Abstract

A polarimetric optical specular event detector (OSED) has been developed to provide spatially and temporally resolved polarimetric data of backscattering in the visible from water wave surfaces. The OSED acquires simultaneous, two-dimensionally resolved images of the remote target in two orthogonal planes of polarization. With the use of plane-polarized illumination the OSED presently can measure, in an ensemble of breaking waves, the equivalent four-element polarization matrix common to polarimetric radars. Upgrade to full Stokes parameter state of polarization measurements is straightforward with the use of present single-aperture, multi-imager CCD camera technology. The OSED is used in conjunction with a coherent pulse-chirped radar (PCR), which also measures the four-element polarization matrix, to provide direct time-correlated identification of backscattering mechanisms operative during wave-breaking events which heretofore have not been described theoretically. We describe the instrument and its implementation, and examples of spatially resolved polarimetric data are displayed as correlated with the PCR backscatter cross section and polarization ratio records.

© 1996 Optical Society of America

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  1. S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
    [CrossRef]
  2. J. W. Wright, “A new model for sea clutter,” IEEE Trans. Antennas Propag. AP-16, 217–223 (1968).
    [CrossRef]
  3. G. R. Valenzuela, “Scattering of electromagnetic waves from the ocean,” in Surveillance of Environmental Pollution and Resources by Electromagnetic Waves, T. Lund, ed., (Reidel, Norwell, Mass., 1978), pp. 196–226.
  4. For scattering geometries in which the plane of incidence includes the direction of the acceleration that is due to gravity the microwave community terms of vertical and horizontal can be considered equivalent to the optical terms of p (parallel) and s (senkrecht)VV then refers to vertically polarized transmission followed by vertically polarized reception as VH refers to vertically polarized transmission followed by horizontally polarized receptionInstead of degree of polarization P the microwave community commonly refers to polarization ratio defined as the ratio of scattering cross-sections HH/VV(dB) = 10 log[(1 + P)/(1 − P)]
  5. P. H. Y. Lee, J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, H. C. Yuen, “X-band microwave backscattering from ocean waves,” J. Geophys. Res. 100, 2591–2611 (1995).
    [CrossRef]
  6. P. H. Y. Lee, J. D. Barter, K. L. Beach, E. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, “Power spectral lineshapes of microwave radiation backscattered from sea surfaces at small grazing angles,” IEE Proc. Radar, Sonar Navig. 142, 252–258 (1995).
    [CrossRef]
  7. P. H. Y. Lee, J. D. Barter, E. Caponi, M. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, “Wind-speed dependence of small-grazing-angle microwave backscattering from sea surfaces,” IEEE Trans. Antennas Propag. AP-44, 333–340 (1996).
    [CrossRef]
  8. J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
    [CrossRef]
  9. J. L. Pezzaniti, R. A. Chipman, “Linear polarization uniformity measurements taken with an imaging polarimeter,” Opt. Eng. 34, 1569–1573 (1995).
    [CrossRef]
  10. J. L. Pezzaniti, R. A. Chipman, “Mueller matrix scatter polarimetry of a diamond-turned mirror,” Opt. Eng. 34, 1593–1598 (1995).
    [CrossRef]
  11. D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schwenke, K. V. Streander, T. W. Leach, C. W. Chambellan, H. K. Hull, L. B. Lacey, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Goldstein, eds., Proc. SPIE1746, 22–33 (1992).
  12. Y. Ohtsuka, K. Oka, “Polarimeter for mapping spatial distribution of dynamic state of polarization,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Gold-stein, eds., Proc. SPIE1746, 42–48 (1992).
  13. K. L. Coulson, V. S. Whitehead, C. Campbell, “Polarized views of the earth from orbital altitude,” in Ocean Optics VII, M. A. Blizard, ed., Proc. SPIE637, 35–41 (1986).
  14. M. L. Skolnik, Introduction to Radar Systems, 2nd ed. (McGraw-Hill, New York, 1980).
  15. P. H. Y. Lee, J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. C. Shelton, H. R. Thompson, M. D. White, R. Yee, “TRW Experiments at OEL-UC Santa Barbara, Part 2: Microwave Backscattering from Breaking Gravity Waves,” TRW report 63817-6001-UT-7.1 (TRW, Redondo Beach, Calif., 17September1995).
  16. E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).
  17. J. A. Lane, J. A. Saxton, “Dielectric dispersion in pure polar liquids at very high radio frequencies. I. Measurements on water, methyl and ethyl alcohols,” Proc. R. Soc. London Ser. A 213, 400–408 (1952).
    [CrossRef]
  18. M. Bass, ed., Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1995), Vol. I and II.
  19. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).
  20. A real surface of positive definite form has two principal curvatures, κ1 and κ2. The mean curvature is defined as KM = (κ1 + κ2)/2. The Gaussian curvature (sometimes called the total curvature) is defined as K = κ1κ2. See, for example, D. J. Struik, Lectures on Classical Differential Geometry, 2nd ed. (Addison-Wesley, Reading, Mass., 1961).
  21. D. E. Barrick, “Rough surface scattering based on the specular point theory,” IEEE Trans. Antennas Propag. AP-16, 449–454 (1968).
    [CrossRef]
  22. P. Wang, Y. Yao, M. P. Tulin, “An efficient numerical tank for non-linear waves, based on the multi-subdomain approach with BEM,” Intl. J. Numer. Methods Fluids 20, 1315–1336 (1995).
    [CrossRef]
  23. M. P. Tulin, Ocean Engineering Laboratory, University of California at Santa Barbara, Santa Barbara, Calif. (personal communication, 1996).
  24. M. W. Long, “On a two-scatterer theory of sea echo,” IEEE Trans. Antennas Propag. AP-22, 667–672 (1974).
    [CrossRef]

