2.1.

System Overview

The wearable OCTA probe with extended DOF proposed in this study adopts the main structure of our previous wearable probe,¹⁸ shown in Fig. 1(a), in addition to the existing three key components (collimator, MEMS mirror, and objective lens), the probe incorporates DOE that can work with the objective lens to generate NB as described in our previous work.²⁴ Figure 1 illustrates the generation of NB using a DOE. By manipulating the beam phase with DOE, multiple foci are generated along the optical axis within the vicinity of the objective lens.²³ These foci collectively form an NB with extended DOF. Each axial focus corresponds to one phase distribution, and the final phase loaded onto the DOE is the superposition of all foci’ phase distributions, as depicted in Fig. 1(b). Through optimization of the initial phase and pixel position of each axial focus, cross-talk between phase distributions corresponding to different focal points is suppressed. This ensures uniform axial intensity of the NB generated by the DOE and suppresses the generation of sidelobes, as illustrated in Fig. 1(c).

Fig. 1

Experimental system configuration and the principle of NB. (a) Setup of the imaging system and a detailed optical configuration of the wearable OCTA probe with extended DOF. SLD: super luminescent diode; MEMS: micro-electromechanical systems. (b) DOE phase pattern for an NB composed of multiple phases to generate m foci. (c) Schematic diagram of generating an NB. (d) Diameters of the used GB and $450\mu \mathrm{m}$ NB along the axial position. (e) Relative intensity of the used GB and $450\mu \mathrm{m}$ NB along the axial position.

Based on our previous finding, imaging the mouse brain with an FOV of about 3 mm requires at least $400\mu \mathrm{m}$ DOF.²⁴ Therefore, the target DOF of the NB used in this experiment was set to $450\mu \mathrm{m}$. The number of required foci is determined by the target DOF, based on the principle that the distance between adjacent focal points should be less than the Rayleigh length (RL), typically set to 0.5 to 0.8 times RL.²³ The Rayleigh length is calculated as $\mathrm{RL}=(\lambda /n)f^2/(\pi r^2)$, where $r$ is the beam waist radius, $n$ is the refractive index, $f$ is the focal length, and $\lambda$ is the center wavelength. In our design, we used a Gaussian beam (GB) diameter of 4.6 mm, resulting in a Rayleigh length of $\sim 18.47\mu \mathrm{m}$. Based on this calculation, we determined that 49 focal points arranged in a $7\times 7$ grid would be sufficient to achieve the desired $450\mu \mathrm{m}$ DOF, ensuring uniform intensity distribution across the depth range with appropriately spaced focal points.

After determining the number of focal points, we found that overlaying the phases of multiple foci leads to uneven axial intensity. To address this, the positions of the foci need to be optimized. We calculate the optimized axial intensity distribution using Fresnel diffraction and further adjust the spacing between adjacent foci based on the current intensity distribution. After this iterative optimization process, we obtain a beam with uniformly distributed axial intensity.

The DOE used in this study features an effective optical area of $1\mathrm{cm}\times 1\mathrm{cm}$, containing $1000\times 1000\text{pixels}$ with a pixel size of $10\mu \mathrm{m}$. The DOE has a physical diameter of 12.7 mm, a thickness of $500\mu \mathrm{m}$, and is mounted in a custom-designed slot with a $700\mu \mathrm{m}$ width for easy installation. The DOE was fabricated using four rounds of lithography, and after fabrication, it was cut into a circular shape with a diameter of 12.7 mm and was inserted into the pre-designed slot in the probe, as shown in Fig. 1(a).

The wearable probe with extended DOF and our homebuilt spectral domain OCT (SD-OCT) system are shown in Fig. 1(a). The light source is a broadband super luminescent diode (SLD-371HP3, Superlum, $850\pm 25\mathrm{nm}$, 15 mW). A $2\times 2$ coupler (BXC45, Thorlabs, Newton, United States) was used to divide the light into the sample arm and reference arm. The reflected light from the two arms was directed to a home-built spectrometer with 0.05 nm resolution, 2048 pixels, and a maximum speed of 70 kHz.

In our customized wearable probe, the beam from the optical fiber was collimated by a collimator and then directed to a two-axis MEMS scanning mirror (A7B1.1, Mirrorcle Tech, Richmond, California) which was put on the front focal plane of an achromatic doublet lens (MAD303-B; diameter, 12.7 mm; focal length, 19 mm) for telecentric scanning. The collimator used is a fiber-coupled fixed-focus collimator (F260APC-850, Thorlabs) with a waist diameter of 3.32 mm. The MEMS scanning mirror has a reflective diameter of 3.6 mm and a maximum tilt range of $\pm 7\mathrm{deg}$.

