Abstract

A new technique based on transmission intensity-quotient ellipsometry has been developed for determining the fibril angle and the relative phase retardation of single, intact pulp fibers. The method uses a polarizing microscope in conjunction with a microscope video camera or CCD camera. Requiring no sample pretreatment, the new method is simple, fast, more accurate than existing methods, and nondestructive of the fiber material. To test the new method, we employed the multiwavelength measurement principle. It is based on the fact that the fibril angle is independent of wavelength, while the relative retardation is inversely proportional to the wavelength used. Measurements were carried out with single pulp fibers as samples under the illumination of different light wavelengths. The measurements and some results are described and presented.

© 1994 Optical Society of America

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References

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  1. R. D. Preston, The Physical Biology of Plant Cell Walls (Chapman & Hall, London, 1974).
  2. D. H. Page, “A method for determining the fibrillar angle in wood tracheids,” J. Microsc. 90, 137–143 (1969).
    [CrossRef]
  3. R. E. Prudhomme, J. Noah, “Determination of fibril angle distribution in wood fibers: a comparison between the x-ray diffraction and the polarized microscope methods,” Wood Fiber 6, 282–289 (1975).
  4. R. E. Mark, P. P. Gillis, “The relationship between fiber modulus and S2 angle,” Tappi 56, 164–167 (1973).
  5. F. El-Hosseiny, D. H. Page, “The mechanical properties of single wood pulp fibres: theories of strength,” Fibre Sci. Technol. 8, 21–30 (1975).
    [CrossRef]
  6. D. H. Page, F. El-Hosseiny, K. Winkler, A. P. S. Lancaster, “Elastic modulus of single wood pulp fibers,” Tappi 60, 114–117 (1977).
  7. D. H. Page, F. El-Hosseiny, “The mechanical properties of single wood pulp fibres. Part VI. Fibril angle and the shape of the stress-strain curve,” J. Pulp Paper Sci. 84, TR99–TR100 (1983).
  8. B. A. Meylan, “Measurement of microfibril angle by x-ray diffraction,” For. Prod. J. 17, 51–58 (1967).
  9. T. Paakkari, R. Serimaa, “A study of the structure of wood cells by x-ray diffraction,” Wood Sci. Technol. 18, 79–85 (1984).
  10. C. M. Crosby, R. E. Marke, “Precise S2 angle determination in pulp fibers,” Sven. Papperstidn. 17, 636–642 (1974).
  11. C. M. Crosby, C. De Zeeuw, R. Marton, “Fibrillar angle variation in red pine determined by Sénarmont compensation,” Wood Sci. Technol. 6, 185–195 (1972).
    [CrossRef]
  12. R. C. Tang, “The microfibrillar orientation in cell-wall layers of Virginia pine tracheids,” Wood Sci. 5, 181–186 (1973).
  13. L. Leney, “A technique for measuring fibril angle using polarized light,” Wood Fiber 13, 13–16 (1981).
  14. W. Holzapfel, C. Ye, “Transmission ellipsometry of Δ and φ based on intensity quotient measurements,” Optik 91, 53–60 (1992).
  15. C. Ye, “Untersuchungen zur photoelastischen Polarisations-modulation optischer Signale,” Ph.D. dissertation (Kassel University, Kassel, Germany; Verlag Shaker Aachen, Germany, 1992).
  16. R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 488–503 (1941).
    [CrossRef]
  17. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1979).
  18. P. S. Theocaris, E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, Berlin, 1979).
  19. A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, New York, 1984), Chap. 5, pp. 132–139.
  20. R. Marton, S. D. McGovern, “Relation of crystallite dimensions and fibrillar orientation to fiber properties,” in The Physics and Chemistry of Wood Fibers, Special Tech. Assoc. Publ. 8 (Technical Association of the Pulp and Paper Industry, Appleton, Wisc., 1970), pp. 153–158.
  21. D. H. Page, F. El-Hosseiny, “The birefringence of wood pulp fibers and the thickness of the Si and S3 layers,” Fall 6, 186–192 (1974).

