Optimizing fluorescence imaging through scattering media using structured light-assisted wavefront shaping

Summary

The scattering of light by biological tissues significantly impedes fluorescence imaging, affecting key aspects such as image resolution, contrast, depth, and the interpretation of fluorescent measurements. To overcome these challenges, we introduce an approach that combines wavefront shaping with image processing. Wavefront shaping adjusts the phase and amplitude of light waves in real time, counteracting scattering-induced aberrations and enhancing image fidelity. Our method optimizes the collection of signals from multiple fluorescent targets, facilitating their precise localization and tracking. Further augmenting this method, we employ a Bessel-Gauss (BG) beam, renowned for its ability to reconstruct its original structure post-interaction with scattering particles. This attribute enhances imaging depth and contrast. Experimental validations conducted across various scattering media confirm the practical feasibility of our approach. Its compatibility with existing microscopy systems offers great potential to advance biological imaging, biomedical diagnostics, and research, paving the way for widespread adoption in various scientific fields.

Graphical abstract

Highlights

• •Wavefront shaping with image processing localizes and enhances hidden fluorescence
• •Image entropy and intensity guide SBGA to optimize image quality and preserve detail
• •Using BG beam for wavefront shaping improves imaging depth and signal strength

Physics; Optics; Computational physics

Introduction

Studying complex biological systems can greatly benefit from deep-tissue imaging and is facilitated by detecting and quantifying fluorescent signals. Biological tissue, as an inhomogeneous medium, poses a major limitation to optical imaging systems by scattering light. This scattering of the incident beam significantly affects the fluorescent image quality, i.e., resolution, contrast, or signal-to-noise ratio (SNR). Consequently, there has been a growing interest in developing methods to optimize the signals of interest. Techniques such as confocal microscopy¹ and two-photon microscopy² attempt to filter out scattered light, utilizing only the non-scattered or ballistic photons. However, ballistic photons decrease exponentially with propagation depth, whereas a large portion of light, although scattered, penetrates deeper into the tissue or similar scattering media.³

In recent years, wavefront shaping techniques^4,5,6,7,8,9 have emerged as an attractive proposition to manipulate and utilize scattered light to motivate innovations for imaging, stimulation, and therapy at depths unattainable with conventional microscopy.^10,11 These methods manipulate the fundamental properties of light, i.e., amplitude, phase, and polarization, to reverse the process of scattering.^12,13 The ability to control scattered light has opened new possibilities for many biomedical applications,^14,15 including imaging systems.^16,17 Given the potential of wavefront shaping methods,¹⁸ there has been a growing interest in developing different methodologies including phase conjugation,^19,20 feedback-based optimization,^21,22 or transmission matrix approaches^23,24 for wavefront shaping.

However, few studies have focused on optimizing multiple hidden fluorescent targets. Most studies have aimed to find a single focus utilizing non-linear fluorescent signal,^25,26 optimize a single fluorescent target,^27,28 or create multiple foci within the speckle pattern.^29,30,31,32 Nevertheless, practical applications require optimization of multiple targets in addition to the utilization of linear signal. To optimize multiple hidden targets simultaneously, unique challenges need to be addressed that require non-traditional approaches. One challenge is to first detect all the targets with very low SNR and to determine the exact position of all the hidden targets. Traditional approaches typically require a predefined target location before optimization. Additionally, finding appropriate metrics that can be used simultaneously to solve the multi-optimization problem is necessary.

We address these challenges by combining wavefront shaping methods with image processing techniques to simultaneously detect and optimize multiple hidden targets with varying fluorescent signal intensities. We demonstrate that this hybrid method can precisely locate deeply buried targets, enhance their fluorescent signal, and therefore improve the fluorescent image quality. We first utilize a simple image analysis technique known as thresholding to classify the image pixels into signal and noise. Subsequently, two well-known image quality metrics, entropy and intensity of the thresholded image, are chosen as the objective functions for the scoring-based genetic algorithm (SBGA), a method we have previously developed.³³

We further demonstrate that higher enhancement and depth penetration can be achieved by substituting the traditional Gaussian input with a Bessel-like beam. Bessel beams are immune to diffractive spreading and have self-healing properties after encountering obstacles or propagating through inhomogeneous media.^34,35 Bessel beams have been used in many applications in which extended penetration or imaging depth is crucial, e.g., fluorescence microscopy or light-sheet microscopy,^36,37 and have been demonstrated to improve SNR.^38,39 Here, we successfully implement our hybrid wavefront shaping method using a Bessel-Gauss (BG) beam as input. BG beams not only maintain the self-healing property inherent in ideal Bessel beams but also exhibit relatively diffraction-free propagation for finite distances.⁴⁰ The results demonstrate that the method is even more powerful with a BG beam compared with the traditional Gaussian beam.

