The illumination systems employed in conventional flexible endoscopes for gastrointestinal applications have traditionally relied on external light sources commonly referred to as cold light. Notable examples of cold-light sources include arc lamps, xenon lamps, and halogen lamps. However, these cold-light sources are characterized by elevated cost, limited operational lifetime, and relatively low efficiency. To address these limitations, the recent trend has seen a shift toward the adoption of light-emitting diodes (LEDs) as replacement light sources. The majority of LED light sources exhibit a Lambertian radiative distribution, as exemplified in Fig. 1. This distribution is characterized by a higher intensity at the center and diminishing luminance toward the periphery [1].

Figure 1. Lambertian light distribution of an light-emitting diodes (LED) light.

In the existing endoscopic lighting system to which the LED light source is applied, the amount of light at the center is relatively high compared to the periphery, so the saturation phenomenon occurs at the center of the image [2]. Because of this phenomenon, it is difficult to detect the patient’s lesion, so it is necessary to study the optimal light distribution to reduce the amount of light at the center and increase the amount at the periphery.

Consequently, this study aims to alleviate the saturation phenomenon observed in images due to the illumination distribution of LED-based endoscopic systems. To achieve this, we propose the design of an illumination distribution characterized by a broad emission angle, as illustrated in Fig. 2. Simultaneously, this design seeks to effectively diminish central intensity and achieve ample intensity at the desired maximum emission angle, by adopting a bat-wing distribution [3]. In light of these premises, the study endeavors to contribute to the optimization of illumination distributions within endoscopy, thereby enhancing the quality of acquired images and ultimately facilitating improved disease detection.

Figure 2. Bat-wing light distribution.

2.1. Alternative Approach Using Bezier Curves for Optical-system Design

Conventional endoscopic illumination systems utilizing Lambertian illumination suffer from the issue of having higher light intensity at the center and lower luminance at the periphery. This characteristic gives rise to image-center saturation, posing a challenge in accurate image interpretation. To mitigate this issue, we aim to transform the illumination pattern into a bat-wing configuration with reduced central intensity and enhanced luminance at the maximum emission angle. However, achieving the bat wing with conventional lens shapes presents limitations. Thus, this paper employs Bezier curves, which offer greater flexibility in shape transformation and lens design [4].

The Bezier curve can be expressed through the trajectory drawn by specific points. It can be expressed using Eqs. (1) and (2). The shape of the Bezier curve changes according to the control points shown in Fig. 3, within range of 0 ≤ t ≤ 1. t is a value that indicates how far the line segment has progressed proportionally. P₁ and P₄ remain fixed points for the lens thickness and diameter, while control points P₂ and P₃ manipulate the Bezier curve [5].

Figure 3. Positions of the coordinates of the Bezier curve.

To implement bat-wing illumination using the Bezier-curve equations, we introduce a merit function for the bat-wing distribution to lower the central intensity with the full width at half maximum (FWHM) to 140°. Optimizing the Bezier curve under these conditions yields the control-point coordinates shown in Table 1. The resulting curve based on these coordinates is illustrated in Fig. 4.

Figure 4. Bezier curve based on the designed coordinates.

TABLE 1. Bezier-curve points.

Coordinate	P1	P2	P3	P4
x	1.00	1.00	1.72	1.80
y	0.00	0.60	0.95	1.01

While utilizing Bezier curves enables the realization of the bat-wing illumination distribution, certain limitations remain in achieving 140° spread and optimal optical efficiency. To overcome these challenges, additional design considerations are essential. Addressing these constraints involves achieving the desired 140° beam angle while enhancing optical efficiency by utilizing total internal reflection at the lens edge. This is achieved by introducing a tapered edge configuration to the lens design. We intricately design the lens by applying this strategy, as illustrated in Fig. 5.

Figure 5. Shape of the designed lens.

Furthermore, because the LED substrate is larger than the diameter of the lens designed using Bezier curves, a gap of a few millimeters arises between the LED and the lens. To counteract the efficiency reduction caused by this gap, a cylindrical lens is applied to maximize efficiency and construct the endoscopic illumination system [6]. The complete configuration of the illumination system is illustrated in Fig. 6; ray-tracing simulations are conducted based on this configuration. The simulation results in Fig. 7 validate a bat-wing illumination with a 140° pattern and 31.15% efficiency.

Figure 6. Designed endoscopic illumination system.

Figure 7. Bat-wing light distribution in the designed endoscopic illumination system.

2.2. Comparative Analysis of Endoscopic Illumination Systems Using a Bezier-based Lens and an Aspherical Lens

To compare the performance of the endoscopic illumination system that is designed based on results from Section 2.1, we test it against a system with a commonly used an aspherical polynomial lens [7].

The optical system now considered uses the same components as the proposed illumination system, but it incorporates an aspherical lens like the one shown in Fig. 8 and parametrized in Table 2, which yields a Lambertian illumination distribution with a beam angle of 132°, as shown in Fig. 9.

Figure 8. Shape of the aspherical lens.

