Figure 6.23 Variation of angular spherical aberration as a function of reciprocal object distance v1 for various refractive indices when the lens has a convex-plano shape with the plano side facing the object. Spherical aberration for a specific f-number is determined by dividing the aberration value shown by ( f-number)3.

6.4THE IMAGE DISPLACEMENT CAUSED BY A PLANOPARALLEL PLATE

From Figure 6.24 it is clear that the longitudinal image displacement caused by the insertion of a thick planoparallel plate into the path of a ray having a convergence angle U is S ¼ BB0, given by

But Y/tan U0 is equal to t, the thickness of the plate. Therefore,

Figure 6.24 Image displacement caused by the insertion of a parallel plate.

where N is the refractive index of the plate. For a paraxial ray this reduces to

s ¼ Nt ðN 1Þ

The plate of glass occupies more space than its “air equivalent,” which is defined as that thickness of air in which a paraxial ray drops or rises by the same amount as in the glass plate. Thus, the useful relationship,

air equivalent ¼ glass thickness=refractive index

DESIGNER NOTE

The inclusion of a flat glass plate in an optical system can impact the ultimate image quality. Microscope cover glasses and dewar windows for infrared detectors are examples where the aberrations induced by a flat glass plate should be accounted for. Consider a flat glass plate placed between the plano-hyperboloid lens in Section 6.1.8 “Plane Surface in Front” and the image it forms. In this case, the added spherical aberration can be effectively mitigated by slightly weakening the conic constant of the lens.