Laser speckle contrast imaging (LSCI) utilizes the high coherence of laser to achieve label-free, fast, and high-resolution imaging of blood flow by analyzing the variations in dynamic speckle patterns [1–7]. Endoscopic LSCI can help surgeons to provide visualization of blood flow in internal tissue, organs, and the endovascular inner wall during minimally invasive surgery [8–14], aiding surgeons in making better-informed decisions.

Recent advancements in endoscopic LSCI have marked significant progress [9,10,15–18]. Zheng et al. first implemented dual-display laparoscopic LSCI in 2018 [15]. They coupled a commercial illumination source directly into the laparoscope and used cross-polarizers to reduce specular reflections. In the subsequent year, Heeman’s team first applied laparoscopic LSCI in human subjects, highlighting its clinical significance in detecting anastomotic leakage [9]. They introduced PerfusiX-Imaging and conducted extensive clinical trials of endoscopic LSCI [14,19,20]. By 2022, Kim et al. had developed a portable, smartphone-based LSCI endoscopy system for easy home use [16]. Concurrently, Peter Kim introduced ActivSight, the first FDA-approved endoscopic LSCI device [21], which is compatible with existing laparoscopic endoscopic systems and enables simultaneous imaging with white light and near-infrared (ICG or LSCI). They also conducted a considerable number of clinical trials to validate the feasibility of using endoscopic LSCI to detect tissue perfusion in surgical procedures [10–12,19]. In 2023, Guo et al. employed a random matrix description method to statistically separate single and multiple scattering components in dual-sensor laparoscopic LSCI, which provided perfusion information for both superficial and deep tissues [17]. In 2024, Markwalderk et al. developed an endoscopic LSCI based on the chip-on-tip CMOS in miniaturization [18].

However, the laser illumination in these studies mostly utilizes an endoscopic low-coherence light illumination solution, where the laser passes through multimode glass fiber bundles and is coupled with the laparoscope’s built-in illumination system [including light cones and built-in lighting glass fiber bundles, as shown in the red dotted box in Fig. 2(a)]. This results in three couplings between the laser and the multimode glass fiber bundles. The laser illumination produced has a small illumination angle, coherence loss, uneven illumination, and a low laser coupling efficiency (30%). The adverse effects of this laser illumination are specifically demonstrated as follows: the small illumination angle leads to a reduced imaging field of view; low coherence and low laser coupling efficiency reduce signal-to-noise ratio (SNR), and may cause a reduction in the linearity and the flow detection range (depending on the camera sensitivity and noise). Also, low-coherence laser illumination has worse blood flow change sensitivity, SNR, and signal-to-background ratio (SBR). Uneven laser illumination introduces different shot noise, dark noise, and quantization noise levels to the detector, causing inaccurate blood flow measurements [22,23]. Additionally, in LSCI, a greater number of photons reaching the detector are preferable under nonoverexposure conditions. Weak laser intensity diminishes the dynamic range of light intensity, thereby reducing LSCI’s sensitivity and SNR [22–25]. For endoscopic LSCI, due to the small aperture of the endoscope and optical system light attenuation, only a tiny fraction of the scattered photons from the sample reach the detector, which is especially impactful during minimally invasive surgery with long working distances, potentially leading to the loss of crucial blood flow information. Therefore, conventional endoscopic LSCI exhibits issues such as a small imaging field of view, limited flow detection range, low blood flow change sensitivity and SNR, inaccurate blood flow measurement caused by uneven laser illumination, and a short effective working distance. These issues severely limit the clinical application of endoscopic LSCI.

In this paper, we first conducted a mathematical analysis of the changes in coherence and speckle contrast of laser after passing through optical fibers. The laser transverse and longitudinal modes, coupled fiber length, and numerical aperture (NA) all have an impact on laser coherence and speckle contrast. We established an effective model for calculating the divergence angle of conical fibers (CFs). And using this model, we designed and fabricated CFs for laser illumination in endoscopic LSCI. Compared to coupling the laser through a multimode fiber (MMF) bundle into laparoscopy (MFBL), the laser passes through multimode glass fiber bundles and is coupled with the laparoscope’s built-in illumination system [including light cones and built-in lighting glass fiber bundles, as shown in the red dotted box in Fig. 2(a)] of conventional endoscopic LSCI; directly coupling laser into a CF of low NA and placing it at the end of the laparoscopic objective, can provide a large illumination field of view, high coherence, high uniformity, and high coupling efficiency laser illumination over short to long working distances. Through phantom and animal experiments, we found that using a low NA CF for laser illumination can expand the imaging field of view, enhance the SNR, allow for more sensitive detection of minute blood flow changes, extend the detectable flow range, and improve the SBR of endoscopic LSCI.

