Abstract

A systematic and straightforward image processing method to extract quantitative phase and refractive index data from weak phase objects is presented, obtained using differential interference contrast (DIC) microscopy. The method is demonstrated on DIC images of optical fibers where a directional integration routine is applied to the DIC images to extract phase and refractive index information using the data obtained across the whole DIC image. By applying the inverse Abel transform to the resultant phase images, an accurate refractive index profile is obtained. The method presented here is compared to the refracted near-field technique, typically used to obtain the refractive index profile of optical fibers, and shows excellent agreement. It is concluded that through careful image processing procedures, DIC microscopy can be successfully implemented to obtain quantitative phase and refractive index information of optical fibers.

© 2008 Optical Society of America

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References

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  1. K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fibre refractive index profiles,” Opt. Quantum Electron. 11, 185-196 (1979).
    [CrossRef]
  2. K. W. Raine, J. G. N. Baines, and D. E. Putland, “Refractive index profiling-state of the art,” J. Lightwave Technol. 7, 1162-1169 (1989).
    [CrossRef]
  3. A. Roberts, E. Ampem-Lassen, A. Barty, K. A. Nugent, G. W. Baxter, N. M. Dragomir, and S. T. Huntington, “Refractive-index profiling of optical fibers with axial symmetry by use of quantitative phase microscopy,” Opt. Lett. 27, 2061-2063 (2002).
    [CrossRef]
  4. E. Ampem-Lassen, S. T. Huntington, N. M. Dragomir, K. A. Nugent, and A. Roberts, “Refractive index profiling of axially symmetric optical fibers: a new technique,” Opt. Express 13, 3277-3282 (2005).
    [CrossRef]
  5. N. M. Dragomir, E. Ampem-Lassen, S. T. Huntington, G. W. Baxter, A. Roberts, and P. M. Farrell, “Refractive index profiling of optical fibers using differential interference contrast microscopy,” IEEE Photon. Technol. Lett. 17, 2149-2151 (2005).
    [CrossRef]
  6. M. Pluta, Advanced Light Microscopy (Elsevier, 1988).
  7. C. Preza, “Phase estimation using rotational diversity for differential interference contrast microscopy,” D.Sc. thesis (Washington University, Sever Institute of Technology, St. Louis, Mo., 1998).
  8. W. Urbanczyk and K. Pietraszkiewicz, “Measurements of stress anisotropy in fiber preform: modification of the dynamic spatial filtering technique,” Appl. Opt. 27, 4117-4122 (1988).
  9. W. Urbanczyk, K. Pietraszkiewicz, and W. A. Wozniak, “Novel bifunctional systems for measuring the refractive index profile and residual stress birefringence in optical fibers and preforms,” Opt. Eng. 31, 491-499 (1992).
    [CrossRef]
  10. M. Kalal and K. A. Nugent, “Abel inversion using fast Fourier transforms,” Appl. Opt. 27, 1956-1959 (1988).
  11. E. B. Van Munster, L. J. Van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149-157 (1997).
    [CrossRef]
  12. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 3rd ed. (Pergamon, 1965), pp. xxviii and 808.
  13. C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72-81 (1997).
    [CrossRef]
  14. Z. Kam, “Microscopic differential interference contrast image processing by line integration (LID) and deconvolution,” Bioimaging 6, 166-176 (1998).
    [CrossRef]
  15. W. Shimada, T. Sato, and T. Yatagai, “Optical surface microtopography using phase-shifting Nomarski microscope,” Proc. SPIE 1332, 525-529 (1991).
    [CrossRef]
  16. B. Heise, A. Sonnleitner, and P. E. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. 66, 312-320 (2005).
    [CrossRef]
  17. M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
    [CrossRef]
  18. B. P. Kouskousis, D. J. Kitcher, S. F. Collins, A. Roberts, and G. W. Baxter, “Refractive index profile of a multi-step fibre using differential interference contrast microscopy,” in COIN-ACOFT 2007, Melbourne, Australia, 2007.
  19. E. Ampem-Lassen, “Studies in photonic device imaging and characterisation,” Ph.D. dissertation (University of Melbourne, School of Physics, 2004).
  20. J. G. Wanguemert-Perez, R. Godoy-Rubio, A. Ortega-Monux, and I. Molina-Fernandez, “Removal of the Gibbs phenomenon and its application to fast-Fourier-transform-based mode solvers,” J. Opt. Soc. Am. A 24, 3772-3780 (2007).
    [CrossRef]
  21. D. Gottlieb and C. W. Shu, “On the Gibbs phenomenon and its resolution,” SIAM Rev. 39, 644-668 (1997).
    [CrossRef]
  22. K. Dossou, S. LaRochelle, and M. Fontaine, “Numerical analysis of the contribution of the transverse asymmetry in the photo-induced index change profile to the birefringence of optical fiber,” J. Lightwave Technol. 20, 1463-1470(2002).
    [CrossRef]
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    [CrossRef]
  24. P. Lu, D. Grobnic, and S. J. Mihailov, “Characterization of the birefringence in fiber Bragg gratings fabricated with an ultrafast-infrared laser,” J. Lightwave Technol. 25, 779-786 (2007).
    [CrossRef]
  25. J. Canning, H. J. Deyerl, H. R. Sorensen, and M. Kristensen, “Ultraviolet-induced birefringence in hydrogen-loaded optical fiber,” J. Appl. Phys. 97, 53104 (2005).
    [CrossRef]
  26. N. M. Dragomir, C. Rollinson, S. A. Wade, A. J. Stevenson, S. F. Collins, G. W. Baxter, P. M. Farrell, and A. Roberts, “Nondestructive imaging of a type I optical fiber Bragg grating,” Opt. Lett. 28, 789-791 (2003).
    [CrossRef]
  27. B. P. Kouskousis, C. M. Rollinson, D. J. Kitcher, S. F. Collins, G. W. Baxter, S. A. Wade, N. M. Dragomir, and A. Roberts, “Quantitative investigation of the refractive-index modulation within the core of a fiber Bragg grating,” Opt. Express 14, 10332-10338 (2006).
    [CrossRef]

