Abstract

A multiple height-transfer interferometric technique was developed to increase the absolute distance measurement capability of a metrology system that uses a tunable laser. Using multiple accurately calibrated reference heights, this technique relaxes the requirement of knowing accurate wavelength information for multiple wavelength interferometry while maintaining its advantages. We present an uncertainty analysis, analyze the primary sources of uncertainties limiting the performance of this technique, and discuss how errors can be minimized. Measurement results of 3D images obtained from a variety of objects are presented. The measurement uncertainty is experimentally demonstrated to be 0.3 μm over 50 mm for two discontinuous surfaces with a confidence level of 95% in a lab environment.

© 2012 Optical Society of America

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References

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  1. J. C. Wyant, “Testing aspherics using two-wavelength holography,” Appl. Opt. 10, 2113–2118 (1971).
    [CrossRef]
  2. Y. Y. Cheng and J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
    [CrossRef]
  3. K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
    [CrossRef]
  4. P. J. de Groot, “Extending the unambiguous range of two-color interferometers,” Appl. Opt. 33, 5948–5953 (1994).
    [CrossRef]
  5. K. H. Bechstein and W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
    [CrossRef]
  6. J. A. Stone and A. Stejskal, “Absolute interferometry with a 670 nm external cavity diode laser,” Appl. Opt. 38, 5981–5994 (1999).
    [CrossRef]
  7. L. Hartmann, K. Meiners-Hagen, and A. Abou-Zeid, “An absolute distance interferometer with two external cavity diode lasers,” Meas. Sci. Technol. 19, 045307 (2008).
    [CrossRef]
  8. H. J. Yang, J. Deibel, S. Nyberg, and K. Riles, “High-precision absolute distance and vibration measurement with frequency scanned interferometry,” Appl. Opt. 44, 3937–3944 (2005).
    [CrossRef]
  9. H. Yu, C. C. Aleksoff, and J. Ni, “A multiple height-transfer interferometric technique,” Opt. Express 19, 16365–16374 (2011).
    [CrossRef]
  10. C. C. Aleksoff and H. Yu, “Discrete step wavemeter,” Proc. SPIE 7790, 77900H (2010).
    [CrossRef]
  11. C. C. Aleksoff, “Multi-wavelength digital holographic metrology,” Proc. SPIE 6311, 63111D (2006).
    [CrossRef]
  12. C. J. Walsh, “Limit to multiwavelength interferometry imposed by frequency instability of the source,” Appl. Opt. 26, 29–31 (1987).
    [CrossRef]
  13. K. Liu and M. G. Littman, “Novel geometry for single-mode scanning of tunable lasers,” Opt. Lett. 6, 117–118 (1981).
    [CrossRef]
  14. International Organization for Standardization, “Guide to the expression of uncertainty in measurement,” (ISO, Geneva, Switzerland, 1995).
  15. C. E. Towers, D. P. Towers, and J. C. Jones, “Optimum frequency selection in multifrequency interferometry,” Opt. Lett. 28, 887–889 (2003).
    [CrossRef]
  16. K. Falaggis, D. P. Towers, and C. E. Towers, “Multiwavelength interferometry: extended range metrology,” Opt. Lett. 34, 950–952 (2009).
    [CrossRef]
  17. K. Falaggis, D. P. Towers, and C. E. Towers, “Method of excess fractions with application to absolute distance metrology: theoretical analysis,” Appl. Opt. 50, 5484–5498 (2011).
    [CrossRef]
  18. K. P. Birch and M. J. Downs, “Correction to the updated Edlen equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
    [CrossRef]
  19. K. Hibino, B. F. D. Oreb, I. Farrant, and K. G. Larkin, “Phase shifting for nonsinusoidal waveforms with phase-shift errors,” J. Opt. Soc. Am. A 12, 761–768 (1995).
    [CrossRef]
  20. D. W. Phillion, “General methods for generating phase-shifting interferometry algorithms,” Appl. Opt. 36, 8098–8115 (1997).
    [CrossRef]
  21. K. A. Goldberg and J. Bokor, “Fourier-transform method of phase-shift determination,” Appl. Opt. 40, 2886–2894 (2001).
    [CrossRef]
  22. J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984).
  23. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]

2011 (2)

2010 (1)

C. C. Aleksoff and H. Yu, “Discrete step wavemeter,” Proc. SPIE 7790, 77900H (2010).
[CrossRef]

2009 (1)

2008 (1)

