Abstract

We formalize the physics of an optical heterodyne accelerometer that allows measurement of low and high velocities from material surfaces under high strain. The proposed apparatus incorporates currently common optical velocimetry techniques used in shock physics, with interferometric techniques developed to self-stabilize and passively balance interferometers in quantum cryptography. The result is a robust telecom-fiber-based velocimetry system insensitive to modal and frequency dispersion that should work well in the presence of decoherent scattering processes, such as from ejecta clouds and shocked surfaces.

© 2010 Optical Society of America

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  1. A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
    [CrossRef]
  2. H. Cummins, N. Knable, L. Gampel, and Y. Yeh, “Frequency shifts in light diffracted by ultrasonic waves in liquid media,” Appl. Phys. Lett. 2, 62–64 (1963).
    [CrossRef]
  3. H. Z. Cummins, N. Knable, and Y. Yeh, “Spurious harmonic generation in optical heterodyning,” Appl. Opt. 2, 823–825(1963).
    [CrossRef]
  4. Y. Yeh and H. Z. Cummins, “Localized fluid flow measurements with an He─Ne laser,” Appl. Phys. Lett. 4, 176–178(1964).
    [CrossRef]
  5. J. W. Forman, Jr., E. W. George, and R. D. Lewis, “Measurement of localized fluid flow velocities in gasses with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).
    [CrossRef]
  6. L. M. Barker and R. E. Hollenbach, “Interferometry technique for measuring the dynamic mechanical properties of materials,” Rev. Sci. Instrum. 36, 1617–1620 (1965).
    [CrossRef]
  7. L. M. Barker, Behavior of Dense Media under High Dynamic Pressures (Gordon & Breach, 1968), p. 483.
  8. L. M. Barker and Hollenbach, “Laser interferometry for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43, 4669–4675 (1972).
    [CrossRef]
  9. W. F. Hemsing, “Velocity sensing interferometer (VISAR) modification,” Rev. Mod. Instrum. 50, 73–78 (1979).
    [CrossRef]
  10. L. Levin, D. Tzach, and J. Shamir, “Fiber optic velocity interferometer with very short coherence length light source,” Rev. Sci. Instrum. 67, 1434–1437 (1996).
    [CrossRef]
  11. L. Fabiny and A. D. Kersey, “Interferometric fiber-optic Doppler velocimeter with high-dynamic range,” IEEE Photon. Technol. Lett. 9, 79–81 (1997).
    [CrossRef]
  12. W. T. Buttler, S. K. Lamoreaux, F. G. Omenetto, and J. R. Torgerson, “Optical velocimetry,” arXiv:0409073v1(2004).
  13. O. T. Strand, D. R. Goosman, C. Martinex, and R. L. Whitworth, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108(2006).
    [CrossRef]
  14. “Quickly” relates to the temporal length of the delay leg, the laser wavelength, the reflector velocity, and the detection and recording system.
  15. W. T. Buttler, “Comment on ‘accuracy limits and window corrections for photon Doppler velocimetry’ [J. Appl. Phys. 101, 013523 (2007)],” J. Appl. Phys. 103, 046102 (2008).
    [CrossRef]
  16. C. H. Bennett, “Quantum cryptography using any 2 nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
    [CrossRef] [PubMed]
  17. P. Townsend, J. G. Rarity, and P. Tapster, “Single photon interference in 10 km long optical fibre interferometer,” Electron. Lett. 29, 634–635 (1993).
    [CrossRef]
  18. P. Townsend, J. G. Rarity, and P. Tapster, “Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel,” Electron. Lett. 29, 1291–1293(1993).
    [CrossRef]
  19. M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracing beam,” Opt. Commun. 72, 341–344 (1989).
    [CrossRef]
  20. A. Muller, J. Bréguet, and N. Gisin, “Experimental demonstration of quantum cryptography using polarized photons in optical-fiber over more than 1 km,” Europhys. Lett. 23, 383–388 (1993).
    [CrossRef]
  21. J. Bréguet, A. Muller, and N. Gisin, “Quantum cryptography with polarized photons in optical fiber—experiment and practical limits,” J. Mod. Opt. 41, 2405–2412 (1994).
    [CrossRef]
  22. D. S. Bethune and W. P. Risk, “Autocompensating quantum cryptography,” New J. Phys. 4, 42 (2002).
    [CrossRef]
  23. This operator, described in Appendix , transmits h-polarized light traveling from left-to-right unchanged, but when the reflected upper path light returns, it rotates h to left-circular (ℓ) polarization for quadrature detection.
  24. What we refer to here is a combination of the shocked surface (reflector) with a Faraday rotator. If the reflector is a mirror, this combination is known as a Faraday mirror: it rotates reflected polarizations by 90° (orthoconjugates).
  25. G. M. B. Bouricius and S. F. Clifford, “An optical interferometer using polarization coding to obtain quadrature phase components,” Rev. Sci. Instrum. 41, 1800–1803(1970).
    [CrossRef]
  26. The δt terms are small enough to be ignored because Δx≈[u(τ)+u(τ+Δt)]/cΔt demonstrating that Δt·ω0[u2(τ+Δt′)−u2(τ)]/c2≪1.
  27. D. H. Dolan, “Foundations of VISAR analysis,” Internal report SAND2006-1950 (Sandia National Laboratories, 2006).
  28. This constant fluctuates as a function of time due to environmental factors.
  29. D. J. Erskine and N. C. Holmes, “White light velocimetry,” Nature 377, 317–320 (1995).
    [CrossRef]

