Abstract

A new, to our knowledge, type of optical device capable of beam redirection and frequency filtering is described. It is based on a transparent elastomeric binary diffraction grating. When light is passed through the device the intensities of the diffraction orders can be modulated by compression of the elastomer in the direction perpendicular to the plane of the grating. Selective filtering of the component frequencies of two-component light (λ = 543.5 nm and λ = 632.8 nm) has been demonstrated. Experimental observations are in agreement with theoretical calculations quantifying the performance of the device.

© 1999 Optical Society of America

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References

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  1. T. R. Ohnstein, J. D. Zook, H. B. French, H. Guckel, T. Earles, J. Klein, P. Magnat, “Tunable IR filters with integral electromagnetic actuators,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 196–199.
  2. O. Solgaard, F. S. A. Sandejas, D. M. Bloom, “Deformable grating optical modulator,” Opt. Lett. 17, 688–690 (1992).
    [CrossRef] [PubMed]
  3. C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP/InGaAs/InP,” IEEE Photon. Technol. Lett. 4, 108–110 (1992).
    [CrossRef]
  4. G. M. Yee, P. A. Hing, N. I. Maluf, G. T. A. Kovacs, “Miniaturized spectrometers for biochemical analysis,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 64–67.
  5. T. A. Kwa, R. F. Wolffenbuttel, “Integrated grating/detector array fabricated in silicon using micromachining techniques,” Sensors Actuators A 31, 259–266 (1992).
    [CrossRef]
  6. J. H. Jerman, D. J. Clift, S. R. Mallison, “A miniature Fabry–Perot interferometer with a corrugated silicon diaphragm support,” Sensors Actuators A 29, 151–158 (1991).
    [CrossRef]
  7. K. Aranti, P. J. French, P. M. Sarro, D. Poenar, R. F. Wolffenbuttel, S. Middelhoek, “Surface micromachined tunable interferometer array,” Sensors Actuators A 43, 17–23 (1994).
    [CrossRef]
  8. R. L. Fork, “Optical frequency filter for ultrashort pulses,” Opt. Lett. 11, 629–631 (1986).
    [CrossRef] [PubMed]
  9. M. Born, E. Wolf, eds., Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chaps. 8.6.1, 8.6.3.
  10. K. Iizuka, Engineering Optics, 2nd ed. (Springer-Verlag, Berlin, 1987), pp. 59–65.
  11. J. A. Rogers, D. Qin, O. J. A. Schueller, G. M. Whitesides, “Elastomeric binary phase gratings for measuring acceleration, displacement, strain and stress,” Rev. Sci. Instrum. 67, 3310–3319 (1996).
    [CrossRef]
  12. J. A. Rogers, O. J. A. Schueller, C. Marzolin, G. M. Whitesides, “Wave-front engineering by use of transparent elastomeric optical elements,” Appl. Opt. 36, 5792–5795 (1997).
    [CrossRef] [PubMed]
  13. Y. Xia, G. M. Whitesides, “Soft lithography,” Angew. Chem. Inter. Ed. Engl. 37, 550–575 (1998).
    [CrossRef]
  14. A. Kumar, G. M. Whitesides, “Features of gold having micrometer to centimeter dimensions can be formed through a combination of stamping with an elastomeric stamp and an alkanethiol ink followed by chemical etching,” Appl. Phys. Lett. 63, 2002–2004 (1993).
    [CrossRef]
  15. A. Kumar, H. A. Biebuyck, G. M. Whitesides, “Patterning self-assembled monolayers: applications in material science,” Langmuir 10, 1498–1511 (1994).
    [CrossRef]

1998 (1)

Y. Xia, G. M. Whitesides, “Soft lithography,” Angew. Chem. Inter. Ed. Engl. 37, 550–575 (1998).
[CrossRef]

1997 (1)

1996 (1)

J. A. Rogers, D. Qin, O. J. A. Schueller, G. M. Whitesides, “Elastomeric binary phase gratings for measuring acceleration, displacement, strain and stress,” Rev. Sci. Instrum. 67, 3310–3319 (1996).
[CrossRef]

1994 (2)

K. Aranti, P. J. French, P. M. Sarro, D. Poenar, R. F. Wolffenbuttel, S. Middelhoek, “Surface micromachined tunable interferometer array,” Sensors Actuators A 43, 17–23 (1994).
[CrossRef]