2007

2006

2005

J. Canning, H. J. Deyerl, H. R. Sorensen, and M. Kristensen, “Ultraviolet-induced birefringence in hydrogen-loaded optical fiber,” J. Appl. Phys. 97, 53104 (2005).
[CrossRef]

B. Heise, A. Sonnleitner, and P. E. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. 66, 312-320 (2005).
[CrossRef]

E. Ampem-Lassen, S. T. Huntington, N. M. Dragomir, K. A. Nugent, and A. Roberts, “Refractive index profiling of axially symmetric optical fibers: a new technique,” Opt. Express 13, 3277-3282 (2005).
[CrossRef]

N. M. Dragomir, E. Ampem-Lassen, S. T. Huntington, G. W. Baxter, A. Roberts, and P. M. Farrell, “Refractive index profiling of optical fibers using differential interference contrast microscopy,” IEEE Photon. Technol. Lett. 17, 2149-2151 (2005).
[CrossRef]

2004

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
[CrossRef]

2003

2002

1998

Z. Kam, “Microscopic differential interference contrast image processing by line integration (LID) and deconvolution,” Bioimaging 6, 166-176 (1998).
[CrossRef]

1997

D. Gottlieb and C. W. Shu, “On the Gibbs phenomenon and its resolution,” SIAM Rev. 39, 644-668 (1997).
[CrossRef]

E. B. Van Munster, L. J. Van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149-157 (1997).
[CrossRef]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72-81 (1997).
[CrossRef]

1992

W. Urbanczyk, K. Pietraszkiewicz, and W. A. Wozniak, “Novel bifunctional systems for measuring the refractive index profile and residual stress birefringence in optical fibers and preforms,” Opt. Eng. 31, 491-499 (1992).
[CrossRef]

1991

W. Shimada, T. Sato, and T. Yatagai, “Optical surface microtopography using phase-shifting Nomarski microscope,” Proc. SPIE 1332, 525-529 (1991).
[CrossRef]

1989

K. W. Raine, J. G. N. Baines, and D. E. Putland, “Refractive index profiling-state of the art,” J. Lightwave Technol. 7, 1162-1169 (1989).
[CrossRef]

1988

1979

K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fibre refractive index profiles,” Opt. Quantum Electron. 11, 185-196 (1979).
[CrossRef]

Ampem-Lassen, E.

