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Traditional endoscopes use fiber bundles to transverse the images and have the disadvantages of large size and poor flexibility. Unlike the single mode fibers just guide the fundamental mode, multi-mode fibers (MMFs) accommodate a large number of guided modes. Accordingly, one MMF can be utilized to transverse imaging for endoscopy. This MMF based endoscope can effectively overcome the above shortcomings. However, there are effects such as modal dispersion and mode coupling in the transmission process of multimode fiber, which will cause the image transmitted in the fiber to be distorted or even unrecognizable. The randomness of fiber shape in fabrication detoriosate the distortion. By measuring the transmission matrix, it is possible to recover the image through MMF. But the overall shape and structure of MMF will change in the operation of endoscope. The transmission characteristics of multimode fiber are only closely related to the fiber geometry, but traditional MMF imaging techniques are applicable when the shape of the optical fiber during imaging is consistent with the shape of the optical fiber when the transmission characteristics are calibrated. This work will focus on solving these problems. This paper explores the imaging technology of single multimode optical fiber, proposes the use of neural network to fit the multimode optical fiber transmission matrix, and calculates the input light field through the reverse transmission matrix and the output speckle light field. The traditional real number network has limited fitting effect on the multimode fiber transmission matrix. Inspired by the physical process of multimode fiber modulation of the light field, the real number network is extended to the field of complex numbers, and complex number operations are implemented in the network in the form of real numbers. This article studies the imaging regularity and effectiveness of multimode fiber under the condition of slight deformation and severe deformation. The neural network fitting method of multi-mode optical fiber transmission matrix used in this paper can maintain its effectiveness within a certain deformation range, and has great application potential in some endoscopic applications.
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