Abstract

In this study, we propose a method to expand the dynamic range of expansion or strain measurement using statistical interferometry. Statistical interferometry is a very accurate interferometric technique that is applicable to practical rough surface objects [Opt. Lett. 16, 883 (1991); J. Opt. Soc. Am. A 18, 1267 (2001)]. It is based on the statistical stability of a fully developed speckle field and was successfully applied to measure the growth of plants in our previous study [Environ. Exp. Bot. 64, 314 (2008); J. For. Res. 12, 393 (2007)]. However, the measurable range of the expansion of the object was restricted to less than one wavelength of the light used. Improvement of the dynamic range is confirmed experimentally in this work by introducing a large expansion up to 300μm while keeping the precision of measurement high. Next, the improved system is applied to monitor plant growth from the subnanometric scale to several hundreds of micrometers under some environmental conditions. These features of the method make it especially worthwhile in botanical and agricultural studies.

© 2010 Optical Society of America

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References

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  1. H. Kadono and S. Toyooka, “Statistical interferometry based on statistics of speckle phase,” Opt. Lett. 16, 883–885 (1991).
    [CrossRef] [PubMed]
  2. H. Kadono, Y. Bitoh, and S. Toyooka, “Statistical interferometry based on a fully developed speckle field: an experimental demonstration with noise analysis,” J. Opt. Soc. Am. A 18, 1267–1274 (2001).
    [CrossRef]
  3. H. Kadono, S. Toyooka, and Y. Iwasaki, “Speckle-shearing interferometry using a liquid-crystal cell as a phase modulator,” J. Opt. Soc. Am. A 8, 2001–2008 (1991).
    [CrossRef]
  4. A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “A novel optical interference method to measure minute elongations in Japanese red pine (Pinus densiflora) seedling roots grown under ectomycorrhizal infection,” Environ. Exp. Bot. 64, 314–321 (2008).
    [CrossRef]
  5. A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “Statistical interferometric investigation of nano-scale root growth: effects of short-term ozone exposure on ectomycorrhizal pine (Pinus densiflora) seedlings,” J. For. Res. 12, 393–402 (2007).
    [CrossRef]
  6. J.C.Dainty, ed., Laser Speckle and Related Phenomena (Springer-Velag, 1975).
  7. A. Oulamara, G. Tribillion, and J. Duvernoy, “Biological activity measurement on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
    [CrossRef]
  8. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1988), pp. 349–399.
    [CrossRef]

2008

A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “A novel optical interference method to measure minute elongations in Japanese red pine (Pinus densiflora) seedling roots grown under ectomycorrhizal infection,” Environ. Exp. Bot. 64, 314–321 (2008).
[CrossRef]

2007

A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “Statistical interferometric investigation of nano-scale root growth: effects of short-term ozone exposure on ectomycorrhizal pine (Pinus densiflora) seedlings,” J. For. Res. 12, 393–402 (2007).
[CrossRef]

2001

1991

1989

A. Oulamara, G. Tribillion, and J. Duvernoy, “Biological activity measurement on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

Bitoh, Y.

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1988), pp. 349–399.
[CrossRef]

Duvernoy, J.

A. Oulamara, G. Tribillion, and J. Duvernoy, “Biological activity measurement on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

Iwasaki, Y.

Kadono, H.

A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “A novel optical interference method to measure minute elongations in Japanese red pine (Pinus densiflora) seedling roots grown under ectomycorrhizal infection,” Environ. Exp. Bot. 64, 314–321 (2008).
[CrossRef]

A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “Statistical interferometric investigation of nano-scale root growth: effects of short-term ozone exposure on ectomycorrhizal pine (Pinus densiflora) seedlings,” J. For. Res. 12, 393–402 (2007).
[CrossRef]

H. Kadono, Y. Bitoh, and S. Toyooka, “Statistical interferometry based on a fully developed speckle field: an experimental demonstration with noise analysis,” J. Opt. Soc. Am. A 18, 1267–1274 (2001).
[CrossRef]

H. Kadono, S. Toyooka, and Y. Iwasaki, “Speckle-shearing interferometry using a liquid-crystal cell as a phase modulator,” J. Opt. Soc. Am. A 8, 2001–2008 (1991).
[CrossRef]

H. Kadono and S. Toyooka, “Statistical interferometry based on statistics of speckle phase,” Opt. Lett. 16, 883–885 (1991).
[CrossRef] [PubMed]

Miwa, M.

A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “A novel optical interference method to measure minute elongations in Japanese red pine (Pinus densiflora) seedling roots grown under ectomycorrhizal infection,” Environ. Exp. Bot. 64, 314–321 (2008).
[CrossRef]

A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “Statistical interferometric investigation of nano-scale root growth: effects of short-term ozone exposure on ectomycorrhizal pine (Pinus densiflora) seedlings,” J. For. Res. 12, 393–402 (2007).
[CrossRef]

Oulamara, A.

A. Oulamara, G. Tribillion, and J. Duvernoy, “Biological activity measurement on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

Rathnayake, A. P.

A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “A novel optical interference method to measure minute elongations in Japanese red pine (Pinus densiflora) seedling roots grown under ectomycorrhizal infection,” Environ. Exp. Bot. 64, 314–321 (2008).
[CrossRef]

A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “Statistical interferometric investigation of nano-scale root growth: effects of short-term ozone exposure on ectomycorrhizal pine (Pinus densiflora) seedlings,” J. For. Res. 12, 393–402 (2007).
[CrossRef]

Toyooka, S.