LSCI uses coherent laser to form speckle patterns, which blur more with faster movement, resulting in reduced speckle contrast. LSCI calculates the scatterer’s movement speed by measuring the speckle contrast [26], $$K=\frac{\sigma }{⟨I⟩}.$$(1)

The laser speckle contrast is not directly proportional to blood flow velocity $v$; it is instead related to the decorrelation time of the speckle intensity fluctuations ${\tau }_c$, which is assumed to be inversely proportional to the flow [26], $$v\propto \frac{1}{{\tau }_c}.$$(2)

The speckle contrast is related to ${\tau }_c$ through Eq. (3) [1], $$K^2=\beta \{\frac{{\tau }_c}{T}+\frac{{\tau }_c^2}{2T^2}[\exp \left(\frac{2T}{{\tau }_c}\right)-1\left]\right\}.$$(3)

In practical applications, $1/K^2$ is commonly used instead of $1/{\tau }_c$ to reduce the time loss associated with iterative calculations. When the integration time $T$ is much greater than the correlation time ${\tau }_c$ ($T/{\tau }_c>100$), the inverse of the square of the contrast can be approximated as being proportional to the flow rate [1,3], $$v\propto \frac{1}{K^2}.$$(4)

In this paper, we use a temporal averaging method to calculate $1/K^2$, with an exposure time of 5 ms and 100 frames.

According to the principles of LSCI in Sections 1 and 2.A, the dynamic range of speckle contrast is crucial for accurate blood flow measurement, as the high dynamic range of speckle contrast leads to a higher SNR [27]. We analyzed the changes in coherence and speckle contrast of the laser passing through a fiber.

The speckle contrast of the laser passing through a fiber is primarily determined by the light source’s coherence and the fiber’s waveguide properties [28–34]. The overall coherence of the light through an MMF is indicated by the sum of the modulus of the complex degree of coherence ($|\gamma |$) across its output surface [2,28,30,31]. $|\gamma |$ is characterized by a central peak $\gamma (r_1,r_2)=\gamma (\rho )=\frac{J_1(2\rho /r_c)}{\rho /r_c}$ and a surrounding complex structure (${\gamma }_{\mathrm{RC}}$, indicating residual coherence), where $r_c$ is the coherence radius, $J_1$ is the Bessel function of the first kind, and $\rho$ is the distance between the two points $r_1$ and $r_2$. The coherent radius [$r_c={\lambda }_0/(\mathit{\pi }\cdot \mathrm{NA})$] is influenced by the fiber’s NA and the light’s central wavelength ${\lambda }_0$. The averaged residual coherence is affected by the source bandwidth, NA, and fiber length (${\gamma }_{\mathrm{RC}}={[1+{(\alpha \tau /t_c)}^2]}^{0.25}$, where $t_c$ is the coherence time, $\tau =L{\mathrm{NA}}^2/(2nc)$ is the total modal dispersion, $\alpha$ is a parameter of one unit order of magnitude between the source bandwidth and the coherence time, $L$ is the length of the fiber, and $n$ is the refractive index of the core layer). These parameters together affect the laser’s coherence after passing through the fiber. Therefore, an increase in the coherence radius (low NA) combined with a higher residual base (narrower spectrum, shorter fiber, and low NA) indicates enhanced coherence in the laser output from the fiber.

Unlike the complex degree of coherence, the speckle contrast can be directly obtained through photography and computation. After passing through a fiber, the speckle contrast $C$ of laser is denoted as [32,33,35] $$C^2={\left[1+0.5\left(\frac{{\pi }^2\mathrm{\Delta }\lambda ·{\mathrm{NA}}^{4}L}{{\lambda }^2{n}_1^2}\right)\right]}^{-0.25},$$(5)where $\mathrm{\Delta }\lambda$ is the spectral width of the laser, NA is the numerical aperture of the fiber, $L$ is the fiber length, $\lambda$ is the central wavelength of the laser, and $n_1$ is the refractive index of the optical fiber core. After the laser passes through the fiber, the speckle contrast $C$ shows a negative correlation with the spectral width, NA, and fiber length, with the NA exerting the most significant impact.

