Analytic merit function based on Buchdahl’s aberration coefficients

Paul N. Robb

doi:10.1364/JOSA.66.001037

Journal of the Optical Society of America
Vol. 66,
Issue 10,
pp. 1037-1041
(1976)
•https://doi.org/10.1364/JOSA.66.001037

Analytic merit function based on Buchdahl’s aberration coefficients

Paul N. Robb

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Paul N. Robb, "Analytic merit function based on Buchdahl’s aberration coefficients," J. Opt. Soc. Am. 66, 1037-1041 (1976)

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Abstract

An equation has been developed that predicts the average size of the spot diagram over the field of view of a lens. The equation is based on an analytic integration of Buchdahl’s aberration polynomials, and is used to supply the figure of merit in an automatic correction computer program. The equation results in aberration balancing through the seventh order, and combines the procedures of optimization and analysis for designers who utilize the geometric spot size as an image quality criterion.

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Equations (27)

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Surface	Curvature	Index	Separation
0	0.000000	1.000000	1.000000 + 12	Object surface
1	0.000000	1.000000	−2.040900 − 01	Entrance pupil
2	2.994900	1.613330	4.210000 − 02
3	−3.193900	1.530000	1.800000 − 02
4	0.541100	1.000000	6.100000 − 02
5	−3.015700	1.548030	1.800000 − 02
6	3.193900	1.000000	4.510000 − 02
7	0.000000	1.000000	3.000000 − 02	Aperture stop
8	0.000000	1.548030	1.500000 − 02
9	3.748500	1.613330	3.010000 − 02
10	−3.143700	1.000000	−6.623763 − 02
11	0.000000	1.000000	9.545974 − 01	Exit pupil
12	0.000000	1.000000	0.000000	Image surface

Term	Value
σ₁	−0.439073983082455035 − 003
σ₂	−0.100488186202487115 − 003
σ₃	0.506484809738067989 − 003
σ₄	−0.564797149425913658 − 003
σ₅	−0.152128370393119686 − 002
μ₁	0.159693347532848129 − 003
μ₂	−0.301166417697754722 − 004
μ₃	−0.192865665244044394 − 004
μ₄	−0.418650036824835560 − 004
μ₅	0.924622460634293073 − 004
μ₆	−0.973172822161019453 − 004
μ₇	−0.139871540474811037 − 003
μ₈	−0.318506492808332063 − 004
μ₉	−0.997330697875487817 − 004
μ₁₀	−0.773272335386523938 − 004
μ₁₁	0.375323594685397964 − 003
μ₁₂	−0.363148882919873296 − 004
τ₁	0.259199007930685713 − 004
τ₂	−0.158859593419589359 − 004
τ₃	−0.123591907564105594 − 004
τ₄	−0.492124365297854265 − 004
τ₅	0.674007367609343389 − 005
τ₆	−0.137750290913369463 − 003
τ₇	0.126071096427357616 − 003
τ₈	0.124138236344091041 − 003
τ₉	0.440148054795477770 − 004
τ₁₀	−0.101809829437487535 − 004
τ₁₁	−0.153320747275632078 − 003
τ₁₂	−0.297684502968293390 − 003
τ₁₃	−0.186874683843572116 − 004
τ₁₄	−0.136566401524981345 − 003
τ₁₅	0.185467746004576876 − 003
τ₁₆	0.157038614340693252 − 003
τ₁₇	0.382983343534922728 − 004
τ₁₈	−0.364208815056422858 − 003
τ₁₉	−0.293505668898173123 − 004
τ₂₀	0.739030883718064567 − 004