L. Hartmann, K. Meiners-Hagen, and A. Abou-Zeid, “An absolute distance interferometer with two external cavity diode lasers,” Meas. Sci. Technol. 19, 045307 (2008).
[CrossRef]

2006 (1)

C. C. Aleksoff, “Multi-wavelength digital holographic metrology,” Proc. SPIE 6311, 63111D (2006).
[CrossRef]

2005 (1)

2003 (1)

2001 (1)

1999 (1)

1998 (1)

K. H. Bechstein and W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

1997 (1)

1995 (1)

1994 (2)

P. J. de Groot, “Extending the unambiguous range of two-color interferometers,” Appl. Opt. 33, 5948–5953 (1994).
[CrossRef]

K. P. Birch and M. J. Downs, “Correction to the updated Edlen equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

1987 (2)

1984 (2)

Y. Y. Cheng and J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
[CrossRef]

J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984).

1982 (1)

1981 (1)

1971 (1)

Abou-Zeid, A.

L. Hartmann, K. Meiners-Hagen, and A. Abou-Zeid, “An absolute distance interferometer with two external cavity diode lasers,” Meas. Sci. Technol. 19, 045307 (2008).
[CrossRef]

Aleksoff, C. C.

H. Yu, C. C. Aleksoff, and J. Ni, “A multiple height-transfer interferometric technique,” Opt. Express 19, 16365–16374 (2011).
[CrossRef]

C. C. Aleksoff and H. Yu, “Discrete step wavemeter,” Proc. SPIE 7790, 77900H (2010).
[CrossRef]

C. C. Aleksoff, “Multi-wavelength digital holographic metrology,” Proc. SPIE 6311, 63111D (2006).
[CrossRef]

Bechstein, K. H.

K. H. Bechstein and W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

Birch, K. P.

K. P. Birch and M. J. Downs, “Correction to the updated Edlen equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Bokor, J.

Cheng, Y. Y.

Creath, K.

de Groot, P. J.

Deibel, J.

Downs, M. J.

K. P. Birch and M. J. Downs, “Correction to the updated Edlen equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Falaggis, K.

Farrant, I.

Fuchs, W.

K. H. Bechstein and W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

Goldberg, K. A.

Greivenkamp, J. E.

J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984).

Hartmann, L.

L. Hartmann, K. Meiners-Hagen, and A. Abou-Zeid, “An absolute distance interferometer with two external cavity diode lasers,” Meas. Sci. Technol. 19, 045307 (2008).
[CrossRef]

Hibino, K.

Ina, H.

Jones, J. C.

Kobayashi, S.

Larkin, K. G.

Littman, M. G.

Liu, K.

Meiners-Hagen, K.

L. Hartmann, K. Meiners-Hagen, and A. Abou-Zeid, “An absolute distance interferometer with two external cavity diode lasers,” Meas. Sci. Technol. 19, 045307 (2008).
[CrossRef]

Ni, J.

Nyberg, S.

Oreb, B. F. D.

Phillion, D. W.

Riles, K.

Stejskal, A.

Stone, J. A.

Takeda, M.

Towers, C. E.

Towers, D. P.

Walsh, C. J.

Wyant, J. C.

Yang, H. J.

Yu, H.

Appl. Opt. (10)

J. Opt. (1)

K. H. Bechstein and W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29, 179–182 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Meas. Sci. Technol. (1)

L. Hartmann, K. Meiners-Hagen, and A. Abou-Zeid, “An absolute distance interferometer with two external cavity diode lasers,” Meas. Sci. Technol. 19, 045307 (2008).
[CrossRef]

Metrologia (1)

K. P. Birch and M. J. Downs, “Correction to the updated Edlen equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Opt. Eng. (1)

J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984).

Opt. Express (1)

Opt. Lett. (3)

Proc. SPIE (2)

C. C. Aleksoff and H. Yu, “Discrete step wavemeter,” Proc. SPIE 7790, 77900H (2010).
[CrossRef]

C. C. Aleksoff, “Multi-wavelength digital holographic metrology,” Proc. SPIE 6311, 63111D (2006).
[CrossRef]

Other (1)

International Organization for Standardization, “Guide to the expression of uncertainty in measurement,” (ISO, Geneva, Switzerland, 1995).

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Figures (13)

Fig. 1.
Fig. 1.

An example plot of power height response function. The location of the main peak corresponds to the object height of 25.4 mm, and the minor peaks are influenced by the selection of multiple wavelengths and system noises.

