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Achromatic phase-shifting for two-wavelength phase-stepping interferometry
15 May 1996
OPTICS COMMUNICATIONS ELSEVIER
Optics Communications 126 ( 1996) 220-222
Achromatic phase-shifting for two-wavelength phase-stepping interferometry P. Hariharan, Maitreyee Roy Department of Physical Optics, School of Physics, University of Sydney, NSW 2006, Australia
Received 15 November 1995; accepted 26 January 1996
Abstract Achromatic phase-shifting can be used with two-wavelength illumination in a polarization interferometer quick and simple method for profiling surfaces exhibiting steps with heights of a few micrometres.
1. Introduction
A problem with interferometric profilers using monochromatic light is ambiguities in the integral interference order that arise at steps on the test surface involving a change in the optical path difference greater than a wavelength. One way to resolve these ambiguities is to use white light and scan the test surface in height. The location of the fringe visibility peak along the scanning axis, for each point on the test surface, then corresponds to the height of the test surface at that point [ l-31. An alternative way to obtain the integral fringe order, which does not involve moving the test surface, is to make measurements, at each point on the test surface, of the fractional interference orders, et and ~2, for two wavelengths, At and AZ. It then follows that (ml + El 1Al =p*
(m:!+c2)A2=f-&
(1)
where p is the optical path difference at this point, and ml and m2 are the integral interference orders for At and A2, respectively. If the fractional interference orders are known with a sufficient degree of accuracy, it is possible to obtain an unambiguous value for p
over an extended range [4]. We show how this method can be implemented conveniently with a polarization interferometer using an achromatic phase-shifter.
2. Theory The measurement range can be extended by subtracting the phase difference ~$1 measured at a wavelength At from the phase difference ~$2 measured at a wavelength A2. The value obtained &q=&
-42.
(2)
corresponds to the phase difference that would have been obtained in measurements made at a synthetic wavelength [ 51
(3) and the repeat distance wavelength.
0030-4018/96/$12.00 @ 1996 Elsevier Science B.V. All rights resewed I8 (96) 00 1 18-6
PN 50030-40
to provide a
is increased
to the synthetic
P Hariharan,
M. Roy/Optics
Communications
126 (1996) 220-222
this phase shift at 594 nm from its nominal 633 nm is less than f0.5”.
CCD camera
4. Measurement H
I
\
I
BS
PI
I
tan #J =
surface Fig.
I,
Schematic
two-wavelength
of a Nomarski
range and accuracy
At each of the wavelengths, four TV frames are acquired corresponding to additional phase shifts of O”, 90”, 180”, and 270’. Since the phase shifts can be taken as the same for both wavelengths, the phase differences ~$1(x, y) and C&(X, y) for the two wavelengths can be calculated to modulo 21r from the two sets of intensity data, for each point in the image, using the simple relation
QI
= '
value at
Q2
hi ‘I 12
221
interferometer
modified for
phase-shifting interferometry.
3. Optical arrangement An optical arrangement that can be used to implement this technique with a polarizing (Nomarski) interferometer is shown schematically in Fig. 1. The illuminating system is modified so that either of two wavelengths, Ai and AZ, can be used. Suitable sources are a red He-Ne laser (AI = 633 nm) and a yellow He-Ne laser (A2 = 594 nm) . Phase shifting cannot be performed in the conventional manner with such an interferometer. However, since the two beams leaving the interferometer are orthogonally polarized, the phase difference between them can be varied by a system consisting of a A/2 plate H mounted between two A/4 plates Qt and Q2 [ 61. The two A/4 plates have their optic axes fixed at an azimuth of 45”, while the A/2 plate can be rotated by known amounts. In this arrangement, a rotation of the h/2 plate by an angle 0 results in one beam acquiring a phase shift 20, while the orthogonally polarized beam acquires a phase shift -26, so that the total phase difference introduced between the two beams is 48. This system has been shown to be a very good approximation to an achromatic phase shifter [ 71. For plates with retardations of A/2 and A/4 at 633 nm, the deviation of
190 -
1210
10 -
1180
(4)
The range of optical path differences over which unambiguous measurements can be made is equal to the synthetic wavelength given by Fq. (3). With red (At = 633 nm) and yellow (A2 = 594 nm) He-Ne lasers, the repeat distance is 9.63 pm, and, in principle, measurements of step changes in height up to +4.8 1 pm can be made. The accuracy of calculations of height using the synthetic wavelength is limited by the fact that the signal-to-noise ratio is reduced by a factor which is equal to the ratio of the synthetic wavelength to the shorter wavelengths at which the actual measurements are made [ 81. However, if the original phase measurements can be made with an accuracy better than 2~/50, the resulting uncertainty in the calculated value of the optical path difference is less than half a wavelength at the original wavelengths. Increased accuracy can then be obtained by using the synthetic wavelength data to calculate the integral order number m for one of the shorter wavelengths at which measurements are made, and using this integral order number, in conjunction with the fractional interference order E measured at this wavelength, in Eq. ( 1) to calculate the actual optical path difference.