1992 (1)

W. Holzapfel, C. Ye, “Transmission ellipsometry of Δ and φ based on intensity quotient measurements,” Optik 91, 53–60 (1992).

1984 (1)

T. Paakkari, R. Serimaa, “A study of the structure of wood cells by x-ray diffraction,” Wood Sci. Technol. 18, 79–85 (1984).

1983 (1)

D. H. Page, F. El-Hosseiny, “The mechanical properties of single wood pulp fibres. Part VI. Fibril angle and the shape of the stress-strain curve,” J. Pulp Paper Sci. 84, TR99–TR100 (1983).

1981 (1)

L. Leney, “A technique for measuring fibril angle using polarized light,” Wood Fiber 13, 13–16 (1981).

1977 (1)

D. H. Page, F. El-Hosseiny, K. Winkler, A. P. S. Lancaster, “Elastic modulus of single wood pulp fibers,” Tappi 60, 114–117 (1977).

1975 (2)

R. E. Prudhomme, J. Noah, “Determination of fibril angle distribution in wood fibers: a comparison between the x-ray diffraction and the polarized microscope methods,” Wood Fiber 6, 282–289 (1975).

F. El-Hosseiny, D. H. Page, “The mechanical properties of single wood pulp fibres: theories of strength,” Fibre Sci. Technol. 8, 21–30 (1975).
[CrossRef]

1974 (2)

C. M. Crosby, R. E. Marke, “Precise S2 angle determination in pulp fibers,” Sven. Papperstidn. 17, 636–642 (1974).

D. H. Page, F. El-Hosseiny, “The birefringence of wood pulp fibers and the thickness of the Si and S3 layers,” Fall 6, 186–192 (1974).

1973 (2)

R. C. Tang, “The microfibrillar orientation in cell-wall layers of Virginia pine tracheids,” Wood Sci. 5, 181–186 (1973).

R. E. Mark, P. P. Gillis, “The relationship between fiber modulus and S2 angle,” Tappi 56, 164–167 (1973).

1972 (1)

C. M. Crosby, C. De Zeeuw, R. Marton, “Fibrillar angle variation in red pine determined by Sénarmont compensation,” Wood Sci. Technol. 6, 185–195 (1972).
[CrossRef]

1969 (1)

D. H. Page, “A method for determining the fibrillar angle in wood tracheids,” J. Microsc. 90, 137–143 (1969).
[CrossRef]

1967 (1)

B. A. Meylan, “Measurement of microfibril angle by x-ray diffraction,” For. Prod. J. 17, 51–58 (1967).

1941 (1)

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1979).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1979).

Crosby, C. M.

C. M. Crosby, R. E. Marke, “Precise S2 angle determination in pulp fibers,” Sven. Papperstidn. 17, 636–642 (1974).

C. M. Crosby, C. De Zeeuw, R. Marton, “Fibrillar angle variation in red pine determined by Sénarmont compensation,” Wood Sci. Technol. 6, 185–195 (1972).
[CrossRef]

De Zeeuw, C.

C. M. Crosby, C. De Zeeuw, R. Marton, “Fibrillar angle variation in red pine determined by Sénarmont compensation,” Wood Sci. Technol. 6, 185–195 (1972).
[CrossRef]

El-Hosseiny, F.

D. H. Page, F. El-Hosseiny, “The mechanical properties of single wood pulp fibres. Part VI. Fibril angle and the shape of the stress-strain curve,” J. Pulp Paper Sci. 84, TR99–TR100 (1983).

D. H. Page, F. El-Hosseiny, K. Winkler, A. P. S. Lancaster, “Elastic modulus of single wood pulp fibers,” Tappi 60, 114–117 (1977).

