Parabasal rays are real rays that make a small angle to the chief ray. They are "real" in the sense that the full form of Snell's Law is used, so that the ray interacts with the real surface curvature and not a plane of equivalent power, and that no approximations are made in the ray-tracing.

Parabasal rays therefore lose all the computational advantages of paraxial rays, but better represent the limiting performance of a system as the aperture goes to zero. In particular, they allow surfaces to be tilted or decentered, to be non-rotationally symmetric, to be diffractive, to be gradient index, etc..

Many calculations require a paraxial reference, as a reference against which the real rays are compared. To ensure that these features work properly, even in systems not well described by first-order optics, ZEMAX uses parabasal rays to compute the limiting properties of the system as the aperture goes to zero.

However, applying paraxial theory to real lenses often causes confusion. To demonstrate this, we are going to trace paraxial rays in a real optical system. We will also trace a parabasal ray, so you can see precisely how the parabasal calculation works, and why it is generally superior.

The file real system.zmx is supplied in the ZIP file available from the last page of this article. It shows a microscope objective working at large NA. It is highly optimized and diffraction limited. The curvature of the final surface (drawn in red) is controlled by a marginal ray angle solve that forces the system to have a "marginal ray angle" of -0.5.
 

Image Space numerical aperture (ISNA) is defined as "the index of image space times the sine of the angle between the paraxial on-axis chief ray and the paraxial on-axis +y marginal ray calculated at the defined conjugates for the primary wavelength." ¹ Now the image space index is 1, so its tempting to think that the ISNA should be sin(0.5) = 0.479. ZEMAX however computes it as 0.447. Why?