Robust wavefront correction using AdamW-enhanced SPGD for computational adaptive optics in optical coherence tomography

Abstract

Computational adaptive optics (CAO) has emerged as an effective approach to correct optical aberrations in optical coherence tomography (OCT) without the need for additional hardware. However, conventional stochastic parallel gradient descent (SPGD) algorithms often suffer from slow convergence, instability, and susceptibility to local minima. In this work, we present an AdamW-enhanced SPGD algorithm that integrates adaptive learning rate control with weight decay to accelerate convergence and stabilize optimization. In addition, an eigenvalue-based sharpness metric is introduced to ensure more robust and stable optimization. The proposed approach was validated using both simulations and two distinct swept-source OCT setups, demonstrating its applicability in realistic imaging conditions. Furthermore, our results enabled cellular-level visualization of the photoreceptor layer and retinal nerve fiber layer in retinal imaging. These findings indicate that the proposed method shows a significant advancement over conventional CAO approaches, expanding the potential for clinical translation of CAO across a variety of ophthalmic applications.

1. Introduction

Optical coherence tomography (OCT) is a powerful noninvasive imaging modality based on interferometric detection, enabling micrometer-scale visualization of biological tissues [1]. Over the past decades, it has become a clinical standard in ophthalmology, particularly for providing high-resolution cross-sectional images of the retina [1–7]. However, when light propagates through the eye, optical properties such as corneal curvature, lens shape, and refractive errors introduce wavefront aberrations, degrading both resolution and contrast. To address this issue, adaptive optics (AO) was introduced, typically employing Shack–Hartmann wavefront sensors and deformable mirrors (DMs) to achieve nearly diffraction-limited imaging [8–10]. However, hardware-based AO increases system complexity and cost, and suffers from a limited depth of focus, which constrains its broader clinical application. Wavefront sensorless adaptive optics has been introduced to reduce system complexity by eliminating direct wavefront sensing, but it still requires physical correction elements such as deformable mirrors [11,12].

As an alternative, computational adaptive optics (CAO) using a phase-stable light source has emerged as an effective approach for aberration correction through post-processing, without relying on physical wavefront sensors or deformable mirrors [13–15]. While CAO can exhibit reduced signal-to-noise ratio compared to hardware-based AO, its simplicity provides a hardware-free alternative for aberration correction in OCT imaging. In OCT systems, CAO methods are commonly classified into three categories: sub-aperture-based methods, guide-star-based methods, and image-metric-based methods [16–19].

Sub-aperture-based CAO estimates wavefront aberrations through cross-correlation between sub-aperture images, which requires sufficiently resolved structural features for reliable shift estimation. In many biological OCT images, particularly those dominated by speckle, the lack of distinct structural features leads to ambiguous correlation peaks and unreliable aberration estimation [16]. Guide-star-based methods depend on the presence of a point-like reference structure, however, in many biological and clinical imaging situations, such references are frequently unavailable or unreliable.

Lastly, image-metric-based CAO has been increasingly employed due to its correction capability and broad applicability. This method estimates wavefront aberrations by optimizing image quality metrics—such as sharpness, entropy, or spatial frequency content [20–25]. Early image-metric-based optimization strategies, including grid search and gradient descent, were introduced but suffered from excessive computational cost and slow convergence [24,25]. To overcome these limitations, stochastic parallel gradient descent (SPGD) was proposed, employing random perturbations to enable robust and efficient correction of higher-order aberrations [16]. Nevertheless, conventional SPGD relies on a fixed gain parameter and is therefore prone to slow convergence, instability under noisy image-metric conditions, and susceptibility to local minima [26].

More recently, advances in deep learning optimization have motivated the application of adaptive optimizer in SPGD algorithms [26]. The approach dynamically adjusts the learning rate using first- and second-order moment estimates, achieving faster and more stable convergence than conventional fixed-gain SPGD. However, the application of such adaptive optimizers to CAO, particularly in OCT, has not yet been fully investigated. Specifically, AdamW, an extension of the Adam optimizer, introduces a decoupled weight decay scheme in which weight decay is applied independently of adaptive gradient scaling [27]. This property enables explicit control of parameter magnitude and leads to more stable and consistent convergence under noisy optimization conditions, making AdamW particularly well suited for SPGD-based CAO-OCT.

