Eq. (1), we enhance the sparsity of the solution by minimizing the l1 norm, expressed as ϕ(x).

Another useful prior is the continuity of the sample. Biological samples typically exhibit smooth and continuous variations^[28]. The continuity depicted in Fig. 1(a) demonstrates the uniform and smooth changes within the sample. Conversely, the traditional low-resolution OCT image reveals the impact of noise and degraded resolution in the grayscale values between adjacent points. The less noise present, the higher the image continuity. Therefore, we use a second-order derivative penalty, denoted as ψ(x), to represent the continuity constraint. It emphasizes piecewise approximation of boundaries between regions of different intensities, enabling globally smooth transitions in the final reconstructed image. Thus, in Eq. (1), we represent the continuity prior constraint as ψ(x).

The specific reconstruction results are shown in Figs. 1(b) and 1(c). The sparsity-only and continuity-only images are generated by independently applying each prior constraint during optimization, while the SC-FROCRT image reflects the combined effect of both. Detailed formulations are provided in Appendix A. The sparse prior achieves high resolution, but due to the disruption caused by noise and random interference, the visual quality of the image is poor. Similarly, the continuous prior effectively suppresses noise and random interference, but it overly smooths the high-frequency information in the image. In contrast, the combined SC priors as constraints effectively reconstruct the structure of the sample.

It is important to ensure that, in OCT two-dimensional (2D) tomographic imaging, the PSF spans at least a 3pixel×3 pixel region to satisfy the Nyquist sampling criterion and achieve the maximum spatial resolution permitted by the optical system^[29]. As illustrated in Fig. 1, we exemplify this spatial continuity by highlighting a 3pixel×3 pixel region centered on a local feature point. In practice, to mitigate noise in OCT images, repeated acquisitions at the same spatial location are typically performed^[6]. But conventional autocorrelation-based noise suppression methods may introduce overlapping artifacts, leading to blurring of fine microstructural details. To address this issue and enhance the robustness of resolution improvement, we not only consider the lateral and axial continuity of OCT images but also explicitly characterize their continuity across frames. Figure 1 demonstrates the 3voxel×3voxel×3 voxel continuity structure, where continuity is preserved not only within individual frames but also across successive temporal acquisitions. This frame-to-frame continuity enables SC-FROCRT to accommodate minor sample displacements while maintaining effective noise suppression.

In summary, continuity and sparsity are considered intrinsic characteristics of OCT images, which can be leveraged as priors to suppress noise and recover high-frequency information. As outlined above, Eq. (1) defines a convex optimization problem. We decompose Eq. (1) into two subproblems: a constrained continuity and sparsity reconstruction subproblem and a deconvolution subproblem. Specifically, the constrained reconstruction is performed within the Split Bregman framework^[35]. Subsequently, a selectable deconvolution module is employed to iteratively refine the deconvolution subproblem. The detailed procedure for solving the convex optimization problem is presented in Appendix A.

To simultaneously achieve high resolution, expanded field-of-view, and isotropic image reconstruction, the SC module proposed in Sec. 2.1 was integrated with our previous research work^[21]. We, thus, established a chained reconstruction framework consisting of three interconnected modules: a conjugate-free module, an SC module, and an isotropic reconstruction module.

Figure 2 shows the SC-FROCRT workflow. We previously developed a 360° full-range multi-angle acquisition system with customizable steps. Conjugate artifacts were suppressed using a simple phase-shifting method by decentering the sample arm pivot, requiring only minor hardware adjustment. The system synchronously captures multi-angle data, which are processed through the SC-FROCRT pipeline.

In the pipeline of the SC-FROCRT algorithm, the multi-angle spectral data collected by the imaging system are first processed by the conjugate-free module. The primary function of this module is to suppress OCT conjugate artifacts and extend the imaging range through the FROCT algorithm (details in Appendix B). Specifically, the raw modulated spectra from multiple angles are transformed into a set of low-resolution images ∑fj. The resulting intermediate outputs are illustrated by the simulated schematic and experimental reconstructions in Fig. 2(b). Although conjugate artifacts are effectively removed at this stage, the intermediate images still exhibit limitations in SNR and resolution. Consequently, the SC module is incorporated in the following stages of the SC-FROCRT workflow to improve image fidelity.

