Abstract

An analytical model is presented that accounts for the effects of self-illumination of a diffusely reflecting test article in luminescent-paint measurements. Contributions from multiple reflections of excitation and emission light are summed to infinite order in closed form. Also included are the effects of spectral leakage resulting from an imperfectly filtered source and imperfectly rejected reflected excitation light. It is shown that the conventional method of determining flow variables from the ratio of flow-on and flow-off signals is adversely affected by self-illumination and spectral leakage. An explicit solution is derived for the associated inversion problem. Sample calculations are presented.

© 1997 Optical Society of America

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References

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  1. J. Kavandi, J. Callis, M. Gouterman, G. Khalil, D. Wright, E. Green, D. Burns, and B. McLachlan, “Luminescent barometry in wind tunnels,” Rev. Sci. Instrum. 61, 3340–3347 (1990).
    [CrossRef]
  2. M. J. Morris, J. F. Donovan, J.T. Kegelman, S. D. Schwab, R. L. Levy, and R. C. Crites, “Aerodynamic applications of pressure sensitive paint,” AIAA J. 31, 419–425 (1993).
    [CrossRef]
  3. B. G. McLachlan and J. H. Bell, “Pressure-sensitive paint in aerodynamic testing,” Exp. Therm. Fluid Sci. 10, 470–485 (1995).
    [CrossRef]
  4. T. Liu, B. T. Campbell, J. P. Sullivan, J. Lafferty, and W. Yanta, “Heat transfer measurements on a waverider at Mach 10 using fluorescent paint,” J. Thermophys. Heat Transf. 9, 605–611 (1995).
    [CrossRef]
  5. G. Havener and L. A. Yates, “Visualizing the flow with CFI,” Aerosp. Am. (June 1994), p. 24.
  6. F. Grum and R. J. Becherer, Optical Radiation Measurements Volume 1: Radiometry (Academic, New York, 1979), p. 37.
  7. C. Asmail, “Bidirectional scattering distribution function (BSDF): a systematized bibliography,” J. Res. Natl. Inst. Stand. Technol. 96, 215–223 (1991).
    [CrossRef]
  8. W. H. Press, S. A. Teukolsky, W.T. Vetterling, and B. M. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge, New York, 1992).

1995 (2)

B. G. McLachlan and J. H. Bell, “Pressure-sensitive paint in aerodynamic testing,” Exp. Therm. Fluid Sci. 10, 470–485 (1995).
[CrossRef]

T. Liu, B. T. Campbell, J. P. Sullivan, J. Lafferty, and W. Yanta, “Heat transfer measurements on a waverider at Mach 10 using fluorescent paint,” J. Thermophys. Heat Transf. 9, 605–611 (1995).
[CrossRef]

1993 (1)

M. J. Morris, J. F. Donovan, J.T. Kegelman, S. D. Schwab, R. L. Levy, and R. C. Crites, “Aerodynamic applications of pressure sensitive paint,” AIAA J. 31, 419–425 (1993).
[CrossRef]

1991 (1)

C. Asmail, “Bidirectional scattering distribution function (BSDF): a systematized bibliography,” J. Res. Natl. Inst. Stand. Technol. 96, 215–223 (1991).
[CrossRef]

1990 (1)

J. Kavandi, J. Callis, M. Gouterman, G. Khalil, D. Wright, E. Green, D. Burns, and B. McLachlan, “Luminescent barometry in wind tunnels,” Rev. Sci. Instrum. 61, 3340–3347 (1990).
[CrossRef]

Asmail, C.

C. Asmail, “Bidirectional scattering distribution function (BSDF): a systematized bibliography,” J. Res. Natl. Inst. Stand. Technol. 96, 215–223 (1991).
[CrossRef]

Becherer, R. J.

F. Grum and R. J. Becherer, Optical Radiation Measurements Volume 1: Radiometry (Academic, New York, 1979), p. 37.

Bell, J. H.

B. G. McLachlan and J. H. Bell, “Pressure-sensitive paint in aerodynamic testing,” Exp. Therm. Fluid Sci. 10, 470–485 (1995).
[CrossRef]

Burns, D.

