Abstract

In this paper, the application of “parallel” moiré deflectometry in measuring the nonlinear refractive index of materials is reported. In “parallel” moiré deflectometry the grating vectors are parallel, and the resulting moiré fringes are also parallel to the grating lines. Compared to “rotational” moiré deflectometry and the Z-scan technique, which cannot easily determine the moiré fringe’s angle of rotation and is sensitive to power fluctuations, respectively, “parallel” moiré deflectometry is more reliable, which allows one to measure the radius of curvature of the light beam by measuring the moiré fringe spacing. The nonlinear refractive index of the sample, including the sense of the change, is obtained from the moiré fringe spacing curve. The method is applied for measuring the nonlinear refractive index of ferrofluids.

© 2011 Optical Society of America

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  1. M. Sheik-bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
    [CrossRef] [PubMed]
  2. M. Sheik-bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [CrossRef]
  3. I. Glatt, Z. Karny, and O. Kafri, “Spatial analysis of the CO2 laser-induced thermal lens in SF6 by moiré deflectometry,” Appl. Opt. 23, 274–277 (1984).
    [CrossRef] [PubMed]
  4. K. Jamshidi-Ghaleh and N. Mansour, “Nonlinear refraction measurements of materials using the moiré deflectometry,” Opt. Commun. 234, 419–425 (2004).
    [CrossRef]
  5. M. H. Majles Ara, S. H. Mousavi, E. Koushki, S. Salmani, A. Gharibi, and A. Ghanadzadeh, “Nonlinear optical responses of Sudan IV doped liquid crystal by z-scan and moiré deflectometry techniques,” J. Mol. Liq. 142, 29–31 (2008).
    [CrossRef]
  6. M. H. Majles Ara, E. Koushki, S. H. Mousavi, S. Salmani, M. Rafizadeh, and A. Gharibi, “Nonlinear optical properties of a dithiooxamide determined by single beam techniques,” Mater. Chem. Phys. 109, 320–324 (2008).
    [CrossRef]
  7. M. H. Majles Ara, S. H. Mousavi, S. Salmani, and E. Koushki, “Measurement of nonlinear refraction of dyes doped liquid crystal using moiré deflectometry,” J. Mol. Liq. 140, 21–24(2008).
    [CrossRef]
  8. S. S. Lin, “Optical properties of TiO2 nanoceramic films as a function of NAl co-doping,” Ceram. Int. 35, 2693–2698 (2009).
    [CrossRef]
  9. S. S. Lin, Y. H. Hung, and S. C. Chen, “Optical properties of TiO2 thin films deposited on polycarbonate by ion beam assisted evaporation,” Thin Solid Films 517, 4621–4625 (2009).
    [CrossRef]
  10. S. S. Lin and D. K. Wu, “The properties of Al-doped TiO2 nanoceramic films deposited by simultaneous rf and dc magnetron sputtering,” Ceram. Int. 36, 87–91 (2010).
    [CrossRef]
  11. S. S. Lin, S. C. Chen, and Y. H. Hung, “TiO2 nanoceramic films prepared by ion beam assisted evaporation for optical application,” Ceram. Int. 35, 1581–1586 (2009).
    [CrossRef]
  12. S. S. Lin, Y. H. Hung, and S. C. Chen, “The properties of TiO2 nanoceramic films prepared by electron beam evaporation,” J. Nanosci. Nanotechnol. 9, 3599–3605 (2009).
    [CrossRef] [PubMed]
  13. S. S. Lin and D. K. Wu, “Enhanced optical properties of TiO2 nanoceramic films by oxygen atmosphere,” J. Nanosci. Nanotechnol. 10, 1099–1104 (2010).
    [CrossRef] [PubMed]
  14. S. A. Akhmanov and S. Yu. Nikitin, Physical Optics(Clarendon, 1997), pp. 320–322.
  15. S. Rasouli and K. Jamshidi-Ghaleh, “Erratum to ‘Nonlinear refraction measurements of materials using the moiré deflectometry’ [K. Jamshidi-Ghaleh, N. Mansour, Opt. Commun. 234, 419 (2004)],” Opt. Commun. 284, 1481–1482(2011).
    [CrossRef]
  16. S. Rasouli and M. T. Tavassoly, “Application of the moiré deflectometry on divergent laser beam to the measurement of the angle of arrival fluctuations and the refractive index structure constant in the turbulent atmosphere,” Opt. Lett. 33, 980–982 (2008).
    [CrossRef] [PubMed]
  17. F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics(Prentice Hall, 1993).
  18. T. Du and W. Luo, “Nonlinear optical effects in ferrofluids induced by temperature and concentration cross coupling,” Appl. Phys. Lett. 72, 272–274 (1998).
    [CrossRef]

