Abstract

A quantitative autocalibrated high-resolution schlieren technique for quantitative measurement of reflective surface shape is proposed. It combines the schlieren principle with the phase-shifting technique that is generally used in interferometry. With an appropriate schlieren filter and appropriately tailored setup, some schlieren fringes are generated. After application of the phase-shift technique, the schlieren phase is calculated and converted into beam deviation values. Theoretical and experimental demonstrations are given. The technique is validated on a reference target, and then its application in a fluid physics experiment is demonstrated. These two examples show the potential of the phase-shifting schlieren technique that in some situations can become competitive with interferometry but with a much better dynamic range and with variable sensitivity. The technique can also be used to measure refractive-index gradients in transparent media.

© 2003 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, Berlin, 2001).
    [CrossRef]
  2. H. Schardin, “Toepler’s schlieren method: basic principles for its use and quantitative evaluation,” in Selected Papers on Schlieren Optics, J. R. Meyer-Arendt, ed., Vol. MS 61 of SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1992), pp. 32–55 (translation of “Das Toeplersche Schlierenverfahren: Grundlagen fur seine Anwendung und quantitative Auswertung,” Forschungsheft 367, Beilage zu Forschung auf dem Gebiete des Ingenieurwesens 1934; translation No. 156 by F. A. Raven for Navy Dept., David Taylor Model Basin, Washington, D.C., 1947).
  3. S. Settles, “Colour-coding Schlieren technique for the optical study of heat and fluid flow,” Int. J. Heat Fluid Flow 6, 3–15 (1985).
    [CrossRef]
  4. J. Shamir, ed., Optical Systems and Processes, Vol. PM65 of SPIE Press Monograph Series (SPIE, Bellingham, Wash., 1999).
    [CrossRef]
  5. P. Hariharan, B. F. Oreb, T. Eiju, “Digital phase-shifting interferometry: a simple error-compensation phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987).
    [CrossRef] [PubMed]
  6. P. Colinet, J. C. Legros, M. G. Velarde, Nonlinear Dynamics of Surface-Tension-Driven Instabilities (Wiley-VCH, Berlin, 2001).
    [CrossRef]

1987

1985

S. Settles, “Colour-coding Schlieren technique for the optical study of heat and fluid flow,” Int. J. Heat Fluid Flow 6, 3–15 (1985).
[CrossRef]

Colinet, P.

P. Colinet, J. C. Legros, M. G. Velarde, Nonlinear Dynamics of Surface-Tension-Driven Instabilities (Wiley-VCH, Berlin, 2001).
[CrossRef]

Eiju, T.

Hariharan, P.

Legros, J. C.

P. Colinet, J. C. Legros, M. G. Velarde, Nonlinear Dynamics of Surface-Tension-Driven Instabilities (Wiley-VCH, Berlin, 2001).
[CrossRef]

Oreb, B. F.

Schardin, H.

H. Schardin, “Toepler’s schlieren method: basic principles for its use and quantitative evaluation,” in Selected Papers on Schlieren Optics, J. R. Meyer-Arendt, ed., Vol. MS 61 of SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1992), pp. 32–55 (translation of “Das Toeplersche Schlierenverfahren: Grundlagen fur seine Anwendung und quantitative Auswertung,” Forschungsheft 367, Beilage zu Forschung auf dem Gebiete des Ingenieurwesens 1934; translation No. 156 by F. A. Raven for Navy Dept., David Taylor Model Basin, Washington, D.C., 1947).

Settles, G. S.

G. S. Settles, Schlieren and Shadowgraph Techniques—Visualizing Phenomena in Transparent Media (Springer-Verlag, Berlin, 2001).
[CrossRef]

Settles, S.

S. Settles, “Colour-coding Schlieren technique for the optical study of heat and fluid flow,” Int. J. Heat Fluid Flow 6, 3–15 (1985).
[CrossRef]

Velarde, M. G.

P. Colinet, J. C. Legros, M. G. Velarde, Nonlinear Dynamics of Surface-Tension-Driven Instabilities (Wiley-VCH, Berlin, 2001).
[CrossRef]

Appl. Opt.

