# Study on Laser Parameter Measurement System Based on Cone-Arranged Fibers and CCD Camera

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}factor, can be obtained by measuring the intensity distribution of one or more axial cross-section spots [1,2,3]. When the spot is large, the measurement system prioritizes the array target composed of attenuation and detection units [4,5,6,7]. The system always has a large aperture, and the calibration of the whole target can conveniently correct the inconsistent responsivity of sampling units. However, its resolution is often limited by the complex unit design. Moreover, the transmittance and response of the units are sensitive to the incident angle in many applications [5,6,7], which is regarded as a significant error source. Since there are frequently variable and unmeasurable skew angles between the beam and the receiving system caused by alignment error, the measurement is expected to be only related to the incident energy, not the incident angle. When the spot is small, a CCD camera is commonly used [8,9,10,11,12,13,14]. The beam can act directly on the CCD array in the camera [8,9] or be imaged on various screens and shot by the camera [1,10,11]. Such methods have the advantage of high resolution [12,13]. However, on the one hand, shooting requires precise space alignment, so fast servo equipment is necessary [12,14], which adds difficulty to practical applications. On the other hand, the measurable spot size is limited by distortion, which is easily caused by the large field of view. Considering these factors, if the cross-section spot is shrunk with high fidelity before shooting, the large spot is measurable by the CCD camera without severe distortion. For the shrinking system, the input maintains a large aperture to facilitate the alignment of the beam, and the reduced output can be relatively fixed to the camera. Compared with the traditional CCD camera shooting, this method combines part of the structure of the array target, such as the large target surface and the sampling units, which not only increases the measurable spot size but also reduces the difficulty of beam alignment and improves the freedom of integration. Compared with the measurement of array targets, this method uses a single attenuator and a commercial CCD camera instead of multiple attenuators and detector units, simplifying the design. In addition, the main factor limiting the resolution changes from the outer diameter of the attenuator or detector to the sampling unit, leading to a significant increase in resolution. In summary, this method of combining the two approaches is of significance to optimize the measurement system.

## 2. Theoretical Model

#### 2.1. Bend Fiber Transmission

- All-glass fiber is suitable for its high laser damage threshold due to low absorption and high-temperature resistance.
- Multimode fiber is more suitable than single-mode fiber because of its larger core diameter and higher laser damage tolerance threshold. The former has a higher duty cycle after the array is integrated, so the spot details the are more accessible [22].

_{eff}to characterize the uniformity of fiber transmittance, as shown in:

_{i}is the total value of the analog digital unit (ADU) in the ith grid. The array composes 20 × 20 fibers, and ADU

_{ave}is the average value of 400 units. As shown in Figure 1c, the relative difference in the ADU

_{ave}per grid is less than 6% for uniform diffuse light, while it reaches 40% for uniform parallel light. The comparison shows that the transmittance of the array fibers should be characterized by the matrix of ADU

_{ave}from uniform diffused light, which has a good consistency; otherwise, Figure 1a will not be so ideal. Furthermore, the less-than-ideal result is believed to be caused by the introduction of imaging errors, which will be explained in detail in the next paragraph. The reason for using the difference in the matrix of ADU

_{ave}of uniformly diffused light to express the difference in fibers’ transmittance is as follows: the diffused input results in the uniform output divergence angle to ensure the fidelity of the measured spot distribution. Specifically, the input diffused light contains multiple modes, with some modes being mixed fully when transmitting in the core if the fiber is bent enough and its length is much greater than the core diameter [27,28]. Other modes, which do not meet the total reflection condition, are coupled to the cladding and disappear. Consider that multiple modes represent multiple angles, and the maximum angle relative to the sidewall section of the core is approximately the critical angle of total reflection θ

_{m}′. Therefore, the output of each fiber should be regarded as the divergent light filled with θ

_{m}, while the relationship between θ

_{m}′, θ

_{m}and NA is shown in the following:

_{0}, n

_{1}, and n

_{2}are the refractive indices of the incident medium, core, and cladding, respectively.