J. Kavandi, J. Callis, M. Gouterman, G. Khalil, D. Wright, E. Green, D. Burns, and B. McLachlan, “Luminescent barometry in wind tunnels,” Rev. Sci. Instrum. 61, 3340–3347 (1990).
[CrossRef]

Callis, J.

J. Kavandi, J. Callis, M. Gouterman, G. Khalil, D. Wright, E. Green, D. Burns, and B. McLachlan, “Luminescent barometry in wind tunnels,” Rev. Sci. Instrum. 61, 3340–3347 (1990).
[CrossRef]

Campbell, B. T.

T. Liu, B. T. Campbell, J. P. Sullivan, J. Lafferty, and W. Yanta, “Heat transfer measurements on a waverider at Mach 10 using fluorescent paint,” J. Thermophys. Heat Transf. 9, 605–611 (1995).
[CrossRef]

Crites, R. C.

M. J. Morris, J. F. Donovan, J.T. Kegelman, S. D. Schwab, R. L. Levy, and R. C. Crites, “Aerodynamic applications of pressure sensitive paint,” AIAA J. 31, 419–425 (1993).
[CrossRef]

Donovan, J. F.

M. J. Morris, J. F. Donovan, J.T. Kegelman, S. D. Schwab, R. L. Levy, and R. C. Crites, “Aerodynamic applications of pressure sensitive paint,” AIAA J. 31, 419–425 (1993).
[CrossRef]

Flannery, B. M.

W. H. Press, S. A. Teukolsky, W.T. Vetterling, and B. M. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge, New York, 1992).

Gouterman, M.

J. Kavandi, J. Callis, M. Gouterman, G. Khalil, D. Wright, E. Green, D. Burns, and B. McLachlan, “Luminescent barometry in wind tunnels,” Rev. Sci. Instrum. 61, 3340–3347 (1990).
[CrossRef]

Green, E.

J. Kavandi, J. Callis, M. Gouterman, G. Khalil, D. Wright, E. Green, D. Burns, and B. McLachlan, “Luminescent barometry in wind tunnels,” Rev. Sci. Instrum. 61, 3340–3347 (1990).
[CrossRef]

Grum, F.

F. Grum and R. J. Becherer, Optical Radiation Measurements Volume 1: Radiometry (Academic, New York, 1979), p. 37.

Kavandi, J.

J. Kavandi, J. Callis, M. Gouterman, G. Khalil, D. Wright, E. Green, D. Burns, and B. McLachlan, “Luminescent barometry in wind tunnels,” Rev. Sci. Instrum. 61, 3340–3347 (1990).
[CrossRef]

Kegelman, J.T.

M. J. Morris, J. F. Donovan, J.T. Kegelman, S. D. Schwab, R. L. Levy, and R. C. Crites, “Aerodynamic applications of pressure sensitive paint,” AIAA J. 31, 419–425 (1993).
[CrossRef]

Khalil, G.

J. Kavandi, J. Callis, M. Gouterman, G. Khalil, D. Wright, E. Green, D. Burns, and B. McLachlan, “Luminescent barometry in wind tunnels,” Rev. Sci. Instrum. 61, 3340–3347 (1990).
[CrossRef]

Lafferty, J.

T. Liu, B. T. Campbell, J. P. Sullivan, J. Lafferty, and W. Yanta, “Heat transfer measurements on a waverider at Mach 10 using fluorescent paint,” J. Thermophys. Heat Transf. 9, 605–611 (1995).
[CrossRef]

Levy, R. L.

M. J. Morris, J. F. Donovan, J.T. Kegelman, S. D. Schwab, R. L. Levy, and R. C. Crites, “Aerodynamic applications of pressure sensitive paint,” AIAA J. 31, 419–425 (1993).
[CrossRef]

Liu, T.

T. Liu, B. T. Campbell, J. P. Sullivan, J. Lafferty, and W. Yanta, “Heat transfer measurements on a waverider at Mach 10 using fluorescent paint,” J. Thermophys. Heat Transf. 9, 605–611 (1995).
[CrossRef]

McLachlan, B.