The collimator, the MEMS mirror, and the objective are integrated through a customized lightweight one-piece 3D-printed mount which is specifically designed and precisely machined to simplify assembly and alignment of the components as well as removal and replacement. This one-piece 3D-printed mount enhances the stability of the probe during mouse movement and minimizes motion artifacts during imaging. The size and weight of this probe increased a little compared with the previous one due to the introduction of DOE, with dimensions of $37\mathrm{mm}\times 34\mathrm{mm}\times 15\mathrm{mm}$, and weighs 10 g. The beam diameter and relative intensity shown in Figs. 1(d) and 1(e) were measured by a microscope system together with a beam profiler with $10\mu \mathrm{m}$ as the axial scanning step size (experimental setup can be found in our previous work²⁴). The NB with the addition of the DOE can maintain a spot size smaller than $8\mu \mathrm{m}$ within an axial range of $450\mu \mathrm{m}$. By contrast, although the traditional GB has a smaller spot size near the focal plane, it rapidly expands along the axial range, only able to maintain a size smaller than $8\mu \mathrm{m}$ within an axial range of $160\mu \mathrm{m}$. Similarly, the intensity of the GB decays rapidly with axial distance, whereas the intensity of the NB remains relatively stable over a larger distance.

Experimental measurements showed that after introducing the DOE, the power in the sample arm was $\sim 57\%$ of the original power. To address the potential impact of sidelobes and insertion loss introduced by the DOE on system performance, we optimized the NB design to balance DOF extension and energy concentration. Figure 2 shows the beam profiles at different axial positions. Six positions with a step size of $80\mu \mathrm{m}$ were selected to demonstrate the $400\mu \mathrm{m}$ axial distance in the middle of the beam. It can be observed that at these axial positions, only a maximum of 8.5% of the energy is dispersed into the sidelobes near the proximal end, with less than 6% energy distributed in the sidelobes at other positions. Most of the energy is concentrated in the central main lobe. Figure 2 demonstrates that this NB has a high energy utilization rate, which is more conducive to imaging biological tissues compared with Bessel beams with a higher proportion of sidelobe energy.^26–28

Fig. 2

Profile of the spot $(x-y)$ and the proportion of sidelobes at different axial positions.

The axial resolution was evaluated by measuring the signal of a mirror, shown in Fig. 3, the full width at half-maximum was measured to be $15\mu \mathrm{m}$. To evaluate the lateral resolution, we imaged the 1951 USAF resolution target. Before the introduction of the DOE, the smallest lines that can be resolved by GB are group 6, element 6. This corresponds to 114 line pairs (lp/mm) and a lateral resolution of $\sim 4.4\mu \mathrm{m}$. After incorporating the DOE, the lateral resolution of the system slightly decreased compared with the resolution of the GB at the focal plane. It could resolve the 6th group, 5th element, corresponding to $102\mathrm{lp}/\mathrm{mm}$, and a lateral resolution of $\sim 4.9\mu \mathrm{m}$. The NB design maintains a relatively stable lateral resolution over the entire axial depth range. Although there is a slight decrease in lateral resolution below $4.9\mu \mathrm{m}$ at deeper locations, the lateral resolution remains within acceptable limits with variations remaining below $8\mu \mathrm{m}$ over the entire $450\mu \mathrm{m}$ depth range.

Fig. 3

Performance of the probe. (a) Experimental estimation of the axial resolution. (b) Experimental estimation of the lateral resolution.

As demonstrated in Fig. 1(b) of our previous work,²⁴ the NB exhibits a significant advantage in terms of extended DOF compared with the GB. The $x-z$ profile and cross-sectional views of the beams reveal that while the NB maintains stable lateral resolution over the extended DOF, the GB, although it offers higher resolution within a shorter DOF, experiences a rapid degradation in resolution as the depth increases. Consequently, although the NB achieves a higher resolution within the extended DOF range, its lateral resolution is slightly reduced compared with the GB at the focal plane. This advantage is particularly beneficial for imaging biological samples with non-flat surfaces, such as the mouse brain, in large FOV imaging.

2.2.

Animal Preparation

All procedures involving mice were approved by the Institutional Animal Care and Use Committee of Tsinghua University. Wild-type mice (C57BL/6, 9 weeks to 3 months old; weight, 20 to 30 g) were used in all the experiments.