In addition to the factors mentioned above, the number of transverse modes $M$ of the laser can lead to a decrease in speckle contrast by $1/\sqrt{M}$ [36]. For a multitransverse mode laser, each transverse mode is independent and incoherent [2,36]. The speckle contrast of a multitransverse mode laser passing through a fiber is essentially equivalent to the superposition of the speckle patterns from multiple single-transverse mode laser passing through the fiber. We have revised Eq. (1) to $$C^2={\left\{M^2\left[1+0.5\left(\frac{{\pi }^2\mathrm{\Delta }{\text{λ}\text{·}\mathrm{\text{NA}}}^{4}L}{{\lambda }^2{n}_1^2}\right)\right]\right\}}^{-0.5}.$$(6)

Therefore, given sufficient laser power, to achieve high coherence and speckle contrast laser illumination in the endoscope, we should use fibers with a low NA and short length to couple single transverse mode laser with narrow linewidths. In endoscopic LSCI, where light utilization is extremely low, the linewidth of the laser can be moderately increased to compensate for laser power, but maintaining a single transverse mode is essential.

Several researchers have analyzed the propagation of laser in conical optical fibers [37–41]. Pisano et al. adjusted the optical input angle of the fiber, changing the axial position of the light at the conical tip without moving the implant, thus stimulating [37] and detecting [38] different positions of the dorsal and ventral striatum in individual mice.

Patiño-Jurado et al. conducted ray-tracing and wave-optics propagation analysis, fabricated a CF with an NA of 0.88 [39], and proposed an analytical expression for calculating the NA of CFs [40]. Petrovic et al. studied the illumination position of different divergence angles under varying cone angles [41]. However, as far as we know, there is still a lack of a comprehensive theoretical model for calculating the divergence angle of CFs. The NA derived from the maximum input angle ${\theta }_{{\mathrm{in}}_{\max }}$ (where ${\theta }_{\mathrm{in}}$ is the angle between the LP wave vector and the optical axis of the fiber before entering the conical tip, ${\theta }_{{\mathrm{in}}_{\max }}$ is the maximum ${\theta }_{\mathrm{in}}$, for example, for an MMF with $\mathrm{NA}=0.22$, ${\theta }_{\mathrm{in}}=0°–8.7°$, and ${\theta }_{{\mathrm{in}}_{\max }}=8.7°$) is flawed, resulting in nonuniform (annular light) or incorrect angle laser illumination (the exit angle corresponding to ${\theta }_{{\mathrm{in}}_{\max }}$ is not necessarily the angle at which the NA is maximized) [39–41]. We will demonstrate this.

In this paper, we find that tracing all LP modes light within the fiber can accurately calculate the distribution of exit angles for CFs. First, the divergence angle of CFs is determined by ${\theta }_{{\mathrm{out}}_{{\mathrm{AM}}_{\max }}}$ [Fig. 1(a), where ${\theta }_{{\mathrm{out}}_{\mathrm{AM}}}$ is the angle between the outgoing light wave vector and the optical axis of the CF, ${\theta }_{{\mathrm{out}}_{{\mathrm{AM}}_{\max }}}$ is the maximum ${\theta }_{{\mathrm{out}}_{\mathrm{AM}}}$, and ${\theta }_{{\mathrm{out}}_{\max }}$ is the maximum angle between the outgoing light wave vector and the optical axis of the conventional fiber]. LP mode light within the MMF is angularly amplified at the conical tip. After each reflection at the conical tip, the angle $\psi$ between the light vector and the normal of the cone ($\alpha$) decreases (${\alpha }_n-{\alpha }_{n-1}=\psi$, where $\psi$ is the cone angle of the CF). After one or more cone reflections, the light reaches the condition of light emergence and is refracted from the conical tip [Fig. 1(b)]. We calculate that when ${\theta }_{\mathrm{in}}>\frac{\pi }{2}-\frac{(2m-1)\psi }{2}-\arcsin (\frac{1}{n})$ [where $m$ is the largest positive integer satisfying the inequality, representing the number of transmissions (including $m-1$ reflection and 1 refraction) of light at the conical tip, $n$ is the refractive index of the fiber core layer], the light will undergo $m$ angle amplification and be refracted from the conical tip; at last, ${\theta }_{{\mathrm{out}}_{\mathrm{AM}}}$ is $${\theta }_{{\mathrm{out}}_{\mathrm{AM}}}=\frac{\pi }{2}-\frac{\psi }{2}-\arcsin \left\{n\sin \right[\frac{\pi }{2}-{\theta }_{\mathrm{in}}-\frac{(2m-1)\psi }{2}\left]\right\}.$$(7)

