Beam Profiling Algorithm - Advanced Optics Laboratory | OPTI 471A, Lab Reports of Optics

Download Beam Profiling Algorithm - Advanced Optics Laboratory | OPTI 471A and more Lab Reports Optics in PDF only on Docsity! Beam Profiling Algorithm The following figure illustrates the case when both beam radius measurements (W1 and W2, or σ1 and σ2) are taken on the same side of the beam waist (W0 or σ0). Given W1 and W2, or σ1 and σ2 and the separation ∆z between the two measurement locations along beam axis, we can find the profiling parameters of the beam using the following algorithm. Geometrical illustration: Based on the basic geometrical properties of beamline diagram (that is, the axial distance from the beam waist is proportional to the beamline distance along the beam line and the proportional factor is kσ0). We can write: 1 0 1z k aσ= and 2 0 2z k aσ= therefore, 2 1 0z z z k dσ∆ = − = From the area of triangle OPQ, we have: 0 1z k d k aσ σ∆ = = , then we can have: 1 zQE a kσ ∆ = = Further more, in triangle OQE, 2 22OE AQ l aσ= = = − 2 2 1 2 1PE QD c l aσ σ σ= = = − = − − and therefore in Triangle PQE, we can have: 2 2d c a= + Thus, 0 2 2 z z kd k c a σ ∆ ∆= = + 2 2 1 1 0a σ σ= − , and 1 0 1z k aσ= 2 2 2 2 0a σ σ= − and 2 0 2z k aσ= 2 0 0z kσ=