Abstract

A special configuration of white-light scanning interferometer is described for measuring the absolute air gap thickness between two planar plates brought into close proximity. The measured gap is not located in any interference arm of the interferometer, but acts as an amplitude-and-phase modulator of the light source. Compared with the common white-light interferometer our approach avoids the influence of the chromatic dispersion of the planar plates on the gap thickness quantification. It covers a large measurement range of from approximate contact to tens of microns with a high resolution of 0.1 nm. Detailed analytical models are presented and signal-processing algorithms based on convolution and correlation techniques are developed. Practical measurements are carried out and the experimental results match well with the analysis and simulation. Short-time and long-time repeatabilities are both tested to prove the high performance of our method.

© 2009 Optical Society of America

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2008 (2)

J. M. Li, C. Liu, X. D. Dai, H. H. Chen, Y. Liang, H. L. Sun, H. Tian, and X. P. Ding, "PMMA microfluidic devices with three-dimensional features for blood cell filtration," J. Micromech. Microeng. 18, 095021 (2008).
[CrossRef]

J. Zhang, Z. H. Lu, and L. J. Wang, "Precision refractive index measurements of air, N2, O2, Ar, and CO2 with a frequency comb," Appl. Opt. 3143-3151 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (4)

C. Ionescu-Zanetti, J. T. Nevill, D. Di Carlo, K. H. Jeong, and L. P. Lee, "Nanogap capacitors: sensitivity to sample permittivity changes," J. Appl. Phys. 99, 24305 (2006).
[CrossRef]

V. Shilpiekandula, "Progress through Mechanics: Small-scale Gaps," Mech. 35, 3-6 (2006).

A. Courteville, R. Wilhelm, and F. Garcia, "A novel, low coherence fibre optic interferometer for position and thickness measurements with unattained accuracy," Proc. of SPIE  6189, 618918 (2006).
[CrossRef]

P. Hlubina, D. Ciprian, J. Lunaek, and M. lesnak, "Thickness of SiO2 thin film on silicon wafer measured by dispersive white-light spectral interferometry,"Appl. Phys. B 84, 511-516 (2006).
[CrossRef]

2005 (3)

A. A. Yu, T. A. Savas, G. S. Taylor, A. Guiseppe-Elie, H. I. Smith, and F. Stellacci, "Supramolecular nanostamping: Using DNA as movable type," Nano Lett. 5, 1061-1064 (2005).
[CrossRef] [PubMed]

G. W. Meindersma, C. M. Guijt, and A. B. De Haan, "Water Recycling and Desalination by Air Gap Membrane Distillation," Environ. Prog. 24, 434-44 (2005).
[CrossRef]

Y. Yasuno, S. Makita, M. Itoh, and T. Yatagai, "Profilometry with line-field Fourier-domain interferometry," Opt. Express 13, 695-701 (2005).
[CrossRef] [PubMed]

2004 (1)

P. Maddaloni, G. Coppola, P. D. Natale, S. D. Nicola, P. Ferraro, M. Gioffré, and M. Iodice, "Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer," IEEE Photonics Technol. Lett. 16, 1349-1351 (2004).
[CrossRef]

2003 (1)

2002 (1)

D. Clifton, A. R. Mount, G. M. Alder, and D. Jardine, "Ultrasonic measurement of the inter-electrode gap in electrochemical machining," Int. J. Mach. Tools Manuf. 42, 1259-1267 (2002).
[CrossRef]

2000 (1)

1999 (1)

E. E. Moon, P. N. Everett, M. W. Meinhold, M. K. Mondol, and H. I. Smith, "Novel mask-wafer gap measurement scheme with nanometer-level detectivity," J. Vac. Sci. Technol. B 17, 2698-2702 (1999).
[CrossRef]

1997 (1)

A. Dhinojwala and S. Granick, "Micron-gap rheo-optics with parallel plates," J. Chem. Phys. 107, 8664-8667 (1997).
[CrossRef]

1996 (2)

E. E. Moon, P. N. Everett, K. Rhee, and H. I. Smith, "Simultaneous measurement of gap and superposition in a precision aligner for x-ray nanolithography," J. Vac. Sci. Technol. B 14, 3969-3973 (1996).
[CrossRef]

