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Design, alignment, and calibration of a focused laser differential interferometer

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Abstract

Methods are presented for systematic selection of optical components and dimensions for the design of both single- and double-focused laser differential interferometers (FLDIs). Step-by-step instructions for the assembly and alignment of each FLDI component are given, including detailed figures of the interferometer fringe behavior, as the required infinite-fringe configuration is approached. Calibration and data post-processing techniques are provided in order to obtain quantitative signals from the FLDI.

© 2021 Optical Society of America

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References

  • View by:

  1. G. Smeets and A. George, “Laser-differential interferometer applications in gas dynamics,” Tech. Rep. 28/73 (French-German Research Institute of Saint-Louis, 1973).
  2. N. J. Parziale, J. E. Shepherd, and H. G. Hornung, “Differential interferometric measurement of instability in a hypervelocity boundary layer,” AIAA J. 51, 750–754 (2013).
    [Crossref]
  3. G. S. Settles and M. R. Fulghum, “The focusing laser differential interferometer, an instrument for localized turbulence measurements in refractive flows,” J. Fluids Eng. 138, 101402 (2016).
    [Crossref]
  4. P. W. Milonni and J. H. Eberly, Laser Physics (Wiley, 2010).
  5. R. A. Soref and D. H. McMahon, “Optical design of Wollaston-prism digital light deflectors,” Appl. Opt. 5, 425–434 (1966).
    [Crossref]
  6. B. F. Bathel, J. M. Weisberger, G. C. Herring, R. A. King, S. B. Jones, R. E. Kennedy, and S. J. Laurence, “Two-point, parallel-beam focused laser differential interferometry with a Nomarski prism,” Appl. Opt. 59, 244–252 (2020).
    [Crossref]
  7. B. E. Schmidt and J. E. Shepherd, “Analysis of focused laser differential interferometry,” Appl. Opt. 54, 8459–8472 (2015).
    [Crossref]
  8. J. M. Lawson, M. C. Neet, I. J. Grossman, and J. M. Austin, “Static and dynamic characterization of a focused laser differential interferometer,” Exp. Fluids 61, 187 (2020).
    [Crossref]

2020 (2)

B. F. Bathel, J. M. Weisberger, G. C. Herring, R. A. King, S. B. Jones, R. E. Kennedy, and S. J. Laurence, “Two-point, parallel-beam focused laser differential interferometry with a Nomarski prism,” Appl. Opt. 59, 244–252 (2020).
[Crossref]

J. M. Lawson, M. C. Neet, I. J. Grossman, and J. M. Austin, “Static and dynamic characterization of a focused laser differential interferometer,” Exp. Fluids 61, 187 (2020).
[Crossref]

2016 (1)

G. S. Settles and M. R. Fulghum, “The focusing laser differential interferometer, an instrument for localized turbulence measurements in refractive flows,” J. Fluids Eng. 138, 101402 (2016).
[Crossref]

2015 (1)

2013 (1)

N. J. Parziale, J. E. Shepherd, and H. G. Hornung, “Differential interferometric measurement of instability in a hypervelocity boundary layer,” AIAA J. 51, 750–754 (2013).
[Crossref]

1966 (1)

Austin, J. M.

J. M. Lawson, M. C. Neet, I. J. Grossman, and J. M. Austin, “Static and dynamic characterization of a focused laser differential interferometer,” Exp. Fluids 61, 187 (2020).
[Crossref]

Bathel, B. F.

Eberly, J. H.

P. W. Milonni and J. H. Eberly, Laser Physics (Wiley, 2010).

Fulghum, M. R.

G. S. Settles and M. R. Fulghum, “The focusing laser differential interferometer, an instrument for localized turbulence measurements in refractive flows,” J. Fluids Eng. 138, 101402 (2016).
[Crossref]

George, A.

G. Smeets and A. George, “Laser-differential interferometer applications in gas dynamics,” Tech. Rep. 28/73 (French-German Research Institute of Saint-Louis, 1973).

Grossman, I. J.

J. M. Lawson, M. C. Neet, I. J. Grossman, and J. M. Austin, “Static and dynamic characterization of a focused laser differential interferometer,” Exp. Fluids 61, 187 (2020).
[Crossref]

Herring, G. C.

Hornung, H. G.

N. J. Parziale, J. E. Shepherd, and H. G. Hornung, “Differential interferometric measurement of instability in a hypervelocity boundary layer,” AIAA J. 51, 750–754 (2013).
[Crossref]

Jones, S. B.

Kennedy, R. E.

King, R. A.

Laurence, S. J.

Lawson, J. M.

J. M. Lawson, M. C. Neet, I. J. Grossman, and J. M. Austin, “Static and dynamic characterization of a focused laser differential interferometer,” Exp. Fluids 61, 187 (2020).
[Crossref]

McMahon, D. H.

Milonni, P. W.

P. W. Milonni and J. H. Eberly, Laser Physics (Wiley, 2010).

Neet, M. C.

J. M. Lawson, M. C. Neet, I. J. Grossman, and J. M. Austin, “Static and dynamic characterization of a focused laser differential interferometer,” Exp. Fluids 61, 187 (2020).
[Crossref]

Parziale, N. J.

N. J. Parziale, J. E. Shepherd, and H. G. Hornung, “Differential interferometric measurement of instability in a hypervelocity boundary layer,” AIAA J. 51, 750–754 (2013).
[Crossref]

Schmidt, B. E.

Settles, G. S.