1996 (1)

P. H. Y. Lee, J. D. Barter, E. Caponi, M. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, “Wind-speed dependence of small-grazing-angle microwave backscattering from sea surfaces,” IEEE Trans. Antennas Propag. AP-44, 333–340 (1996).
[CrossRef]

1995 (6)

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

J. L. Pezzaniti, R. A. Chipman, “Linear polarization uniformity measurements taken with an imaging polarimeter,” Opt. Eng. 34, 1569–1573 (1995).
[CrossRef]

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix scatter polarimetry of a diamond-turned mirror,” Opt. Eng. 34, 1593–1598 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, H. C. Yuen, “X-band microwave backscattering from ocean waves,” J. Geophys. Res. 100, 2591–2611 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, E. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, “Power spectral lineshapes of microwave radiation backscattered from sea surfaces at small grazing angles,” IEE Proc. Radar, Sonar Navig. 142, 252–258 (1995).
[CrossRef]

P. Wang, Y. Yao, M. P. Tulin, “An efficient numerical tank for non-linear waves, based on the multi-subdomain approach with BEM,” Intl. J. Numer. Methods Fluids 20, 1315–1336 (1995).
[CrossRef]

1974 (1)

M. W. Long, “On a two-scatterer theory of sea echo,” IEEE Trans. Antennas Propag. AP-22, 667–672 (1974).
[CrossRef]

1968 (2)

D. E. Barrick, “Rough surface scattering based on the specular point theory,” IEEE Trans. Antennas Propag. AP-16, 449–454 (1968).
[CrossRef]

J. W. Wright, “A new model for sea clutter,” IEEE Trans. Antennas Propag. AP-16, 217–223 (1968).
[CrossRef]

1952 (1)

J. A. Lane, J. A. Saxton, “Dielectric dispersion in pure polar liquids at very high radio frequencies. I. Measurements on water, methyl and ethyl alcohols,” Proc. R. Soc. London Ser. A 213, 400–408 (1952).
[CrossRef]

1951 (1)

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

Barrick, D. E.

D. E. Barrick, “Rough surface scattering based on the specular point theory,” IEEE Trans. Antennas Propag. AP-16, 449–454 (1968).
[CrossRef]

Barter, J. D.

P. H. Y. Lee, J. D. Barter, E. Caponi, M. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, “Wind-speed dependence of small-grazing-angle microwave backscattering from sea surfaces,” IEEE Trans. Antennas Propag. AP-44, 333–340 (1996).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, H. C. Yuen, “X-band microwave backscattering from ocean waves,” J. Geophys. Res. 100, 2591–2611 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, E. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, “Power spectral lineshapes of microwave radiation backscattered from sea surfaces at small grazing angles,” IEE Proc. Radar, Sonar Navig. 142, 252–258 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. C. Shelton, H. R. Thompson, M. D. White, R. Yee, “TRW Experiments at OEL-UC Santa Barbara, Part 2: Microwave Backscattering from Breaking Gravity Waves,” TRW report 63817-6001-UT-7.1 (TRW, Redondo Beach, Calif., 17September1995).

Beach, K. L.

P. H. Y. Lee, J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, H. C. Yuen, “X-band microwave backscattering from ocean waves,” J. Geophys. Res. 100, 2591–2611 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, E. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, “Power spectral lineshapes of microwave radiation backscattered from sea surfaces at small grazing angles,” IEE Proc. Radar, Sonar Navig. 142, 252–258 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. C. Shelton, H. R. Thompson, M. D. White, R. Yee, “TRW Experiments at OEL-UC Santa Barbara, Part 2: Microwave Backscattering from Breaking Gravity Waves,” TRW report 63817-6001-UT-7.1 (TRW, Redondo Beach, Calif., 17September1995).

Campbell, C.

K. L. Coulson, V. S. Whitehead, C. Campbell, “Polarized views of the earth from orbital altitude,” in Ocean Optics VII, M. A. Blizard, ed., Proc. SPIE637, 35–41 (1986).