In this study, we calculate the relationship between ${\theta }_{{\mathrm{out}}_{\mathrm{AM}}}$ and ${\theta }_{\mathrm{in}}$ for MMF (core/cladding/coating layer, 400/420/600 μm, $\mathrm{NA}=0.22$, $n_{\mathrm{core}}=1.458,n_{\mathrm{clad}}=1.441$, Chunhui, China) with cone angles ranging from 10° to 100° [as shown in Fig. 1(c), ${\theta }_{\mathrm{in}}=0°–8.7°$] based on the model. At $\psi =20°$, 40°, 50°, 60°, 70°, the ${\theta }_{{\mathrm{in}}_{\max }}$ corresponds to the ${\theta }_{{\mathrm{out}}_{{\mathrm{AM}}_{\max }}}$; however, this is not the case in other scenarios. Due to the relatively large ${\theta }_{{\mathrm{out}}_{{\mathrm{AM}}_{\min }}}$ produced by these cone angles, the resulting laser illumination is annular. To verify the applicability of our model, we analyze and process fibers at representative angles [Fig. 1(d), $\psi =19.7°$, 35.7°, 29.1°, 88.9°] and present the actual exit light distribution of the corresponding cone angle [Fig. 1(e); we laid the CFs on a sheet of white paper and took photos with a mobile phone]. In this paper, we aim to achieve uniform laser illumination suitable for a laparoscopic imaging field of view size (26003BA, STORZ, $\mathrm{FOV}=64°$ [42]). Through simulations, we find that $\psi =19.7°$ and $\psi =35.7°$ can achieve the corresponding angle of laser illumination (${\theta }_{{\mathrm{out}}_{{\mathrm{AM}}_{\max }}}\approx 30°$, and with the inherent divergence angle of the LP mode [43], the exit angle can reach about 32°), as shown in Fig. 1(d). Specifically, $\psi =19.7°$ (${\theta }_{{\mathrm{out}}_{\mathrm{AM}}}=8.3°–29.5°$) offers a broader distribution of ${\theta }_{{\mathrm{out}}_{\mathrm{AM}}}$ compared to $\psi =35.7°$ (${\theta }_{{\mathrm{out}}_{\mathrm{AM}}}=12.4°–29.4°$), and in the fabricated CFs, the $\psi =19.7°$ fiber exhibits an extremely uniform distribution of laser illumination, while the $\psi =35.7°$ fiber shows a ring-shaped illumination pattern with weaker middle and stronger edges [Fig. 1(e)]. At $\psi =29.1°$ and 88.9°, ${\theta }_{{\mathrm{in}}_{\max }}$ is not the angle at which ${\theta }_{{\mathrm{out}}_{\mathrm{AM}}}$ is maximized. Simulation results show that the exit light distribution at $\psi =29.1°$ presents a solid center (corresponding to ${\theta }_{\mathrm{in}}=2.9°–8.7°$), which is verified by the actual exit light distribution chart [Fig. 1(e), $\psi =29.1°$]. We also observed an interesting phenomenon where the simulation results at $\psi =88.9°$ show that parts of ${\theta }_{{\mathrm{out}}_{\mathrm{AM}}}$ are greater than 90° and parts less than 90°, with the smaller angles presenting an annular distribution [Fig. 1(e)], which is also confirmed by the actual exit light distribution [Fig. 1(e), $\psi =88.9°$].

We believe this model enables users to select the conical angle that best meets their usage requirements, in accordance with the available manufacturing capabilities. We use a CF with $\psi =19.7°$ to produce uniform laser illumination suitable for the viewing field for laparoscopic imaging of 64°.

