Abstract

We propose a multiple height-transfer interferometric technique based on concepts from both multiple wavelength interferometry and wavelength scanning interferometry. Conventional multiple wavelength interferometry requires accurate wavelength information for large step height measurement, while wavelength scanning interferometry is limited by mode-hop-free tuning range. Using the multiple reference heights, it is possible to bypass the wavelength determinations and achieve large step height measurement using relative phase changes. By applying this technique with a proposed multiple height calibration artifact, we experimentally demonstrated accuracy better than 1 micron over 100 mm in a workshop environment.

© 2011 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010 (2)

2008 (2)

2006 (1)

C. C. Aleksoff, “Multi-wavelength digital holographic metrology,” Proc. SPIE 6311, 63111D, 63111D-7 (2006).
[CrossRef]

2005 (1)

2002 (1)

S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13(9), 1382–1387 (2002).
[CrossRef]

2000 (1)

J. C. Marron and K. W. Gleichman, “Three-dimensional imaging using a tunable laser source,” Opt. Eng. 39(1), 47–51 (2000).
[CrossRef]

1999 (1)

1998 (1)

K. H. Bechstein and W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29(3), 179–182 (1998).
[CrossRef]

1984 (2)

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

Y. Y. Cheng and J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23(24), 4539–4543 (1984).
[CrossRef] [PubMed]

Aleksoff, C. C.

C. C. Aleksoff and H. Yu, “Discrete step wavemeter,” Proc. SPIE 7790, 77900H, 77900H-10 (2010).
[CrossRef]

C. C. Aleksoff, “Multi-wavelength digital holographic metrology,” Proc. SPIE 6311, 63111D, 63111D-7 (2006).
[CrossRef]

Bechstein, K. H.

K. H. Bechstein and W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29(3), 179–182 (1998).
[CrossRef]

Cheng, Y. Y.

Davies, A.

Deibel, J.

Fuchs, W.

K. H. Bechstein and W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29(3), 179–182 (1998).
[CrossRef]

Ghim, Y. S.

Gleichman, K. W.

J. C. Marron and K. W. Gleichman, “Three-dimensional imaging using a tunable laser source,” Opt. Eng. 39(1), 47–51 (2000).
[CrossRef]

Greivenkamp, J. E.

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

Howard, L.

Le Floch, S.

Lee, C. C.

S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13(9), 1382–1387 (2002).
[CrossRef]

Lévêque, S.

Lu, S. H.

S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13(9), 1382–1387 (2002).
[CrossRef]

Marron, J. C.

J. C. Marron and K. W. Gleichman, “Three-dimensional imaging using a tunable laser source,” Opt. Eng. 39(1), 47–51 (2000).
[CrossRef]

McLeod, R. R.

Moore, E. D.

Nyberg, S.

Riles, K.

Salvadé, Y.

Schuhler, N.

Stejskal, A.

Stone, J. A.

Suratkar, A.

Wyant, J. C.

Yang, H. J.

Yu, H.

C. C. Aleksoff and H. Yu, “Discrete step wavemeter,” Proc. SPIE 7790, 77900H, 77900H-10 (2010).
[CrossRef]

Appl. Opt. (4)

J. Opt. (1)

K. H. Bechstein and W. Fuchs, “Absolute interferometric distance measurements applying a variable synthetic wavelength,” J. Opt. 29(3), 179–182 (1998).
[CrossRef]

Meas. Sci. Technol. (1)

S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13(9), 1382–1387 (2002).
[CrossRef]

Opt. Eng. (2)

J. C. Marron and K. W. Gleichman, “Three-dimensional imaging using a tunable laser source,” Opt. Eng. 39(1), 47–51 (2000).
[CrossRef]

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

Opt. Express (2)

Proc. SPIE (2)

C. C. Aleksoff, “Multi-wavelength digital holographic metrology,” Proc. SPIE 6311, 63111D, 63111D-7 (2006).
[CrossRef]

C. C. Aleksoff and H. Yu, “Discrete step wavemeter,” Proc. SPIE 7790, 77900H, 77900H-10 (2010).
[CrossRef]

Other (2)

P. Hariharan, Optical interferometry (Academic Press, 2003).

A. J. Lewis, Absolute length measurement using multiple-wavelength phase-stepping interferometry (University of London, 1993).

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Figures (6)

Fig. 1
Fig. 1

Michelson set-up with reference and measurement heights

Fig. 2
Fig. 2

An example plot of power height response function. The location of 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 noise.

Fig. 3
Fig. 3

Overview of MHTIT scheme

Fig. 4
Fig. 4

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

Fig. 5
Fig. 5

Schematic of calibration system layout

Fig. 6
Fig. 6

Front view of z-gage

Tables (3)

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Table 1 Wavelength Acquisition Interval Centered at 800 nm for Several Heights

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Table 2 Stainless Steel Gage Block Measurement Results

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Table 3 Uncertainty Estimates

Equations (12)

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Φ b , n = 2 π q b , n + ϕ b , n = 4 π h b λ n
Φ s , n = 2 π ( q b , n q s , n ) + ( ϕ b , n ϕ s , n ) = 4 π h s λ n
Δ Φ s , m , n = 4 π h s ( 1 λ m 1 λ n ) = 4 π h s Λ m n
Λ m . n = λ n λ m λ n λ m
Δ Φ o , m , n Δ Φ r , m , n = h o h r
| λ m λ n | < λ m λ n 2 h Δ λ m , n
h 1 2 π q n 1 + Δ ϕ n 1 = h 2 2 π q n 2 + Δ ϕ n 2 = = h M 1 2 π q n M 1 + Δ ϕ n M 1 = h M 2 π q n M + Δ ϕ n M
h o 2 π q n + Δ ϕ n = h r e f Δ Φ n
2 π q n + Δ ϕ n = h o h r e f Δ Φ n
r ( h o ) = n = 2 N e i h o Δ Φ n h r e f + i Δ ϕ n
| r ( h o ) | 2 = | n = 2 N e i h o Δ Φ n h r e f + i Δ ϕ n | 2 = N 1 + 2 n = 2 N m > n N cos [ ( Δ Φ n Δ Φ m ) h o h r e f + Δ ϕ n Δ ϕ m ]
H = arg max ( | r ( h o ) | 2 )

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