Int. J. Heat Fluid Flow

S. Settles, “Colour-coding Schlieren technique for the optical study of heat and fluid flow,” Int. J. Heat Fluid Flow 6, 3–15 (1985).
[CrossRef]

Other

J. Shamir, ed., Optical Systems and Processes, Vol. PM65 of SPIE Press Monograph Series (SPIE, Bellingham, Wash., 1999).
[CrossRef]

P. Colinet, J. C. Legros, M. G. Velarde, Nonlinear Dynamics of Surface-Tension-Driven Instabilities (Wiley-VCH, Berlin, 2001).
[CrossRef]

G. S. Settles, Schlieren and Shadowgraph Techniques—Visualizing Phenomena in Transparent Media (Springer-Verlag, Berlin, 2001).
[CrossRef]

H. Schardin, “Toepler’s schlieren method: basic principles for its use and quantitative evaluation,” in Selected Papers on Schlieren Optics, J. R. Meyer-Arendt, ed., Vol. MS 61 of SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1992), pp. 32–55 (translation of “Das Toeplersche Schlierenverfahren: Grundlagen fur seine Anwendung und quantitative Auswertung,” Forschungsheft 367, Beilage zu Forschung auf dem Gebiete des Ingenieurwesens 1934; translation No. 156 by F. A. Raven for Navy Dept., David Taylor Model Basin, Washington, D.C., 1947).

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Figures (13)

Fig. 1
Fig. 1

Schematic drawing of the Schlieren system working in reflection.

Fig. 2
Fig. 2

Conventional Schlieren: (a) arrangement of the knife-edge, (b) typical response curve.

Fig. 3
Fig. 3

PSS: (a) arrangement of the filter, (b) typical response curve.

Fig. 4
Fig. 4

Definitions of axes and coordinates in the theoretical approach.

Fig. 5
Fig. 5

Experimental evidence of schlieren fringes: gray level versus mirror rotation angle. Filled circles are measurement points.

Fig. 6
Fig. 6

Angle of a beam reflected by a lens’s front surface.

Fig. 7
Fig. 7

(a) Schlieren fringes and (b) phases obtained from the beam deviation produced by a 1-m focal-length lens surface.

Fig. 8
Fig. 8

Beam’s deviation angle versus its position.

Fig. 9
Fig. 9

Lens surface profile deduced from integration of the curve in Fig. 8.

Fig. 10
Fig. 10

Two of the five shifted images acquired after heating of the bottom plate.

Fig. 11
Fig. 11

Processed images: (a) wrapped phase, (b) unwrapped phase.

Fig. 12
Fig. 12

Profile of the liquid-gas interface over a convection pattern.

Fig. 13
Fig. 13

(a) One of the five fringe images. (b) Wrapped phase image obtained with a large amount of liquid surface deformation close to the border of the experimental cell. (c) Surface profile of the liquid deduced from integration on one line profile of (b).

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

tanαΛ=Λ/f2.
Ssx, y=δx-xs, y-ys.
EIx1, y2=V1λfFSsx, ytx1, y1,
EIIx2, y2=V1λfFEIx1, y1=Tx2+xsλf, y2+ysλf.
EIIIx3, y3=V1λfFTx2+xsλf, y2+ysλfhx2, y2
EIIIx3, y3=λf2FVλfTx2+xsλf, y2+ysλfFVλfhx2, y2 exp-2πiλfx3xs +y3yst-x3, -y3Hx3λf, y3λf,
ICCDx3, y3=-a/2a/2  dxsdysexp-2πiλfx3xs+y3yst-x3, -y3Hx3λf, y3λf2,
tx1, y1=expikxx1=exp2πiλf ηx3, kx=2πλf η=2πλsinθ.
ICCDη-a/2a/2dxs|hη-xs|2.
hx=1+cos2πΛ x+ϕ,
ICCDη=a+b cos2πΛ η+ϕ,
η=fθ.
α=2 arctand/R.

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