Caponi, E.

P. H. Y. Lee, J. D. Barter, E. Caponi, M. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, “Wind-speed dependence of small-grazing-angle microwave backscattering from sea surfaces,” IEEE Trans. Antennas Propag. AP-44, 333–340 (1996).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, E. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, “Power spectral lineshapes of microwave radiation backscattered from sea surfaces at small grazing angles,” IEE Proc. Radar, Sonar Navig. 142, 252–258 (1995).
[CrossRef]

Caponi, M.

P. H. Y. Lee, J. D. Barter, E. Caponi, M. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, “Wind-speed dependence of small-grazing-angle microwave backscattering from sea surfaces,” IEEE Trans. Antennas Propag. AP-44, 333–340 (1996).
[CrossRef]

Chambellan, C. W.

D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schwenke, K. V. Streander, T. W. Leach, C. W. Chambellan, H. K. Hull, L. B. Lacey, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Goldstein, eds., Proc. SPIE1746, 22–33 (1992).

Chipman, R. A.

J. L. Pezzaniti, R. A. Chipman, “Linear polarization uniformity measurements taken with an imaging polarimeter,” Opt. Eng. 34, 1569–1573 (1995).
[CrossRef]

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix scatter polarimetry of a diamond-turned mirror,” Opt. Eng. 34, 1593–1598 (1995).
[CrossRef]

Coulson, K. L.

K. L. Coulson, V. S. Whitehead, C. Campbell, “Polarized views of the earth from orbital altitude,” in Ocean Optics VII, M. A. Blizard, ed., Proc. SPIE637, 35–41 (1986).

Dunn, R. B.

D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schwenke, K. V. Streander, T. W. Leach, C. W. Chambellan, H. K. Hull, L. B. Lacey, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Goldstein, eds., Proc. SPIE1746, 22–33 (1992).

Elmore, D. F.

D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schwenke, K. V. Streander, T. W. Leach, C. W. Chambellan, H. K. Hull, L. B. Lacey, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Goldstein, eds., Proc. SPIE1746, 22–33 (1992).

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).

Hindman, C. L.

P. H. Y. Lee, J. D. Barter, E. Caponi, M. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, “Wind-speed dependence of small-grazing-angle microwave backscattering from sea surfaces,” IEEE Trans. Antennas Propag. AP-44, 333–340 (1996).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, H. C. Yuen, “X-band microwave backscattering from ocean waves,” J. Geophys. Res. 100, 2591–2611 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, E. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, “Power spectral lineshapes of microwave radiation backscattered from sea surfaces at small grazing angles,” IEE Proc. Radar, Sonar Navig. 142, 252–258 (1995).
[CrossRef]

Hull, H. K.

D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schwenke, K. V. Streander, T. W. Leach, C. W. Chambellan, H. K. Hull, L. B. Lacey, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Goldstein, eds., Proc. SPIE1746, 22–33 (1992).

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

Lacey, L. B.

D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schwenke, K. V. Streander, T. W. Leach, C. W. Chambellan, H. K. Hull, L. B. Lacey, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Goldstein, eds., Proc. SPIE1746, 22–33 (1992).

Lake, B. M.

P. H. Y. Lee, J. D. Barter, E. Caponi, M. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, “Wind-speed dependence of small-grazing-angle microwave backscattering from sea surfaces,” IEEE Trans. Antennas Propag. AP-44, 333–340 (1996).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, H. C. Yuen, “X-band microwave backscattering from ocean waves,” J. Geophys. Res. 100, 2591–2611 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, E. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, “Power spectral lineshapes of microwave radiation backscattered from sea surfaces at small grazing angles,” IEE Proc. Radar, Sonar Navig. 142, 252–258 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. C. Shelton, H. R. Thompson, M. D. White, R. Yee, “TRW Experiments at OEL-UC Santa Barbara, Part 2: Microwave Backscattering from Breaking Gravity Waves,” TRW report 63817-6001-UT-7.1 (TRW, Redondo Beach, Calif., 17September1995).

Lane, J. A.

J. A. Lane, J. A. Saxton, “Dielectric dispersion in pure polar liquids at very high radio frequencies. I. Measurements on water, methyl and ethyl alcohols,” Proc. R. Soc. London Ser. A 213, 400–408 (1952).
[CrossRef]

Leach, T. W.

D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schwenke, K. V. Streander, T. W. Leach, C. W. Chambellan, H. K. Hull, L. B. Lacey, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Goldstein, eds., Proc. SPIE1746, 22–33 (1992).

Lee, P. H. Y.

