Abstract

A method to determine f-number for an imaging system is discussed. This method uses Ronchi test and is different in that the value of f-number of the system can be determined without depending on any particular parameters. Two different sizes of aperture for a common system were investigated and the corresponding f-numbers were compared with those calculated by a lens design software. In addition, the determined f-numbers are proved to be consistent with other values obtained in this study.

© 2009 Optical Society of America

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References

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  1. R. Ditteon, Modern Geometrical Optics, Wiley, New York (1998).
  2. G. Smith and D.A. Atchison, The Eye and Visual Optical Instruments, Cambridge University Press (1997).
    [CrossRef]
  3. R.R. Shannon, The Art and Science of Optical Design, Cambridge University Press (1997).
  4. S. Lee and J. Sasian, "Ronchigram quantification via a non-complementary dark-space effect," Opt. Express 17, 1854-1858 (2009).
    [CrossRef] [PubMed]
  5. There are many different versions, but we adopted one. J. C. Wyant and K. Creath, "Basic Wavefront Aberration Theory for Optical Metrology," in Applied Optics and Optical Engineering, XI, 1992, Academic Press, Inc.
  6. ZEMAX Optical Design Program, ZEMAX Development Corporation, www.zemax.com.

2009 (1)

Opt. Express (1)

Other (5)

There are many different versions, but we adopted one. J. C. Wyant and K. Creath, "Basic Wavefront Aberration Theory for Optical Metrology," in Applied Optics and Optical Engineering, XI, 1992, Academic Press, Inc.

ZEMAX Optical Design Program, ZEMAX Development Corporation, www.zemax.com.

R. Ditteon, Modern Geometrical Optics, Wiley, New York (1998).

G. Smith and D.A. Atchison, The Eye and Visual Optical Instruments, Cambridge University Press (1997).
[CrossRef]

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

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Figures (3)

Fig. 1.
Fig. 1.

Ronchi test setup for measuring transverse ray aberrations in a beam.

Fig. 2.
Fig. 2.

Representing Ronchi images with two different apertures (a) 20 mm and (b) 30 mm.

Fig. 3.
Fig. 3.

Two important Zernike polynomial coefficients, a 3 in black and a 8 in red as a function of ruling’s location, determined by Ronchi test with two different apertures of (a) 20 mm and (b) 30 mm.

Tables (1)

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Table 1. F-number measured with those calculated by ZEMAX for 2 different sizes of aperture.

Equations (13)

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ε ( i ) x = 2 ( F / # ) k = 1 35 a k Z ( i ) k x
ε ( i ) y = 2 ( F / # ) k = 1 35 a k Z ( i ) k y
AZ Z T = 1 2 ( F / # ) E Z T
A = ( a 1 a 2 a 35 ) .
E ( ε x ( 1 ) ε x ( 2 ) ε x ( N x ) ε y ( 1 ) ε y ( 2 ) ε y ( N y ) ) ,
Z = ( Z ( 1 ) 1 x Z ( 2 ) 1 x Z ( N x ) 1 x Z ( 1 ) 1 y Z ( 2 ) 1 y Z ( N y ) 1 y Z ( 1 ) 2 x Z ( 2 ) 2 x Z ( N x ) 2 x Z ( 1 ) 2 y Z ( 2 ) 2 y Z ( N y ) 2 y Z ( 1 ) 34 x Z ( 2 ) 34 x Z ( N x ) 34 x Z ( 1 ) 34 y Z ( 2 ) 34 y Z ( N y ) 34 x Z ( 1 ) 35 x Z ( 2 ) 35 x Z ( N x ) 35 x Z ( 1 ) 35 y Z ( 2 ) 35 y Z ( N y ) 35 y ) .
A = 1 2 ( F / # ) E Z T ( Z Z T ) 1 .
Δ a 3 = Δ a 3 , F / # = 1 ( F / # )
Δ a 3 = < Δ a 3 , F / # = 1 > ( F / # ) .
0 W 20 = δz 8 ( F / # ) 2 ,
Δ ( 0 W 20 ) = Δz 8 ( F / # ) 2 .
Δ a 3 = Δ z 16 ( F / # ) 2 .
F / # = Δ z 16 < Δ a 3 , F / # = 1 > .

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