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The experimental setup of this study is illustrated in Fig. 1a. In brief, a laser beam with a wavelength λ of 650 nm was emitted from the light source and expanded using a telescope comprising lenses L1 (f = 50 mm) and L2 (f = 75 mm). A conical lens, L3, with an inclination angle α of 5° was employed to transform the Gaussian beam into a Bessel beam. The 4f system comprised a lens L4 (f = 50 mm) and a 20× objective lens (NA = 0.4), and it was placed in a suitable position to focus the laser, thus providing a dense Bessel beam pattern, as shown in Fig. 1b. Next, the seven-core fibre was introduced into the optical path and placed slightly off-axis as the Bessel beam was transmitted through the fibre. The resultant transmission pattern, as shown in Fig. 1c, was captured using an objective lens (50×, NA = 0.42) and CMOS-1 camera. Note that the experimental pattern is similar to the simulated pattern shown in Fig. 1c. For the experiment, a commercial MCF (YOFC) with a core diameter of 8 μm, core spacing of 41.5 μm, and cladding diameter of 150 μm was employed. A self-designed, high-precision, electronically controlled optical fibre rotation apparatus was built; this apparatus enables the rotation of a fibre with a minimum rotation step of 0.075° while minimising the self-twisting of the fibre. White light was injected into the MCF at fibre end-face A, and a fibre core distribution pattern was obtained at fibre end-face B. The fibre core distribution image was captured using an objective lens (40×, NA = 0.6) camera (CMOS-2) to map the transmission pattern to the corresponding core distribution, as shown in Fig. 1d. The distance between the laser beam transmitted position and end-face of the fibre was restricted at 150 µm.
Fig. 1 Experimental setup. a Converting a Gaussian beam into Bessel beam using a cone lens and by focusing the laser using a 4f system. The high-precision optical fibre rotation apparatus and image capture devices are used to control fibre rotation and image acquisition. b Bessel beam pattern generated using a cone lens and captured by CMOS-1. c Experimental and simulated pattern of a Bessel beam transmitted through a seven-core fibre. d Seven-core fibre core distribution; here, a light-emitting diode point light source propagates white light at the fibre end-face A, and the core distribution image is captured at fibre end-face B.
The correlation that exists between the specific transmission pattern and corresponding fibre core distribution can be established using the Pearson correlation coefficient44,45, which evaluates the similarity between the reference and measured patterns. Herein, the calculation of the correlation coefficient was extended in two dimensions, as follows.
$${\rho }_{d}\left(X,{Y}_{d}\right)=\frac{1}{\left(M\times N-1\right)}\sum _{i=1}^{M}\sum _{j=1}^{N}\left(\frac{\left({X}_{i,j}-{\mu }_{X}\right)\left({Y}_{d,i,j}-{\mu }_{{Y}_{d}}\right)}{{\sigma }_{X}{\sigma }_{Yd}}\right) $$ (1) where X is the measured 2D pattern corresponding to a 2D data matrix, with values ranging from 0 to 255; $ {X}_{i,j} $ is the pixel point in row i and column j of the X pattern; $ {Y}_{d} $ represents the d-th reference pattern obtained from the reference dataset; and $ {Y}_{d,i,j} $ is the pixel point in row i and column j of the $ {Y}_{d} $ pattern. Note that the variables $ \,{\mu }_{X},\;{\mu }_{{Y}_{d}} $ and $ {\sigma }_{X},\;{\sigma }_{Yd} $ can be calculated using X and $ {Y}_{d} $, which represent the mean and standard deviations, respectively. A single pattern consists of M rows and N columns, and each measured X pattern returns a parameter $\, {\rho }_{d} $, which reflects the similarity to the d-th reference patterns. The most similar pattern returns the maximum $\, \rho $ value. Thus, a connection between the measured pattern and d-th fibre core distribution with the highest Pearson correlation coefficient can be established. Because the cores of a seven-core fibre are arranged based on the vertex and centre of a regular hexagon, the measured core distribution angle can be simplified to 0°–60°.
Bessel-beam-based side-view measurement of seven-core fibre internal core distribution
- Light: Advanced Manufacturing , Article number: (2024)
- Received: 04 June 2023
- Revised: 13 December 2023
- Accepted: 13 December 2023 Published online: 26 January 2024
doi: https://doi.org/10.37188/lam.2024.002
Abstract: Accurate knowledge of the internal core distribution of multicore fibres (MCFs) is essential, given their widespread application, including in fibre splicing, bundle fan-in/fan-out, mode coupling, writing gratings, and fibre drawing. However, the extensive use of MCFs is restricted by the limited methods available to precisely measure the fibre core distribution, as the measurement accuracy determines the performance of the product. In this study, a side-view and nondestructive scheme based on Bessel beam illumination was proposed for measuring the internal core distribution of a seven-core fibre. Bessel beams offer a large focal length in a scattering medium, and exhibit a unique pattern when propagating in an off-axis medium with a spatially varying refractive index. The results revealed that a long focal length and unique pattern influence the image contrast in the case of Bessel beams, which differs from a typical Gaussian beam. Further, high-precision measurement of a seven-core fibre core distribution based on a Bessel beam was demonstrated using a digital correlation method. A deep learning approach was used to improve the measurement precision to 0.2° with an accuracy of 96.8%. The proposed side-view Bessel-beam-based method has the potential to handle more complex MCFs and photonic crystal fibres.
Research Summary
Nondestructive measurement: non-diffraction structured light improves image contrast
An imaging method based on structured light illumination shows promise for nondestructive measurement of specialty optical fibre internal core distribution. Structured light, such as Bessel beams, have a long depth of focus because they are mathematically non-diffraction. Fei Xu from China's Nanjing University and colleagues now report development of structured light imaging, achieving high contrast imaging results using Bessel beams as an illumination source to image media with complex internal structures. Because of the long focus depth and non-diffraction of Bessel beams, imaging blurring caused by light scattering is reduced. The team demonstrated the application of nondestructive measurement in high precision measurement of seven-core fibre core distribution.
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