Light Beam Deflector Performance: a Comparative Analysis

J. David Zook

doi:10.1364/AO.13.000875

Applied Optics
Vol. 13,
Issue 4,
pp. 875-887
(1974)
•https://doi.org/10.1364/AO.13.000875

Light Beam Deflector Performance: a Comparative Analysis

J. David Zook

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J. David Zook, "Light Beam Deflector Performance: a Comparative Analysis," Appl. Opt. 13, 875-887 (1974)

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Abstract

The performance of various types of analog light beam deflectors is summarized, and their relative positions in a deflector hierarchy are defined. The three types of deflectors considered are (1) mechanical (galvanometer) mirror deflectors, (2) acoustooptic deflectors, and (3) analog electrooptic deflectors. Material figures of merit are defined and compared, and the theoretical trade-off between speed and resolution is given for each type of deflector.

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Parameter	Value	Comment
α	4	Coil radius is allowed to distort by one-fourth (1/α) of the conductor thickness at maximum rotational speed
β	1	A square mirror is assumed.
γ	4	The coil is twice as long as it is wide (l = γR).
θ ₀	0.3 rad	Half-angle of uniform field
B	20,000 G	This is the maximum field attainable with available pole pieces.
K _H	0.26 W/cm²	Conservative estimate of heat dissipation in 301 Servomotor.
ρ _e	2.8 × 10⁻⁶ Ω cm	Resistivity of Al
ρ _c	2.7 g/cm³	Density of Al
v _sc	6.4 × 10⁵ cm/sec	Velocity of sound in Al
v _sm	12.9 × 10⁶ cm/sec	Velocity of sound in Be
ρ _m	1.82	Density of Be
λ	0.63 × 10⁻⁴ cm	Wavelength of He–Ne laser
Λ	0.25	This corresponds to 10,000 spots from Eq. (10).
W	1.161 cm	Calculated from Eq. (16)
θ _p	0.2154 rad	θ _p = (28/39)θ₀ from Eq. (16) and (10)
v _a ²Λ^−1/2	319,200 cm^3/2/sec²	From Eq. (11)
v _b Λ^1/2	4,348,000 cm^3/2/sec	From Eq. (12)
v _c	1,810,000 cm/sec	From Eq. (13)
ω ₀	3012 rad/sec	From Eq. (18)
R	0.7068 cm	From Eq. (17)
t _m	0.03325 cm	From Eq. (5)
J _m	0.009162 g cm²	From Eq. (4)
t _c	0.01797 cm	From Eq. (5)
W _c	0.1196 cm	W _c = (22/39)θ₀R from Eq. (8)
J _c	0.01912 g cm²	J _c = 2ρ _c t _c w _c (l + 2R/3)R²
I _m	6.909 A turns	From Eq. (7)
τ _m	55,220 dyne cm	τ = 2RlBI _m
ω ₀	3011 rad/sec	ω₀² = τ _m /θ _p (J _m + J _c ) (This is a consistency check)
τ _A	1.04 msec	τ _A = π/ω₀

	KD₂PO₄ (KD*P)	LiNbO₃ (LN)	Sr_0.75Ba_0.25Nb₂O₆ (SBN)
n	1.50	2.20	2.30
r _ij	r₆₃ = 2.4 × 10⁻⁹ cm/V	r₃₃ = 3.10 × 10⁻⁹ cm/V	r₃₃ = 1.34 × 10⁻⁷ cm/V
eλ/2n³r (eλ = 10⁻⁴ cm)	6170 V	1520 V	31 V
κ = ∊ _j /∊₀	49	26.4	6500
f _ij = r _ij /∊ _j	0.055 m²/C	0.133 m²/C	0.0233 m²/C
n ⁷	17.1	250	340
(n⁷r²)/[∊(eλ)³]	2.26 × 10⁷J⁻¹	103 × 10⁷J⁻¹	1061 × 10⁷J⁻¹
Maximum demonstrated (Δn) _p	8.1 × 10⁻⁵	0.001	0.003
Maximum W (see text)	7 cm	2 cm	1 cm
L/W	55.5	19.1	11.3
Maximum N _R (e = 1.6)	1050	1280	1130

Parameter	Value	Comment
α	4	Coil radius is allowed to distort by one-fourth (1/α) of the conductor thickness at maximum rotational speed
β	1	A square mirror is assumed.
γ	4	The coil is twice as long as it is wide (l = γR).
θ ₀	0.3 rad	Half-angle of uniform field
B	20,000 G	This is the maximum field attainable with available pole pieces.
K _H	0.26 W/cm²	Conservative estimate of heat dissipation in 301 Servomotor.
ρ _e	2.8 × 10⁻⁶ Ω cm	Resistivity of Al
ρ _c	2.7 g/cm³	Density of Al
v _sc	6.4 × 10⁵ cm/sec	Velocity of sound in Al
v _sm	12.9 × 10⁶ cm/sec	Velocity of sound in Be
ρ _m	1.82	Density of Be
λ	0.63 × 10⁻⁴ cm	Wavelength of He–Ne laser
Λ	0.25	This corresponds to 10,000 spots from Eq. (10).
W	1.161 cm	Calculated from Eq. (16)
θ _p	0.2154 rad	θ _p = (28/39)θ₀ from Eq. (16) and (10)
v _a ²Λ^−1/2	319,200 cm^3/2/sec²	From Eq. (11)
v _b Λ^1/2	4,348,000 cm^3/2/sec	From Eq. (12)
v _c	1,810,000 cm/sec	From Eq. (13)
ω ₀	3012 rad/sec	From Eq. (18)
R	0.7068 cm	From Eq. (17)
t _m	0.03325 cm	From Eq. (5)
J _m	0.009162 g cm²	From Eq. (4)
t _c	0.01797 cm	From Eq. (5)
W _c	0.1196 cm	W _c = (22/39)θ₀R from Eq. (8)
J _c	0.01912 g cm²	J _c = 2ρ _c t _c w _c (l + 2R/3)R²
I _m	6.909 A turns	From Eq. (7)
τ _m	55,220 dyne cm	τ = 2RlBI _m
ω ₀	3011 rad/sec	ω₀² = τ _m /θ _p (J _m + J _c ) (This is a consistency check)
τ _A	1.04 msec	τ _A = π/ω₀

	KD₂PO₄ (KD*P)	LiNbO₃ (LN)	Sr_0.75Ba_0.25Nb₂O₆ (SBN)
n	1.50	2.20	2.30
r _ij	r₆₃ = 2.4 × 10⁻⁹ cm/V	r₃₃ = 3.10 × 10⁻⁹ cm/V	r₃₃ = 1.34 × 10⁻⁷ cm/V
eλ/2n³r (eλ = 10⁻⁴ cm)	6170 V	1520 V	31 V
κ = ∊ _j /∊₀	49	26.4	6500
f _ij = r _ij /∊ _j	0.055 m²/C	0.133 m²/C	0.0233 m²/C
n ⁷	17.1	250	340
(n⁷r²)/[∊(eλ)³]	2.26 × 10⁷J⁻¹	103 × 10⁷J⁻¹	1061 × 10⁷J⁻¹
Maximum demonstrated (Δn) _p	8.1 × 10⁻⁵	0.001	0.003
Maximum W (see text)	7 cm	2 cm	1 cm
L/W	55.5	19.1	11.3
Maximum N _R (e = 1.6)	1050	1280	1130

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Equations (57)

Applied Optics