P. H. Y. Lee, J. D. Barter, E. Caponi, M. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, “Wind-speed dependence of small-grazing-angle microwave backscattering from sea surfaces,” IEEE Trans. Antennas Propag. AP-44, 333–340 (1996).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, H. C. Yuen, “X-band microwave backscattering from ocean waves,” J. Geophys. Res. 100, 2591–2611 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, E. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, “Power spectral lineshapes of microwave radiation backscattered from sea surfaces at small grazing angles,” IEE Proc. Radar, Sonar Navig. 142, 252–258 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. C. Shelton, H. R. Thompson, M. D. White, R. Yee, “TRW Experiments at OEL-UC Santa Barbara, Part 2: Microwave Backscattering from Breaking Gravity Waves,” TRW report 63817-6001-UT-7.1 (TRW, Redondo Beach, Calif., 17September1995).

Lites, B. W.

D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schwenke, K. V. Streander, T. W. Leach, C. W. Chambellan, H. K. Hull, L. B. Lacey, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Goldstein, eds., Proc. SPIE1746, 22–33 (1992).

Long, M. W.

M. W. Long, “On a two-scatterer theory of sea echo,” IEEE Trans. Antennas Propag. AP-22, 667–672 (1974).
[CrossRef]

Ohtsuka, Y.

Y. Ohtsuka, K. Oka, “Polarimeter for mapping spatial distribution of dynamic state of polarization,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Gold-stein, eds., Proc. SPIE1746, 42–48 (1992).

Oka, K.

Y. Ohtsuka, K. Oka, “Polarimeter for mapping spatial distribution of dynamic state of polarization,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Gold-stein, eds., Proc. SPIE1746, 42–48 (1992).

Pezzaniti, J. L.

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix scatter polarimetry of a diamond-turned mirror,” Opt. Eng. 34, 1593–1598 (1995).
[CrossRef]

J. L. Pezzaniti, R. A. Chipman, “Linear polarization uniformity measurements taken with an imaging polarimeter,” Opt. Eng. 34, 1569–1573 (1995).
[CrossRef]

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Rice, S. O.

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

Rungaldier, H.

P. H. Y. Lee, J. D. Barter, E. Caponi, M. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, “Wind-speed dependence of small-grazing-angle microwave backscattering from sea surfaces,” IEEE Trans. Antennas Propag. AP-44, 333–340 (1996).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, H. C. Yuen, “X-band microwave backscattering from ocean waves,” J. Geophys. Res. 100, 2591–2611 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, E. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, “Power spectral lineshapes of microwave radiation backscattered from sea surfaces at small grazing angles,” IEE Proc. Radar, Sonar Navig. 142, 252–258 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. C. Shelton, H. R. Thompson, M. D. White, R. Yee, “TRW Experiments at OEL-UC Santa Barbara, Part 2: Microwave Backscattering from Breaking Gravity Waves,” TRW report 63817-6001-UT-7.1 (TRW, Redondo Beach, Calif., 17September1995).

Saxton, J. A.

J. A. Lane, J. A. Saxton, “Dielectric dispersion in pure polar liquids at very high radio frequencies. I. Measurements on water, methyl and ethyl alcohols,” Proc. R. Soc. London Ser. A 213, 400–408 (1952).
[CrossRef]

Schwenke, J. A.

D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schwenke, K. V. Streander, T. W. Leach, C. W. Chambellan, H. K. Hull, L. B. Lacey, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Goldstein, eds., Proc. SPIE1746, 22–33 (1992).

Shelton, J. C.

P. H. Y. Lee, J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, H. C. Yuen, “X-band microwave backscattering from ocean waves,” J. Geophys. Res. 100, 2591–2611 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, E. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, “Power spectral lineshapes of microwave radiation backscattered from sea surfaces at small grazing angles,” IEE Proc. Radar, Sonar Navig. 142, 252–258 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. C. Shelton, H. R. Thompson, M. D. White, R. Yee, “TRW Experiments at OEL-UC Santa Barbara, Part 2: Microwave Backscattering from Breaking Gravity Waves,” TRW report 63817-6001-UT-7.1 (TRW, Redondo Beach, Calif., 17September1995).

Skolnik, M. L.

M. L. Skolnik, Introduction to Radar Systems, 2nd ed. (McGraw-Hill, New York, 1980).

Skumanich, A. P.

D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schwenke, K. V. Streander, T. W. Leach, C. W. Chambellan, H. K. Hull, L. B. Lacey, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Goldstein, eds., Proc. SPIE1746, 22–33 (1992).

Streander, K. V.

D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schwenke, K. V. Streander, T. W. Leach, C. W. Chambellan, H. K. Hull, L. B. Lacey, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Goldstein, eds., Proc. SPIE1746, 22–33 (1992).

Struik, D. J.

A real surface of positive definite form has two principal curvatures, κ1 and κ2. The mean curvature is defined as KM = (κ1 + κ2)/2. The Gaussian curvature (sometimes called the total curvature) is defined as K = κ1κ2. See, for example, D. J. Struik, Lectures on Classical Differential Geometry, 2nd ed. (Addison-Wesley, Reading, Mass., 1961).

Thompson, H. R.