A. Kumar, H. A. Biebuyck, G. M. Whitesides, “Patterning self-assembled monolayers: applications in material science,” Langmuir 10, 1498–1511 (1994).
[CrossRef]

1993 (1)

A. Kumar, G. M. Whitesides, “Features of gold having micrometer to centimeter dimensions can be formed through a combination of stamping with an elastomeric stamp and an alkanethiol ink followed by chemical etching,” Appl. Phys. Lett. 63, 2002–2004 (1993).
[CrossRef]

1992 (3)

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP/InGaAs/InP,” IEEE Photon. Technol. Lett. 4, 108–110 (1992).
[CrossRef]

T. A. Kwa, R. F. Wolffenbuttel, “Integrated grating/detector array fabricated in silicon using micromachining techniques,” Sensors Actuators A 31, 259–266 (1992).
[CrossRef]

O. Solgaard, F. S. A. Sandejas, D. M. Bloom, “Deformable grating optical modulator,” Opt. Lett. 17, 688–690 (1992).
[CrossRef] [PubMed]

1991 (1)

J. H. Jerman, D. J. Clift, S. R. Mallison, “A miniature Fabry–Perot interferometer with a corrugated silicon diaphragm support,” Sensors Actuators A 29, 151–158 (1991).
[CrossRef]

1986 (1)

Aranti, K.

K. Aranti, P. J. French, P. M. Sarro, D. Poenar, R. F. Wolffenbuttel, S. Middelhoek, “Surface micromachined tunable interferometer array,” Sensors Actuators A 43, 17–23 (1994).
[CrossRef]

Biebuyck, H. A.

A. Kumar, H. A. Biebuyck, G. M. Whitesides, “Patterning self-assembled monolayers: applications in material science,” Langmuir 10, 1498–1511 (1994).
[CrossRef]

Bloom, D. M.

Clift, D. J.

J. H. Jerman, D. J. Clift, S. R. Mallison, “A miniature Fabry–Perot interferometer with a corrugated silicon diaphragm support,” Sensors Actuators A 29, 151–158 (1991).
[CrossRef]

Cremer, C.

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP/InGaAs/InP,” IEEE Photon. Technol. Lett. 4, 108–110 (1992).
[CrossRef]

Earles, T.

T. R. Ohnstein, J. D. Zook, H. B. French, H. Guckel, T. Earles, J. Klein, P. Magnat, “Tunable IR filters with integral electromagnetic actuators,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 196–199.

Ebbinghaus, G.

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP/InGaAs/InP,” IEEE Photon. Technol. Lett. 4, 108–110 (1992).
[CrossRef]

Emeis, N.

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP/InGaAs/InP,” IEEE Photon. Technol. Lett. 4, 108–110 (1992).
[CrossRef]

Fork, R. L.

French, H. B.

T. R. Ohnstein, J. D. Zook, H. B. French, H. Guckel, T. Earles, J. Klein, P. Magnat, “Tunable IR filters with integral electromagnetic actuators,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 196–199.

French, P. J.

K. Aranti, P. J. French, P. M. Sarro, D. Poenar, R. F. Wolffenbuttel, S. Middelhoek, “Surface micromachined tunable interferometer array,” Sensors Actuators A 43, 17–23 (1994).
[CrossRef]

Guckel, H.

T. R. Ohnstein, J. D. Zook, H. B. French, H. Guckel, T. Earles, J. Klein, P. Magnat, “Tunable IR filters with integral electromagnetic actuators,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 196–199.

Heise, G.

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP/InGaAs/InP,” IEEE Photon. Technol. Lett. 4, 108–110 (1992).
[CrossRef]

Hing, P. A.

G. M. Yee, P. A. Hing, N. I. Maluf, G. T. A. Kovacs, “Miniaturized spectrometers for biochemical analysis,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 64–67.

Iizuka, K.

K. Iizuka, Engineering Optics, 2nd ed. (Springer-Verlag, Berlin, 1987), pp. 59–65.

Jerman, J. H.

J. H. Jerman, D. J. Clift, S. R. Mallison, “A miniature Fabry–Perot interferometer with a corrugated silicon diaphragm support,” Sensors Actuators A 29, 151–158 (1991).
[CrossRef]

Klein, J.

T. R. Ohnstein, J. D. Zook, H. B. French, H. Guckel, T. Earles, J. Klein, P. Magnat, “Tunable IR filters with integral electromagnetic actuators,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 196–199.

