The specific definition for each polynomial ray aberration term computed in six current lens design programs is presented. A comparison between programs was performed that found significant variances in term definitions. Several anomalous term computations are reported. In addition, certain characteristics of the compared programs are contrasted, and a consistent aberration term definition scheme is recommended for adoption by all programs.
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Definitions, Programs, and AberrationsThe definition for each aberration term in six lens design programs is tabulated with the BASE TERM reference. All dependencies on ρ, θ, and
in each term are omitted for clarity.
NOTES:
Tangential terms imply θ = 0° in Eq. (2) and sagittal terms imply θ = 90°.
Comparison was made on the following programs in September 1972 on the current versions as of that date. Organization marketing each program is also given.
FLAIR 43 computes polynomial aberrations in two separate subroutines which are denoted by THØRD and SWØRD. Subroutine SWØRD computes all 37 coefficients comprising the third, fifth and seventh orders.
Same for CDC Computer Optics Package (C.O.P.) or TROPEL versions.
Also called circular coma.
This is one of the 14 COMBO predefined terms. In addition, σi (i = 1, …,5) and μj (j = 1, …,12) are available as separate terms.
In ACCOS V and CORR, μ11 can be formed by summing 5th order tangential linear astigmation (TAST5) and 5th order Petzval, and μ10 by adding five times TAST5 to 5th order Petzval.
GIH is the Gaussian image height.
Page 76 of Reference 2.
Table II
Characteristics of the Compared Programs Pertaining to Their Aberration Subsection (s)
COMPUTES TERMS FOR SYSTEMS WHICH CONTAIN CONICAL SURFACE(S)
YES
YES
YES
YES
YES
YES
COMPUTES TERMS FOR SYSTEMS WHICH CONTAIN POLYNOMIAL ASPHERIC SURFACE (S)
YES
YES
YES
NO
YES
YES
HIGHEST ORDER OF SPHERICAL CONTRIBUTION COMPUTED
7th
7th
3rd (THØD) 7th (SWØD)
5th
3rd
7th
OPTION FOR USER DEFINED SUMS OF TERMS (TOTAL CONTRIBUTIONS)
YES
YES
NO
14 predefined sums are available
NO
NO
OPTION FOR USER DEFINED INTER-SURFACE SUMS OF TERMS (PARTIAL CONTRIBUTIONS)
YES
YES
NO
Currently being added
NO
NO
TERMS AVAILABLE IN DESIGN PROCESS
YES
YES
NO
YES
As bound
YES
INDIVIDUAL COEFFICIENTS AVAILABLE IN DESIGN PROCESS
NO
NO
NO
YES
As bound
NO
TERMS DEFINED IN USERS MANUAL
NO
NO
Partially
YES
In annotated output package available from CDC
YES
NOTES:
individual surface term-values need to be multiplied by the focal ratio to determine-actual surface contributions. Totals are internally multiplied by the system focal ratio.
Capable of designing zoom systems and multiple configurations by using polynomial aberrations.
All coefficients through the 7th order are available in analysis mode only.
“Wave form” of terms only are available.
Tables (2)
Table I
Definitions, Programs, and AberrationsThe definition for each aberration term in six lens design programs is tabulated with the BASE TERM reference. All dependencies on ρ, θ, and
in each term are omitted for clarity.
NOTES:
Tangential terms imply θ = 0° in Eq. (2) and sagittal terms imply θ = 90°.
Comparison was made on the following programs in September 1972 on the current versions as of that date. Organization marketing each program is also given.
FLAIR 43 computes polynomial aberrations in two separate subroutines which are denoted by THØRD and SWØRD. Subroutine SWØRD computes all 37 coefficients comprising the third, fifth and seventh orders.
Same for CDC Computer Optics Package (C.O.P.) or TROPEL versions.
Also called circular coma.
This is one of the 14 COMBO predefined terms. In addition, σi (i = 1, …,5) and μj (j = 1, …,12) are available as separate terms.
In ACCOS V and CORR, μ11 can be formed by summing 5th order tangential linear astigmation (TAST5) and 5th order Petzval, and μ10 by adding five times TAST5 to 5th order Petzval.
GIH is the Gaussian image height.
Page 76 of Reference 2.
Table II
Characteristics of the Compared Programs Pertaining to Their Aberration Subsection (s)
COMPUTES TERMS FOR SYSTEMS WHICH CONTAIN CONICAL SURFACE(S)
YES
YES
YES
YES
YES
YES
COMPUTES TERMS FOR SYSTEMS WHICH CONTAIN POLYNOMIAL ASPHERIC SURFACE (S)
YES
YES
YES
NO
YES
YES
HIGHEST ORDER OF SPHERICAL CONTRIBUTION COMPUTED
7th
7th
3rd (THØD) 7th (SWØD)
5th
3rd
7th
OPTION FOR USER DEFINED SUMS OF TERMS (TOTAL CONTRIBUTIONS)
YES
YES
NO
14 predefined sums are available
NO
NO
OPTION FOR USER DEFINED INTER-SURFACE SUMS OF TERMS (PARTIAL CONTRIBUTIONS)
YES
YES
NO
Currently being added
NO
NO
TERMS AVAILABLE IN DESIGN PROCESS
YES
YES
NO
YES
As bound
YES
INDIVIDUAL COEFFICIENTS AVAILABLE IN DESIGN PROCESS
NO
NO
NO
YES
As bound
NO
TERMS DEFINED IN USERS MANUAL
NO
NO
Partially
YES
In annotated output package available from CDC
YES
NOTES:
individual surface term-values need to be multiplied by the focal ratio to determine-actual surface contributions. Totals are internally multiplied by the system focal ratio.
Capable of designing zoom systems and multiple configurations by using polynomial aberrations.
All coefficients through the 7th order are available in analysis mode only.
“Wave form” of terms only are available.
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