Another key parameter of CAO performance is the choice of image quality metric, which serves as the objective function for optimization. While previous approaches such as Shannon entropy and energy concentration have been commonly employed [16,26], eigenvalue-based image sharpness metrics have been widely adopted in image quality assessment and autofocus applications [23,28,29]. The method quantifies image sharpness by normalizing the image, constructing a Gram matrix, and evaluating its singular values or eigenvalues, where larger eigenvalues correspond to dominant structural information in the image [28]. Validated in digital holography by Ghosh et al., this metric provides a monotonic response to focus changes and outperforms entropy-based metrics in terms of robustness and focus detection accuracy, even under noisy conditions [23].

Here, we propose an AdamW-enhanced SPGD algorithm for CAO in OCT imaging. By integrating the random perturbation framework of SPGD with the adaptive learning-rate adjustment and weight decay of AdamW, the method achieves faster and more stable convergence. Furthermore, combined with an eigenvalue-based metric, the algorithm further ensures robust optimization under high order aberrations. We validate its efficacy through numerical simulations, phantom experiments, and in-vivo retinal OCT imaging, highlighting its potential to enhance real-time CAO performance and facilitate clinical application.

2. Methods

2.1. Image formation theory and computational aberration correction

The process of image formation in a coherent optical system can be modeled using Fourier optics. Let $g(x,y)$ represent the aberration-free complex image field in the spatial domain. Optical aberrations are represented by a phase function, ${\varphi }_a(u,v)$ , which modulates the phase of the pupil plane field, and the resultant aberrated image field $g_a(x,y)$ can be expressed as:

$$g_a(x,y)={\mathcal{F}}^{-1}\{\mathcal{F}\{g(x,y)\}\cdot e^{i{\varphi }_a(u,v)}\}$$ (1)

where $\mathcal{F}$ and ${\mathcal{F}}^{-1}$ denote the Fourier transforms and inverse Fourier transforms, respectively [2]. This equation expresses how phase aberrations in the pupil plane modulate the spatial frequency content of the image, resulting in a distorted image field in the spatial domain. We note that Eq. (1) represents a simplified numerical formulation for computational implementation. A rigorous OCT image formation model includes additional amplitude terms and coordinate scaling factors, as described in prior studies on OCT image formation and computational adaptive optics [15,16,30].

In this study, the aberration phase in the pupil plane, ${\varphi }_a(u,v)$ , is modeled as a linear combination of Zernike polynomials [31],

$${\phi }_a(u,v)=\sum _{n=4}^N{A}_n{Z}_n(u,v)$$ (2)

where $Z_n$ are the Zernike polynomials, $A_n$ are corresponding coefficients of wavefront distortions, and N indicates the number of Zernike modes included. We note that the first three Zernike modes correspond to piston, tip, and tilt, which account for misalignment effects of the imaging system, and were excluded [16,26].

To evaluate the sharpness of the reconstructed image during wavefront correction, an eigenvalue-based metric was employed [23,28]. The input image was first normalized using energy normalization (i.e., L2 norm) and then mean-centered, where $\tilde{X}$ indicates the resulting zero-mean normalized image matrix, X. From this matrix, a Gram matrix, G can be constructed as,

$$G(X)=\frac{1}{m}\tilde{X}{\tilde{X}}^{\mathrm{\top }}.$$ (3)

where m denotes the dimension of the image (i.e., the number of rows of the image matrix). The sharpness metric is then defined as the sum of all eigenvalues, $\mathrm{\lambda },$ of G, given by

$$S_{\text{eig}}(X)=\sum _{i=1}^m{\lambda }_i(G).$$ (4)

We note that using the Gram matrix, instead of full singular value decomposition, avoids the heavy computational cost while providing an equivalent sharpness metric based on squared singular values [28]. Specifically, a sharper image exhibits stronger spatial correlations, leading to higher energy concentration and consequently larger eigenvalues in the Gram matrix. To improve the robustness of the eigenvalue-based metric, the top and bottom 2% of eigenvalues were removed. This follows prior eigenvalue-based sharpness and autofocusing studies, where dominant components are sensitive to magnification effects and the least dominant components are primarily noise-dominated [23,28,29].

