As a relay image transmission device, the image transmission performance of the optical fiber panel will always affect the imaging quality of the system, which will lead to the reduction of the modulation transfer function of the imaging system, affect the centroid positioning error of the detection space point target, and introduce noise. The image transmission performance of the fiber optic panel is mainly determined by the performance and parameter indicators of the fiber optic panel. The main performance and parameter indicators of the panel include the numerical aperture of the panel, fiber arrangement, fill factor, transmittance, resolution and some other indicators. It is of great significance to study the effects of different optical fiber panel performance and parameter indicators on the image transmission capability of optical fiber panels, and to find the performance parameters of optical fiber panels that can achieve excellent image transmission capabilities. Next, take the optical fiber panel as an example for analysis, and the analysis results can also be applied to other optical fiber imaging devices.

The numerical aperture of the optical fiber panel is the numerical aperture of the optical fiber monofilament. The numerical aperture of the optical fiber monofilament is only determined by the refractive index of the optical fiber core and the cladding medium, and its size depends on the relative refractive index difference of the optical fiber core and cladding. Regardless of fiber geometry.

The larger the numerical aperture, the stronger the light-gathering ability of the fiber optic panel, and the higher the image brightness of the final fiber exit end face. From the perspective of increasing the amount of light passing through the fiber optic panel, the larger the numerical aperture, the better. The ideal maximum numerical aperture of the fiber is 1. At this time, the aperture angle of the fiber is 90°. All hemispherical rays of the heart. However, in reality, it is difficult to achieve an ideal level due to the difference in refractive index between the core layer and the cladding layer of the optical fiber. At present, the numerical aperture of the fiber optic panels produced by existing manufacturers can generally reach or be close to 0.6, and the numerical aperture of some fiber optic components can reach 0.8 or even 0.9. This kind of fiber is achieved at the expense of other fiber performance indicators. High numerical aperture can achieve its excellent light collection performance in specific environmental conditions, but it is not universal.

The fill factor is an extremely important structural parameter of the fiber optic panel, expressed as K, which is defined as the ratio of the effective light transmission area (S) of the fiber optic panel to the total area (S0) of the fiber optic panel. Then the fill factor of the fiber panel can be expressed as K = S/S0. According to the previous chapters, it can be seen that only the core layer of the fiber can transmit light, then the filling factor (Kf) of a single fiber is expressed as the ratio of the area of the fiber core layer to the area of the fiber single filament. Let the fiber diameter be d, the fiber core diameter is dc, the fill factor of a single fiber is expressed as:

Under the condition that the diameter of the fiber remains unchanged, the larger the diameter of the fiber core, the higher the fill factor of the fiber panel. The increase of the fiber core means the thinning of the fiber cladding. Cross-light between optical fibers affects the image transmission quality of the optical fiber panel. General fiber cladding thickness for making fiber optic panels
The thickness is roughly controlled at 1~2μm. In the actual processing and drawing process, the fiber cladding is generally controlled to be about one-tenth of the fiber diameter.
The sum of the core area of all the fibers in the fiber optic panel is the effective light transmission area of the fiber optic panel, and the total area of the fiber optic panel is the sum of the areas of all the fibers in the panel plus the total gap area between the fibers. The total gap area is determined by the fiber arrangement of the fiber optic panel. The optical fiber arrangement of the fiber optic panel mainly includes square arrangement, regular hexagonal arrangement, etc.

Let K f – square be the filling factor of the optical fiber monofilaments in a square arrangement, and K f – hexagon be the filling factor of the optical fiber monofilaments in a regular hexagonal arrangement, as shown in Figure 2.3. Find the fill factor for both arrangements.

Among them, S fiber is the area of a single fiber filament, S square is the area of a square with side length d, S hexagon is the area of a regular hexagon with side length d/√3, and K f – square = 0.7854,
K f – hexagon = 0.9069. It is concluded that the filling factor of the fiber optic panel with the optical fibers arranged in a regular hexagon is larger than that of the fiber optic panel arranged in a square, so the use of the fiber optic panel arranged in a regular hexagon can increase the light throughput of the fiber optic panel itself, and improve the efficiency of the optical fiber panel. Panel imaging capability.

Therefore, the fill factor of the optical fiber panel can be expressed as the product of the fill factor of the optical fiber monofilament and the fill factor of the optical fiber panel. The fill factor of the fiber optic panels with two different arrangements can be given by:

Therefore, considering the factor that the larger the filling factor of the fiber optic panel, the more light passing through the fiber, it can be seen that under the same fiber material parameters, the image transmission performance of the fiber optic panel arranged in a regular hexagonal close-packed arrangement is better than that of a square close-packed arrangement. Arranged fiber optic panels, and considering the stability of the internal structure of the fiber optic panels, the fiber optic panels that are also arranged in a regular hexagon are more advantageous. At present, 70% of the optical fiber imaging devices manufactured at home and abroad are arranged in a regular hexagon, and the drawing method is well controlled and the space utilization rate is high. The advantages. At present, the fill factor of fiber optic panels with regular hexagonal arrangement of fibers is about 60% ~ 90%.