The SC module processes the multi-angle low-resolution image set ∑fj, performing iterative super-resolution reconstruction guided by prior knowledge of the sample. The specific reconstruction procedures and algorithmic details have been elaborated in Sec. 2.1. Upon completion of this module, the intermediate outputs comprise a set of multi-angle super-resolved images ∑rj. As illustrated in the simulated and experimental images in Fig. 2(b), although there is notable enhancement in both SNR and resolution, the reconstructed images still fall short of fulfilling the demands for high-resolution, wide field-of-view, isotropic imaging. In particular, resolution anisotropy-induced distortions remain uncorrected, and the loss of structural information due to the limitations of single-angle scanning persists. Additionally, minor reconstruction errors may arise from the inevitable presence of non-optimal regularization parameters during sparse-continuous iterative processing. Consequently, following this stage, the SC-FROCRT algorithm applies a final Fourier synthesis-based isotropic reconstruction step to achieve accurate recovery of the sample structure.

In the final stage, the multi-angle super-resolved images ∑rj are processed through the Fourier synthesis module. This step effectively alleviates the backscattering-induced signal occlusion caused by highly reflective structural features in single-angle imaging, thus minimizing the loss of critical image details^[16]. Moreover, the integration of multi-angle data within this module facilitates the correction of residual artifacts introduced during the sparse-continuous iterative reconstruction. Additionally, the SC module approach offers distinct advantages. It not only enhances the SNR and contrast of the input images—delivering high-quality low-noise datasets for Fourier synthesis—but also improves fine structural recovery through super-resolution enhancement across multiple viewing angles.

Overall, the synergy of the three modules enables SC-FROCRT to achieve high-resolution, wide field-of-view, and isotropic OCT reconstruction.

As shown in Fig. 2, the sample is placed in a standard circular tube and immersed in an appropriate liquid solution to meet the registration requirements for OCRT reconstruction. For the tape phantom and aloe samples, we used water as the medium. The raw spectral data of the tape phantom and aloe samples are consistent with those used in our previous publication^[21]. In the present study, we reprocess these datasets using the proposed SC-FROCRT method to demonstrate its improvement in resolution and image quality. The corresponding results are presented in the subsequent sections. For the cleared mouse leg bone and spinal cord samples, we used the ultimate 3D imaging of solvent-cleared organ (uDISCO) reagent^[36]. The tube is immersed in the same fluid as the sample and mounted on a computer-controlled rotation stage synchronized with OCT imaging.

During data acquisition, a phase shift (approximately π/2) between adjacent A-scans is introduced by decentering the scanning pivot point in the sample arm, enabling subsequent FROCT signal processing, as detailed in Refs. [18,21]. The system has a central wavelength of 1310 nm and a bandwidth of 60 nm, with 2048 A-scans per frame. The frame rate is 20 frames per second (fps). The axial FWHM resolution is 18 µm in air, and the lateral resolution at the focal plane is 25 µm (determined using en face imaging of a USAF resolution target). We selected a 6° angular step for image acquisition, which demonstrated good performance in the reconstruction results^[13]. Due to the substantial increase in data volume required for 3D reconstruction of cleared mouse brain samples, the sampling interval was reduced, and image acquisition was conducted at 12° angular increments.

The spectral reconstruction calculation of multi-angle images obtained through the conjugate artifact removal algorithm and the corresponding sparse-continuous iterative optimization algorithm were performed on a personal computer with an Intel Core i7-9700k CPU (3.6 GHz) running Windows 10 (64-bit). All methods were implemented in MATLAB (R2019b). Before the Fourier synthesis algorithm was applied, the generated multi-angle images needed to be cropped to ensure uniform size, making comparisons consistent. In this study, images were resized to 1024 (axial) pixel × 512 (lateral) pixel. These images were then transferred to the OCRT reconstruction pipeline on a Sitonholy (Beijing, China) IW4200-4G workstation (Xeon CPU E52650 v4, 2.2–2.9 GHz) with 128 GB RAM, where OCRT reconstruction was performed with a total of 100 iterations in a PyThon (v3.5.6) environment.

For reconstruction, the 2D image size was set to [1024, 512] (axial × lateral). For 3D reconstruction, the size was reduced to [512, 256] to balance computation with resolution. All raw OCT data were normalized to prevent grayscale overflow during iterative reconstruction. Notably, for all samples, the OCT image was acquired with the reference plane positioned at the surface of the sample, while the FROCT image was acquired with the reference plane placed at the center of the sample. The performance of the SC iterative module depends critically on appropriate regularization. For each sample type, the specific values of regularization parameters [αs,αc] are listed in Table 1.