Results

Identifying multiple objective functions

The excitation wavefront is distorted as it propagates through a scattering medium, limiting the contrast and information retrieved from the collected image. Here, our goal is to recover the signals hidden by scattering media. Traditional feedback-based wavefront shaping employs a spatial light modulator (SLM) to shape the incident wavefront $\left(\overrightarrow{u}s\right)$, based on the feedback from a single localized target or multiple predefined target positions. However, our approach does not require predefined localization of targets. Although most studies on multiple targets focus on achieving uniform intensity distribution within the defined spots in speckle,^29,30,33,41 we aim to optimize fluorescent targets with varying intensities without utilizing the speckle.

To achieve enhanced imaging while preserving maximum detail such as intensity variation and distribution, we select image entropy and intensity as our objective functions. SBGA³³ utilizes these metrics to compute an optimal solution, which is then configured on the SLM to obtain an enhanced image. Based on Shannon’s entropy from information theory, image entropy serves as a measure of the information present within an image.⁴² The entropy, $H$, of an image is defined as follows:

$$H=-\sum _{i=0}^{2^n-1}P\left(w_i\right){\log }_{2}P\left(w_i\right)$$ (Equation 1)

where $P\left(w_i\right)$ is the probability of finding the intensity level $w_i$ at pixel $i$, and $2^n$ represents the number of available intensity levels for an $n$-bit grayscale image.⁴³ The use of image entropy has been extensively applied in computational image restoration across various fields, including astronomy.^44,45 Here, we show how incorporating wavefront shaping techniques can utilize image entropy to enhance fluorescent signals.

Maximizing entropy of image $\left(S\right)$ ensures the enhancement of image details, provided that $S$ does not merely amplify random noise.⁴⁶ To address this, we apply a thresholding technique⁴⁷ that differentiates target pixels, which correspond to fluorescent targets, from background or noise pixels. The thresholding method involves defining a single threshold value, $\tau$, calculated by finding the maximum intensity level, $w_{\max }$, in the initial image and adjusting it by a correction factor, $t_c$, such that $\tau =w_{\max }\times t_c$. The correction factor $\left(0\le t_c\le 0.5\right)$ is inversely related to the SNR. In cases where $w_{\max }$ in the initial image is low, a higher $t_c$ is used to separate targets from noise (Figure S16A). The thresholding operation is defined as:

$$g\left(x,y\right)=\{\begin{array}{cc}f\left(x,y\right)& \text{if}f\left(x,y\right)>\tau \\ 0& \text{if}f\left(x,y\right)\le \tau \end{array}$$ (Equation 2)

where $G$, the resulting thresholded image, consists of pixel values $g\left(x,y\right)$ as described by Equation 2. Additional information on thresholding is given in the STAR Methods section. The SBGA now assigns scores, $s_{\mathcal{H}}$ and $s_{\mathcal{I}}$, based on each solution’s ability to optimize the entropy $\left(\mathcal{H}\right)$ and intensity $\left(\mathcal{I}\right)$ of the thresholded image. The intensity of the thresholded image, $\mathcal{I}$, is measured as the average contribution of all pixels $\left(m\times n\right)$ in $G$:

$$\mathcal{I}=\frac{1}{mn}\sum _{x=1}^m\sum _{y=1}^{n}g\left(x,y\right)$$ (Equation 3)

An illustration of our method is presented in Figure 1. Initially, a set of phase masks $\left({\overrightarrow{u}}_1,{\overrightarrow{u}}_2,\dots ,{\overrightarrow{u}}_n\right)$ is randomly generated and displayed on the SLM. The camera records the corresponding images $\left(S_1,S_2,\dots ,S_n\right)$. Entropy and intensity values ($\mathcal{H}$ and $\mathcal{I}$) are computed from the thresholded images $\left(G_1,G_2,\dots ,G_n\right)$, and the phase masks are assigned scores ($s_{\mathcal{H}}$ and $s_{\mathcal{I}}$). The algorithm then ranks the phase masks based on their combined score $\left(s_{\mathcal{H}}+s_{\mathcal{I}}\right)$ and eliminates solutions with lower scores. This process continues through a series of generations to find the optimal input wavefront ${\overrightarrow{u}}_{opt}$ that maximizes the combined score:

$${\overrightarrow{u}}_{opt}=\underset{\overrightarrow{u}}{\arg \max }\left(s_{\mathcal{H}}+s_{\mathcal{I}}\right)$$ (Equation 4)

Figure 1.

