Abstract

The resultant increment of the wave-front aberration of a lens system which is produced by a small change of the constructional parameter in the system can be represented by the equation

w/xiΔxi=w1/xiΔxi-NK(1-cosuK)s¯K/xiΔxi,

where w and Δxi denote the wave-front aberration and the increment of the constructional parameter, respectively. The first term of the right-hand side of the equation represents the increment of the wave-front aberration with respect to the original reference sphere and the second term shows the increment produced by the focal shift due to the change of the constructional parameter.

The numerical result obtained from the equation showed fairly good agreement with that obtained by the actual ray tracing.

© 1959 Optical Society of America

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References

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  1. F. D. Cruickshank, Proc. Phys. Soc. (London) 58, 296 (1946).
    [Crossref]
  2. P. C. Foote, J. Opt. Soc. Am. 38, 590 (1948).
    [Crossref]
  3. W. M. Stempel, J. Opt. Soc. Am. 38, 925 (1948).
    [Crossref]
  4. N. J. Rumsay, J. Opt. Soc. Am. 41, 229 (1951).
    [Crossref]
  5. A. E. Glancy, J. Opt. Soc. Am. 41, 389 (1951).
    [Crossref] [PubMed]
  6. T. Suzuki, Technol. Repts. Osaka Univ. 2, 37 (1952).
  7. T. Suzuki, Technol. Repts. Osaka Univ. 3, 215 (1953).
  8. H. H. Hopkins, Wave Theory of Aberrations (Oxford University Press, London, 1950), p. 29.
  9. W. S. S. Blaschke, Optica Acta 3, 10 (1956).
    [Crossref]

1956 (1)

W. S. S. Blaschke, Optica Acta 3, 10 (1956).
[Crossref]

1953 (1)

T. Suzuki, Technol. Repts. Osaka Univ. 3, 215 (1953).

1952 (1)

T. Suzuki, Technol. Repts. Osaka Univ. 2, 37 (1952).

1951 (2)

1948 (2)

P. C. Foote, J. Opt. Soc. Am. 38, 590 (1948).
[Crossref]

W. M. Stempel, J. Opt. Soc. Am. 38, 925 (1948).
[Crossref]

1946 (1)

F. D. Cruickshank, Proc. Phys. Soc. (London) 58, 296 (1946).
[Crossref]

Blaschke, W. S. S.

W. S. S. Blaschke, Optica Acta 3, 10 (1956).
[Crossref]

Cruickshank, F. D.

F. D. Cruickshank, Proc. Phys. Soc. (London) 58, 296 (1946).
[Crossref]

Foote, P. C.

Glancy, A. E.

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Oxford University Press, London, 1950), p. 29.

Rumsay, N. J.

Stempel, W. M.

W. M. Stempel, J. Opt. Soc. Am. 38, 925 (1948).
[Crossref]

Suzuki, T.

T. Suzuki, Technol. Repts. Osaka Univ. 3, 215 (1953).

T. Suzuki, Technol. Repts. Osaka Univ. 2, 37 (1952).

J. Opt. Soc. Am. (4)

Optica Acta (1)

W. S. S. Blaschke, Optica Acta 3, 10 (1956).
[Crossref]

Proc. Phys. Soc. (London) (1)

F. D. Cruickshank, Proc. Phys. Soc. (London) 58, 296 (1946).
[Crossref]

Technol. Repts. Osaka Univ. (2)

T. Suzuki, Technol. Repts. Osaka Univ. 2, 37 (1952).

T. Suzuki, Technol. Repts. Osaka Univ. 3, 215 (1953).

Other (1)

H. H. Hopkins, Wave Theory of Aberrations (Oxford University Press, London, 1950), p. 29.

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Figures (2)

Fig. 1
Fig. 1

Change of the wave-front aberration due to the change of the curvature of the ith refracting surface. ( w ¯ * w * - w ¯ w ) shows the increment of the wave-front aberration. Ti and Ti* denote the original and new refracting surfaces, respectively.

Fig. 2
Fig. 2

Relation between the increment of the wave-front aberration (NPP*〉−NPQ〉) and the increment of the curvature of the refracting surface. The curvatures of T* and T surfaces are (RR) and R, respectively.

Tables (2)

Tables Icon

Table I Constructional parameters of the test lens.

Tables Icon

Table II Rates of changes of the wave-front aberrations with respect to the small change of the curvature of the fifth refracting surface.

Equations (17)

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w / x i Δ x i = w 1 / x i Δ x i - N K ( 1 - cos u K ) s ¯ K / x i Δ x i ,
Δ w 1 = [ P i P i * ] - [ P i Q i ] ,
Δ w 2 = - N K ( 1 - cos u K ) Δ s ¯ K ,
Δ w = Δ w 1 + Δ w 2 .
Δ w 1 = [ P P * ] - [ PQ ] = N P P * - N PQ ,
PQ = P P * cos ( i - i ) .
Δ w 1 = P P * { N - N cos ( i - i ) }
Δ w 1 = - P P * cos i Δ ( N cos i ) ,
PO = PH + HO = r cos i + s cos u ,
h = r sin i = s sin u ,
AO = r + s ,
P O / r = 1 cos i { 1 - cos ( u + i ) } .
P P * = - P O / r Δ r .
Δ w 1 = { 1 - cos ( u + i ) } Δ ( N cos i ) Δ r ,
Δ w 1 = - 1 / R 2 { 1 - cos ( u + i ) } Δ ( N cos i ) Δ R ,
Δ s ¯ K = s ¯ K / R i Δ R i ,
Δ w 2 = - N K ( 1 - cos u K ) s ¯ K / R i Δ R i .