E. Ampem-Lassen, S. T. Huntington, N. M. Dragomir, K. A. Nugent, and A. Roberts, “Refractive index profiling of axially symmetric optical fibers: a new technique,” Opt. Express 13, 3277-3282 (2005).
[CrossRef]

N. M. Dragomir, E. Ampem-Lassen, S. T. Huntington, G. W. Baxter, A. Roberts, and P. M. Farrell, “Refractive index profiling of optical fibers using differential interference contrast microscopy,” IEEE Photon. Technol. Lett. 17, 2149-2151 (2005).
[CrossRef]

A. Roberts, E. Ampem-Lassen, A. Barty, K. A. Nugent, G. W. Baxter, N. M. Dragomir, and S. T. Huntington, “Refractive-index profiling of optical fibers with axial symmetry by use of quantitative phase microscopy,” Opt. Lett. 27, 2061-2063 (2002).
[CrossRef]

E. Ampem-Lassen, “Studies in photonic device imaging and characterisation,” Ph.D. dissertation (University of Melbourne, School of Physics, 2004).

Arnison, M. R.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
[CrossRef]

Aten, J. A.

E. B. Van Munster, L. J. Van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149-157 (1997).
[CrossRef]

Baines, J. G. N.

K. W. Raine, J. G. N. Baines, and D. E. Putland, “Refractive index profiling-state of the art,” J. Lightwave Technol. 7, 1162-1169 (1989).
[CrossRef]

Barty, A.

Baxter, G. W.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 3rd ed. (Pergamon, 1965), pp. xxviii and 808.

Canning, J.

J. Canning, H. J. Deyerl, H. R. Sorensen, and M. Kristensen, “Ultraviolet-induced birefringence in hydrogen-loaded optical fiber,” J. Appl. Phys. 97, 53104 (2005).
[CrossRef]

Cogswell, C. J.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
[CrossRef]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72-81 (1997).
[CrossRef]

Collins, S. F.

Deyerl, H. J.

J. Canning, H. J. Deyerl, H. R. Sorensen, and M. Kristensen, “Ultraviolet-induced birefringence in hydrogen-loaded optical fiber,” J. Appl. Phys. 97, 53104 (2005).
[CrossRef]

Dossou, K.

Dragomir, N. M.

Farrell, P. M.

N. M. Dragomir, E. Ampem-Lassen, S. T. Huntington, G. W. Baxter, A. Roberts, and P. M. Farrell, “Refractive index profiling of optical fibers using differential interference contrast microscopy,” IEEE Photon. Technol. Lett. 17, 2149-2151 (2005).
[CrossRef]

N. M. Dragomir, C. Rollinson, S. A. Wade, A. J. Stevenson, S. F. Collins, G. W. Baxter, P. M. Farrell, and A. Roberts, “Nondestructive imaging of a type I optical fiber Bragg grating,” Opt. Lett. 28, 789-791 (2003).
[CrossRef]

Fontaine, M.

Godoy-Rubio, R.

Gottlieb, D.

D. Gottlieb and C. W. Shu, “On the Gibbs phenomenon and its resolution,” SIAM Rev. 39, 644-668 (1997).
[CrossRef]

Grobnic, D.

Hariharan, P.

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72-81 (1997).
[CrossRef]

Heise, B.

B. Heise, A. Sonnleitner, and P. E. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. 66, 312-320 (2005).
[CrossRef]

Huntington, S. T.

Kalal, M.

Kam, Z.

Z. Kam, “Microscopic differential interference contrast image processing by line integration (LID) and deconvolution,” Bioimaging 6, 166-176 (1998).
[CrossRef]

Kitcher, D. J.

