2022
DOI: 10.3390/s22051765
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Reconstructing the Spatial Parameters of a Laser Beam Using the Transport-of-Intensity Equation

Abstract: A simple method for reconstructing the spatial parameters of a laser beam, based on the transport-of-intensity equation, is presented. Registration of cross-section intensity distributions in several planes was carried out using a single CMOS camera. The processing of the experimental measurements with the help of specialized software helped to reconstruct all of the spatial parameters, namely, the radius and position of the waist, Rayleigh length, angular divergence, quality parameter M2 The method was compar… Show more

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Cited by 9 publications
(7 citation statements)
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“…Then, at the second stage, the wavefront radius of curvature R (z 2 ) is calculated by approximating the obtained phase values ϕ (z 2 ) of the laser beam with a hyperbolic dependence according to the following equations [18,19]: where z R is a Rayleigh length, w (z) is the laser beam radius at the level 1/e 2 and w 0 denotes the beam waist radius. At the final stage, based on the reconstructed spatial characteristics of the laser beam that passed through the optical lens, the refractive index of the lens is determined.…”
Section: Methods and Approachesmentioning
confidence: 99%
“…Then, at the second stage, the wavefront radius of curvature R (z 2 ) is calculated by approximating the obtained phase values ϕ (z 2 ) of the laser beam with a hyperbolic dependence according to the following equations [18,19]: where z R is a Rayleigh length, w (z) is the laser beam radius at the level 1/e 2 and w 0 denotes the beam waist radius. At the final stage, based on the reconstructed spatial characteristics of the laser beam that passed through the optical lens, the refractive index of the lens is determined.…”
Section: Methods and Approachesmentioning
confidence: 99%
“…If calculating the effective spot size of laser beam during cutting, the value can be estimated by plugging in half of the material thickness into variable ( z ) of Equation (). [ 116 ] This assumes fine focus is set to the center of the material. If fine focus were set on top of the material, the effective spot size would become the size of the beam waist.zR=[ Wo2BPP]×1000$$z_{\text{R}} = \left[\right.…”
Section: Nitinol Manufacturing Processesmentioning
confidence: 99%
“…The beam product parameter is a measure of how a beam compares to a theoretical gaussian beam distribution and is defined by Equation (1). [116] BPP…”
Section: Relevant Equationsmentioning
confidence: 99%
“…Three-dimensional (3D) image visualization is a significant issue for many applications, such as unmanned autonomous vehicles, media content, defense, and so on [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ]. To visualize 3D images, various methods can be utilized, such as time of flight, stereoscopic imaging, holography, and integral imaging [ 1 , 9 , 10 , 11 ]. By utilizing incoherent light with a general camera, integral imaging [ 1 , 9 , 12 , 13 , 14 ] can be used.…”
Section: Introductionmentioning
confidence: 99%