lens - Why do old-school catadioptric lenses have a fixed aperture?

Pretty much what it says on the tin. As far as I can tell, catadioptric telephoto lenses (operating on a similar principle to many telescopes; using mirrors rather than refraction) fell out of favour after the 1980s because of their fixed focal length and aperture. Now, fixed focal length I understand, but what are the engineering issues that prevent a variable aperture on a cato lens?

Now, I'm not asking why they fell out of favour, but rather why they have this specific limitation.

Answer

The mirror lens has an advantage in that it is completely free from chromatic aberrations. All other lens systems are degraded by longitudinal and transverse chromatic aberrations. These are brought about as the image forming rays pass through a transparent lens. The mirror lens avoids this because the mirror’s silvering is on the surface of the lens; thus the image forming rays never enter. Thus the mirror lens is able to deliver a well-defined image with high magnification.

Another benefit of the mirror lens is its short barrel. This is achieved by causing the image forming rays to double back on themselves. This is possible as the main or objective mirror lens is placed at the rear of the tube. The objective mirror’s shape causes the rays to converge. These travel to the front of the tube where they encounter a smaller secondary first surface mirror. This secondary mirror directs the rays to the back of the tube. These image forming exit the tube via a hole drilled in the center of the primary mirror. The rays exit and an image is projected on film or digital sensor.

This is a catadioptic system that features a shortened barrel free of chromatic aberrations. The system is however not free from the remaining six aberrations that plague all optical systems. The catadioptic system features a thin transparent lens at the tubes entrance. This lens is used to make some corrections that mitigate some of the aberrations. Thus this corrector lens allows for a simpler shape (figure) of the objective mirror.

The key to the folded (shortened) optical path is the up-front second mirror. The problem is, this secondary mirror blocks a significant amount of light that would have entered if the systems were a conventional transparent lens design. The shadow of this obstructing secondary mirror will image if the lens is stopped down to the smaller f/numbers (tiny diameter). Additionally the obstructing secondary makes it almost impossible to install a mechanical iris diaphragm. We are forced to control exposure via shutter speed or ISO setting or both.