Obstruction

"Obstruction" in optical instruments such as telescopes means that parts of the "original" free aperture are covered, or obstructed, by other things, typically parts of the instrument such as secondary mirrors. This effect is inherent in many common designs of reflecting telescopes such as the Newtonian and the Cassegrain telescopes and most of their derivates including Schmidt camera, Schmidt Cassegrain and Schmidt Maksutov telescopes.

Independent of the optical quality of particular instruments, obstruction has the effect to make images less defined, less contrasty, and less sharp. As one would expect, the effects depend on the amount of obstruction. Also, there is a minor effect on image brightness, as obstruction reduces the free aperture, and thus the light-collecting area. Thierry Legault has described the effects of obstruction for central, circular obstructions (typical for secondary mirrors), nicely illustrated with Lunar and planetary images which were then "artificially obstructed" (by computer simulation) in two steps (20 and 33 % obstruction). He finds that an instrument with free (circular) aperture of diameter D and (circular) obstruction of diameter d has

  1. the image definition (contrast, sharpness) equivalent to that of an unobstructed instrument with effective aperture D_eff:
    D_eff = D - d

  2. the light-gathering power of an unobstructed telescope with aperture D_lg (very straightforward):
    D_lg = sqrt( D^2 - d^2 )
This leads to the following table of equivalences for 33% obstructed reflectors (Newtons, Cassegrains, etc): 
Reflector diameter   
 33 % obstruction                  300   250   225   200   150   110
Equivalent diameter of refractor 
 about image definition            200   170   150   130   100    73
Equivalent diameter of refractor 
 about light gathering             280   235   210   190   140   100
where the first equivalence (image definition) has its main impact on binary star separation, planetary and Lunar details observing, while the second equivalence roughly determins limiting magnitudes and deepsky observing.

It should be emphasized that other effects may have much higher limiting effects on image definition/sharpness, in particulary atmospheric seeing conditions and instrumental misadjustment.

What remains obscure in Thierry's discussion of this objective, at least to the present author, is how he arrives at his conclusion No. 3, that obstruction is of minor effect on high-contrast structures, and thus his Equivalent Diameters about planetary and lunar resolution; these should IMHO identically equated to the equivalence about image definition. To the present author, this point appears to be a personal and perhaps personally biased opinion of Thierry who is a very successful observer and photographer with obstructed astronomical instruments. If there is any justification for his view, an explanation for his impression might be that the effect of aperture on image definition is not so prominent for high-contrast objects such as Lunar craters.

References:

  • Thierry Legault's obstruction page

    Hartmut Frommert [contact]

    [Spider] @ [SEDS]