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Coma in the Newtonian Telescope
by James Mulherin
The dominant optical aberration in the Newtonian telescope is off-axis coma. In the eyepiece, coma adds a V-shaped flare to a star’s image that points inward toward the center of the field of view (fov). The amount of coma apparent in a Newtonian telescope is a function of the focal ratio of the telescope. A fast (short focal length) telescope will exhibit more coma in off-axis star images than a slow (long focal length) telescope. Also, for a given focal ratio, coma is linearly proportional to field position. A star located further away from the optical axis (the center of the fov) will exhibit more coma than a star located close to the optical axis.
In this article we explain how coma forms in off-axis star images. We then describe the relationships between coma, field position and focal ratio. The article then gives examples, for comparative purposes, that show the amount of coma apparent in Newtonian telescopes over a range of focal ratios. Finally, we discuss the effects of off-axis coma on image quality when observing different types of astronomical objects.
How Coma is Formed
The surface of a Newtonian telescope’s primary mirror is parabolic. The parabola is the only geometric Surface that will focus a bundle of parallel rays to a point. Except for the limitations due to diffraction and atmospheric turbulence (seeing), a perfect parabola would focus a bundle of parallel rays to an infinitely small point. However, this is only true if that bundle of rays is parallel to the axis of the parabola or parallel to the optical axis of the telescope. When you center a star in the fov of a telescope the above condition is met and there is no coma in the image.
When a bundle of parallel rays from a star strikes the parabolic mirror at an angle, the star image is formed off the optical axis, or decentered in the fov. The parabola does not reflect this bundle of angled rays to a perfect point. Instead, the star appears as a bright spot with a V-shaped comatic flare. To understand how this comatic flare is formed, imagine subdividing the mirror’s surface into a series of thin annular rings of increasing diameter. Start by covering all of the rings except the inner one, just outside the obstruction caused by the secondary mirror. The parabolic mirror will reflect the light striking this ring and the image that it forms will be a tiny ring in the focal plane. Now cover this first ring and uncover the next ring out. Light reflected from this next ring will be focused to a slightly larger ring in the focal plane and this ring will be slightly further away from the optical axis than the previous one. Continuing this process we find that the star’s image is simply the summation of these ever widening rings that are shifted outward in the focal plane. The spot diagrams in figures 1 and 2 demonstrate this effect by showing the same off axis star image; first with the mirror’s full aperture exposed, then with only the outermost ring of the mirrors aperture exposed. The V-shaped appearance of the star image is due to the concentration of light where the rings overlap.
Figure 1- Off-Axis Coma - Full Aperture of F/4 Mirror Exposed
Figure 2-- Off-Axis Coma – Only Outermost Ring of F/4 Mirror Exposed
Coma and Field Position
The amount of coma in a star’s image is directly proportional to its distance from the optical axis. There are two ways to specify this off-axis field position. You can specify a star’s angular position relative to the center of the fov (this is the angle that the star’s bundle of parallel rays makes relative to the optical axis of the telescope), or you can specify the star’s linear distance from the center of the fov, measured directly in the focal plane. In the interest of clarity, we choose the later method and specify field position as the linear distance from the center of the fov to the star’s image. Using this method to specify field position, all telescopes of a given focal ratio have the same amount of off-axis coma, regardless of aperture. For example, a 10” F/4 has the same amount of coma as a 20” F/4 at the edge of a 30-mm diameter fov. We will make use of this fact when we compare coma in telescopes with different focal ratios. First, we will use the following example to define some measurement standards. Figure 3 below shows the appearance of off-axis coma in an F/4 Newtonian telescope across a 30-mm diameter fov.
Figure 3 -- Coma in an F/4 Newtonian Telescope
Each spot diagram in the above matrix shows the appearance of a star’s image at different field positions. The field positions sampled are the center of the fov and successively larger off-axis distances in 3-mm increments. The largest off axis distance is 15-mm away from the optical axis. Because these distances are radial, and because coma is symmetrical about the optical axis, this set of spot diagrams represents performance across a 30-mm diameter fov. The following information is shown in the diagram:
- The star’s field position, measured radially in millimeters from the optical axis, is listed directly below each spot.
- In the upper left corner of the diagram there is a scale bar indicating scale in microns (there are 1000 microns in one millimeter). In this case the scale is 210-microns.
- At the bottom of the diagram, the Root-Mean-Square (RMS) and geometric spot radius in microns is listed for each field position. The RMS radius is a statistical measure of how well the energy is concentrated in the star image. For example, at field position two (3-mm off axis) the RMS spot radius is 11.723-microns. This means that most of the energy in the star image falls within 11.7-microns of the star’s centroid, or within a circle of about 23.4-microns diameter.
