Abstract

New parameters for calculation of third-order aberration coefficients (Seidel aberration coefficients) are introduced. The formulas for Seidel aberration coefficients are linear in these new variables. With these new variables it is possible to calculate the shape and the refractive index of the glass of the individual lenses of the optical system, which was not possible before.

© 2002 Optical Society of America

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References

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  1. B. Havelka, Geometrical Optics I (Czech Academy of Science Press, Prague, 1955).
  2. D. Argentieri, Ottica Industriale (Hoepli, Milano, Italy, 1942).
  3. H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, Oxford, UK, 1950).
  4. G. G. Slyusarev, Aberration and Optical Design Theory (Adam Hilger, London, 1984).
  5. A. Cox, A System of Optical Design (Focal, New York, 1964).
  6. P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997).
  7. A. Mikš, Applied Optics (Czech Technical University Press, Prague, 2000).
  8. A. C. Conrady, Applied Optics and Optical Design (Part I, Oxford, U. Press, New York, 1929; Part II, Dover, New York, 1960).
  9. H. Haferkorn, Bewertung Optisher Systeme (VEB Deutscher Verlag der Wissenschaften, Berlin, 1986).
  10. W. T. Welford, Aberrations of the Symmetrical Optical Systems (Academic, London, 1974).

Argentieri, D.

D. Argentieri, Ottica Industriale (Hoepli, Milano, Italy, 1942).

Conrady, A. C.

A. C. Conrady, Applied Optics and Optical Design (Part I, Oxford, U. Press, New York, 1929; Part II, Dover, New York, 1960).

Cox, A.

A. Cox, A System of Optical Design (Focal, New York, 1964).

Haferkorn, H.

H. Haferkorn, Bewertung Optisher Systeme (VEB Deutscher Verlag der Wissenschaften, Berlin, 1986).

Havelka, B.

B. Havelka, Geometrical Optics I (Czech Academy of Science Press, Prague, 1955).

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, Oxford, UK, 1950).

Macdonald, J.

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

Mikš, A.

A. Mikš, Applied Optics (Czech Technical University Press, Prague, 2000).

Mouroulis, P.

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

Slyusarev, G. G.

G. G. Slyusarev, Aberration and Optical Design Theory (Adam Hilger, London, 1984).

Welford, W. T.

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

Other (10)

B. Havelka, Geometrical Optics I (Czech Academy of Science Press, Prague, 1955).

D. Argentieri, Ottica Industriale (Hoepli, Milano, Italy, 1942).

H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, Oxford, UK, 1950).

G. G. Slyusarev, Aberration and Optical Design Theory (Adam Hilger, London, 1984).

A. Cox, A System of Optical Design (Focal, New York, 1964).

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

A. Mikš, Applied Optics (Czech Technical University Press, Prague, 2000).

A. C. Conrady, Applied Optics and Optical Design (Part I, Oxford, U. Press, New York, 1929; Part II, Dover, New York, 1960).

H. Haferkorn, Bewertung Optisher Systeme (VEB Deutscher Verlag der Wissenschaften, Berlin, 1986).

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

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Equations (94)