2.2. Principle of AdamW-enhanced SPGD algorithm

To optimize the Zernike coefficients for aberration correction, we employed a stochastic parallel gradient descent (SPGD) algorithm enhanced with an AdamW-style adaptive update scheme [16,26,27]. The optimization process begins by initializing the Zernike coefficient vector, $A_n$ , and generating a normalized random perturbation vector, $\delta$ , for each iteration.

The sharpness of the reconstructed image can be evaluated using an eigenvalue-based metric under both positive and negative perturbations as

$$S_{+}=S_{eig}(A_n+\sigma \delta A_n)and{S}_{-}=S_{eig}(A_n-\sigma \delta A_n).$$ (5)

where $\sigma$ was empirically set to 10⁻⁴. The gradient-like estimate can be evaluated as

$$gra{d}_n=(S_{+}-S_{-})\delta$$ (6)

which guides the update of first and second moment terms in the Adam optimizer framework as

$$m_n={\beta }_1{m}_{n-1}+(1-{\beta }_1)gra{d}_n,$$ (7)

$$v_n={\beta }_2{v}_{n-1}+(1-{\beta }_2)gra{d_n}^2.$$ (8)

Since these estimates are biased toward zero in the early stages of optimization, bias correction is applied as follows,

$$\widehat{m_n}=\frac{m_n}{1-{\beta }_1^n},$$ (9)

$$\widehat{v_n}=\frac{v_n}{1-{\beta }_2^n}.$$ (10)

Finally, the Zernike coefficients are updated using the AdamW-style adaptive update scheme, incorporating both adaptive learning rate and weight decay as,

$$A_{n+1}=A_n-{\alpha }_n\left(\frac{\widehat{m_n}}{\sqrt{\widehat{v_n}}+ϵ}+d{A}_n\right)$$ (11)

where ${\alpha }_n$ is a learning rate that changes with each iteration, $ϵ$ is a stabilizing constant to avoid division by zero, and d is a regularization term for weight decay. Learning rate, ${\alpha }_n$ , is defined as,

$${\alpha }_n={\alpha }_{min}+\frac{1}{2}({\alpha }_{max}-{\alpha }_{min})\left(1+cos\frac{\pi n}{T}\right)$$ (12)

where ${\alpha }_{max}$ and ${\alpha }_{min}$ represent the maximum and minimum learning rates, respectively, and T is the total number of iterations. This learning rate allows a relatively large step size during the early stages to accelerate convergence, followed by progressively smaller updates near the optimum, improving stability.

In our implementation, we set the total number of iterations, $T=2000$ , with hyperparameters ${\beta }_1=0.9,{\beta }_2=0.999$ , $ϵ={10}^{-8}$ , and $d={10}^{-4}$ . The learning rate parameters were set to ${\alpha }_{max}=0.02$ and ${\alpha }_{min}=0.002$ , following the cosine annealing schedule described in Eq. (12). This maximum iteration count, 2000, was determined based on an empirical convergence criterion. The optimization was considered complete when the mean absolute change of Zernike aberrations, evaluated over a sliding window of 100 iterations, fell below 0.001. Note that this threshold may vary depending on the image size and content. Figure 1 presents the overall flow of the AdamW-enhanced reconstruction process.

Fig. 1.

Flowchart of AdamW-enhanced SPGD algorithm

2.3. Numerical simulation of AdamW-enhanced SPGD algorithm

For the purpose of evaluating the performance of the proposed optimization algorithm, we conducted a series of numerical simulations using a complex amplitude image of a USAF resolution target with a size of 150 × 150 pixels. A set of known aberrations was applied to the image, and the effectiveness of the aberration correction was evaluated.

First, we compared the correction performance for seven low-order Zernike aberration modes between the conventional SPGD algorithm [16] and the proposed AdamW-enhanced SPGD. The accuracy of the corrected coefficients was quantified by evaluating the root-mean-square (RMS) error between the estimated and ground truth Zernike vectors. RMS values were computed by averaging the coefficient errors over 100 independent optimization runs. A detailed comparison of the optimization objectives and frameworks between the two algorithms is summarized in Table 1. Next, to evaluate the algorithm’s ability to recover more complex wavefront distortions, total of 12 Zernike modes including higher-order aberrations (HOAs) were applied and corrected. RMS error was also calculated to compare the performance of both optimization methods.

Table 1. Comparison of conventional SPGD and AdamW-enhanced SPGD algorithms.