Illustrative diagram detailing the steps of the method

Images $\left(S_1,S_2,\dots ,S_n\right)$ are captured with different phase masks $\left({\overrightarrow{u}}_1,{\overrightarrow{u}}_2,\dots ,{\overrightarrow{u}}_n\right)$. The optimal phase mask $\left({\overrightarrow{u}}_{opt}\right)$ is determined by simultaneously maximizing the entropy $\left(\mathcal{H}\right)$ and intensity $\left(\mathcal{I}\right)$ of the thresholded images $\left(G_1,G_2,\dots ,G_n\right)$.

Additionally, we enhance the method by replacing the Gaussian beam with a BG beam to improve both enhancement and penetration depth.

Experimental setup

A home-built optical microscope is used for the experimental demonstration and is illustrated in Figure 2. A continuous wave helium-neon laser ($\lambda =632.8\text{nm}$) beam is expanded and directed onto a phase-only SLM (Santec SLM-200). A half-wave plate is used to control the incident beam polarization. A 4$f$ imaging system and a microscope objective MO1 (10$\times$, numerical apertur (NA) $=$ 0.3) transmit the beam reflected by the SLM to excite fluorescent microspheres (carboxylate-modified polystyrene beads, 40 nm diameter, 633/720) hidden behind scattering sample. The fluorescent microspheres were randomly dispersed on a microscope slide, which was then placed behind the scattering layer for the experiments, unless stated otherwise. The distance between the slide and the scattering layer was $\sim$5 mm. The emitted signal is collected by a second microscope objective MO2 (20×, NA $=$ 0.4) through a band-pass filter (center wavelength = 720 nm) and captured by a camera (Thorlabs CS2100M).

Figure 2.

The experimental setup. Laser beam ($\lambda =632.8$ nm) directed toward a spatial light modulator (SLM) through a half-wave plate (HWP) and a beam splitter (BS)

The reflected beam from the SLM is focused onto the scattering sample by a microscope objective (MO1). Fluorescent emission is filtered through a longpass filter and captured by a camera.

We place an axicon⁴⁸ $\left(\alpha =0.5°\right)$ before the scattering medium when a BG beam is utilized in the experiments. The axicon can be placed either before or after the SLM, as long as the BG beam is formed after MO1, without any phase modulation. An iris is placed before MO1 to ensure that the aperture size is not limited by MO1. No other changes in the optical setup were made for the experiments using the BG beam, except for the introduction of the axicon. Future studies could be extended to evaluate the performance of both Gaussian and BG beams with varying experimental parameters.⁴⁹

The BG beam can also be generated using a digital hologram displayed on a second SLM (Figure S17). Further details about the alternative setup are given in the STAR Methods section. MATLAB scripts are used to control the camera and the SLM.

Simultaneous optimization of multiple targets

To empirically validate our approach, we conducted experiments aimed at optimizing fluorescent signals through various scattering media, including pig skin tissue, ground-glass diffusers (GGD), and parafilm. The GGD (Thorlabs DG10-120-MD) has a thickness of 2.0 mm and 120 grit. The mean free path of the diffuser is 0.33 mm, calculated using the procedure described in Balasubramaniam et al.⁵⁰ The scattering mean free path of parafilm has been characterized and estimated to be $170\mu m$ with an anisotropy factor of $g\approx 0.80$.^27,51,52,53 The physical and optical properties of pig skin have been extensively studied,^{54,55,56,57,58} and it is popular for its similarity to human skin.^59,60,61 The mean free path of photons and anisotropy factor of pig skin have been estimated to be 0.17 mm and 0.72, respectively.^62,63

The experiment began by randomly dispersing fluorescent beads on a microscope slide, which were then concealed behind four layers of parafilm. We captured the fluorescent signals both before and after the optimization process. Figure 3A displays the initial image, which shows limited information due to the scattering of incident light by the media.

Figure 3.