_{m}= 27.4°) is a ring. Suppose applying lateral force causes the bending of the fiber. In that case, the ring width gradually increases as the curvature increases and becomes a solid circle with an outer diameter more significant than the initial ring. The far-field distribution characterizes the divergence angle of the output beam. The result means that the curvature will affect the divergence angle complexly. For an ideal camera imaging system with a lens, as long as the output surface of the array is imaged through the camera, the difference in the output divergence angle does not seem to affect the image captured. This effect is enormous, to the extent that the measured results deviate by 40% from the actual output, as shown in Figure 1b,c. The reasons are as follows: 1. The difference in divergence angle leads to the difference in the amount of incoming light of the camera, limited to the field diaphragm. 2. The focal planes of the output of each fiber cannot be unified, and the diffused spot generated by defocusing is on the image plane. In addition, the degree of diffusing is different and is not easy to determine. When calculating the intensity distribution of the captured images in the pooling grids, some errors are difficult to eliminate simply by using the algorithm. Brighter spots appear more frequently in the lower half of the array, as shown in Figure 1b. Considering that the small output end is located in the lower half of the receiving surface in the actual system, there is reason to believe that the relatively large radius of curvature brings a smaller output divergence angle to this area, resulting in a higher intensity of the shot spots.

#### 2.2. Fiber-Homogenizer Model

_{N}is the output light intensity in the normal direction of the homogenizer surface, and I

_{θ}is the output light intensity in the direction of the angle θ with the normal. A 1064 nm laser is taken for normal incidence and three fibers with large bending differences are randomly selected for experiments. Using three-dimensional graphs and PIB curves to characterize simulated and experimental spots, as shown in Figure 2, the RMSE of PIB curves belonging to the simulated spot (a) and the three experimental spots (b), (c), and (d) are very low, being 1.10%, 1.16%, and 1.15%, respectively, proving that our homogenizer can be seen as a Lambertian material. In addition, the PIB curves of spots (b), (c), and (d) are almost overlapped, which can be seen in Figure 2e. A uniform Gaussian model is, therefore, feasibly able to simulate 400 homogenized spots.

## 3. Methods

#### 3.1. Instrument Design

#### 3.2. Computational Correction

_{m}

_{×m}, where m × m is the camera resolution. Secondly, the experimental spot provided in Section 2.2 is used as the model. Assuming that the unit in the first row (column) can affect that in the 20th row (column) in the farthest case, the spot model needs to be processed with average pooling by grids of 39 × 39 to obtain P

_{39}

_{×39}. Thirdly, L

_{m×m}is used to filter the measured image A

_{m×m}and averagely pool it to obtain the matrix A′

_{20}

_{×20}as a known quantity and solve the actual spot A′′

_{20}

_{×20}by:

_{1}

_{×400}is reshaped into A′′

_{20}

_{×20}, and the actual output of 400 fibers can be obtained.

^{−7}, and the total power P

_{sum}can be solved as

_{sum}is the total value of the image’s ADU. Furthermore, power density I can also be calculated by γ.

## 4. Results and Discussions

_{m}is calculated as 12.7°, according to Equation (2). However, the power is reduced to 68.3% and 72.8% of the actual power (normal incident) at 12° and −12°, respectively. It is known that the application object of theoretical NA and θ

_{m}is the meridian ray in a straight fiber, which is the ray in any plane through the central axis of the fiber. In actual application scenarios, the full incidence at θ

_{m}and the bending of the fiber will cause the light to be refracted into the cladding and become gradually lost there. In addition, the RMSE increased to approximately 6% at this angle, indicating that the loss is non−uniform for fibers, which is caused by the difference in the bending shape of each fiber. In summary, θ

_{m}can only be used as a reference for the system’s allowable incident angle. However, when switching to the fiber with a larger theoretical NA, the allowable incident angle of the system will be positively affected as the critical incident angle that meets the total reflection condition is increased. In addition, the system has good performance in the range of measurable laser beam width and light intensity; for the former, the maximum is 66.7% of the array aperture (Gaussian beam), which is generally 76 mm. In this case, the power received by the array reaches 99% of the total power of the laser beam [31]. As for the minimum, the spot needs to cover at least ten fibers in the radial direction so as not to affect the subsequent interpolation calculation and spot recovery [32]; therefore, the minimum laser beam width needs to reach 33.4% of the array aperture, that is, 38 mm. Regarding the allowable light intensity, the minimum is in the order of mW/cm

^{2}, taking into account the data in the power density calibration in Section 3.2; the maximum is in the order of kW/cm

^{2}, taking into account the test experiment of the total reflection metal target used and the laser damage threshold of the sampling fibers [33].

## 5. Conclusions

- The CCD camera can shoot large spots without the distortion caused by a large field of view for the cross−section spot is shrunk with high fidelity.
- The sampling resolution is higher and the design is simpler compared with the traditional array target.
- The allowed incident angle range is acceptable. The measurement of the total power and the power density distribution of the spots has high accuracy when the beam’s incident angle is between −8° and 8°.