P. H. Y. Lee, J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. C. Shelton, H. R. Thompson, M. D. White, R. Yee, “TRW Experiments at OEL-UC Santa Barbara, Part 2: Microwave Backscattering from Breaking Gravity Waves,” TRW report 63817-6001-UT-7.1 (TRW, Redondo Beach, Calif., 17September1995).

Tomczyk, S.

D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schwenke, K. V. Streander, T. W. Leach, C. W. Chambellan, H. K. Hull, L. B. Lacey, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Goldstein, eds., Proc. SPIE1746, 22–33 (1992).

Tulin, M. P.

P. Wang, Y. Yao, M. P. Tulin, “An efficient numerical tank for non-linear waves, based on the multi-subdomain approach with BEM,” Intl. J. Numer. Methods Fluids 20, 1315–1336 (1995).
[CrossRef]

M. P. Tulin, Ocean Engineering Laboratory, University of California at Santa Barbara, Santa Barbara, Calif. (personal communication, 1996).

Valenzuela, G. R.

G. R. Valenzuela, “Scattering of electromagnetic waves from the ocean,” in Surveillance of Environmental Pollution and Resources by Electromagnetic Waves, T. Lund, ed., (Reidel, Norwell, Mass., 1978), pp. 196–226.

Wang, P.

P. Wang, Y. Yao, M. P. Tulin, “An efficient numerical tank for non-linear waves, based on the multi-subdomain approach with BEM,” Intl. J. Numer. Methods Fluids 20, 1315–1336 (1995).
[CrossRef]

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

White, M. D.

P. H. Y. Lee, J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. C. Shelton, H. R. Thompson, M. D. White, R. Yee, “TRW Experiments at OEL-UC Santa Barbara, Part 2: Microwave Backscattering from Breaking Gravity Waves,” TRW report 63817-6001-UT-7.1 (TRW, Redondo Beach, Calif., 17September1995).

Whitehead, V. S.

K. L. Coulson, V. S. Whitehead, C. Campbell, “Polarized views of the earth from orbital altitude,” in Ocean Optics VII, M. A. Blizard, ed., Proc. SPIE637, 35–41 (1986).

Williams, A. B.

P. H. Y. Lee, J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, H. C. Yuen, “X-band microwave backscattering from ocean waves,” J. Geophys. Res. 100, 2591–2611 (1995).
[CrossRef]

Wright, J. W.

J. W. Wright, “A new model for sea clutter,” IEEE Trans. Antennas Propag. AP-16, 217–223 (1968).
[CrossRef]

Yao, Y.

P. Wang, Y. Yao, M. P. Tulin, “An efficient numerical tank for non-linear waves, based on the multi-subdomain approach with BEM,” Intl. J. Numer. Methods Fluids 20, 1315–1336 (1995).
[CrossRef]

Yee, R.

P. H. Y. Lee, J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, H. C. Yuen, “X-band microwave backscattering from ocean waves,” J. Geophys. Res. 100, 2591–2611 (1995).
[CrossRef]

P. H. Y. Lee, J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. C. Shelton, H. R. Thompson, M. D. White, R. Yee, “TRW Experiments at OEL-UC Santa Barbara, Part 2: Microwave Backscattering from Breaking Gravity Waves,” TRW report 63817-6001-UT-7.1 (TRW, Redondo Beach, Calif., 17September1995).

Yuen, H. C.

P. H. Y. Lee, J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, H. C. Yuen, “X-band microwave backscattering from ocean waves,” J. Geophys. Res. 100, 2591–2611 (1995).
[CrossRef]

Commun. Pure Appl. Math. (1)

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

IEE Proc. Radar, Sonar Navig. (1)

P. H. Y. Lee, J. D. Barter, K. L. Beach, E. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, “Power spectral lineshapes of microwave radiation backscattered from sea surfaces at small grazing angles,” IEE Proc. Radar, Sonar Navig. 142, 252–258 (1995).
[CrossRef]

IEEE Trans. Antennas Propag. (4)

P. H. Y. Lee, J. D. Barter, E. Caponi, M. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, “Wind-speed dependence of small-grazing-angle microwave backscattering from sea surfaces,” IEEE Trans. Antennas Propag. AP-44, 333–340 (1996).
[CrossRef]

J. W. Wright, “A new model for sea clutter,” IEEE Trans. Antennas Propag. AP-16, 217–223 (1968).
[CrossRef]

D. E. Barrick, “Rough surface scattering based on the specular point theory,” IEEE Trans. Antennas Propag. AP-16, 449–454 (1968).
[CrossRef]

M. W. Long, “On a two-scatterer theory of sea echo,” IEEE Trans. Antennas Propag. AP-22, 667–672 (1974).
[CrossRef]

Intl. J. Numer. Methods Fluids (1)

