High-speed Shack-Hartmann wavefront sensor design with commercial off-the-shelf optics

Jeffrey J. Widiker; Scott R. Harris; Bradley D. Duncan

doi:10.1364/AO.45.000383

Applied Optics
Vol. 45,
Issue 2,
pp. 383-395
(2006)
•https://doi.org/10.1364/AO.45.000383

High-speed Shack–Hartmann wavefront sensor design with commercial off-the-shelf optics

Jeffrey J. Widiker, Scott R. Harris, and Bradley D. Duncan

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Jeffrey J. Widiker, Scott R. Harris, and Bradley D. Duncan, "High-speed Shack-Hartmann wavefront sensor design with commercial off-the-shelf optics," Appl. Opt. 45, 383-395 (2006)

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Abstract

Several trade-offs relevant to the design of a two-dimensional high-speed Shack–Hartmann wavefront sensor are presented. Also outlined are some simple preliminary experiments that can be used to establish critical design specifications not already known. These specifications include angular uncertainty, maximum measurable wavefront tilt, and spatial resolution. A generic design procedure is then introduced to enable the adaptation of a limited selection of CCD cameras and lenslet arrays to the desired design specifications by use of commercial off-the-shelf optics. Although initially developed to aid in the design of high-speed (i.e., megahertz-frame-rate) Shack–Hartmann wavefront sensors, our method also works when used for slower CCD cameras. A design example of our procedure is provided.

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Parameter	$θ_{\max}$	$σ_{θ}$	$W_{spot}$	SSR
$f_{μ}$	↓	↓	↑	—
Δ	↑	↑	↓	↓
λ	↓	↓	↑	—
CCD pixel size^a	—	↑	—	—
CCD fill factor	—	↓	—	—

Parameter	Condition	Increase	Decrease
		$θ_{\max}$
	>1	$σ_{θ}$	A
		SSR
$\| M_{1} \|$
			$θ_{\max}$
	<1	A	$σ_{θ}$
			SSR

			$W_{spot}$
	+	$θ_{\max}$
			σ_θ
f _s
		$W_{spot}$
	−		$θ_{\max}$
		σ_θ


			A
	>1	W_spot
			σ_θ
$\| M_{2} \|$
		A
	<1		W_spot
		σ_θ

Alteration	$θ_{\max} (µrad)$	$σ_{θ} (µrad)$	$SSR ({mm}^{- 1})$	Sampled Area $(mm \times mm)$	Spot Size		$\| M_{1} \|$	$f_{s} (m)$	$\| M_{2} \|$
Alteration	$θ_{\max} (µrad)$	$σ_{θ} (µrad)$	$SSR ({mm}^{- 1})$	Sampled Area $(mm \times mm)$	(mm)	(pixels)	$\| M_{1} \|$	$f_{s} (m)$	$\| M_{2} \|$
None	4904	2083.3	3.049	$14.4 \times 14.4$	92.6	1	1	∞	1
Introduction of 4-F system	1349	572.9	0.838	$52.5 \times 52.5$	92.6	1	0.275	∞	1
Introduction of singlet lens	1520	640.0	0.915	$48.1 \times 48.1$	90.4	1	0.3	1	1
Introduction of relay lens	1520	1.15	0.915	$7.63 \times 7.63$	1000	10	0.3	1	11.1
Iteration 1	1520	28.96	0.915	$19.2 \times 19.2$	400	4	0.3	1	4.42
Iteration 2	1520	8.27	0.915	$10.9 \times 10.9$	700	7	0.3	1	7.74
Iteration 3	1520	18.52	0.915	$15.3 \times 15.3$	500	5	0.3	1	5.53
Iteration 4	1520	11.87	0.915	$12.8 \times 12.8$	600	6	0.3	1	6.64
Desired	>1500	<15	>0.833	Most possible	NA^a	NA	NA	NA	NA

Parameter	$θ_{\max}$	$σ_{θ}$	$W_{spot}$	SSR
$f_{μ}$	↓	↓	↑	—
Δ	↑	↑	↓	↓
λ	↓	↓	↑	—
CCD pixel size^a	—	↑	—	—
CCD fill factor	—	↓	—	—

Parameter	Condition	Increase	Decrease
		$θ_{\max}$
	>1	$σ_{θ}$	A
		SSR
$\| M_{1} \|$
			$θ_{\max}$
	<1	A	$σ_{θ}$
			SSR

			$W_{spot}$
	+	$θ_{\max}$
			σ_θ
f _s
		$W_{spot}$
	−		$θ_{\max}$
		σ_θ


			A
	>1	W_spot
			σ_θ
$\| M_{2} \|$
		A
	<1		W_spot
		σ_θ

Abstract

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Equations (28)

Applied Optics