Fig. 2.
Fig. 2.

Illustration of the ShaPix holographic metrology system and insertion of the reference array using excess light and pixels.

Fig. 3.
Fig. 3.

The measurement of an automotive valve body (a) photograph and (b) 3D result.

Fig. 4.
Fig. 4.

The measurement of an automotive pump housing (a) photograph and (b) 3D result.

Fig. 5.
Fig. 5.

Measurements of a 50.8 mm step height.

Fig. 6.
Fig. 6.

Measured variation of the interference phase of reference interferometer.

Fig. 7.
Fig. 7.

Layout of multiple reference heights.

Fig. 8.
Fig. 8.

Simulation results, (a) standard deviation and (b) outlier rate.

Fig. 9.
Fig. 9.

Near common optical path configuration.

Fig. 10.
Fig. 10.

Fourier fringe analysis on a simulated retroreflector surface: (a) simulated fringe pattern; (b) the log display of FT magnitude; (c) the phase map of FT.

Fig. 11.
Fig. 11.

Simulated fringe patterns in five different situations: (a) rotated, high modulation, no filter; (b) nonrotated, low modulation, no filter; (c) rotated, low modulation, no filter; (d) rotated, low modulation, Gaussian filter; (e) rotated, low modulation, Gaussian filter.

Fig. 12.
Fig. 12.

Alignment error geometry.

Fig. 13.
Fig. 13.

Schematic of a first-order rotation invariant module.

Tables (1)

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Table 1. OPDs of Four Array Designs

Equations (24)

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hmeas=hrefΔΦmeasΔΦref.
ΔΦ=4πhref(1λm1λn)=4πhrefΛmn,
h12πqn1+Δϕn1=h22πqn2+Δϕn2==hM12πqnM1+ΔϕnM1=hM2πqnM+ΔϕnM,
2πqn+Δϕn=hmeashrefΔΦn,
r(ho)=n=2NeihoΔΦnhref+iΔϕn.
|r(ho)|2=|n=2NeihoΔΦnhref+iΔϕn|2=N1+2n=2Nm>nNcos[(ΔΦnΔΦm)hohref+ΔϕnΔϕm],
H=argmax(|r(ho)|2).
U(hm)={i[hmXi·U(Xi)]2}1/2=hm[(U(hr)hr)2+(U(ΔΦr)ΔΦr)2+(U(ΔΦm)ΔΦm)2]1/2,
U(hm)=hm[(U(hr)hr)2+(U(ΔΦr)4πhrΛ)2+(U(ΔΦm)4πhmΛ)2]1/2=[hm2(U(hr)hr)2+hm2(U(ΔΦr)4πhrΔλλ2)2+(U(ΔΦm)4πΔλλ2)2]1/2,
εϕ=Δλ+ελλ24πh1Δλλ24πh1=ελλ24πh1.
h1λ24ελ.
OPD=OPL1OPL2=n2(L1+ΔL)n1L1=ΔnL1+n2ΔL,
H(x,y)=xsin(αx)+ysin(αy)+Ho,
In=IO+IR+2IOIRcos{4πλH(x,y)+Δn},
Sn=[InIOIR]W(x,y),
sn={IOIR{w[fx1λsin(αx),fy1λsin(αy)]exp(4πiλH0)exp(iΔn)}+IOIR{w[fx+1λlsin(αx),fy+1λlsin(αy)]exp(4πiλH0)exp(iΔn)}},
Δh=h(1cosθ)+dsinθ,hθ2/2+θd.
hx=Bx(A1x+A2x)/2,
R=[cosθsinθ0sinθcosθ0001],T1=[10xc01yc001],T2=[10xc01yc001].
T2RT1=[cosθsinθxcxccosθ+ycsinθsinθcosθycyccosθxcsinθ001].
T2RT1A1={xcosθ+xcxccosθdsinθ+ycsinθ,xcosθ+yc+dcosθyccosθxcsinθ,1}T2RT1A2={xcosθ+xcxccosθ+dsinθ+ycsinθ,xcosθ+ycdcosθyccosθxcsinθ,1}T2RT1B={xc+hcosθxccosθ+ycsinθ,ycyccosθ+hsinθxcsinθ,1}.
(T2RT1B(T2RT1A2+T2RT1A1)/2){1,0,0},=xc+hcosθxccosθ+ycsinθ+(2xc+2xccosθ2ycsinθ)/2,=hcosθ.
d1d2=mn,
hG=BxnA1x+mA2xm+n.

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