The Geometric spot radius is simply the radius within which all of the energy falls. For the field position in the example above (3-mm off axis), if you were to draw a circle around the star’s image to enclose all of the energy, that circle would have a radius of 18-microns (36-microns diameter).
Coma and Focal Ratio
As mentioned earlier, the amount of off-axis coma in a Newtonian telescope is also a function of focal ratio. A fast telescope will exhibit more coma than a slow telescope. For comparison, figures 4, 5 and 6 show spot diagrams for Newtonian telescopes with focal ratios of F/4.5, F/5.0 and F/5.5. As in the F/4 example above, the spot diagrams in the figures below cover the same 30-mm diameter fov.
Figure 4 -- Coma in an F/4.5 Newtonian
Figure 5 -- Coma in an F/5 Newtonian
Figure 6 -- Coma in an F/5.5 Newtonian
Coma and Image Quality
All of the spot diagram examples above are for relatively fast Newtonian telescopes and the comatic aberration is fairly large. In each case, the optical performance of the telescope is diffraction limited only over a fairly small area at the center of the fov. Over most of the fov, the comatic aberration appears to be relatively large. In practice, the effect of this comatic aberration on image quality in a large Newtonian telescope depends on the type of object observed.
Diffuse objects such as nebulae and galaxies are objects with large and small-scale detail throughout but they typically have no well defined edges. In fact, the more aperture you have, the more you see of the object. What you perceive as edges and where they are perceived literally depends on your telescope’s light gathering ability. The effect of off axis coma on what detail you can resolve visually or photographically is practically imperceptible. Effectively, the telescope forms an image of an object with indistinct edges. The coma makes the edges slightly less distinct, but by an amount that is imperceptible by any practical measure.
The effect is similar on globular clusters, except for the stars in the core of the cluster that are resolved. But if the star cluster is centered in the eyepiece the stars in its core are close to the center of the telescope’s fov and thus sharp. So again, the net effect of off-axis coma is negligible.
When observing an open cluster you will see coma in stars near the edge of the fov. In any other image that features stars sprinkled across the fov, coma will be noticeable. For most observers, this is an acceptable tradeoff given the many benefits of a large aperture Newtonian telescope.
When observing planets the optical performance of the telescope is diffraction limited as long as the planet is held near the center of the fov. Keeping the planet centered can be a challenge however, if you are looking for fine detail as the planet drifts across the center of the fov in a Dobsonian telescope. In addition, when looking for fine detail, the inherent limitations due to coma in a large aperture Newtonian telescope will often be compounded by the effects of atmospheric seeing. A large aperture telescope is often “seeing limited” due to turbulence in the Earth’s atmosphere.
For planetary observing, many observers insist that a 4” to 6” aperture apochromatic refractor is the best choice of instrument. However, a large aperture Newtonian telescope can achieve similar performance be applying an off-axis mask to the telescope. The spot diagrams in Figure 7 show the results of installing a 6” off-axis mask on an 18” F/4.5 Newtonian. The result is an un-obstructed 6” F/13.5 off-axis Newtonian telescope with significantly less comatic aberration. Stopping down to the smaller aperture for planetary observing will also help defeat some of the effects of atmospheric seeing.
Figure 7 -- 18” F/4.5 with 6” F/13.5 Off-Axis Mask
A Note On Eyepiece Aberrations
In the above discussion it is assumed that eyepiece aberrations do not contribute significantly to the final image quality of the telescope/eyepiece system. In reality this is rarely the case. When examined independent of a telescope, the dominant aberrations in most eyepiece designs are field curvature and astigmatism. Usually, these eyepiece aberrations are larger than the telescope’s comatic aberration and they are the aberrations most prominent in the image. In the eyepiece, the combination of astigmatism and coma give the star a squashed, V-shaped appearance. The effect of eyepiece field curvature is to cause stars at the edge of the fov to appear slightly defocused when stars at the center of the fov are in sharp focus.
To understand why eyepiece aberrations are so large, note that the eyepiece is actually a small refracting telescope being used in reverse. The eyepiece is designed to re-collimate “point-like” star images produced by the telescope so that your eye can refocus them onto your retina. Now consider that most modern eyepiece designs have an apparent fov of between 60 and 80 degrees! Correcting astigmatism and field curvature over such a wide fov requires a complex and expensive eyepiece design. The Nagler eyepiece is an example of a commercially available design that goes to the expense of correcting eyepiece astigmatism (and they are priced accordingly). That is why the Nagler design works so well with fast Newtonians.
About the Author
James Mulherin is the president of Optical Mechanics and a master optician. James manages the optics shop at Optical Mechanics and is a leading expert in the design and fabrication of astronomical optics.
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