P. Wang, Y. Yao, M. P. Tulin, “An efficient numerical tank for non-linear waves, based on the multi-subdomain approach with BEM,” Intl. J. Numer. Methods Fluids 20, 1315–1336 (1995).
[CrossRef]

J. Geophys. Res. (1)

P. H. Y. Lee, J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, H. C. Yuen, “X-band microwave backscattering from ocean waves,” J. Geophys. Res. 100, 2591–2611 (1995).
[CrossRef]

Opt. Eng. (3)

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

J. L. Pezzaniti, R. A. Chipman, “Linear polarization uniformity measurements taken with an imaging polarimeter,” Opt. Eng. 34, 1569–1573 (1995).
[CrossRef]

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix scatter polarimetry of a diamond-turned mirror,” Opt. Eng. 34, 1593–1598 (1995).
[CrossRef]

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J. A. Lane, J. A. Saxton, “Dielectric dispersion in pure polar liquids at very high radio frequencies. I. Measurements on water, methyl and ethyl alcohols,” Proc. R. Soc. London Ser. A 213, 400–408 (1952).
[CrossRef]

Other (12)

M. Bass, ed., Handbook of Optics, 2nd ed. (McGraw-Hill, New York, 1995), Vol. I and II.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

A real surface of positive definite form has two principal curvatures, κ1 and κ2. The mean curvature is defined as KM = (κ1 + κ2)/2. The Gaussian curvature (sometimes called the total curvature) is defined as K = κ1κ2. See, for example, D. J. Struik, Lectures on Classical Differential Geometry, 2nd ed. (Addison-Wesley, Reading, Mass., 1961).

G. R. Valenzuela, “Scattering of electromagnetic waves from the ocean,” in Surveillance of Environmental Pollution and Resources by Electromagnetic Waves, T. Lund, ed., (Reidel, Norwell, Mass., 1978), pp. 196–226.

For scattering geometries in which the plane of incidence includes the direction of the acceleration that is due to gravity the microwave community terms of vertical and horizontal can be considered equivalent to the optical terms of p (parallel) and s (senkrecht)VV then refers to vertically polarized transmission followed by vertically polarized reception as VH refers to vertically polarized transmission followed by horizontally polarized receptionInstead of degree of polarization P the microwave community commonly refers to polarization ratio defined as the ratio of scattering cross-sections HH/VV(dB) = 10 log[(1 + P)/(1 − P)]

D. F. Elmore, B. W. Lites, S. Tomczyk, A. P. Skumanich, R. B. Dunn, J. A. Schwenke, K. V. Streander, T. W. Leach, C. W. Chambellan, H. K. Hull, L. B. Lacey, “The advanced Stokes polarimeter: a new instrument for solar magnetic field research,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Goldstein, eds., Proc. SPIE1746, 22–33 (1992).

Y. Ohtsuka, K. Oka, “Polarimeter for mapping spatial distribution of dynamic state of polarization,” in Polarization Analysis and Measurement, R. A. Chipman, D. H. Gold-stein, eds., Proc. SPIE1746, 42–48 (1992).

K. L. Coulson, V. S. Whitehead, C. Campbell, “Polarized views of the earth from orbital altitude,” in Ocean Optics VII, M. A. Blizard, ed., Proc. SPIE637, 35–41 (1986).

M. L. Skolnik, Introduction to Radar Systems, 2nd ed. (McGraw-Hill, New York, 1980).

P. H. Y. Lee, J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. C. Shelton, H. R. Thompson, M. D. White, R. Yee, “TRW Experiments at OEL-UC Santa Barbara, Part 2: Microwave Backscattering from Breaking Gravity Waves,” TRW report 63817-6001-UT-7.1 (TRW, Redondo Beach, Calif., 17September1995).

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).

M. P. Tulin, Ocean Engineering Laboratory, University of California at Santa Barbara, Santa Barbara, Calif. (personal communication, 1996).

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Figures (23)

Fig. 1
Fig. 1

Schematic diagram of the OSED showing the IR filtering, splitting, and polarization analysis of the received light. The CCD imager outputs are displayed on black-and-white TV monitors and acquired by a color frame grabber with digital signal processing capabilities for quantitative analysis and display. The p- and s-polarization image cartoons illustrate that, although polarized image features may not be distinguishable in the normal (sum-image) view, they become prominent in the difference and can be displayed quantitatively in the degree-of-polarization false-color image.

Fig. 2
Fig. 2

Schematic diagram of plan and elevation views illustrating the mounting of the OSED with respect to the PCR to allow synchronized recording of the same field of view in which the geometric requirement for observation of specular events is identical for each instrument. The toe-in half-angles of the PCR and OSED shown in the plan view are αμ = 1.5° and α v ≅ 5°, respectively. In the elevation view, the grazing angle θ g is indicated. The 3-dB beam width of the microwave radiation pattern is indicated by the dotted lines. The elliptical footprint represents the intersection of the approximately conical microwave radiation pattern with the mean water level.