5. Conclusions This technique can be implemented conveniently with a polarization interference microscope. Since the phase-shifter is placed in the orthogonally polarized
223
P: Hurihurun.
M. Roy/Optics
beams leaving the interferometer, very little modification of the optical system is required. Because polarization interferometers are very stable and the rotation of the A/2 plate can be controlled precisely, very accurate measurements of step changes in surface height up to a few micrometres can be made,
Communicalions
126 (1996) 220-222
Appl. Optics 29 (1990) 3775. 131 B.S. Lee and T.C. Strand, Appl. Optics 29 (1990) 3784. [4] t? Hariharan, Optical Interferometry (Academic Press, 121 G.S. Kino and S.S.C. Chim,
Sydney, 1985) p. 119. [S] P Hariharan and M. Roy, J. Mod. Optics 41 (1994) 2197. [6] t? Hariharan and P E. Ciddor, Optics Commun. It0 ( 1994)
13. 171 Y.-Y.Cheng and J.C. Wyant. Appl. Optics 23 (1984) 4539. 181 K. Creath. Appl. Optics 26 (1987)
References II
1 M. Davidson,
K. Kaufman, 1. Mazor and E Cohen, in: Integrated Circuit Metrology, Inspection and Process Control, Proc. SPIE, Vol. 775 (Bellingham, Washington: SPIE, 1987) p, 233.
2810.
OPTICS COMMUNICATIONS ELSEVIER
Optics Communications 126 ( 1996) 220-222
Achromatic phase-shifting for two-wavelength phase-stepping interferometry P. Hariharan, Maitreyee Roy Department of Physical Optics, School of Physics, University of Sydney, NSW 2006, Australia
Received 15 November 1995; accepted 26 January 1996
Abstract Achromatic phase-shifting can be used with two-wavelength illumination in a polarization interferometer quick and simple method for profiling surfaces exhibiting steps with heights of a few micrometres.
1. Introduction
A problem with interferometric profilers using monochromatic light is ambiguities in the integral interference order that arise at steps on the test surface involving a change in the optical path difference greater than a wavelength. One way to resolve these ambiguities is to use white light and scan the test surface in height. The location of the fringe visibility peak along the scanning axis, for each point on the test surface, then corresponds to the height of the test surface at that point [ l-31. An alternative way to obtain the integral fringe order, which does not involve moving the test surface, is to make measurements, at each point on the test surface, of the fractional interference orders, et and ~2, for two wavelengths, At and AZ. It then follows that (ml + El 1Al =p*
(m:!+c2)A2=f-&
(1)
where p is the optical path difference at this point, and ml and m2 are the integral interference orders for At and A2, respectively. If the fractional interference orders are known with a sufficient degree of accuracy, it is possible to obtain an unambiguous value for p
over an extended range [4]. We show how this method can be implemented conveniently with a polarization interferometer using an achromatic phase-shifter.
2. Theory The measurement range can be extended by subtracting the phase difference ~$1 measured at a wavelength At from the phase difference ~$2 measured at a wavelength A2. The value obtained &q=&
-42.
(2)
corresponds to the phase difference that would have been obtained in measurements made at a synthetic wavelength [ 51
(3) and the repeat distance wavelength.
0030-4018/96/$12.00 @ 1996 Elsevier Science B.V. All rights resewed I8 (96) 00 1 18-6
PN 50030-40
to provide a
is increased
to the synthetic
P Hariharan,
M. Roy/Optics
Communications
126 (1996) 220-222
this phase shift at 594 nm from its nominal 633 nm is less than f0.5”.