	Conventional SPGD [16]	AdamW-Enhanced SPGD
Optimization objective	Image entropy minimization ◦Uses Shannon entropy, $E=-sum(I\times logI)$ where I indicates intensity.	Eigenvalue-based sharpness maximization ◦Normalize and mean-center image matrix, $\tilde{X}$ ◦Construct Gram matrix,     $G(X)=\frac{1}{m}\tilde{X}{\tilde{X}}^{\mathrm{\top }}.$ ◦Define sharpness metric as the sum of eigenvalues,       $S_{\text{eig}}(X)=\sum _{i=1}^m{\mathrm{\lambda }}_i(G).$
Optimization framework	◦Random Bernoulli perturbations applied to Zernike coefficients ◦Gradient approximated by    $\mathrm{\Delta }E=E_{+}+E_{-}$ ◦Coefficients updated as,   $A_{n+1}=A_n+\gamma \mathrm{\Delta }E\cdot \delta A_n$	◦Same random perturbation scheme ◦First and second moments of gradient estimated as   $m_n={\beta }_1{m}_{n-1}+(1-{\beta }_1)gra{d}_n$   $v_n={\beta }_2{v}_{n-1}+(1-{\beta }_2)gra{d_n}^2$ ◦Bias-corrected adaptive updates as   $\widehat{m_n}=\frac{m_n}{1-{\beta }_1^n},\widehat{v_n}=\frac{v_n}{1-{\beta }_2^n}$ ◦Coefficients updated as,   $A_{n+1}=A_n-{\alpha }_n\left(\frac{\widehat{m_n}}{\sqrt{\widehat{v_n}}+ϵ}+d{A}_n\right)$
Learning rate	◦ Fixed global step size γ.	◦ Adaptive learning rate per coefficient
Weight decay	◦ Not used.	◦ Uses weight decay

Finally, to test the robustness of the method with respect to the reference image, we repeated the same correction task using another complex amplitude image of a cameraman with the same size (150 × 150 pixels). The same 12-mode aberration set was applied and corrected, and the resulting RMS errors were evaluated. In this experiment, we evaluated four conditions by combining two optimization strategies: conventional SPGD and AdamW-enhanced SPGD with two objective metrics: entropy-based and eigenvalue-based. The resulting Zernike coefficient errors and RMS values were analyzed to assess the performance of each condition.

2.4. Application of AdamW-Enhanced SPGD aberration correction for OCT imaging

To experimentally validate the proposed AdamW-enhanced SPGD aberration correction algorithm, we applied it to two distinct Swept source OCT (SS-OCT) imaging setups: a benchtop phantom imaging system and a human retinal imaging platform, both based on stretched-pulse mode-locked (SPML) swept sources.

For OCT imaging, we employed a SS-OCT system previously described in detail by Lee et al [14]. Imaging was performed using a two-axis galvanometer scanner followed by a beam expander composed of two lenses (f = 40 mm and f = 75 mm), and a commercial objective lens (LCPLN20XIR, Olympus, NA = 0.45). The source was an SPML swept laser centered at 1290 nm with a bandwidth of 100 nm and a repetition rate of 10 MHz, providing an axial resolution of 10 µm in air. A low-scattering tissue phantom was prepared by dispersing TiO₂ powder (TI-602, Atlantic Equipment Engineers, Inc.) into polydimethylsiloxane (PDMS) following the protocol of Ayers et al. [32], where the diameter of TiO₂ particles is known to be under 1 μm [33]. For in-vivo human retinal imaging, we used a beam expander composed of f = 60 mm and f = 80 mm lenses. The source was a 1050-nm SPML swept laser operating at a 4.7 MHz repetition rate, which provided an axial resolution of 8 µm in tissue and a transverse resolution of 3.1 µm with a 6.8-mm beam diameter on the cornea. The basic optical setup of this OCT imaging system is illustrated in Figure S1 in the Supplement 1 ^{(1.8MB, pdf)} .