Kovacs, G. T. A.

G. M. Yee, P. A. Hing, N. I. Maluf, G. T. A. Kovacs, “Miniaturized spectrometers for biochemical analysis,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 64–67.

Kumar, A.

A. Kumar, H. A. Biebuyck, G. M. Whitesides, “Patterning self-assembled monolayers: applications in material science,” Langmuir 10, 1498–1511 (1994).
[CrossRef]

A. Kumar, G. M. Whitesides, “Features of gold having micrometer to centimeter dimensions can be formed through a combination of stamping with an elastomeric stamp and an alkanethiol ink followed by chemical etching,” Appl. Phys. Lett. 63, 2002–2004 (1993).
[CrossRef]

Kwa, T. A.

T. A. Kwa, R. F. Wolffenbuttel, “Integrated grating/detector array fabricated in silicon using micromachining techniques,” Sensors Actuators A 31, 259–266 (1992).
[CrossRef]

Magnat, P.

T. R. Ohnstein, J. D. Zook, H. B. French, H. Guckel, T. Earles, J. Klein, P. Magnat, “Tunable IR filters with integral electromagnetic actuators,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 196–199.

Mallison, S. R.

J. H. Jerman, D. J. Clift, S. R. Mallison, “A miniature Fabry–Perot interferometer with a corrugated silicon diaphragm support,” Sensors Actuators A 29, 151–158 (1991).
[CrossRef]

Maluf, N. I.

G. M. Yee, P. A. Hing, N. I. Maluf, G. T. A. Kovacs, “Miniaturized spectrometers for biochemical analysis,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 64–67.

Marzolin, C.

Middelhoek, S.

K. Aranti, P. J. French, P. M. Sarro, D. Poenar, R. F. Wolffenbuttel, S. Middelhoek, “Surface micromachined tunable interferometer array,” Sensors Actuators A 43, 17–23 (1994).
[CrossRef]

Ohnstein, T. R.

T. R. Ohnstein, J. D. Zook, H. B. French, H. Guckel, T. Earles, J. Klein, P. Magnat, “Tunable IR filters with integral electromagnetic actuators,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 196–199.

Poenar, D.

K. Aranti, P. J. French, P. M. Sarro, D. Poenar, R. F. Wolffenbuttel, S. Middelhoek, “Surface micromachined tunable interferometer array,” Sensors Actuators A 43, 17–23 (1994).
[CrossRef]

Qin, D.

J. A. Rogers, D. Qin, O. J. A. Schueller, G. M. Whitesides, “Elastomeric binary phase gratings for measuring acceleration, displacement, strain and stress,” Rev. Sci. Instrum. 67, 3310–3319 (1996).
[CrossRef]

Rogers, J. A.

J. A. Rogers, O. J. A. Schueller, C. Marzolin, G. M. Whitesides, “Wave-front engineering by use of transparent elastomeric optical elements,” Appl. Opt. 36, 5792–5795 (1997).
[CrossRef] [PubMed]

J. A. Rogers, D. Qin, O. J. A. Schueller, G. M. Whitesides, “Elastomeric binary phase gratings for measuring acceleration, displacement, strain and stress,” Rev. Sci. Instrum. 67, 3310–3319 (1996).
[CrossRef]

Sandejas, F. S. A.

Sarro, P. M.

K. Aranti, P. J. French, P. M. Sarro, D. Poenar, R. F. Wolffenbuttel, S. Middelhoek, “Surface micromachined tunable interferometer array,” Sensors Actuators A 43, 17–23 (1994).
[CrossRef]

Schier, M.

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP/InGaAs/InP,” IEEE Photon. Technol. Lett. 4, 108–110 (1992).
[CrossRef]

Schueller, O. J. A.

J. A. Rogers, O. J. A. Schueller, C. Marzolin, G. M. Whitesides, “Wave-front engineering by use of transparent elastomeric optical elements,” Appl. Opt. 36, 5792–5795 (1997).
[CrossRef] [PubMed]

J. A. Rogers, D. Qin, O. J. A. Schueller, G. M. Whitesides, “Elastomeric binary phase gratings for measuring acceleration, displacement, strain and stress,” Rev. Sci. Instrum. 67, 3310–3319 (1996).
[CrossRef]

Solgaard, O.

Stoll, L.

