Haze of surface random systems: An approximate analytic approach

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 79, Issue 6, 2009, Pages

  Simonsen, Ingve ^a,b   Larsen, Åge ^c   Andreassen, Erik ^c   Ommundsen, Espen ^d   Nord Varhaug, Katrin ^e  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^b NORDITA   (Denmark)

^c SINTEF MATERIALS AND CHEMISTRY   (Norway)

^d NORNER AS   (Norway)

^e REC Wafer AS   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTIC APPROACH; ANALYTIC APPROXIMATION; ANALYTIC EXPRESSIONS; ANGLE OF INCIDENCE; ANGULAR INTERVALS; BLOWN POLYETHYLENE FILMS; CORRELATION FUNCTION; CORRELATION LENGTHS; GAUSSIAN; INCIDENT LIGHT; LARGE REGIONS; MONTE CARLO SIMULATION; PARAMETER SPACES; PERTURBATION THEORY; RANDOM SYSTEMS; RANDOMLY ROUGH SURFACES; ROUGHNESS MEASURE; SPECULAR DIRECTION; TRANSMITTED LIGHT;

ANGULAR DISTRIBUTION; METAL ANALYSIS; MONTE CARLO METHODS; PERTURBATION TECHNIQUES; POWER SPECTRUM; SURFACE PROPERTIES; SURFACE ROUGHNESS;

POLYMER FILMS;

EID: 66749117813     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.79.063813     Document Type: Article

References (69)