2008 (1)

W. T. Buttler, “Comment on ‘accuracy limits and window corrections for photon Doppler velocimetry’ [J. Appl. Phys. 101, 013523 (2007)],” J. Appl. Phys. 103, 046102 (2008).
[CrossRef]

2006 (2)

O. T. Strand, D. R. Goosman, C. Martinex, and R. L. Whitworth, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108(2006).
[CrossRef]

D. H. Dolan, “Foundations of VISAR analysis,” Internal report SAND2006-1950 (Sandia National Laboratories, 2006).

2004 (1)

W. T. Buttler, S. K. Lamoreaux, F. G. Omenetto, and J. R. Torgerson, “Optical velocimetry,” arXiv:0409073v1(2004).

2002 (1)

D. S. Bethune and W. P. Risk, “Autocompensating quantum cryptography,” New J. Phys. 4, 42 (2002).
[CrossRef]

1997 (1)

L. Fabiny and A. D. Kersey, “Interferometric fiber-optic Doppler velocimeter with high-dynamic range,” IEEE Photon. Technol. Lett. 9, 79–81 (1997).
[CrossRef]

1996 (1)

L. Levin, D. Tzach, and J. Shamir, “Fiber optic velocity interferometer with very short coherence length light source,” Rev. Sci. Instrum. 67, 1434–1437 (1996).
[CrossRef]

1995 (1)

D. J. Erskine and N. C. Holmes, “White light velocimetry,” Nature 377, 317–320 (1995).
[CrossRef]

1994 (1)

J. Bréguet, A. Muller, and N. Gisin, “Quantum cryptography with polarized photons in optical fiber—experiment and practical limits,” J. Mod. Opt. 41, 2405–2412 (1994).
[CrossRef]

1993 (3)

A. Muller, J. Bréguet, and N. Gisin, “Experimental demonstration of quantum cryptography using polarized photons in optical-fiber over more than 1 km,” Europhys. Lett. 23, 383–388 (1993).
[CrossRef]

P. Townsend, J. G. Rarity, and P. Tapster, “Single photon interference in 10 km long optical fibre interferometer,” Electron. Lett. 29, 634–635 (1993).
[CrossRef]

P. Townsend, J. G. Rarity, and P. Tapster, “Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel,” Electron. Lett. 29, 1291–1293(1993).
[CrossRef]

1992 (1)

C. H. Bennett, “Quantum cryptography using any 2 nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
[CrossRef] [PubMed]

1989 (1)

M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracing beam,” Opt. Commun. 72, 341–344 (1989).
[CrossRef]

1979 (1)

W. F. Hemsing, “Velocity sensing interferometer (VISAR) modification,” Rev. Mod. Instrum. 50, 73–78 (1979).
[CrossRef]

1972 (1)

L. M. Barker and Hollenbach, “Laser interferometry for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43, 4669–4675 (1972).
[CrossRef]

1970 (1)