B. P. Kouskousis, C. M. Rollinson, D. J. Kitcher, S. F. Collins, G. W. Baxter, S. A. Wade, N. M. Dragomir, and A. Roberts, “Quantitative investigation of the refractive-index modulation within the core of a fiber Bragg grating,” Opt. Express 14, 10332-10338 (2006).
[CrossRef]

B. P. Kouskousis, D. J. Kitcher, S. F. Collins, A. Roberts, and G. W. Baxter, “Refractive index profile of a multi-step fibre using differential interference contrast microscopy,” in COIN-ACOFT 2007, Melbourne, Australia, 2007.

Klement, P. E.

B. Heise, A. Sonnleitner, and P. E. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. 66, 312-320 (2005).
[CrossRef]

Kouskousis, B. P.

B. P. Kouskousis, C. M. Rollinson, D. J. Kitcher, S. F. Collins, G. W. Baxter, S. A. Wade, N. M. Dragomir, and A. Roberts, “Quantitative investigation of the refractive-index modulation within the core of a fiber Bragg grating,” Opt. Express 14, 10332-10338 (2006).
[CrossRef]

B. P. Kouskousis, D. J. Kitcher, S. F. Collins, A. Roberts, and G. W. Baxter, “Refractive index profile of a multi-step fibre using differential interference contrast microscopy,” in COIN-ACOFT 2007, Melbourne, Australia, 2007.

Kristensen, M.

J. Canning, H. J. Deyerl, H. R. Sorensen, and M. Kristensen, “Ultraviolet-induced birefringence in hydrogen-loaded optical fiber,” J. Appl. Phys. 97, 53104 (2005).
[CrossRef]

Larkin, K. G.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
[CrossRef]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72-81 (1997).
[CrossRef]

LaRochelle, S.

Lu, P.

Mihailov, S. J.

Molina-Fernandez, I.

Nugent, K. A.

Ortega-Monux, A.

Pietraszkiewicz, K.

W. Urbanczyk, K. Pietraszkiewicz, and W. A. Wozniak, “Novel bifunctional systems for measuring the refractive index profile and residual stress birefringence in optical fibers and preforms,” Opt. Eng. 31, 491-499 (1992).
[CrossRef]

W. Urbanczyk and K. Pietraszkiewicz, “Measurements of stress anisotropy in fiber preform: modification of the dynamic spatial filtering technique,” Appl. Opt. 27, 4117-4122 (1988).

Pluta, M.

M. Pluta, Advanced Light Microscopy (Elsevier, 1988).

Preza, C.

C. Preza, “Phase estimation using rotational diversity for differential interference contrast microscopy,” D.Sc. thesis (Washington University, Sever Institute of Technology, St. Louis, Mo., 1998).

Putland, D. E.

K. W. Raine, J. G. N. Baines, and D. E. Putland, “Refractive index profiling-state of the art,” J. Lightwave Technol. 7, 1162-1169 (1989).
[CrossRef]

Raine, K. W.

K. W. Raine, J. G. N. Baines, and D. E. Putland, “Refractive index profiling-state of the art,” J. Lightwave Technol. 7, 1162-1169 (1989).
[CrossRef]

Roberts, A.

Rollinson, C.

Rollinson, C. M.

Sato, T.

W. Shimada, T. Sato, and T. Yatagai, “Optical surface microtopography using phase-shifting Nomarski microscope,” Proc. SPIE 1332, 525-529 (1991).
[CrossRef]

Sheppard, C. J. R.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
[CrossRef]

Shimada, W.

W. Shimada, T. Sato, and T. Yatagai, “Optical surface microtopography using phase-shifting Nomarski microscope,” Proc. SPIE 1332, 525-529 (1991).
[CrossRef]

Shu, C. W.

D. Gottlieb and C. W. Shu, “On the Gibbs phenomenon and its resolution,” SIAM Rev. 39, 644-668 (1997).
[CrossRef]

Smith, N. I.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
[CrossRef]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72-81 (1997).
[CrossRef]

Sonnleitner, A.

B. Heise, A. Sonnleitner, and P. E. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. 66, 312-320 (2005).
[CrossRef]

Sorensen, H. R.

J. Canning, H. J. Deyerl, H. R. Sorensen, and M. Kristensen, “Ultraviolet-induced birefringence in hydrogen-loaded optical fiber,” J. Appl. Phys. 97, 53104 (2005).
[CrossRef]

Stevenson, A. J.

