High image definition -
a physical explanation to Kutter's book title

In the following the superiority of the unobstructed reflecting telescope with its refractor-like sharpness and contrast performance shall be pointed out.

The optical and physical relations mentioned have been depicted as simply as possible and mathematical formulae have been fully omitted to allow the open-minded newcomer to deepen his optical knowledge in the realm of amateur astronomy.



Kutter´s frequently applied term "high image definition" basically refers to:

• detail reproduction resp. discriminating power, physically called "resolution"
• optimum contrast performance
• complete absence of chromatic abberations

Both first items solely rely on the schief´s as well as the refractor´s obstruction-free light path while the third quality feature is reserved only to the physically effect of reflection. Whereas a high and expensive deal of effords is practised in order to compensate sufficiently for the chromatic aberrations inherent to the refraction of light.

The superiority of the refractor versus the reflecting telescope is obvious in particular in the range of smaller apertures and is therefore discussed passionately especially by amateur astronomers.

In the literature there is usually quite a summary justification for the inferiority of the reflecting telescope, arguing it would react more sensitive on air turbulences due to the open tube construction. Further on it is said that the accuracy demand for a reflecting surface is four times higher than for the four refracting surfaces of a doublet achromat.

But these arguments are not the real reason, rather there is a fundamental difference between the light path of the two instrument types: the refractor forms the star light to a telescope image exploiting the full extension of the objective plane while the central light penetration is masked out by the reflecting telescopes´ inevitable secondary mirror. Subsequently this will be explained in detail.

A mathematical point of light, as given by a fixed star, does not get an infinitely small image when projected by a lens, but rather a definite large disk, surrounded by a number of different bright light rings. The rays of light coming from the star are diffracted at the rim of the lens and get pulled apart to a diffraction figure.

From the point of view of geometric optics, that means only a slight loss of light, not having a real influence on the quality of the image. Seen from the point of view of the wave optics, this obstruction is of severe importance, since that diffraction figure is the smallest light spot any astronomical image scenery is composed of. The smaller and pin-shaped our "pixels" (picture elements) are, the higher is the gain of resolution and contrast in the image depicted!

Generally, the radius of the central disc (also called Airy disk) is based on the wave nature of a vibrating light quant and depends only on the aperture of the lens and the wavelength of the light rays. As for light diffraction no remedy exists, we have to deal with that.

Besides the absolute size of the diffraction disk, the light distribution within this entity is important as well. In the chapter: "The Oblique Telescope - Optical Aspects" this is explained thoroughly. It is shown there, how the diffraction forming light distributes on the central diffraction disk and on the surrounding rings in case of an ideal lens, and an imaging mirror obstructed by spider vanes. One can see, how fatally the spot-shaped image information blows up and how the close vicinity of the central pixel as a carrier of image information gets also brightened up causing a noticable loss of contrast.

The relations are unfortunately still somewhat more complex: besides the diffraction disk as the smallest possible collimation of a parallel bundle of rays, the so-called spot diagram exists telling us how well (sometimes rather badly!) the rays are collimated as a function of their distance from the optical axis..

Fortunately, we have the free choice of an optical design, as well as an appropriate aperture ratio at hand. Both have a decisive influence on the size of the diffraction disk for off-axis light rays, outside in the field. A genious computer simulation by David Stewick makes this evaluable: WINSPOT.EXE, available by free download, that can examine various diagrams of spot collimation.

Indeed, the widespread, fast Newtonian parabolic mirror isn´t by far the non-plus ultra of astro-optics. Even in diffraction theory its imaging properties are to be criticised because the un-equaling long focusing rays of its various zones adversely affect the diffracion image by phase inequality. Each observer recognizes this from the limited ability of enlarging photographs from a fast parabolic miror.

Let us have a look at the spot diagram of a F/5-Newton telescope still being not really fast versus that of a schiefspiegler in anastigmatical design, F/28.

So we are going to compare the following telescopes:

• parabolic mirror (Newton) with an imaging aperture of 150 mm, F = 750 mm and a given field of view of sema-angle .75 degrees (three times full moon diameter)
• Kutter telescope with two imaging surfaces of aperture 150 mm, F = 4200 mm and .25 degrees of given field (simple full moon diameter)

The radius of a diffraction disk, e.g. in the green light (500 nm) is calculated by the following rule of thumb: r = 1.22 * lambda * focal length / aperture

Putting in real numbers leads to:
r (Newton) = 1.22 * .0005 mm * 750 mm / 150 mm = .003 mm (diameter .006 mm)
r (Kutter) = 1.22 * .0005 mm 4200 mm / 150 mm = .017 mm (diameter .034 mm)

So the Kutter diffraction disk is five to six times larger than the one to the Newton, meaning the latter is superior in respect of resolving power, but only on the optical axis.