U. Schnell, R. Dandliker, and S. Gray, "Dispersive white-light interferometry for absolute distance measurement with dielectric multilayer systems on the target," Opt. Lett. 21, 528-530 (1996).
[CrossRef] [PubMed]

1994 (1)

B. Karp and G. Adam, "Small gap width measurement with a finite X-ray source", NDT&E International  27, 21-25 (1994).
[CrossRef]

1983 (1)

D. C. Flanders and T. M. Lyszcarz, "A precision wide-range optical gap measurement technique," J. Vac. Sci. Technol. B 1, 1196-1199 (1983).
[CrossRef]

1972 (1)

P. A. Flournoy, R. W. McClure, and G. Wyntjes, "White-Light Interferometric Thickness Gauge," App. Opt. 11, 1907-1915 (1972).
[CrossRef]

1969 (1)

S. E. EVLASOV, "Evaluating the quality of optical surfaces by the width of interference fringes," Meas. Tech.  12, 942-943 (1969).
[CrossRef]

Adam, G.

B. Karp and G. Adam, "Small gap width measurement with a finite X-ray source", NDT&E International  27, 21-25 (1994).
[CrossRef]

Alder, G. M.

D. Clifton, A. R. Mount, G. M. Alder, and D. Jardine, "Ultrasonic measurement of the inter-electrode gap in electrochemical machining," Int. J. Mach. Tools Manuf. 42, 1259-1267 (2002).
[CrossRef]

Bae, J. H.

Chen, H. H.

J. M. Li, C. Liu, X. D. Dai, H. H. Chen, Y. Liang, H. L. Sun, H. Tian, and X. P. Ding, "PMMA microfluidic devices with three-dimensional features for blood cell filtration," J. Micromech. Microeng. 18, 095021 (2008).
[CrossRef]

Ciprian, D.

P. Hlubina, D. Ciprian, J. Lunaek, and M. lesnak, "Thickness of SiO2 thin film on silicon wafer measured by dispersive white-light spectral interferometry,"Appl. Phys. B 84, 511-516 (2006).
[CrossRef]

Clifton, D.

D. Clifton, A. R. Mount, G. M. Alder, and D. Jardine, "Ultrasonic measurement of the inter-electrode gap in electrochemical machining," Int. J. Mach. Tools Manuf. 42, 1259-1267 (2002).
[CrossRef]

Coppola, G.

P. Maddaloni, G. Coppola, P. D. Natale, S. D. Nicola, P. Ferraro, M. Gioffré, and M. Iodice, "Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer," IEEE Photonics Technol. Lett. 16, 1349-1351 (2004).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, and S. D. Nicola, "Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer," Appl. Opt.  42, 3882-3887 (2003).
[CrossRef] [PubMed]

Courteville, A.

A. Courteville, R. Wilhelm, and F. Garcia, "A novel, low coherence fibre optic interferometer for position and thickness measurements with unattained accuracy," Proc. of SPIE  6189, 618918 (2006).
[CrossRef]

Dai, X. D.

J. M. Li, C. Liu, X. D. Dai, H. H. Chen, Y. Liang, H. L. Sun, H. Tian, and X. P. Ding, "PMMA microfluidic devices with three-dimensional features for blood cell filtration," J. Micromech. Microeng. 18, 095021 (2008).
[CrossRef]

Dandliker, R.

De Haan, A. B.

G. W. Meindersma, C. M. Guijt, and A. B. De Haan, "Water Recycling and Desalination by Air Gap Membrane Distillation," Environ. Prog. 24, 434-44 (2005).
[CrossRef]

Dhinojwala, A.

A. Dhinojwala and S. Granick, "Micron-gap rheo-optics with parallel plates," J. Chem. Phys. 107, 8664-8667 (1997).
[CrossRef]

Di Carlo, D.

C. Ionescu-Zanetti, J. T. Nevill, D. Di Carlo, K. H. Jeong, and L. P. Lee, "Nanogap capacitors: sensitivity to sample permittivity changes," J. Appl. Phys. 99, 24305 (2006).
[CrossRef]

Ding, X. P.

