Abstract

This paper proposes a simple noninvasive method that makes it possible to calculate the inner design parameters of the cemented doublet using measurements of its chosen paraxial optical and geometrical parameters without any damage to the system under testing (e.g., dismantling). Derived formulas are based on the knowledge of measured values of the lenses thicknesses, the radii of curvatures of the first and the last doublet’s surfaces, the paraxial focal length, and positions of the object and the image focal point. Practical usefulness of the proposed method is demonstrated on the real measurement of a known doublet.

© 2016 Optical Society of America

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References

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  1. M. Herzberger, Modern Geometrical Optics (Interscience, 1958).
  2. A. Mikš, Applied Optics (Czech Technical University, 2009).
  3. M. Berek, Grundlagen der Praktischen Optik (Walter de Gruyter & Co., 1970).
  4. M. Born and E. Wolf, Principles of Optics (Oxford University, 1964).
  5. W. T. Welford, Aberrations of the Symmetrical Optical Systems (Academic, 1974).
  6. A. Miks, J. Novak, and P. Novak, “Generalized refractive tunable-focus lens and its imaging characteristics,” Opt. Express 18, 9034–9047 (2010).
    [Crossref]
  7. D. Malacara, Optical Shop Testing (Wiley, 2007).
  8. G. V. Kreopalova, N. L. Lazareva, and D. T. Puriajev, Optical Measurements (Maschinostroenie, 1987).
  9. J. Picht, Meß- und Prüfmethoden der optischen Fertigung (Akademie-Verlag, 1953).
  10. J. Flügge, Einführung in die Messung der optischen Grundgrössen (Verlag Braun, 1954).
  11. B. Dorband, H. Miller, and H. Gross, Handbook of Optical Systems, Vol. 5 of Metrology of Optical Components and Systems (Wiley, 2012).
  12. http://www.zygo.com/ .
  13. http://www.trioptics.com/ .
  14. http://www.oeg-messtechnik.de/ .
  15. A. Miks and J. Novak, “Experimental method of determination of parameters of cemented doublet,” Appl. Opt. 54, 7940–7943 (2015).
    [Crossref]
  16. L. E. Scales, Introduction to Non-linear Optimization (Springer, 1985).
  17. E. M. T. Hendrix and B. G. Toth, Introduction to Nonlinear and Global Optimization (Springer, 2010).
  18. http://www.meopta.com/en/ .

2015 (1)

2010 (1)

Berek, M.

M. Berek, Grundlagen der Praktischen Optik (Walter de Gruyter & Co., 1970).

Born, M.

M. Born and E. Wolf, Principles of Optics (Oxford University, 1964).

Dorband, B.

B. Dorband, H. Miller, and H. Gross, Handbook of Optical Systems, Vol. 5 of Metrology of Optical Components and Systems (Wiley, 2012).

Flügge, J.

J. Flügge, Einführung in die Messung der optischen Grundgrössen (Verlag Braun, 1954).

Gross, H.

B. Dorband, H. Miller, and H. Gross, Handbook of Optical Systems, Vol. 5 of Metrology of Optical Components and Systems (Wiley, 2012).

Hendrix, E. M. T.

E. M. T. Hendrix and B. G. Toth, Introduction to Nonlinear and Global Optimization (Springer, 2010).

Herzberger, M.

M. Herzberger, Modern Geometrical Optics (Interscience, 1958).

Kreopalova, G. V.

G. V. Kreopalova, N. L. Lazareva, and D. T. Puriajev, Optical Measurements (Maschinostroenie, 1987).

Lazareva, N. L.

G. V. Kreopalova, N. L. Lazareva, and D. T. Puriajev, Optical Measurements (Maschinostroenie, 1987).

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 2007).

Miks, A.

Mikš, A.

A. Mikš, Applied Optics (Czech Technical University, 2009).

Miller, H.

B. Dorband, H. Miller, and H. Gross, Handbook of Optical Systems, Vol. 5 of Metrology of Optical Components and Systems (Wiley, 2012).

Novak, J.

Novak, P.

Picht, J.

J. Picht, Meß- und Prüfmethoden der optischen Fertigung (Akademie-Verlag, 1953).

Puriajev, D. T.

G. V. Kreopalova, N. L. Lazareva, and D. T. Puriajev, Optical Measurements (Maschinostroenie, 1987).

Scales, L. E.

L. E. Scales, Introduction to Non-linear Optimization (Springer, 1985).

Toth, B. G.

E. M. T. Hendrix and B. G. Toth, Introduction to Nonlinear and Global Optimization (Springer, 2010).

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical Systems (Academic, 1974).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Oxford University, 1964).

Appl. Opt. (1)

Opt. Express (1)

Other (16)

D. Malacara, Optical Shop Testing (Wiley, 2007).

G. V. Kreopalova, N. L. Lazareva, and D. T. Puriajev, Optical Measurements (Maschinostroenie, 1987).

J. Picht, Meß- und Prüfmethoden der optischen Fertigung (Akademie-Verlag, 1953).

J. Flügge, Einführung in die Messung der optischen Grundgrössen (Verlag Braun, 1954).

B. Dorband, H. Miller, and H. Gross, Handbook of Optical Systems, Vol. 5 of Metrology of Optical Components and Systems (Wiley, 2012).

http://www.zygo.com/ .

http://www.trioptics.com/ .

http://www.oeg-messtechnik.de/ .

L. E. Scales, Introduction to Non-linear Optimization (Springer, 1985).

E. M. T. Hendrix and B. G. Toth, Introduction to Nonlinear and Global Optimization (Springer, 2010).

http://www.meopta.com/en/ .

M. Herzberger, Modern Geometrical Optics (Interscience, 1958).

A. Mikš, Applied Optics (Czech Technical University, 2009).

M. Berek, Grundlagen der Praktischen Optik (Walter de Gruyter & Co., 1970).

M. Born and E. Wolf, Principles of Optics (Oxford University, 1964).

W. T. Welford, Aberrations of the Symmetrical Optical Systems (Academic, 1974).

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Figures (1)

Fig. 1.
Fig. 1. Optical scheme of cemented doublet.

Tables (1)

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Table 1. Comparison of Nominal and Calculated Values of Inner Parameters of Cemented Doublet

Equations (10)

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ϕ=ϕ1+ϕ2+ϕ3D1(ϕ1ϕ2+ϕ1ϕ3)D2(ϕ1ϕ3+ϕ2ϕ3)+D1D2ϕ1ϕ2ϕ3,
sF=n0(D1ϕ2+D1ϕ3+D2ϕ3D1D2ϕ2ϕ31)/ϕ,
sF=n3(D1ϕ1+D2ϕ1+D2ϕ2D1D2ϕ1ϕ21)/ϕ,
s=n0n3(D1+D2D1D2ϕ2)ssFϕϕ(sFs),
ϕ1=(n1n0)/r1,ϕ2=(n2n1)/r2,ϕ3=(n3n2)/r3,
D1=d1/n1,D2=d2/n2.
n2=d2+ϕ2d2(sFsF+r1r3r3sFr1sF)d2+r3ϕr3(d1r1)+ϕ2sF(d2sF+r3sFd2r1r1r3).
n1=ϕd1n2r3(r1sF)r1(d2n2d2+n2r3)ϕn2r3sF(d1r1).
r2=d1[d2(n21)n2r3+1](n1n2)n1[ϕsF+d1(n21)n1r3+d2(n21)n2r3+1],
r2=d2[d1(n11)n1r11](n1n2)n2[ϕsF+d1(n11)n1r1+d2(n11)n2r11].

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