The transmittance performance of the fiber optic panel is a standard for evaluating the light transmittance performance of the fiber optic panel, which is defined as the ratio of the outgoing luminous flux of the panel to the incident luminous flux. expressed as the following formula

Among them, I represents the outgoing luminous flux, and i₀ represents the incident luminous flux. When analyzing the transmittance of the fiber optic panel, in order to prevent part of the incident light from entering the fiber optic panel, the incident angle of the incident light should be set to be less than or equal to the aperture angle of the fiber optic panel, so that all the incident light can be received by the fiber optic panel. When analyzing the transmittance of the optical fiber panel, it can be shown that the light transmission performance is reduced due to the optical fiber itself. The transmittance of the fiber optic panel is mainly determined by two factors. The first part is the transmittance of the single fiber we mentioned above, which is mainly caused by the optical energy loss caused by the following three factors: Fresnel reflection loss on the fiber end face. , the total reflection loss of the interface between the fiber core and the cladding, the absorption and scattering loss of the fiber material, etc.

(1) Fresnel reflection loss of fiber end face
When light is incident on the input end face of the fiber from the ambient medium, a part of the light will always be lost after being reflected by the incident end face of the fiber. This phenomenon is defined as the Fresnel reflection loss of the fiber end face. There are two decisive factors for this loss, one is the incident angle of the beam, and research shows that controlling the change of the incident angle of the same beam, the reflection loss of the incident end face of the fiber also changes accordingly. When the beam is incident vertically, the reflection loss of the incident end face of the optical fiber is the lowest. With the increase of the incident angle of the beam, the reflection loss of the end face also increases. When the incident angle of the beam is within the range of the aperture angle of the fiber, the reflection loss coefficient of the fiber end face of the incident beam can be approximated to the reflection loss coefficient of the fiber end face when the beam is vertically incident. The reflection loss coefficient of the fiber end face when light is vertically incident can be expressed as:

If only the Fresnel reflection loss of the entrance and exit end faces of the fiber is considered, the transmittance of a single fiber of the fiber can be expressed as the following formula:

(2) Total reflection loss at the interface between fiber core and cladding
Since the optical fiber panel is drawn by a process such as wire drawing, it is inevitable that there will be interface defects between the optical fiber core layer and the cladding layer, resulting in total reflection loss between the interfaces. Set the interface total reflection loss coefficient as β, then the actual reflection coefficient of the interface between the fiber core and cladding is expressed as (1-β). Studies have shown that if the fiber is made of glass, the total reflection loss coefficient at the core-clad interface of the fiber is about 0.0005. If the fiber material is plastic, the total reflection loss coefficient at the core-clad interface of the fiber is about 0.01. There is an existing fiber of length L, if only the total reflection loss between the core layer and the cladding interface of the fiber is considered, the transmittance of the fiber should be expressed as:

Among them, qm represents the number of total reflections per unit length of fiber filament.

(3) Absorption and scattering loss of fiber material

The absorption and scattering loss of the optical fiber material mainly refers to the optical loss of the optical fiber core layer, which is generally caused by the different materials and processing technology of the optical fiber core layer. Set the absorption loss coefficient of the core material to α. If only the absorption loss of the fiber core material is considered, the transmittance of the fiber should be expressed as the following exponential form:

Among them, secα’ represents the optical path length of a unit length of the optical fiber, and L represents the length of the optical fiber.

To sum up, considering the effects of the Fresnel reflection loss on the fiber end face, the total reflection loss at the interface between the fiber core and the cladding, and the absorption and scattering losses of the fiber material, the transmittance of the fiber monofilament can be obtained. Overrate expression:

The second factor that determines the transmittance is the fill factor of the fiber optic panel. As mentioned in the previous section, the fill factor of a fiber optic panel represents the proportion of the effective light-passing area of a fiber optic panel to the total panel area.
The larger the fill factor, the larger the effective light-passing area of the fiber optic panel.
In the case of the same fiber material, the larger the core diameter ratio of a single fiber, the larger the fill factor of the fiber panel, and the higher the light integral transmittance of the panel. Similarly, when the parameters and materials of the optical fibers are completely the same, that is, when the optical energy loss of a single optical fiber is completely the same, the optical fiber panel with the fibers arranged in a regular hexagon is more transparent than the optical fiber panel with the fibers arranged in a square shape. The pass rate is higher and the light transmission ability is stronger.
The fill factor of a fiber optic panel with fibers arranged in a regular hexagon can be expressed as:

The transmittance of the fiber optic panel with the fibers arranged in a regular hexagon can be expressed as:

Different from communication fibers, fiber optic panels and other fiber optic imaging devices generally operate in the visible light band, about 400nm to 800nm. And because the image transmission fiber is drawn from a multi-mode fiber with a thick core and a thin cladding, the image transmission attenuation is fast, and the attenuation level is approximately 1dB/m. In practical applications, the thickness of the fiber panel can be controlled at about 100mm. Even within 50mm, far less than 1m in length, the degree of energy attenuation in the process of optical fiber image transmission is low, and the light transmittance is high. To sum up, considering the above two factors that affect the transmittance of the optical fiber panel, if you want to improve the optical transmittance performance of the optical fiber panel, it is not only necessary to improve the optical transmittance performance of the optical fiber monofilament, but also to improve the fill factor of the optical fiber panel and Reduce the thickness of fiber optic panels

Resolution is an important indicator used to characterize and evaluate the image transmission performance of fiber optic panels. It is defined as the minimum distance between two image points in space that the fiber optic panel can resolve, and its unit is usually expressed as the logarithm of the line spacing that can be resolved per millimeter ( lp/mm). Obviously, the higher the resolution of the fiber optic panel, the better the image transmission performance, the transmission image
the higher the clarity. Under the ideal premise of uniform drawing, regular arrangement and good optical insulation of each monofilament in the optical fiber panel, the resolution of the optical fiber panel and other optical fiber imaging devices is mainly determined by the spacing of adjacent optical fiber monofilaments and the optical fiber arrangement.
Assuming that the sampling value d0 of the spacing between adjacent optical fibers is the fiber diameter d, the resolution of the optical fiber panel is the reciprocal of twice the sampling spacing of the single fiber, that is, 1/2d0 = 1/2d. Due to the different arrangement of the fibers in the fiber optic panel and different sampling directions, the distance between the two adjacent monofilaments (sampling spacing d0) is different, and ultimately the resolution of the fiber optic panel is also different.
The following figure shows the structure of the fiber optic panel with different arrangements, and marks the sampling spacing in different sampling directions.

The lowest resolution obtained by an optical fiber panel of a certain arrangement along any sampling direction is defined as the limit resolution of the optical fiber panel of this arrangement. The limiting resolution of a fiber optic panel with fibers arranged in a square can be expressed as

The limiting resolution of the fiber optic panel with the fibers arranged in a regular hexagon can be expressed as:

Under the premise of the same diameter of the fiber filaments, the limit resolution of the fiber optic panel with the fibers arranged in a regular hexagon is higher than that of the fiber optic panel with the fibers arranged in a square shape. Therefore, selecting a fiber optic panel with fibers arranged in a regular hexagon can achieve higher imaging resolution and higher image clarity.
Finally, it is obvious that the resolution of the fiber optic panel is related to the diameter of the fiber. It is also possible to reduce the diameter of the fiber monofilament by improving the fiber manufacturing process technology, so as to achieve a higher resolution of the fiber optic panel.

(1) Cross-sectional area of fiber optic panel When the fiber diameter and fiber arrangement are determined, the cross-sectional area of the fiber panel determines the field of view that the fiber relay imaging system can observe and the amount of information transmitted by the image. In a concentric optical camera, the exit end face of the fiber optic panel should be coupled with the image sensor and should be matched in shape, so the fiber The cross-sectional shape of the panel is rectangular, but since the imaging focal plane of the concentric objective lens is hemispherical, the cross-section of the incident end face of the optical fiber panel is a hemispherical curved surface. According to the cross-sectional size of the optical fiber imaging device, it can be divided into small-section optical fiber imaging device and large-section optical fiber imaging device. Optical fiber imaging devices with small cross sections are generally used in various medical and industrial fiber endoscopes, and the cross-sectional diameter is generally less than 3 mm; optical fiber imaging devices with large cross sections are generally used in military sighting instruments, such as periscopes and hand-held weapons. Optical fiber sights, etc., as well as relay imaging devices as concentric optical cameras, generally have a cross-sectional area greater than 5mm × 5mm.

(2) Length of fiber optic panel Since the fiber optic panel is a passive optical fiber imaging device, and the longer the length of the fiber optic panel, the lower the light transmittance, so in the case of no active lighting, the thickness of the fiber optic panel should be as much as possible on the premise of meeting the structural requirements. shortened.

(3) Wire breakage rate During the processing of the fiber optic panel, it has been drawn twice. Due to the drawing process, ambient temperature and other factors, it is inevitable that the fiber cannot pass through, such as broken wires, dark wires, etc., in the final image. Black spots are generated, and what’s more, a group of broken wires will be generated, covering the target information. At present, the processing technology of optical fiber panels has become mature, and there are regulations on the problem of wire breakage. The wire breakage rate of small-section optical fiber imaging devices should be less than 0.3‰, and the wire-breaking rate of large-section optical fiber imaging devices should be less than 0.8‰.