J. M. Li, C. Liu, X. D. Dai, H. H. Chen, Y. Liang, H. L. Sun, H. Tian, and X. P. Ding, "PMMA microfluidic devices with three-dimensional features for blood cell filtration," J. Micromech. Microeng. 18, 095021 (2008).
[CrossRef]

Everett, P. N.

E. E. Moon, P. N. Everett, M. W. Meinhold, M. K. Mondol, and H. I. Smith, "Novel mask-wafer gap measurement scheme with nanometer-level detectivity," J. Vac. Sci. Technol. B 17, 2698-2702 (1999).
[CrossRef]

E. E. Moon, P. N. Everett, K. Rhee, and H. I. Smith, "Simultaneous measurement of gap and superposition in a precision aligner for x-ray nanolithography," J. Vac. Sci. Technol. B 14, 3969-3973 (1996).
[CrossRef]

Ferraro, P.

P. Maddaloni, G. Coppola, P. D. Natale, S. D. Nicola, P. Ferraro, M. Gioffré, and M. Iodice, "Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer," IEEE Photonics Technol. Lett. 16, 1349-1351 (2004).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, and S. D. Nicola, "Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer," Appl. Opt.  42, 3882-3887 (2003).
[CrossRef] [PubMed]

Flanders, D. C.

D. C. Flanders and T. M. Lyszcarz, "A precision wide-range optical gap measurement technique," J. Vac. Sci. Technol. B 1, 1196-1199 (1983).
[CrossRef]

Flournoy, P. A.

P. A. Flournoy, R. W. McClure, and G. Wyntjes, "White-Light Interferometric Thickness Gauge," App. Opt. 11, 1907-1915 (1972).
[CrossRef]

Garcia, F.

A. Courteville, R. Wilhelm, and F. Garcia, "A novel, low coherence fibre optic interferometer for position and thickness measurements with unattained accuracy," Proc. of SPIE  6189, 618918 (2006).
[CrossRef]

Gioffré, M.

P. Maddaloni, G. Coppola, P. D. Natale, S. D. Nicola, P. Ferraro, M. Gioffré, and M. Iodice, "Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer," IEEE Photonics Technol. Lett. 16, 1349-1351 (2004).
[CrossRef]

Granick, S.

A. Dhinojwala and S. Granick, "Micron-gap rheo-optics with parallel plates," J. Chem. Phys. 107, 8664-8667 (1997).
[CrossRef]

Gray, S.

Guijt, C. M.

G. W. Meindersma, C. M. Guijt, and A. B. De Haan, "Water Recycling and Desalination by Air Gap Membrane Distillation," Environ. Prog. 24, 434-44 (2005).
[CrossRef]

Guiseppe-Elie, A.

A. A. Yu, T. A. Savas, G. S. Taylor, A. Guiseppe-Elie, H. I. Smith, and F. Stellacci, "Supramolecular nanostamping: Using DNA as movable type," Nano Lett. 5, 1061-1064 (2005).
[CrossRef] [PubMed]

Hlubina, P.

P. Hlubina, D. Ciprian, J. Lunaek, and M. lesnak, "Thickness of SiO2 thin film on silicon wafer measured by dispersive white-light spectral interferometry,"Appl. Phys. B 84, 511-516 (2006).
[CrossRef]

Iodice, M.

P. Maddaloni, G. Coppola, P. D. Natale, S. D. Nicola, P. Ferraro, M. Gioffré, and M. Iodice, "Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer," IEEE Photonics Technol. Lett. 16, 1349-1351 (2004).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, and S. D. Nicola, "Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer," Appl. Opt.  42, 3882-3887 (2003).
[CrossRef] [PubMed]

Ionescu-Zanetti, C.

C. Ionescu-Zanetti, J. T. Nevill, D. Di Carlo, K. H. Jeong, and L. P. Lee, "Nanogap capacitors: sensitivity to sample permittivity changes," J. Appl. Phys. 99, 24305 (2006).
[CrossRef]

Itoh, M.

Jardine, D.

D. Clifton, A. R. Mount, G. M. Alder, and D. Jardine, "Ultrasonic measurement of the inter-electrode gap in electrochemical machining," Int. J. Mach. Tools Manuf. 42, 1259-1267 (2002).
[CrossRef]

Jeong, K. H.