Subsequently, to evaluate the performance of the AdamW-enhanced SPGD aberration correction, we first performed imaging process of a phantom. Thereafter, to demonstrate the potential clinical applications, we applied the algorithm to in-vivo human retinal imaging, visualizing photoreceptors layer (PRL) and retinal nerve fiber layer (RNFL) with cellular-level resolution. Retinal image was obtained from a healthy volunteer under protocols approved by the Institutional Review Board of the Korea Advanced Institute of Science and Technology. Written informed consent was obtained prior to imaging, and all procedures adhered to the Declaration of Helsinki. Detailed subject information, including the imaged eye, age, gender, and spectacle or contact lens prescription, is provided in Table S1 in the Supplement 1 ^{(1.8MB, pdf)} .

3. Results

3.1. Comparative simulation of AdamW-enhanced and conventional SPGD algorithms using a USAF resolution target image

To evaluate the effectiveness of the AdamW-enhanced SPGD algorithm, we performed a comparative simulation against the conventional SPGD approach, using a complex amplitude image of a simulated USAF resolution target (Fig. 2(a)). The aberrated images (Fig. 2(b1) and 2(b2)) were generated by applying predefined Zernike phase errors to the initial wavefront. Specifically, two sets of Zernike aberrations were evaluated in this study. The first set included 7 low-order modes ranging from Z₄ to Z₁₀, covering astigmatism, coma, defocus, and trefoil components. The second set incorporated five additional high-order modes from Z₁₁ to Z₁₅, resulting in a total of 12 aberration modes for correction. Random phase shifts of either +1 or −1 radian were applied to each Zernike mode in the aberration sets. Specifically, in the low-order simulation, modes Z₄, Z₅, Z₇, and Z₁₀ were assigned a phase shift of +1 radian, while Z₆, Z₈, and Z₉ were assigned −1 radian. In the simulation including high-order aberrations, phase shifts of +1 radian were applied to modes Z₄, Z₅, Z₇, Z₁₀, Z₁₁, Z₁₂, and Z₁₄, whereas −1 radian shifts were assigned to modes Z₆, Z₈, Z₉, Z₁₃, and Z₁₅ (Fig. 2(e1) and 2(e2)).

Fig. 2.

Comparison of low-order and high-order aberration correction performance between conventional SPGD and AdamW-enhanced SPGD algorithms. (a) Initial complex amplitude of simulated USAF resolution target. (b1) and (b2) Aberrated intensity images with low-order and high-order Zernike distortions, respectively. (c1) Corrected image of low-order and high-order aberration case using conventional SPGD, respectively. (d1) and (d2) Corrected image of low-order and high-order aberration case using AdamW-enhanced SPGD, respectively. (e1) and (e2) Estimated Zernike coefficients for low-order and high-order aberration, respectively.

Subsequently, we applied the conventional SPGD and the proposed AdamW-enhanced SPGD algorithms to perform aberration correction (Fig. 2(c) and 2(d)). For the conventional SPGD, the perturbation magnitude, $\delta$ was set to 0.2 and a gain coefficient was set to $\gamma =-0.05$ . In the case of low-order aberrations, both algorithms were able to significantly recover the image quality. The AdamW-enhanced algorithm converged in only 411 iterations, whereas the conventional SPGD required 726 iterations to reach the stopping criterion. Moreover, the AdamW-enhanced method achieved a noticeably lower RMS error (0.1755 and 0.2692, respectively). In the high-order aberration case, the AdamW-enhanced SPGD algorithm successfully converged after 1086 iterations with RMS error of 0.2039, while the conventional SPGD failed to converge within the same maximum iteration limit. The result demonstrates the improved convergence behavior and robustness of the proposed method, especially in the presence of high-order aberrations. Quantitative analysis of the estimated Zernike coefficients is presented in Fig. 2(e). We note that, on a system equipped with an AMD Ryzen AI 7 350 CPU and 32 GB RAM and implemented in MATLAB, the computational cost for image size of 200 × 200 pixels was approximately 3.35 ms per iteration (3.35 s per 1000 iterations) or conventional SPGD and 4.90 ms per iteration for the AdamW-enhanced SPGD.