Simultaneous optimization of multiple targets

(A–F) (Top row) Results with four layers of parafilm showing the image captured (A) before and (B) after optimization, and (C) comparison of targets’ intensity before and after the optimization process. (Bottom row) Results with ground glass diffuser showing fluorescent targets (D) before and (E) after applying the method, and (F) a comparison of multiple targets’ intensities before and after optimization. See also Figure S1.

Post-optimization, enhanced details are evident in the images, as demonstrated in Figure 3B. Figure 3C quantifies this enhancement, showing the targets’ intensities before and after optimization.

Further experiments were conducted using a GGD as the scattering medium, yielding analogous outcomes. The difference between the images captured before and after optimization is apparent from Figures 3D and 3E. The optimization process successfully enhanced the visibility of previously undetectable fluorescent beads, as illustrated in Figure 3F.

For these experiments, we selected a correction factor $\left(t_c\right)$ of 0.40 and ran the optimization over 400 generations. The resultant images were normalized to the maximum intensity value obtained post-optimization and cropped to focus on the regions of interest. Additionally, an experiment was repeated five times with a GGD over 300 generations. The intensity ratio after and before optimization (enhancement) and 95$\%$ confidence interval (CI) was found to be 2.48 $\pm$ 0.19, as shown in Figure S1.

BG beam achieves higher enhancement

We further demonstrate that utilizing BG beams can achieve higher enhancement in wavefront shaping applications. BG beams were generated using an axicon, and their intensity profile is displayed in Figure S2. Initially, both Gaussian and BG beams were employed to focus light at a predefined target through a scattering medium.

The experimental parameters, including the number of generations, mutation rate, and number of controlled input channels (SLM superpixels), were consistent for experiments utilizing both beams. As illustrated in Figure S3, the BG beam achieved an enhancement approximately 3.13 times higher than that of the Gaussian beam. Here, enhancement is defined as the ratio of final intensity obtained after optimization to the average intensity found before optimization. Similar results were observed with the alternative setup in which a second SLM was used to generate the BG beam (Figure S17).

Subsequent experiments, aimed to optimize multiple targets hidden behind scattering samples, demonstrated that both Gaussian and BG beams achieved enhancement, as shown in Figure 4. However, BG beam achieved a notably higher enhancement after undergoing the same number of generations. This is particularly evident in Figures 4C and 4F, where the BG beam not only achieved greater enhancement but also revealed targets that remained obscured even after optimization with the Gaussian beam. These targets, visible only after optimization with the BG beam, are highlighted by white rectangles in Figure 4F. The comparison of intensity profiles along the white dashed lines, shown in the insets, indicates that the BG beam consistently achieved higher intensities compared with the Gaussian beam.

Figure 4.

BG beam achieves higher enhancement

(A–F) The first column presents fluorescence intensity before optimization. The second and third columns display the results after optimization with Gaussian and BG beams, respectively. (A) Before and (B) after optimization with Gaussian beam, (C) fluorescent target after optimization with BG beam (parafilm), (D) before and (E) after applying the method with Gaussian beam, (F) multiple targets become apparent after optimization with BG beam (glass diffuser). Intensity profiles plotted along the white dashed lines are shown as insets. See also and Figures S2–S4.

Furthermore, an experiment to optimize a fluorescent target hidden behind the scattering medium (GGD) utilizing both beams was repeated five times. The optimization process was run over 300 generations each time. It can be seen from Figure S4F that for each experiment, the BG beam achieved higher intensity than the Gaussian beam. The ratio of the maximum intensities achieved by these beams and the 95$\%$ CI was found to be 2.78 $\pm$ 0.69. After optimization, the SNR was found to be 2.05 times higher with the BG beam than with the Gaussian beam, based on the average of five trials. Subsequently, the experiment was extended to run over a greater number of generations. The experiment with the BG beam was run for 1,800 generations and was then repeated with the Gaussian beam. The experiment with the Gaussian beam was run for an additional 500 generations. However, the BG beam demonstrated a consistently higher intensity trend compared with the Gaussian beam, as shown in Figure S5.

BG and Gaussian beams’ performance with increasing scattering media thickness

Our experiments were extended to include pig skin tissue to emulate human skin scattering.

For this experiment, the fluorescent beads were directly placed on the skin sample. The results obtained with 2- and 3-mm-thick pig skin are shown in the first and second rows of Figure 5, respectively. The performance disparity between the Gaussian and BG beams became more pronounced as the tissue thickness increased. Figures 5G and 5H display the progression of intensity and entropy over generations for both beams, respectively. As the tissue thickness increased, the ratios of maximum intensity and entropy achieved by the BG and Gaussian beams also increased. Figure S6 further demonstrates that the intensity ratio escalated with increasing thickness of the scattering medium (parafilm layers), underscoring the advantages of utilizing BG beams for thicker tissue samples.

