Abstract

A new instrument, the polarization phase-shifting point-diffraction interferometer, has been developed by use of a birefringent pinhole plate. The interferometer uses polarization to separate the test and reference beams, interfering what begin as orthogonal polarization states. The instrument is compact, simple to align, and vibration insensitive and can phase shift without moving parts or separate reference optics. The theory of the interferometer is presented, along with properties and fabrication techniques for the birefringent pinhole plate and a new model used to determine the quality of the reference wavefront from the pinhole as a function of pinhole size and test optic aberrations. The performance of the interferometer is also presented, along with a detailed error analysis and experimental results.

© 2006 Optical Society of America

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References

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  1. O. Y. Kwon, "Multichannel phase-shifted Interferometer," Opt. Lett. 9, 59-61 (1984).
    [CrossRef] [PubMed]
  2. H. Kadono, T. Nobukatsu, and T. Asakura, "New common-path phase shifting interferometer using a polarization technique," Appl. Opt. 26, 898-904 (1987).
    [CrossRef] [PubMed]
  3. H. Kadono, M. Ogusu, and S. Toyooka, "Phase shifting common path interferometer using a liquid-crystal phase modulator," Opt. Commun. 110, 391-400 (1994).
    [CrossRef]
  4. C. R. Mercer and K. Creath, "Liquid-crystal point-diffraction interferometer for wave-front measurements," Appl. Opt. 35, 1633-1642 (1996).
    [CrossRef] [PubMed]
  5. M. Totzeck, N. Kerwein, A. Tavrov, E. Rosenthal, and H. J. Tiziani, "Quantitative Zernike phase-contrast microscopy by use of structured birefringent pupil-filters and phase-shift evaluation," in Interferometry XI: Techniques and Analysis, K.Creath and J.Schmit, eds., Proc. SPIE 4777, 1-11 (2002).
  6. J. C. Wyant, "Recent Investigations of interferometry and applications to optical testing," in Los Alamos Conference on Optics 1979, D. H. Liebenberg, ed., Proc. SPIE 190, 507-511 (1979).
  7. W. H. Steel, Interferometery (Cambridge U. Press, 1983).
  8. I. J. Hodgkinson and Q. H. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, 1997).
    [CrossRef]
  9. I. Hodgkinson and Q. H. Wu, "Review of birefringent and chiral optical interference coatings," in Optical Interference Coating, 2001 OSA Technical Digest (Optical Society of America, 2001), pp. FA1-FA3.
  10. A. Street, "How a FIB works," Integrated Reliability, retrieved 22 May, 2002, http://www.irsi.com/Site1/fibwork.html.
  11. C. Friedrich, "Micromilling tools," Michigan Technological University, Department of Mechanical Engineering-Engineering Mechanics, retrieved 22 May 2002, http://www.me.mtu.edu/∼microweb/chap7/ch7-1.htm (1998).
  12. R. M. Neal, "Polarization phase-shifting point-diffraction interferometer," Ph.D. dissertation (University of Arizona, 2003).
  13. K. A. Goldberg, E. Tejnil, and J. Bokor, "A 3-D numerical study of pinhole diffraction to predict the accuracy of EUV point diffraction interferometry," in Extreme Ultraviolet Lithography, Vol. 4 of OSA Trends in Optics and Photonics (Optical Society of America, 1996), pp. 133-137.

2003 (1)

R. M. Neal, "Polarization phase-shifting point-diffraction interferometer," Ph.D. dissertation (University of Arizona, 2003).

2002 (1)

M. Totzeck, N. Kerwein, A. Tavrov, E. Rosenthal, and H. J. Tiziani, "Quantitative Zernike phase-contrast microscopy by use of structured birefringent pupil-filters and phase-shift evaluation," in Interferometry XI: Techniques and Analysis, K.Creath and J.Schmit, eds., Proc. SPIE 4777, 1-11 (2002).

2001 (1)

I. Hodgkinson and Q. H. Wu, "Review of birefringent and chiral optical interference coatings," in Optical Interference Coating, 2001 OSA Technical Digest (Optical Society of America, 2001), pp. FA1-FA3.

