By the use of an electronic computer, automatic correction concerning aberration of optical systems by the least square method is devised.
Let the difference coefficients of aberrations φ
i (
i=1, ····,
m) by the variation of variables β
f (
j=1, ····,
n) of a lens be denoted by
aij.
When the amount of change
li of aberrations φ
i and the weighting factors
wi of φ
i are given, the amounts
Δβ
j of variation of β
j are given by
_??_(_??_
wiaijaik)
Δβ
j=(_??_
wiliaik).
The determinant
D of the coefficient matrix is expressed by
_??_
where the summation is carried out over all combinations of
n integers γ
1<γ
2<····<γ
n chosen from 1, 2, ····
m.
If the number
n of variables happens to be larger than the number
m of equations,
D will be always zero, and the least square method will not hold. When
m_??_
n,
D is expressed by the square sum of determinants of
mCn matrixes. If the values of
mCn is large (say more than 50) the chance of
D=0 is very little. The program of automatic correction by the least square method is worked out and applied to a Tessar type lens and a Gauss type lens with satisfactory results.
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