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1s-1s=1f=ϕ,
ϕ=(n-1)1r-1r,
m=ss=11+sϕ.
X=r+rr-r.
Y=s+ss-s.
r=2(n-1)ϕ(X+1),r=2(n-1)ϕ(X-1).
Y=s+ss-s=m+1m-1=-1-2sϕ=1-2sϕ.
SI=i=1Khi4Mi,
SII=i=1Khi3h¯iMi+i=1Khi2Ni,
SIII=i=1Khi2h¯i2Mi+2i=1Khih¯iNi+i=1Kϕi,
SIV=i=1K ϕini,
SV=i=1Khih¯i3Mi+3i=1Kh¯i2Ni+i=1K h¯ihi 3+1niϕi,
Mi=ϕi3(AiXi2+BiXiYi+CiYi2+Di),
Ni=ϕi2(EiXi+FiYi),
Ai=ni+24ni(ni-1)2,Bi=ni+1ni(ni-1),
Ci=3ni+24ni,
Di=ni24(ni-1)2,Ei=Bi/2,Fi=2ni+12ni,
ϕi=(ni-1)1ri-1ri=1si-1si,
Xi=ri+riri-ri,
Yi=si+sisi-si=mi+1mi-1=-1-2siϕi,
Yi+1=hiϕihi+1ϕi+1(Yi-1)-1.
ri=2(ni-1)ϕi(Xi+1),ri=2(ni-1)ϕi(Xi-1).
h¯jhj=h¯1h1+i=2j di-1hi-1hi,
h¯1=s1s¯1s¯1-s1,
M¯i=AiXi2+Di,
N¯i=EiXi.
δs=-2H2M¯
δm=H2(M¯+N¯/2),
M¯i=14 ni+2ni(ni-1)2Xi2+ni2(ni-1)2,
N¯i=12 ni+1ni(ni-1)Xi.
M¯i=Di+AiEi2N¯i2,
Di=ni24(ni-1)2,AiEi2=ni(ni+2)(ni+1)2.
n=1.5,A/E2=0.84;
n=2.0,A/E2=0.89.
M¯i=Di+0.86N¯i2.
Mi=ϕi3(M¯i+2N¯iYi+1.06Yi2),
Ni=ϕi2(N¯i+1.31Yi),
M¯i=fi3Mi-2 fi2NiYi+1.56Yi2,
N¯i=fi2Ni-1.31Yi,
D=M¯-0.86N¯2.
n=DD-0.5.
1<D<2.76.
r=2(n-1)ϕ(X+1),r=2(n-1)ϕ(X-1).
1s=ϕ2(-Y-1),1s=ϕ2(-Y+1).
M¯=M(ϕ=1, m=-1),
N¯=N(ϕ=1, m=-1),
M¯0=M(ϕ=1, m=0),N¯0=N(ϕ=1, m=0),
M¯=M(ϕ=1, m=),N¯=N(ϕ=1, m=).
M=ϕ3(M¯+2NY¯+1.06Y2),
N=ϕ2(N¯+1.31Y),
M¯=f3M-2 f2NY+1.56Y2,
N¯=f2N-1.31Y,
M=ϕ3M¯0+2N¯0(Y+1)+2.62Y+1.06Y2+1.56,
N=ϕ2[N¯0+1.31(Y+1)],
M¯0=f3M-2 f2N(Y+1)+2.62Y+1.56Y2+1.06,
N¯0=f2N-1.31(Y+1),
M=ϕ3M¯+2N¯(Y-1)-2.62Y+1.06Y2+1.56,
N=ϕ2[N¯+1.31(Y-1)],
M¯=f3M-2 f2N(Y-1)-2.62Y+1.56Y2+1.06,
N¯=f2N-1.31(Y-1).
M¯=M¯0+2N¯0+1.56,N¯=N¯0+1.31,
M¯=M¯-2N¯+1.56,N¯=N¯-1.31,
M¯0=M¯-2N¯+1.06,N¯0=N¯-1.31,
M¯0=M¯-4N¯+5.24,N¯0=N¯-2.62,
M¯=M¯+2N¯+1.06,N¯=N¯+1.31,
M¯=M¯0+4N¯0+5.24,N¯=N¯0+2.62.
CI=i=1Khi2 ϕiviPiλ,
CII=i=1Khih¯i ϕiviPiλ,
v=nd-1nF-nC,Pλ=nF-nλnF-nC,
i=12ϕi=ϕ,i=12 ϕivi=0.
i=12ϕi=ϕ,i=12 ϕivi=0,i=12 ϕiviPid=0.
P1d=P2d.
i=13ϕi=ϕ,i=13 ϕivi=0,
i=13 ϕiviPid=0,i=13 ϕiviPig=0.
exactvalues:n2=1.61644,X2=1.4435,
calculated values:n2=1.62020,X2=1.4525,
difference:δn2=0.00376,δX2=0.0080.
γ=h1/h2=-f1/f2,d=f1+f2.
S1=h14(M1+M2/γ4),
SII=h22(dM2/γ+γ2N1+N2).
K=M1(γ-1),N¯2=-N¯1+K,
M¯2=2N¯1+(2-γ)M1-1.06,
D2=D1-(1.72N¯1-1)K-0.86K2.
f2=-f1/γ,d=f1+f2,
E1=0.5(n1+1)/[n1(n1-1)],N¯1=E1X1,
D1=0.25n12/(n1-1)2,M¯1=D1+0.86N¯12,
M1=Mˆ1-2N¯1+1.06,K=M1(γ-1),
D2=D1+(1.72N¯1-1)K-0.86K2,
n2=D2/(D2-0.5),N¯2=-N¯1+K,
E2=0.5(n2+1)/[n2(n2-1)],X2=N¯2/E2,
r1=2 f1(n1-1)/(X1+1),
r1=2 f1(n1-1)/(X1-1),
r2=2 f2(n2-1)/(X2+1),
r2=2 f2(n2-1)(X2-1).

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