1998 (1)

C. Friedrich, "Micromilling tools," Michigan Technological University, Department of Mechanical Engineering-Engineering Mechanics, retrieved 22 May 2002, http://www.me.mtu.edu/∼microweb/chap7/ch7-1.htm (1998).

1997 (1)

I. J. Hodgkinson and Q. H. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, 1997).
[CrossRef]

1996 (2)

K. A. Goldberg, E. Tejnil, and J. Bokor, "A 3-D numerical study of pinhole diffraction to predict the accuracy of EUV point diffraction interferometry," in Extreme Ultraviolet Lithography, Vol. 4 of OSA Trends in Optics and Photonics (Optical Society of America, 1996), pp. 133-137.

C. R. Mercer and K. Creath, "Liquid-crystal point-diffraction interferometer for wave-front measurements," Appl. Opt. 35, 1633-1642 (1996).
[CrossRef] [PubMed]

1994 (1)

H. Kadono, M. Ogusu, and S. Toyooka, "Phase shifting common path interferometer using a liquid-crystal phase modulator," Opt. Commun. 110, 391-400 (1994).
[CrossRef]

1987 (1)

1984 (1)

1983 (1)

W. H. Steel, Interferometery (Cambridge U. Press, 1983).

1979 (1)

J. C. Wyant, "Recent Investigations of interferometry and applications to optical testing," in Los Alamos Conference on Optics 1979, D. H. Liebenberg, ed., Proc. SPIE 190, 507-511 (1979).

Asakura, T.

Bokor, J.

K. A. Goldberg, E. Tejnil, and J. Bokor, "A 3-D numerical study of pinhole diffraction to predict the accuracy of EUV point diffraction interferometry," in Extreme Ultraviolet Lithography, Vol. 4 of OSA Trends in Optics and Photonics (Optical Society of America, 1996), pp. 133-137.

Creath, K.

Friedrich, C.

C. Friedrich, "Micromilling tools," Michigan Technological University, Department of Mechanical Engineering-Engineering Mechanics, retrieved 22 May 2002, http://www.me.mtu.edu/∼microweb/chap7/ch7-1.htm (1998).

Goldberg, K. A.

K. A. Goldberg, E. Tejnil, and J. Bokor, "A 3-D numerical study of pinhole diffraction to predict the accuracy of EUV point diffraction interferometry," in Extreme Ultraviolet Lithography, Vol. 4 of OSA Trends in Optics and Photonics (Optical Society of America, 1996), pp. 133-137.

Hodgkinson, I.

I. Hodgkinson and Q. H. Wu, "Review of birefringent and chiral optical interference coatings," in Optical Interference Coating, 2001 OSA Technical Digest (Optical Society of America, 2001), pp. FA1-FA3.

Hodgkinson, I. J.

I. J. Hodgkinson and Q. H. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, 1997).
[CrossRef]

Kadono, H.

H. Kadono, M. Ogusu, and S. Toyooka, "Phase shifting common path interferometer using a liquid-crystal phase modulator," Opt. Commun. 110, 391-400 (1994).
[CrossRef]

H. Kadono, T. Nobukatsu, and T. Asakura, "New common-path phase shifting interferometer using a polarization technique," Appl. Opt. 26, 898-904 (1987).
[CrossRef] [PubMed]

Kerwein, N.

M. Totzeck, N. Kerwein, A. Tavrov, E. Rosenthal, and H. J. Tiziani, "Quantitative Zernike phase-contrast microscopy by use of structured birefringent pupil-filters and phase-shift evaluation," in Interferometry XI: Techniques and Analysis, K.Creath and J.Schmit, eds., Proc. SPIE 4777, 1-11 (2002).

Kwon, O. Y.

Mercer, C. R.

Neal, R. M.

R. M. Neal, "Polarization phase-shifting point-diffraction interferometer," Ph.D. dissertation (University of Arizona, 2003).

Nobukatsu, T.

Ogusu, M.