These were tuned empirically to optimize the trade-off between resolution enhancement and noise robustness. Both the SC module and the Fourier synthesis module used adaptive iteration strategies. For high-SNR samples (e.g., the multilayer phantom and aloe tissue), 12–15 SC iterations were sufficient for convergence. In contrast, for solvent-cleared samples with lower SNR, the number of SC iterations (LoopSC) was increased to 20 to preserve structural fidelity. The iteration count for the Fourier synthesis step (LoopF) followed the same principle—set to 100 for high-quality samples and increased to 150 for low-SNR transparent tissues. The system’s PSF was characterized using a two-step approach. First, one-dimensional (1D) axial and lateral PSFs were measured separately using planar mirror imaging, then merged to construct a 2D PSF. To further improve accuracy, we followed the approach described in Ref. [23], imaging 10 µm polystyrene microspheres. Multiple microspheres near the direct current (DC) center were averaged to obtain a more stable PSF profile.

To further compare the quality of the reconstructed images, two commonly used quantitative metrics were adopted to evaluate the performance of the proposed method. Since OCT samples lack ground truth data, we employed a non-labeled SNR metric to evaluate the SNR of the reconstructed images. Non-labeled SNR is defined as the ratio of mean intensity in a foreground region containing structure to the standard deviation of intensity in a background region: SNR=10lgμfσb,(2)where μf and σb represent the mean intensity of a foreground region and the standard deviation of intensity in a background region, respectively.

The gradient-based sharpness index (GSI) is a widely used sharpness metric that estimates image clarity based on local gradient magnitude^[17]. It is particularly suitable for OCT where reference ground truth is unavailable. The GSI is computed as GSI=1N∑x,y[Gx(x,y)]2+[Gy(x,y)]2,(3)where Gx and Gy are the gradients of the OCT image along the lateral and axial directions, respectively. This formulation reflects the energy of rapidly changing regions, which correlates with visual sharpness.

Furthermore, for characterizing image resolution, the Fourier ring correlation (FRC) technique is an excellent evaluation metric^[37]. The FRC was developed to evaluate the global effective resolution in general, describing the highest reliable cut-off frequency of an image. This effective resolution, or equivalently the spectral SNR, is one crucial super-resolution image quality metric, reflecting the authentic resolvability or the uncertainty: FRC(ri)=∑r∈riF1(r)·F2(r)*∑r∈riF12(r)·∑r∈riF22(r),(4)where F1 and F2 are the Fourier transforms of the two images and ri is the ith frequency bin. The calculation of FRC resolution requires two independent frames of identical content under the same imaging conditions.

To validate the reconstruction performance of the SC-FROCRT technique, we first conducted imaging experiments on a multi-layer tape phantom sample placed inside a glass capillary tube with an inner diameter of 3.5 mm. The multilayer-rolled sample forms an anisotropic structure, enabling evaluation of resolution enhancement and isotropic reconstruction across methods.

Figure 3(a) illustrates the evolution of reconstruction results from OCT to SC-FROCRT, corresponding to the outputs of each of the three modules. The OCT reconstruction suffers from insufficient resolution and speckle noise and shot noise interference, making it difficult to discern the layered structure of the tape. While the FROCT method expands the imaging range by removing conjugate artifacts, allowing for deeper structural information capture, the lateral resolution is compromised due to the filtering process of conjugate artifact removal. This is particularly evident in the line scan comparison presented in Fig. 3(b).

The SC-FROCT method enhances the FROCT image through the SC module, resulting in substantial improvements in both SNR and resolution. It sharpens the boundaries of the layered structure, making the transitions between layers more distinct. However, despite this enhancement in resolution, some image information remains lost in the occluded region beneath the top layer of the tape, as indicated by the dashed box in Fig. 3(b). Ultimately, the SC-FROCRT method provides high-resolution isotropic imaging with extended range, clearly revealing the annular layered structure of the tape, while maintaining uniform high resolution in both lateral and axial directions. Additionally, it compensates for the missing backscattered information from the single-angle SC module reconstruction.