Figure 2(a) shows our laparoscopic LSCI system. A medical cold-light source is coupled into the laparoscope (26003BA, STORZ, Germany) through multimode glass fiber bundles (Chunhui, China, $\mathrm{NA}=0.6$) to provide bright-field illumination. A long-pass dichroic mirror (FF750-SDi02-$25\times 36$, Semrock, USA) splits the light from the sample into visible and near-infrared light for bright-field imaging and LSCI, respectively. An RGB camera (acA1920-155uc, Basler, Germany) captures the visible light signal from the sample, while a mono camera (acA1920-155um, Basler, Germany) with an added filter ($785\mathrm{nm}\pm 2\mathrm{nm}$, Chroma) captures the LSCI signal. The laser diode LD785-SE400 is installed on the temperature control mount TCLDM9, which is controlled by the LD current controller LDC205C and the LD temperature controller TED200C to make the LD work stably at the set power. The incident end of the CF is designed as the SMA905 interface and is fixed on the three-axis translation mount CXYZ05A through the fiber adapter SM05SMA. The XYZ position of the CXYZ05A is adjusted to maximize the laser coupling efficiency.

Additionally, we designed and fabricated two CF fixing components for a 0° viewing angle laparoscope and a 30° viewing angle laparoscope. To protect the tip of the CF, we designed a quartz glass protective case to safeguard the tapered structure, as shown in the lower left corner of Fig. 2(b-1). For the 0° viewing angle laparoscope, the CF is glued into the linear groove in the 0° medical-grade stainless steel tube [shown in the blue area in Fig. 2(b-2)], and the external part of the laparoscope is glued inside the 0° tube through a curing adhesive [Fig. 2(b-1)]. For the 30° viewing angle laparoscope, we have designed a deflecting optical fiber component placed at the front end of the 30° tube [Fig. 2(c-1)]. This device features a helical cylindrical groove inside [as shown in the dark yellow area in Fig. 2(c-1)], ensuring that the illumination axis of the CF precisely aligns with the 30° laparoscope’s viewing angle. The upper section of the CF is directly fixed into the linear groove in the 30° tube [as shown in the blue area in Fig. 2(c-2)], while the rear section of the CF is first fixed into the helical cylindrical groove of the deflecting optical fiber component. The deflecting optical fiber component, along with the CF, is then secured in the trapezoidal groove of the 30° tube [as shown in Fig. 2(c-2)]. The diameter of the helical structure is 1 mm. Due to the tiny outer diameter of the CF (hundreds of micrometers) and deflecting optical fiber component (inner diameter identical to outer diameter of the laparoscope, with a thickness of 1 mm), this external fiber method minimally increases the laparoscopic system’s space requirements.

To compare the advantages of the CF with MFBL, we evaluated the (1) laser illumination field of view, (2) uniformity of illumination (reflected by LSCI of the phantom), (3) speckle contrast, and (4) coupling efficiency of CF and MFBL.

Under both illumination methods, the laser was projected onto a standard Lambertian phantom (uniformity range $\pm 1\%$, JY-BRT, Hangxin, China), and the scattered light was captured by the mono camera of the laparoscopic LSCI system (Basler, aca1920-155um). Our data analysis was performed by MATLAB R2021a.

Under laser illumination both of the CF and MFBL, we captured images of a standard Lambertian phantom at various working distances. Due to the MMF effect, laser illumination through the fiber results in speckle illumination. We first applied median filtering to the obtained images to eliminate the effects of speckles. Next, we set the threshold intensity to $1/e$ of the average light intensity and calculated the ratio of pixel number with an intensity of 1 to the total pixel number.

As shown in Figs. 3(a) and 3(b), the CF provides more uniform laser illumination compared to the MFBL. To demonstrate that, due to the nonuniform illumination of MFBL, different laser intensities correspond to different $1/K^2$ values at the same flow rate, resulting in higher $1/K^2$ values in the center and lower values on the sides. In contrast, the CF provides uniform illumination, leading to uniform $1/K^2$ values across the field of view. The long axis of the phantom tube was aligned parallel to the long axis of the camera. We calculated the temporal contrast for a lipid emulsion phantom flowing with 8 mm/s at a working distance of 50 mm, and then performed $1/K^2$ fitting for the phantom tube within the field of view.

Under laser illumination of the CF and MFBL, we analyzed the laser-illuminated standard Lambertian phantom imaging results at various working distances using a $7\times 7$ sliding window to calculate the statistics of the standard deviation of light intensity divided by the average light intensity.

