Abstract

We demonstrate the use of a mirror as a viewing diaphragm to generate a built-in diffracted reference beam in schlieren diffraction interferometry (SDI). The use of a mirror edge as a diffracting element instead of a conventional knife edge considerably enhances the contrast of the schlieren pattern, and it is shown to be equal to that of a phase knife edge. This increase in contrast is due to the fact that the otherwise unutilized diffracted beam in SDI is recombined in the described folding mirror geometry.

© 2006 Optical Society of America

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References

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  1. G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, 2001).
  2. E. B. Temple, "Quantitative measurement of gas density by means of light interference in a schlieren system," J. Opt. Soc. Am. 47, 91-100 (1957).
    [CrossRef]
  3. A. Hanenkamp and W. Merzkirch, "Investigation of the properties of a sharp-focusing schlieren system by means of Fourier analysis," Opt. Lasers Eng. 44, 159-169 (2006).
    [CrossRef]
  4. H. Kleine, H. Gronig, and K. Takayama, "Simultaneous shadow, schlieren and interferometric visualization of compressible flows," Opt. Lasers Eng. 44, 170-189 (2006).
    [CrossRef]
  5. A. Srivastava, K. Muralidhar, and P. K. Panigrahi, "Reconstruction of the concentration field around a growing KDP crystal with schlieren tomography," Appl. Opt. 44, 5381-5392 (2005).
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  6. E. Garbusi, J. A. Ferrari, and C. D. Perciante, "Harmonic suppression and defect enhancement using schlieren processing," Appl. Opt. 44, 2963-2969 (2005).
    [CrossRef] [PubMed]
  7. D. R. Jonassen, G. S. Settles, and Michael D. Tronosky, "Schlieren 'PIV' for turbulent flows," Opt. Lasers Eng. 44, 190-207 (2006).
    [CrossRef]
  8. A. Eder and M. Jordan, "The schlieren technique," in Optical Measurements, Techniques and Applications, F. Mayinger, and O. Feldmann, eds. (Springer-Verlag, 2001), pp. 5-16.
  9. N. Pollock, "A simple laser interferometer for wind tunnel flow visualization," J. Phys. E 13, 1062-1066 (1980).
    [CrossRef]
  10. J. A. Ferrari and E. M. Frins, "One-beam interferometer by beam folding," Appl. Opt. 41, 5313-5316 (2002).
    [CrossRef] [PubMed]
  11. M. Born and E. Wolf, Principles of Optics (Pergamon, 1970), pp. 449-453.
  12. S. Ganci, "Maggi-Rubinowicz transformation for phase apertures," J. Opt. Soc. Am. A 3, 2094-2100 (1986).
    [CrossRef]
  13. J. Ojeda-Castañeda, "Foucault, wire, and phase modulation tests," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 306-309.
  14. R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, "Knife-edge diffraction pattern as an interference phenomenon: an experimental reality," Opt. Laser Technol. (to be published).
  15. A. K. Aggarwal and S. K. Kaura, "Further applications of point diffraction interferometer," J. Opt. (Paris) 17, 135-138 (1986).
    [CrossRef]
  16. J. S. Goldmeer, D. L. Urban, and Z. Yuan, "Measurement of gas-phase temperatures in flames with a point-diffraction interferometer," Appl. Opt. 40, 4816-4823 (2001).
    [CrossRef]

2006 (3)

A. Hanenkamp and W. Merzkirch, "Investigation of the properties of a sharp-focusing schlieren system by means of Fourier analysis," Opt. Lasers Eng. 44, 159-169 (2006).
[CrossRef]

H. Kleine, H. Gronig, and K. Takayama, "Simultaneous shadow, schlieren and interferometric visualization of compressible flows," Opt. Lasers Eng. 44, 170-189 (2006).
[CrossRef]

D. R. Jonassen, G. S. Settles, and Michael D. Tronosky, "Schlieren 'PIV' for turbulent flows," Opt. Lasers Eng. 44, 190-207 (2006).
[CrossRef]

2005 (2)

2002 (1)

2001 (1)

1986 (2)

S. Ganci, "Maggi-Rubinowicz transformation for phase apertures," J. Opt. Soc. Am. A 3, 2094-2100 (1986).
[CrossRef]

A. K. Aggarwal and S. K. Kaura, "Further applications of point diffraction interferometer," J. Opt. (Paris) 17, 135-138 (1986).
[CrossRef]

1980 (1)

N. Pollock, "A simple laser interferometer for wind tunnel flow visualization," J. Phys. E 13, 1062-1066 (1980).
[CrossRef]

1957 (1)

Aggarwal, A. K.

