Читать книгу Optical Engineering Science - Stephen Rolt - Страница 66

The list below sets out the WFE dependence of the five Gauss-Seidel aberrations on pupil function, p, and field angle, θ.

 Spherical Aberration: ΦSA ∝ p4

 Coma: ΦCO ∝ p3θ

 Field Curvature: ΦFC ∝ p2θ2

 Astigmatism: ΦAS ∝ p2θ2

 Distortion: ΦDI ∝ pθ3

To quantify each aberration, we can define a coefficient, K, which describes the magnitude (in units of length) of the aberration. In addition, as well as normalising the pupil function, we can also normalise the field angle by introducing the quantity, h, which represents the ratio, θ/θ₀, the ratio of the field angle to the maximum field angle.

(3.37)

(3.38)

(3.39)

(3.40)

(3.41)

The reader should take particular note of the form of Eq. (3.40). The description of astigmatism here is such that the mean defocus over all orientations of the ray fan is taken to be zero. However, other representations adopt the convention that the defocus is zero for the sagittal ray and the balance of the astigmatism is incorporated into the field curvature. That is to say, in these conventions, the astigmatism is taken to be proportional to cos²φ, rather than cos2φ, as in Eq. (3.40). Of course, in using cos²φ, an average defocus of the same form as field curvature is introduced, hence the reason for adopting the convention used here. If the field curvature and astigmatism were redefined according to that convention, then the following revised description would apply:

(3.42)

(3.43)