The ends of a capillary glass tube square outside and round inside (Cnpowder, China, to reduce specular reflection), were connected to a 100 μL microsyringe (Gaoge, China) and a glass dish containing a 2% lipid emulsion solution (Kelun, China) through the PVC tube. A precision infusion pump (TJ-4A, Longer Pump, China) was used to steadily push the lipid emulsion solution into the PVC tube, ensuring both the capillary glass tube and the PVC tube were filled with the solution without air bubbles. The exposure time of the mono CMOS was set to 5 ms, and the flow rate of the lipid emulsion in the capillary tube, controlled by the infusion pump, ranged from 2 to 20 mm/s, with a step size of 2 mm/s. At each speed, 100 frames of speckle images were captured for data analysis. Based on working distances from short to long, we selected ROI pixel areas from $50\times 50$ to $10\times 10$ for data analysis. To ensure the robustness of the system, each data set was recorded 5 times.

All experimental procedures were performed according to guidelines from the Huazhong University of Science and Technology, which have been approved by the Institutional Animal Ethics Committee of Huazhong University of Science and Technology, involving 5 male and 5 female rats. Anesthesia was maintained through intraperitoneal injections of 6 mg/kg thiamylal sodium and 8 mg/g chloral hydrate. The rats were placed in a supine position, shaved, and then subjected to a laparotomy to expose the mesentery. Ischemia was induced by clamping specific blood vessels with hemostatic forceps, and reperfusion was simulated by releasing the clamps. The working distance was set at 50 mm with an exposure time of 5 ms. Upon completion of the experiments, euthanasia was carried out on all animals according to the protocol.

As illustrated in Figs. 3(a) and 3(b), the CF demonstrates superior performance in terms of illumination field, uniformity, speckle contrast, and intensity compared to the MFBL. Between 2 and 5 mm, the illumination/imaging field increases rapidly with working distance due to the considerably smaller diameter of the illumination fiber compared to the imaging aperture. From 5 to 50 mm, CF offers a larger illumination field than MFBL, with the CF illumination/imaging field ratio approaching 1, while MFBL is around 0.6, as shown in Fig. 3(c). At a working distance of 2–5 mm, both the CF and MFBL exhibit near-dark field illumination, resulting in relatively low speckle contrast [as depicted in Fig. 3(d)]. Within a 5 to 50 mm working distance, CF (0.6) shows a higher speckle contrast compared to MFBL (0.4), with CF’s speckle contrast dynamic range being approximately 1.5 times that of MFBL. Uniform laser illumination is crucial for LSCI [22–25]. At a working distance of 50 mm, temporal contrast analysis of phantoms under CF and MFBL laser illumination was performed. Figure 3(e) shows that CF maintains nearly equal $1/K^2$ across the entire field, whereas MFBL exhibits higher central $1/K^2$ with lower values at the edges, a result of the central-strong, edge-weak illumination of MFBL [as depicted in Fig. 3(a)], which severely undermines the performance of endoscopic LSCI. The signal intensity of LSCI directly affects the dynamic range of the speckle patterns recorded by the camera, thereby influencing the accuracy of LSCI. Thus, sufficient laser power is essential for illuminating the sample [1,2,22]. Measurements of the output power and coupling efficiency for CF and MFBL were conducted [Fig. 3(f)], with the CF showing a coupling efficiency of $>95\%$. In contrast, due to the triple laser coupling process into the fiber bundle and limited transmission efficiency, the MFBL exhibits a lower coupling efficiency (approximately 30%).

We find that the CF, as the laser illumination of endoscopic LSCI, performs best in terms of illumination field of view, illumination uniformity, speckle contrast, and coupling efficiency, which is extremely favorable for endoscopic LSCI.