Figure 5.

Comparison of BG and Gaussian beams’ performance with increasing scattering media thickness

(A–H) Top and bottom rows present results with 2- and 3-mm-thick pig skin samples, respectively. (A) Before and (B) after optimization with Gaussian beam, (C) fluorescent targets after optimization with BG beam, (D) before and (E) after optimization with Gaussian beam, (F) multiple targets enhanced after optimization with BG beam, (G) intensity and (H) entropy improvement over generations by both beams. The circles are the result fit by line or dashed line. See also Figure S6.

Preserving information about relative intensity

We also demonstrate that the method can preserve information about the relative intensity differences among targets.

Initially, the intensity differences between targets were recorded without any scattering medium. As depicted in Figures 6A and 6D, target 1 exhibited higher intensity compared with target 2, with a ratio of approximately 1.48. When a scattering medium (parafilm) was introduced to the excitation path, information about relative intensity was obscured, as shown in Figures 6B and 6E. However, after optimization, the relative intensity information was successfully retrieved, with target 1 again exhibiting higher intensity than target 2, with a ratio of approximately 1.5, as shown in Figures 6C and 6F.

Figure 6.

Preserving information about the relative intensity differences

(A–F) (A) Intensity differences between targets without any scattering sample, (B) after hiding targets behind a scattering medium, and (C) simultaneously optimized targets. Intensity profiles of the targets (D) without any scattering medium, (E) with scattering medium, and (F) after optimization. See also Figure S7.

Another example using a GGD is shown in Figure S7. The experiment was run over 300 generations and repeated five times. The targets and their intensity profiles without scattering medium are shown in Figures S7A and S7D, respectively. Figures S7B and S7C show the targets before and after optimization through the scattering medium, and Figures S7E and S7F show their corresponding intensity profiles. The difference between the intensities of target 1 $\left(I_{t1}\right)$ and target 2 $\left(I_{t2}\right)$ is defined as $\Delta I=I_{t1}-I_{t2}$. The normalized $\Delta I$ across the five experiments is shown in Figure S7G. The 95% CI was found to be 0.53 ± 0.09, with the interval entirely above 0, confirming that target 1 consistently exhibited higher intensity than target 2.

Locating targets after movement

We further demonstrate the robust tracking ability of our method, capable of locating and optimizing targets even after intentional movement.

Fluorescent beads were placed on a stage programmed to move in both the $x$ and $y$ directions every 100 generations over a total of 300 generations. The results of this experiment are illustrated in Figure 7. Despite the shifts in position during the optimization process, the method effectively located and optimized the targets through the scattering medium (parafilm), confirming its efficacy in tracking changes in target positions.

Figure 7.

Locating targets after movement

Reference lines (dashed white lines) indicate the initial positions of the targets. Hidden fluorescent targets optimized across three different locations (Positions 1, 2, and 3). See also Figure S8 and Table S1.

Additionally, the Pearson correlation coefficient was calculated to compare the regions of interest after every 100 generations to ensure the same targets were detected after movement (see Figure S8; Table S1).

Optimizing fluorescent targets through moth antenna and wing

We extended the application of our method to act as a sensing tool within biological specimens, particularly useful for structures traditionally challenging for available microscopic techniques due to pigmentation. We applied our method to localize and optimize fluorescent targets within the wings and antennae of the North American hawk moth (Manduca sexta).

Tracking fluorescent signals across structures such as moth antennae reveals vital information regarding physiological processes that influence behaviors such as host seeking, mating, and oviposition.⁶⁴ Conventional microscopy techniques, such as confocal microscopy, are generally limited to transparent structures or require the clearing of pigmented tissues.^64,65 Our method successfully locates and enhances fluorescent signals through opaque moth antennae and wings without requiring any tissue clearing.

For the experiment, the moth was cold-anesthetized and injected in the abdomen with a fluorescent solution. Figures 8A and 8B show the moth and the injection site, respectively. Images of the antenna and wing regions where fluorescence was detected are displayed in Figures 8C and 8D, respectively. Before and after optimization images of fluorescent targets through antenna are shown in Figures 8E and 8F, and through wing vein in Figures 8G and 8H.

Figure 8.

Optimizing fluorescent targets through moth antenna and wing

(A) Image of the moth used in the experiment.