G. M. B. Bouricius and S. F. Clifford, “An optical interferometer using polarization coding to obtain quadrature phase components,” Rev. Sci. Instrum. 41, 1800–1803(1970).
[CrossRef]

1968 (1)

L. M. Barker, Behavior of Dense Media under High Dynamic Pressures (Gordon & Breach, 1968), p. 483.

1965 (2)

J. W. Forman, Jr., E. W. George, and R. D. Lewis, “Measurement of localized fluid flow velocities in gasses with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).
[CrossRef]

L. M. Barker and R. E. Hollenbach, “Interferometry technique for measuring the dynamic mechanical properties of materials,” Rev. Sci. Instrum. 36, 1617–1620 (1965).
[CrossRef]

1964 (1)

Y. Yeh and H. Z. Cummins, “Localized fluid flow measurements with an He─Ne laser,” Appl. Phys. Lett. 4, 176–178(1964).
[CrossRef]

1963 (2)

H. Cummins, N. Knable, L. Gampel, and Y. Yeh, “Frequency shifts in light diffracted by ultrasonic waves in liquid media,” Appl. Phys. Lett. 2, 62–64 (1963).
[CrossRef]

H. Z. Cummins, N. Knable, and Y. Yeh, “Spurious harmonic generation in optical heterodyning,” Appl. Opt. 2, 823–825(1963).
[CrossRef]

1958 (1)

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
[CrossRef]

Barker, L. M.

L. M. Barker and Hollenbach, “Laser interferometry for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43, 4669–4675 (1972).
[CrossRef]

L. M. Barker, Behavior of Dense Media under High Dynamic Pressures (Gordon & Breach, 1968), p. 483.

L. M. Barker and R. E. Hollenbach, “Interferometry technique for measuring the dynamic mechanical properties of materials,” Rev. Sci. Instrum. 36, 1617–1620 (1965).
[CrossRef]

Bennett, C. H.

C. H. Bennett, “Quantum cryptography using any 2 nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
[CrossRef] [PubMed]

Bethune, D. S.

D. S. Bethune and W. P. Risk, “Autocompensating quantum cryptography,” New J. Phys. 4, 42 (2002).
[CrossRef]

Bouricius, G. M. B.

G. M. B. Bouricius and S. F. Clifford, “An optical interferometer using polarization coding to obtain quadrature phase components,” Rev. Sci. Instrum. 41, 1800–1803(1970).
[CrossRef]

Bréguet, J.

J. Bréguet, A. Muller, and N. Gisin, “Quantum cryptography with polarized photons in optical fiber—experiment and practical limits,” J. Mod. Opt. 41, 2405–2412 (1994).
[CrossRef]

A. Muller, J. Bréguet, and N. Gisin, “Experimental demonstration of quantum cryptography using polarized photons in optical-fiber over more than 1 km,” Europhys. Lett. 23, 383–388 (1993).
[CrossRef]

Buttler, W. T.

W. T. Buttler, “Comment on ‘accuracy limits and window corrections for photon Doppler velocimetry’ [J. Appl. Phys. 101, 013523 (2007)],” J. Appl. Phys. 103, 046102 (2008).
[CrossRef]

W. T. Buttler, S. K. Lamoreaux, F. G. Omenetto, and J. R. Torgerson, “Optical velocimetry,” arXiv:0409073v1(2004).

Clifford, S. F.

G. M. B. Bouricius and S. F. Clifford, “An optical interferometer using polarization coding to obtain quadrature phase components,” Rev. Sci. Instrum. 41, 1800–1803(1970).
[CrossRef]

Cummins, H.

H. Cummins, N. Knable, L. Gampel, and Y. Yeh, “Frequency shifts in light diffracted by ultrasonic waves in liquid media,” Appl. Phys. Lett. 2, 62–64 (1963).
[CrossRef]

Cummins, H. Z.

Y. Yeh and H. Z. Cummins, “Localized fluid flow measurements with an He─Ne laser,” Appl. Phys. Lett. 4, 176–178(1964).
[CrossRef]

H. Z. Cummins, N. Knable, and Y. Yeh, “Spurious harmonic generation in optical heterodyning,” Appl. Opt. 2, 823–825(1963).
[CrossRef]

Dolan, D. H.

D. H. Dolan, “Foundations of VISAR analysis,” Internal report SAND2006-1950 (Sandia National Laboratories, 2006).

Erskine, D. J.