A. K. Aggarwal and S. K. Kaura, "Further applications of point diffraction interferometer," J. Opt. (Paris) 17, 135-138 (1986).
[CrossRef]

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, "Knife-edge diffraction pattern as an interference phenomenon: an experimental reality," Opt. Laser Technol. (to be published).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1970), pp. 449-453.

Chhachhia, D. P.

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, "Knife-edge diffraction pattern as an interference phenomenon: an experimental reality," Opt. Laser Technol. (to be published).

Eder, A.

A. Eder and M. Jordan, "The schlieren technique," in Optical Measurements, Techniques and Applications, F. Mayinger, and O. Feldmann, eds. (Springer-Verlag, 2001), pp. 5-16.

Ferrari, J. A.

Frins, E. M.

Ganci, S.

Garbusi, E.

Goldmeer, J. S.

Gronig, H.

H. Kleine, H. Gronig, and K. Takayama, "Simultaneous shadow, schlieren and interferometric visualization of compressible flows," Opt. Lasers Eng. 44, 170-189 (2006).
[CrossRef]

Hanenkamp, A.

A. Hanenkamp and W. Merzkirch, "Investigation of the properties of a sharp-focusing schlieren system by means of Fourier analysis," Opt. Lasers Eng. 44, 159-169 (2006).
[CrossRef]

Jonassen, D. R.

D. R. Jonassen, G. S. Settles, and Michael D. Tronosky, "Schlieren 'PIV' for turbulent flows," Opt. Lasers Eng. 44, 190-207 (2006).
[CrossRef]

Jordan, M.

A. Eder and M. Jordan, "The schlieren technique," in Optical Measurements, Techniques and Applications, F. Mayinger, and O. Feldmann, eds. (Springer-Verlag, 2001), pp. 5-16.

Kaura, S. K.

A. K. Aggarwal and S. K. Kaura, "Further applications of point diffraction interferometer," J. Opt. (Paris) 17, 135-138 (1986).
[CrossRef]

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, "Knife-edge diffraction pattern as an interference phenomenon: an experimental reality," Opt. Laser Technol. (to be published).

Kleine, H.

H. Kleine, H. Gronig, and K. Takayama, "Simultaneous shadow, schlieren and interferometric visualization of compressible flows," Opt. Lasers Eng. 44, 170-189 (2006).
[CrossRef]

Kumar, R.

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, "Knife-edge diffraction pattern as an interference phenomenon: an experimental reality," Opt. Laser Technol. (to be published).

Merzkirch, W.

A. Hanenkamp and W. Merzkirch, "Investigation of the properties of a sharp-focusing schlieren system by means of Fourier analysis," Opt. Lasers Eng. 44, 159-169 (2006).
[CrossRef]

Muralidhar, K.

Ojeda-Castañeda, J.

J. Ojeda-Castañeda, "Foucault, wire, and phase modulation tests," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 306-309.

Panigrahi, P. K.

Perciante, C. D.

Pollock, N.

N. Pollock, "A simple laser interferometer for wind tunnel flow visualization," J. Phys. E 13, 1062-1066 (1980).
[CrossRef]

Settles, G. S.

D. R. Jonassen, G. S. Settles, and Michael D. Tronosky, "Schlieren 'PIV' for turbulent flows," Opt. Lasers Eng. 44, 190-207 (2006).
[CrossRef]

G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, 2001).

Sharma, A. K.

