Laser beam cleanup using improved model-based wavefront sensorless adaptive optics

Bing Dong; Rui Wang

doi:10.3788/COL201614.031406

Journals >Chinese Optics Letters >Volume 14 >Issue 3 >Page 031406 > Article

Chinese Optics Letters
Vol. 14, Issue 3, 031406 (2016)

Laser beam cleanup using improved model-based wavefront sensorless adaptive optics

Bing Dong^* and Rui Wang

Author Affiliations

School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China

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DOI: 10.3788/COL201614.031406 Cite this Article Set citation alerts

Bing Dong, Rui Wang. Laser beam cleanup using improved model-based wavefront sensorless adaptive optics[J]. Chinese Optics Letters, 2016, 14(3): 031406 Copy Citation Text

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Abstract

An improved model-based wavefront sensorless adaptive optics algorithm is proposed for laser beam cleanup. Deformable mirror (DM) eigenmodes are used to replace traditional Lukosz modes in order to avoid DM fitting errors. The traditional method is based on a sophisticated calibration process and solving linear equations. In our method, coefficients of DM eigenmodes are estimated by adding bidirectional modal biases into the system and then solving parabolic equations. The calibration process is omitted in our method, which makes it more feasible. From simulation and experimental results, the corrective accuracy of the improved method is higher than the traditional one.

φ = \sum_{i = 4}^{N} a_{i} L_{i} = a \cdot L,

(1)

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\int_{0}^{2 π} \int_{0}^{1} \nabla L_{j} \cdot \nabla L_{j^{'}} r d r d θ = π δ_{j j^{'}},

(2)

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〈 ρ^{2} 〉 \propto \iint_{P} {| \nabla φ |}^{2} d A .

(3)

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\iint_{P} {| \nabla φ |}^{2} d A = π \sum_{i = 4}^{N} a_{i}^{2} .

(4)

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〈 ρ^{2} 〉 = μ {| a |}^{2},

(5)

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J = \int_{ρ} \int_{θ} I (ρ, θ) (1 - ρ^{2} / R^{2}) ρ d ρ d θ = 1 - \frac{μ}{R^{2}} {| a |}^{2},

(6)

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\hat{a} \approx T^{- 1} (W - W_{0}),

(7)

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\nabla ω = (\nabla U) {SV}^{T} .

(8)

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U = ω {({SV}^{T})}^{- 1} .

(9)

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{\begin{cases} J_{0} = 1 - \frac{μ}{R^{2}} \sum_{k \neq i} a_{k}^{' 2} - \frac{μ}{R^{2}} a_{i}^{' 2}, \\ J_{+} = 1 - \frac{μ}{R^{2}} \sum_{k \neq i} a_{k}^{' 2} - \frac{μ}{R^{2}} {(a_{i}^{'} + b_{i}^{'})}^{2}, \\ J_{-} = 1 - \frac{μ}{R^{2}} \sum_{k \neq i} a_{k}^{' 2} - \frac{μ}{R^{2}} {(a_{i}^{'} - b_{i}^{'})}^{2} . \end{cases}

(10)

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a_{i}^{'} = \frac{b_{i}^{'} (J_{+} - J_{-})}{2 J_{+} - 4 J_{0} + 2 J_{-}} .

(11)

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ε = 1 - \frac{σ_{res}}{σ_{0}},

(12)

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Bing Dong, Rui Wang. Laser beam cleanup using improved model-based wavefront sensorless adaptive optics[J]. Chinese Optics Letters, 2016, 14(3): 031406

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