Abstract

We present a method for absolute testing of axicon surfaces in a null test setup. The absolute test exploits the symmetry of axicons, which allows us to introduce a shift of the surface under test in both the axial and rotational directions while still maintaining the null test condition. With two shifts of the surface under test and four measurements, the interferometer and null optics error can be removed. The absolute surface local deviation can be obtained by wavefront reconstruction with a double-side spiral-path direct integration method. A simulation of the method, including typical systematic as well as statistical errors as input, is presented to estimate the error propagation. Experimental absolute test results of a 90° axicon surface are given.

© 2011 Optical Society of America

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  1. V. Belyi, A. Forbes, N. Kazak, N. Khilo, and P. Ropot, Opt. Express 18, 1966 (2010).
    [CrossRef] [PubMed]
  2. O. Brzobohatý, T. Cizmár, and P. Zemánek, Opt. Express 16, 12688 (2008).
    [PubMed]
  3. J. Hayes, K. L. Underwood, J. S. Loomis, R. E. Parks, and J. C. Wyant, Appl. Opt. 20, 235 (1981).
    [CrossRef] [PubMed]
  4. M. Deangelis, S. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Lasers Eng. 39, 155 (2003).
    [CrossRef]
  5. D. Kupka, P. Schlup, and R. A. Bartels, Appl. Opt. 47, 1200 (2008).
    [CrossRef] [PubMed]
  6. S. Reichelt and H. J. Tiziani, Opt. Commun. 220, 23 (2003).
    [CrossRef]
  7. K. Mantel, E. Geist, I. Harder, N. Lindlein, and G. Leuchs, Opt. Lett. 34, 3178 (2009).
    [CrossRef] [PubMed]
  8. E. E. Bloemhof, Opt. Lett. 35, 2346 (2010).
    [CrossRef] [PubMed]
  9. F. Roddier and C. Roddier, Appl. Opt. 30, 1325 (1991).
    [CrossRef] [PubMed]
  10. W. Zou and J. P. Rolland, J. Opt. Soc. Am. A 22, 938 (2005).
    [CrossRef]
  11. P. Hariharan, B. F. Oreb, and W. Zhou, J. Mod. Opt. 33, 251 (1986).
  12. J. Nam and J. Rubinstein, J. Opt. Soc. Am. A 25, 1697 (2008).
    [CrossRef]
  13. S. Reichelt, M. Daffner, H. J. Tiziani, and R. Freimann, J. Mod. Opt. 49, 1069 (2002).
    [CrossRef]
  14. J. Ma, C. Pruss, M. Häfner, B. Heitkamp, R. Zhu, Z. Gao, C. Yuan, and W. Osten, “Systematic analysis of the measurement of cone angles using high line density computer-generated holograms,” Opt. Eng. (to be published).

2010

2009

2008

2005

2003

M. Deangelis, S. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Lasers Eng. 39, 155 (2003).
[CrossRef]

S. Reichelt and H. J. Tiziani, Opt. Commun. 220, 23 (2003).
[CrossRef]

2002

S. Reichelt, M. Daffner, H. J. Tiziani, and R. Freimann, J. Mod. Opt. 49, 1069 (2002).
[CrossRef]

1991

1986

P. Hariharan, B. F. Oreb, and W. Zhou, J. Mod. Opt. 33, 251 (1986).

1981

Bartels, R. A.

Belyi, V.

Bloemhof, E. E.

Brzobohatý, O.

Cizmár, T.

Daffner, M.

S. Reichelt, M. Daffner, H. J. Tiziani, and R. Freimann, J. Mod. Opt. 49, 1069 (2002).
[CrossRef]

Deangelis, M.

M. Deangelis, S. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Lasers Eng. 39, 155 (2003).
[CrossRef]

Ferraro, P.

M. Deangelis, S. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Lasers Eng. 39, 155 (2003).
[CrossRef]

Finizio, A.

M. Deangelis, S. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Lasers Eng. 39, 155 (2003).
[CrossRef]

Forbes, A.

Freimann, R.

S. Reichelt, M. Daffner, H. J. Tiziani, and R. Freimann, J. Mod. Opt. 49, 1069 (2002).
[CrossRef]

Gao, Z.

J. Ma, C. Pruss, M. Häfner, B. Heitkamp, R. Zhu, Z. Gao, C. Yuan, and W. Osten, “Systematic analysis of the measurement of cone angles using high line density computer-generated holograms,” Opt. Eng. (to be published).

Geist, E.

Häfner, M.

J. Ma, C. Pruss, M. Häfner, B. Heitkamp, R. Zhu, Z. Gao, C. Yuan, and W. Osten, “Systematic analysis of the measurement of cone angles using high line density computer-generated holograms,” Opt. Eng. (to be published).

Harder, I.

Hariharan, P.

P. Hariharan, B. F. Oreb, and W. Zhou, J. Mod. Opt. 33, 251 (1986).

Hayes, J.

Heitkamp, B.

J. Ma, C. Pruss, M. Häfner, B. Heitkamp, R. Zhu, Z. Gao, C. Yuan, and W. Osten, “Systematic analysis of the measurement of cone angles using high line density computer-generated holograms,” Opt. Eng. (to be published).

Kazak, N.

Khilo, N.

Kupka, D.

Leuchs, G.

Lindlein, N.

Loomis, J. S.

Ma, J.

J. Ma, C. Pruss, M. Häfner, B. Heitkamp, R. Zhu, Z. Gao, C. Yuan, and W. Osten, “Systematic analysis of the measurement of cone angles using high line density computer-generated holograms,” Opt. Eng. (to be published).