Fig. 3
Fig. 3

Schematic diagram of the signal processing and archiving arrangements. The image processing board resides in and is controlled by a computer. Analyzed images are displayed on a separate monitor. The MOD recorder is used to archive synchronous black-and-white frames of data as the red and green color channels of one color image. VGA, videographics array; SVHS, Superior Video Home System.

Fig. 4
Fig. 4

Schematic diagram of the high-contrast, unpolarized target used for the alignment calibration of the OSED. x and y describe the horizontal and vertical dimensions of a target patch.

Fig. 5
Fig. 5

Schematic diagram of the misalignment geometry and nomenclature. The different cross hatchings indicate the images of the two cameras and their overlap. The unit cell defines a minimum cell that includes representatives of all misaligned cell populations. δ is a small, relative translation misalignment at an arbitrary angle ϕ from the horizontal.

Fig. 6
Fig. 6

Pixel-by-pixel summed view of the NIST-style target illustrating the resolution obtainable with this instrument at a range of 10 m. The line pairs are labeled as lp/cm. The target is surrounded by an incomplete representation of the checkerboard target arrangement. The circular targets at the bottom of the view are polarized targets that are not distinguishable by pixel intensity in this view (see Fig. 11).

Fig. 7
Fig. 7

Statistically defined misaligned pixel fraction fstat plotted against the deliberate areal misaligned pixel fraction fareal.

Fig. 8
Fig. 8

Effective relative misalignment of p- and s-polarization images expressed in pixel widths as a function of deliberate misalignment fraction. Maximum pixel misalignment for this target is ~92 pixels.

Fig. 9
Fig. 9

Estimates of uncertainty in the degree-of-polarization measurement plotted against local target brightness at optimum spatial alignment. Two statistical estimates are shown based on the interpretation of the target data as representing spatial misalignment (Alignment) or spatial photosensitivity variation (Photometric). Target brightness is displayed as the digitizer integer output in the 0–255 range or ADC units (adu).

Fig. 10
Fig. 10

Measured degree of polarization of a linearly polarized target plotted as a function of the angle ϕ between the plane of polarization and the s-polarization plane of the OSED.

Fig. 11
Fig. 11

Composite figure illustrating the input black-and-white images from the p- and s-polarization images in the lower left and lower right panels, respectively. The two-color archived image appears in the upper left panel, and the difference image appears in the upper right panel. p- and s-polarized targets are also provided in the lower left and right of each panel to illustrate the appearance of each polarization at each stage of analysis.

Fig. 12
Fig. 12

Schematic diagram of the basic double-bounce backscatter reflection geometry. θ g is the grazing angle of one reflection and the angle of incidence of the other.

Fig. 13
Fig. 13

Comparison of the expected degree of polarization to be presented by a double-bounce backscatter event (with vertical plane of incidence) to the PCR (λμ ≈ 3 cm, x-band) and the OSED (λ v ≈ 580 nm, visible) assuming fresh water. Note that the expected degree of polarization in the optical is ~0.25 at the maximum polarization in the microwave regime.

Fig. 14
Fig. 14

Schematic diagram of the paraxial ray geometry involved in the surface curvature. y o and y i are the object size (OSED illuminator lamps) and image size (in the curved reflecting surface). A o and A d are the areas of the object and detector (CCD imager). a m is the area on the reflecting surface that defines the effective detector collection solid angle with respect to the object A o . B o is the surface brightness of the object. s o , s i , and s d are the object, image, and detector distances, respectively, from the reflecting surface. f is the paraxial focal length of the spherical reflecting surface of radius r.

Fig. 15
Fig. 15

100-s time record of radar backscatter cross section in which wave-breaking events appear as the sharp bursts of all radar polarization components. The colors represent: red = HH, yellow = VV, green = VH, and blue = HV. The IRIG start time for the record (to within ~90 ms), printed in the upper right corner, is used to correlate this time record with specific OSED image frames.

Fig. 16
Fig. 16

10-s excerpt from the record of Fig. 15 showing the times of the three OSED image frames of Figs. 1820. Three representative times were chosen to illustrate PCR to OSED correlations early in the breaking event (Fig. 18, 35.66 s), at the peak of the breaking event (Fig. 19, 36.16 s), and late in the breaking event (Fig. 20, 36.79 s).

Fig. 17
Fig. 17

Scale template that defines the spatial scales in the field of view of the OSED and the false color degree-of-polarization linear scale. Note that the luminance in this view does not contain any information of relative image intensity. A combination of luminance and hue has been chosen to portray only degree of polarization. Regions of zero-summed intensity are painted black. Scattered, colored, single pixels are the result of acquisition noise and division by small sum intensity in the process of calculation of the degree of polarization. The spatial scale indicates the centerline of the wave tank surface at the mean water line along the x axis. Radial range from the radar in meters is indicated along the x axis. 0.5-m distances to right and left of the centerline are indicated with dotted lines for comparison because the nominal 3-dB-footprint width of the PCR is 1 m at a 10-m range.

