Dominant off-axis aberration in the Newtonian is coma; astigmatism is low in comparison. Image surface deformation is field curvature, with distortion being zero with the stop at mirror surface. All three aberration are independent of mirror conic, which means that they are equally affecting both types of the Newtonian telescope, those with spherical and those with paraboloidal primary. Following are relations specifying the aberrations.

● lower-order coma, from Eq. 12-13 and 15.1, after substitutions, as the P-V and RMS wavefront error at diffraction focus for object at infinity is given as:

respectively, with α being the field angle (α=h/ƒ, h being the linear height in the image plane, and ƒ the mirror focal length). Note that this is double the error given by Eq. 12, which expresses only the peak aberration.

In units of the λ=0.00055mm wavelength, the coma wavefront errors are, slightly rounded off:

for D and h in mm (or with the numerical factor 38 and 6.7 replaced by 965 and 170, respectively, for D in inches).

For the 0.80 Strehl ratio, ωλ=1/√180, which corresponds to the field angle α=F2/90D in radians, for D in mm (α=F2/2286D for D in inches), or the linear height in the image plane

in radians, or α'=38F2/D in arc minutes, for D in mm (α'=1.5F2/D for D in inches). Evidently, unlike the linear quality field, which only changes in proportion to F3, quality angular field changes in proportion to F2 and in inverse proportion to the aperture diameter D.

As Eq. 70 implies, the wavefront error of coma in the Newtonian is inversely proportional to the square of its ƒ-ratio for given angular field radius, and to the third power of it for given linear field radius. Thus it decreases exponentially with the increase in focal ratio, as illustrated on a simplified scheme below.

Also, Eq. 70 shows, coma of the concave mirror is independent of its conic. It, however, changes with the stop position and object distance, as described in 2.2. Coma (it also contains specifics on geometric, or ray aberration). In terms of object distance o and mirror radius of curvature R, the coma wavefront error changes in proportion to (o+R)/o, with R being, according to the sign convention, negative. Thus, mirror coma diminishes with the object distance, falling to zero for object at the center of curvature (o=-R).

What is usually seen of the coma in the eyepiece, with sufficiently bright stars, roughly corresponds to the dense 1/3 of its geometric blur (sagittal coma). Its angular size needs to be ~5 arc minutes to be clearly recognized by an average eye. Since the angular size of sagittal coma in the eyepiece (neglecting eyepiece distortion) is 3.75ε/F2, in arc minutes, with ε being the eyepiece apparent viewing semi-angle in degrees, the viewing angle in the eyepiece at which the geometric sagittal coma would become obvious to most people is given by ε~1.33F2. This means that one could see it at the edge of a 42° AFOV eyepiece at ƒ/4, regardless of its focal length.

 However, what we see in the eyepiece is not a ray spot, but an actual diffraction image deformed by the aberration. The above "geometric" angle at which sagittal coma becomes visible is noticeably reduced in conventional eyepieces, due to significant additional blurring caused by eyepiece astigmatism. Also, in order for the comatic deformation to be seen in the actual star image, this image has to be noticeably deformed by the aberration. For coma, that occurs as the aberration decidedly exceeds ~1 wave P-V on the wavefront (or, as the full size blur exceeds four times the Airy disc diameter, and the sagittal coma is nearly 1.5 times the Airy disc diameter). At this aberration level, and beyond, the actual visible blur of relatively bright stars roughly resembles the form and size of geometric sagittal coma. As the error diminishes below ~1 wave P-V, the effect gradually transforms into one-sided intensity distribution asymmetry visible in the diffraction rings, but with the spurious disc still well defined. 

From Eq. 70, the field height at which the coma error becomes large enough (~1.25 wave P-V) to begin to resemble sagittal coma in the actual star image can be approximated by h~F3/30, in mm. For an ƒ/4 mirror, that corresponds to ~2.1mm (FIG. 73). For the magnification level needed to enlarge the actual comatic image of a bright star with this amount of coma to 5 arc minutes apparent size, the eyepiece focal length is approximately f~1.3F. Hence an average observer, with a 5mm eyepiece and an ƒ/4 mirror, can expect to notice coma on bright stars from ~2mm off-axis out. With an ƒ/6 mirror, it will take an 8mm eyepiece to show coma becoming apparent some 7mm off-axis (which would require 80+ degrees AFOV); higher magnification will reveal little of the characteristic comatic deformation inside 7mm off-axis, due to the deformation becoming less apparent with the decreasing wavefront error. Compromised image sharpness, however, will be noticeable well within the 7mm-radius field circle.

Due to eyepiece astigmatism, which increases with the square of eyepiece field angle, comatic-like deformation in the eyepiece grows rapidly toward the field edge. For given linear field radius in the image plane, eyepiece astigmatism increases in inverse proportion to the square of the focal ratio as transverse aberration (i.e. ray spot size) and inversely to the cube of it as wavefront error (lens astigmatism, given by Eq. 22, increases with the square of entrance beam width, which is inversely proportional to mirror focal ratio, and inversely to lens' focal length, which is proportional to the mirror focal ratio for given aperture and nominal magnification). Therefore, its proportion to mirror coma at given linear field radius remains constant regardless of mirror focal ratio.