2011 (1)

S. Rasouli and K. Jamshidi-Ghaleh, “Erratum to ‘Nonlinear refraction measurements of materials using the moiré deflectometry’ [K. Jamshidi-Ghaleh, N. Mansour, Opt. Commun. 234, 419 (2004)],” Opt. Commun. 284, 1481–1482(2011).
[CrossRef]

2010 (2)

S. S. Lin and D. K. Wu, “The properties of Al-doped TiO2 nanoceramic films deposited by simultaneous rf and dc magnetron sputtering,” Ceram. Int. 36, 87–91 (2010).
[CrossRef]

S. S. Lin and D. K. Wu, “Enhanced optical properties of TiO2 nanoceramic films by oxygen atmosphere,” J. Nanosci. Nanotechnol. 10, 1099–1104 (2010).
[CrossRef] [PubMed]

2009 (4)

S. S. Lin, S. C. Chen, and Y. H. Hung, “TiO2 nanoceramic films prepared by ion beam assisted evaporation for optical application,” Ceram. Int. 35, 1581–1586 (2009).
[CrossRef]

S. S. Lin, Y. H. Hung, and S. C. Chen, “The properties of TiO2 nanoceramic films prepared by electron beam evaporation,” J. Nanosci. Nanotechnol. 9, 3599–3605 (2009).
[CrossRef] [PubMed]

S. S. Lin, “Optical properties of TiO2 nanoceramic films as a function of NAl co-doping,” Ceram. Int. 35, 2693–2698 (2009).
[CrossRef]

S. S. Lin, Y. H. Hung, and S. C. Chen, “Optical properties of TiO2 thin films deposited on polycarbonate by ion beam assisted evaporation,” Thin Solid Films 517, 4621–4625 (2009).
[CrossRef]

2008 (4)

M. H. Majles Ara, S. H. Mousavi, E. Koushki, S. Salmani, A. Gharibi, and A. Ghanadzadeh, “Nonlinear optical responses of Sudan IV doped liquid crystal by z-scan and moiré deflectometry techniques,” J. Mol. Liq. 142, 29–31 (2008).
[CrossRef]

M. H. Majles Ara, E. Koushki, S. H. Mousavi, S. Salmani, M. Rafizadeh, and A. Gharibi, “Nonlinear optical properties of a dithiooxamide determined by single beam techniques,” Mater. Chem. Phys. 109, 320–324 (2008).
[CrossRef]

M. H. Majles Ara, S. H. Mousavi, S. Salmani, and E. Koushki, “Measurement of nonlinear refraction of dyes doped liquid crystal using moiré deflectometry,” J. Mol. Liq. 140, 21–24(2008).
[CrossRef]

S. Rasouli and M. T. Tavassoly, “Application of the moiré deflectometry on divergent laser beam to the measurement of the angle of arrival fluctuations and the refractive index structure constant in the turbulent atmosphere,” Opt. Lett. 33, 980–982 (2008).
[CrossRef] [PubMed]

2004 (1)

K. Jamshidi-Ghaleh and N. Mansour, “Nonlinear refraction measurements of materials using the moiré deflectometry,” Opt. Commun. 234, 419–425 (2004).
[CrossRef]

1998 (1)

T. Du and W. Luo, “Nonlinear optical effects in ferrofluids induced by temperature and concentration cross coupling,” Appl. Phys. Lett. 72, 272–274 (1998).
[CrossRef]

1997 (1)

S. A. Akhmanov and S. Yu. Nikitin, Physical Optics(Clarendon, 1997), pp. 320–322.

1993 (1)

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics(Prentice Hall, 1993).