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, "Knife-edge diffraction pattern as an interference phenomenon: an experimental reality," Opt. Laser Technol. (to be published).

Srivastava, A.

Takayama, K.

H. Kleine, H. Gronig, and K. Takayama, "Simultaneous shadow, schlieren and interferometric visualization of compressible flows," Opt. Lasers Eng. 44, 170-189 (2006).
[CrossRef]

Temple, E. B.

Urban, D. L.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1970), pp. 449-453.

Yuan, Z.

Appl. Opt. (4)

J. Opt. (1)

A. K. Aggarwal and S. K. Kaura, "Further applications of point diffraction interferometer," J. Opt. (Paris) 17, 135-138 (1986).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Phys. E (1)

N. Pollock, "A simple laser interferometer for wind tunnel flow visualization," J. Phys. E 13, 1062-1066 (1980).
[CrossRef]

Opt. Lasers Eng. (3)

A. Hanenkamp and W. Merzkirch, "Investigation of the properties of a sharp-focusing schlieren system by means of Fourier analysis," Opt. Lasers Eng. 44, 159-169 (2006).
[CrossRef]

H. Kleine, H. Gronig, and K. Takayama, "Simultaneous shadow, schlieren and interferometric visualization of compressible flows," Opt. Lasers Eng. 44, 170-189 (2006).
[CrossRef]

D. R. Jonassen, G. S. Settles, and Michael D. Tronosky, "Schlieren 'PIV' for turbulent flows," Opt. Lasers Eng. 44, 190-207 (2006).
[CrossRef]

Other (5)

A. Eder and M. Jordan, "The schlieren technique," in Optical Measurements, Techniques and Applications, F. Mayinger, and O. Feldmann, eds. (Springer-Verlag, 2001), pp. 5-16.

G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, 2001).

J. Ojeda-Castañeda, "Foucault, wire, and phase modulation tests," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 306-309.

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, "Knife-edge diffraction pattern as an interference phenomenon: an experimental reality," Opt. Laser Technol. (to be published).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1970), pp. 449-453.

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Figures (4)

Fig. 1
Fig. 1

Diffraction geometry of the mirror edge. XY is a spherical wavefront incident on the mirror edge K, path 1 denotes the geometrical wave U g , path 2 denotes the diffracted U d + diffracted-reflected wave U d , and A is a point situated on the illuminated boundary of K. Closeup around point A is shown on top.

Fig. 2
Fig. 2

Schematic of the experimental setup. Path 1 denotes the geometrical wave U g , path 2 denotes the diffracted U d + diffracted-reflected wave U d , S is focus formed by an imaging lens ( L 2 ) .

Fig. 3
Fig. 3

Schematic representation of two different positions (I and II) of the diffracting element K in the Airy pattern.

Fig. 4
Fig. 4

Experimental results of an optical glass plate held in a mount with (a) classical SDI (Airy disk blocked with knife edge), (b) knife edge striking the Airy disk, and (c) mirror edge striking the Airy disk.

Equations (6)

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U ( P 1 ) = U g ( P 1 ) + U d ( P 1 ) ,
U g ( P 1 ) = ( A / R ) exp ( j k R ) , when   P 1   is   in   the direct   beam = 0 , when   P 1   is   in geometrical   shadow,
U d ( P 1 ) = U d ( P 1 ) + U d ( P 1 ) = ( A / 4 π ) [ 1 exp ( j k Δ ) ] Σ exp { j k ( r + s ) } × cos ( n A , s ) sin ( r , d l ) × d l / { r s [ 1 + cos ( r , s ) ] } ,
U d ( P 1 ) = ( A / 4 π ) Σ exp { j k ( r + s ) } cos ( n A , s ) × sin ( r , d l ) d l / { r s [ 1 + cos ( r , s ) ] } ,
U d ( P 1 ) = ( A / 4 π ) Σ exp { j k ( r + s + Δ ) } cos ( n B , s ) × sin ( r , d l ) d l / { r s [ 1 + cos ( r , s ) ] } ,
cos ( n A , s ) = cos ( n B , s ) .

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