- Measurement resolution can be improved further without the limitations of complex unit structure. For example, the hexagonal fiber layout will be an optimization direction for the higher fiber packing density than the square layout.
- When it is needed to focus on a larger angle, a fiber with higher NA should be considered. The system’s actual NA and the fiber’s theoretical NA are predicted to have a linear correlation, and the relevant theoretical discussion and experimental verification are worth studying.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Kaplan, A.F.H. Analysis and modeling of a high−power Yb: Fiber laser beam profile. Opt. Eng.
**2011**, 50, 054201. [Google Scholar] [CrossRef] - Pan, S.; Ma, J.; Zhu, R.; Tu, B.; Zhou, W. Actual−time complex amplitude reconstruction method for beam quality M
^{2}factor measurement. Opt. Express**2017**, 25, 20142. [Google Scholar] [CrossRef] [PubMed] - Wang, F.; Xie, Y.J.; Ji, Y.F.; Duan, L.H.; Ye, X.S. A compound detector array for the measurement of large area laser beam intensity distribution. In Proceedings of the 2nd International Symposium on Laser Interaction with Matter, Xi’an, China, 16 May 2013. [Google Scholar] [CrossRef]
- Zhang, L.; Wang, Z.B.; Shao, B.B.; Yang, P.L.; Tao, M.M. Near-Infrared Detecting Array for High Energy Laser Beam Diagnostics. Adv. Mater. Res.
**2012**, 571, 156–159. [Google Scholar] [CrossRef] - Feng, G.B.; Yang, P.L.; Wang, Q.S.; Liu, F.H.; Ye, X.S. Intensity laser far-field spot intensity distribution measurement technology. High Power Laser Part. Beams
**2013**, 25, 1615–1619. (In Chinese) [Google Scholar] [CrossRef] - Higgs, C.; Grey, P.C.; Mooney, J.G.; Hatch, R.E.; Carlson, R.R.; Murphy, D.V. Dynamic target board for ABL-ACT performance characterization. In Proceedings of the Airborne Laser Advanced Technology II, Orlando, FL, USA, 5 April 1999. [Google Scholar] [CrossRef]
- Raj, V.; Swapna, M.S.; Sankararaman, S. Unwrapping the laser beam quality through nonlinear time series and fractal analyses: A surrogate approach. Opt. Laser Technol.
**2021**, 140, 107029. [Google Scholar] [CrossRef] - Ji, K.H.; Hou, T.R.; Li, J.B.; Meng, L.Q.; Han, Z.G.; Zhu, R.H. Fast measurement of the laser beam quality factor based on phase retrieval with a liquid lens. Appl. Opt.
**2019**, 58, 2765–2772. [Google Scholar] [CrossRef] - Schmidt, O.A.; Schulze, C.; Flamm, D.; Brüning, R.; Kaiser, T.; Schröter, S.; Duparré, M. Actual-time determination of laser beam quality by modal decomposition. Opt. Express
**2011**, 19, 6741–6748. [Google Scholar] [CrossRef] [PubMed] - Bonora, S.; Beydaghyan, G.; Haché, A.; Ashrit, P.V. Mid-IR laser beam quality measurement through vanadium dioxide optical switching. Opt. Lett.
**2013**, 38, 1554–1556. [Google Scholar] [CrossRef] - Ke, Y.; Zeng, C.L.; Xie, P.Y.; Jiang, Q.S.; Liang, K.; Yang, Z.Y.; Zhao, M. Measurement system with high accuracy for laser beam quality. Appl. Opt.
**2015**, 54, 4876–4880. [Google Scholar] [CrossRef] [PubMed] - Zhao, Y.Y.; Xiao, Z.J.; Liang, X.; Bao, L. Study of zero position variation for an optical sight by using a CCD. J. Opt. Technol.
**2019**, 86, 374–378. [Google Scholar] [CrossRef] - Nemoto, K.; Nayuki, T.; Fujii, T.; Goto, N.; Kanai, Y. Optimum control of the laser beam intensity profile with a deformable mirror. Appl. Opt.
**1997**, 36, 7689–7695. [Google Scholar] [CrossRef] [PubMed] - Kim, S.; Lee, M.; Park, J.; Lee, K.; Hwang, I. Solar tracking system for lighting fiber. In Proceedings of the Conference on Lasers and Electro-Optics (CLEO)—Laser Science to Photonic Applications, San Jose, CA, USA, 8 June 2014. [Google Scholar] [CrossRef]
- Röpke, U.; Bartelt, H.; Unger, S.; Schuster, K.; Kobelke, J. Two-dimensional high-precision fiber waveguide arrays for coherent light propagation. Opt. Express
