Abstract

Measurements of wavefront deformations can be carried out with the help of lateral shearing interferometers. Here the focus is on a setup providing two shears along orthogonal directions simultaneously to generate the data needed for a reconstruction. We describe a diffractive solution using Ronchi phase gratings with a suppressed zeroth order for both the doubling of the wavefront under test and the bidirectional shearing unit. A series arrangement of the gratings offers an on-axis geometry, which minimizes the systematic errors of the test. For illumination, an extended incoherent monochromatic light source is used. High-contrast fringes can be obtained by tailoring the degree of coherence via a periodic intensity distribution.

© 2011 Optical Society of America

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References

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2002

G. Fütterer, M. Lano, N. Lindlein, and J. Schwider, “Lateral shearing interferometer for phase-shift mask measurement at 193 nm,” Proc. SPIE 4691, 541–551 (2002).
[CrossRef]

2001

C. Siegel, F. Löwenthal, and J. Balmer, “A wave front sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

1998

J. Schwider, “DOE-based interferometry,” Optik 108, 181–196 (1998).

1997

1996

T. Dresel, “Optimization of symmetric Dammann gratings with a multidimensional error feedback algorithm,” Opt. Commun. 129, 19–26 (1996).
[CrossRef]

1990

1984

1983

1981

1980

1979

1977

1971

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Balmer, J.

C. Siegel, F. Löwenthal, and J. Balmer, “A wave front sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Büeler, M.

M. Mrochen, M. Büeler, and T. Seiler, “Ophthalmologische Optik und Laser,” Research report (Augenklinik Universitätsspital Zürich, 2000/2001).

Burow, R.

Chellappa, R.

R. T. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” in Proceedings of the IEEE Conference on Transactions on Pattern Analysis and Machine Intelligence (IEEE, 1988), pp. 439–451.
[CrossRef]

Dammann, H.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Dresel, T.

T. Dresel, “Optimization of symmetric Dammann gratings with a multidimensional error feedback algorithm,” Opt. Commun. 129, 19–26 (1996).
[CrossRef]

Elssner, K.-E.

Frankot, R. T.

R. T. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” in Proceedings of the IEEE Conference on Transactions on Pattern Analysis and Machine Intelligence (IEEE, 1988), pp. 439–451.
[CrossRef]

Fried, D. L.

Fütterer, G.

G. Fütterer, M. Lano, N. Lindlein, and J. Schwider, “Lateral shearing interferometer for phase-shift mask measurement at 193 nm,” Proc. SPIE 4691, 541–551 (2002).
[CrossRef]

G. Fütterer, “UV-Shearing Interferometrie zur Vermessung lithographischer “Phase Shift” Masken und VUV-Strukturierung,” Ph.D. dissertation (University Erlangen-Nürnberg, 2002).

Görtler, K.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Grzanna, J.

Harder, I.

I. Harder, “Laterales DUV-Shearing Interferometer mit reduzierter zeitlicher und räumlicher Kohärenz,” Ph.D. dissertation (University Erlangen-Nürnberg, 2003).

Herrmann, J.

Hudgin, R. H.

Hunt, B. R.

Kobayashi, S.

Koliopoulos, C. L.

Lano, M.

G. Fütterer, M. Lano, N. Lindlein, and J. Schwider, “Lateral shearing interferometer for phase-shift mask measurement at 193 nm,” Proc. SPIE 4691, 541–551 (2002).
[CrossRef]

Lindlein, N.

G. Fütterer, M. Lano, N. Lindlein, and J. Schwider, “Lateral shearing interferometer for phase-shift mask measurement at 193 nm,” Proc. SPIE 4691, 541–551 (2002).
[CrossRef]

Lohmann, A. W.

Löwenthal, F.

C. Siegel, F. Löwenthal, and J. Balmer, “A wave front sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing, Series in Pure and Applied Optics (Wiley, 2007).
[CrossRef]

Merkel, K.

Mrochen, M.

M. Mrochen, M. Büeler, and T. Seiler, “Ophthalmologische Optik und Laser,” Research report (Augenklinik Universitätsspital Zürich, 2000/2001).

Schreiber, H.

Schwider, J.

Seiler, T.

M. Mrochen, M. Büeler, and T. Seiler, “Ophthalmologische Optik und Laser,” Research report (Augenklinik Universitätsspital Zürich, 2000/2001).

Siegel, C.

C. Siegel, F. Löwenthal, and J. Balmer, “A wave front sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

Spolaczyk, R.

Takeda, M.

Thomas, J. A.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Appl. Opt.

J. Opt. Soc. Am.

Opt. Commun.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

T. Dresel, “Optimization of symmetric Dammann gratings with a multidimensional error feedback algorithm,” Opt. Commun. 129, 19–26 (1996).
[CrossRef]

C. Siegel, F. Löwenthal, and J. Balmer, “A wave front sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

Optik

J. Schwider, “DOE-based interferometry,” Optik 108, 181–196 (1998).

Proc. SPIE

G. Fütterer, M. Lano, N. Lindlein, and J. Schwider, “Lateral shearing interferometer for phase-shift mask measurement at 193 nm,” Proc. SPIE 4691, 541–551 (2002).
[CrossRef]

Other

I. Harder, “Laterales DUV-Shearing Interferometer mit reduzierter zeitlicher und räumlicher Kohärenz,” Ph.D. dissertation (University Erlangen-Nürnberg, 2003).