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP/InGaAs/InP,” IEEE Photon. Technol. Lett. 4, 108–110 (1992).
[CrossRef]

Whitesides, G. M.

Y. Xia, G. M. Whitesides, “Soft lithography,” Angew. Chem. Inter. Ed. Engl. 37, 550–575 (1998).
[CrossRef]

J. A. Rogers, O. J. A. Schueller, C. Marzolin, G. M. Whitesides, “Wave-front engineering by use of transparent elastomeric optical elements,” Appl. Opt. 36, 5792–5795 (1997).
[CrossRef] [PubMed]

J. A. Rogers, D. Qin, O. J. A. Schueller, G. M. Whitesides, “Elastomeric binary phase gratings for measuring acceleration, displacement, strain and stress,” Rev. Sci. Instrum. 67, 3310–3319 (1996).
[CrossRef]

A. Kumar, H. A. Biebuyck, G. M. Whitesides, “Patterning self-assembled monolayers: applications in material science,” Langmuir 10, 1498–1511 (1994).
[CrossRef]

A. Kumar, G. M. Whitesides, “Features of gold having micrometer to centimeter dimensions can be formed through a combination of stamping with an elastomeric stamp and an alkanethiol ink followed by chemical etching,” Appl. Phys. Lett. 63, 2002–2004 (1993).
[CrossRef]

Wolffenbuttel, R. F.

K. Aranti, P. J. French, P. M. Sarro, D. Poenar, R. F. Wolffenbuttel, S. Middelhoek, “Surface micromachined tunable interferometer array,” Sensors Actuators A 43, 17–23 (1994).
[CrossRef]

T. A. Kwa, R. F. Wolffenbuttel, “Integrated grating/detector array fabricated in silicon using micromachining techniques,” Sensors Actuators A 31, 259–266 (1992).
[CrossRef]

Xia, Y.

Y. Xia, G. M. Whitesides, “Soft lithography,” Angew. Chem. Inter. Ed. Engl. 37, 550–575 (1998).
[CrossRef]

Yee, G. M.

G. M. Yee, P. A. Hing, N. I. Maluf, G. T. A. Kovacs, “Miniaturized spectrometers for biochemical analysis,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 64–67.

Zook, J. D.

T. R. Ohnstein, J. D. Zook, H. B. French, H. Guckel, T. Earles, J. Klein, P. Magnat, “Tunable IR filters with integral electromagnetic actuators,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 196–199.

Angew. Chem. Inter. Ed. Engl. (1)

Y. Xia, G. M. Whitesides, “Soft lithography,” Angew. Chem. Inter. Ed. Engl. 37, 550–575 (1998).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Kumar, G. M. Whitesides, “Features of gold having micrometer to centimeter dimensions can be formed through a combination of stamping with an elastomeric stamp and an alkanethiol ink followed by chemical etching,” Appl. Phys. Lett. 63, 2002–2004 (1993).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP/InGaAs/InP,” IEEE Photon. Technol. Lett. 4, 108–110 (1992).
[CrossRef]

Langmuir (1)

A. Kumar, H. A. Biebuyck, G. M. Whitesides, “Patterning self-assembled monolayers: applications in material science,” Langmuir 10, 1498–1511 (1994).
[CrossRef]

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

J. A. Rogers, D. Qin, O. J. A. Schueller, G. M. Whitesides, “Elastomeric binary phase gratings for measuring acceleration, displacement, strain and stress,” Rev. Sci. Instrum. 67, 3310–3319 (1996).
[CrossRef]

Sensors Actuators A (3)

T. A. Kwa, R. F. Wolffenbuttel, “Integrated grating/detector array fabricated in silicon using micromachining techniques,” Sensors Actuators A 31, 259–266 (1992).
[CrossRef]

J. H. Jerman, D. J. Clift, S. R. Mallison, “A miniature Fabry–Perot interferometer with a corrugated silicon diaphragm support,” Sensors Actuators A 29, 151–158 (1991).
[CrossRef]

K. Aranti, P. J. French, P. M. Sarro, D. Poenar, R. F. Wolffenbuttel, S. Middelhoek, “Surface micromachined tunable interferometer array,” Sensors Actuators A 43, 17–23 (1994).
[CrossRef]

Other (4)

M. Born, E. Wolf, eds., Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chaps. 8.6.1, 8.6.3.

K. Iizuka, Engineering Optics, 2nd ed. (Springer-Verlag, Berlin, 1987), pp. 59–65.

T. R. Ohnstein, J. D. Zook, H. B. French, H. Guckel, T. Earles, J. Klein, P. Magnat, “Tunable IR filters with integral electromagnetic actuators,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 196–199.