D. J. Erskine and N. C. Holmes, “White light velocimetry,” Nature 377, 317–320 (1995).
[CrossRef]

Fabiny, L.

L. Fabiny and A. D. Kersey, “Interferometric fiber-optic Doppler velocimeter with high-dynamic range,” IEEE Photon. Technol. Lett. 9, 79–81 (1997).
[CrossRef]

Forman, J. W.

J. W. Forman, Jr., E. W. George, and R. D. Lewis, “Measurement of localized fluid flow velocities in gasses with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).
[CrossRef]

Gampel, L.

H. Cummins, N. Knable, L. Gampel, and Y. Yeh, “Frequency shifts in light diffracted by ultrasonic waves in liquid media,” Appl. Phys. Lett. 2, 62–64 (1963).
[CrossRef]

George, E. W.

J. W. Forman, Jr., E. W. George, and R. D. Lewis, “Measurement of localized fluid flow velocities in gasses with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).
[CrossRef]

Gisin, N.

J. Bréguet, A. Muller, and N. Gisin, “Quantum cryptography with polarized photons in optical fiber—experiment and practical limits,” J. Mod. Opt. 41, 2405–2412 (1994).
[CrossRef]

A. Muller, J. Bréguet, and N. Gisin, “Experimental demonstration of quantum cryptography using polarized photons in optical-fiber over more than 1 km,” Europhys. Lett. 23, 383–388 (1993).
[CrossRef]

Goosman, D. R.

O. T. Strand, D. R. Goosman, C. Martinex, and R. L. Whitworth, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108(2006).
[CrossRef]

Hemsing, W. F.

W. F. Hemsing, “Velocity sensing interferometer (VISAR) modification,” Rev. Mod. Instrum. 50, 73–78 (1979).
[CrossRef]

Hollenbach, R. E.

L. M. Barker and R. E. Hollenbach, “Interferometry technique for measuring the dynamic mechanical properties of materials,” Rev. Sci. Instrum. 36, 1617–1620 (1965).
[CrossRef]

Holmes, N. C.

D. J. Erskine and N. C. Holmes, “White light velocimetry,” Nature 377, 317–320 (1995).
[CrossRef]

Kersey, A. D.

L. Fabiny and A. D. Kersey, “Interferometric fiber-optic Doppler velocimeter with high-dynamic range,” IEEE Photon. Technol. Lett. 9, 79–81 (1997).
[CrossRef]

Knable, N.

H. Z. Cummins, N. Knable, and Y. Yeh, “Spurious harmonic generation in optical heterodyning,” Appl. Opt. 2, 823–825(1963).
[CrossRef]

H. Cummins, N. Knable, L. Gampel, and Y. Yeh, “Frequency shifts in light diffracted by ultrasonic waves in liquid media,” Appl. Phys. Lett. 2, 62–64 (1963).
[CrossRef]

Lamoreaux, S. K.

W. T. Buttler, S. K. Lamoreaux, F. G. Omenetto, and J. R. Torgerson, “Optical velocimetry,” arXiv:0409073v1(2004).

Levin, L.

L. Levin, D. Tzach, and J. Shamir, “Fiber optic velocity interferometer with very short coherence length light source,” Rev. Sci. Instrum. 67, 1434–1437 (1996).
[CrossRef]

Lewis, R. D.

J. W. Forman, Jr., E. W. George, and R. D. Lewis, “Measurement of localized fluid flow velocities in gasses with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).
[CrossRef]

Martinelli, M.

M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracing beam,” Opt. Commun. 72, 341–344 (1989).
[CrossRef]

Martinex, C.

O. T. Strand, D. R. Goosman, C. Martinex, and R. L. Whitworth, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108(2006).
[CrossRef]

Muller, A.

J. Bréguet, A. Muller, and N. Gisin, “Quantum cryptography with polarized photons in optical fiber—experiment and practical limits,” J. Mod. Opt. 41, 2405–2412 (1994).
[CrossRef]

A. Muller, J. Bréguet, and N. Gisin, “Experimental demonstration of quantum cryptography using polarized photons in optical-fiber over more than 1 km,” Europhys. Lett. 23, 383–388 (1993).
[CrossRef]

Omenetto, F. G.

