Abstract

We study the effects of an extended light source on the calibration of an interference microscope, also referred to as an optical profiler. Theoretical and experimental numerical aperture (NA) factors for circular and linear light sources along with collimated laser illumination demonstrate that the shape of the light source or effective aperture cone is critical for a correct NA factor calculation. In practice, more-accurate results for the NA factor are obtained when a linear approximation to the filament light source shape is used in a geometric model. We show that previously measured and derived NA factors show some discrepancies because a circular rather than linear approximation to the filament source was used in the modeling.

© 2004 Optical Society of America

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References

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  1. J. E. Greivnekamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 2nd ed., D Malacara, ed. (Wiley, New York, 1992), pp. 501–598.
  2. G. Schulz, “Deduction of theory,” in Contributions to Interference of Microscopy, W. Krug, J. Rienitz, G. Schulz, eds., translated by J. H. Dickson (Hilger and Watts, London, 1964), pp. 282–296.
  3. C. J. R. Sheppard, K. G. Larkin, “Effect of numerical aperture on interference spacing,” Appl. Opt. 34, 4731–4734 (1995).
    [CrossRef]
  4. J. Biegen, “Calibration requirements for Mirau and Linnik microscope interferometers,” Appl. Opt. 28, 1972–1974 (1989).
    [CrossRef] [PubMed]
  5. Measurement was performed with a Wyko NT 3300 optical profiler (Veeco Instruments, Tucson, Ariz.).
  6. Measurement was performed with a Wyko NT 8000 optical profiler (Veeco Instruments, Tucson, Ariz.).
  7. A. Dubois, J. Selb, L. Vabre, A.-C. Boccara, “Phase measurements with wide-aperture interferometers,” Appl. Opt. 39, 2326–2331 (2000).
    [CrossRef]

2000 (1)

1995 (1)

1989 (1)

Biegen, J.

Boccara, A.-C.

Bruning, J. H.

J. E. Greivnekamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 2nd ed., D Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

Dubois, A.

Greivnekamp, J. E.

J. E. Greivnekamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 2nd ed., D Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

Larkin, K. G.

Schulz, G.

G. Schulz, “Deduction of theory,” in Contributions to Interference of Microscopy, W. Krug, J. Rienitz, G. Schulz, eds., translated by J. H. Dickson (Hilger and Watts, London, 1964), pp. 282–296.

Selb, J.

Sheppard, C. J. R.

Vabre, L.

Appl. Opt. (3)

Other (4)

J. E. Greivnekamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 2nd ed., D Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

G. Schulz, “Deduction of theory,” in Contributions to Interference of Microscopy, W. Krug, J. Rienitz, G. Schulz, eds., translated by J. H. Dickson (Hilger and Watts, London, 1964), pp. 282–296.

Measurement was performed with a Wyko NT 3300 optical profiler (Veeco Instruments, Tucson, Ariz.).

Measurement was performed with a Wyko NT 8000 optical profiler (Veeco Instruments, Tucson, Ariz.).

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Figures (6)

Fig. 1
Fig. 1

Illustration of an effective aperture cone.

Fig. 2
Fig. 2

Schematic diagram of the interferometer and illumination system shown in Ref. 2. The illumination is through one side of the Michelson interferometer.

Fig. 3
Fig. 3

Schematic diagram of the Köhler illuminator for telecentric objectives.

Fig. 4
Fig. 4

OPD model for this paper. RP and ST 1-T 1 P represent two rays from one point in the light source reaching point P on the reference surface and reaching point T 1 on the test surface and reflecting back to point P on the reference surface. The OPD between these two rays is the sum of distance AT 1 and T 1 P. The pair of dashed lines (UP and VT 2-T 2 P) represents OPD at P contributed by the other point in the light source. The OPD for point P is the average of OPDs from all possible contributions by all points of the light source.

Fig. 5
Fig. 5

Central obscuration in the Mirau interferometer that determines the minimum of illumination angle.

Fig. 6
Fig. 6

Diagram showing images of the illumination aperture (dotted curve), pupil of the objective (dashed curve), and the effective aperture (solid curve).

Tables (1)

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Table 1 Values for NA Factors

Equations (8)

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m¯= 1Cp cos φ+h sin φ cos χdΩΩ,
m¯=pC1+cos u2,
Uh=0u P1φP2φRφexp-2ikd cos φ×sin φdφ,
Pφ=cosn φ.
OPD=ATi+TiP=d/cos α+d cos β/cos α,
α=2θ-φ, β=α-φ.
m¯=i=1nOPDin.
β=1+0.25NA2+0.1NA4+0.086NA6.

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