CCD camera
4. Measurement H
I
\
I
BS
PI
I
tan #J =
surface Fig.
I,
Schematic
two-wavelength
of a Nomarski
range and accuracy
At each of the wavelengths, four TV frames are acquired corresponding to additional phase shifts of O”, 90”, 180”, and 270’. Since the phase shifts can be taken as the same for both wavelengths, the phase differences ~$1(x, y) and C&(X, y) for the two wavelengths can be calculated to modulo 21r from the two sets of intensity data, for each point in the image, using the simple relation
QI
= '
value at
Q2
hi ‘I 12
221
interferometer
modified for
phase-shifting interferometry.
3. Optical arrangement An optical arrangement that can be used to implement this technique with a polarizing (Nomarski) interferometer is shown schematically in Fig. 1. The illuminating system is modified so that either of two wavelengths, Ai and AZ, can be used. Suitable sources are a red He-Ne laser (AI = 633 nm) and a yellow He-Ne laser (A2 = 594 nm) . Phase shifting cannot be performed in the conventional manner with such an interferometer. However, since the two beams leaving the interferometer are orthogonally polarized, the phase difference between them can be varied by a system consisting of a A/2 plate H mounted between two A/4 plates Qt and Q2 [ 61. The two A/4 plates have their optic axes fixed at an azimuth of 45”, while the A/2 plate can be rotated by known amounts. In this arrangement, a rotation of the h/2 plate by an angle 0 results in one beam acquiring a phase shift 20, while the orthogonally polarized beam acquires a phase shift -26, so that the total phase difference introduced between the two beams is 48. This system has been shown to be a very good approximation to an achromatic phase shifter [ 71. For plates with retardations of A/2 and A/4 at 633 nm, the deviation of
190 -
1210
10 -
1180
(4)
The range of optical path differences over which unambiguous measurements can be made is equal to the synthetic wavelength given by Fq. (3). With red (At = 633 nm) and yellow (A2 = 594 nm) He-Ne lasers, the repeat distance is 9.63 pm, and, in principle, measurements of step changes in height up to +4.8 1 pm can be made. The accuracy of calculations of height using the synthetic wavelength is limited by the fact that the signal-to-noise ratio is reduced by a factor which is equal to the ratio of the synthetic wavelength to the shorter wavelengths at which the actual measurements are made [ 81. However, if the original phase measurements can be made with an accuracy better than 2~/50, the resulting uncertainty in the calculated value of the optical path difference is less than half a wavelength at the original wavelengths. Increased accuracy can then be obtained by using the synthetic wavelength data to calculate the integral order number m for one of the shorter wavelengths at which measurements are made, and using this integral order number, in conjunction with the fractional interference order E measured at this wavelength, in Eq. ( 1) to calculate the actual optical path difference.
5. Conclusions This technique can be implemented conveniently with a polarization interference microscope. Since the phase-shifter is placed in the orthogonally polarized
223
P: Hurihurun.
M. Roy/Optics
beams leaving the interferometer, very little modification of the optical system is required. Because polarization interferometers are very stable and the rotation of the A/2 plate can be controlled precisely, very accurate measurements of step changes in surface height up to a few micrometres can be made,
Communicalions
126 (1996) 220-222
Appl. Optics 29 (1990) 3775. 131 B.S. Lee and T.C. Strand, Appl. Optics 29 (1990) 3784. [4] t? Hariharan, Optical Interferometry (Academic Press, 121 G.S. Kino and S.S.C. Chim,
Sydney, 1985) p. 119. [S] P Hariharan and M. Roy, J. Mod. Optics 41 (1994) 2197. [6] t? Hariharan and P E. Ciddor, Optics Commun. It0 ( 1994)
13. 171 Y.-Y.Cheng and J.C. Wyant. Appl. Optics 23 (1984) 4539. 181 K. Creath. Appl. Optics 26 (1987)
References II
1 M. Davidson,
K. Kaufman, 1. Mazor and E Cohen, in: Integrated Circuit Metrology, Inspection and Process Control, Proc. SPIE, Vol. 775 (Bellingham, Washington: SPIE, 1987) p, 233.
2810.