(B) Microscopic image of the injection site in the abdomen.

(C–H) Images of (C) antenna and (D) wing sections where fluorescent signals were optimized. Overlays of white light and fluorescent images of the moth antenna (E) before and (F) after optimization. Overlays of fluorescent targets and white light images of the wing (G) before and (H) after optimization. See also Figure S9.

Discussion

In this study, we combined wavefront shaping with entropy-based image processing to demonstrate that key details, such as intensity difference and distribution among targets, can be preserved. Moreover, the method has shown the ability to locate and enhance targets even when they shift positions during the optimization process. By employing non-diffractive BG beams, we achieved significantly higher enhancement compared with Gaussian beams, as illustrated in Figures 4 and 5. The unique propagation characteristics of BG beams, which maintain their spatial structures deep within scattering media, increase the SNR and contribute to this enhanced performance.^66,67

During optimization, the number of non-zero elements in the thresholded image $\left(G\right)$ may vary with each generation, allowing the discovery of new targets that were not detected initially. The exceptional propagation properties of BG beams, coupled with dynamic updates to the thresholded image, facilitate increased enhancement and the optimization of a greater number of targets.

Additionally, we present simulation results to further analyze the recovery of relative target intensities by the optimization process. The speckle pattern is simulated using a transmission matrix with random amplitudes and phases.⁶⁸ Here, fluorescent targets are modeled as matrices with Gaussian intensity distributions dispersed within a larger sparse matrix, and the sparse matrix is multiplied by the speckle to mimic the fluorescent signal. Figure S10A shows that multiple targets were enhanced after optimization. As shown in Figure S10B, the original intensity order of the targets (without scattering, black) was distorted by scattering (red) and was restored after optimization (blue). Furthermore, Figure S10C presents the relationship between enhancement and initial intensity, with a Spearman’s $\rho =0.2$, indicating weak correlation and demonstrating that the optimization process is effective across targets of varying initial intensities.

Our method has been primarily applied to optimizing multiple targets, as demonstrated in our experimental results. However, it can be adapted for single-target optimization by adjusting the objective function to entropy minimization from maximization. Figure S11 shows the simulation result when the objective function is changed from maximizing to minimizing entropy. With entropy minimization, the algorithm tends to converge to the brightest target found before optimization.

Optimizing multiple targets may reduce individual target intensity due to increasing the intensity of multiple modes of the scattering sample’s transmission matrix at once²²; nevertheless, detecting signals from multiple sources is crucial in many applications, such as studying biological systems and diagnosing diseases. Our method offers flexibility to optimize either multiple targets or a single target by simply adjusting the objective functions accordingly. This adaptability allows the method to cater to various specific requirements, extending its application to recognizing patterns and more complex imaging scenarios. Figure S12 shows simulated results for ring and square patterns before and after optimization.

Moreover, detecting fluorescent signals in a reflection setup is crucial for practical and non-invasive applications. We tested our method using reflection geometry, where the fluorescent signal is detected by a camera (scientific complementary metal oxide semiconductor (sCMOS), CAM2) from the same side as the incident beam. Figure S13 describes the experimental setup, and Figure S14 shows the reflected and transmitted signals before and after optimization through scattering media (GGD and parafilm). This confirms the method’s effectiveness in both transmission and reflection geometries.

Outlook and challenges

As we continue to develop and refine our imaging technique, a number of pivotal challenges and opportunities present themselves. These will not only test the scalability and adaptability of our approach but also determine its long-term viability and integration into existing medical and scientific frameworks.

Scalability and adaptation

Future research should focus on expanding the applicability of our method across a wider range of biological systems, including various tissue types and larger anatomical structures. This will involve overcoming physical and computational barriers that may arise as we scale the technique, ensuring it remains effective and practical for clinical diagnostics.

Comparative effectiveness

It is imperative to conduct comprehensive comparative studies against established imaging technologies such as optical coherence tomography and magnetic resonance imaging. These studies should evaluate not only the relative cost and effectiveness but also the ease with which our method can be integrated into existing medical workflows, ensuring it offers a tangible improvement over current options.

Stability and maintenance

The long-term stability of wavefront shaping in a clinical setting is crucial. Research should continue into the optimization’s durability and the potential need for recalibration, guaranteeing the method’s reliability for continuous and routine medical use.