Mantel, K.

Nam, J.

Nicola, S.

M. Deangelis, S. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Lasers Eng. 39, 155 (2003).
[CrossRef]

Oreb, B. F.

P. Hariharan, B. F. Oreb, and W. Zhou, J. Mod. Opt. 33, 251 (1986).

Osten, W.

J. Ma, C. Pruss, M. Häfner, B. Heitkamp, R. Zhu, Z. Gao, C. Yuan, and W. Osten, “Systematic analysis of the measurement of cone angles using high line density computer-generated holograms,” Opt. Eng. (to be published).

Parks, R. E.

Pierattini, G.

M. Deangelis, S. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Lasers Eng. 39, 155 (2003).
[CrossRef]

Pruss, C.

J. Ma, C. Pruss, M. Häfner, B. Heitkamp, R. Zhu, Z. Gao, C. Yuan, and W. Osten, “Systematic analysis of the measurement of cone angles using high line density computer-generated holograms,” Opt. Eng. (to be published).

Reichelt, S.

S. Reichelt and H. J. Tiziani, Opt. Commun. 220, 23 (2003).
[CrossRef]

S. Reichelt, M. Daffner, H. J. Tiziani, and R. Freimann, J. Mod. Opt. 49, 1069 (2002).
[CrossRef]

Roddier, C.

Roddier, F.

Rolland, J. P.

Ropot, P.

Rubinstein, J.

Schlup, P.

Tiziani, H. J.

S. Reichelt and H. J. Tiziani, Opt. Commun. 220, 23 (2003).
[CrossRef]

S. Reichelt, M. Daffner, H. J. Tiziani, and R. Freimann, J. Mod. Opt. 49, 1069 (2002).
[CrossRef]

Underwood, K. L.

Wyant, J. C.

Yuan, C.

J. Ma, C. Pruss, M. Häfner, B. Heitkamp, R. Zhu, Z. Gao, C. Yuan, and W. Osten, “Systematic analysis of the measurement of cone angles using high line density computer-generated holograms,” Opt. Eng. (to be published).

Zemánek, P.

Zhou, W.

P. Hariharan, B. F. Oreb, and W. Zhou, J. Mod. Opt. 33, 251 (1986).

Zhu, R.

J. Ma, C. Pruss, M. Häfner, B. Heitkamp, R. Zhu, Z. Gao, C. Yuan, and W. Osten, “Systematic analysis of the measurement of cone angles using high line density computer-generated holograms,” Opt. Eng. (to be published).

Zou, W.

Appl. Opt.

J. Mod. Opt.

P. Hariharan, B. F. Oreb, and W. Zhou, J. Mod. Opt. 33, 251 (1986).

S. Reichelt, M. Daffner, H. J. Tiziani, and R. Freimann, J. Mod. Opt. 49, 1069 (2002).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

S. Reichelt and H. J. Tiziani, Opt. Commun. 220, 23 (2003).
[CrossRef]

Opt. Eng.

J. Ma, C. Pruss, M. Häfner, B. Heitkamp, R. Zhu, Z. Gao, C. Yuan, and W. Osten, “Systematic analysis of the measurement of cone angles using high line density computer-generated holograms,” Opt. Eng. (to be published).

Opt. Express

Opt. Lasers Eng.

M. Deangelis, S. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, Opt. Lasers Eng. 39, 155 (2003).
[CrossRef]

Opt. Lett.

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Figures (5)

Fig. 1
Fig. 1

Shifting positions required for the absolute test. Test setup for testing an axicon in reflection with (a) a null lens, (b) axial translation, and (c) rotation.

Fig. 2
Fig. 2

Measurement configuration of CGH and axicon surface. Effective rays of CGH with r i and r o as the boundaries’ radii.

Fig. 3
Fig. 3

SDI diagram. Red point at left, starting point of the integration; blue point at upper right, target point of the integration.

Fig. 4
Fig. 4

(a) Simulation of an absolute axicon measurement on a model interferometer with system error and (b) measuring a surface under test with errors, yielding the (c) reconstruction error.

Fig. 5
Fig. 5

(a) Experimental result is split into the (b) systematic error and the (c) surface topography error.

Equations (8)

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Φ ( ρ , θ ) = ϕ axicon ( ρ , θ ) + ϕ sys ( ρ , θ ) + ϕ noise ( ρ , θ ) + ϕ mis ( ρ , θ ) .
Φ ± Δ θ ( ρ , θ ) = ϕ axicon ( ρ , θ ± Δ θ ) + ϕ sys ( ρ , θ ) .
r i = Z 0 × tan ( α / 2 ) ,
r o = 2 × h × tan ( α / 2 ) + r i ,
Φ ± Δ z ( ρ , θ ) = ϕ axicon ( ρ ± Δ Z × cot ( α / 2 ) , θ ) + ϕ sys ( ρ , θ ) .
Φ Δ θ ( ρ , θ ) Φ Δ θ ( ρ , θ ) = ϕ ( ρ , θ + Δ θ ) ϕ ( ρ , θ Δ θ ) ,
Φ Δ z ( ρ , θ ) Φ Δ z ( ρ , θ ) = ϕ ( ρ + Δ ρ , θ ) ϕ ( ρ Δ ρ , θ ) .
( Φ Δ x ( x , y ) Φ Δ y ( x , y ) ) = ( Δ x 0 0 Δ y ) ( cos θ sin θ / ρ sin θ cos θ / ρ ) ( Φ Δ z / ( 2 × Δ ρ ) Φ Δ θ / ( 2 × Δ θ ) ) .

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