C. Ionescu-Zanetti, J. T. Nevill, D. Di Carlo, K. H. Jeong, and L. P. Lee, "Nanogap capacitors: sensitivity to sample permittivity changes," J. Appl. Phys. 99, 24305 (2006).
[CrossRef]

Karp, B.

B. Karp and G. Adam, "Small gap width measurement with a finite X-ray source", NDT&E International  27, 21-25 (1994).
[CrossRef]

Kim, J. K.

Kim, M. S.

Lee, L. P.

C. Ionescu-Zanetti, J. T. Nevill, D. Di Carlo, K. H. Jeong, and L. P. Lee, "Nanogap capacitors: sensitivity to sample permittivity changes," J. Appl. Phys. 99, 24305 (2006).
[CrossRef]

Li, J. M.

J. M. Li, C. Liu, X. D. Dai, H. H. Chen, Y. Liang, H. L. Sun, H. Tian, and X. P. Ding, "PMMA microfluidic devices with three-dimensional features for blood cell filtration," J. Micromech. Microeng. 18, 095021 (2008).
[CrossRef]

Liang, Y.

J. M. Li, C. Liu, X. D. Dai, H. H. Chen, Y. Liang, H. L. Sun, H. Tian, and X. P. Ding, "PMMA microfluidic devices with three-dimensional features for blood cell filtration," J. Micromech. Microeng. 18, 095021 (2008).
[CrossRef]

Liu, C.

J. M. Li, C. Liu, X. D. Dai, H. H. Chen, Y. Liang, H. L. Sun, H. Tian, and X. P. Ding, "PMMA microfluidic devices with three-dimensional features for blood cell filtration," J. Micromech. Microeng. 18, 095021 (2008).
[CrossRef]

Lu, Z. H.

J. Zhang, Z. H. Lu, and L. J. Wang, "Precision refractive index measurements of air, N2, O2, Ar, and CO2 with a frequency comb," Appl. Opt. 3143-3151 (2008).
[CrossRef] [PubMed]

Lunaek, J.

P. Hlubina, D. Ciprian, J. Lunaek, and M. lesnak, "Thickness of SiO2 thin film on silicon wafer measured by dispersive white-light spectral interferometry,"Appl. Phys. B 84, 511-516 (2006).
[CrossRef]

Lyszcarz, T. M.

D. C. Flanders and T. M. Lyszcarz, "A precision wide-range optical gap measurement technique," J. Vac. Sci. Technol. B 1, 1196-1199 (1983).
[CrossRef]

Maddaloni, P.

P. Maddaloni, G. Coppola, P. D. Natale, S. D. Nicola, P. Ferraro, M. Gioffré, and M. Iodice, "Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer," IEEE Photonics Technol. Lett. 16, 1349-1351 (2004).
[CrossRef]

Makita, S.

McClure, R. W.

P. A. Flournoy, R. W. McClure, and G. Wyntjes, "White-Light Interferometric Thickness Gauge," App. Opt. 11, 1907-1915 (1972).
[CrossRef]

Meindersma, G. W.

G. W. Meindersma, C. M. Guijt, and A. B. De Haan, "Water Recycling and Desalination by Air Gap Membrane Distillation," Environ. Prog. 24, 434-44 (2005).
[CrossRef]

Meinhold, M. W.

E. E. Moon, P. N. Everett, M. W. Meinhold, M. K. Mondol, and H. I. Smith, "Novel mask-wafer gap measurement scheme with nanometer-level detectivity," J. Vac. Sci. Technol. B 17, 2698-2702 (1999).
[CrossRef]

Mondol, M. K.

E. E. Moon, P. N. Everett, M. W. Meinhold, M. K. Mondol, and H. I. Smith, "Novel mask-wafer gap measurement scheme with nanometer-level detectivity," J. Vac. Sci. Technol. B 17, 2698-2702 (1999).
[CrossRef]

Moon, E. E.

E. E. Moon, P. N. Everett, M. W. Meinhold, M. K. Mondol, and H. I. Smith, "Novel mask-wafer gap measurement scheme with nanometer-level detectivity," J. Vac. Sci. Technol. B 17, 2698-2702 (1999).
[CrossRef]

E. E. Moon, P. N. Everett, K. Rhee, and H. I. Smith, "Simultaneous measurement of gap and superposition in a precision aligner for x-ray nanolithography," J. Vac. Sci. Technol. B 14, 3969-3973 (1996).
[CrossRef]

Mount, A. R.

