Let me guess: You decided to clean your primary mirror and realized that the secondary was covered by dust too. Why not dismounting it, clean it properly and mount it again? 

At that time, you didn't know about one small detail: To collimate a fast Newtonian telescope isn't an easy task. Why and how? Let see that together

What is a fast Newtonian telescope?

A "fast" Newtonian telescope is a telescope with a small F/D ratio, means the ratio of the focal length to aperture size. As you already know, an optical train with an F/D ration of 5 is usually rated "f/5". 

There is no common understanding about how fast is fast; Some astronomers consider that a Newtonian telescope with F/D <5 is fast, and some others set the limit at 4. 

In the past, fast Newtonian were easy to identify because there mere mostly parabolic mirrors, or even sometimes hyperbolic for the most expensive astrographs (Takahashi Epsilon, as one of the most iconic one). This definition tend to become obsolete, since more and more entry-level f/5 telescope also use parabolic mirrors. 

Why do I bother you with this definition?

Because of that:

Why is collimation so important?

You have probably seen those beautiful spot diagrams somewhere 

Source: https://rcopticalsystems.com/telescopes/aberration_color.html 

In this example, a simulation shows the spread of luminous flux of a perfect point star, depending on its distance to the optical center (or to be precise, depending on the angle between the ray of light and the optical axis). This phenomenon is called the coma. 

As you can see, the further the star is from the center, the more distorted it is. We now understand the importance of have the center... centered. This means that the optical axis should ideally hit the center of the sensor, so that each corner of the sensor is at an equal distance of the optical center. 

What happens if this is not the case: the farthest corner will have a higher coma and as we all know, large distorted stars are particularly unsightly. 

Life is harder with fast Newtonians

If you want to know more about the theory and find the source of this article, please refer to that excellent website:

https://www.telescope-optics.net/newtonian_collimation.htm

Allow me to copy and paste the introduction of this article:

The difficulty in aligning optical elements of the Newtonian reflector arises from its diagonally oriented flat mirror, causing apparent shift of the projection of its surface away from the primary, in the view of the focuser opening. Due to this effect, in a perfectly aligned instrument (FIG. 116, top), with the center of the flat coinciding with the point of intersection of primary's and focuser axes - positioned at right angle - observing with the eye at the focal point, the flat appears off the focuser axis, shifted away from the primary. Also, image of the primary mirror in the reflected view of the flat appears decentered with respect to the flat, while in fact their respective centers do lie on the optical axis, and are perfectly aligned with the focuser axis. 

Can you see it in the above picture? The alpha angle is bigger than beta, causing an asymmetric luminous flux, and therefore asymmetric flats, when the telescope is "perfectly aligned" which means that center of the secondary mirror is exactly located at the intersection between the primary's optical axis and the focuser's axis.

I know. This last sentence caused some headaches.  

Does is mean that a flat field is also asymmetrical? Actually, yes. And not even a little, as you can see in the picture below:

Source: https://www.cloudynights.com/articles/cat/articles/how-to/passive-tool-collimation-and-the-newtonian-r1947

Partial offset and full offset

So what? Shall we send the telescope to our astronomy dealer?

Before we do this, let's try to collimate by ourselves. The first thing we need to decide is which offset type we are going to use. 

1. Partial offset: Secondary toward Primary

2. Full offset: Secondary toward Primary and away from focuser offset

It is no bigger effort to perform a full offset collimation compared to the partial offset, and the result is noticeably better. Therefore, it is worth spending the extra 5 minutes.

Full offset collimation step by step

Ready? Go!

Aligning the secondary mirror under the focuser

This is one of the most underrated steps! First step is to place the secondary mirror in central position, by adjusting the 3 or 4 screws holding the spider. The distance between the holders and the tube must be equal, as shown below

For the second step, I use 2 pieces of paper: One is located in the tube (shown in orange), under the secondary mirror on the opposite side of the focuser. It helps to see the mirror better

The other paper (shown in blue) is rolled up and inserted in the focuser tube. I use a fairly thick paper for a better result. For an even better result, you can even cut the end at 45°. This paper helps to locate the mirror along the axis of the optical tube (green arrow).

