Optical design; Fiber bundle imaging; Telecentric

In order to solve the problem that the conventional optical system can not be placed apart in different areas, fiber bundle imaging optical system is needed. With a flexible fiber bundle, the detection target can be imaged onto the sensor. This paper uses a fiber bundle with φ8mm, length 50mm, resolution 30lp/mm, hexagonal arrangement, and 0.3 numerical aperture as the main component.

The front objective and rear magnifying optical system of the optical system are designed. It provides a complete imaging solution for fiber bundle imaging. Through the glass fitting of the designed optical system, the results show that the field of view of the system can reach 35°, the numerical aperture of the front objective is 0.29, the numerical aperture of the rear optical system is 0.3, the modular transfer function of the front objective lens can reach 0.38 in 30 lp/mm,, and the modular transfer function of the rear magnifying optical system can reach 0.65 in 30 lp/mm,. It meets the requirements of field of view, numerical aperture matching, resolution and other parameters for fiber bundle imaging system. Furthermore, the selected glass are Chengdu Guangming’s existing products, the system has high feasibility.

Optical fiber is a filamentous fiber that has the function of transmitting light, images, and other kinds of optical information. Fiber bundle arranges multiple optical fibers with the same length in a certain order, so that it can be bent freely and transmit images. It has been widely used in modern military reconnaissance, clinical care, non-destructive testing, aerospace equipment and other fields.

As an arbitrarily bendable images transmission device, compared with the conventional optical imaging device, fiber bundle has excellent characteristics such as larger freedom and transmitting images under complex spatial conditions, which breaks the layout structure as a straight line or a broken line in the conventional optical system. With the rapid development of domestic optical fiber bundle manufacturing technologies, optical fiber bundles with high resolution, large cross-section, and high transmission index can be produced, and the performance of optical fiber bundles continues to increase, fiber bundle imaging system design is called for higher requirements. The traditional design can’t meet the requirements, new designs are needed.

Generally, the front system not only needs to meet the requirements of field of view, but also needs to match the numerical aperture of the fiber bundle. At the same time, the image-side telecentric light path is also needed. The rear system, as the amplification of the exit image of the fiber bundle, requires the design of an object-side telecentricity and satisfies the requirement the numerical aperture matching principle.

The existing designs mostly use aspheric surfaces and add diffraction elements to achieve better image quality. These methods increase the complexity of the system and increase the manufacturing cost of the system Meanwhile, systematic simulation analysis of the front system, fiber bundle, and the rear system is still a blank at home and abroad.Systematic simulation analysis is necessary to improve the existing design method, which helps to analyze the aberrations caused by the light during the transmission, and to optimize the entire optical system.

In this paper, a φ8mm fiber bundle with 30lp/mm limit resolution and 0.3 numerical aperture is selected as the main component, then do the systematic simulation of the fiber bundle imaging system. Firstly, we the introduce composition of fiber bundle imaging system and the principle of optical design. Then we do the analysis of the front and rear system.

Finally, we simulate the whole fiber bundle imaging system. The field of view is 35°, the minimum modulation transfer function at 30 lp/mm is 0.38, and the RMS of the final image plane is less than 0.011 mm. The system has the characteristics of large field of view, resolution reaching the limit of the device, easy manufacturing, and low cost. It provides a reliable design method for the development of the fiber bundle imaging system.

Figure 1. shows the constitute of fiber bundle imaging optics. It mainly consists of target, front objective lens, fiber bundle, rear amplifying system and detector. Target is firstly imaged on the front end of fiber bundle by the front objective lens, the image is transmitted to the rear end through fiber bundle, and the rear amplifying system magnifies the image to the detector. Fiber bundle is the core components of this optical system. Its resolution, numerical aperture, and other characteristics determine the design criteria of the front and rear systems.

Fig 1. Constitute of fiber bundle imaging system

Light transmission in fiber follows total reflection condition. Therefore, in order to make all light can be transmitted from front to the rear, numerical aperture of the incident light should be less than the numerical aperture of the fiber. At the same time, due to field of view of the system, there must be off-axis rays. If only the matching of the numerical aperture is satisfied, part of the rays will be blocked for off-axis location. In order to ensure that both on-axis and off-axis rays enter the fiber bundle, front lens must be designed to imaging-side telecentric lens. For the rear amplifying lens, the numerical aperture should be greater than or equal to the numerical aperture of the fiber bundle.