Let us have a look at the spot diagrams of both systems. The Newton has got an excellent paraxial collimation, which in theory would be much smaller than its diffraction disk (represented by a black ring). However the F/5-Newton suffers huge coma at the field´s edge, so even at .75 degrees of angular distance to the center (at 1.5 * full moon diameters) its collimation degrades to a monstrous blop!

If we consider that the pixels on the edge of our Newton consist out of such "blobs", it is clear that a coma-corrector is a must for any photographic use of the Newtonian reflector !


The Kutter performs in a completely different way: the collimation at its field´s rim (light distribution in the focal plane) is hardly worse than in the center. So we get a nearly diffraction limited field with sharpest imaging at the view fields´ rim. There is no objection to mounting even big CCD sensors of expensive digital cameras in the focal plane in order to get high resolution photos of the moon, without additional investment in optical correctors!


If you download WINSPOT, you can easily verify the following interesting facts by yourself:

• looking at the 150/750-Newton from the above example: a field of approximately 1.5 * full moon examined at the field´s rim leads to a similar spot size as with the schiefspiegler (but does not have its ultimate contrast power)
• the diffraction limited field of this F/5-Newton (spot size at its field´s rim no bigger than its difraction disk) is just 9 arc-minutes, corresponding to about 10 diameters of Jupiter, only.

But apart from this main feature "resolution or power of separation" of the obstruction-free Kutter telescope, there are other favourable characteristics in terms of visual perfection. Let us take the widespread Cassegrain telescope. Especially for this the priority seems to be shifted towards convenient overall size and maintainability. This fact leads to a significant trade-off in optical perfection and from the technical point of view appears to be totally inappropriate, which can be shown easyly. For example take a reflecting telescope with 200 mm aperture and 4000 mm focal length due to its optical perfection (spherical mirror producible with pinpoint accuracy!).

A Newton would be virtually impossible because of its great overall length. Therefore, we design a Cassegrainian, where 4000 mm focal length can be put into a tube of only about 900 mm lenght, first of all a good advantage in terms of transportability and set up. Such an arrangement with a system aperture ratio F/20 yields to:

• primary mirror of 1000 mm focal length, F / 5
• secondary mirror of -320 mm focal length and about 60 mm aperture, approximately F / 5.3

But beware: in terms of the required accuracy of the main Cassegrainian mirror in respect to that of the Newton, the further consideration of this system shows that the primary Cassegrain F / 5 mirror needs to have an accuracy 64 times !!! higher than that of an F/20 Newton of equal size.

Even if manufacturing such a mirror would consistently succeed well in high volume make, the fact remains that all deformations caused by temperature and gravity effects would be magnified in the same ratio as compared with the Newton, induced by the high post-magnification of the Cassegrain secondary mirror! Ludwig Schupmann was already aware of this fact posting the term "optical detour" for this hazardous design principle.

Considering further that the Cassegrain secondary mirror features an obstruction of 60 mm divided by 200 mm, equal to .3 thus reducing the diffraction disk´s contrast by almost 60%, it is not not hard to realize that the compact and easy to handle Cassegrainian is totally inferior to the schiefspiegler

So optical design features of the Kutter telescope are clearly defined:

• unobstructed path of rays in terms of a minimum diffraction disk and best possible contrast
• the aperture ratio of the primary mirror must be slow (max. 1:12) on order to keep spherical aberrations small.
• ong focal length without a big optical detour, allocating the forces of the optical system evenly over the primary and secondary mirror.
• the secondary convex mirror can have the same radius of curvature as the primary mirror has (a pleasant advantage easing the grinding process). Thus the Petzval condition is fulfilled and the image plane is flattened.
• the schiefspieglers maximum aperture should remain below 400 mm; scaling it up to large reflecting telescopes is not possible.

So the advantage of the Kutter telescope compared to a similar Newtonian or Cassegrainan is given by the absence of unwanted diffractions of the secondary mirror and its spider vanes. Resolving power and contrast reside on the same level as with the apochromatic refracting telescope thus being beneficial especially for lunar and planetary observations.

For all these reasons, schiefspieglers have been for long the telescopes of choice for the puristic lunar and planetary observer who won´t afford an expensive APO of reasonable aperture.

Finally, the inclined reader may oversee the author´s note on a widely spread phenomenon. Heading to the point without further preface - who would desire a refracting telescope for himself, with large, deep scratches and a central, blind spot on his Fraunhofer lens? In case of the "poor man's telescope" (a Russell W. Porter neologism), such scratches are taken as a matter of course, called "spider vanes" and "secondary mirror"!

And this although - from an optical point of view - it is undisputed that spider vanes as well as secondary mirrors come along with the same physically caused loss of optical power as scratches do.