D. Clifton, A. R. Mount, G. M. Alder, and D. Jardine, "Ultrasonic measurement of the inter-electrode gap in electrochemical machining," Int. J. Mach. Tools Manuf. 42, 1259-1267 (2002).
[CrossRef]

Natale, P. D.

P. Maddaloni, G. Coppola, P. D. Natale, S. D. Nicola, P. Ferraro, M. Gioffré, and M. Iodice, "Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer," IEEE Photonics Technol. Lett. 16, 1349-1351 (2004).
[CrossRef]

Nevill, J. T.

C. Ionescu-Zanetti, J. T. Nevill, D. Di Carlo, K. H. Jeong, and L. P. Lee, "Nanogap capacitors: sensitivity to sample permittivity changes," J. Appl. Phys. 99, 24305 (2006).
[CrossRef]

Nicola, S. D.

P. Maddaloni, G. Coppola, P. D. Natale, S. D. Nicola, P. Ferraro, M. Gioffré, and M. Iodice, "Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer," IEEE Photonics Technol. Lett. 16, 1349-1351 (2004).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, and S. D. Nicola, "Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer," Appl. Opt.  42, 3882-3887 (2003).
[CrossRef] [PubMed]

Podoleanu, A. G.

Rhee, K.

E. E. Moon, P. N. Everett, K. Rhee, and H. I. Smith, "Simultaneous measurement of gap and superposition in a precision aligner for x-ray nanolithography," J. Vac. Sci. Technol. B 14, 3969-3973 (1996).
[CrossRef]

Savas, T. A.

A. A. Yu, T. A. Savas, G. S. Taylor, A. Guiseppe-Elie, H. I. Smith, and F. Stellacci, "Supramolecular nanostamping: Using DNA as movable type," Nano Lett. 5, 1061-1064 (2005).
[CrossRef] [PubMed]

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V. Shilpiekandula, "Progress through Mechanics: Small-scale Gaps," Mech. 35, 3-6 (2006).

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A. A. Yu, T. A. Savas, G. S. Taylor, A. Guiseppe-Elie, H. I. Smith, and F. Stellacci, "Supramolecular nanostamping: Using DNA as movable type," Nano Lett. 5, 1061-1064 (2005).
[CrossRef] [PubMed]

E. E. Moon, P. N. Everett, M. W. Meinhold, M. K. Mondol, and H. I. Smith, "Novel mask-wafer gap measurement scheme with nanometer-level detectivity," J. Vac. Sci. Technol. B 17, 2698-2702 (1999).
[CrossRef]

E. E. Moon, P. N. Everett, K. Rhee, and H. I. Smith, "Simultaneous measurement of gap and superposition in a precision aligner for x-ray nanolithography," J. Vac. Sci. Technol. B 14, 3969-3973 (1996).
[CrossRef]

Stellacci, F.

A. A. Yu, T. A. Savas, G. S. Taylor, A. Guiseppe-Elie, H. I. Smith, and F. Stellacci, "Supramolecular nanostamping: Using DNA as movable type," Nano Lett. 5, 1061-1064 (2005).
[CrossRef] [PubMed]

Sun, H. L.

J. M. Li, C. Liu, X. D. Dai, H. H. Chen, Y. Liang, H. L. Sun, H. Tian, and X. P. Ding, "PMMA microfluidic devices with three-dimensional features for blood cell filtration," J. Micromech. Microeng. 18, 095021 (2008).
[CrossRef]

Taylor, G. S.

A. A. Yu, T. A. Savas, G. S. Taylor, A. Guiseppe-Elie, H. I. Smith, and F. Stellacci, "Supramolecular nanostamping: Using DNA as movable type," Nano Lett. 5, 1061-1064 (2005).
[CrossRef] [PubMed]

Tian, H.