**2007**, 15, 6894–6899. [Google Scholar] [CrossRef] [PubMed] - Heyvaert, S.; Ottevaere, H.; Kujawa, I.; Buczynski, R.; Raes, M.; Terryn, H.; Thienpont, H. Numerical characterization of an ultra-high NA coherent fiber bundle part I: Modal analysis. Opt. Express
**2013**, 21, 21991–22011. [Google Scholar] [CrossRef] [PubMed] - Luo, J.; Qin, L.A.; Hou, Z.H.; Guan, W.L.; Zhu, W.Y.; Zhang, S.L.; Tan, F.F. Optical fiber transmission characteristics in laser spot distribution measurement system. Acta Opt.
**2021**, 41, 146–152. (In Chinese) [Google Scholar] [CrossRef] - Boechat, A.A.P.; Su, D.; Hall, D.R.; Jones, J.D.C. Bend loss in large core multimode optical fiber beam delivery systems. Appl. Opt.
**1991**, 30, 321–327. [Google Scholar] [CrossRef] [PubMed] - Jeong, Y.; Sahu, J.K.; Payne, D.N.; Nilsson, J. Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power. Opt. Express
**2004**, 12, 6088–6092. [Google Scholar] [CrossRef] [PubMed] - Yalin, A.P. High power fiber delivery for laser ignition applications. Opt. Express
**2013**, 21, A1102–A1112. [Google Scholar] [CrossRef] [PubMed] - Pask, C.; Snyder, A.W. Multimode optical fibers: Interplay of absorption and radiation losses. Appl. Opt.
**1976**, 15, 1295–1298. [Google Scholar] [CrossRef] [PubMed] - Velamuri, A.V.; Patel, K.; Sharma, I.; Gupta, S.S.; Gaikwad, S.; Krishnamurthy, P.K. Investigation of Planar and Helical Bend Losses in Single- and Few-Mode Optical Fibers. J. Light. Technol.
**2019**, 37, 3544–3556. [Google Scholar] [CrossRef] - Donlagic, D. A low bending loss multimode fiber transmission system. Opt. Express
**2009**, 17, 22081–22095. [Google Scholar] [CrossRef] [PubMed] - Goto, Y.; Nakajima, K.; Matsui, T.; Kurashima, T.; Yamamoto, F. Influence of Cladding Thickness on Transmission Loss and its Relationship with Multicore Fiber Structure. J. Light. Technol.
**2015**, 33, 4942–4949. [Google Scholar] [CrossRef] - Haggans, C.W.; Singh, H.; Varner, W.F.; Wang, J. Narrow-Depressed Cladding Fiber Design for Minimization of Cladding Mode Losses in Azimuthally Asymmetric Fiber Bragg Gratings. J. Light. Technol.
**1998**, 16, 902–909. [Google Scholar] [CrossRef] - Varghese, B.; Rajan, V.; Leeuwen, T.G.V.; Steenbergen, W. Evaluation of a multimode fiber optic low coherence interferometer for path length resolved Doppler measurements of diffuse light. Rev. Sci. Instrum.
**2007**, 78, 7664–7667. [Google Scholar] [CrossRef] - Smith, R.C.G.; Sarangan, A.M.; Jiang, Z.; Marciante, J.R. Direct measurement of bend-induced mode deformation in large-mode-area fibers. Opt. Express
**2012**, 20, 4436–4443. [Google Scholar] [CrossRef] - Gambling, W.A.; Payne, D.N.; Matsumura, H. Mode conversion coefficients in optical fibers. Appl. Opt.
**1975**, 14, 1538–1542. [Google Scholar] [CrossRef] - Berrocal, E.; Meglinski, I.; Jermy, M. New model for light propagation in highly inhomogeneous polydisperse turbid media with applications in spray diagnostics. Opt. Express
**2005**, 13, 9181–9195. [Google Scholar] [CrossRef] - Schermer, R.T. Mode scalability in bent optical fibers. Opt. Express
**2007**, 15, 15674–15701. [Google Scholar] [CrossRef] - Pang, M.; Gao, X.; Rong, J. Technical requirements and uncertainty of far field laser spot centroid measurement using array detection method. Optik
**2015**, 126, 5881–5885. [Google Scholar] [CrossRef] - Cheng, Y.L.; He, F.; Tan, F.F. Research on the laser spot restoration method of detector array target. Laser Infrared
**2020**, 50, 749–753. [Google Scholar] [CrossRef] - Guan, W.L.; Tan, F.F.; Hou, Z.H. Research on Wide Angle Array Detection Technology for High Power Density Laser. Acta Opt. Sin.
**2022**, 42, 0214002. [Google Scholar] [CrossRef]