W. T. Buttler, S. K. Lamoreaux, F. G. Omenetto, and J. R. Torgerson, “Optical velocimetry,” arXiv:0409073v1(2004).

Rarity, J. G.

P. Townsend, J. G. Rarity, and P. Tapster, “Single photon interference in 10 km long optical fibre interferometer,” Electron. Lett. 29, 634–635 (1993).
[CrossRef]

P. Townsend, J. G. Rarity, and P. Tapster, “Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel,” Electron. Lett. 29, 1291–1293(1993).
[CrossRef]

Risk, W. P.

D. S. Bethune and W. P. Risk, “Autocompensating quantum cryptography,” New J. Phys. 4, 42 (2002).
[CrossRef]

Schawlow, A. L.

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
[CrossRef]

Shamir, J.

L. Levin, D. Tzach, and J. Shamir, “Fiber optic velocity interferometer with very short coherence length light source,” Rev. Sci. Instrum. 67, 1434–1437 (1996).
[CrossRef]

Strand, O. T.

O. T. Strand, D. R. Goosman, C. Martinex, and R. L. Whitworth, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108(2006).
[CrossRef]

Tapster, P.

P. Townsend, J. G. Rarity, and P. Tapster, “Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel,” Electron. Lett. 29, 1291–1293(1993).
[CrossRef]

P. Townsend, J. G. Rarity, and P. Tapster, “Single photon interference in 10 km long optical fibre interferometer,” Electron. Lett. 29, 634–635 (1993).
[CrossRef]

Torgerson, J. R.

W. T. Buttler, S. K. Lamoreaux, F. G. Omenetto, and J. R. Torgerson, “Optical velocimetry,” arXiv:0409073v1(2004).

Townes, C. H.

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
[CrossRef]

Townsend, P.

P. Townsend, J. G. Rarity, and P. Tapster, “Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel,” Electron. Lett. 29, 1291–1293(1993).
[CrossRef]

P. Townsend, J. G. Rarity, and P. Tapster, “Single photon interference in 10 km long optical fibre interferometer,” Electron. Lett. 29, 634–635 (1993).
[CrossRef]

Tzach, D.

L. Levin, D. Tzach, and J. Shamir, “Fiber optic velocity interferometer with very short coherence length light source,” Rev. Sci. Instrum. 67, 1434–1437 (1996).
[CrossRef]

Whitworth, R. L.

O. T. Strand, D. R. Goosman, C. Martinex, and R. L. Whitworth, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108(2006).
[CrossRef]

Yeh, Y.

Y. Yeh and H. Z. Cummins, “Localized fluid flow measurements with an He─Ne laser,” Appl. Phys. Lett. 4, 176–178(1964).
[CrossRef]

H. Cummins, N. Knable, L. Gampel, and Y. Yeh, “Frequency shifts in light diffracted by ultrasonic waves in liquid media,” Appl. Phys. Lett. 2, 62–64 (1963).
[CrossRef]

H. Z. Cummins, N. Knable, and Y. Yeh, “Spurious harmonic generation in optical heterodyning,” Appl. Opt. 2, 823–825(1963).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

H. Cummins, N. Knable, L. Gampel, and Y. Yeh, “Frequency shifts in light diffracted by ultrasonic waves in liquid media,” Appl. Phys. Lett. 2, 62–64 (1963).
[CrossRef]

Y. Yeh and H. Z. Cummins, “Localized fluid flow measurements with an He─Ne laser,” Appl. Phys. Lett. 4, 176–178(1964).
[CrossRef]

J. W. Forman, Jr., E. W. George, and R. D. Lewis, “Measurement of localized fluid flow velocities in gasses with a laser Doppler flowmeter,” Appl. Phys. Lett. 7, 77–78 (1965).
[CrossRef]

Electron. Lett. (2)

P. Townsend, J. G. Rarity, and P. Tapster, “Single photon interference in 10 km long optical fibre interferometer,” Electron. Lett. 29, 634–635 (1993).
[CrossRef]

P. Townsend, J. G. Rarity, and P. Tapster, “Enhanced single photon fringe visibility in a 10 km-long prototype quantum cryptography channel,” Electron. Lett. 29, 1291–1293(1993).
[CrossRef]

Europhys. Lett. (1)

