Page 137 - Modern Optical Engineering The Design of Optical Systems

120 Chapter Six

TABLE 6.2 The Paraxial Surface Chromatic Contributions of the
Lens Described on p 119
SRF PAC SAC PLC SLC
1 –0.255960 –0.178181 –0.025295 –0.017608
2 –0.187385 –0.130444 0.209488 0.145831
3 0.419729 0.297051 –0.290034 –0.205263
4 0.287842 0.203711 0.229879 0.162690
5 –– –– –– ––
6 –0.063021 –0.043871 –0.154461 –0.107525
7 –0.223595 –0.155651 0.057824 0.040253
SUM –0.022389 –0.007385 0.027401 0.018377

transverse astigmatism (0.5NA[x T x S ]), PTZ3 is the transverse
Petzval field curvature, and DIS3 is the third-order transverse dis-
tortion. These correspond to the coefficients B 1 through B 5 in Eqs. 5.1
and 5.2.
Although this chapter has dealt with the calculation of the first-
and third-order aberration surface contributions, the following fifth-
order calculations are typically available in optical software programs,
so we include sample calculations at this point. For convenience, we
repeat the aberration power series expansion equations (Eqs. 5.1
and 5.2) from the previous chapter. The terms h and s, are the frac-
tional object height (0<h<1) and the fractional pupil coordinates
(0<s<1).

y′ A s cos A h
1 2
2
3
2
B s cos B s h(2 cos 2 ) (3B B )sh cos B h 3
1 2 3 4 5
5
3 2
4
2
C s cos (C C cos 2 )s h (C C cos )s h cos
1 2 3 4 6
2 3
5
7
4
(C C cos 2 )s h C sh cos C h D s cos . . . (5.1)
7 8 10 12 1
TABLE 6.3 The Third Order Surface Aberration Contributions
SRF SA3 CMA3 AST3 PTZ3 DIS3
1 –0.709019 –0.070068 –0.006924 –0.330897 –0.033385
2 –0.755360 0.844458 –0.944066 –0.036241 1.095939
3 2.049816 –1.416428 0.978756 0.300215 –0.883772
4 0.493011 0.393733 0.314447 0.351763 0.532055
5 –– –– –– –– ––
6 –0.035845 –0.087854 –0.215325 –0.060510 –0.676055
7 –1.229178 0.317877 –0.082206 –0.334022 0.107641
SUM –0.186575 –0.018282 0.044681 –0.109691 0.142422