Figure 4(a) shows a local magnified comparison of the key region in Fig. 3(b), highlighting the resolution improvements with SC-FROCRT. The SC-FROCRT method achieves a higher GSI than intermediate steps, indicating improved spatial resolution. The GSI value for FROCT is lower than that of OCT, which aligns with the known degradation in lateral resolution caused by the angular averaging process in FROCT. Figure 4(b) presents the lateral line scan signal intensity distribution for the region marked in Fig. 4(a). Resolution comparisons based on the ridge structures in the tape phantom were conducted following the spatial frequency evaluation principles described in ISO 12233:2024^[38]. The analysis reveals that the FROCT methods result in blurred boundaries, with only 4–5 layers of the tape structure being distinguishable. The SC-FROCT reconstruction reaches the super-resolution limit on lateral resolution that has deteriorated, where continuity becomes the dominant factor, preventing resolution of the tape structure. SC-FROCRT shows clear peak distributions and accurately reconstructs the 7-layer structure. The pixel distribution between layers L1–L7 is uniform, which strongly corresponds to the actual structure of the simulated sample. Figure 4(c) compares the FRC curves. OCT shows the lowest FRC due to conjugate artifacts and noise. FROCT eliminates conjugate artifacts but has low resolution. SC-FROCT improves FRC, while SC-FROCRT outperforms all methods across spatial frequencies.

To comprehensively evaluate the reconstruction performance of the SC-FROCRT method across different directions, we conducted ablation experiments and quantitatively compared the FROCRT, H-FROCRT, and SC-FROCRT methods. FROCRT is based on our previous work^[21], while H-FROCRT uses BM3D denoised multi-angle FROCT images before isotropic reconstruction.

Figure 5(a) shows that FROCRT identifies the basic layered structure but struggles with blurred boundaries. H-FROCRT improves uniformity and layer contrast but lacks resolution improvement. SC-FROCRT offers the best performance in boundary contrast and resolution, preserving more structural detail. Figure 5(b) shows that SC-FROCRT maintains the best FRC correlation in the high-frequency range and achieves a 1.32-fold improvement in the FRC metric over FROCRT. The line scan in Fig. 5(c) demonstrates that SC-FROCRT provides balanced high resolution laterally and axially, with consistent spatial resolution across directions. These ablation results decisively confirm the comprehensive benefits of the SC-FROCRT method in maintaining structural detail, enhancing resolution, and ensuring isotropic imaging. SC-FROCRT outperforms both FROCRT and H-FROCRT in terms of GSI, also demonstrating the advantage of incorporating the SC module.

A distinctive characteristic of plant tissue samples is their large nuclear structures. The unique cell wall structure of plant cells is represented as sparse, linear features in OCT images, making them ideal for validating OCT imaging techniques. In our experiment, we applied the SC-FROCRT method to an ex vivo aloe sample. The aloe sample was imaged inside a 4 mm inner diameter glass tube, as shown in Fig. 6.

Figure 6(a) compares the imaging results of the FROCRT and SC-FROCRT techniques. The SC-FROCRT reconstruction shows finer structural details in the plant tissue, with significantly enhanced contrast in the cell wall regions and minimal structural blurring. In Fig. 6(b), two regions of interest from Fig. 6(a) (Region 1 and Region 2) are enlarged to compare reconstruction results from four methods: OCT, FROCT, H-FROCT, and SC-FROCT. H-FROCT, processed with BM3D denoising, improves SNR but not resolution. SC-FROCT reduces noise and enhances resolution. But due to the high sparsity of the aloe tissue, the SC module produces overly sparse visual artifacts, resulting in a discontinuous appearance of the tissue structure. This phenomenon can be more clearly observed in the global image in Appendix C.

Figure 6(c) presents enlarged views of Region 1 and Region 3, showing reconstruction results from OCRT, FROCRT, H-FROCRT, and SC-FROCRT. SC-FROCRT provides the best imaging performance, achieving clearer and more accurate cell wall reconstruction, and effectively correcting SC-FROCT’s errors. Figures 6(d)–6(f) compare the performance of different reconstruction methods, presenting results for the SNR, line scan intensity distribution, and 2D frequency spectrum of the PSF. Specifically, as shown in the line scan comparison, Fig. 6(e) demonstrates that the SC-FROCRT displays sharper peak features, enabling a clear distinction between adjacent cell wall structures. In contrast, the FROCRT exhibits a peak-valley fusion, leading to reduced clarity in the cell wall resolution. Fourier domain image analysis [Fig. 6(f)] further shows that SC-FROCRT exhibits a broader spectral bandwidth, indicating an overall improvement in image resolution. Detailed global image information for each of the reconstruction methods described above can be found in Appendix C.

We further applied the SC-FROCRT technique to the tomographic reconstruction of an ex vivo tissue-cleared mouse spleen, validating the ability to enhance image quality in more complex sample structures. The tomographic images of the cleared mouse spleen are shown in Fig. 7(a). Since tissue-cleared samples require immersion in a specific uDISCO agent, the OCT and FROCT methods failed to produce high-quality, high-contrast spleen structures. Although SC-FROCT images reconstructed via the SC module offer improved resolution, they still suffer from anisotropic resolution and residual speckle noise due to single-angle acquisition. In contrast, SC-FROCRT employs multi-angle Fourier synthesis, which not only corrects resolution anisotropy but also effectively suppresses speckle artifacts, resulting in clearer preservation of the spleen’s internal structures.