Biocompatibility and safety

The biological impact of prolonged exposure to BG beams, particularly on sensitive or live tissues, must be thoroughly assessed. Understanding any phototoxic effects and establishing protocols to mitigate them will be essential for the method’s acceptance and success in clinical applications.

Automation and usability

Simplifying the operation of our imaging process and enhancing its automation will make the technology accessible to medical personnel who lack specialized training in optics. This will lower barriers to adoption and facilitate broader clinical use.

Broadening applications

Investigating the potential for non-medical applications, such as environmental monitoring and industrial non-destructive testing, could significantly broaden the market and utility of the technology, opening up new avenues for deployment.

Economic analysis

A detailed economic feasibility study will elucidate the cost implications of clinical implementation. This analysis is critical to understanding the economic viability for widespread adoption and will help identify any financial barriers to its deployment.

Reflection geometry enhancements

Given the promising results in both transmission and reflection geometries, further enhancing the method’s performance in reflection-based applications could greatly extend its utility in non-invasive diagnostic procedures.

Addressing these challenges and opportunities will not only enhance the capabilities of our method but also expand its practical applications, ensuring it meets the diverse needs of modern biomedical imaging. The continuous development and adaptation of this technology holds the potential to revolutionize the way we visualize and understand complex biological systems in medical fields and beyond.

In conclusion, we have introduced a versatile method capable of optimizing multiple fluorescent targets simultaneously, demonstrating significant improvements when combined with BG beams. The method’s ability to track and optimize the positions of targets after movement, and its effectiveness in various imaging configurations including reflection, makes it a powerful tool for biological imaging and biomedical diagnostics. Furthermore, the compatibility of our approach with existing microscopic systems offers a promising avenue for advancing medical diagnostics and research.

Limitations of the study

This method assumes a sparse distribution of targets, which requires a sparse matrix representation for optimization. Although this is well-suited for detecting sparsely labeled fluorescent targets, which is often desired in biological imaging, it can be extended to samples with a higher target density. However, for densely packed samples, the image must be segmented into smaller regions for individual region optimization. Figure S15 demonstrates this approach, where the algorithm optimizes smaller segments effectively, despite failing to optimize an entire dense sample at once.

It is important to note that the method allows targets to be moved any distance within the field of view and still be tracked. However, the optimization of targets requires 100 generations. Similar to other feedback-based wavefront shaping methods,^69,70 the speed is limited by the equipment, e.g., the SLM refresh rate. It is possible to speed up the process by using faster SLMs.

Resource availability

Lead contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Nazifa Rumman (rumman@uic.edu).

Materials availability

This study did not generate new unique materials.

Data and code availability

Data included in this manuscript and the supplemental information will be made available by the lead contact upon reasonable request.

Acknowledgments

P.B., E.F., A.D., and M.N. acknowledge the support by a grant from the Gordon and Betty Moore Foundation to the American Society for Cell Biology for the PAIR-UP Imaging Science Program. N.R. and M.N. acknowledge the support of the US Department of Energy (DOE) under grant No DE-SC0024676.

Author contributions

Conceptualization, N.R.; methodology, N.R. and T.W.; validation, N.R. and P.B.; formal analysis, N.R., P.B., and T.W.; investigation, N.R., P.B., and T.W.; writing, N.R., P.B., T.W., M.N., E.F., T.A.S., and A.D.; visualization, N.R. and A.M.; supervision, T.A.S., and M.N.; all authors discussed the results and commented on the manuscript.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Software and algorithms
MATLAB	The MathWorks, Inc	https://www.mathworks.com
Python (Anaconda)	Anaconda, Inc.	https://www.anaconda.com

Experimental model and subject details

Adult Manduca sexta (Lepidoptera: Sphingidae) were obtained from a laboratory colony maintained at Case Western Reserve University (Cleveland, OH, USA). Moths were reared from larvae under controlled environmental conditions (25 $\pm$ 1°C, 16:8 h light:dark photoperiod, 60–70% relative humidity) on an artificial wheat germ–based diet until pupation, after which pupae were maintained under the same environmental conditions until adult eclosion. Sex was determined at the pupal stage by examination of the abdominal tip. Eclosed adults were kept in a plexiglass cage with access to a 25% sucrose solution. Insects are not regulated under the Institutional Animal Care and Use Committee (IACUC) guidelines; however, all handling and experimental procedures followed accepted ethical standards for invertebrate research at Rensselaer Polytechnic Institute.