The craniotomy surgery was performed in the following manner: Initially, mice were anesthetized with isoflurane (3% for induction, 1.5% during surgery). Subsequently, a toe pinch test was carried out to ensure the depth of anesthesia. After confirming the mouse’s proper anesthesia, it was carefully positioned on a stereotactic frame while maintaining its body temperature with a heating pad. Before commencing the surgery, the ophthalmic ointment was applied topically to safeguard the corneal surfaces from drying and potential damage due to extended exposure to the illuminating light source. A scalp incision was made, followed by conducting a craniotomy using a drill.²⁹ Once the skull was carefully removed, the brain was covered with 2% agarose and then a cover glass (with a thickness of 0.17 mm and a diameter of 6 mm) was affixed to the skull to minimize any motion of the exposed brain. In addition, a custom aluminum head post was securely attached to the skull using dental cement.

2.3.

Data Acquisition and Processing

In this work, we employed a stepwise raster scanning procedure to collect volumetric data. The slow scanner ($y$) was driven by a step waveform with a total of 800 steps. At each step, five consecutive B-scans were acquired to analyze dynamic flow signals. Each of these B-scans consisted of 1024 A-lines in the fast-scanning direction. Adjacent B-scans were paired for blood flow extraction at each scanning step $y$. The original spectral interference fringe signal $S$ $(k,x,t)$ underwent a Fourier transformation along the wavenumber direction, resulting in the backscattered profile $C_{\mathrm{OCT}}$ $(z,x,t)$ in the depth domain. This profile included both amplitude $I$ and phase $\mathrm{\Phi }$ information:

The cross-sectional angiogram was then created by subtracting the amplitude component $I$ $(z,x,t)$ between paired B-scans:

Then, the OCTA signals at each step $y$ were averaged to improve flow contrast. Performing this process for all $y$ values, OCTA volumetric data containing microvasculature flow information can be obtained. The enface angiograms are obtained by performing maximum intensity projection along the axial direction.

3.1.

OCT Structural Imaging Performance

The GB and NB were tested with $5\mu \mathrm{m}$ polystyrene (PS) beads (XFJ100, XFnano) embedded in ultrasound gel (Ultrasonic Coupling, Cofoe). The phantom with beads concentration around $2\times {10}^5/{\mathrm{mm}}^3$ was degassed with a centrifuge (10 min at 15,000 rpm, H1850, Cence). During the experiment, the probe is fixed on a bracket with the sample placed underneath. The integration time of the spectrometer was set to $20\mu \mathrm{s}$, with 1024 A-scan in one B-scan. As shown in Fig. 4(a), the B-scan image acquired using the GB demonstrates recognizable beads only within a range of $\sim 160\mu \mathrm{m}$ near the focal plane, indicated by the red dashed line. This means that the GB maintains a lateral resolution above $8\mu \mathrm{m}$ only within this axial range, with areas farther from the focus displaying significant defocusing. By contrast, the NB provides a much wider range of distinguishable particles, maintaining a lateral resolution above $8\mu \mathrm{m}$ over a $450\mu \mathrm{m}$ axial range, achieving a 2.8-fold increase in DOF. As shown in Fig. 4(b), the NB allows for clear particle imaging across a larger depth range, with regions well above the red dashed line still displaying sharp and detailed features. This demonstrates that the NB can maintain high-resolution imaging over a significantly extended depth range.

Fig. 4

B-scan imaging results of $5\mu \mathrm{m}$ polystyrene microspheres with wearable probe using GB (a) and $450\mu \mathrm{m}$ NB (b). Scale bars at bottom left, $300\mu \mathrm{m}$.

To better illustrate the differences between the two and the advantages of the NB, a 3D scan of the sample was performed with a lateral FOV of $3\mathrm{mm}\times 2.6\mathrm{mm}$, with 1024 sampling points on the fast axis and 800 in the slow axis. The volumetric visualization of the 3D data is shown in Fig. 5. The imaging results of GB are shown in Figs. 5(a)–5(c). Figure 5(a) shows the overall effect, and the red box in it is zoomed in as Fig. 5(b), where the particles at the top are clearly imaged with high resolution, but the resolution rapidly decreases with depth, and the particles at the bottom are significantly widened due to beam defocus. By contrast, the imaging results using the $450\mu \mathrm{m}$ NB show no defocus phenomenon, as depicted in Figs. 5(d)–5(f). In Fig. 5(e), an enlarged view of the red box in Fig. 5(d), high-resolution imaging is maintained throughout the entire depth range, with particle sizes remaining consistent without the widening observed in Fig. 5(b). Figures 5(c) and 5(f) show the enface results of the volumetric data obtained using GB and NB, respectively, further highlighting the defocus phenomenon of the GB outside the DOF and the long focal depth advantage of the NB.