1990 (1)

M. Sheik-bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

1989 (1)

1984 (1)

Akhmanov, S. A.

S. A. Akhmanov and S. Yu. Nikitin, Physical Optics(Clarendon, 1997), pp. 320–322.

Chen, S. C.

S. S. Lin, Y. H. Hung, and S. C. Chen, “The properties of TiO2 nanoceramic films prepared by electron beam evaporation,” J. Nanosci. Nanotechnol. 9, 3599–3605 (2009).
[CrossRef] [PubMed]

S. S. Lin, S. C. Chen, and Y. H. Hung, “TiO2 nanoceramic films prepared by ion beam assisted evaporation for optical application,” Ceram. Int. 35, 1581–1586 (2009).
[CrossRef]

S. S. Lin, Y. H. Hung, and S. C. Chen, “Optical properties of TiO2 thin films deposited on polycarbonate by ion beam assisted evaporation,” Thin Solid Films 517, 4621–4625 (2009).
[CrossRef]

Du, T.

T. Du and W. Luo, “Nonlinear optical effects in ferrofluids induced by temperature and concentration cross coupling,” Appl. Phys. Lett. 72, 272–274 (1998).
[CrossRef]

Ghanadzadeh, A.

M. H. Majles Ara, S. H. Mousavi, E. Koushki, S. Salmani, A. Gharibi, and A. Ghanadzadeh, “Nonlinear optical responses of Sudan IV doped liquid crystal by z-scan and moiré deflectometry techniques,” J. Mol. Liq. 142, 29–31 (2008).
[CrossRef]

Gharibi, A.

M. H. Majles Ara, S. H. Mousavi, E. Koushki, S. Salmani, A. Gharibi, and A. Ghanadzadeh, “Nonlinear optical responses of Sudan IV doped liquid crystal by z-scan and moiré deflectometry techniques,” J. Mol. Liq. 142, 29–31 (2008).
[CrossRef]

M. H. Majles Ara, E. Koushki, S. H. Mousavi, S. Salmani, M. Rafizadeh, and A. Gharibi, “Nonlinear optical properties of a dithiooxamide determined by single beam techniques,” Mater. Chem. Phys. 109, 320–324 (2008).
[CrossRef]

Glatt, I.

Hagan, D. J.

M. Sheik-bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Hung, Y. H.

S. S. Lin, Y. H. Hung, and S. C. Chen, “Optical properties of TiO2 thin films deposited on polycarbonate by ion beam assisted evaporation,” Thin Solid Films 517, 4621–4625 (2009).
[CrossRef]

S. S. Lin, S. C. Chen, and Y. H. Hung, “TiO2 nanoceramic films prepared by ion beam assisted evaporation for optical application,” Ceram. Int. 35, 1581–1586 (2009).
[CrossRef]

S. S. Lin, Y. H. Hung, and S. C. Chen, “The properties of TiO2 nanoceramic films prepared by electron beam evaporation,” J. Nanosci. Nanotechnol. 9, 3599–3605 (2009).
[CrossRef] [PubMed]

Jamshidi-Ghaleh, K.

S. Rasouli and K. Jamshidi-Ghaleh, “Erratum to ‘Nonlinear refraction measurements of materials using the moiré deflectometry’ [K. Jamshidi-Ghaleh, N. Mansour, Opt. Commun. 234, 419 (2004)],” Opt. Commun. 284, 1481–1482(2011).
[CrossRef]

K. Jamshidi-Ghaleh and N. Mansour, “Nonlinear refraction measurements of materials using the moiré deflectometry,” Opt. Commun. 234, 419–425 (2004).
[CrossRef]

Kafri, O.

Karny, Z.

Koushki, E.

