Abstract

An adjustable Wollaston-like prism is characterized for use in shearing- and differential schlieren-interferometry with laser and white-light illumination. We demonstrate that a polycarbonate prism under mechanical loading behaves identically to Wollaston's classical birefringent beam splitter. A linear relationship is found between the pure bending moment applied to the polycarbonate prism and the resulting light-beam-divergence angle. The utility of this prism in shearing-interferometry is shown by using it in place of the knife-edge in small and large schlieren optical systems. It is inexpensive to fabricate, and it yields adjustable beam-divergence angles over a range of at least 0–24 arc min.

© 2008 Optical Society of America

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References

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  1. M. Françon, "Interférences par double réfraction en lumière blanche," Revue d'Optique 31, 65-80 (1952).
  2. G. Nomarski, "Remarques sur le fonctionnement des dispositifs interférientiels à polarisation," J. Phys. Radium 17, 15-35 (1956).
  3. R. Chevalerias, Y. Latron, and C. Veret, "Methods of interferometry applied to the visualization of flow in wind tunnels," J. Opt. Soc. Am. 47, 703-706 (1957).
    [CrossRef]
  4. M. Philbert, "Emploi de la strioscopie interférentielle en aérodynamique," Rech. Aeronaut. 65, 19-27 (1958).
  5. W. Merzkirch, "A simple schlieren interferometer system," AIAA J. 3, 1974-1976 (1965).
    [CrossRef]
  6. R. D. Small, V. Sernas, and R. H. Page, "Single beam schlieren-interferometer using a Wollaston prism," Appl. Opt. 11, 858-862 (1972).
    [CrossRef] [PubMed]
  7. G. Smeets, "Observational techniques related to differential interferometry," in Proceedings of 11th International Congress on High Speed Photography, P. J. Rolls, ed. (Chapman & Hall, 1975), pp. 283-288.
  8. H. Oertel and H. Oertel, Jr., Optische Strömungsmesstechnik (G. Braun, 1989).
  9. W. Merzkirch, Flow Visualization (Academic, 1987).
  10. J. M. Desse, "Recent contribution in color interferometry and applications to high-speed flows," Opt. Lasers Eng. 44, 304-320 (2006).
    [CrossRef]
  11. S. R. Sanderson, "Shock wave interactions in hypervelocity flow," Ph.D. dissertation (California Institute of Technology, 1995).
  12. S. R. Sanderson, "Simple, adjustable beam splitting element for differential interferometers based on photoelastic birefringence of a prismatic bar," Rev. Sci. Instrum. 76, 113703 (2005).
    [CrossRef]
  13. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  14. J. E. Shigley and C. R. Mischke, Mechanical Engineering Design, 6th ed. (McGraw-Hill, 2001).
  15. R. B. Heywood, Photoelasticity for Designers (Pergamon Press, 1969).
  16. J. W. Dally and W. F. Riley, Experimental Stress Analysis, 3rd ed. (McGraw-Hill, 1991).
  17. A. Wineman and R. Kolberg, "Mechanical response of beams of a nonlinear viscoelastic material," Polym. Eng. Sci. 35, 345-350 (1995).
    [CrossRef]
  18. G. L. Cloud, "Mechanical-optical properties of polycarbonate resin and some relations with material structure," Exp. Mech. 9, 489-499 (1969).
    [CrossRef]
  19. I. Newton, Opticks (Dover, 1952) (reprinted from 4th ed., 1730).
  20. G. M. Carlomagno, "A Wollaston prism interferometer used as a reference beam interferometer," in Proceedings of Flow Visualization IV, Paris, 1986, C. Veret, ed. (Hemisphere, 1987), pp. 105-110.
  21. G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, 2001).