Fig. 5

3D imaging results of $5\mu \mathrm{m}$ polystyrene microspheres with wearable probe using GB and $450\mu \mathrm{m}$ NB. (a) 3D imaging by GB. (d) 3D imaging by $450\mu \mathrm{m}$ NB, the red box in panels (a) and (d) is zoomed in as panels (b) and (e). (c) and (f) En face $(x-y)$ images of the 3D volumetric data acquired by GB and $450\mu \mathrm{m}$ NB, respectively.

3.2.

OCTA Imaging Performance

The connection between the probe and the mouse brain was described in our previous work.¹⁸ After wearing, the GB focus was placed at the axial position corresponding to the center of the imaging FOV. The imaging results are shown in Fig. 6. We took 800 B-scans in the slow scanner direction, and at each step, we repeated the B-scan five times; each of these B-scans consisted of 1024 A-lines in the fast-scanning direction, and the FOV was set to be $2.5\mathrm{mm}\times 2\mathrm{mm}$. Figure 6(a) shows the enface result of the OCT data. Two positions were selected in the image (indicated by the red and yellow dashed lines), and corresponding OCT cross-sectional images are presented in Figs. 6(d) and 6(g). In Fig. 6(d), it can be observed that there is a height difference along the selected line. The height difference along this line is $\sim 200\mu \mathrm{m}$. However, the maximum height difference was measured from the entire OCT 3D point cloud, representing the difference between the highest and lowest points across the entire OCT 3D surface, which was found to be $385\mu \mathrm{m}$. The GB could only maintain a resolution better than $8\mu \mathrm{m}$ within an axial range of $160\mu \mathrm{m}$, which is insufficient to cover the height difference of the sample surface; therefore, an obvious defocus phenomenon (the upper right corner position) can be observed in the GB-OCTA imaging result, shown in Fig. 6(b). After introducing the DOE, the wearable probe could maintain lateral resolution better than $8\mu \mathrm{m}$ in $450\mu \mathrm{m}$, which exceeds the maximum height difference of the sample surface. Therefore, as shown in the NB-OCTA imaging result in Fig. 6(c), clear imaging could be achieved throughout the entire FOV without defocusing issues.

Fig. 6

Imaging performance of the probe. (a) OCT image of the mouse brain, FOV, $2.5\mathrm{mm}\times 2\mathrm{mm}$, scale bar at bottom left, $500\mu \mathrm{m}$. (b) GB-OCTA image of the same region as panel (a). (c) NB-OCTA image of the same region as panel (a). Cross-sectional images of the red dash lines in panels (a)–(c) are shown in panels (d)–(f). Cross-sectional images of the yellow dash lines in panels (a)–(c) are shown in panels (g)–(i).

The advantages of NB-OCTA can also be observed from the comparison of the cross-sectional images. As shown in Figs. 6(e) and 6(f), the cross-sections represent the OCTA results at the positions corresponding to the red dashed lines in Figs. 6(b) and 6(c). The blood vessels are labeled by the blue lines in Figs. 6(e) and 6(f) are within the DOF of GB, thus achieving high resolution and signal-to-noise ratio (SNR) in both GB and NB imaging results. However, the blood vessels indicated by the red arrows in Fig. 6(f) are outside the GB focal range, thus only exhibiting high resolution and SNR in NB-OCTA. The clarity of the signal at the same position in Fig. 6(e) is significantly weaker than in Fig. 6(f). In addition, the contrast-to-noise ratio (CNR) and SNR were calculated using the signal intensity and background intensity across the entire enface image, rather than selecting a specific region. Higher CNR helps to distinguish blood vessels from surrounding tissue, whereas higher SNR improves image clarity and visibility of details, aiding in the evaluation of vascular connectivity. In Fig. 6(b), $\mathrm{CNR}=20.57\mathrm{dB}$ and $\mathrm{SNR}=22.84\mathrm{dB}$; in Fig. 6(c), $\mathrm{CNR}=21.95\mathrm{dB}$ and $\mathrm{SNR}=25.81\mathrm{dB}$, both demonstrating better performance of the NB.