A comparison of multi-angle stacked reconstruction images using the methods mentioned above is shown in Fig. 7(b), showing SC-FROCRT’s consistent superiority in reconstruction quality. This method clearly delineates internal structures, especially the cavities and morphology formed by spleen trabeculae. FROCRT improves internal structure display but is limited in resolving microstructures, as shown in the magnified comparison in Fig. 7(c). Figure 7(d) shows the lateral reconstruction intensity comparison of the three methods in Fig. 7(c), highlighting the differences in resolution performance. The subsequent SNR results confirm that SC-FROCRT reconstruction achieves a 12 dB advantage over the other two reconstruction methods. Detailed global result comparison can also be found in Appendix C.

The femur joint contains complex trabecular bone structures, which differ significantly from the surrounding dense cortical bone. These subtle trabecular structures present as weak echo signals in OCT imaging and are particularly affected by low image contrast and noise of the trabecular bone structure, whose intensity is comparable to that of the background, thereby limiting their effective resolution in conventional reconstructions. This limitation confines the applicability of OCT technology in bone tissue studies. To address this issue, we applied the SC-FROCRT technique to the tissue-cleared mouse femur joint.

Figure 8(a) presents a clear comparison of the overall reconstruction between the SC-FROCRT and FROCT methods. It is encouraging that FROCT covers the entire depth of the bone, allowing information from inside the bone cavity to be captured. However, due to signal attenuation and occlusion by the cortical bone, it is challenging to differentiate structures within the bone cavity in single-angle images. In contrast, the SC-FROCRT substantially improves the overall image quality, not only clearly outlining the cortical bone contour but also distinguishing the trabecular structures inside the bone cavity.

Figure 8(b) provides a comparison of the imaging performance for various single-angle reconstruction techniques. Figure 8(c) illustrates the results after multi-angle reconstruction, with histogram matching applied to the OCRT and FROCRT images for improved visual comparison. Although histogram matching enhanced the image contrast, the reconstructions from traditional methods still exhibited blurred trabecular bone structures, and the boundary between the trabecular and cortical bones remained indistinct, making it difficult to accurately resolve the structures. Figure 8(d) presents further detailed reconstruction results for a localized region. Figure 8(e) compares the lateral intensity curves at gap1 and gap2. The SC-FROCRT method’s curves show clear peak and valley features, distinguishing the trabecular bone structure, in contrast to the flat curves produced by OCRT and FROCRT. Figure 8(f) shows the FRC analysis, which further highlights the spatial resolution advantage of the SC-FROCRT method, achieving a 1.51-fold improvement compared to FROCRT.

For larger tissue-cleared mouse brain samples, we conducted multi-angle 3D data acquisition to validate the application of the SC-FROCRT reconstruction method in the 3D reconstruction of biological tissues. Given the larger size of the mouse brain sample, the scan was centered at the junction between the olfactory bulb and brain regions, as shown in Fig. 9.

Figure 9(a) presents the global angle of the 3D reconstruction, where the regional segmentation of the mouse brain’s structure is clearly visible. The external contour of the brain tissue is clearly defined. To further showcase the isotropic high-resolution capability of the SC-FROCRT method, we selected four tomographic slices at different depths along the z axis for demonstration, as shown in Figs. 9(b1)–9(b4). Figure 9(b1) shows the complete reconstruction of the top structure of the olfactory bulb, with a clear comparison to the SC-FROCT reconstruction, highlighting the detailed contours and fine internal structures, especially the two lobes’ prominent structure and layering. Figure 9(b2) compares SC-FROCRT reconstruction with the original images, demonstrating accurate isotropic distortion correction in mouse brain tomography. The highlighted reflective surfaces are caused by high-reflection cavities between brain regions. Figures 9(b3) and 9(b4) provide a broader view of the structural features of the mouse brain. Figure 9(c) provides the actual structural image of the mouse brain tissue, which is used for a direct visual comparison with the SC-FROCRT reconstruction results. The dashed box in the image indicates the region that was scanned and reconstructed in this study. The image clearly illustrates the slanted morphology of the actual mouse brain imaging region.