G. Fütterer, “UV-Shearing Interferometrie zur Vermessung lithographischer “Phase Shift” Masken und VUV-Strukturierung,” Ph.D. dissertation (University Erlangen-Nürnberg, 2002).

J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1990), Vol.  28, pp. 271–359.
[CrossRef]

R. T. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” in Proceedings of the IEEE Conference on Transactions on Pattern Analysis and Machine Intelligence (IEEE, 1988), pp. 439–451.
[CrossRef]

M. Mrochen, M. Büeler, and T. Seiler, “Ophthalmologische Optik und Laser,” Research report (Augenklinik Universitätsspital Zürich, 2000/2001).

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

D. Malacara, Optical Shop Testing, Series in Pure and Applied Optics (Wiley, 2007).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Talbot interferogram of a phase object representing spherical aberration with an ablation depth of 9 μm . The image was taken at the first Talbot distance of 127 mm from an amplitude Ronchi grating having a period of 200 μm .

Fig. 2
Fig. 2

Measurement of a Zernike phase plate representing spherical aberration with an ablation depth of 6 μm using a Fizeau interferometer in double pass. (a) Evaluated phase. (b) Waviness of the surface due to point by point ablation. To show the waviness of the phase data, a global Zernike fit was subtracted from the evaluated phase values.

Fig. 3
Fig. 3

Scheme of the diffractive solution of a bidirectional shearing interferometer. The first two gratings are used for wavefront doubling producing two laterally separated copies of an incoming nearly planar wavefront. The following shearing unit consists of two identical gratings with orthogonally oriented substructures of identical periods. The arrow on the right indicates the direction of the lateral movement of the first shearing grating for producing the wanted phase shift.

Fig. 4
Fig. 4

Overview over the relative intensities of the diffracted waves for ideal Ronchi phase gratings with suppressed zeroth order in a series arrangement. Parasitic diffraction orders propagating parallel to the optical axis contribute only marginally to the resulting interference pattern.

Fig. 5
Fig. 5

Scheme of the experimental setup (a detailed description is given in the text). The wavelength of the He–Ne laser is 633 nm ; the period of the used gratings is 7.6 μm . This leads to a diffraction angle of ± 4.8 ° for the plus and minus first orders. The axial distance of the shearing gratings is therefore about 0.8 mm .

Fig. 6
Fig. 6

Fringe pattern produced by a small rotation of the second grating of the shearing unit.

Fig. 7
Fig. 7

Demonstration of the lateral movement of the wavefront copies due to a rotation of the first grating of the wavefront doubling unit. For small rotation angles, this will be mainly an up/down movement of the two shearing images.

Fig. 8
Fig. 8

Diffraction pattern fanned out by the 9 × 9 spot binary Dammann phase grating on the rotating scatterer.

Fig. 9
Fig. 9

Plot of the degree of coherence along one shear direction, according to Eq. (3). The values used for calculation are B = 20 mm , λ = 633 nm , f = 160 mm (lenses L1 and L2), G = 0.8 mm , β = 2 . This corresponds to the characteristics of the experimental setup. The measured PMMA probes have a diameter of 5 mm . The shear value S of 0.25 mm proved to deliver good results. S is calculated according to Eq. (4). Note that high contrast reoccurs periodically.

Fig. 10
Fig. 10

Shearing images for a single shear direction showing the periodic reoccurrence of the contrast with increasing shears. Shear values from left to right: one times basic shear, one and a half times, two times, two and a half times, and three times.

Fig. 11
Fig. 11

Double-circle mask selects a lune in the measuring field. The selection procedure of the mask with the interferogram can be assisted if a multiple of the basic shear is adjusted. At left is the shear used for the measurement; at right, the threefold shear is applied to the setup as well as to the selection masks to support the alignment of the masks with the rims of the measuring fields.

Fig. 12
Fig. 12

Unwrapped phase for x- and y-slope data for a phase object representing secondary spherical aberration with an ablation depth of 6 μm . The contour lines have a spacing of 0.6 waves; the figure shows a peak-to-valley of 5.1 waves on the left-hand side and 5.4 waves on the right-hand side.

Fig. 13
Fig. 13

Repeatability test for one slope component: difference of two consecutive measurements with the basic shear. The data were smoothed with a 5 × 5 kernel. The smoothed data show a peak-to-valley value of 0.007 waves and an rms of 0.0004 waves.

Fig. 14
Fig. 14

Zernike fit of the wavefront deviation of a circular phase object with a diameter of 5 mm , reconstructed from the two slope data fields illustrated in Fig. 12. The contour lines have a spacing of 0.5 waves; the figure shows a peak-to-valley of 9.6 waves, matching the expected value and shape given by the PMMA probe under test. The Zernike fit is calculated for a maximum degree of 10.

Equations (5)

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A ( ξ , η ) jinc 2 ( B λ f ξ 2 + η 2 ) ; jinc ( x ) = 2 J 1 ( π x ) π x b = 2 × 1.22 λ f B ,
I ( ξ , η ) [ jinc 2 ( B λ f ξ 2 + η 2 ) comb ( 1 G ξ , 1 G η ) ] rect ( 1 W ξ , 1 W η ) .
| γ 12 ( p , q ) | | [ chat ( 2 f B p 2 + q 2 ) comb ( G λ p , G λ q ) ] sinc ( W λ p , W λ q ) | p = ( x 1 x 2 ) f ; q = ( y 1 y 2 ) f .
S = β λ f G .
j 4 g 2 ; j = 0 , 1 , 2 , 3 , 4 .

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