Resolution is an important for optical system. The resolution of the fiber bundle is currently limited by the limited manufacturing level. The resolution of the front and rear optical system only needs to be matched with the resolution of the fiber bundle. In particular, for the front lens, since the fiber’s front end is a plane, the field curvature of the image plane needs to be corrected.

Front optical system is necessary to consider the field of view, resolution, numerical aperture matching, off-axis and on-axis aberrations, and telecentric light path. At the same time, it is necessary to control the exit image height of the edge field and the incident angle of the principal rays of the exit rays on the image plane for optimization, so as to realize the telecentricity in the image side. What’s more, the length of system must be limited for the size requirement. The front lens are designed in five-piece negative-positive structure. The system has field of view of 35°, focal length of 5 mm, relative aperture of f/1.72, total length of 72 mm, and image numerical aperture of 0.29. The design of front optical system is shown in Figure 2.

Fig 2. Design of front optical system

The rear optical system plays a role in amplifying the image in the rear end of the fiber bundle. The diagonal thereof of 1-inch detector is 16 mm. Therefore, the vertical magnification of the rear optical system is about 1:2. Meanwhile, the resolution, numerical aperture matching and telecentric light path need to be considered.

Finally, the total length of the system is also an important consideration. In optimization, magnification of the entire system, incident angle of the first surface, and the total length of the system must be limited. The rear lens are designed in five-piece structure. Focal length of the system is 13.7mm, total length of the system is 17.4mm, magnification ratio is 2, and the numerical aperture of the object is 0.3. The optical design of the rear optical system is shown in Figure 3.

Fig. 3. Design of rear optical system

The resolution, field curvature, and spot diagram of front optical system are mainly observed and analyzed. Results are shown in Figure 4.

Fig 4. (a)Front optical system modulation transfer function diagram. (b) Front optical system field curvature diagram. (c) Front optical system spot diagram

It can be seen that at 30 lp/mm, the modulation transfer function is approximately 0.38, which can meet the resolution requirements of the system. The maximum field curvature of the system at full field of view is less than 0.1, which can meet the requirements for the flatness of the system. The RMS of the full field of view is 0.02mm. The image points are relatively concentrated, which can meet the needs of fiber bundle imaging system.

The resolution and spot diagram of rear optical system are mainly observed and analyzed. Results are shown in Figure 5.

Fig. 5. (a) Rear optical system optical modulation transfer function diagram. (b) Rear optical system spot diagram

It can be seen that at 30 lp/mm, the modulation transfer function is greater than 0.7, which can meet the resolution requirements of the system. The RMS of the entire system is a maximum of 0.011mm. The image points are relatively concentrated, which can meet the needs of fiber bundle imaging system.

The selected fiber bundle is simulated as a radius of 4 mm and length of 50 mm. The material is quartz glass with numerical aperture of 0.3. The total length of the system is 140 mm, focal length is 6.4 mm, image-side relative aperture is f/2.15, and total system field of view is 35°. The solid model and the Seidel aberration diagram are shown in Figure 6.

As we can see from the Seidel aberration diagram, aberrations of the fiber bundle imaging system are well controlled.

The larger residual aberration is distortion caused by large field of view, which is acceptable and has no effect on imaging quality. Because aspherical surfaces and free-form surfaces are not used in this design, and the glass are all produced by Chengdu Guangming. This system is simple, easy to manufacture, low cost, and highly implementable.

Fig. 6. (a)Solid model of fiber bundle imaging system. (b) Fiber bundle imaging system Seidel aberration diagram.

In this paper, according to the requirements of resolution and numerical aperture matching of the front objective lens and the rear optical system, we choose the initial structure reasonably, control the optimization parameters, and research on the design and optimizing method of large field of view fiber bundle imaging system. A large field of view fiber bundle imaging system is simulated and analyzed, and a reliable simulation result is obtained. The results show that the total length is 140mm, the focal length is 6.4mm, relative aperture is f/2.15, the total field of view of the system is 35°, and the minimum full-field modulation transfer function is 0.38. Seidel aberration is small and meets the imaging requirements. Due to the use of a good design, the entire system is simple, easy to manufacture, low cost, and highly implementable.