In this paper, we present the SC-FROCRT method, which achieves high resolution, expanded field-of-view, and isotropic image reconstruction. In the SC-FROCRT method, we developed a super-resolution model and applied iterative optimization to the images obtained from a conjugate image removal system. Furthermore, we integrated this super-resolution model with the previously established FROCRT method. Our results show that SC-FROCRT significantly enhances the resolution of FROCRT, with an average 1.41-fold improvement in the FRC metric. When compared to conventional OCT imaging, SC-FROCRT optimizes resolution, field-of-view, and isotropy, achieving superior performance beyond traditional methods.

The SC-FROCRT method enhances resolution through the SC module, which utilizes sparse continuous priors for iterative reconstruction. Unlike traditional super-resolution techniques prone to noise and error, the SC module ensures robust performance. To demonstrate the SC module’s super-resolution capabilities, we conducted an additional comparative experiment, as shown in Appendix D. The Fourier synthesis module optimizes both conjugate image removal and the SC module. The optimization of the conjugate image removal module by the Fourier synthesis module was previously discussed in Ref. [21]. However, the sparse continuous prior used in the SC module may occasionally lead to reconstruction artifacts, as seen in the aloe tissue reconstruction comparisons in Fig. 6 and Appendix C. The overly sparse cell wall structures in plant tissues cause discontinuities in super-resolved reconstructions, which can distort fine structural details. However, the Fourier synthesis module further refines the reconstruction, yielding a more accurate and realistic representation of the cell walls. Thus, the SC-FROCRT method is not merely a combination of innovations but leverages the complementary strengths of each approach to optimize performance. To further validate the structural fidelity of the SC-FROCRT reconstruction, we performed high-resolution light sheet fluorescence microscopy (LSFM) imaging on the cleared mouse femoral joint sample (corresponding to Fig. 8) for direct comparison. The imaging was conducted using the Zeiss Lightsheet 7 system, which provides autofluorescence-based volumetric imaging with an isotropic resolution of 2.53 µm, serving as a high-resolution reference for comparison. As shown in Fig. 10, although grayscale contrast differs between LSFM and OCT-based images due to their fundamentally distinct contrast mechanisms, the underlying anatomical structures exhibit strong spatial consistency. This structural agreement between modalities provides additional evidence supporting the accuracy and reliability of the SC-FROCRT method. Furthermore, edge resolution and power spectral analysis offer quantitative validation of the enhanced fidelity achieved by SC-FROCRT.

However, as a computational method, SC-FROCRT also faces challenges similar to those of its predecessors. The data acquisition mechanism of OCRT limits its applicability in in vivo scenarios. For live imaging, it is preferable to rotate the imaging probe rather than the sample. In such cases, special attention must be given to the configuration of the sample stage to ensure alignment between the rotation centers of the sample and the imaging probe. The recently proposed 3DOCRT technique introduces a 3D data acquisition approach based on concave lenses, offering a new pathway for in vivo SC-FROCRT imaging. Meanwhile, the current algorithm’s inability to respond in real time poses a limitation for real-time applications. Fortunately, advancements in deep learning technology present a promising strategy for accelerating the entire algorithmic process. By using a generative adversarial approach in the Fourier synthesis module to establish the relationship between multi-angle images and refractive index spectra, we significantly reduced synthesis time. Research in Ref. [17] introduces a novel approach, showing that deep learning can effectively reduce the angular requirements for Fourier synthesis reconstruction, thereby enhancing computational efficiency.

We also applied SC-FROCRT to the 3D reconstruction of large-scale tissue-cleared mouse brains. The results showed discrepancies compared to 2D tomography, mainly due to the limited imaging depth of OCT, leading to signal loss for depths beyond 5 mm, as seen in Fig. 9(b4). Looking forward, SC-FROCRT has the potential to provide more accurate structural reconstructions for smaller tissue slices. For larger biological tissues, combining SC-FROCRT with more advanced methods for expanding imaging depth would significantly enhance its utility for the analysis of diverse tissue structures. In conclusion, we believe SC-FROCRT has immense potential for achieving high-resolution isotropic tissue tomography and offers considerable value to the broader research community.

Acknowledgment. Figures 3 and 4 present the reconstruction results for tape and aloe samples. The original spectral data were acquired in our previous work[21], which laid the foundation for the present analysis. We gratefully acknowledge the efforts of the team involved in the original data acquisition. This work was supported by the National Key Research and Development Program of China (No. 2022YFB4702902), the Beijing Municipal Natural Science Foundation (No. 4232077), and the National Natural Science Foundation of China (No. 62275023).