Urbanczyk, W.

W. Urbanczyk, K. Pietraszkiewicz, and W. A. Wozniak, “Novel bifunctional systems for measuring the refractive index profile and residual stress birefringence in optical fibers and preforms,” Opt. Eng. 31, 491-499 (1992).
[CrossRef]

W. Urbanczyk and K. Pietraszkiewicz, “Measurements of stress anisotropy in fiber preform: modification of the dynamic spatial filtering technique,” Appl. Opt. 27, 4117-4122 (1988).

Van Munster, E. B.

E. B. Van Munster, L. J. Van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149-157 (1997).
[CrossRef]

Van Vliet, L. J.

E. B. Van Munster, L. J. Van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149-157 (1997).
[CrossRef]

Waagaard, O. H.

Wade, S. A.

Wanguemert-Perez, J. G.

White, K. I.

K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fibre refractive index profiles,” Opt. Quantum Electron. 11, 185-196 (1979).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 3rd ed. (Pergamon, 1965), pp. xxviii and 808.

Wozniak, W. A.

W. Urbanczyk, K. Pietraszkiewicz, and W. A. Wozniak, “Novel bifunctional systems for measuring the refractive index profile and residual stress birefringence in optical fibers and preforms,” Opt. Eng. 31, 491-499 (1992).
[CrossRef]

Yatagai, T.

W. Shimada, T. Sato, and T. Yatagai, “Optical surface microtopography using phase-shifting Nomarski microscope,” Proc. SPIE 1332, 525-529 (1991).
[CrossRef]

Appl. Opt.

Bioimaging

Z. Kam, “Microscopic differential interference contrast image processing by line integration (LID) and deconvolution,” Bioimaging 6, 166-176 (1998).
[CrossRef]

IEEE Photon. Technol. Lett.

N. M. Dragomir, E. Ampem-Lassen, S. T. Huntington, G. W. Baxter, A. Roberts, and P. M. Farrell, “Refractive index profiling of optical fibers using differential interference contrast microscopy,” IEEE Photon. Technol. Lett. 17, 2149-2151 (2005).
[CrossRef]

J. Appl. Phys.

J. Canning, H. J. Deyerl, H. R. Sorensen, and M. Kristensen, “Ultraviolet-induced birefringence in hydrogen-loaded optical fiber,” J. Appl. Phys. 97, 53104 (2005).
[CrossRef]

J. Lightwave Technol.

J. Microsc.

E. B. Van Munster, L. J. Van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149-157 (1997).
[CrossRef]

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7-12(2004).
[CrossRef]

J. Opt. Soc. Am. A

Microsc. Res. Tech.

B. Heise, A. Sonnleitner, and P. E. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. 66, 312-320 (2005).
[CrossRef]

Opt. Eng.

W. Urbanczyk, K. Pietraszkiewicz, and W. A. Wozniak, “Novel bifunctional systems for measuring the refractive index profile and residual stress birefringence in optical fibers and preforms,” Opt. Eng. 31, 491-499 (1992).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fibre refractive index profiles,” Opt. Quantum Electron. 11, 185-196 (1979).
[CrossRef]

Proc. SPIE

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72-81 (1997).
[CrossRef]

W. Shimada, T. Sato, and T. Yatagai, “Optical surface microtopography using phase-shifting Nomarski microscope,” Proc. SPIE 1332, 525-529 (1991).
[CrossRef]

SIAM Rev.

D. Gottlieb and C. W. Shu, “On the Gibbs phenomenon and its resolution,” SIAM Rev. 39, 644-668 (1997).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 3rd ed. (Pergamon, 1965), pp. xxviii and 808.

B. P. Kouskousis, D. J. Kitcher, S. F. Collins, A. Roberts, and G. W. Baxter, “Refractive index profile of a multi-step fibre using differential interference contrast microscopy,” in COIN-ACOFT 2007, Melbourne, Australia, 2007.

E. Ampem-Lassen, “Studies in photonic device imaging and characterisation,” Ph.D. dissertation (University of Melbourne, School of Physics, 2004).