2006 (1)

J. M. Desse, "Recent contribution in color interferometry and applications to high-speed flows," Opt. Lasers Eng. 44, 304-320 (2006).
[CrossRef]

2005 (1)

S. R. Sanderson, "Simple, adjustable beam splitting element for differential interferometers based on photoelastic birefringence of a prismatic bar," Rev. Sci. Instrum. 76, 113703 (2005).
[CrossRef]

1995 (1)

A. Wineman and R. Kolberg, "Mechanical response of beams of a nonlinear viscoelastic material," Polym. Eng. Sci. 35, 345-350 (1995).
[CrossRef]

1972 (1)

1969 (1)

G. L. Cloud, "Mechanical-optical properties of polycarbonate resin and some relations with material structure," Exp. Mech. 9, 489-499 (1969).
[CrossRef]

1965 (1)

W. Merzkirch, "A simple schlieren interferometer system," AIAA J. 3, 1974-1976 (1965).
[CrossRef]

1958 (1)

M. Philbert, "Emploi de la strioscopie interférentielle en aérodynamique," Rech. Aeronaut. 65, 19-27 (1958).

1957 (1)

1956 (1)

G. Nomarski, "Remarques sur le fonctionnement des dispositifs interférientiels à polarisation," J. Phys. Radium 17, 15-35 (1956).

1952 (1)

M. Françon, "Interférences par double réfraction en lumière blanche," Revue d'Optique 31, 65-80 (1952).

AIAA J. (1)

W. Merzkirch, "A simple schlieren interferometer system," AIAA J. 3, 1974-1976 (1965).
[CrossRef]

Appl. Opt. (1)

Exp. Mech. (1)

G. L. Cloud, "Mechanical-optical properties of polycarbonate resin and some relations with material structure," Exp. Mech. 9, 489-499 (1969).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Radium (1)

G. Nomarski, "Remarques sur le fonctionnement des dispositifs interférientiels à polarisation," J. Phys. Radium 17, 15-35 (1956).

Opt. Lasers Eng. (1)

J. M. Desse, "Recent contribution in color interferometry and applications to high-speed flows," Opt. Lasers Eng. 44, 304-320 (2006).
[CrossRef]

Polym. Eng. Sci. (1)

A. Wineman and R. Kolberg, "Mechanical response of beams of a nonlinear viscoelastic material," Polym. Eng. Sci. 35, 345-350 (1995).
[CrossRef]

Rech. Aeronaut. (1)

M. Philbert, "Emploi de la strioscopie interférentielle en aérodynamique," Rech. Aeronaut. 65, 19-27 (1958).

Rev. Sci. Instrum. (1)

S. R. Sanderson, "Simple, adjustable beam splitting element for differential interferometers based on photoelastic birefringence of a prismatic bar," Rev. Sci. Instrum. 76, 113703 (2005).
[CrossRef]

Revue d'Optique (1)

M. Françon, "Interférences par double réfraction en lumière blanche," Revue d'Optique 31, 65-80 (1952).

Other (11)

G. Smeets, "Observational techniques related to differential interferometry," in Proceedings of 11th International Congress on High Speed Photography, P. J. Rolls, ed. (Chapman & Hall, 1975), pp. 283-288.

H. Oertel and H. Oertel, Jr., Optische Strömungsmesstechnik (G. Braun, 1989).

W. Merzkirch, Flow Visualization (Academic, 1987).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

J. E. Shigley and C. R. Mischke, Mechanical Engineering Design, 6th ed. (McGraw-Hill, 2001).

R. B. Heywood, Photoelasticity for Designers (Pergamon Press, 1969).

J. W. Dally and W. F. Riley, Experimental Stress Analysis, 3rd ed. (McGraw-Hill, 1991).

I. Newton, Opticks (Dover, 1952) (reprinted from 4th ed., 1730).

G. M. Carlomagno, "A Wollaston prism interferometer used as a reference beam interferometer," in Proceedings of Flow Visualization IV, Paris, 1986, C. Veret, ed. (Hemisphere, 1987), pp. 105-110.

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

S. R. Sanderson, "Shock wave interactions in hypervelocity flow," Ph.D. dissertation (California Institute of Technology, 1995).