M. H. Majles Ara, S. H. Mousavi, E. Koushki, S. Salmani, A. Gharibi, and A. Ghanadzadeh, “Nonlinear optical responses of Sudan IV doped liquid crystal by z-scan and moiré deflectometry techniques,” J. Mol. Liq. 142, 29–31 (2008).
[CrossRef]

M. H. Majles Ara, E. Koushki, S. H. Mousavi, S. Salmani, M. Rafizadeh, and A. Gharibi, “Nonlinear optical properties of a dithiooxamide determined by single beam techniques,” Mater. Chem. Phys. 109, 320–324 (2008).
[CrossRef]

M. H. Majles Ara, S. H. Mousavi, S. Salmani, and E. Koushki, “Measurement of nonlinear refraction of dyes doped liquid crystal using moiré deflectometry,” J. Mol. Liq. 140, 21–24(2008).
[CrossRef]

Lin, S. S.

S. S. Lin and D. K. Wu, “The properties of Al-doped TiO2 nanoceramic films deposited by simultaneous rf and dc magnetron sputtering,” Ceram. Int. 36, 87–91 (2010).
[CrossRef]

S. S. Lin and D. K. Wu, “Enhanced optical properties of TiO2 nanoceramic films by oxygen atmosphere,” J. Nanosci. Nanotechnol. 10, 1099–1104 (2010).
[CrossRef] [PubMed]

S. S. Lin, S. C. Chen, and Y. H. Hung, “TiO2 nanoceramic films prepared by ion beam assisted evaporation for optical application,” Ceram. Int. 35, 1581–1586 (2009).
[CrossRef]

S. S. Lin, Y. H. Hung, and S. C. Chen, “The properties of TiO2 nanoceramic films prepared by electron beam evaporation,” J. Nanosci. Nanotechnol. 9, 3599–3605 (2009).
[CrossRef] [PubMed]

S. S. Lin, “Optical properties of TiO2 nanoceramic films as a function of NAl co-doping,” Ceram. Int. 35, 2693–2698 (2009).
[CrossRef]

S. S. Lin, Y. H. Hung, and S. C. Chen, “Optical properties of TiO2 thin films deposited on polycarbonate by ion beam assisted evaporation,” Thin Solid Films 517, 4621–4625 (2009).
[CrossRef]

Luo, W.

T. Du and W. Luo, “Nonlinear optical effects in ferrofluids induced by temperature and concentration cross coupling,” Appl. Phys. Lett. 72, 272–274 (1998).
[CrossRef]

Majles Ara, M. H.

M. H. Majles Ara, E. Koushki, S. H. Mousavi, S. Salmani, M. Rafizadeh, and A. Gharibi, “Nonlinear optical properties of a dithiooxamide determined by single beam techniques,” Mater. Chem. Phys. 109, 320–324 (2008).
[CrossRef]

M. H. Majles Ara, S. H. Mousavi, S. Salmani, and E. Koushki, “Measurement of nonlinear refraction of dyes doped liquid crystal using moiré deflectometry,” J. Mol. Liq. 140, 21–24(2008).
[CrossRef]

M. H. Majles Ara, S. H. Mousavi, E. Koushki, S. Salmani, A. Gharibi, and A. Ghanadzadeh, “Nonlinear optical responses of Sudan IV doped liquid crystal by z-scan and moiré deflectometry techniques,” J. Mol. Liq. 142, 29–31 (2008).
[CrossRef]

Mansour, N.

K. Jamshidi-Ghaleh and N. Mansour, “Nonlinear refraction measurements of materials using the moiré deflectometry,” Opt. Commun. 234, 419–425 (2004).
[CrossRef]

Mousavi, S. H.

M. H. Majles Ara, S. H. Mousavi, E. Koushki, S. Salmani, A. Gharibi, and A. Ghanadzadeh, “Nonlinear optical responses of Sudan IV doped liquid crystal by z-scan and moiré deflectometry techniques,” J. Mol. Liq. 142, 29–31 (2008).
[CrossRef]

M. H. Majles Ara, S. H. Mousavi, S. Salmani, and E. Koushki, “Measurement of nonlinear refraction of dyes doped liquid crystal using moiré deflectometry,” J. Mol. Liq. 140, 21–24(2008).
[CrossRef]

M. H. Majles Ara, E. Koushki, S. H. Mousavi, S. Salmani, M. Rafizadeh, and A. Gharibi, “Nonlinear optical properties of a dithiooxamide determined by single beam techniques,” Mater. Chem. Phys. 109, 320–324 (2008).
[CrossRef]

Nikitin, S. Yu.

