I was reading this question on mirror lenses and the answers taught me a lot about mirror lenses. It is pretty obvious to me why they have donut bokeh (central obstruction) and why they are fixed aperture (an iris would be difficult to insert into the light path) but it isn't at all obvious why a mirror lens should have poor contrast.
I'm wondering why.
The loss of contrast is due to the central obstruction; that is, the "hole of the donut" that blocks light from getting through the center of the lens.
In a diffraction-limited telescope or lens, the point spread function—basically an image of a point source, like a star—is the Fourier transform of the aperture. For a circular aperture, like most lenses, this is a Bessel J1 function, also known as a Jinc, or an Airy disk:
When you obstruct the center of the aperture, turning it into a donut, the Fourier transform changes in a way that transfers power out of the central bright spot, into the first ring. The effect is to lower the contrast of the image.
This web page has examples of the point spread function for all sorts of obstructed apertures, so you can see the effect clearly.
Contrary to the popular myth, only local contrast (i.e. sharpness) drop is caused by central obstruction and its associated point spread function. The difference between refracting and mirror lens is detectable but it is not that big.
This can be easily verified by placing a small black circle in front of your regular lens. The obstruction will not wash out the image, mirror lens style.
Now, the overall low contrast, or fogginess, perceived as a distinguishing feature of mirror lens is a result of light scattering from mirror surfaces. Regular glass lenses also scatter some light but to much less degree. This has something to do with physics associated with reflecting and refracting surfaces and coatings used on lenses and mirrors - but I don't know the details.
