8.1.2. Newtonian collimation

There are two drawbacks of this type of alignment: (1) uneven illumination of the outer field, and (2) difficulty of determining the correct visual alignment of the three components. The former is pretty much insignificant in visual use, since the uneven illumination falloff at the two opposite sides of the field are unlikely to be noticed. The latter does present practical difficulty, although it is possible to determine and produce an image of the proper visual alignment for a particular telescope, and use it as a guide.

Much more common alternatives are those that are based on near-concentric visual alignment of the focuser, diagonal, primary mirror in the diagonal's view and diagonal's reflection in the primary. One of them achieves this by offsetting the diagonal by sliding it down along its surface plane, until it becomes visually centered in the focuser's view. It also evens up field illumination, without introducing any form of mechanical.

The other is a conventional 3-step collimation procedure, in which the diagonal is centered in the focuser by shifting it toward primary. It also achieves near-concentric visual alignment and even field illumination, but at a price of introducing some forms of misalignment, some generally negligible, some others possibly not (FIG. 116, bottom). This collimation mode is sometimes referred to as partial offset, as opposed to offset, or full offset when the flat shifts diagonally along its surface. A better terminology, suggested by Don Pensack, is unidirectional and bidirectional diagonal offset, respectively.

The starting assumption is that all three elements are in near-perfect mechanical alignment, with the diagonal center nearly coinciding with the focuser and tube axis point of intersection, and the primary nearly centered around tube axis as well. Focuser axis is perpendicular to the tube axis. Mirrors are likely to be deviating somewhat from their perfect orientation but, for the sake of illustration, we'll assume they are close to it (diagonal deviations from 45-degree angle - or in the plane orthogonal to it - will affect the position of primary's reflection in it, while primary's deviation from orthogonal to the axis position will affect position of diagonal's reflection in it, which is centered around primary's optical axis).

Following calculation, assuming surface rotation around their center point (except when acknowledged otherwise), and omitting negligible factors (such as depth of the primary) is not strict in mathematical sense, but should give close approximations practically as good as exact values for the range of amateur Newtonian telescopes.

The first step of this procedure (FIG. 116 bottom, 1) is centering the diagonal in the focuser's view by shifting it axially toward the primary. The needed axial shift ∆a (to distinguish it from the offsetting shift ∆) to equalize apparent visual angles α and β for the top and bottom half of the diagonal, respectively, resulting in the apparent and actual center of the diagonal coincide, requires the equality (a-∆a)/(H-a+∆a)=(a+∆a)/(H+a+∆a), which solves to:

where A=2a is the diagonal's minor axis, and H the height of focus above the diagonal's center. By neglecting ∆a in brackets with three parameters (i.e. neglecting that the focus-to-diagonal separation will increase by ∆a after primary's tilt), it simplifies to a close approximation ∆a~a2/H = A2/4H.

The shift has, however, separated reflected (imaginary) axis of the primary from the focuser axis, inducing decenter error. At this point, primary's axis is shifted toward the primary by ∆a linearly, which brings to the field center off-axis field point of identical height, with the P-V wavefront error of coma, according to Eq. 73.1, given by ω=6.7∆a/F3. For 300mm f/5 Newtonian with the focus height H=250mm, diagonal's minor semi-axis a=35mm and corresponding axial shift ∆a=4.9mm, this gives ω=0.26 wave RMS.

The next step, with the diagonal centered in the focuser's view, is to bring reflection of the primary in the diagonal's view (i.e. on the surface of the diagonal) to the diagonal's center, making the two concentric. Since the axial shift resulted in nearly equalized apparent angles α and β, the primary reflection is also nearly centered in the secondary, and only slightly shifted toward tube opening due to focuser axis being displaced upward from primary's axis. Centering of the primary reflection is accomplished by tilting the diagonal clockwise, by an angle given as:

in radians (for this small angles, practically identical to tanγ), f being the mirror focal length. Obviously, an imaginary ray coinciding with the focuser axis will be now, after reflection from the diagonal, directed toward the center of the primary.

However, the diagonal tilt directs the "reflected" primary's axis - with the best image point on it - further away from the field center (FIG. 116, bottom 2). At this point, with both, diagonal and primary in its view centered in the focuser's view, the total RMS wavefront error of coma in the field center is that of decenter and tilt combined, or ω=(6.7∆a/F3)+13.4γH/F3 (the latter from Eq. 73, substituting γ for τ and multiplying with 57.3x60 for the conversion from arc minutes to radians, with the result reduced by a factor H/f for the focuser). For the same 300mm f/5 Newtonian, that comes to γ=0.00196 and the combined RMS wavefront error of coma ω=0.31 wave.

The final step is bringing the deflected optical axis of the primary - i.e. the focal point - back to the field center, in the middle of the focuser. This is accomplished by tilting the primary clockwise, so that its optical axis tilts upwards until it nearly coincides with the focuser axis "reflected" from the diagonal. The required angle of tilt equals 2γ. Since diagonal's reflection in the primary is centered around primary's axis (since the diagonal is axially centered itself), bringing primary's axis to the center of the focuser is, in terms of the view in the focuser, bringing diagonal's reflection in the primary to the center of the view, that is, making it concentric with both, diagonal and primary's reflection in it.

 As a result of primary's axis now coinciding with the focuser axis "reflected" from the diagonal, the two axes hit nearly identical point at the diagonal, and nearly coincide in the focuser. In other words, the point of best image is brought to nearly coincide with the focuser axis, that is, with the field center (note that the focal point is now slightly higher, effectively by the amount of diagonal's axial shift).