The GB-OCTA and NB-OCTA enface images were first normalized. A threshold was then applied to generate binary images to differentiate blood vessels from the background. The threshold was selected based on the grayscale pixel values of the enface images and empirical observation. Regions corresponding to blood vessels, with higher intensity than the threshold, were assigned a value of 1, whereas regions corresponding to the background, with lower intensity than the threshold, were assigned a value of 0. This binary vessel map was represented as a skeleton map ($M$). $\overline{I(x,y){|}_{M(x,y)=1}}$ is the mean value of the intensities of the pixels that corresponded to the skeleton map in the enface OCTA image, $\overline{I(x,y){|}_{\mathrm{Bck}}}$ represents the average intensity of pixels in the background (tissue) area of the enface image, and ${\sigma }_{I(x,y)|\mathrm{Bck}}$ is the standard deviation of the background signals.

In the experiment described above, the FOV was $2.5\mathrm{mm}\times 2\mathrm{mm}$. This time, the orientation of the wearable probe was kept unchanged, the FOV was expanded by 20% to image a region of $3\mathrm{mm}\times 2.4\mathrm{mm}$, and the acquisition scheme remained the same at $1024\times 800\times 5$. Due to the enlargement of the imaging field, the maximum height difference increased from 385 to $425\mu \mathrm{m}$, and as a result, the GB-OCTA imaging shown in Fig. 7(b) exhibits more pronounced defocusing (as shown in the upper right corner of the image), whereas the $450\mu \mathrm{m}$ DOF of the NB can still cover the maximum height difference of $425\mu \mathrm{m}$. Therefore, the imaging result of NB-OCTA in Fig. 7(c) can still maintain high-resolution imaging without defocusing throughout the whole FOV.

Fig. 7

Imaging performance of the probe. (a) OCT image of the mouse brain, FOV, $3\mathrm{mm}\times 2.4\mathrm{mm}$, scale bar at bottom left, $500\mu \mathrm{m}$. (b) GB-OCTA image of the same region as panel (a). (c) NB-OCTA image of the same region as panel (a). Cross-sectional images of the red dash lines in panels (a)–(c) are shown in panels (d)–(f). Cross-sectional images of the yellow dash lines in panels (a)–(c) are shown in panels (g)–(i).

Similarly, the comparison of OCTA cross-sectional images shown in Figs. 7(e) and 7(f) also highlights the advantages of NB-OCTA, and the blood vessel labeled by the red arrow in Fig. 7(f) exhibits higher resolution and SNR in NB-OCTA. In Fig. 7(b), $\mathrm{CNR}=15.49\mathrm{dB}$ and $\mathrm{SNR}=19.77\mathrm{dB}$; in Fig. 7(c), $\mathrm{CNR}=16.37\mathrm{dB}$ and $\mathrm{SNR}=22.07\mathrm{dB}$, demonstrating better performance of the NB in the wearable probe.

To further demonstrate the advantage of the NB in the wearable probe, the same FOV of Fig. 7 is used, and the position of the beam focus is adjusted by changing the number of spacers in the probe. This experiment focuses the GB at three different axial positions ($z=50\mu \mathrm{m}$, $z=0\mu \mathrm{m}$, $z=-50\mu \mathrm{m}$), as shown in Figs. 8(b)–8(d). The enface image acquired with NB is shown in Fig. 8(a). The yellow, red, blue, and green boxes in Figs. 8(a)–8(d) are zoomed in Fig. 8(e), indicating axial positions of $-170\mu \mathrm{m}$, $-60\mu \mathrm{m}$, $60\mu \mathrm{m}$, and $130\mu \mathrm{m}$, respectively, for $450\mu \mathrm{m}$ NB-OCTA, high resolution is maintained at all four positions, whereas for GB-OCTA, no matter where the focus is, the DOF of the beam cannot cover the height difference of the sample surface ($425\mu \mathrm{m}$), so there will always be positions out of focus. This experiment provides a more comprehensive explanation of the necessity of using NB in the wearable probe.

Fig. 8

OCTA imaging of mouse brain ($3\mathrm{mm}\times 2.4\mathrm{mm}$) with wearable probe using GB and $450\mu \mathrm{m}$ NB. (a) Enface $(x-y)$ image acquired by $450\mu \mathrm{m}$ NB, scale bars at bottom left, $300\mu \mathrm{m}$. (b) Enface $(x-y)$ image acquired by GB with the focal position at $z=50\mu \mathrm{m}$. (c) Enface $(x-y)$ image acquired by GB with the focal position at $z=0\mu \mathrm{m}$. (d) Enface $(x-y)$ image acquired by GB with the focal position at $z=-50\mu \mathrm{m}$. The yellow, red, blue, and green boxes in panels (a–d) are zoomed in panel (e), indicating axial positions of $-170\mu \mathrm{m}$, $-60\mu \mathrm{m}$, $60\mu \mathrm{m}$, and $130\mu \mathrm{m}$, respectively.