Abstract

A method to determine the location of the paraxial image plane of an imaging system is discussed. This method uses a recently developed quantitative Ronchi test and is different in that the location of paraxial image plane of the system can be determined from the measured Ronchigrams alone. We validate the location determined by the method by modifying the optical setup and comparing the retrieved f-number of the system to the theoretical prediction.

© 2010 OSA

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References

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  1. C. Donald, O’Shea, Elements of Modern Optical Design, John Wiley & Sons, New York (1985).
  2. P. Mouroulis, and J. Macdonald, Geometrical Optics and Optical Design, Oxford University Press, New York (1997).
  3. R. R. Shannon, The Art and Science of Optical Design, Cambridge University Press, Cambridge (1997).
  4. V. N. Mahajan, “Zernike polynomials and aberration balancing,” Proc. of SPIE Vol. 5173, edited by P.Z. Mouroulis, W.J. Smith, and R.B. Johnson (SPIE, Bellingham, WA, 2003).
  5. For example,Y. Nakano and K. Murata, “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24(19), 3162 (1985).
    [CrossRef] [PubMed]
  6. S. Lee and J. Sasian, “Ronchigram quantification via a non-complementary dark-space effect,” Opt. Express 17(3), 1854–1858 (2009).
    [CrossRef] [PubMed]
  7. S. Lee, “Direct determination of f-number by using Ronchi test,” Opt. Express 17(7), 5107–5111 (2009).
    [CrossRef] [PubMed]
  8. There are many different conventions, but we followed the one in J. C. Wyant and K. Creath, “Basic Wavefront Aberration Theory for Optical Metrology,” in Applied Optics and Optical Engineering, XI, 1992, Academic Press, Inc.

2009 (2)

1985 (1)

Appl. Opt. (1)

Opt. Express (2)

Other (5)

There are many different conventions, but we followed the one in J. C. Wyant and K. Creath, “Basic Wavefront Aberration Theory for Optical Metrology,” in Applied Optics and Optical Engineering, XI, 1992, Academic Press, Inc.

C. Donald, O’Shea, Elements of Modern Optical Design, John Wiley & Sons, New York (1985).

P. Mouroulis, and J. Macdonald, Geometrical Optics and Optical Design, Oxford University Press, New York (1997).

R. R. Shannon, The Art and Science of Optical Design, Cambridge University Press, Cambridge (1997).

V. N. Mahajan, “Zernike polynomials and aberration balancing,” Proc. of SPIE Vol. 5173, edited by P.Z. Mouroulis, W.J. Smith, and R.B. Johnson (SPIE, Bellingham, WA, 2003).

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Figures (4)

Fig. 1
Fig. 1

Ronchi test setup for measuring transverse ray aberrations in a beam. Notice that the aperture is located behind the test lens and that the location of the aperture was varied.

Fig. 2
Fig. 2

A set of typical Ronchigrams. The ruling is in vertical orientation for (a) and (b) and horizontal orientation for (c) and (d). (A) and (c) are 0-phase and (b) and (d) are π-phase.

Fig. 3
Fig. 3

Defocus a3 (black squares) and spherical aberration a8 (red circles) for the aperture stop located at 4 mm are drawn as a function of ruling’s longitudinal position. The accompanied lines are the fitted lines.

Fig. 4
Fig. 4

(a) The f-number and (b) the primary spherical aberration a 8 are drawn as a function of the aperture location, z AS. The black lines show the theoretical values with respect to those for the initial aperture location at 0 mm, respectively.

Tables (1)

Tables Icon

Table 1 The F/#, the primary spherical aberration a 8, and the locations of the paraxial image plane in terms of Ronchi ruling locations, determined by the quantitative Ronchi test are listed for several locations of the aperture.

Equations (3)

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0 W 20 = d z 8 ( F/# ) 2 ,
F/# = ( F/# ) 0 z AS D 0 ,
a 8 = a 8 , 0 ( F/# ( F/# ) 0 ) 4 ,

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