A. Muller, J. Bréguet, and N. Gisin, “Experimental demonstration of quantum cryptography using polarized photons in optical-fiber over more than 1 km,” Europhys. Lett. 23, 383–388 (1993).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

L. Fabiny and A. D. Kersey, “Interferometric fiber-optic Doppler velocimeter with high-dynamic range,” IEEE Photon. Technol. Lett. 9, 79–81 (1997).
[CrossRef]

J. Appl. Phys. (2)

L. M. Barker and Hollenbach, “Laser interferometry for measuring high velocities of any reflecting surface,” J. Appl. Phys. 43, 4669–4675 (1972).
[CrossRef]

W. T. Buttler, “Comment on ‘accuracy limits and window corrections for photon Doppler velocimetry’ [J. Appl. Phys. 101, 013523 (2007)],” J. Appl. Phys. 103, 046102 (2008).
[CrossRef]

J. Mod. Opt. (1)

J. Bréguet, A. Muller, and N. Gisin, “Quantum cryptography with polarized photons in optical fiber—experiment and practical limits,” J. Mod. Opt. 41, 2405–2412 (1994).
[CrossRef]

Nature (1)

D. J. Erskine and N. C. Holmes, “White light velocimetry,” Nature 377, 317–320 (1995).
[CrossRef]

New J. Phys. (1)

D. S. Bethune and W. P. Risk, “Autocompensating quantum cryptography,” New J. Phys. 4, 42 (2002).
[CrossRef]

Opt. Commun. (1)

M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracing beam,” Opt. Commun. 72, 341–344 (1989).
[CrossRef]

Phys. Rev. (1)

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
[CrossRef]

Phys. Rev. Lett. (1)

C. H. Bennett, “Quantum cryptography using any 2 nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
[CrossRef] [PubMed]

Rev. Mod. Instrum. (1)

W. F. Hemsing, “Velocity sensing interferometer (VISAR) modification,” Rev. Mod. Instrum. 50, 73–78 (1979).
[CrossRef]

Rev. Sci. Instrum. (4)

L. Levin, D. Tzach, and J. Shamir, “Fiber optic velocity interferometer with very short coherence length light source,” Rev. Sci. Instrum. 67, 1434–1437 (1996).
[CrossRef]

L. M. Barker and R. E. Hollenbach, “Interferometry technique for measuring the dynamic mechanical properties of materials,” Rev. Sci. Instrum. 36, 1617–1620 (1965).
[CrossRef]

O. T. Strand, D. R. Goosman, C. Martinex, and R. L. Whitworth, “Compact system for high-speed velocimetry using heterodyne techniques,” Rev. Sci. Instrum. 77, 083108(2006).
[CrossRef]

G. M. B. Bouricius and S. F. Clifford, “An optical interferometer using polarization coding to obtain quadrature phase components,” Rev. Sci. Instrum. 41, 1800–1803(1970).
[CrossRef]

Other (8)

The δt terms are small enough to be ignored because Δx≈[u(τ)+u(τ+Δt)]/cΔt demonstrating that Δt·ω0[u2(τ+Δt′)−u2(τ)]/c2≪1.

D. H. Dolan, “Foundations of VISAR analysis,” Internal report SAND2006-1950 (Sandia National Laboratories, 2006).

This constant fluctuates as a function of time due to environmental factors.

“Quickly” relates to the temporal length of the delay leg, the laser wavelength, the reflector velocity, and the detection and recording system.

This operator, described in Appendix , transmits h-polarized light traveling from left-to-right unchanged, but when the reflected upper path light returns, it rotates h to left-circular (ℓ) polarization for quadrature detection.

What we refer to here is a combination of the shocked surface (reflector) with a Faraday rotator. If the reflector is a mirror, this combination is known as a Faraday mirror: it rotates reflected polarizations by 90° (orthoconjugates).

L. M. Barker, Behavior of Dense Media under High Dynamic Pressures (Gordon & Breach, 1968), p. 483.

W. T. Buttler, S. K. Lamoreaux, F. G. Omenetto, and J. R. Torgerson, “Optical velocimetry,” arXiv:0409073v1(2004).

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Figures (8)

Fig. 1
Fig. 1

This VISAR-like geometry presents an optical heterodyne accelerometer, where early light that travels the long path is superposed with later light that travels the short path. (Subsequent improvements to the early concept, which include an etalon, polarizers, and wave plates, are omitted.)