3.2. Robustness analysis with different reference images and objective metrics

To further validate the algorithm under different image conditions, we used the cameraman image as an alternative reference input and compared the performance of four optimization-metric combinations. Specifically, we evaluated four conditions by combining two optimization strategies—conventional SPGD and AdamW-enhanced SPGD—with two different objective function metrics: entropy-based and eigenvalue-based. In this simulation, we applied the same set of 12 Zernike aberration modes (Z₄ to Z₁₅) as in the USAF target experiment described in Section 3.1. Performance was quantitatively analyzed based on the error in estimated Zernike coefficients and the resulting RMS values. For the conventional SPGD, the perturbation magnitude $\delta$ was set to 0.2. The gain coefficient $\gamma$ was set to −0.25 for the entropy metric and −200 for the eigenvalue metric. In contrast, the AdamW-enhanced SPGD algorithm employed the same set of hyperparameters used in the previous experiment. For reference, a separate validation of the objective functions (entropy-based and eigenvalue-based) under a single Zernike defocus perturbation is provided in Supplement 1 ^{(1.8MB, pdf)} Fig. S2.

Figure 3(a1) and 3(a2) show the complex field of the reference image. After introducing 12-mode Zernike phase aberrations, the degraded intensity image and corresponding pupil-phase distortion are described in Fig. 3(b1) and 3(b2), respectively. The exemplary result of convergence behavior is visualized in Fig. 3(c), where the normalized objective function values are plotted over 2000 iterations. Among the four methods, the AdamW-enhanced SPGD with eigenvalue metric achieved the fastest and most stable convergence. In contrast, the conventional SPGD with entropy exhibited the slowest convergence and frequent oscillations. Coefficient recovery results are shown in Fig. 3(d1–3(d4). The AdamW–Eigenvalue method exhibited the best overall performance, converging in 1147 iterations with the lowest RMS error of 0.1151. This was followed by AdamW–Entropy (1219 iterations, RMS 0.1489), SPGD–Eigenvalue (1401 iterations, RMS 0.1198), while SPGD–Entropy failed to converge within the maximum iteration limit of 2000 and resulted in the highest error (RMS 0.2183). The result shows that AdamW optimization significantly enhances the performance of SPGD-based aberration correction, and that eigenvalue-based metrics provide more stable convergence than entropy-based approaches. Furthermore, the AdamW-enhanced SPGD achieved this performance without any hyperparameter adjustment, showing robustness and adaptability across different image types and objective metrics.

Fig. 3.

Robustness analysis of aberration correction using different reference image (cameraman) with same 12-mode Zernike aberrations. (a1) Amplitude and (a2) phase of initial complex field of cameraman image. (b1) Intensity image after applying 12-mode Zernike phase aberrations (b2) Distorted phase map in pupil plane. (c) Representative convergence curves of normalized objective function values over iterations according to different optimization methods and metrics. (d1)–(d4) Comparison of estimated Zernike coefficients against ground truth.

3.3. Validation of algorithm via phantom-based OCT imaging

To evaluate the effectiveness of the proposed aberration correction algorithm on point-like structures, we performed experiments using a low-scattering phantom composed of TiO₂ particles embedded in PDMS. A representative en-face complex image was extracted from a volumetric OCT dataset at a depth of approximately 404 μm, distant from the focal plane. As shown in Fig. 4(a1)–(a2), the initial projection image was notably blurred, with reduced contrast and poorly localized scatterers due to the cumulative effects of defocus and higher-order aberrations. After applying AdamW-enhanced SPGD, the reconstructed image (Fig. 4(b1)–(b2)) showed a marked improvement in contrast and sharpness. The point-like scatterers became clearly resolved with enhanced signal localization, indicating successful wavefront correction. The estimated Zernike coefficients obtained during optimization are shown in Fig. 4(c). We note that the Zernike defocus coefficient (Z4, in radians) represents the wavefront phase variation across the pupil plane and does not directly correspond to the physical axial displacement in the image plane. The result was achieved without modifying any hyperparameters from the previous simulation, demonstrating the robustness of the proposed method across different imaging conditions. Thus, we can conclude that the proposed method is robust and accurate for correcting complex phase distortions.

Fig. 4.

En-face image of phantom before and after computational aberration correction. (a) Initial projection image of phantom sample dataset at a depth of 404 μm from the focal plane. (b) Reconstructed image after wavefront correction using AdamW-enhanced SPGD algorithm. (c) Estimated aberration using proposed aberration correction algorithm. Scale bars (a1) and (b1): 20 μm, (a2) and (b2): 5 μm.