S. A. Akhmanov and S. Yu. Nikitin, Physical Optics(Clarendon, 1997), pp. 320–322.

Pedrotti, F. L.

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics(Prentice Hall, 1993).

Pedrotti, L. S.

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics(Prentice Hall, 1993).

Rafizadeh, M.

M. H. Majles Ara, E. Koushki, S. H. Mousavi, S. Salmani, M. Rafizadeh, and A. Gharibi, “Nonlinear optical properties of a dithiooxamide determined by single beam techniques,” Mater. Chem. Phys. 109, 320–324 (2008).
[CrossRef]

Rasouli, S.

S. Rasouli and K. Jamshidi-Ghaleh, “Erratum to ‘Nonlinear refraction measurements of materials using the moiré deflectometry’ [K. Jamshidi-Ghaleh, N. Mansour, Opt. Commun. 234, 419 (2004)],” Opt. Commun. 284, 1481–1482(2011).
[CrossRef]

S. Rasouli and M. T. Tavassoly, “Application of the moiré deflectometry on divergent laser beam to the measurement of the angle of arrival fluctuations and the refractive index structure constant in the turbulent atmosphere,” Opt. Lett. 33, 980–982 (2008).
[CrossRef] [PubMed]

Said, A. A.

M. Sheik-bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

M. Sheik-bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

Salmani, S.

M. H. Majles Ara, S. H. Mousavi, E. Koushki, S. Salmani, A. Gharibi, and A. Ghanadzadeh, “Nonlinear optical responses of Sudan IV doped liquid crystal by z-scan and moiré deflectometry techniques,” J. Mol. Liq. 142, 29–31 (2008).
[CrossRef]

M. H. Majles Ara, E. Koushki, S. H. Mousavi, S. Salmani, M. Rafizadeh, and A. Gharibi, “Nonlinear optical properties of a dithiooxamide determined by single beam techniques,” Mater. Chem. Phys. 109, 320–324 (2008).
[CrossRef]

M. H. Majles Ara, S. H. Mousavi, S. Salmani, and E. Koushki, “Measurement of nonlinear refraction of dyes doped liquid crystal using moiré deflectometry,” J. Mol. Liq. 140, 21–24(2008).
[CrossRef]

Sheik-bahae, M.

M. Sheik-bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

M. Sheik-bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

Tavassoly, M. T.

Van Stryland, E. W.

M. Sheik-bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

M. Sheik-bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

Wei, T.

M. Sheik-bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Wu, D. K.

S. S. Lin and D. K. Wu, “The properties of Al-doped TiO2 nanoceramic films deposited by simultaneous rf and dc magnetron sputtering,” Ceram. Int. 36, 87–91 (2010).
[CrossRef]

S. S. Lin and D. K. Wu, “Enhanced optical properties of TiO2 nanoceramic films by oxygen atmosphere,” J. Nanosci. Nanotechnol. 10, 1099–1104 (2010).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

T. Du and W. Luo, “Nonlinear optical effects in ferrofluids induced by temperature and concentration cross coupling,” Appl. Phys. Lett. 72, 272–274 (1998).
[CrossRef]

Ceram. Int. (3)

S. S. Lin and D. K. Wu, “The properties of Al-doped TiO2 nanoceramic films deposited by simultaneous rf and dc magnetron sputtering,” Ceram. Int. 36, 87–91 (2010).
[CrossRef]

S. S. Lin, S. C. Chen, and Y. H. Hung, “TiO2 nanoceramic films prepared by ion beam assisted evaporation for optical application,” Ceram. Int. 35, 1581–1586 (2009).
[CrossRef]

S. S. Lin, “Optical properties of TiO2 nanoceramic films as a function of NAl co-doping,” Ceram. Int. 35, 2693–2698 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

J. Mol. Liq. (2)

M. H. Majles Ara, S. H. Mousavi, E. Koushki, S. Salmani, A. Gharibi, and A. Ghanadzadeh, “Nonlinear optical responses of Sudan IV doped liquid crystal by z-scan and moiré deflectometry techniques,” J. Mol. Liq. 142, 29–31 (2008).
[CrossRef]