Fig. 2
Fig. 2

Unbalanced Mach–Zehnder geometry is characterized by a long and short arm for each Mach–Zehnder. The sender prepares and divides a dim, weak coherent pulse in two (“single-photon” superposition), adds a random phase ϕ, and sends the photon to her cohort who adds a random phase β used to determine the random phase ϕ. Simple analysis reveals the “single-photon” can travel either the short-short, short-long or long-short, or the long-long paths, with interference occurring at the middle time only with unbalanced intensities.

Fig. 3
Fig. 3

In the autocompensating geometry, a horizontally (h) polarized “single photon” is transmitted from left to right through the fiber circulator (C) to the BS that causes a superposition. In the upper arm, the λ / 2 wave plate rotates the h polarization to vertical (v) before passing the superposition through the PBS toward the optics on the right that reflect the photon before adding a random phase β and directing the photon back to the transmitter for phase analysis. Because the polarizations were rotated by the orthoconjugating Faraday mirror (FM) [24], the paths are passively switched by the PBS, balancing and stabilizing the interferometer.

Fig. 4
Fig. 4

These elements define an autocompensating telecom- fiber-based optical heterodyne accelerometer; the individual elements are described in detail in the text and legend. Optical paths where light travels in both directions are marked with double-ended arrows, and optical paths where light travels in only one direction are marked with single-ended arrows.

Fig. 5
Fig. 5

Notional experimental geometry that requires an ability to determine the velocity of a material sample that has experienced a high-pressure impulse—shock wave.

Fig. 6
Fig. 6

Interference path lengths P 1 and P 2 demonstrate that light formed at an earlier time interferes with light formed at a later time. The paths define the relevant Doppler-shifted angular frequencies, and the relative path lengths that determine the relative phase difference, relating velocities. (Individual optical elements within P 1 and P 2 are defined within the text.)

Fig. 7
Fig. 7

Polarization operator P ^ (left image) composed of the three polarization optics (right image) labeled Q (quarter-wave retarder), F (22.5° Faraday rotator), and H (half-wave retarder).

Fig. 8
Fig. 8

Upper half of each figure shows the polarization effects of the operator elements as light transmits from left to right and the lower half as light transmits from right-to-left after the light reflects from the shocked sample back into the optical channel and into the uMZ: (a) describes the operation of P ^ , (b) the operation of H, and (c) the operation of F when combined with the reflection from the surface of the shocked sample.

Equations (8)

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ψ 0 = A 0 [ 1 0 ] g ( τ ; ω 0 ) = A 0 [ h ] g ( τ ; ω 0 ) ,
ψ 1 = A 0 2 [ 1 0 ] g ( τ ; ω 0 ) = A 0 2 [ h ] g ( τ ; ω 0 ) , ψ 2 = A 0 2 [ 0 1 ] g ( τ + Δ t ; ω 0 ) = A 0 2 [ v ] g ( τ + Δ t ; ω 0 ) .
ψ = A 0 2 ( [ v ] g ( τ ; ω 0 ) + [ h ] g ( τ + Δ t ; ω 0 ) ) ,
ϕ 1 = ω 0 x 1 2 Δ x c + ω 1 x 1 + 2 L c , ϕ 2 = ω 0 x 1 + 2 L Δ x c + ω 2 x 1 Δ x c ,
ω 1 ω D ( τ ) = ω 0 ( 1 + 2 u ( τ ) c ) , ω 2 ω D ( τ + Δ t ) = ω 0 ( 1 + 2 u ( τ + Δ t ) c ) ,
Δ ϕ = ( ω 0 ω 1 ) 2 L c + ( ω 0 ω 2 ) Δ x c + ( ω 2 ω 1 ) x 1 c .
Δ ϕ 2 = { ϕ 0 if     u 1 = u 2 = 0 ω 0 u 1 c Δ t if     u 1 = u 2 0 ω 0 ( u 1 c Δ t u 2 u 1 c x 1 c ) if    u 1 u 2 ,
u ( τ + Δ t ) u ( τ ) Δ t T a ( τ ) T = u ( τ ) + K Δ ϕ 2 π ,

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