A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “A novel optical interference method to measure minute elongations in Japanese red pine (Pinus densiflora) seedling roots grown under ectomycorrhizal infection,” Environ. Exp. Bot. 64, 314–321 (2008).
[CrossRef]

A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “Statistical interferometric investigation of nano-scale root growth: effects of short-term ozone exposure on ectomycorrhizal pine (Pinus densiflora) seedlings,” J. For. Res. 12, 393–402 (2007).
[CrossRef]

H. Kadono, Y. Bitoh, and S. Toyooka, “Statistical interferometry based on a fully developed speckle field: an experimental demonstration with noise analysis,” J. Opt. Soc. Am. A 18, 1267–1274 (2001).
[CrossRef]

H. Kadono and S. Toyooka, “Statistical interferometry based on statistics of speckle phase,” Opt. Lett. 16, 883–885 (1991).
[CrossRef] [PubMed]

H. Kadono, S. Toyooka, and Y. Iwasaki, “Speckle-shearing interferometry using a liquid-crystal cell as a phase modulator,” J. Opt. Soc. Am. A 8, 2001–2008 (1991).
[CrossRef]

Tribillion, G.

A. Oulamara, G. Tribillion, and J. Duvernoy, “Biological activity measurement on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

Environ. Exp. Bot.

A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “A novel optical interference method to measure minute elongations in Japanese red pine (Pinus densiflora) seedling roots grown under ectomycorrhizal infection,” Environ. Exp. Bot. 64, 314–321 (2008).
[CrossRef]

J. For. Res.

A. P. Rathnayake, H. Kadono, S. Toyooka, and M. Miwa, “Statistical interferometric investigation of nano-scale root growth: effects of short-term ozone exposure on ectomycorrhizal pine (Pinus densiflora) seedlings,” J. For. Res. 12, 393–402 (2007).
[CrossRef]

J. Mod. Opt.

A. Oulamara, G. Tribillion, and J. Duvernoy, “Biological activity measurement on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Other

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1988), pp. 349–399.
[CrossRef]

J.C.Dainty, ed., Laser Speckle and Related Phenomena (Springer-Velag, 1975).

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Figures (11)

Fig. 1
Fig. 1

Optical system of statistical interferometry.

Fig. 2
Fig. 2

Phasors corresponding to the phase changes that are due to the expansions of the object.

Fig. 3
Fig. 3

Probability density distribution p ϕ ( ϕ ) of experimentally obtained speckle phase with antisymmetrical phase difference Δ ψ a = 0.34 rad from the virtual phase, ψ v = π / 2 .

Fig. 4
Fig. 4

Expansion of the dynamic range (a) before and (b) after renewal of reference patterns, Phasor 1 and Phasor 3 .

Fig. 5
Fig. 5

Stability of experimental system. An aluminum plate under a constant temperature was measured, and the standard deviation of the object phase was 0.0053 rad .

Fig. 6
Fig. 6

Optical system for measuring large in-plane expansion. One laser beam is incident onto a fixed metal plate and the other beam is incident onto a movable plate mounted on a PZT stage.

Fig. 7
Fig. 7

Difference between the measured expansions and those given by a PZT driven with a sine wave of amplitude 4000 nm and period 600 s .

Fig. 8
Fig. 8

Measurement of large expansion with a mechanical stage. The amplitude of the to-and-fro linear translation was 300 μm at a speed of 1 step / s , and repeatability was found to be 1.87 nm .

Fig. 9
Fig. 9

Growth or strain of a rice plant leaf over 10 s . Leaf is growing approximately linearly, and the growth rate was calculated to be 6.58 μ strain / s from regression fit indicated by straight line.

Fig. 10
Fig. 10

Long-term growth behavior of a rice plant leaf under alternation of illumination using a white fluorescent lamp.

Fig. 11
Fig. 11

Short-term growth rate of a rice plant leaf obtained from growth shown in Fig. 10. Each growth rate was calculated over 10 s .

Equations (14)

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p ϕ ( ϕ ) = 1 2 π ( π < ϕ π ) ,
Δ ψ = 2 π λ Δ x sin θ .
I 1 ( x ) = I 0 ( x ) [ 1 + γ ( x ) cos ( ϕ ( x ) + ψ 1 ) ] , I 2 ( x ) = I 0 ( x ) [ 1 + γ ( x ) cos ( ϕ ( x ) ) ] , I 3 ( x ) = I 0 ( x ) [ 1 + γ ( x ) cos ( ϕ ( x ) + ψ 3 ) ] ,
ψ 1 = ψ 3 = ψ v .
ϕ ( x ) = tan 1 I 1 ( x ) I 3 ( x ) I 1 ( x ) + I 3 ( x ) 2 I 2 ( x ) · cos ψ v 1 sin ψ v .
ψ 1 = ψ v Δ ψ s + Δ ψ a , ψ 3 = ψ v + Δ ψ s + Δ ψ a .
Phasor 1 = Phasor 2 , 1 ψ r , Phasor 3 = Phasor 2 , 1 + ψ r .
Δ ψ ( t i ) = ψ ( t i ) | I 1 , I 2 , i , I 3 ψ ( t 1 ) | I 1 , I 2 , 1 , I 3 , ( i = 1 , 2 , 3 N ) .
Phasor 1 = Phasor 2 , k ψ r , Phasor 3 = Phasor 2 , k + ψ r .
Δ ψ ( t j ) = ψ ( t k + j ) | I 1 , I 2 , ( k + j ) , I 3 ψ ( t k ) | I 1 , I 2 , k , I 3 , ( j = 1 , 2 , 3 N k ) .
Δ x ( t j ) = Δ ψ ( t j ) λ / 2 π sin θ .
Δ x ( t i ) = Δ x ( t k ) + Δ x ( t j ) .
N e = A CCD 2 π α 2 .
α = 0.61 λ z w .

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