For a more precise adjustment, you can also try to use a metal ruler but this technique isn't easy to implement, and the risk of damaging the mirror is high.

"How precise shall all this be?" 

I'd say 0,1mm for the spider (distances "a" and "b"), and 0,5mm for the axial adjustment (green arrow) or better. 

Aligning the secondary mirror

The game now is to place the laser spot in the middle of the primary mirror, by tilting the secondary mirror without changing its axial position. In other words: make this fine tuning with the 3 adjustment screws, and don't touch the central pivot screw!

The mirror's position is modified every time a screw is tightened? OK don't worry, it's all normal. Just repeat this step until it works

Aligning the primary mirror

What sounds like a difficult task is actually the easiest one. Most of the telescopes have 3 fine-tuning screws and 3 locking screws. 

The game is now to reflect the laser spot back to the secondary mirror, and finally back to the laser collimator

Did it work? Congrats! You just made a normal collimation, as you would do for an f/8 telescope, and it would be more than sufficient. 

Let's summarize: The laser beam now perfectly hits the center of the secondary, is then reflected at an exact angle of 90° and deviated toward the primary, hitting the primary at its very middle, back to the secondary, deviated again at 90°C back to where it exactly comes from.

The optical train is now perfectly aligned but as we explained before, it shouldn't be! 

Let's add some disorder now

Full-offset collimation

You understood the theory and you successfully performed a normal collimation. You are now close to touching the holy grail.

After all, it's just about moving the secondary mirror on the plane of its own surface right? 

Let me be frank: it is not easy at all. I tried several methods and miserably failed. Here is a description of a simple technique I developed to make my life easier (and works so far)

In our case: M = 70mm, F=4, and therefore offset = 4.375mm

The radial offset is quite easy to tune. On the picture below, the upper part of the spider needs to be unscrewed, while the lower part must be screwed and tightened. 

The axial offset is a more delicate step. It is difficult to measure the axial offset correctly but since we can accept a small mechanical tolerance, I decided to print a target with a small hole located where the laser beam must pass. Once it is done, the mirror is off-center

The mirror needs now to be axially moved toward the primary mirror. But now that the laser collimator is inserted, the the target can't be seen. 

This is where the inspection mirror is used. Please be carfull not to reflect the laser in your eyes. Even if those lasers are harmless for a short time, it's better not to...

Now that the dual offset technique has been succesfully done, we probably modified the rotation of the secondary mirror. By adjusting the 3 fine-tuning screws, we can now bring the laser to the donut indicating the center of the primary mirror. The primary mirror needs also to be tuned according to the conventional collimation rules explained before. 

We are almost done.

Final adjustment of the primary mirror

The 2nd and 3rd steps described in the article https://www.telescope-optics.net/newtonian_collimation.htm explain how to tilt the secondary and primary mirrors. I don't know how to do this with conventional equipment but anyhow, it shouldn't be necessary since we are using a laser collimator which shall ensure that the luminous flux is at its maximum in the middle of the sensor (if the sensor is perfectly centered of course).

It's now time to mount the corrector, filter wheel, and camera back again. Use the chance to remove the dust from the coma corrector with the compressed gas. Camera is wired, luminance filter is in position and flat panel is on. 

At that final stage, I allow myself a very small adjustment of the primary mirror in order to align the flat field and the sensor. I assume it's because my sensor isn't perfectly aligned with the center. Never mind, it works!

As you can see on the second picture, the hot spot (ie. the brightest part) is slightly off-center, but this will be compensated by the master flat.

The purple corners (ie. the least bright part) represent the vignetting. Unequal corners have two negative consequences:

1. One of the corners will be underexposed. Even with a good master flat, it will capture less photons, resuting into a lower signal and a lower SNR. An inesthetic noise could appear in this corner.

2. The underexposed corner is also the furthest from the optical center. This corner will have more coma than the others, and it is pratically impossible to compensate it during the postprocessing without serious side effects.