F. El-Hosseiny, D. H. Page, “The mechanical properties of single wood pulp fibres: theories of strength,” Fibre Sci. Technol. 8, 21–30 (1975).
[CrossRef]

D. H. Page, F. El-Hosseiny, “The birefringence of wood pulp fibers and the thickness of the Si and S3 layers,” Fall 6, 186–192 (1974).

Gdoutos, E. E.

P. S. Theocaris, E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, Berlin, 1979).

Gillis, P. P.

R. E. Mark, P. P. Gillis, “The relationship between fiber modulus and S2 angle,” Tappi 56, 164–167 (1973).

Holzapfel, W.

W. Holzapfel, C. Ye, “Transmission ellipsometry of Δ and φ based on intensity quotient measurements,” Optik 91, 53–60 (1992).

Jones, R. C.

Lancaster, A. P. S.

D. H. Page, F. El-Hosseiny, K. Winkler, A. P. S. Lancaster, “Elastic modulus of single wood pulp fibers,” Tappi 60, 114–117 (1977).

Leney, L.

L. Leney, “A technique for measuring fibril angle using polarized light,” Wood Fiber 13, 13–16 (1981).

Mark, R. E.

R. E. Mark, P. P. Gillis, “The relationship between fiber modulus and S2 angle,” Tappi 56, 164–167 (1973).

Marke, R. E.

C. M. Crosby, R. E. Marke, “Precise S2 angle determination in pulp fibers,” Sven. Papperstidn. 17, 636–642 (1974).

Marton, R.

C. M. Crosby, C. De Zeeuw, R. Marton, “Fibrillar angle variation in red pine determined by Sénarmont compensation,” Wood Sci. Technol. 6, 185–195 (1972).
[CrossRef]

R. Marton, S. D. McGovern, “Relation of crystallite dimensions and fibrillar orientation to fiber properties,” in The Physics and Chemistry of Wood Fibers, Special Tech. Assoc. Publ. 8 (Technical Association of the Pulp and Paper Industry, Appleton, Wisc., 1970), pp. 153–158.

McGovern, S. D.

R. Marton, S. D. McGovern, “Relation of crystallite dimensions and fibrillar orientation to fiber properties,” in The Physics and Chemistry of Wood Fibers, Special Tech. Assoc. Publ. 8 (Technical Association of the Pulp and Paper Industry, Appleton, Wisc., 1970), pp. 153–158.

Meylan, B. A.

B. A. Meylan, “Measurement of microfibril angle by x-ray diffraction,” For. Prod. J. 17, 51–58 (1967).

Noah, J.

R. E. Prudhomme, J. Noah, “Determination of fibril angle distribution in wood fibers: a comparison between the x-ray diffraction and the polarized microscope methods,” Wood Fiber 6, 282–289 (1975).

Paakkari, T.

T. Paakkari, R. Serimaa, “A study of the structure of wood cells by x-ray diffraction,” Wood Sci. Technol. 18, 79–85 (1984).

Page, D. H.

D. H. Page, F. El-Hosseiny, “The mechanical properties of single wood pulp fibres. Part VI. Fibril angle and the shape of the stress-strain curve,” J. Pulp Paper Sci. 84, TR99–TR100 (1983).

D. H. Page, F. El-Hosseiny, K. Winkler, A. P. S. Lancaster, “Elastic modulus of single wood pulp fibers,” Tappi 60, 114–117 (1977).

F. El-Hosseiny, D. H. Page, “The mechanical properties of single wood pulp fibres: theories of strength,” Fibre Sci. Technol. 8, 21–30 (1975).
[CrossRef]

D. H. Page, F. El-Hosseiny, “The birefringence of wood pulp fibers and the thickness of the Si and S3 layers,” Fall 6, 186–192 (1974).

D. H. Page, “A method for determining the fibrillar angle in wood tracheids,” J. Microsc. 90, 137–143 (1969).
[CrossRef]

Preston, R. D.