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Figures (16)

Fig. 1
Fig. 1

Photo of a Sanderson prism loading fixture, showing dimensions r and ℓ and the dial indicator used to measure deflection Δ y .

Fig. 2
Fig. 2

Simple z-type schlieren system setup modified for laser-illuminated differential interferometry. P represents a polarizing filter.

Fig. 3
Fig. 3

Dimensional drawing of mount and loading fixture for applying a pure bending moment to a polycarbonate Sanderson prism. Many of the dimensions shown are discretionary, but it is important to maintain symmetrically equal distances from the axis of the thumbscrew to the two loading-pin and two support-pin contact points with the Sanderson prism.

Fig. 4
Fig. 4

St. Venant's effect near the loading contact point of the prism.

Fig. 5
Fig. 5

Example double image of vertical wire in test region created by a Sanderson prism (laser illumination, test section diameter = 108   mm ).

Fig. 6
Fig. 6

Beam-divergence angle ε versus image separation or overlap distance d, comparing the geometric-optics requirement with experimental Sanderson-prism results from Eq. (5).

Fig. 7
Fig. 7

Comparison of candle-plume interferograms at equivalent 3.2   arc   min beam-divergence angles and a finite-fringe setting under laser illumination: (a) Wollaston prism and (b) Sanderson prism.

Fig. 8
Fig. 8

Comparison of candle plume interferograms at equivalent 3.2   arc   min beam-divergence angles and infinite fringe setting under laser illumination: (a) Wollaston prism and (b) Sanderson prism.

Fig. 9
Fig. 9

White-light fringe pattern comparison at ε = 3.2 arc   min : (a) Wollaston prism and (b) Sanderson prism. The dark central fringe of the Newton's-ring colors is marked by a white arrow in each case.

Fig. 10
Fig. 10

White-light interferograms of a candle plume using Wollaston and Sanderson prisms at finite-fringe setting: (a) Wollaston prism at ε = 3.2   arc   min , (b) Sanderson prism at ε = 2.4   arc min , and (c) Sanderson prism at ε = 5   arc   min .

Fig. 11
Fig. 11

Z-type schlieren system modified for symmetric white-light differential interferometry with dual birefringent prisms.

Fig. 12
Fig. 12

Examples of white-light interferograms of a candle plume using the Sanderson prism at infinite-fringe setting. Image rows from top to bottom show ε = 2.9 , 4.8, and 6.7   arc   min , respectively. In each row three examples are shown of the different background colors available.

Fig. 13
Fig. 13

White-light interferograms of a candle plume using the Sanderson prism at large beam-divergence angles: (a) ε = 12 arc   min , (b) ε = 24   arc   min .

Fig. 14
Fig. 14

White-light Sanderson-prism interferograms of the shock diamonds in a 1 mm diameter supersonic air jet, ε = 13 arc   min , illustrating complete image separation in the horizontal direction. Three different choices of background-fringe color are shown.

Fig. 15
Fig. 15

White-light interferograms with Wollaston and Sanderson prisms in Penn State's 1   m aperture coincident schlieren system. Top row, candle plume; bottom row, human thermal plume and cough. (a) Wollaston prism and (b–d) Sanderson prism.

Fig. 16
Fig. 16

Pseudo-schlieren images, actually infinite-fringe differential interferograms of weak air currents rising from fingers: (a) Wollaston and (b) Sanderson prisms, both with ε = 3.2   arc   min .

Tables (1)

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Table 1 Sanderson Prism Dimensions and Aspect Ratios

Equations (7)

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ε ( C 1 + C 2 ) M z b I z z ,
M z = 24 E I z z Δ y 4 r 2 3 l 2 ,
( C 1 + C 2 ) = λ f σ ,
λ f σ = λ r f σ , r ,
ε = λ f σ 24 E Δ y b 4 r 2 3 l 2 .
ε = d f 2 .
ε max = 2 λ b f σ h S y ,

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