J. M. Li, C. Liu, X. D. Dai, H. H. Chen, Y. Liang, H. L. Sun, H. Tian, and X. P. Ding, "PMMA microfluidic devices with three-dimensional features for blood cell filtration," J. Micromech. Microeng. 18, 095021 (2008).
[CrossRef]

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J. Zhang, Z. H. Lu, and L. J. Wang, "Precision refractive index measurements of air, N2, O2, Ar, and CO2 with a frequency comb," Appl. Opt. 3143-3151 (2008).
[CrossRef] [PubMed]

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A. Courteville, R. Wilhelm, and F. Garcia, "A novel, low coherence fibre optic interferometer for position and thickness measurements with unattained accuracy," Proc. of SPIE  6189, 618918 (2006).
[CrossRef]

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[CrossRef]

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A. A. Yu, T. A. Savas, G. S. Taylor, A. Guiseppe-Elie, H. I. Smith, and F. Stellacci, "Supramolecular nanostamping: Using DNA as movable type," Nano Lett. 5, 1061-1064 (2005).
[CrossRef] [PubMed]

Zhang, J.

J. Zhang, Z. H. Lu, and L. J. Wang, "Precision refractive index measurements of air, N2, O2, Ar, and CO2 with a frequency comb," Appl. Opt. 3143-3151 (2008).
[CrossRef] [PubMed]

App. Opt. (1)

P. A. Flournoy, R. W. McClure, and G. Wyntjes, "White-Light Interferometric Thickness Gauge," App. Opt. 11, 1907-1915 (1972).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. B (1)

P. Hlubina, D. Ciprian, J. Lunaek, and M. lesnak, "Thickness of SiO2 thin film on silicon wafer measured by dispersive white-light spectral interferometry,"Appl. Phys. B 84, 511-516 (2006).
[CrossRef]

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G. W. Meindersma, C. M. Guijt, and A. B. De Haan, "Water Recycling and Desalination by Air Gap Membrane Distillation," Environ. Prog. 24, 434-44 (2005).
[CrossRef]

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P. Maddaloni, G. Coppola, P. D. Natale, S. D. Nicola, P. Ferraro, M. Gioffré, and M. Iodice, "Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer," IEEE Photonics Technol. Lett. 16, 1349-1351 (2004).
[CrossRef]

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D. Clifton, A. R. Mount, G. M. Alder, and D. Jardine, "Ultrasonic measurement of the inter-electrode gap in electrochemical machining," Int. J. Mach. Tools Manuf. 42, 1259-1267 (2002).
[CrossRef]

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C. Ionescu-Zanetti, J. T. Nevill, D. Di Carlo, K. H. Jeong, and L. P. Lee, "Nanogap capacitors: sensitivity to sample permittivity changes," J. Appl. Phys. 99, 24305 (2006).
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[CrossRef]

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E. E. Moon, P. N. Everett, M. W. Meinhold, M. K. Mondol, and H. I. Smith, "Novel mask-wafer gap measurement scheme with nanometer-level detectivity," J. Vac. Sci. Technol. B 17, 2698-2702 (1999).
[CrossRef]

E. E. Moon, P. N. Everett, K. Rhee, and H. I. Smith, "Simultaneous measurement of gap and superposition in a precision aligner for x-ray nanolithography," J. Vac. Sci. Technol. B 14, 3969-3973 (1996).
[CrossRef]

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[CrossRef]

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[CrossRef]

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V. Shilpiekandula, "Progress through Mechanics: Small-scale Gaps," Mech. 35, 3-6 (2006).

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[CrossRef]

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Proc. of SPIE (1)

A. Courteville, R. Wilhelm, and F. Garcia, "A novel, low coherence fibre optic interferometer for position and thickness measurements with unattained accuracy," Proc. of SPIE  6189, 618918 (2006).
[CrossRef]

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[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

(a) Schematic of experimental setup to characterize the tiny gap between two planar plates; (b) Modulation of the light source by the multi-beam interference occuring at the gap.

Fig. 2.
Fig. 2.

Simulated I—Δ signal in which local curves produced by C1 to C7 in Eq. 4 are observed with their spacings remarked; a and b show the shapes of the local curves by C1 and C2 .

Fig. 3.
Fig. 3.

Simulated I—Δ signal for the common white-light scanning interferometer. (a) two local curves before consideration of the dispersion of the cover plate; (b) two local curves after considering the dispersion.

Fig. 4.
Fig. 4.