1. J. L. White, Y. Matsukura, H. J. Kang, and H. Yamane, Int. Polym. Process. 1, 83 (1987).
2. M. S. Edmondson and S. E. Pirtle, J. Plast. Film Sheeting 9, 334 (1993). 10.1177/875608799300900406
3. M. B. Johnson, G. L. Wilkes, A. M. Sukhadia, and D. C. Rohlfing, J. Appl. Polym. Sci. 77, 2845 (2000). 10.1002/1097-4628(20000923)77:13<2845::AID- APP6>3.0.CO;2-7
4. E. Andreassen, Å. Larsen, K. Nord-Varhaug, M. Skar, and H. Øysæd, Polym. Eng. Sci. 42, 1082 (2002). 10.1002/pen.11014
5. M. S. Pucci and R. N. Shroff, Polym. Eng. Sci. 26, 569 (1986). 10.1002/pen.760260808
6. A. M. Sukhadia, J. Plast. Film Sheeting 16, 54 (2000). 10.1106/YPU9-CJW7-ACQY-WALP
7. H. Zweifel, Plastics Additives Handbook, 5th ed. (Hanser, Munich, 2001).
8. S. Cheruvu, F. Y.-K. Lo, S. C. Ong, and T.-K. Su, International Patent No. WO 95/13317 (1995).
9. H. Ashizawa, J. E. Spruiell, and J. L. White, Polym. Eng. Sci. 24, 1035 (1984). 10.1002/pen.760241307
10. P. F. Smith, I. Chun, G. Liu, D. Dimitriev, J. Rasburn, and G. J. Vancso, Polym. Eng. Sci. 36, 2129 (1996). 10.1002/pen.10609
11. F. C. Stehling, C. S. Speed, and L. Westerman, Macromolecules 14, 698 (1981). 10.1021/ma50004a047
12. A. Larena and G. Pinto, Polym. Eng. Sci. 33, 742 (1993). 10.1002/pen.760331204
13. S. W. Shang and R. D. Kamla, J. Plast. Film Sheeting 11, 21 (1995).
14. F. M. Willmouth, in Optical Properties of Polymers, edited by, G. H. Meeten, (Elsevier, London, 1986), p. 265.
15. ASTM Standard D 1003-95: Standard Test Method for Haze and Luminous Transmittance of Transparent Plastics, 2000.
16. ASTM Standard E 430-91, Standard Test Method for Measurement of Gloss of High-Gloss Surfaces by Goniophotometry, 1991.
17. Y. Kikuta, Y. Miyasaka, T. Asuke, H. Yamanashi, and T. Taka, Bunseki Kagaku 45, 347 (1996).
18. N. D. Huck and P. L. Clegg, SPE Trans. 1, 121 (1961).
19. M. Kojima, J. H. Magill, J. S. Lin, and S. N. Magonov, Chem. Mater. 9, 1145 (1997). 10.1021/cm960505h
20. L. Wang, T. Huang, M. R. Kamal, A. D. Rey, and J. Teh, Polym. Eng. Sci. 40, 747 (2000). 10.1002/pen.11204
21. L. Wang, M. R. Kamal, and A. D. Rey, Polym. Eng. Sci. 41, 358 (2001). 10.1002/pen.10734
22. A. M. Sukhadia, D. C. Rohlfing, M. B. Johnson, and G. L. Wilkes, J. Appl. Polym. Sci. 85, 2396 (2002). 10.1002/app.10874
23. J. W. S. Rayleigh, The Theory of Sound (Dover, New York, 1945), Vols. 1 and 2.
24. P. Beckmann and A. Spizzichino, The Scattering from Electromagnetic Waves from Rough Surfaces (Artech House, Boston, 1963).
25. F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon Press, Oxford, UK, 1979).
26. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (IOP, Bristol, 1991).
27. L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (John Wiley & Sons, New York, 2000), Vol. 1.
28. L. Tsang, J. A. Kong, K.-H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (John Wiley & Sons, New York, 2001), Vol. 2.
29. L. Tsang and J. A. Kong, Scattering of Electromagnetic Waves: Advanced topics (John Wiley & Sons, New York, 2001), Vol. 3.
30. M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University Press, Cambridge, 1999).
31. I. Simonsen, Ph.D. thesis, The Norwegian University of Science and Technology
32. Available from http://www.phys.ntnu.no/ingves/Thesis/
33. I. Simonsen, e-print arXiv:cond-mat/0408017.
34. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005). 10.1016/j.physrep.2004.11.001
35. I. Simonsen, D. Vandembroucq, and S. Roux, Phys. Rev. E 61, 5914 (2000). 10.1103/PhysRevE.61.5914
36. I. Simonsen, D. Vandembroucq, and S. Roux, J. Opt. Soc. Am. A Opt. Image Sci. Vis. 18, 1101 (2001). 10.1364/JOSAA.18.001101
37. X.-L. Zhou and S.-H. Chen, Phys. Rep. 257, 223 (1995). 10.1016/0370-1573(94)00110-O
38. S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, Phys. Rev. B 38, 2297 (1988). 10.1103/PhysRevB.38.2297
39. D. K. G. de Boer, Phys. Rev. B 49, 5817 (1994) 10.1103/PhysRevB.49.5817
40. D. K. G. de Boer, Phys. Rev. B 51, 5297 (1995). 10.1103/PhysRevB.51.5297
41. A. V. Andreev, Phys. Lett. A 219, 349 (1996). 10.1016/0375-9601(96)00469- 0
42. A. A. Maradudin and T. A. Leskova, Waves Random Media 7, 395 (1997).
43. A. A. Maradudin, I. Simonsen, T. A. Leskova, and E. R. Méndez, Opt. Lett. 24, 1257 (1999). 10.1364/OL.24.001257
44. E. R. Méndez, Appl. Phys. Lett. 81, 798 (2002). 10.1063/1.1495900
45. J. C. Stover, Optical Scattering: Measurements and Analysis, 2nd ed. (SPIE Optical Engineering Press, Bellingham, WA, 1995).
46. E. C. Teague, CIRP Ann. 30, 563 (1981). 10.1016/S0007-8506(07)60168-1
47. R. Alexander-Katz and R. G. Barrera, J. Polym. Sci., Part B: Polym. Phys. 36, 1321 (1998). 10.1002/(SICI)1099-0488(199806)36:8<1321::AID-POLB7>3.0. CO;2-U
48. E. Bahar, B. S. Lee, G. R. Huang, and R. D. Kubik, Radio Sci. 30, 545 (1995). 10.1029/94RS03161
49. W. T. Welford, Opt. Quantum Electron. 9, 269 (1977). 10.1007/BF00619527
50. J. D. Jackson, Classical Electrodynamics, 2nd ed. (John Wiley & Sons, New York, 1975).
51. M. E. Nadal and E. A. Thompson, J. Coat. Technol. 72, 61 (2000). 10.1007/BF02720526
52. E. R. Méndez, R. G. Barrera, and R. Alexander-Katz, Physica A 207, 137 (1994). 10.1016/0378-4371(94)90364-6
53. F. W. Billmeyer and Y. Chen, Color Res. Appl. 10, 219 (1985). 10.1002/col.5080100410
54. The actual angular interval depends on the type of haze one wants to measure, e.g., narrow- or wide-angle haze, and it depends on the actual standard one desires to comply with. For instance, one should notice that the angular interval may be different for reflection and transmission.
55. Haze is often also indicated by using a "percentage notation" so that a haze of 1 corresponds to a haze of 100%.
56. One should, however, be aware that this is only fully true if a plane incident wave is used. On the other hand, if an incident beam of finite width is applied, one can, at least in principle, get a nonvanishing, but small, haze value even for an ideal scattering system.
57. A. A. Maradudin, I. Simonsen, T. A. Leskova, and E. R. Méndez, Waves Random Media 11, 529 (2001). 10.1088/0959-7174/11/4/308
58. J. Shen and A. A. Maradudin, Phys. Rev. B 22, 4234 (1980). 10.1103/PhysRevB.22.4234
59. R. M. Fitzgerald and A. A. Maradudin, Waves Random Media 4, 275 (1994). 10.1088/0959-7174/4/3/004
60. Surface Polaritons, edited by, V. M. Agranovich, and, D. L. Mills, (North-Holland, Amsterdam, 1982).
61. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964).
62. J. A. Sánchez-Gil, A. A. Maradudin, and E. R. Méndez, J. Opt. Soc. Am. A Opt. Image Sci. Vis. 12, 1547 (1995). 10.1364/JOSAA.12.001547
63. Gloss is normally only used in the context of reflection. Furthermore, the angles of incidence that haze and gloss refer to, are often different (and standard dependent).
64. I. Simonsen, Å. G. Larsen, E. Andreassen, E. Ommundsen, and K. Nord-Varhaug, Phys. Status Solidi B 242, 2995 (2005). 10.1002/pssb.200562235
65. A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. 203, 255 (1990). 10.1016/0003-4916(90)90172-K
66. I. Simonsen, T. A. Leskova, A. A. Maradudin, and O. Hunderi, Proc. SPIE 4100, 65 (2000). 10.1117/12.401667
67. D. Bicout and C. Brosseau, J. Phys. I (France) 2, 2047 (1992). 10.1051/jp1:1992266
68. E. I. Chaikina, Appl. Opt. 37, 1110 (1998). 10.1364/AO.37.001110
69. In the language of rough surface scattering this is called the Rayleigh hypothesis in honor of Lord Rayleigh who first suggested its use. Formally this hypothesis amounts to assuming that the asymptotic expressions for the field above and below the surface [Eqs. 5] can be used all the way down to the rough interface and consequently used to fulfill the boundary conditions.