Abstract

We present a surprising modification of optical interferometry. A so-called spiral phase element in the beam path of a standard microscope results in an interferogram of phase samples, for which the interference fringes have the shape of spirals instead of closed contour lines as in traditional interferograms. This configuration overrides the basic problem of interferometry, i.e., that elevations and depressions cannot be distinguished. Therefore a complete sample profile can be reconstructed from a single exposure, promising, e.g., high-speed metrology with a single laser pulse. The method is easy to implement, it does not require a spatially separated reference beam, and it is optimally stable against environmental noise.

© 2005 Optical Society of America

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References

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2005 (1)

2004 (2)

2003 (1)

2000 (1)

1992 (2)

N. Heckenberg, R. R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

1984 (1)

R. Smyth and R. Moore, Opt. Eng. 23, 361 (1984).

1965 (1)

Bernet, S.

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 1965).

Campos, J.

Cheng, X.

Cottrell, D. M.

Crabtree, K.

Davis, J. A.

Ding, J.

Fürhapter, S.

Guo, C.

Heckenberg, N.

Jesacher, A.

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

McDuff, R. R.

McNamara, D. E.

Moore, R.

R. Smyth and R. Moore, Opt. Eng. 23, 361 (1984).

Moreno, I.

Ren, X.

Ritsch-Marte, M.

Senthilkumaran, P.

Shafer, D.

Shannon, R. R.

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Smith, C. P.

Smyth, R.

R. Smyth and R. Moore, Opt. Eng. 23, 361 (1984).

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Wang, H.

Weekley, R. E.

White, A. G.

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Figures (3)

Fig. 1
Fig. 1

Reconstruction of a simulated phase profile by the method of spiral interferometry. (a) Simulated sample profile of a surface or a refractive structure. (b) Normal interferogram. The closed-contour lines do not distinguish between elevations and depressions. (c) Spiral interferogram obtained by filtering with the modified spiral phase-contrast method. Depending on the topography, the spirals change their rotational direction. (d) A single contour line of the spiral interferogram. (e) Processed contour line. The local direction of the line is proportional to the surface height, modulo one wavelength, which allows a unique height to be assigned to each single point of the contour line. (f) Reconstructed surface profile by interpolation between the sampling points given by the contour line.

Fig. 2
Fig. 2

Sketch of the experimental setup. A phase sample at a microscope sample stage is illuminated with light from a laser diode. The transmitted light is collected by a microscope objective. A relay lens ( L 1 ) is used to image the Fourier transform of the image wave at a SLM displaying a phase hologram. The light diffracted from the SLM into the first diffraction order is imaged through lens L 2 at a CCD camera, after the other diffraction orders are blocked. At the left the central section of a spiral phase hologram is sketched, which is displayed at the SLM (gray levels correspond to phase values). The modification necessary to produce the described spiral fringes is done by substituting a blazed grating (indicated above), which diffracts the zero-order Fourier spot of the incident image wave, for a circular area about the central singularity. At the image detector this zero-order Fourier component evolves into a plane wave, which interferes with the remainder of the image wave, as required for spiral interferometry.

Fig. 3
Fig. 3

Experimentally obtained interferogram of an oil drop smeared on a glass coverslip. (a) Normal contourlike interference fringes. (b) Spiral interferogram of the same sample region obtained after filtering with the modified spiral phase hologram (the blazed grating in a small central area; upper left in Fig. 2). (c) Section of the spiral interferogram to be processed. (d) Single contour line of the spiral interferogram. (e) Surface profile reconstructed by processing the contour line and fitting the surface at the obtained sampling points.

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