G. S. Settles and M. R. Fulghum, “The focusing laser differential interferometer, an instrument for localized turbulence measurements in refractive flows,” J. Fluids Eng. 138, 101402 (2016).
[Crossref]

Shepherd, J. E.

B. E. Schmidt and J. E. Shepherd, “Analysis of focused laser differential interferometry,” Appl. Opt. 54, 8459–8472 (2015).
[Crossref]

N. J. Parziale, J. E. Shepherd, and H. G. Hornung, “Differential interferometric measurement of instability in a hypervelocity boundary layer,” AIAA J. 51, 750–754 (2013).
[Crossref]

Smeets, G.

G. Smeets and A. George, “Laser-differential interferometer applications in gas dynamics,” Tech. Rep. 28/73 (French-German Research Institute of Saint-Louis, 1973).

Soref, R. A.

Weisberger, J. M.

AIAA J. (1)

N. J. Parziale, J. E. Shepherd, and H. G. Hornung, “Differential interferometric measurement of instability in a hypervelocity boundary layer,” AIAA J. 51, 750–754 (2013).
[Crossref]

Appl. Opt. (3)

Exp. Fluids (1)

J. M. Lawson, M. C. Neet, I. J. Grossman, and J. M. Austin, “Static and dynamic characterization of a focused laser differential interferometer,” Exp. Fluids 61, 187 (2020).
[Crossref]

J. Fluids Eng. (1)

G. S. Settles and M. R. Fulghum, “The focusing laser differential interferometer, an instrument for localized turbulence measurements in refractive flows,” J. Fluids Eng. 138, 101402 (2016).
[Crossref]

Other (2)

P. W. Milonni and J. H. Eberly, Laser Physics (Wiley, 2010).

G. Smeets and A. George, “Laser-differential interferometer applications in gas dynamics,” Tech. Rep. 28/73 (French-German Research Institute of Saint-Louis, 1973).

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)

Fig. 1.
Fig. 1. FLDI schematic with component annotations in boldface. ${\textbf L}$ = laser, ${\textbf B}$ = beam waist, ${\textbf D}$ = diverging lens, ${{\textbf P}_{{\textbf 1}}}$ = quarter-wave plate, ${\textbf W} ``{{\textbf P}_{\textbf i}}$ = Wollaston prisms, ${{\textbf F}_{\textbf i}}$ = focusing lenses, ${{\textbf P}_{{\textbf 2}}}$ = linear polarizer, ${\textbf{PD}}$ = photodetector. ${{ S }_{i}}$ are dimensions. Reprinted and modified with permission from Springer Nature Customer Service Centre GmbH: Springer Verlag [8], 2020.
Fig. 2.
Fig. 2. DFLDI pitch-side principal rays for incorrect (top) and correct (bottom) primary Wollaston prism (${\textbf W}{{\textbf P}_{\textbf A}}$) positioning. In the correct configuration, all four rays are parallel in the test section. Note the transverse ($x$) scale is exaggerated.
Fig. 3.
Fig. 3. Schematic of DFLDI pitch-side optics conceptualized as two optical subsystems for application of ray-tracing matrix analysis.
Fig. 4.
Fig. 4. Fringe pattern obtained by translating receiving prism/polarizer pair along beam path ($z$ direction).
Fig. 5.
Fig. 5. Curving of single fringe near the infinite fringe alignment location.
Fig. 6.
Fig. 6. Effect of rotating Wollaston prism on fringes.

Equations (18)

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q f = A q n + B C q n + D .
M = M 5 M 4 M 3 M 2 M 1 = [ 1 S 2 0 1 ] [ 1 0 1 / f 2 1 ] [ 1 S 1 0 1 ] [ 1 0 1 / f 1 1 ] [ 1 S 4 0 1 ] = [ A B C D ] .
q ( z n ) = [ 1 R ( z n ) + i λ L π w 2 ( z n ) ] 1 .
Δ x = 2 S 3 tan ( θ 2 ) S 3 θ .
r [ r ϕ ] .
r out = M i ( r in ± r WP ) .
r WP [ 0 θ / 2 ] .
M i [ 1 d 2 i f i d 1 i d 1 i d 2 i f i + d 2 i 1 f i d 1 i f i + 1 ] .
r out a,b = M B ( ( 1 ) a M B r W P A + ( 1 ) b r W P B ) a , b { 0 , 1 } .
1 2 { 1 f B ( d 1 A d 1 A d 2 A f A + d 2 A ) θ A + ( 1 d 1 B f B ) × [ ( 1 d 1 A f A ) θ A + θ B ] } = 0.
F f A f B , Θ θ A θ B , X d 1 A f A , Y d 1 B f B , K d 1 B + d 2 A f B .
Y = Θ ( K F 1 ) X + [ 1 + Θ ( 1 K ) ] .
d 1 A = f A X = f A K 1 K 1 F .
Δ x 1 = | r o u t 1 , 1 r o u t 2 , 1 | = | r o u t 1 , 2 r o u t 2 , 2 | ,
Δ x 2 = | r o u t 1 , 1 r o u t 1 , 2 | = | r o u t 2 , 1 r o u t 2 , 2 | .
Δ x 1 = [ ( d 1 A d 1 A d 2 A f A + d 2 A ) ( d 2 B f B 1 ) ( d 1 B d 1 B d 2 B f B + d 2 B ) ( d 1 A f A 1 ) ] θ A .
Δ x 2 = 2 f B tan ( θ B 2 ) f B θ B .
V = A sin ( Δ Φ Δ Φ 0 ) + D ,

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