3.4. In-vivo visualization of photoreceptors and retinal nerve fiber layer

To validate the in-vivo performance of the proposed computational aberration correction algorithm, OCT imaging of the human retina was conducted. For in-vivo retinal imaging, axial motion correction was performed prior to aberration correction to compensate for motion-induced phase instability [14]. Under our implementation, this step required on the order of tens of seconds (approximately 30 seconds for a 500 × 500 pixel dataset). Figure 5 shows en-face projection images of the PRL and RNFL, before and after wavefront correction. The raw PRL image (Fig. 5(a1)) shows a blurred appearance with poorly defined cone mosaic. Similarly, the initial RNFL projection (Fig. 5(b1)) exhibits blurred axonal bundles.

Fig. 5.

High-resolution PRL and RNFL projections after computational aberration correction processing. (a1) and (b1) Initial projections of PRL and RNFL, respectively. (a2) and (b2) Reconstructed image after wavefront and defocus correction using AdamW-enhanced SPGD and ISAM. Scale bars 250 μm

After applying the AdamW-enhanced SPGD algorithm with interferometric synthetic aperture microscopy (ISAM) [13,14], the reconstructed images (Fig. 5(a2), (b2)) show marked improvements in spatial resolution and contrast. In the corrected PRL image, individual photoreceptors become clearly resolved, while the RNFL projection reveals fine structural details of the nerve fiber bundles. The result demonstrates the capability of our proposed method in reconstructing cellular retinal structures.

4. Discussion

In this study, we proposed a novel computational aberration correction algorithm that integrates an AdamW-enhanced adaptive optimization scheme with the conventional SPGD approach. Specifically, the proposed method integrates stochastic perturbation with adaptive learning rate and weight decay, resulting in significantly faster and more stable convergence, particularly for high-order aberration correction. Furthermore, by applying an eigenvalue-based sharpness metric, our proposed algorithm demonstrated more stable convergence compared with the conventional Shannon entropy metric. Importantly, the proposed AdamW-enhanced SPGD maintained consistent performance with the same hyperparameters not only across different reference images (e.g., USAF resolution target and cameraman image) but also in experimental data, including phantom and in-vivo retinal images, demonstrating its robustness and generalizability.

One of the recent variants of SPGD, the adaptive-gain SPGD (AGSPGD) algorithm [26], incorporates Adam-like moment-based adaptation, in which first- and second-moment statistics are accumulated to adaptively regulate the gain coefficient and improve convergence compared with conventional SPGD. We note that AGSPGD does not include an explicit parameter decay term. Moreover, prior validations of AGSPGD have primarily focused on PSF-level numerical simulations or simplified optical configurations, and the algorithm was originally evaluated using intensity-based objective functions. In this work, we further evaluated AGSPGD under the same eigenvalue-based objective metric used in our framework. In this evaluation, the proposed AdamW-enhanced SPGD leads to higher coefficient-recovery accuracy, as demonstrated in Supplement 1 ^{(1.8MB, pdf)} Fig. S3.

Given these improvements in robustness and accuracy, the proposed algorithm is suited for retinal OCT imaging, where reliable wavefront correction is critical for clinical evaluation. In particular, our algorithm enabled cellular-level reconstruction of the PRL and the RNFL. Structural alterations in the PRL are known to serve as sensitive biomarkers for photoreceptor degeneration and age-related macular diseases, while the enhanced visualization of fine axon bundle structures in the RNFL could facilitate early detection and longitudinal monitoring of neurodegenerative diseases of the retina, such as glaucoma and diabetic retinopathy [34–38]. These results demonstrate that our approach provides fast and reliable aberration correction, thereby facilitating its integration into the clinical field, where high-resolution imaging must be achieved within clinically acceptable time frames.

In conclusion, the proposed AdamW-enhanced SPGD algorithm achieves rapid and stable convergence even in the presence of complex high-order aberrations and exhibits robust performance across diverse imaging conditions. We expect that the successful validation in real OCT imaging will significantly broaden the scope of clinical applications for computational adaptive optics.

Funding

National Research Foundation of Korea https://ror.org/013aysd81 ( 2020R1A2C3009667); Korea Advanced Institute of Science and Technology https://ror.org/05apxxy63 ( NYU-KAIST Partnership (Project No. 2024-05)).

Disclosures

The authors declare no conflicts of interest.

Data availability

All data for supporting the conclusion have been included in the manuscript. Other data may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 ^{(1.8MB, pdf)} for supporting content.