R. D. Preston, The Physical Biology of Plant Cell Walls (Chapman & Hall, London, 1974).

Prudhomme, R. E.

R. E. Prudhomme, J. Noah, “Determination of fibril angle distribution in wood fibers: a comparison between the x-ray diffraction and the polarized microscope methods,” Wood Fiber 6, 282–289 (1975).

Serimaa, R.

T. Paakkari, R. Serimaa, “A study of the structure of wood cells by x-ray diffraction,” Wood Sci. Technol. 18, 79–85 (1984).

Tang, R. C.

R. C. Tang, “The microfibrillar orientation in cell-wall layers of Virginia pine tracheids,” Wood Sci. 5, 181–186 (1973).

Theocaris, P. S.

P. S. Theocaris, E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, Berlin, 1979).

Winkler, K.

D. H. Page, F. El-Hosseiny, K. Winkler, A. P. S. Lancaster, “Elastic modulus of single wood pulp fibers,” Tappi 60, 114–117 (1977).

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, New York, 1984), Chap. 5, pp. 132–139.

Ye, C.

W. Holzapfel, C. Ye, “Transmission ellipsometry of Δ and φ based on intensity quotient measurements,” Optik 91, 53–60 (1992).

C. Ye, “Untersuchungen zur photoelastischen Polarisations-modulation optischer Signale,” Ph.D. dissertation (Kassel University, Kassel, Germany; Verlag Shaker Aachen, Germany, 1992).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, New York, 1984), Chap. 5, pp. 132–139.

Fall (1)

D. H. Page, F. El-Hosseiny, “The birefringence of wood pulp fibers and the thickness of the Si and S3 layers,” Fall 6, 186–192 (1974).

Fibre Sci. Technol. (1)

F. El-Hosseiny, D. H. Page, “The mechanical properties of single wood pulp fibres: theories of strength,” Fibre Sci. Technol. 8, 21–30 (1975).
[CrossRef]

For. Prod. J. (1)

B. A. Meylan, “Measurement of microfibril angle by x-ray diffraction,” For. Prod. J. 17, 51–58 (1967).

J. Microsc. (1)

D. H. Page, “A method for determining the fibrillar angle in wood tracheids,” J. Microsc. 90, 137–143 (1969).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Pulp Paper Sci. (1)

D. H. Page, F. El-Hosseiny, “The mechanical properties of single wood pulp fibres. Part VI. Fibril angle and the shape of the stress-strain curve,” J. Pulp Paper Sci. 84, TR99–TR100 (1983).

Optik (1)

W. Holzapfel, C. Ye, “Transmission ellipsometry of Δ and φ based on intensity quotient measurements,” Optik 91, 53–60 (1992).

Sven. Papperstidn. (1)

C. M. Crosby, R. E. Marke, “Precise S2 angle determination in pulp fibers,” Sven. Papperstidn. 17, 636–642 (1974).

Tappi (2)

R. E. Mark, P. P. Gillis, “The relationship between fiber modulus and S2 angle,” Tappi 56, 164–167 (1973).

D. H. Page, F. El-Hosseiny, K. Winkler, A. P. S. Lancaster, “Elastic modulus of single wood pulp fibers,” Tappi 60, 114–117 (1977).

Wood Fiber (1)

R. E. Prudhomme, J. Noah, “Determination of fibril angle distribution in wood fibers: a comparison between the x-ray diffraction and the polarized microscope methods,” Wood Fiber 6, 282–289 (1975).

Wood Fiber (1)

L. Leney, “A technique for measuring fibril angle using polarized light,” Wood Fiber 13, 13–16 (1981).

Wood Sci. Technol. (1)

T. Paakkari, R. Serimaa, “A study of the structure of wood cells by x-ray diffraction,” Wood Sci. Technol. 18, 79–85 (1984).

Wood Sci. (1)

R. C. Tang, “The microfibrillar orientation in cell-wall layers of Virginia pine tracheids,” Wood Sci. 5, 181–186 (1973).