As described in Section 2.F, flow velocity phantom experiments were conducted under CF and MFBL laser illumination at various working distances ($\mathrm{WD}=10$, 20, 50, 80 mm), with the flow velocity of the lipid emulsion controlled between 2 and 20 mm/s. Overall, as shown in Fig. 4(a), the CF demonstrated a superior linear fit across all working distances and the entire velocity range, with higher blood flow velocity measurement sensitivity and smaller measurement error [the shaded area in Fig. 4(a) represents the measurement error of the five recorded results as described in Section 2.F]. Specifically, Fig. 4(b) indicates that the MFBL had a high linear fit ($R^2=0.97-0.99$) in the 2 to 20 mm/s range at WDs of 10 to 20 mm, but at $\mathrm{WD}=50\mathrm{mm}$, the linearity was almost absent ($R^2=0.448$) in the 12 to 20 mm/s range. At $\mathrm{WD}=80\mathrm{mm}$, linearity was only observed in the 2 to 10 mm/s range ($R^2=0.79$), with no linearity in the 12 to 20 mm/s range ($R^2=0.31$). The CF maintained a linear fit close to 1 ($R^2=0.993-0.999$) across the entire velocity range at working distances of 10 to 20 mm. At $\mathrm{WD}=50\mathrm{mm}$ and 80 mm, high linearity ($R^2=0.99-0.993$) was also observed in the 2 to 10 mm/s range, with a slight reduction in the 12 to 20 mm/s range ($R^2=0.95-0.97$). As depicted in Fig. 4(c), with increasing working distance, the MFBL showed a significant reduction in flow velocity measurement sensitivity [$\eta$, $\eta =(1/K^2(v_2)-1/K^2(v_1))/(v_2-v_1)$] in the 12 to 20 mm/s range (6.74 to 14.9) compared to the 2 to 10 mm/s range (29.51 to 26.28) at $\mathrm{WD}=10\mathrm{mm}$ and 20 mm, following the same trend as that at $\mathrm{WD}=50\mathrm{mm}$ and 80 mm. In contrast, the CF at $\mathrm{WD}=10\mathrm{mm}$ and 20 mm showed only a slight decrease in the 12 to 20 mm/s range (32.7 to 31.3) compared to the 2 to 10 mm/s range (33.4 to 33.3) and exhibited a gradual reduction in $\eta$ with increased working distance and speed, yet remaining overall higher than the MFBL. In conclusion, the CF outperforms MFBL in terms of a broader velocity measurement range, higher linear fit, and increased blood flow velocity measurement sensitivity across short to long working distances. It is worth noting that although high coherence leads to a low $1/K^2$, due to the presence of camera noise, high signal intensity results in a higher $1/K^2$ [22,23,44], and the laser output power of the CF is about 3 times that of the MFBL, all of which ultimately result in the CF exhibiting a higher $1/K^2$.

We first imaged the rats’ mesentery under CF and MFBL laser illumination, as shown in Fig. 5. MFBL laser illumination produced restricted angle, low speckle contrast, weak intensity, and uneven illumination [Fig. 5(a)]. In contrast, CF laser illumination resulted in large angle, high dynamic range of speckle contrast, relatively higher intensity, and even illumination [Fig. 5(b)]. The LSCI results under MFBL laser illumination exhibited a low SNR, poor SBR, significant variations in LSCI results across different light intensities, and extremely poor performance at the edges [Fig. 5(c)]. Under CF laser illumination, the LSCI results showed qualitative improvements in SNR, SBR, and edge imaging performance [Fig. 5(d)].

To simulate relatively minor blood flow changes in animal experiments, we performed a unilateral mesenteric vessel occlusion [45] (both ends of the intestinal tract are not blocked; in this scenario, the blood flow alterations are minor). We conducted mesenteric vessel temporary occlusion and reperfusion experiments in rats under laser illumination of CF and MFBL. The entire procedure lasted 120 s. At a working distance of 50 mm, we initially recorded the rat’s mesenteric blood supply under normal conditions for 20 s, then temporarily occluded the venous return of the upper left mesentery [red circle in Fig. 6(a-2)] using a hemostatic clamp for 50 s, and finally released the hemostatic clamp to allow blood reperfusion for 50 s. As demonstrated in the endoscopic LSCI results in Figs. 6(a)–6(c), overall, the CF exhibited higher SBR and SNR, with the ischemia–reperfusion process being more pronounced. Notably, due to the significantly weaker light intensity at the edges of the MFBL, this discrepancy became even more pronounced [Figs. 6(b) and 6(c)].

To quantitatively describe the advantages of CF in blood flow monitoring, we selected four representative ROIs in Fig. 6(c-1): the main trunk vessel closest to the ligation site (ROI 1); the branch supplying the ligated vessel (ROI 2); the distal branch of the ligated vessel (ROI 3); and a branch not apparently implicated in the ligation process (ROI 4). We calculated the $1/K^2$ for these four ROIs under CF and MFBL before, during, and after ligation, as detailed in Fig. 6(d). Under MFBL, ROIs 1 and 2 showed significant ischemia–reperfusion, but ROIs 3 and 4 remained mostly unchanged. Under CF, ROIs 1 and 2 exhibited more pronounced ischemia–reperfusion changes. Notably, during reperfusion, ROI 2 experienced a reduction in blood flow compared to before ligation, a phenomenon not observed under MFBL. Furthermore, a significant ischemia–reperfusion process was observed in ROI 3 under CF, and surprisingly, in the nonligated vessel branch (ROI 4), no significant blood flow change was noted during ischemia, but a decrease in flow was detected during reperfusion, which was also not seen under MFBL. This could be due to the influence of the reperfusion process in adjacent ligated vessels, leading to a reduced flow rate of ROI 4.