M. Pluta, Advanced Light Microscopy (Elsevier, 1988).

C. Preza, “Phase estimation using rotational diversity for differential interference contrast microscopy,” D.Sc. thesis (Washington University, Sever Institute of Technology, St. Louis, Mo., 1998).

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Figures (10)

Fig. 1
Fig. 1

Normalized DIC image of a CF2-082 multistep-index fiber covering an area of approximately 1024 × 1024 pixels having a pixel spacing of approximately 0.23 μm .

Fig. 2
Fig. 2

Extracted phase image of a CF2-082 multistep fiber having the same dimensions as the measured image. Diagonal streaking is evident, which is due to random walk accumulation of uncorrelated noise along the direction of integration and the unknown integration constant.

Fig. 3
Fig. 3

(a) Two-dimensional Fourier transform of the remaining background after subtraction of the averaged row. (b) Vertical bandpass filter applied to averaged row image. (c) Resultant background image after vertical bandpass filter.

Fig. 4
Fig. 4

(a) Extracted phase image of the CF2-082 multistep fiber from the measured DIC image after a third-degree polynomial fit was applied to remove horizontal nonuniformity of the background illumination in the phase image. (b) Simulated phase image of the CF2-082 multistep fiber modeled to replicate the same imaging conditions as the measured DIC image covering an area of 1024 × 1024 pixels having a pixel spacing of approximately 0.23 μm .

Fig. 5
Fig. 5

Schematic representation of the multistep fiber structure.

Fig. 6
Fig. 6

Line profile through the phase image of a multistep fiber obtained from simulated and experimentally obtained data, where the solid curve represents the extracted phase profile from the measured DIC image, and the dotted curve represents the phase profile through the simulated phase image.

Fig. 7
Fig. 7

Refractive index profile obtained from the phase image shown in Fig. 4a. (a) Surface plot of the change in refractive index through the various regions of the fiber as a function of position, where the color bar displays the change in refractive index. (b) Line profile through the simulated and extracted refractive index distribution of the multistep fiber, where I–IV specify the varying regions of the fiber. The point plot represents a line profile through the refractive index distribution from the simulated image, and the solid curve represents a line profile through the refractive index distribution from the measured image.

Fig. 8
Fig. 8

Normalized DIC image of the Corning SMF28 optical fiber covering an area of approximately 1024 × 1024 pixels having a pixel spacing of approximately 0.173 μm .

Fig. 9
Fig. 9

Extracted phase image of the SMF28 optical fiber from the measured DIC image, where a third-degree polynomial fit is applied to the outer boundaries of the fiber to correct uneven illumination in the phase image

Fig. 10
Fig. 10

Refractive index profile obtained from the phase image shown in Fig. 10. (a) Surface plot of the change in refractive index from the cladding as a function of position, where the color bar displays the varying colors used to highlight the change in refractive index. (b) Line profile through the extracted refractive index distribution of the SMF28 optical fiber. The dotted curve represents a line profile through the refractive index distribution from RNF method, and the solid curve represents a line profile through the refractive index distribution calculated from the measured image.

Tables (1)

Tables Icon

Table 1 Comparison between the Refractive Index Differences for the Radial Integration Method Applied to a Measured Differential Interference Contrast Image with the Specifications of the Calibrated Multistep Fiber

Equations (3)

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i ( x , y ) = I 0 sin 2 ( Δ τ ̲ τ ̲ φ ( x , y ) + Δ θ ) ,
Δ n ( r , y ) = λ 2 π 0 R φ ( x , y ) x d x r 2 x 2 ,
{ 2 k 0 ( n 1 R 1 2 x 2 ) + k 0 n 0 ( d 2 R 4 2 x 2 ) for R 4 | x | R 1 2 k 0 n 4 ( R 4 2 x 2 ) + 2 k 0 n 3 ( R 3 2 x 2 R 4 2 x 2 ) ) + 2 k 0 n 2 ( R 2 2 x 2 R 3 2 x 2 ) + 2 k 0 n 1 ( R 1 2 x 2 R 2 2 x 2 ) + k 0 n 0 ( d 2 R 1 2 x 2 ) for | x | R 1 } ,

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