Secondary mirror rotation and tilt is somewhat a confusing subject. Many have noticed after collimating their scopes with laser collimators by adjusting the secondary mirror to redirect the laser beam to the primary center then adjust the primary mirror to have the laser retrace its path back to the source, they can rotate the secondary mirror slightly and repeat the collimation steps successfully. Does this make sense? How can we introduce a rotation “error” then still get the laser beam to hit the primary center and retrace its path? Are we eliminating the introduced rotation “error” by “tilt” adjustments or are we hiding the rotation error by the “tilt” adjustments.
Well, let us talk about the term “tilt”. When we tilt the secondary mirror using one of the 3 (or 4) adjustment set screws, we are actually performing a rotation and displacement – mathematically speaking. That is, there is a “rotation” element when we tilt the secondary mirror. The axis of this rotation is perpendicular to the plane that includes both the central secondary bolt and the set screw being adjusted. That means, each set screw adjustment will rotate the secondary mirror slightly about a unique axis. Really, there are 4 rotation axes when we adjust the secondary mirror. The first is the rotation around the central bolt – the obvious rotation axis. The remaining three (assuming your secondary mirror has 3 set screws) are at 120 degrees apart and “perpendicular” to tube axis.
Back to the first paragraph, when we introduce a slight rotation error around the central bolt after having completed a successful collimation, we can negate and eliminate that error by only adjusting the set screws. The inherent rotation elements introduced by the secondary mirror set screws will negate the original rotation error. The end result is a scope with a perfect axially aligned – just like it was before the introduction of the rotation error. So, what is the difference between both setups? The appearance of the secondary mirror will be different – though it might not be noticeable.
Let us consider the following hypothetical experiment. Imagine a square mirror placed at a 45 degree angle as shown in figure “A”. Assume we have the ability to rotate the mirror about all 3 axes (X, Y, and Z) . A laser beam racing down the Y axis will end up reflecting off the mirror surface in the direction of the -Z axis as shown in figure “B”. Figure “C” is the same setup but shown from the Y axis perspective. Rotation around the Z axis is similar to rotating the secondary mirror round the central bolt. Rotations around the X and Y axes are similar to set screw adjustments.
Now, if we rotate the square mirror around the Z axis counter-clockwise by 45 degrees, we will introduce a rotation error and the reflected laser beam will significantly off-target. Can we eliminate the Z rotation error by introducing new rotations only via the X and Y axes? The answer is YES. By rotating the mirror around the Y axis by 35.26 degree clockwise followed by a 15 degree clockwise rotation around the X axis, we will end up succeeding in redirecting the laser beam down the -Z axis again as shown in figure “D”. But the mirror appearance is different.
How can this be? Well, the final location of the mirror in our example is equivalent to rotating the mirror by 58.64 degrees around its axis – an axis that is perpendicular to the mirror surface and runs through its center. The final mirror surface planar position is exactly the same and the laser beam will see the exact same thing in figures “C” and “D”. Bear in mind that straight laser beams do not interact with the secondary mirror edge and therefore are insensitive to the appearance/shape of the secondary mirror. Only the planar position of the secondary mirror in 3D will impact the laser beam reflection – not its shape.