(a) Random noise with the amplitude of the 4mW is simulated and added into the simulated signal for a 10 µm gap. (b) Central Curve with noise. (c) Side Curve with noise. (e) Simulated Central Peak. (f) Convolution calculation between the simulated Central Peak as in (e) and the whole signal reduces largely the influence of the noise. (f) Central Curve after noise noise filtering. (g) Side Curve after noise filtering. From (f) and (g) the gap thickness can be easily iendified.

Fig. 5.
Fig. 5.

(a) Simulated signal for a 2 µm gap, in which the three local curves are combined partly to make the gap thickness quantification very difficult; (b) Recorded data for the Central Curve when the gap is thick enough to make the two side peaks go beyond the PZR scanning range.

Fig. 6.
Fig. 6.

Simulated signal for a 2 µm gap, in which the Central Curve has been subtracted and the Side Peaks return to their ideal positions.

Fig. 7.
Fig. 7.

Simulated signal for a 400 nm gap, in which the central peak has been subtracted and side peaks are so close as to be combined together.

Fig. 8.
Fig. 8.

(a) Simulated curve for a 400 nm gap with 2mW peak-to-peak random noise. (b) Results of the correlation calculation between (a) and the curves in the database.

Fig. 9.
Fig. 9.

(a) Experimental setup to measure the gap thickness; (b) Flexure based mechanism to hold the PZT driving the moving mirror.

Fig. 10.
Fig. 10.

(a-1), (b-1) and (c-1) are the experimental curves detected by the photodetector for four gaps, from which the gap thickness is determined to be 10.1258 µm, 6.3733 µm, 1.6514 µm and 494.3 nm. (a-2), (b-2) and (c-2) present the simulated signal for the 10.1258 µm, 6.3733 µm, 1.6514 µm gaps with consideration of all the practical parameters; (d-2): Result of the correlation calculation between the experimental data in (d-1) and the simulated signals in the database for gap thicknesses from 1 nm to 1 µm.

Tables (1)

Tables Icon

Table 1. TABLE I MEASUREMENTS FOR EXAMINING THE SHORT-TERM AND LONG-TERM REPEATABILITIES

Equations (17)

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E1 =Einputr1;
E2 =Einputt1r2t1'eiφ1 ;
E3 =Einputt1t2r3t2't1'ei(δ+φ1) ;
E4 =Einputt1 t2 t3 r4 t3 ' t2 ' t1'ei(δ+φ1+φ2)
δ=2πλ 2 na h cos α ; φ1 =2πλ 2 n1 h1 cos β ; φ2 =2πλ 2 n2 h2 cos γ ;
Egap =E1+E2+E3+E4
=Einput (r1+t1r2t1'eiφ1+t1t2r3t2't1'ei(δ+φ1)+t1t2t3r4t3't2't1ei(δ+φ1+φ2))
C1 =14 λ1λ2 (a2+b2+c2+d2) cos 4πΔλ d λ
C2 =14 λ1λ2bc cos 4π(nah+Δ)λ d λ 14 λ1λ2 b c cos 4π(nahΔ)λ d λ
C3 =14 λ1λ2ab cos 4π[n1(λ)h1+Δ]λ d λ 14 λ1λ2 ab cos 4π[n1(λ)h1Δ]λ d λ
C4 =14 λ1λ2cd cos 4π[n2(λ)h2+Δ]λ d λ 14 λ1λ2 cd cos 4π[n2(λ)h2Δ]λ d λ
C5 =14 λ1λ2ac cos 4π[(n1(λ)h1+nah+Δ]λ d λ +14 λ1λ2 ac cos 4π[n1(λ)h1+nahΔ]λ d λ
C6 =14 λ1λ2bd cos 4π[(n2(λ)h2+nah+Δ]λ d λ +14 λ1λ2 bd cos 4π[n2(λ)h2+nahΔ]λ d λ
C7 =14 λ1λ2ad cos 4π[(n1(λ)h1+nah+n2(λ)h2+Δ]λ d λ
14 λ1λ2ab cos 4π[(n1(λ)h1+nah+n2(λ)h2Δ]λ d λ
I=M1 +λ1λ2M2 cos 4πΔλ d λ λ1λ2M3 cos 4π[n1(λ)h1Δ]λ d λ
+λ1λ2M4 cos 4π[n1(λ)h1+nahΔ]λ d λ +.....

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