J	S(J)
1	−0.114551564155943532 − 007
2	0.153535758247054299 − 008
3	− 0.322287240848374533 − 007
4	0.336399820245911459 − 007
5	0.000000000000000000
6	0.728489592050546948 − 009
7	−0.741213821561096584 − 010
8	−0.860998771073142758 − 010
9	0.167367629056714154 − 008
10	0.150953181377502015 − 008
11	0.254353153987298823 − 008
12	−0.711787031724773450 − 009
13	−0.286561469855709262 − 009
14	−0.121125450729696982 − 010
15	0.286582583457478236 − 008
16	0.269576404268654863 − 008
17	0.000000000000000000
18	−0.800934535533570135 − 009
19	−0.123134643682443363 − 009
20	−0.130978058779854913 − 009
21	0.123722144622024723 − 008
22	−0.226485349012083027 − 010
23	0.258086796292358830 − 008
24	0.634829833693267361 − 009
25	0.761660962526396291 − 009
26	0.745005846125645090 − 010
27	0.296149753431151525 − 011
28	0.296949263120178899 − 008
29	0.323331211717207836 − 008
30	0.267282887316007029 − 010
31	0.627450544219722486 − 010
32	0.260593066727410921 − 009
33	0.373653430212802853 − 009
34	0.222236729432103997 − 010
35	0.255092424932314672 − 008
36	0.165664572452623135 − 010
37	0.000000000000000000
	Average rms spot radius
	σ 0.126760330532988931 − 003

Surface	Curvature	Index	Separation
0	0.000000	1.000000	1.000000 + 12	Object surface
1	0.000000	1.000000	−2.040900 − 01	Entrance pupil
2	2.994900	1.613330	4.210000 − 02
3	−3.193900	1.530000	1.800000 − 02
4	0.541100	1.000000	6.100000 − 02
5	−3.015700	1.548030	1.800000 − 02
6	3.193900	1.000000	4.510000 − 02
7	0.000000	1.000000	3.000000 − 02	Aperture stop
8	0.000000	1.548030	1.500000 − 02
9	3.748500	1.613330	3.010000 − 02
10	−3.143700	1.000000	−6.623763 − 02
11	0.000000	1.000000	9.545974 − 01	Exit pupil
12	0.000000	1.000000	0.000000	Image surface

Term	Value
σ₁	−0.439073983082455035 − 003
σ₂	−0.100488186202487115 − 003
σ₃	0.506484809738067989 − 003
σ₄	−0.564797149425913658 − 003
σ₅	−0.152128370393119686 − 002
μ₁	0.159693347532848129 − 003
μ₂	−0.301166417697754722 − 004
μ₃	−0.192865665244044394 − 004
μ₄	−0.418650036824835560 − 004
μ₅	0.924622460634293073 − 004
μ₆	−0.973172822161019453 − 004
μ₇	−0.139871540474811037 − 003
μ₈	−0.318506492808332063 − 004
μ₉	−0.997330697875487817 − 004
μ₁₀	−0.773272335386523938 − 004
μ₁₁	0.375323594685397964 − 003
μ₁₂	−0.363148882919873296 − 004
τ₁	0.259199007930685713 − 004
τ₂	−0.158859593419589359 − 004
τ₃	−0.123591907564105594 − 004
τ₄	−0.492124365297854265 − 004
τ₅	0.674007367609343389 − 005
τ₆	−0.137750290913369463 − 003
τ₇	0.126071096427357616 − 003
τ₈	0.124138236344091041 − 003
τ₉	0.440148054795477770 − 004
τ₁₀	−0.101809829437487535 − 004
τ₁₁	−0.153320747275632078 − 003
τ₁₂	−0.297684502968293390 − 003
τ₁₃	−0.186874683843572116 − 004
τ₁₄	−0.136566401524981345 − 003
τ₁₅	0.185467746004576876 − 003
τ₁₆	0.157038614340693252 − 003
τ₁₇	0.382983343534922728 − 004
τ₁₈	−0.364208815056422858 − 003
τ₁₉	−0.293505668898173123 − 004
τ₂₀	0.739030883718064567 − 004

Abstract

Cited By

Tables (4)

Equations (27)

Journal of the Optical Society of America