Читать книгу Optical Engineering Science - Stephen Rolt - Страница 62

The third Gauss-Seidel term produced is known as field curvature. The OPD associated with field curvature is second order in both field angle and pupil function. Furthermore, there is no dependence upon ray fan angle, as the WFE is circularly symmetric. Unlike in the case for coma, behaviour is identical for the tangential and sagittal ray fans.

(3.30)

From Eq. (3.30), in the case of a single field point, the effect of a quadratic dependence of WFE on pupil function is to produce a uniform defocus. That is to say, a uniform defocus produces a characteristic quadratic pupil dependence in the WFE. The extent of this defocus is proportional to the square of the field angle, producing a curved surface which intersects the paraxial focal plane at zero field angle – the optical axis. If this field curvature were the only aberration, then this curved surface would produce a perfectly sharp image for all these field points. That is to say, with the presence of field curvature, the ideal focal surface is a curved surface or sphere rather than a plane. This is illustrated in Figure 3.15.

Figure 3.15 shows both the tangential and sagittal focal surfaces (S and T), with the optimum focal surface lying between the two. Ideally, for field curvature, the imaging surface should be curved, following the ideal focal surface. If, for instance, only a plane imaging surface is available, then this need not be located at the paraxial focus. This surface can, in principle, be located at an offset, such that the rms WFE is minimised across all fields. In calculating the rms WFE, this would be weighted according to area across all object space, as represented by a circle centred on the optical axis whose radius is the maximum object height.

Figure 3.15 Field curvature.

Figure 3.16 Ray fan plots illustrating field curvature.

Clearly, the OPD fan for field curvature is a series of parabolic curves whose height is proportional to the square of the field angle. There is no distinction between the sagittal and tangential fans. Similarly, the ray fans show a series of linear plots whose magnitude is also proportional to the square of the field angle. A series of ray fan plots for field curvature is shown in Figure 3.16.

In view of the symmetry associated with field curvature, the geometrical spot consists of a uniform blur spot whose size increases in proportion to the square of the field angle. In addition, this spot is centred on the chief ray; unlike in the case for coma, there is no centroid shift with respect to the chief ray.