For the experiment, the moth was cold-anesthetized and injected in the abdomen with a fluorescent solution prepared by diluting approximately 20 $\mu l$ of 2% solids (0.04 $\mu m$ diameter fluorescent (633/720) carboxylate-modified microspheres) in 200 $\mu l$ of deionized water.

Pig skin was obtained from a local butcher shop. The tissue was from Sus scrofa domesticus (domestic pig). No live animal procedures were conducted here.

Method details

Defined parameters for the optimization algorithm (SBGA)

The number of generations used for the experiments presented here was 300 unless stated otherwise. The initial population consisted of 30 phase masks and the number of offsprings created in each generation was 15. The phase masks were represented by a matrix $H\times W$ where the number of SLM superpixels was $H=W=130$ and the mutation rate was $2.7\%$. All the parameters defined for the experiments comparing the performance of BG and Gaussian beams were held consistent.

Thresholding

The correction factor $\left(t_c\right)$ is used to determine the threshold value $\left(\tau \right)$. The correction factor needs to be chosen such that $w_{\min }<\tau \le \frac{w_{\max }}{2}$. The minimum intensity level $\left(w_{\min }\right)$ can be obtained from the background image. Figure S16A presents the range of correction factors with different $w_{\max }$ values, as observed in our experiments. For example, from Figure 2A, $w_{\max }$ was determined to be 218, indicating that $t_c$ would range from 0.31 to 0.50 (from Figure S16A). Figures S16B and S16C display the thresholded images when $t_c=0.2$ and $t_c=0.8$, respectively, resulting in $\tau <w_{\min }$ and $\tau >\frac{w_{\max }}{2}$. This causes the number of non-zero elements (nz) to be either too large, which fails to separate target and background pixels, or too small, which fails to locate all targets. Figure S16D shows the thresholded image with $t_c=0.4$, which was used for the experiment (Figure 2). While the thresholding value was experimentally determined in this work, an adaptive approach could be used in future applications.

Additional experiment with an alternate setup

An alternate experimental setup with two SLMs was implemented to focus light through a scattering medium using Gaussian and BG beams. In this setup, the BG beam was generated before the focusing lens (L1) by encoding the transfer function of an axicon as a hologram on the first SLM.⁷¹ When using the Gaussian beam, the SLM (SLM1) acted as a mirror and did not introduce any phase modulation. The second SLM (SLM2) was used for wavefront shaping (Figure S17A).

Experiments were carried out over 300 generations with both beams to create a single focus through a ground glass diffuser. This experiment was repeated three times, each at a different target position in the scattering medium. The intensities at the defined target positions were recorded across generations, and the average intensity progression of three experiments is shown in Figure S17B. It can be observed that BG beam resulted in higher enhancement.

Quantification and statistical analysis

To demonstrate the reproducibility and consistency of the experiments, selected experiments were repeated, and the 95% confidence interval (CI) was estimated (Figures S1, S4, and S7).

To compute the 95% CI, the standard deviation (SD) was found from the mean of the data points obtained from the repeated experiments. The standard error of the mean (SEM) was calculated as:

$$\text{SEM}=\frac{\text{SD}}{\sqrt{n}}$$ (Equation 5)

where $n$ is the number of experiments. The 95% CI was calculated as:

$$\text{CI}=\text{Mean}\pm t\times \text{SEM}$$ (Equation 6)

where $t$ is the $t$-score corresponding to a 95% confidence level, obtained from the Student’s $t$-distribution with degrees of freedom $df=n-1$. For $n=5$ experiments, $t$ was found to be 2.776.

Enhancement of fluorescent targets is defined as the the ratio of the intensity after optimization $\left(I_{aft}\right)$ to the intensity before optimization $\left(I_{bef}\right)$. For results presented in Figure S1, enhancement was calculated individually for all targets, as shown in Figure S1E. The mean enhancement of the targets within each experiment was then computed and used to estimate the 95% CI, as shown in Figure S1F.

Additionally, to evaluate correlation between enhancement and initial target intensity, Spearman’s rank correlation coefficient $\left(\rho \right)$ was computed (Figure S10). Spearman’s $\rho$ measures the strength of the monotonic relationship between two variables, and Spearman’s $\rho$ close to zero indicates weak or no correlation. It is calculated as:

$$\rho =1-\frac{6\sum d_i^2}{n\left(n^2-1\right)}$$ (Equation 7)

where $d_i$ is the difference between the ranks of the two variables for the $i$-th observation, and $n$ is the total number of observations.

Published: August 25, 2025