Wave-theory analysis of acousto-optic Bragg diffraction image formation

David J. Mehrl; Zeh Chen Liu; Adrian Korpel

doi:10.1364/AO.32.005112

Applied Optics
Vol. 32,
Issue 26,
pp. 5112-5118
(1993)
•https://doi.org/10.1364/AO.32.005112

Wave-theory analysis of acousto-optic Bragg diffraction image formation

David J. Mehrl, Zeh Chen Liu, and Adrian Korpel

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David J. Mehrl, Zeh Chen Liu, and Adrian Korpel, "Wave-theory analysis of acousto-optic Bragg diffraction image formation," Appl. Opt. 32, 5112-5118 (1993)

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Abstract

We analyze anastigmatic Bragg diffraction imaging by use of an efficient numerical method that makes use of a plane-wave spectrum formalism applicable to weak acousto-optic diffraction involving three-dimensional light and sound fields. Results from this wave-theory analysis are compared with previous results derived on the basis of ray theory, and are shown to be in good agreement, thus corroborating the validity of both techniques.

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Description	Value
λ (Light wavelength)	0.422 μm
Λ (Sound wavelength)	0.1 mm
K/k ≅ 2ϕ_B	4.22 mrad
W _L (Waist of incident light at O)	0.896 μm
W _s (Waist of sound at Q)	50 μm
r₀ (Position of sound source)	x₀ = −2.61 cm
	y₀ = 0 cm
	z₀ = − 1.08 cm

Description	Value
Distance of sound source from origin	$\bar{Q O} = \sqrt{{x_{0}}^{2} + {z_{0}}^{2}} = 2.83 cm$
Angle between sound source and the Z axis	α₀ = tan⁻¹(x₀/z₀) = 1.18 rad
Distance between centers of vertical and horizontal line foci	$Δ z = (K / k) \bar{Q O} / sin α_{0} = 129$ μm
Angular extent of incident light [See Eq. (13)]	ϕ_max = ϕ_max′ = ${\tilde{W}}_{ϕ}$ = λ/πW _L = 0.0150 rad
Extent of horizontal focus along the X axis	Δx = 2Δz sin ϕ_max = 38.55 μm
Extent of horizontal focus along the horizontal focus line	Δq = Δ/sin α₀ = 41.7 μm
Extent of vertical focus along the vertical focus line	Δy = 2Δz sin ϕ_max′ = 38.55 μm
Waist of light, in the horizontal extent, at the vertical focus line	δx_min = λ/(2 sin ϕ_max) = 1.412 μm
Waist of light, in the vertical extent, at horizontal focus line	δy_min = λ/(2sin ϕ′_max) = 1.412 μm

Description	Value
λ (Light wavelength)	0.422 μm
Λ (Sound wavelength)	0.1 mm
K/k ≅ 2ϕ_B	4.22 mrad
W _L (Waist of incident light at O)	0.896 μm
W _s (Waist of sound at Q)	50 μm
r₀ (Position of sound source)	x₀ = −2.61 cm
	y₀ = 0 cm
	z₀ = − 1.08 cm

Description	Value
Distance of sound source from origin	$\bar{Q O} = \sqrt{{x_{0}}^{2} + {z_{0}}^{2}} = 2.83 cm$
Angle between sound source and the Z axis	α₀ = tan⁻¹(x₀/z₀) = 1.18 rad
Distance between centers of vertical and horizontal line foci	$Δ z = (K / k) \bar{Q O} / sin α_{0} = 129$ μm
Angular extent of incident light [See Eq. (13)]	ϕ_max = ϕ_max′ = ${\tilde{W}}_{ϕ}$ = λ/πW _L = 0.0150 rad
Extent of horizontal focus along the X axis	Δx = 2Δz sin ϕ_max = 38.55 μm
Extent of horizontal focus along the horizontal focus line	Δq = Δ/sin α₀ = 41.7 μm
Extent of vertical focus along the vertical focus line	Δy = 2Δz sin ϕ_max′ = 38.55 μm
Waist of light, in the horizontal extent, at the vertical focus line	δx_min = λ/(2 sin ϕ_max) = 1.412 μm
Waist of light, in the vertical extent, at horizontal focus line	δy_min = λ/(2sin ϕ′_max) = 1.412 μm

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Equations (15)

Applied Optics