Abstract

In this Letter, we introduce an algorithm that overcomes limitations in shape measurement by holographic microscopic methods in cases of micro-optical elements with high NA, such as microlenses. The presented algorithm provides a simple method for shape reconstruction from interferometrically measured phase. The algorithm is based on the analysis of local ray transition through the measured object. We develop algorithms for holographic configurations working in transmission and reflection. The accuracy of the developed algorithms is proved by experiments and extensive simulations. We present an experiment in a holographic Mach–Zehnder configuration where we have measured and successfully reconstructed the height distribution of spherical and cylindrical microlenses with NA up to 0.3.

© 2011 Optical Society of America

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References

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  1. H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
    [CrossRef]
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    [CrossRef]
  3. T. Colomb, N. Pavillon, J. Kühn, E. Cuche, Ch. Depeursinge, and Y. Emery, Opt. Lett. 35, 1840 (2010).
    [CrossRef] [PubMed]
  4. T. Kozacki, M. Józwik, and R. Joźwicki, Opto-Electron. Rev. 17, 211 (2009).
    [CrossRef]
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2010 (1)

2009 (1)

T. Kozacki, M. Józwik, and R. Joźwicki, Opto-Electron. Rev. 17, 211 (2009).
[CrossRef]

2007 (1)

T. Miyashita, Jpn. J. Appl. Phys. 46, 5391 (2007).
[CrossRef]

2006 (1)

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

2001 (1)

1998 (1)

Angelsky, O. V.

Colomb, T.

Cox, R.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Cuche, E.

Depeursinge, Ch.

Emery, Y.

Hanson, S. G.

Herzig, H. P.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Jozwicki, R.

T. Kozacki, M. Józwik, and R. Joźwicki, Opto-Electron. Rev. 17, 211 (2009).
[CrossRef]

Józwik, M.

T. Kozacki, M. Józwik, and R. Joźwicki, Opto-Electron. Rev. 17, 211 (2009).
[CrossRef]

Kozacki, T.

T. Kozacki, M. Józwik, and R. Joźwicki, Opto-Electron. Rev. 17, 211 (2009).
[CrossRef]

Kühn, J.

Maksimyak, P. P.

Miyashita, T.

T. Miyashita, Jpn. J. Appl. Phys. 46, 5391 (2007).
[CrossRef]

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Naessens, K.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Ottevaere, H.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Pavillon, N.

Rohrbach, A.

Ryukhtin, V. V.

Singer, W.

Taghizadeh, M.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Thienpont, H.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Völkel, R.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Woo, H. J.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Appl. Opt. (1)

J. Opt. A (1)

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

T. Miyashita, Jpn. J. Appl. Phys. 46, 5391 (2007).
[CrossRef]

Opt. Lett. (1)

Opto-Electron. Rev. (1)

T. Kozacki, M. Józwik, and R. Joźwicki, Opto-Electron. Rev. 17, 211 (2009).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Plane wave local ray refraction by a microlens under test.

Fig. 2
Fig. 2

Plane wave local ray reflection from a microlens under test.

Fig. 3
Fig. 3

Error of height reconstruction using the LRA and TEA methods for spherical microlenses of NA 0.3, radius of curvature 167 μm , diameter 200 μm , substrate refractive index 1.5, and wavelength 0.5 μm .

Fig. 4
Fig. 4

Area where shape was reconstructed with peak-to-valley ratio (PV) error smaller than λ / 20 for cylindrical microlenses with diameter 100 μm and different radii of curvature from phase measurement for microlenses in transmission and in reflection.

Fig. 5
Fig. 5

Measurement results of a spherical microlens of NA = 0.18 .

Fig. 6
Fig. 6

Difference between shapes reconstructed using the LRA and TEA methods for a spherical microlens of NA = 0.18 (cross section through the vertex of the microlens).

Fig. 7
Fig. 7

Measurement results of cylindrical microlens of NA = 0.3 .

Fig. 8
Fig. 8

Difference between shapes reconstructed using the LRA and TEA methods for a cylindrical microlens of NA = 0.3 .

Equations (6)

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k n = [ k x n , k y n , k z n ] = [ φ ( x ) , ( k 0 2 Δ φ ( x ) ) 1 / 2 ] .
φ ( x ) = OPD n h m = n h k 0 h k 0 2 / k z n .
h ( x ) = φ ( x ) ( n k 0 k 0 2 k z n 1 ) 1 ,
x s = φ ( x ) φ ( x ) k 0 1 ( n k z n k 0 ) 1 ,
h ( x + x s ) = φ ( x ) ( k 0 + k 0 2 k z n 1 ) 1 ,
x s = φ ( x ) φ ( x ) ( k z n k 0 + k 0 2 ) 1 .

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