Abstract

Signature characteristics of several materials under CO2 laser illumination are measured using a laboratory reflectometer. The reflectometer is a monostatic direct-detection system. Measured quantities include sample correlation, statistical signal distribution and its mean and standard deviations, and reflectivity of diffuse materials. Measured density distribution and number of speckle cells are compared with theoretical predictions. The measurements show that the flame-sprayed aluminum is well suited as a high-reflectivity diffuse standard, while sandpapers in general exhibit specular characteristics at near-normal incidence to the sample surface.

© 1984 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. H. Shapiro, Appl. Opt. 21, 3398 (1982).
    [CrossRef] [PubMed]
  2. R. A. Brandewie, W. C. Davis, Appl. Opt. 11, 1526 (1972).
    [CrossRef] [PubMed]
  3. M. J. Post, R. A. Richter, R. J. Keeler, R. M. Hardesty, T. R. Lawrence, F. F. Hall, Appl. Opt. 19, 2828 (1980).
    [CrossRef] [PubMed]
  4. O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widen, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).
  5. M. J. Kavaya, R. T. Menzies, U. P. Oppenheim, P. H. Flamant, D. A. Haner, Appl. Opt. 22, 2619 (1983).
    [CrossRef] [PubMed]
  6. J. Y. Wang, Appl. Opt. 21, 464 (1982).
    [CrossRef] [PubMed]
  7. J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975).
    [CrossRef]
  8. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965), 6.631.
  9. Manufactured by Ace Metalizing of Sante Fe Springs, Calif.
  10. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), p. 210.
  11. Ref. 3; their values were obtained through comparison with data published by Kronstein et al. [J. Opt. Soc. Am. 53, 458 (1963)] using an integrating sphere experiment. Thus, strictly speaking, these values should be applied to a system with unpolarized receiver. However, most of the reflected radiation from these two sandpapers remains in the same polarization state as the incident beam, and their results are applicable to a coherent lidar system.
    [CrossRef]

1983 (1)

1982 (2)

1981 (1)

O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widen, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).

1980 (1)

1972 (1)

1963 (1)

Bolander, G.

O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widen, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).

Brandewie, R. A.

Davis, W. C.

Flamant, P. H.

Goodman, J. W.

J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965), 6.631.

Gullberg, K.

O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widen, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).

Hall, F. F.

Haner, D. A.

Hardesty, R. M.

Kavaya, M. J.

Keeler, R. J.

Kronstein,

Lawrence, T. R.

Menzies, R. T.

Oppenheim, U. P.

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), p. 210.

Post, M. J.

Renhorn, I.

O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widen, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).

Richter, R. A.

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965), 6.631.

Shapiro, J. H.

Steinvall, O.

O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widen, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).

Wang, J. Y.

Widen, A.

O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widen, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widen, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).

Other (4)

J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975).
[CrossRef]

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965), 6.631.

Manufactured by Ace Metalizing of Sante Fe Springs, Calif.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), p. 210.

Cited By

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

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Reflectometer coordinate systems.

Fig. 2
Fig. 2

Optical schematic of monostatic reflectometer.

Fig. 3
Fig. 3

Two typical beam profiles at the target plane.

Fig. 4
Fig. 4

Typical line trace of the sampled signal.

Fig. 5
Fig. 5

Sample correlation of flame-sprayed aluminum.

Fig. 6
Fig. 6

Comparisons of histograms with theoretical predictions: (a) L2 = 2.62 m, 200-μm circular aperture; (b) L2 = 2.62 m, 2-mm square aperture; (c) L2 = 0.76 m, 2-mm square aperture.

Fig. 7
Fig. 7

Normalized mean received signal vs π D 2 / 4 L 2 2 for FSA (θ = ϕ = 0°).

Fig. 8
Fig. 8

Mean received signal vs beam incidence angle: (a) flame-sprayed aluminum; (b) 400-A silicon carbide; (c) Norton 320-A silicon carbide.

Fig. 9
Fig. 9

Number of speckle cells vs Am/Ac (ϕ = θ = 0°).

Fig. 10
Fig. 10

Number of speckle cells vs target aspect angle (2-mm square aperture, L2 = 2.62 m, ϕ = 0°).

Tables (1)

Tables Icon

Table I Mean Reflectivities of Flame-Sprayed Aluminum and Sandpaper at Several Polarization and Beam Incident Angles (Transmitter Polarization: Vertical, ϕ = 0°)

Equations (18)

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

U 0 ( ρ ) = k exp ( j k L 1 ) 2 π j L 1 d 2 r U 0 ( r ) exp ( j k ρ - r 2 2 L 1 ) ,
U r ( ρ ) = U 0 ( ρ ) T ˜ ( ρ ) ,
U r ( r ) = k exp ( j k L 2 ) 2 π j L 2 d 2 ρ U r ( ρ ) exp ( j k ρ - r 2 2 L 2 ) .
S = P t d 2 r U r ( r ) 2 ,
U r ( ρ 1 ) U r * ( ρ 2 ) = λ 2 T d π δ ( ρ 1 - ρ 2 ) ,
0 ρ d ρ J 0 ( β ρ r 1 ) J 0 ( β ρ r 2 ) = δ ( r 1 - r 2 ) β 2 r 1 r 2 ,
S = P t ( T d π ) π D 2 4 L 2 2 ,
P ( S ) = ( μ S ) μ S μ - 1 exp ( - μ S S ) Γ ( μ ) ,
P ( S ) = 1 S exp ( - S S ) .
γ ( Δ r ) = exp ( - π Δ r 2 2 A c ) ,
μ = { A c A m erf ( A c A m ) - ( A c π A m ) [ 1 - exp ( - π A m A c ) ] } - 2 ,
U 0 ( ρ ) 2 = 1 π α 0 2 exp ( - ρ 2 α 0 2 ) ,
γ ( Δ r ) = d 2 ρ U 0 ( ρ ) 2 exp ( j k L 2 Δ r · ρ ) .
γ ( Δ r ) = 2 α 0 2 0 ρ d ρ exp ( - ρ 2 α 0 2 ) J 0 ( k ρ Δ r L 2 ) .
γ ( Δ r ) = exp ( - α 0 2 π 2 Δ r 2 λ 2 L 2 2 ) .
A c = π 4 ( 2 λ L 2 π α 0 ) 2 ,
Δ = 2 λ L 0 π α 0 .
r = i = 1 N ( Y i - Y ) ( Y i + n - Y ) [ i = 1 N ( Y i - Y ) 2 i = 1 N ( Y i + n - Y ) 2 ] 1 / 2 ,

Metrics