H. Kadono, M. Ogusu, and S. Toyooka, "Phase shifting common path interferometer using a liquid-crystal phase modulator," Opt. Commun. 110, 391-400 (1994).
[CrossRef]

Rosenthal, E.

M. Totzeck, N. Kerwein, A. Tavrov, E. Rosenthal, and H. J. Tiziani, "Quantitative Zernike phase-contrast microscopy by use of structured birefringent pupil-filters and phase-shift evaluation," in Interferometry XI: Techniques and Analysis, K.Creath and J.Schmit, eds., Proc. SPIE 4777, 1-11 (2002).

Steel, W. H.

W. H. Steel, Interferometery (Cambridge U. Press, 1983).

Street, A.

A. Street, "How a FIB works," Integrated Reliability, retrieved 22 May, 2002, http://www.irsi.com/Site1/fibwork.html.

Tavrov, A.

M. Totzeck, N. Kerwein, A. Tavrov, E. Rosenthal, and H. J. Tiziani, "Quantitative Zernike phase-contrast microscopy by use of structured birefringent pupil-filters and phase-shift evaluation," in Interferometry XI: Techniques and Analysis, K.Creath and J.Schmit, eds., Proc. SPIE 4777, 1-11 (2002).

Tejnil, E.

K. A. Goldberg, E. Tejnil, and J. Bokor, "A 3-D numerical study of pinhole diffraction to predict the accuracy of EUV point diffraction interferometry," in Extreme Ultraviolet Lithography, Vol. 4 of OSA Trends in Optics and Photonics (Optical Society of America, 1996), pp. 133-137.

Tiziani, H. J.

M. Totzeck, N. Kerwein, A. Tavrov, E. Rosenthal, and H. J. Tiziani, "Quantitative Zernike phase-contrast microscopy by use of structured birefringent pupil-filters and phase-shift evaluation," in Interferometry XI: Techniques and Analysis, K.Creath and J.Schmit, eds., Proc. SPIE 4777, 1-11 (2002).

Totzeck, M.

M. Totzeck, N. Kerwein, A. Tavrov, E. Rosenthal, and H. J. Tiziani, "Quantitative Zernike phase-contrast microscopy by use of structured birefringent pupil-filters and phase-shift evaluation," in Interferometry XI: Techniques and Analysis, K.Creath and J.Schmit, eds., Proc. SPIE 4777, 1-11 (2002).

Toyooka, S.

H. Kadono, M. Ogusu, and S. Toyooka, "Phase shifting common path interferometer using a liquid-crystal phase modulator," Opt. Commun. 110, 391-400 (1994).
[CrossRef]

Wu, Q. H.

I. Hodgkinson and Q. H. Wu, "Review of birefringent and chiral optical interference coatings," in Optical Interference Coating, 2001 OSA Technical Digest (Optical Society of America, 2001), pp. FA1-FA3.

I. J. Hodgkinson and Q. H. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, 1997).
[CrossRef]

Wyant, J. C.

J. C. Wyant, "Recent Investigations of interferometry and applications to optical testing," in Los Alamos Conference on Optics 1979, D. H. Liebenberg, ed., Proc. SPIE 190, 507-511 (1979).

Appl. Opt. (2)

Opt. Commun. (1)

H. Kadono, M. Ogusu, and S. Toyooka, "Phase shifting common path interferometer using a liquid-crystal phase modulator," Opt. Commun. 110, 391-400 (1994).
[CrossRef]

Opt. Lett. (1)

Other (9)

M. Totzeck, N. Kerwein, A. Tavrov, E. Rosenthal, and H. J. Tiziani, "Quantitative Zernike phase-contrast microscopy by use of structured birefringent pupil-filters and phase-shift evaluation," in Interferometry XI: Techniques and Analysis, K.Creath and J.Schmit, eds., Proc. SPIE 4777, 1-11 (2002).

J. C. Wyant, "Recent Investigations of interferometry and applications to optical testing," in Los Alamos Conference on Optics 1979, D. H. Liebenberg, ed., Proc. SPIE 190, 507-511 (1979).