Wood Sci. Technol. (1)

C. M. Crosby, C. De Zeeuw, R. Marton, “Fibrillar angle variation in red pine determined by Sénarmont compensation,” Wood Sci. Technol. 6, 185–195 (1972).
[CrossRef]

Other (6)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1979).

P. S. Theocaris, E. E. Gdoutos, Matrix Theory of Photoelasticity (Springer-Verlag, Berlin, 1979).

A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, New York, 1984), Chap. 5, pp. 132–139.

R. Marton, S. D. McGovern, “Relation of crystallite dimensions and fibrillar orientation to fiber properties,” in The Physics and Chemistry of Wood Fibers, Special Tech. Assoc. Publ. 8 (Technical Association of the Pulp and Paper Industry, Appleton, Wisc., 1970), pp. 153–158.

R. D. Preston, The Physical Biology of Plant Cell Walls (Chapman & Hall, London, 1974).

C. Ye, “Untersuchungen zur photoelastischen Polarisations-modulation optischer Signale,” Ph.D. dissertation (Kassel University, Kassel, Germany; Verlag Shaker Aachen, Germany, 1992).

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Figures (15)

Fig. 1
Fig. 1

Schematic representation of the layer structure of a single wood fiber: φ, fibril angle (see text).

Fig. 2
Fig. 2

Single pulp fiber (represented by the S2 layer) in a polarizing microscope. The two fiber walls are described by two linear retarders of the same relative retardation Δ and the same orientation angle φ (fibril angle) with opposite senses (see text).

Fig. 3
Fig. 3

Block diagram of the experimental setup.

Fig. 4
Fig. 4

(a) Polarizing micrograph (λ = 600 nm) of unbleached commercial pine kraft pulp. (b) Measured fiber segment (420×) where the intensity I(A) at the two marked points in the center region was measured.

Fig. 5
Fig. 5

Measured fibril angle φ and relative retardation Δ of the pulp fiber in Fig. 4(b) versus wavelength λ: (a) φ and (b) Δ for point 1 and (c) φ and (d) Δ for point 2.

Fig. 6
Fig. 6

Detected intensity dependence I(A) (λ = 600 nm) at point 1 of the fiber shown in Fig. 4(b) in the polarizing microscope used for the test measurements.

Fig. 7
Fig. 7

(a) Polarizing micrograph (λ = 600 nm) of unbleached laboratory-made pine kraft pulp. (b) Measured fiber segment (420×) where the intensity I(A) at the two marked points in the center region was measured.

Fig. 8
Fig. 8

Measured fibril angle φ and relative retardation Δ of the pulp fiber in Fig. 7(b) versus wavelength λ: (a) φ and (b) Δ for point 1 and (c) φ and (d) Δ for point 2.

Fig. 9
Fig. 9

Detected intensity dependence I(A) (λ = 600 nm) at point 1 of the fiber shown in Fig. 7(b) in the polarizing microscope used for the test measurements. The large amplitude change of I(A) implies a similar situation to that experienced with the quotient method when the PSA arrangement is used (see text).

Fig. 10
Fig. 10

(a) Polarizing micrograph (λ = 600 nm) of a bleached commercial pine kraft pulp fiber. (b) Measured segment (420×) where the intensity I(A) at the two marked points in the center region was measured.

Fig. 11
Fig. 11

Measured fibril angle φ and relative retardation Δ of the pulp fiber in Fig. 10(b) versus wavelength λ: (a) φ and (b) Δ for point 1 and (c) φ and (d) Δ for point 2.

Fig. 12
Fig. 12

(a) Polarizing micrograph (λ = 600 nm) of a bleached laboratory-made pine kraft pulp fiber (springwood). (b) Measured fiber segment (650×) where the intensity I(A) at the two marked points in the center region was measured.

