J. Eur. Opt. Society-Rapid Publ. 21, 8( 2025) 81
vol. XI( Optical Science Center, University of Arizona and WYKO, Corporation, Tucson, AZ, USA, 1992).
10 Mejia Y, Exact relations between wave aberration and the sagitta difference, and between ray aberration and the slope difference, OPTIK. International Journal for Light and Electron Optics 123, 730( 2012).
11 Mouroulis P, Macdond J, Geometrical optics and Optical Design( Oxford, New York, NY, USA, 1997), pp. 201 – 203.
12 Hamilton WR, Theory of Systems of Rays, Transactions of the Royal Irish Academy 15, 69 – 174( 1828).
13 Restrepo J, Stoerck P, Ihrke I, Ray and wave aberrations revisited: a Huygens construction yield exact relations, J Opt. Soc. Am. A 33( 1), 1 – 13( 2022).
14 Lin PD, Seidel primary ray aberration coefficients for objects placed at finite and infinite distances, Opt Express 28( 9), 19740 – 19754( 2020).
15 Lin PD, Alternative method for computing primary wavefront aberrations using Taylor series expansion of optical path length, OPTIK International Journal for Light and Electron Optics 248, 168134( 2021).
16 Lin PD, Optical path length difference of ray path inside reference sphere: a new approach for determining wavefront aberrations in axially symmetrical systems with object at infinity, J. Opt. Soc. Am. A 41, 1616 – 1628( 2024).
17 Lin PD, It is a sufficient condition only, not a necessary and sufficient condition, for decomposing wavefront aberrations, J. Eur. Opt. Society-Rapid Publ. 18( 3), 1 – 4( 2022).
18 Laikin M, Lens Design, 2nd ed.( Marcel Dekker Inc., New York, NY, USA, 1995), p. 71.
Appendix
Zemax simulation can provide the peak values of ay aberrations( i. e., spherical aberration D1, coma D2, astigmatism D3, field curvature D4, and distortion D5) and wavefront aberrations( denoted as spherical aberration W040, coma W131, astigmatism W222, field curvature W220S, and distortion W311). Their values are identical in object and image spaces, leading that we have the following equations:
D1 ¼ B 1 q 3 max ¼ B e = 1q 3 e = max;
D2 ¼ B 2 h 0 q 2 max ¼ B e = 2h 0 q 2 e = max; ðA1Þ ðA2Þ
D3 ¼ B 3 h 2
0 q max ¼ B e = 3 h 2 0 q e = max; ðA3Þ
D4 ¼ B 4 h 2
0 q max ¼ B e = 4 h 2 0 q e = max; ðA4Þ
D5 ¼ B 5 h 3
0 ¼ B e = 5h 3
0; ðA5Þ
W 040 ¼ C 040 q 4 max = t 0 ¼ C e = 040 q 4 e = max = t 0;
W 131 ¼ C 131 h 0 q 3 max = t 0 ¼ C e = 131 h 0 q 3 e = max = t 0; ðA6Þ
ðA7Þ
W 222 ¼ C 222 h 2
0 q2 max = t 0 ¼ C e = 222 h 2 0 q2 e = max = t 0; ðA8Þ
W 220S ¼ C 220 h 2
0 q2 max = t 0 ¼ C e = 220 h 2 0 q2 e = max = t 0; ðA9Þ
W 311 ¼ C 311 h 3
0 q max = t 0 ¼ C e = 311 h 3 0 q e = max = t 0; ðA10Þ
where B j and B e / j( j = 1 – 5) are ray aberration coefficients in object and image spaces. q max and q e / max are respectively the maximum radii of the entrance and exit pupils. C 040, C 131, C 222, C 220, C 311( C coefficients) are wavefront aberration coefficients in object space, and C e / 040, C e / 131, C e / 222, C e / 220, C e / 311( C e coefficients) are wavefront aberration coefficients in image space. Thus one can obtain the aberration coefficients, B j( listed in No. 4), B e / j( given in No. 12), C, and C e from the Zemax’ speakvaluesofwavefront and ray aberrations.