We conducted a real-time analysis of several ROIs under CF laser illumination (adding ROI 5 from the right distal vessel) throughout the ischemia–reperfusion process and revealed intriguing phenomena, as detailed in Fig. 6(e). At the onset of ligation ($t=20\mathrm{s}$), the $1/K^2$ in ROIs 1, 2, and 3 dropped rapidly, with the extent of decrease being $\mathrm{ROI}1>\mathrm{ROI}3>\mathrm{ROI}2$. Interestingly, during ischemia (20–70 s), the blood flow in ROIs 1, 2, and 3 increased to varying degrees, while ROI 4 showed almost no change in flow rate during normal and ischemic conditions. After releasing the hemostatic clamp, the blood flow in ROIs 1, 2, and 3 increased but remained lower than before ligation, whereas ROI 4 experienced a slight decrease in flow rate, and ROI 5 exhibited almost no change in blood flow throughout the ischemia–reperfusion process.

To demonstrate that CF offers superior performance in terms of SNR and SBR, we magnified the areas within the white, black, and red boxes in Fig. 6(b-1), corresponding to the LSCI results under MFBL [Figs. 7(a), 7(c), 7(e)] and CF [Figs. 7(b), 7(d), 7(f)]; it becomes distinctly noticeable that the CF achieves a significant enhancement in SNR and SBR.

In Figs. 7(a) and 7(b), the CF laser illumination shows more pronounced ischemia–reperfusion phenomena compared to MFBL [as shown in Fig. 6(d)]. For a detailed quantitative evaluation, we performed $1/K^2$ fitting along the designated white lines in Figs. 7(c) and 7(e) under both CF and MFBL. As depicted in Fig. 7(g), in the region of the main vessel, the CF distinctly displays the intricate network of smaller vessels (comprising both arteries and veins) within the main vessel, whereas MFBL, with its weaker edge illumination, can hardly visualize the main vessel and suffers from extremely low SNR. At the distal branch of the vessel [as shown in Fig. 7(h)], the CF also demonstrates higher SNR and SBR.

Therefore, compared to the MFBL, the CF offers a larger effective imaging field of view, higher SBR and SNR in animal imaging, while also enabling more effective detection of subtle blood flow changes.

In this paper, we initially analyzed the reasons for the poor performance of conventional endoscopic LSCI, which uses a low-coherence illumination scheme resulting in narrow angles, poor coherence, uniformity, and low coupling efficiency laser illumination. We introduced a new endoscopic laser illumination method that directly couples a single-mode, narrow-bandwidth laser into a CF of low NA, achieving wide-angle, high-coherence, and uniform laser illumination with high coupling efficiency in the endoscope. Additionally, we established an effective model for calculating the divergence angle of CFs. Through phantom and animal experiments, we demonstrated that using a CF for laser illumination, compared to conventional endoscopic LSCI methods, can broaden the imaging field of view, enhance the SNR, enable more sensitive detection of minute blood flow changes, expand the detectable flow range, and improve SBR of endoscopic LSCI. Given the ultrafine size of the CF (several hundred micrometers), this external fiber method minimally increases the laparoscopic system’s space requirements. The laser illumination characteristics produced by CFs are highly advantageous for endoscopic LSCI, which probably enhances its potential for clinical adoption. Furthermore, the CF is also suitable for other environments requiring wide-angle, high-coherence, and uniform laser illumination.

Acknowledgment. We thank the Optical Bioimaging Core Facility of WNLO-HUST for the support in data acquisition.Author Contributions.J.Y. conceived the project, constructed the computational model for the divergence angle of conical optical fibers, processed the data, and wrote the manuscript. J.Y., Q.H., T.S., and Y.Y. conducted the phantom experiments. J.Y., L.M., and S.Y. optimized the optical system. J.Y., Q.H., T.S., and Y.Y. performed animal experiments. S.F. provided guidance on algorithms. P.L. and J.L. supervised the research and offered constructive feedback on the entire project. All authors discussed the simulation and experimental results and contributed to the writing of the manuscript.