G. M. Yee, P. A. Hing, N. I. Maluf, G. T. A. Kovacs, “Miniaturized spectrometers for biochemical analysis,” in Proceedings of the Solid State Sensor and Actuator Workshop (Elsevier, Lausanne, Switzerland, 1996), pp. 64–67.

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Figures (5)

Fig. 1
Fig. 1

(a) Coordinates used in the calculations. (b) Scheme of the experimental setup. PDMS, polydimethylsiloxane.

Fig. 2
Fig. 2

(a) Calculated dependence of the intensities of the zero and the first orders as functions of the phase angle. (b) Effect of the deformation of the grating during compression on the intensity of the zero-order beam. Even with a conservative estimate of the constant, C = 20, the intensity curves with and without the stress correction are in good agreement across the operational range of the device (∊ < ∼6%). In both cases the calculations were carried out with values of d 0 = 1.8 µm and λ = 543.5 nm.

Fig. 3
Fig. 3

Intensities of the zero and the first orders as functions of the compressive strain ∊. The filled circles represent the zero order, and the open circles the first order results. The curves show the theoretical values.

Fig. 4
Fig. 4

Ratios of the intensities of the red to the green beams (filled circles) and the green to the red beams (open circles) when diffracted into the zero and the first orders.

Fig. 5
Fig. 5

Plots of the theoretical intensities of light filtered into the zero order as a function of both the wavelength (in the visible) and the compressive strain ∊ for the 1.8-µm grating and the 2.2-µm grating. The calculations were carried out by use of Eq. (9a) with a value for the constant of C = 10.

Equations (24)

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τx=expiϕfor nL<x<n+12L1otherwise, n=0, ±1, ±2,, ±N/2   
Uf=-N+1L/2N+1L/2 τxexp-i2πxfdx=m=-N/2m=N/2mL-L/2mL+L/2 τxexp-i2πxfdx.
Uf=m=- δf-mL1L-L/2L/2 τyexp-i2πyfdy.
Imf=|Umf|2=1L2-L/2L/2 τyexp-i2πym/Ldy2
I0ϕ=1+cos ϕ2,
I1ϕ=21-cos ϕπ2.
ϕ=2πne-nairdλ.
Δϕ=2πne-naird-d0λ=2πΔnΔdλ.
Δϕ  2πΔnd0λΔHH,
I0,corrϕ=1+cos ϕ2+C21-cos ϕ,
I1,corrϕ=2π2cos2πC/21-cos ϕ.
Uf=m=-N/2m=N/2exp-i2πfmL×-L/2L/2 τyexp-i2πfydy.
Uf=limNm=-N/2m=N/2exp-i2πfmL×-L/2L/2 τyexp-i2πfydy,
Uf=limNsinπfLN+1sinπfL-L/2L/2 τyexp-i2πfydy.
limNsinπfLN+1sinπfL=m=-m=1L δf-mL,
I0ϕ=1L2-L/2L/2 τydy-L/2L/2 τ*ydy=1L2L2+L2expiϕL2+L2exp-iϕ=142+expiϕ+exp-iϕ=1+cos ϕ2, I1ϕ=1L2-L/2L/2 τyexp-i2πyLdy×-L/2L/2 τ*yexpi2πyLdy =1L2L2π21-expiϕ1-exp-iϕ=1π22-expiϕ+exp-iϕ=21-cos ϕπ2.
dz=-TzE z,
Δϕ=2πΔnΔdλ,  Δd  dz,  z=d0,
Δϕ  2πΔnλ d0z.
Δϕ  2πΔnd0ΔHλH.
τx=expiϕfor nL-Δx2<x<n+12L+Δx2n=0, ±1, ±2,, ±N/21otherwise.
I0,corrϕ=1L2-L/2L/2 τydy2 =1L2L2-Δx+L2+Δxexpiϕ2,
I0,corrϕ=1+cos ϕ2+C21-cos ϕ,
I1,corrϕ=1L2-L/2L/2 τyexp-π2iyLdy2 =1L2iLπcosπΔxL1-expiϕ2=2π2cos2πC/21/21-cos ϕ.

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