Figure 9. Light distribution for the illumination system using the aspherical lens.

TABLE 2. Coefficients of the aspherical lens.

Category	Figure
Radius	−3.00
Conic Constant (k)	−0.01
4th order	−0.60
6th order	1.000 × 10−5
8th order	1.013 × 10−2
10th order	−0.10033
12th order	1.1718 × 10−2
14th order	3.637 × 10−3
16th order	1.250 × 10−2
18th order	2.150 × 10−3
20th order	3.775 × 10−4

To compare the two systems, we define a region upon which a 140° beam angle is irradiated. Receiver dimensions are set in this region, and the simulation environment is established by placing them 15 mm away from the optical center, as shown in Fig. 10.

Figure 10. Simulation environment with receiver.

In the initial stage of analysis, we carry out simulations to observe the illuminance distribution of the bat-wing system designed in Section 2.1 and the Lambertian system, within the area irradiated by the endoscopic illumination system.

The illuminance simulation results are represented lum view picture and graphically using a cross-section. The x-axis variable D on each graph indicates the location of the irradiated area. Observing the circular regions marked on the graphs, it becomes evident that the bat-wing illumination system disperses the intensity from the center toward the periphery, compared to the Lambertian system. Furthermore, a broader central illuminance distribution area is observed, with increased peripheral brightness. Notably, the central illuminance of the bat-wing illumination system is found to be 18.66% lower than that of the Lambertian system.

Finally, for the purpose of effective disease detection with endoscopic imaging, the luminance distribution entering the endoscopic imaging system is of paramount importance. A uniform luminance distribution within the field of view (FOV) of 140° enhances comfortable disease detection. To irradiate in this manner, we employ a spatial lum meter applied to the receiver, based on the optical center of the endoscopic imaging system, to compare the bat-wing and Lambertian illumination systems, and then we conduct luminance simulations. In the case of the illumination simulations in Figs. 11 and 12, the optical phenomenon irradiated inside the human body is analyzed when the endoscopic lighting system is actually inserted into the body.

Figure 11. Illuminance lum view of illumination systems: (a) bat-wing distribution using a Bezier-curve, (b) Lambertian distribution with aspherical lens.

Figure 12. Illuminance simulation results for the illumination systems with bat-wing and Lambertian distributions: (a) x-coordinate cross-section, (b) y-coordinate cross-section.

The results of the luminance simulations demonstrate a 17.31% reduction in central luminance entering the endoscopic imaging system. As shown in Figs. 13 and 14, it is evident that the bat-wing distribution illumination system exhibits higher luminance values around the region of large emission angle. This signifies the ability of the imaging system to secure a broader peripheral field of view when viewing the image through the endoscopic imaging system. In the case of the luminance simulations in Figs. 13 and 14, the scene received by the optical system when the surface irradiated by the lighting system is photographed with an endoscopic imaging system are analyzed.

Figure 13. Luminance lum view of illumination systems: (a) Bat-wing distribution using a Bezier-curve, (b) Lambertian distribution with aspherical lens.

Figure 14. Luminance simulation results for the illumination systems with bat-wing and Lambertian distributions: (a) x-coordinate cross-section, (b) y-coordinate cross-section.

In conclusion, it can be recognized that the saturation issue present in Lambertian-distribution illumination, where the central area exhibits higher illuminance and brightness compared to the surrounding regions, can be mitigated by employing illumination with a bat-wing distribution.

In this paper, we have presented the design of an endoscopic illumination system incorporating Bezier curves to achieve a FOV of 140° with bat-wing illumination. This design aims to mitigate the issue of image-center saturation caused by the illumination of conventional miniature flexible endoscopes.

The designed endoscopic illumination system successfully met the criteria of bat-wing illumination with a 140° beam angle and a luminous efficiency of 31.15%. To substantiate its practical performance, we conducted a comprehensive comparison between the proposed bat-wing illumination system and a conventional illumination system employing an aspherical lens and exhibiting Lambertian illumination. Through illuminance and luminance simulations, our results indicated that the bat-wing illumination system effectively decreased the central luminance and brightness by 18.66% and 17.31% respectively, when compared to the system employing the aspherical lens. Moreover, the bat-wing illumination system ensures higher luminous output in peripheral regions. Consequently, the proposed system significantly alleviates image-center saturation issues.

We believe that the bat-wing illumination based on Bezier curves, as introduced in this paper, has the potential to be applied to various optical setups. This research can significantly improve the diagnostic accuracy and quality of endoscopic images by mitigating the challenge of image-center saturation in different endoscopic imaging contexts.

This work was supported by a Development of high-performance smart gastroscope system (GK18D0100, Develo-pment and commercialization of AI & motorization technology based high-performance smart gastroscope system) grant, funded by the Korea Medical Device Development Fund.

Korea Medical Device Development Fund; Development and commercialization of AI & motorization technology based high-performance smart gastroscope system (Grant no. KMDF_PR_20210526_0002-2021-05).

The authors declare no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.