Abstract

The bender-bimorph beam steerer is a piezoelectrically driven optical device capable of pointing a light beam of several centimeters diameter anywhere in a several degree wide field of view with a control bandwidth of several hundred hertz. Its operation depends on the mechanical motion of a piezoelectric bender-bimorph to tilt a mirror, which in turn deflects the light beam. Fundamental relationships governing the operation of such a device constrain the product of mirror diameter, scan amplitude, and control bandwidth so that optimization of a bender-bimorph beam steerer system is a matter of trade-off considerations. A theoretical analysis of bender-bimorph performance is carried out. Expressions are derived for the resonant frequency of a loaded bimorph and its deflection. Graphs of these expressions are presented with several parameters treated as variables. For the numerical calculations, a very light beryllium mirror the same width as the bimorph is assumed. Some experimental data were collected and compared with the predicted performance (i.e., resonant frequency and deflection). The comparison verified the theoretical expressions.

© 1970 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. R. J. Roark, Formulas for Stress and Strain (McGraw–Hill Book Co., New York, 1954).
  2. Clevite Electronic Components Bulletin No. 9234, January1962.

Roark, R. J.

R. J. Roark, Formulas for Stress and Strain (McGraw–Hill Book Co., New York, 1954).

Other (2)

R. J. Roark, Formulas for Stress and Strain (McGraw–Hill Book Co., New York, 1954).

Clevite Electronic Components Bulletin No. 9234, January1962.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Deflection of light beam.

Fig. 2
Fig. 2

Bender-bimorph scanner.

Fig. 3
Fig. 3

Slab elongation.

Fig. 4
Fig. 4

Application of forces.

Fig. 5
Fig. 5

Angular deflection.

Fig. 6
Fig. 6

Resonant frequency fr and peak-to-peak deflection ϕp-p vs length l of a 1-mm thick bimorph.

Fig. 7
Fig. 7

Resonant frequency fr and peak-to-peak deflection ϕp-p vs length l of a 0.5-mm thick bimorph.

Fig. 8
Fig. 8

Number of resolution elements n vs mirror diameter d for various peak-to-peak deflection angles.

Tables (1)

Tables Icon

Table I Values of Constants

Equations (35)

Equations on this page are rendered with MathJax. Learn more.

d = 4 F l 3 / Y w t 3 ,
k = Y w t 3 / 4 l 3 .
f r = N ( t / l 2 ) ,
f r = ( 1 / 2 π ) ( k / m e ) 1 2 .
m e = k / 4 π 2 f r 2 .
m e = Y w l t / 16 π 2 N 2 .
f load = 1 2 π [ k / ( m e + m l ) ] 1 2 = 1 2 π ( k / m e ) 1 2 [ 1 + ( m l / m e ) ] 1 2 = f r [ 1 + ( m l / m e ) ] 1 2 .
f load = N ( t / l 2 ) [ 1 + ( 16 m l π 2 N 2 / Y w l t ) ] 1 2 .
Δ x = E d 31 l ,
Δ x = ( V / t ) d 31 l .
Δ x 1 = 2 F l / t w Y .
l = α R , l + Δ x 2 = α [ R + ( t / 4 ) ] .
Δ x 2 = α ( t / 4 ) .
α = 2 M F ( Y I / F ) 1 2 tan [ 1 2 × l ( Y I / F ) 1 2 ] ,
M = F ( t / 4 ) ,
I = 1 12 ( t / 2 ) 3 w .
α = 24 l F / Y w t 2 .
Δ x 1 / t = 2 F l / t 2 w F ,
Δ x 1 / t = α / 12 .
Δ x 2 = 3 Δ x 1 ,
Δ x = 4 Δ x 1 .
α = 3 d 31 l V / t 2 .
ϕ = 2 α .
ϕ p p = 12 d 31 l V peak / t 2 .
θ = λ / d .
ϕ p p = n θ = n λ / d ,
n = 12 d 31 l d V p e a k / λ t 2 .
m l = 1 4 π d 2 t l ρ l ,
t l = d / 6 .
m l = 0.153 d 3 .
V p max = E max t / 2 .
f load = N ( t / l 2 ) [ 1 + ( 24.2 N 2 w 2 / Y l t ) ] 1 2 .
f load = 1.45 × 10 5 ( t / l 2 ) [ 1 + ( 0.77 w 2 / l t ) ] 1 2 .
ϕ p p = ( 1.55 × 10 5 l V peak ) / t 2 ( degrees ) .
n = d ϕ p p / λ ( 57.3 ) ,

Metrics