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# Astronomy Calculations

## Depth of Focus

I have written a lot about focus motor and temperature compensating. Then we need some numbers of have much focus precision we need. When shall the motor change the focus when temperature changes.

The depth of focus depends mainly on three things:

• The seeing, i It could be from 1" to 10", a seeing of 2" (2 arc second) is very good.

Seeing, Wiki

• The opening of the telescope, the focal ratio.

F-number, Wiki

• The wavelength you observing at. The resolution of the telescope are different at H-alpha compare to the blue wavelengths.

Normally when talking about optics in the visually wavelengths, about 380 (blue) nm to 650 (red) nm we use the green / yellow wavelength 550 nm as a reference.

If you only take photos of the H-alpha red glow you maybe should use 656 nm instead. If doing photographing in the UV spectrum, then maybe 350 nm is better to use as the reference.

Wavelength, Wiki

Here I try to sort it out:

It start to calculate as soon you change or write new figures in the white or dark red boxes. Do not exceed the maximum number of characters, delete characters if necessary.

Note:
You use the information on your own risk! There can always be a mistake in my equations behind the calculations, check that the result is correct. Let me know if you find something wrong and I try to correct it. Some calculations are very simple done and not correct in the small details.

### What wavelength to use as reference?

Note:
Shorter wavelengths (blue, UV) set higher demands of the focuser resolution. When doing RGB (color) images, set wavelength to 350 nm (blue).

Wavelength
(300 to 999 nm)

Opening diameter
(1 to 999 mm)

### Calculated theoretical optical data (point object like stars):

Resolution (Rayleigh limit) Airy disc (2x Rayleigh limit) FWHM (Full Width Half Max)
= Calculated results = Calculated results = Calculated results
arc seconds arc seconds arc seconds

### What is the focal length of the telescope or lens?

focal length including reducer or Barlow
(1 to 9999 mm)

### Calculated focal ratio:

= Calculated results focal ratio

### Calculated projected spot size diameter on the sensor:

= Calculated results micrometer (spot size FWHM)

Seeing disc angle (FWHM at chosen wavelength)
(1 to 10.0 arc seconds)

= Calculated results micrometer (spot size FWHM)

### Calculated Depth of Focus:

You can not say exactly where it's out of focus, it's more of a personal taste. I used focal ratio x FWHM disc size in these calculations:

focal ratio depth of focus (theoretical) depth of focus (seeing)
= Calculated results = +/-Calculated results = +/-Calculated results
micrometer micrometer

From these figures you know how much you can tolerate it to be out of focus. Example, if the temperature change the focal length or telescope tube length equal to above or more, then you have to start the focus motor and adjust focus.

I think it could be wise to design the gear box so that you use the whole length of your focus draw tube, but no less resolution then 1/5 of the above numbers, i.e. if you get +/-10 micrometers depth of focus, then not more then 2 micrometer per step, just my opinion. Design after the strongest demands, wavelength and focal ratio you have.

Normally it's the seeing that limit your resolution. When doing planetary imaging with Lucky Imaging it's maybe the opening of the telescope that's limit, if the telescope is of good quality.