Abstract

In this paper, formulas are described for the calculation of the third-order aberration (Seidel) coefficients for a thick lens in air. The explicit analytic dependence of individual aberration coefficients on a lens thickness is presented. Such formulas make it possible to analyze an influence of the lens thickness on lens aberration properties and the replacement of a thick lens optical system by a thin lens model.

© 2012 Optical Society of America

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References

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  1. M. Herzberger, Strahlenoptik (Springer, 1931).
  2. A. Mikš, Applied Optics (Czech Technical University, 2009).
  3. M. Berek, Grundlagen der praktischen optik (Walter de Gruyter, 1970).
  4. H. Chretien, Calcul des Combinaisons Optiques (Masson, 1980).
  5. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  6. W. T. Welford, Aberrations of Optical Systems (Taylor & Francis, 1986).
  7. C. G. Wynne, “Primary aberrations and conjugate change,” Proc. R. Soc. London Sect. B 65, 429–437 (1952).
    [CrossRef]
  8. W. Smith, Modern Optical Engineering (McGraw-Hill, 2000).
  9. Lambda Research, http://lambdares.com/ .

1952

C. G. Wynne, “Primary aberrations and conjugate change,” Proc. R. Soc. London Sect. B 65, 429–437 (1952).
[CrossRef]

Berek, M.

M. Berek, Grundlagen der praktischen optik (Walter de Gruyter, 1970).

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Chretien, H.

H. Chretien, Calcul des Combinaisons Optiques (Masson, 1980).

Herzberger, M.

M. Herzberger, Strahlenoptik (Springer, 1931).

Mikš, A.

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

Smith, W.

W. Smith, Modern Optical Engineering (McGraw-Hill, 2000).

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Taylor & Francis, 1986).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Wynne, C. G.

C. G. Wynne, “Primary aberrations and conjugate change,” Proc. R. Soc. London Sect. B 65, 429–437 (1952).
[CrossRef]

Proc. R. Soc. London Sect. B

C. G. Wynne, “Primary aberrations and conjugate change,” Proc. R. Soc. London Sect. B 65, 429–437 (1952).
[CrossRef]

Other

W. Smith, Modern Optical Engineering (McGraw-Hill, 2000).

Lambda Research, http://lambdares.com/ .

M. Herzberger, Strahlenoptik (Springer, 1931).

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

M. Berek, Grundlagen der praktischen optik (Walter de Gruyter, 1970).

H. Chretien, Calcul des Combinaisons Optiques (Masson, 1980).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

W. T. Welford, Aberrations of Optical Systems (Taylor & Francis, 1986).

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Figures (2)

Fig. 1.
Fig. 1.

General optical system with K spherical surfaces.

Fig. 2.
Fig. 2.

Influence of lens thickness on Seidel aberration coefficients (X=0, d=0.1fmm).

Tables (1)

Tables Icon

Table 1. Third-Order Aberrations for Thick Lens of Different Shape

Equations (23)

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niσi=niσi+hi(nini)/ri,hi+1=hidiσi,σi+1=σi,ni+1=ni,ni/sini/si=(nini)/ri,si+1=sidi,i=1,2,,K,
m=y0/y0=n1σ1/nKσK,
2nKσKδx=Ux(Uy2+Ux2)σK3SI+2UyUxtanω1σK2σ¯1SII+Uxtan2ω1σKσ¯12(SIII+H2SIV),
2nKσKδy=Uy(Uy2+Ux2)σK3SI+(3Uy2+Ux2)tanω1σK2σ¯1SII+Uytan2ω1σKσ¯12(3SIII+H2SIV)+tan3ω1σ¯13SV,
SI=i=1KAi,SII=i=1KAiBi,SIII=i=1KAiBi2,SIV=i=1KCi,SV=i=1K(AiBi2+H2Ci)Bi,
Ai=hi(σi+1σi1/ni+11/ni)2(σi+1ni+1σini),Bi=σ¯i+1σ¯iσi+1σi,Ci=1hi(σi+1niσini+1),
H=n1σ1y0=nKσKy0=n1(h¯1σ1h1σ¯1)=nK(h¯KσKhKσ¯K).
X=r2+r1r2r1,r1=(n1)φ(X+1)(φd(X21)+nn+1),φ1=n1r1,φ2=φφ11dφ1/n,r2=1nφ2.
SI=S0I+d[φ1(φ1n)2(φ1n2)n3(n1)2],
S0I=1(n1)2[n+2nφ12(2n+1)φ1+n2]
SII=S0II+d[(φ1n)2(φ1n2)n3(n1)2],
S0II=φ1(n+1)n2n(1n)
SIII=φ1n2(φ1n2)[d(nφ1)+n(1n)]2n3(n1)2(nφ1d).
SIII1d[(φ1n2)(φ12n+φ1n)n3(n1)].
SIV=φ1n+φ11φ1dn1n+dφ1(1φ1)n2.
SV=n21n2n3(φ11)(n1)2+(φ1n2)α12n3(n1)2(nφ1d)2(φ1n)α1,
α1=nφ1d+dnn2.
SVd(2φ13)n2+(φ11)n+φ1n3.
d=(A±n(n1)D)/B,
A=n(n1)[2n3+φ12(n+1)2φ1n(n+1)],B=2(φ1n)2(φ1n2),D=φ1[φ13(n+1)24φ1n(φ1n)(n2+n+1)4n4].
d=n1,SI=(nn1)2,SII=0,SIII=0,SIV=1n,SV=1n2n2.
r1=2(n1)/n,r2=r1,d=2r1,φ1=(n1)/r1,φ2=(1φ1)/(1dφ1/n).
SI=n4(n1)214,SII=12n1/2n(n1),SIII=3n1n21,SIV=1,SV=2(3n1)(n1)n3.

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