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Journals >Photonics Research >Volume 10 >Issue 7 >Page 1777 > Article

Photonics Research
Vol. 10, Issue 7, 1777 (2022)

Adaptive optics wavefront correction using a damped transpose matrix of the influence function

Boyu Gu^1、2、3 and Yuhua Zhang^1、2、*

Author Affiliations

¹Doheny Eye Institute, Pasadena, California 91103, USA

²Department of Ophthalmology, University of California - Los Angeles, Los Angeles, California 90095, USA

³Currently at School of Computer and Information Engineering, Tianjin Chengjian University, Tianjin 300384, China

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DOI: 10.1364/PRJ.452364 Cite this Article Set citation alerts

Boyu Gu, Yuhua Zhang. Adaptive optics wavefront correction using a damped transpose matrix of the influence function[J]. Photonics Research, 2022, 10(7): 1777 Copy Citation Text

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Abstract

To assess the performance of adaptive optics and predict an optimal wavefront correction, we built a wavefront reconstructor with a damped transpose matrix of the influence function. Using an integral control strategy, we tested this reconstructor with four deformable mirrors in an experimental system, an adaptive optics scanning laser ophthalmoscope, and an adaptive optics near-confocal ophthalmoscope. Testing results proved that this reconstructor could ensure a stable and precise correction for wavefront aberration compared to a conventional optimal reconstructor formed by the inverse matrix of the influence function. This method may provide a helpful tool for testing, evaluating, and optimizing adaptive optics systems.

A = U Σ V^{T},

(1)

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Σ = [\begin{matrix} σ_{1} & 0 & \dots & 0 \\ 0 & σ_{2} & \dots & 0 \\ ⋮ & ⋮ & □ & ⋮ \\ 0 & 0 & \dots & σ_{r} \end{matrix}],

(2)

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X = A^{+} W = {(U Σ V^{T})}^{+} W = V Σ^{+} U^{T} W,

(3)

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Σ^{+} = [\begin{matrix} 1 / σ_{1} & 0 & \dots & 0 \\ 0 & 1 / σ_{2} & \dots & 0 \\ ⋮ & ⋮ & □ & ⋮ \\ 0 & 0 & \dots & 1 / σ_{r} \end{matrix}],

(4)

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X = V [\begin{matrix} 1 / σ_{1} & 0 & \dots & 0 \\ 0 & 1 / σ_{2} & \dots & 0 \\ ⋮ & ⋮ & □ & ⋮ \\ 0 & 0 & \dots & 1 / σ_{r} \end{matrix}] U^{T} W .

(5)

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X = c A^{T} W,

(6)

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A^{T} = {(U Σ V^{T})}^{T} = V (Σ^{T}) U^{T},

(7)

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X = V [\begin{matrix} c σ_{1} & 0 & \dots & 0 \\ 0 & c σ_{2} & \dots & 0 \\ ⋮ & ⋮ & □ & ⋮ \\ 0 & 0 & \dots & c σ_{r} \end{matrix}] U^{T} W .

(8)

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X_{i} = c A^{T} W + X_{i - 1},

(9)

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X_{i} = c [A^{T} \sum_{j = 1}^{m} a_{j} [\begin{matrix} \partial Z_{j} / \partial x \\ \partial Z_{j} / \partial y \end{matrix}]] + X_{i - 1},

(10)

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X_{i} = g A^{+} W + X_{i - 1},

(11)

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X_{i} = g [A^{+} \sum_{j = 1}^{m} a_{j} [\begin{matrix} \partial Z_{j} / \partial x \\ \partial Z_{j} / \partial y \end{matrix}]] + X_{i - 1},

(12)

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{RMS}_{Zernike} = \sqrt{\sum_{j = 1}^{m} a_{j}^{2}} .

(13)

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{RMS}_{deflection} = \sqrt{\sum_{i = 1}^{n} (Δ x_{i}^{2} + Δ y_{i}^{2}) / n},

(14)

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A_{i} = ([\begin{matrix} B_{i}^{x push} \\ B_{i}^{y push} \end{matrix}] - [\begin{matrix} B_{i}^{x pull} \\ B_{i}^{x pull} \end{matrix}]) / 2 p,

(15)

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A = [A_{1}, A_{2}, \dots, A_{N}] .

(16)

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r (P, Q) = \frac{\sum_{i, j} (p_{i, j} - p_{m}) (q_{i, j} - q_{m})}{\sqrt{\sum_{i, j} {(p_{i, j} - p_{m})}^{2} \sum_{i, j} {(q_{i, j} - q_{m})}^{2}}},

(17)

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Boyu Gu, Yuhua Zhang. Adaptive optics wavefront correction using a damped transpose matrix of the influence function[J]. Photonics Research, 2022, 10(7): 1777

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