W. H. Steel, Interferometery (Cambridge U. Press, 1983).

I. J. Hodgkinson and Q. H. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, 1997).
[CrossRef]

I. Hodgkinson and Q. H. Wu, "Review of birefringent and chiral optical interference coatings," in Optical Interference Coating, 2001 OSA Technical Digest (Optical Society of America, 2001), pp. FA1-FA3.

A. Street, "How a FIB works," Integrated Reliability, retrieved 22 May, 2002, http://www.irsi.com/Site1/fibwork.html.

C. Friedrich, "Micromilling tools," Michigan Technological University, Department of Mechanical Engineering-Engineering Mechanics, retrieved 22 May 2002, http://www.me.mtu.edu/∼microweb/chap7/ch7-1.htm (1998).

R. M. Neal, "Polarization phase-shifting point-diffraction interferometer," Ph.D. dissertation (University of Arizona, 2003).

K. A. Goldberg, E. Tejnil, and J. Bokor, "A 3-D numerical study of pinhole diffraction to predict the accuracy of EUV point diffraction interferometry," in Extreme Ultraviolet Lithography, Vol. 4 of OSA Trends in Optics and Photonics (Optical Society of America, 1996), pp. 133-137.

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Figures (14)

Fig. 1
Fig. 1

Conventional PDI.

Fig. 2
Fig. 2

Operation of the PDI Plate.

Fig. 3
Fig. 3

Operation of the PPSPDI.

Fig. 4
Fig. 4

Operation of the PPSPDI Plate.

Fig. 5
Fig. 5

Characteristic normal columnar structure for bidirectionally deposited birefringent films.[8]

Fig. 6
Fig. 6

Focused ion-beam-etched pinhole in a silicon thin film.

Fig. 7
Fig. 7

Peak-to-valley and rms phase errors versus thin film retardance.

Fig. 8
Fig. 8

Peak-to-valley and rms phase errors versus thin film alignment angle.

Fig. 9
Fig. 9

Peak-to-valley and rms phase errors versus final analyzer angle.

Fig. 10
Fig. 10

Reference wavefront error versus spherical aberration for various pinhole sizes.

Fig. 11
Fig. 11

Reference wavefront error versus astigmatism for various pinhole sizes.

Fig. 12
Fig. 12

Reference wavefront error versus coma for various pinhole sizes.

Fig. 13
Fig. 13

Comparison of measurements of the test lens made with a commercial phase-shifting Fizeau interferometer and with the PPSPDI.

Fig. 14
Fig. 14

Subtraction of two consecutive measurements: OPDs, optical path differences.

Equations (25)