M. H. Majles Ara, S. H. Mousavi, S. Salmani, and E. Koushki, “Measurement of nonlinear refraction of dyes doped liquid crystal using moiré deflectometry,” J. Mol. Liq. 140, 21–24(2008).
[CrossRef]

J. Nanosci. Nanotechnol. (2)

S. S. Lin, Y. H. Hung, and S. C. Chen, “The properties of TiO2 nanoceramic films prepared by electron beam evaporation,” J. Nanosci. Nanotechnol. 9, 3599–3605 (2009).
[CrossRef] [PubMed]

S. S. Lin and D. K. Wu, “Enhanced optical properties of TiO2 nanoceramic films by oxygen atmosphere,” J. Nanosci. Nanotechnol. 10, 1099–1104 (2010).
[CrossRef] [PubMed]

Mater. Chem. Phys. (1)

M. H. Majles Ara, E. Koushki, S. H. Mousavi, S. Salmani, M. Rafizadeh, and A. Gharibi, “Nonlinear optical properties of a dithiooxamide determined by single beam techniques,” Mater. Chem. Phys. 109, 320–324 (2008).
[CrossRef]

Opt. Commun. (2)

K. Jamshidi-Ghaleh and N. Mansour, “Nonlinear refraction measurements of materials using the moiré deflectometry,” Opt. Commun. 234, 419–425 (2004).
[CrossRef]

S. Rasouli and K. Jamshidi-Ghaleh, “Erratum to ‘Nonlinear refraction measurements of materials using the moiré deflectometry’ [K. Jamshidi-Ghaleh, N. Mansour, Opt. Commun. 234, 419 (2004)],” Opt. Commun. 284, 1481–1482(2011).
[CrossRef]

Opt. Lett. (2)

Thin Solid Films (1)

S. S. Lin, Y. H. Hung, and S. C. Chen, “Optical properties of TiO2 thin films deposited on polycarbonate by ion beam assisted evaporation,” Thin Solid Films 517, 4621–4625 (2009).
[CrossRef]

Other (2)

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics(Prentice Hall, 1993).

S. A. Akhmanov and S. Yu. Nikitin, Physical Optics(Clarendon, 1997), pp. 320–322.

Supplementary Material (1)

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup. D.F., L 1 , L 2 , G 1 , G 2 , L 3 , S.F., D, and L 4 stand for neutral density filter, focusing lens, collimating lens, first grating, second grating, Fourier transforming lens, spatial filter, diffuser, and imaging lens, respectively.

Fig. 2
Fig. 2

Typical moiré patterns recorded at different distances of the sample from the focal plane for laser power 70 mW . The corresponding video can be observed in the background (Media 1 DVI, 1.79 M B ).

Fig. 3
Fig. 3

Behavior of moiré fringe period at various z, with theoretical fits on the experimental data for two laser powers, 25 and 70 mW .

Equations (10)

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I ( ρ , z ) = I 0 w 0 2 w 2 ( z ) exp [ 2 ρ 2 w 2 ( z ) ] ,
Δ n ( ρ , z ) = n 2 I 0 w 0 2 w 2 ( z ) exp [ 2 ρ 2 w 2 ( z ) ] .
Δ n ( ρ , z ) n 2 I 0 w 0 2 w 2 ( z ) [ 1 2 ρ 2 w 2 ( z ) ] .
f s ( z ) = π w 4 ( z ) 8 n 2 s P = f s ( 0 ) ( 1 + z 2 z 0 2 ) 2 ,
d m = d 2 δ d ,
d m = | r | d Z k .
( A B C D ) = ( 1 0 1 f 2 1 ) ( 1 f 2 z 0 1 ) ( 1 0 1 f s ( z ) 1 ) ( 1 f 1 + z 0 1 ) ( 1 0 1 f 1 1 ) .
r ( z ) = L 2 S ( z ) f t ( z ) ,
r ( z ) = L 2 + f 2 2 z f s ( z ) f 2 2 z 2 f 2 .
d m ( z ) = d Z k | { L 2 + f 2 2 z f 2 2 z 2 f s ( 0 ) ( 1 + z 2 z 0 2 ) 2 f 2 } | .

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