J. Kavandi, J. Callis, M. Gouterman, G. Khalil, D. Wright, E. Green, D. Burns, and B. McLachlan, “Luminescent barometry in wind tunnels,” Rev. Sci. Instrum. 61, 3340–3347 (1990).
[CrossRef]

McLachlan, B. G.

B. G. McLachlan and J. H. Bell, “Pressure-sensitive paint in aerodynamic testing,” Exp. Therm. Fluid Sci. 10, 470–485 (1995).
[CrossRef]

Morris, M. J.

M. J. Morris, J. F. Donovan, J.T. Kegelman, S. D. Schwab, R. L. Levy, and R. C. Crites, “Aerodynamic applications of pressure sensitive paint,” AIAA J. 31, 419–425 (1993).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W.T. Vetterling, and B. M. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge, New York, 1992).

Schwab, S. D.

M. J. Morris, J. F. Donovan, J.T. Kegelman, S. D. Schwab, R. L. Levy, and R. C. Crites, “Aerodynamic applications of pressure sensitive paint,” AIAA J. 31, 419–425 (1993).
[CrossRef]

Sullivan, J. P.

T. Liu, B. T. Campbell, J. P. Sullivan, J. Lafferty, and W. Yanta, “Heat transfer measurements on a waverider at Mach 10 using fluorescent paint,” J. Thermophys. Heat Transf. 9, 605–611 (1995).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W.T. Vetterling, and B. M. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge, New York, 1992).

Vetterling, W.T.

W. H. Press, S. A. Teukolsky, W.T. Vetterling, and B. M. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge, New York, 1992).

Wright, D.

J. Kavandi, J. Callis, M. Gouterman, G. Khalil, D. Wright, E. Green, D. Burns, and B. McLachlan, “Luminescent barometry in wind tunnels,” Rev. Sci. Instrum. 61, 3340–3347 (1990).
[CrossRef]

Yanta, W.

T. Liu, B. T. Campbell, J. P. Sullivan, J. Lafferty, and W. Yanta, “Heat transfer measurements on a waverider at Mach 10 using fluorescent paint,” J. Thermophys. Heat Transf. 9, 605–611 (1995).
[CrossRef]

AIAA J. (1)

M. J. Morris, J. F. Donovan, J.T. Kegelman, S. D. Schwab, R. L. Levy, and R. C. Crites, “Aerodynamic applications of pressure sensitive paint,” AIAA J. 31, 419–425 (1993).
[CrossRef]

Exp. Therm. Fluid Sci. (1)

B. G. McLachlan and J. H. Bell, “Pressure-sensitive paint in aerodynamic testing,” Exp. Therm. Fluid Sci. 10, 470–485 (1995).
[CrossRef]

J. Res. Natl. Inst. Stand. Technol. (1)

C. Asmail, “Bidirectional scattering distribution function (BSDF): a systematized bibliography,” J. Res. Natl. Inst. Stand. Technol. 96, 215–223 (1991).
[CrossRef]

J. Thermophys. Heat Transf. (1)

T. Liu, B. T. Campbell, J. P. Sullivan, J. Lafferty, and W. Yanta, “Heat transfer measurements on a waverider at Mach 10 using fluorescent paint,” J. Thermophys. Heat Transf. 9, 605–611 (1995).
[CrossRef]

Rev. Sci. Instrum. (1)

J. Kavandi, J. Callis, M. Gouterman, G. Khalil, D. Wright, E. Green, D. Burns, and B. McLachlan, “Luminescent barometry in wind tunnels,” Rev. Sci. Instrum. 61, 3340–3347 (1990).
[CrossRef]

Other (3)

W. H. Press, S. A. Teukolsky, W.T. Vetterling, and B. M. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge, New York, 1992).

G. Havener and L. A. Yates, “Visualizing the flow with CFI,” Aerosp. Am. (June 1994), p. 24.

F. Grum and R. J. Becherer, Optical Radiation Measurements Volume 1: Radiometry (Academic, New York, 1979), p. 37.

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Figures (7)

Fig. 1
Fig. 1

Ideal situation for luminescent-paint measurements: excitation light (blue) is converted into emission light (red) at the surface.