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d pinhole 1.22 λ  ( f # working ) .
d pinhole 1.22 λ  ( f # working ) ,
R = ( n e n o ) t λ = Δ n t λ ,
t = λ 2 Δ n .
Δ n λ = Δ n 633 [ 1 + c ( 1 λ 2 1 633 2 ) ] ,
[ E x Output E y Output ] = [ Final   Element ] [ 2nd Element ] × [ 1st Element ] [ E x Input E y Input ] .
A Test = 1 2 [ 1 0 0 e ] ( 1 1 ) ,
A Ref = 1 2 [ 1 0 0 e i δ ] ( A A ) ,
A Test = 1 2 [ e i Δ 0 0 e i Δ ] [ 1 0 0 e i δ ] ( 1 1 ) ,
A Ref = 1 2 [ e i Δ 0 0 e i Δ ] [ 1 0 0 e i δ ] ( A A ) .
A Test = 1 2 [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] Rotation   Matrix (- θ ) [ 0.8 e i ϕ 0 0 1 ] Retarder   of Retardance   ϕ   and 0.8   Diattenuation [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] Rotation   Matrix  ( θ ) [ e i Δ 0 0 e i Δ ] [ 1 0 0 e i δ ] ( 1 1 ) ,
A Ref = 1 2 [ 1 0 0 e i δ ] ( 0.6 0.6 ) .
A Test = 1 2 [ cos ( ψ ) 2 cos ( ψ ) sin ( ψ ) cos ( ψ ) sin ( ψ ) sin ( ψ ) 2 ] [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] [ 0.8 e i ϕ 0 0 1 ] [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] [ e i Δ 0 0 e i Δ ] [ 1 0 0 e i δ ] ( 1 1 ) ,
A Ref = 1 2 [ cos ( ψ ) 2 cos ( ψ ) sin ( ψ ) cos ( ψ ) sin ( ψ ) sin ( ψ ) 2 ] [ 1 0 0 e i δ ] ( 0.6 0.6 ) .
I ( δ , Δ , ϕ ) = 0.59 + 0.0 9 cos ( δ ) + 0.03 cos ( Δ ) + 0.03 cos ( δ + Δ ) + 0.2 cos ( δ ϕ ) 0.2 cos ( δ + ϕ ) + 0.24 cos ( Δ + ϕ ) 0.24 cos ( δ + Δ + ϕ ) .
Output   phase = arc t a n [ 0.6 sin ( Δ ) 0.8 sin ( ϕ ) 0.48 sin ( Δ + ϕ ) 0.18 + 0.6 cos ( Δ ) 0.48 cos ( Δ + ϕ ) ] .
I ( δ , Δ , θ ) = 0.18 0.48 cos ( Δ ) cos 2 ( θ ) + 0.32 cos 4 ( θ ) 1.08 cos ( δ + Δ ) cos ( θ ) sin ( θ ) + 1.44 cos ( δ ) cos 3 ( θ ) sin ( θ ) + 0.6 cos ( Δ ) sin 2 ( θ ) + 0.82 cos 2 ( θ ) sin 2 ( θ ) 1.8 cos ( δ ) cos ( θ ) sin 3 ( θ ) + 0.5 sin 4 ( θ ) .
Output   phase = arc t a n [ 0.54 cos ( Δ + 2 θ ) 0.54 cos ( Δ 2 θ ) 0.36 cos ( θ ) sin ( θ ) 2.16 cos ( Δ ) cos ( θ ) sin ( θ ) + 0.81 sin ( 4 θ ) ] .
Output   phase = arc   tan [ 0.27 cos ( Δ 4 ψ ) 0.27 cos ( Δ + 4 ψ ) + 1.08 cos ( 2 ψ ) sin ( Δ ) 0.77 + 1.14 cos ( Δ ) 0.03 cos ( Δ 4 ψ ) 0.59 cos ( 4 ψ ) 0.03 cos ( Δ + 4 ψ ) 0.6 sin ( Δ 2 ψ ) + 0.6 sin ( Δ + 2 ψ ) + 2.72 cos ( ψ ) sin ( ψ ) ] .
U ( x p , y p ) = c y l [ ( x p     2 + y p     2 ) 1 / 2 d 1 ] exp [ i 2 π W ( x p , y p ) ] ,
U ( x 2 , y 2 ) = { cyl [ ( x 2     2 + y 2     2 ) 1 / 2 d 1 ] exp [ i 2 π W ( x 2 , y 2 ) ] } × cyl [ ( x 2     2 + y 2     2 ) 1 / 2 d 2 ] ,
U ( x 3 , y 3 ) = cyl [ ( x 3     2 + y 3     2 ) 1 / 2 d 1 ] exp [ i 2 π W ( x 3 , y 3 ) ] ∗∗ { cyl [ ( x 3     2 + y 3     2 ) 1 / 2 d 2 ] } ,
U ( x p , y p ) = cyl [ ( x p     2 + y p     2 ) 1 / 2 d 1 ] exp [ i 2 π W 40 ( x p     2 + y p     2 ) 2 ] ,
U ( x p , y p ) = cyl [ ( x p     2 + y p     2 ) 1 / 2 d 1 ] exp [ i 2 π W 22 y p     2 ] ,
U ( x p , y p ) = cyl [ ( x p     2 + y p     2 ) 1 / 2 d 1 ] × exp [ i 2 π W 31 ( x p     2 + y p     2 ) y p ] ,

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