Fig. 13
Fig. 13

(a) Polarizing micrograph (λ = 600 nm) of a bleached laboratory-made pine kraft pulp fiber (summerwood). (b) Measured segment (650×) where the intensity I(A) at the two marked points in the center region was measured.

Fig. 14
Fig. 14

Measured fibril angle φ and relative retardation Δ of the pulp fiber in Fig. 12(b) versus wavelength λ: (a) φ and (b) Δ for point 1 and (c) φ and (d) Δ for point 2.

Fig. 15
Fig. 15

Measured fibril angle φ and relative retardation Δ of the pulp fiber in Fig. 13(b) versus wavelength λ: (a) φ and (b) Δ for point 1 and (c) φ and (d) Δ for point 2.

Equations (20)

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T s = R ( φ ) [ exp ( j Δ / 2 ) 0 0 exp ( j Δ / 2 ) ] R ( φ ) R ( φ ) × [ exp ( j Δ / 2 ) 0 0 exp ( j Δ / 2 ) ] R ( φ ) ,
R ( φ ) = ( cos φ sin φ sin φ cos φ ) ,
T s = [ a b c d ] ,
a = sin 2 ( 2 φ ) + cos ( Δ ) cos 2 ( 2 φ ) j cos ( 2 φ ) sin ( Δ ) ,
b = sin ( 4 φ ) sin 2 ( Δ 2 ) ,
c = b = sin ( 4 φ ) sin 2 ( Δ 2 ) ,
d = sin 2 ( 2 φ ) + cos ( Δ ) cos 2 ( 2 φ ) + j cos ( 2 φ ) sin ( Δ ) .
E = I 0 ( cos A sin A 0 0 ) ( a b c d ) ( cos P sin P ) .
I ( A ) = I 0 { [ c 2 cos 2 P + a d sin 2 P + c 2 ( a + d ) sin 2 P ] sin 2 A + [ a d cos 2 P + b 2 sin 2 P + b 2 ( a + d ) sin 2 P ] cos 2 A + 1 2 [ c ( a + d ) cos 2 P + b ( a + d ) sin 2 P + 1 2 ( a 2 + d 2 + 2 b c ) sin 2 P ] sin 2 A } .
I ( A ) = I 0 2 ( 1 + T 1 sin 2 A + T 2 cos 2 A ) ,
T 1 = 1 + 8 cos 2 ( 2 φ ) sin 2 ( Δ 2 ) [ cos 2 ( 2 φ ) sin 2 ( Δ 2 ) 1 ] ,
T 2 = 2 sin ( 4 φ ) sin 2 ( Δ 2 ) [ 2 cos 2 ( 2 φ ) sin 2 ( Δ 2 ) 1 ] .
T 1 = I ( A = 45 ° ) I ( A = 135 ° ) I ( A = 45 ° ) + I ( A = 135 ° ) ,
T 2 = I ( A = 0 ° ) I ( A = 90 ° ) I ( A = 0 ° ) + I ( A = 90 ° ) .
tan 2 φ 1 = 2 T 2 [ 2 ( 1 + T 1 ) ] 1 / 2 { 2 [ 2 ( 1 + T 1 ) ] 1 / 2 } ,
tan 2 φ 2 = 2 T 2 [ 2 ( 1 + T 1 ) ] 1 / 2 { 2 + [ 2 ( 1 + T 1 ) ] 1 / 2 } , T 1 ± 1 ;
cos Δ 1 = 1 1 cos 2 ( 2 φ 1 ) { 1 1 2 [ 2 ( 1 + T 1 ) ] 1 / 2 } ,
cos Δ 2 = 1 1 cos 2 ( 2 φ 2 ) { 1 + 1 2 [ 2 ( 1 + T 1 ) ] 1 / 2 } .
Δ = 360 ° λ d ( n 1 n 2 ) ,
φ 11 φ 21 , Δ 11 / Δ 21 λ 2 / λ 1 .

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