Fig. 2
Fig. 2

Deviation from the ideal situation as a result of spectral leakage through the source and camera filters. The dotted beams give rise to unwanted signal contributions.

Fig. 3
Fig. 3

Deviation from the ideal situation as a result of self-illumination at the emission (red) and excitation (blue) wavelengths. The dotted beam, in particular, gives rise to an unwanted signal contribution when measurements are performed on the horizontal surface. Contributions from multiple reflections are not shown.

Fig. 4
Fig. 4

Two-plate geometry used for the numerical example. The wide arrows indicate that the surface, the flow field, and the resulting shock extend infinitely in both directions. The parameter s measures the position along the cross section of the surface, with -1 ≤ s ≤ 3.

Fig. 5
Fig. 5

Assumed distributions of illumination (F) and pressure (P) on the surface from Fig. 4.

Fig. 6
Fig. 6

Calculated signals on the surface from Fig. 4, through different reflection orders M, for both flow-off (top) and flow-on (bottom) conditions.

Fig. 7
Fig. 7

Actual and reconstructed flow-on pressures on the surface from Fig. 4. Shown, in order of increasing accuracy, are the results of a conventional calculation [correcting for neither self-illumination (SI) nor spectral leakage (SL)]; a calculation that corrects for spectral leakage only; and a calculation that corrects for both self-illumination and spectral leakage.

Tables (1)

Tables Icon

Table 1 Pressure Reconstruction Errors for the Test Case from Figs. 4 and 5 as a Function of the Number of Recursions of Eq. (3.12)a

Equations (50)

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

ηP=η01+kP,
Lbluem+1xi=RblueπEbluemxi,
Lredm+1xi=ηxiπEbluemxi+RredπEredmxi.
Eλmxi=Saxi,xjLλmxjdSj,
axi, xjmax0,nˆi· xijnˆj· xjixij4,
Lλxi=m=1Lλmxi, λ=red, blue.
Sxi=KredLredxi+KblueLbluexi,
Aij1πaxi, xjΔSj,
η˜xiηxiηref,
FxiηrefπKredEblue0xi.
δsEred0Eblue0Rredηref,
δcKblueKredRblueηref.
SredmxiKredLredmxi,
SbluemxiKblue/δcLbluemxi.
Sxi=m=1Sredmxi+δcSbluemxi,
Sblue1xi=Fxi,
Sred1xi=Fxiη˜xi+δs,
Sbluem+1xi=Rbluej=1NAijSbluemxj,
Sredm+1xi=η˜xiSbluem+1xi+Rredj=1N AijSredmxj.
AλijRλAij, λ=red, blue.
m=0Aλm=I-Aλ-1Vλ,
S=SSL+VredVblueFDMη˜,
SSL=δsVred+δcVblueF.
Sxi=Fxiη˜xi.
η˜onxiSonxiSoffxi.
CF=Soff,
C=δsVred+δcVblue+VredVblue.
F=C-1Soff.
I-AredS-SSLi=VblueFiη˜i,
η˜onxi=1+I-AredSon-SoffiVblueC-1Soffi.
VblueC-1=11+δI-Ared-1I-Ared,
δδc+δs,
δc1+δ+δs1+δRblueRred.
u01-AredSoff,
uku0+Areduk-1.
Dxi1+δSonxi-Soffxi.
η˜onxi=1+Dxi-AredDiSoffxi-ui. 
η˜onxi=Sonxi-AredSoniSoffxi-AredSoffi.
η˜onxi=1+δSonxiSoffxi-δ.
Ãij=nˆi·xijnˆj·xji2xij3Δsj,
η˜s=1+kPref1+kPs,
ΔΩi=ΔSixij2nˆi·xijxij,
Δ2Pλmxi=LλmxjΔSjnˆj·xjixji ΔΩi,
ΔEλmxi=Δ2PλmxiΔSi.
ΔEλmxi=axi, xjLλmxjΔSj,
Sxi=Fxiη˜xi+δ,
η˜onxi=η˜onxi+δ1+δ.
SA=FAη˜A+βredFBη˜B1-βblue21-βred2,
η˜on,A=η˜on,A+η˜on,B-η˜on,AfAB,
fAB=βredFBFA+βredFB1.

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