Fig. 18
Fig. 18

OSED image frame synchronized with t = 35.66 s in the PCR record (Fig. 16). The wave crest has just begun to turn forward sufficiently to present specular facets to the PCR and OSED. Note the green hue (s polarization), which is in agreement with the dominant HH signal in Fig. 16. This figure directly verifies that wave breaking can give rise to super events.

Fig. 19
Fig. 19

OSED image frame synchronized with t = 36.16 s in the PCR record (Fig. 16). The wave crest has long since crashed into the front face and dissolved into a disordered surface including foam and droplets. The frame has been chosen to illustrate the large white (unpolarized) regions in the wave crest along with the pronounced polarization structure, including red (p polarized) and green (s polarized) regions. Also the reflection of the bright, isotropically scattering wave crest foam in the front face of the wave gives rise to broad regions of s-polarized light (green, shading to blue directly under the crest region) that is due to the preferential absorption of p-polarized light near Brewster incidence. This figure directly verifies that wave breaking can give rise to Brewster events.

Fig. 20
Fig. 20

OSED image frame synchronized with t = 36.79 s in the PCR record (Fig. 16). The Brewster reflection on the front apron of the wave has largely disappeared, and the wave crest has become predominantly red in agreement with Fig. 16 in which the HH signal has dropped below the VV. This figure directly verifies that wave breaking can give rise to both specular and vertical events.

Fig. 21
Fig. 21

Comparison of the OSED s-polarization intensity integrated over the field of view in unpolarized illumination to the PCR HH + VH cross section for the time window 30–40 s. Cross sections are relative, so that differences of absolute level are not physically significant.

Fig. 22
Fig. 22

Comparison of the OSED p-polarization intensity integrated over the field of view in unpolarized illumination to the PCR VV + HV cross section for the time window 30–40 s. Cross sections are relative, so that differences of absolute level are not physically significant.

Fig. 23
Fig. 23

Comparison of the OSED polarization ratio in unpolarized illumination to a modified PCR polarization ratio of HH + VH cross section to VV + HV cross section for the time window 30–40 s.

Equations (26)

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I sum = ( I s + I p ) / 2 ,
I dif = ( I s - I p + 255 ) / 2 ,
f AREAL = δ x y + δ y x - 2 δ x δ y x y ,
δ x = δ cos ϕ , δ y = δ sin ϕ ,
f areal = 2 δ π ( x + y - δ x y ) .
σ dif 2 = f stat I sum 2 ,
δ = x + y 2 { 1 - [ 1 - 2 π f stat x y ( x + y ) 2 ] 1 / 2 } .
P = I dif - 255 / 2 I sum ,
d P = 1 I sum [ d I dif - P d I sum ] ,
d I dif = I dif x δ x + I dif y δ y I sum ρ , d I sum = I sum x δ x + I sum y δ y I sum ρ ,
d P align δ ρ ( 1 + P 2 ) 1 / 2 ,
d P photo σ dif I sum ( 1 + P 2 ) 1 / 2 = f stat 1 / 2 ( 1 + P 2 ) 1 / 2 .
P meas = I 1 - I 2 I 1 + I 2 , I 1 = i 01 + cos 2 ( ϕ - δ 1 ) , I 2 = i 02 + sin 2 ( ϕ - δ 2 ) , i 01 = 0.023 ,             δ 1 = 2.3 ° , i 02 = 0.012 ,             δ 2 = 1.1 ° ,
n = 8.14 - i 2 ,
n = 1.33 - i 4.98 × 10 - 9 .
1 s o + 1 s i = - 2 r - 2 κ ,
m j = y i y o = 1 1 + 2 κ j s o ,
Π A d = α r B 0 A 0 a m s o 2 .
a m A d = ( - s i 1 s d - s i 1 ) ( - s i 2 s d - s i 2 ) = [ ( 1 + s d m 1 s o ) ( 1 + s d m 2 s o ) ] - 1 ,
Π Π κ = 0 = [ ( 1 + κ 1 2 s d s o s d + s o ) ( 1 + κ 2 2 s d s o s d + s o ) ] - 1 = [ ( 1 + κ 1 R 0 ) ( 1 + κ 2 R 0 ) ] - 1 = ϕ 1 ϕ 2 ϕ 0 2 ,
κ max 0.036 cm - 1
d min 2 κ max 28 cm
ϕ = ϕ 0 ( 1 + κ R 0 ) - 1 .
δ ϕ = ϕ 0 ( 1 + κ R 0 ) - 2 r 0 δ κ .
κ max R 0 ϕ 0 ϕ res 72 pixels 2 pixels 1 ,
κ max ϕ 0 R 0 ϕ res = 72 pixels 10.45 m × 2 pixels = 0.036 cm - 1 .

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