If we express the coma blur length (Eq. 17) in arc minutes, it comes to 645h/DF3. Angular size of this blur on the retina is multiplied by telescope magnification M, to 645hM/DF3. Setting 645hM/DF3=3 gives the field radius h at which angular size of the coma blur is three arc minutes as h=DF3/215M. Average P-V wavefront error of astigmatism in a conventional eyepiece is approximated by W~0.02ƒe(α/F)2 in units of 550nm wavelength, where ƒe is the ep focal length, and α is the ep field angle (AFOV/2). Substituting α~57.3h/ƒe gives WA~66h2/ƒeF2, with the astigmatism wavefront error relating to that of coma (WC=37.9h/F3, also in units of the wavelength) as 1.7hF/ƒe.

The combined visible blur size can be, at least roughly, approximated as larger than coma-alone blur by a factor of 1+(WA/WC). If we assume that only about the bright 1/3 of the coma blur (sagittal coma) is visible, which is most often the case (the exception are bright stars, especially in large apertures) then the combined blur is roughly three times smaller.

Graph below illustrates how quality visual field in the Newtonian telescope varies with coma alone. Note that D/M in the above equations is, for convenience, replaced by the pupil diameter P.

The green plots, for the field radius with the angular sagittal coma within 3 arc minutes, would represent the field quality with zero eyepiece astigmatism. The red plots, for the entire coma blur (tangential coma) are probably more representative, at least as a rough guide, considering that eyepiece astigmatism commonly enlarges the final blur. Somewhat larger blur, 3-5 arc minutes is still acceptable, and toward field edge, as much as 6-9 arc minutes is tolerable. The inset with diffraction pattern illustrates how eyepiece astigmatism combines with coma in producing the actual combined blur (ray spot on white background corresponds to 1 wave P-V of coma, next at right to it; the bottom 1/3 of the spot is sagittal coma).

The 1 wave of coma is characterized by Sidgwick as limit to tolerable, visually. Obviously, it may not be so at high enough magnifications, and/or with significant eyepiece astigmatism present. In a 200mm f/5 Newtonian, coma is that strong at 3.3mm off axis. In the 10mm f.l. eyepiece, tangential coma is already 8.5 arc minutes, and sagittal near to 3. Average eyepiece astigmatism P-V wavefront error at this field height (close to 20-degree field angle) is nearly three times stronger than coma's, enlarging sagittal coma to roughly 11 arc minutes - quite obvious for most observers.

Field curvature in the Newtonian is relatively weak, with no significant effect on visual observing. 
 

● lower-order astigmatism, from Eq. 18, after substitutions (for θ=0), as the P-V and RMS wavefront error at best focus, for object at infinity, are:

with ƒ being the mirror focal length.

In units of the l=0.00055mm wavelength, the errors are:

for D in mm (or with the numerical factor 227 replaced by 5766 for D in inches).

The field angle at which astigmatism reaches 0.80 Strehl is α=√F/622D in radians, or at the off-axis height in the image plane of h=αƒ. It has no significance, with the coma error being absolutely dominant at this field angle. The two aberrations' RMS wavefront errors equalize for the field angle α=1/6F in radians, or for the h=D/6 height in the image plane, after which the astigmatism quickly becomes the dominant aberration.

The wavefront error doesn't change with object distance. However, it does change with the stop position. More details on this, as well as on the geometric (ray) aberration in 2.3. Astigmatism.

● field curvature: Petzval curvature of a concave mirror is Rp=R/2, R being the mirror radius. Due to the presence of astigmatism, actual best image curvature is different from the Petzval. Also, it varies with the stop position. For the stop at the surface, best, or "median" image surface equals the negative of mirror's focal length:

which makes it positive (concave toward mirror) for mirror oriented to the left, regardless of mirror conic. Position of the aperture stop influences mirror astigmatism, which in turn causes changes in the median image curvature. As Eq. 39 shows, it varies somewhat with the conic. For a paraboloid, best image surface is flat with the stop at half the focal length from mirror, and with the stop at the focal length away mirror astigmatism is cancelled, but image curvature equals R/2 (convex toward mirror). For a sphere, best astigmatic field is flat for the stop at (1-0.51/2) focal lengths from mirror, and astigmatism is cancelled for the stop at the center of curvature.

Miscollimation sensitivity of a Newtonian is determined by the diameter and F-number of the primary mirror. Sources of miscollimation are: (1) primary tilt/decenter, (2) flat tilt/decenter/despace, (3) focuser tilt/decenter and (4) tube/structural flow resulting in any of the former. As a result, axial image point is shifted away from the field center, and replaced with certain amount of off-axis coma.

Expressing the linear center field shift as 2τƒ/(60x57.3), for τ the mirror tilt angle in arc minutes and ƒ the focal length, and substituting it for h in Eq. 70.1 (right), gives the RMS wavefront error of coma shifted to the field center (in units of 0.00055mm wavelength) as:

for the aperture diameter D in mm (for D in inches, ωt = τD/10F2).

Assigning H to the diagonal-to-focus separation, and H' to the focus height in the focuser (measured from the focuser base), the miscollimation sensitivity per arc minute of tilt is smaller by a factor H/ƒ for the diagonal, and by a factor of H'/2ƒ for the focuser, respectively, with ƒ being the mirror focal length.

Sensitivity to decenter - also in units of 550nm wavelength - is identical for all three, mirror, flat and focuser, and given by:

for the decenter ∆ in mm. It is also the despace sensitivity of the flat for despace in mm.

More details on collimating Newtonian on the following page.