The measurement method of the telescope focusing system backlash described in this article was discovered suddenly when I was checking two autofocus curves with a friend some time ago. At that time, a friend sent me two pictures of autofocus curves. The curves are very smooth and fitting well, but the focus position differs by about 400 steps. Normally there shouldn't be such a big difference. Then my friend told me that the backlash compensation direction of the two focusing is different. One is IN and the other is OUT. Then I realized that this difference is actually the overall backlash of the telescope focusing system including the telescope focuser and the electronic focuser. A few days later, I have a clear sky and I repeated the measurement method. This article is an introduction to this method. Hope this method will be useful for astrophotographers.

The accuracy of focusing affects the quality of astrophotography images. When capturing deep space objects, most people use electronic automatic focusers plus auto-focusing software to obtain accurate focus. Normally we use overshoot backlash compensation method during auto-focusing. When using this backlash compensation method, the input backlash compensation value can be larger than the actual backlash. If the backlash compensation value is smaller than the actual backlash, the backlash cannot be completely eliminated during focusing, which will affect the focusing result. Therefore, knowing the backlash of your equipment will help you choose the right backlash compensation parameters for auto-focusing and get a better focusing result.

This article introduces an accurate and easy-to-operate method for measuring the backlash of the telescope focusing system. In our tests the equipment we used and their parameters are as follows:

Telescope: SkyRover 102 APO Pro

Aperture: 102mm

Focal length: 714

Electronic focuser: Oasis Focuser

Focusing resolution: 0.8μm/step

Software: Sequence Generator Pro

Specific Method

The actual operation is very simple. What we need to do is just performing two (or two groups of) DSO auto-focusing operations.

Step 1:

Use other method to estimate the backlash of your focuser system, and set a value 50%~100% larger than the estimated backlash as the backlash compensation parameter in the auto-focus software to ensure that the backlash can be completely eliminated during the auto-focusing process.

Step 2:

Perform a group of auto-focusing operations. Choose Overshoot backlash compensation method, and choose IN for compensation direction. In one of my measurement tests, auto-focusing operation was repeated 6 times continuously, and the obtained focus positions were 20701, 20701, 20704, 20707, 20703, and 20708. The actual focusing curves are shown in Figure 1 at the end of this article.

Step 3:

Perform another group of auto-focusing operations. Comparing to the previous group, the only difference is that the compensation direction is set to OUT. The other parameters remain unchanged. In my measurement test, this time the auto-focusing operation was performed 6 times again, and the obtained focus positions were 20940, 20948, 20954, 20954, 20961, and 20965. The actual focusing curves are shown in Figure 2.

Step 4:

Now we can calculate the backlash. The average value of the focus position is 20704 when the backlash compensation direction is IN, and the average value is 20954 when the backlash compensation direction is OUT. The difference between them is 250 steps, which is the backlash of the focusing system. This value is similar to the backlash we estimate by other methods.

Fundamental

Every time auto-focusing operation completes, the telescope focuser moves to the focus position, which means that the actual position of the telescope focuser is the same after each successful focusing operation (Here we assume the focusing is accurate and errors are ignored).

When using SGP auto-focusing function and the backlash compensation direction is set to IN, the movement direction of the motor is inward when returning to the focus position. At this time there is no backlash in the inward direction. When the backlash compensation direction is set to OUT, the movement direction of the motor is outward when returning to the focus position. At this time there is no backlash in the outward direction. This means that when changing between the two states, the actual position of the telescope focuser does not change, but the directions of the backlashes are opposite., Since the backlash in one direction is always zero, We can see the steps the motor moves are just equals the backlash of the focuser system when the state is changed from one to the other. So the difference between the number of the focus positions of the two states is the value of the backlash.

Note: When using software other than SGP, the definition of the backlash compensation direction may be different.

Let’s analyze the process in an ideal and simplest way.

1. After each auto-focusing in the first group completed, the final motor movement direction is inward. The focus position is p1. At this time, if we continue to move the motor in the inward direction, there will be no backlash and each step will drive the telescope focuser to move inward. We assume that x steps are moved in the inward direction in this state,.

2. Then we start to move the motor in the outward direction. This process can be considered as two stages. In the first stage, b steps are moved to completely eliminate the backlash, and the telescope focuser does not actually move. In the second stage y steps are moved, and the telescope focuser reaches the position p2. The physical positions ofp2 and p1 are the same., Now we have the following equation:

p1 - x + b + y = p2

Since the actual position of the telescope focuser is the same at the positions of p1 and p2, then x and y must be the same. So now we can get the following equation:

b = p2 – p1

Therefore, the backlash value can be obtained by calculating the difference between the focus positions of the two groups of auto-focusing.

In each direction of backlash compensation, we performed a group of auto-focusing instead of a single auto-focusing. In this way, not only can the average value of a group of focus positions be taken, but more importantly, the difference of each focus position in the group can be used to evaluate the focus accuracy, and then evaluate the accuracy of the measured backlash.

Advantages of this measurement method

In fact, as long as we have a way to move the telescope focuser accurately to a same position, it can be used to measure the backlash. The measurement method described in this article has the following advantages:

1. Astrophotographers can simply use the DSO equipment they have at hand and don’t’ need any additional tools, such as calipers.

2. With this method the measurement has a good accuracy. The measurement accuracy is roughly equivalent to the auto-focusing accuracy. For example, based on the group of auto-focusing result shown in Figure 1, the focus position after each auto-focusing is only a maximum of 7 steps difference, less than 6 μm. Therefore, it can be estimated that the error of the measured backlash is roughly within the range of about 10 steps.

3. The equipment and software used by the measurement are exactly the same as the actual equipment and software used for DSO capturing. This avoids introducing other additional errors.

4. The measurement can be done easily. As long as we re ready to capture deep space objects, we can do this measurement.

The above measurement method requires that the auto-focusing is accurate.

The auto-focusing curves of our test are shown as follows.

Figure 1 Curves when compensation direction is IN

Figure 2 Curves when compensation direction is OUT