**Figure 1.**Array spots: (

**a**) array spots with skylight; (

**b**) array spots with direct sunlight; (

**c**) the contrast of the η

_{eff}of the two types of spots: the fluctuation of η

_{eff}with direct sunlight, as the light source is much larger than that with skylight. The number of the fiber is defined as follows. The number increases one by one in each row in the array from left to right and increases in each column from top to bottom.

**Figure 2.**Simulated and experimental results: (

**a**) simulated spot; (

**b**) experimental spot of fiber #1; (

**c**) experimental spot of fiber #2; (

**d**) experimental spot of fiber #3; (

**e**) PIB curves of four spots.

**Figure 3.**System diagram: the upper half of the diagram shows the light transmission process without the homogenizer (part of the spots of the array), while the lower half shows the process with the homogenizer. (

**a**) Different divergence angles of the output array beams without the homogenizer; (

**b**) captured array spots with mutual crosstalk that are not easy to divide; (

**c**) output beams that become array diffusers; (

**d**) captured array spots with mutual crosstalk that can be predicted by the model and removed by the algorithm; (

**e**) array spots after positioning and gridding; (

**f**) array spots after crosstalk removal; and (

**g**) restored spots.

**Figure 4.**(

**a**) Schematic diagram of mutual crosstalk between spots; (

**b**) calibration curve of total power.

**Figure 5.**(

**a**) Actual spot collected by the diffuse reflection screen; (

**b**) spot measured by the system; (

**c**) centroid section lines of the two types of spots in the x-direction; (

**d**) centroid section lines of the two types of spots in the y-direction; (

**e**) PIB curves of the two types of spots.

**Figure 6.**(

**a**) PIB curves of the measured spots at different incident angles and the actual spot; (

**b**) absolute value of the measured total power and their ratios relative to the true power when the incident angle changes between −16° and 16°; (

**c**) RMSEs of the PIB curves of the measured spots and the actual spot.

Instrument | Feature | Specification |
---|---|---|

Laser | Wavelength | 1064 nm |

Polarization | Linear | |

Output power | 1~100 W, continuously adjustable | |

Working mode | Continuous wave | |

Diffuse reflection screen | Diffuse reflectance ratio | >99% |

Material | Thermoplastic resin | |

Filter | Central wavelength | 1064 nm |

Bandwidth | 8 nm | |

Attenuators | Type | Absorptive neutral density |

Optical density (OD) | 2~5 | |

Lenses | Focal for actual spot | 12 mm/F 1.4 |

Focal for reduced spot (with extension ring) | 50 mm/F 1.4 | |

CCD camera | Camera | Allied Vision Prosilica GT |

Sensor | Sony ICX674ALG | |

Pixels | 1936 (H) × 1456 (V) | |

Pixel size with lens for actual spot | 121 μm (H) × 121 μm (V) | |

Pixel size with lens for reduced spot | 5 μm (H) × 5 μm (V) |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Luo, J.; Qin, L.; Hou, Z.; Zhang, S.; Zhu, W.; Guan, W. Study on Laser Parameter Measurement System Based on Cone-Arranged Fibers and CCD Camera. *Sensors* **2022**, *22*, 7892.
https://doi.org/10.3390/s22207892

**AMA Style**

Luo J, Qin L, Hou Z, Zhang S, Zhu W, Guan W. Study on Laser Parameter Measurement System Based on Cone-Arranged Fibers and CCD Camera. *Sensors*. 2022; 22(20):7892.
https://doi.org/10.3390/s22207892

**Chicago/Turabian Style**

Luo, Jie, Laian Qin, Zaihong Hou, Silong Zhang, Wenyue Zhu, and Wenlu Guan. 2022. "Study on Laser Parameter Measurement System Based on Cone-Arranged Fibers and CCD Camera" *Sensors* 22, no. 20: 7892.
https://doi.org/10.3390/s22207892