Page 138 - Modern Optical Engineering The Design of Optical Systems

Third-Order Aberration Theory and Calculation 121

TABLE 6.4 The Fifth-Order Surface Contribution for the Lens on p 119
SRF SA5 CMA5 AST5 PTZ5 DIS5 SA7
1 –0.061946 –0.001202 0.000323 –0.004476 0.000474 –0.006382
2 –0.154199 0.189546 –0.060252 –0.007701 0.056437 –0.028360
3 0.394409 –0.354457 0.033863 0.007252 –0.026296 0.073525
4 0.110416 0.055693 0.021076 0.016469 0.052491 0.033928
5 –– –– –– –– –– ––
6 –0.015016 –0.022169 –0.023359 –0.004057 –0.053149 –0.006118
7 –0.148238 0.092127 0.011081 0.008735 –0.014342 –0.017923
SUM 0.125426 –0.040462 –0.017268 0.025173 0.015616 0.048670

x′ A s sin
1
2
3
2
B s sin B s h sin 2 (B B )sh sin
1 2 3 4
5
4
2
3
2
C s sin C s h sin 2 (C C cos )s h sin
1 3 5 6
4
3
7
2
C s h sin 2 C sh sin D s sin . . . (5.2)
9 11 1
Table 6.4 lists the fifth-order analogs of the five Seidel aberrations
listed in Table 6.3, plus the seveth-order spherical aberration term.
These correspond to the coefficients C 1 , C 3 , (C 10 C 11 )/4, (5C 11 C 10 )/4,
C 12 , and D 1 in Eqs. 5.1 and 5.2.
Table 6.5 gives the Buchdahl fifth-order coefficient values (C 1 , C 2 . . .)
for the Eqs. 5.1 and 5.2.
TABLE 6.5 The Fifth Order Buchdahl Aberrations Surfaces Contributions of the Lens
on p 119
SRF C1/2 C3/4 C5/6 C7/8 C9/10 C11/12
1 –0.061946 –0.001202 –0.018301 0.006375 0.006542 0.004799
–0.007324 –0.018538 0.033213 0.008183 0.006092 0.000474
2 –0.154199 0.189546 –0.169776 0.361953 0.134015 –0.067954
0.314507 –0.468290 –0.243766 0.248751 –0.308963 0.056437
3 0.394409 –0.354457 0.226035 –0.313680 –0.109803 0.041115
–0.574065 0.624135 0.280642 –0.193903 0.176565 –0.026296
4 0.110416 0.055693 0.049073 0.017082 0.025061 0.037545
0.108491 0.094590 –0.066253 0.009050 0.121850 0.052491
5 –– –– –– –– –– ––
–– –– –– –– –– ––
6 –0.015016 –0.022169 –0.034561 0.026508 –0.008375 –0.027415
–0.045089 –0.083140 0.024848 0.002542 –0.120850 –0.053149
7 –0.148238 0.092127 –0.008556 –0.076892 –0.043850 0.019815
0.141897 –0.039780 0.047409 –0.055757 0.064138 –0.014342
SUM 0.125426 –0.040462 0.043914 0.021346 0.003592 0.007905
–0.061583 0.108976 0.076092 0.018867 –0.061167 0.015616