Autofocus Step Size Calculator

Get the autofocus step size for your focuser, telescope and camera in each capture program, then check it on a simulated run.

The Focus Step Calculator works out the autofocus Step Size for your Focuser, Telescope and Camera in nine Capture Programs, including N.I.N.A., KStars / Ekos and ASIAIR, and then tests it on a simulated Autofocus Run. Put simply, it tells you how many motor steps apart the points of a run should be.

How to use it

Start with your Focus motor. If yours sits on the focuser knob, such as a ZWO EAF or EAFN, the Askar WAF, the Celestron Focus Motor, a Pegasus FocusCube 3 or Motor Focus Kit, a SESTO SENSO 3, a QHY Q-Focuser or a generic stepper, Steps per turn fills in for you, and typing your own number makes the motor Custom. The SESTO SENSO 3 and the QHY go on the fine-focus knob, so the travel you measure is the fine knob’s. If your focuser has its motor built in, such as an ESATTO or an iOptron iAFS, it comes with its maker’s travel per step and you have nothing to measure.
Next, enter the Travel per turn in mm. This is how far the drawtube moves when the knob the motor drives makes one full turn. It differs between focusers, even of one model, so until you fill it in, the screen shows how to measure it. For a more precise figure, turn the knob five times and divide by 5.
Enter your Backlash in steps. Each program’s overshoot is then shown as at least 1.2 times that value.
Pick your Telescope, or type its Aperture and Focal length in mm, and choose a Barlow / reducer if you use one. Then pick your Camera, or type its Pixel size in µm.
Under Star size, choose your Seeing, from Excellent (2″) to Bad (5″). Once you have done a real run, enter the lowest star size it measured in Lowest HFR measured, in pixels. A program that reports diameter asks for HFD instead.
Now read the Step size for the selected program, along with the Critical focus zone and the Star size at focus. If one motor step is more than a quarter of the zone, a warning appears.
Select a Capture Program in the table to see its Settings to enter, written in the program’s own words, such as Autofocus step size in N.I.N.A. or Initial step size in KStars / Ekos. If your program uses a different number of points, type another odd number in Points. Rerun draws a fresh run.

How it works

During an Autofocus Run, the Capture Program moves the focuser through 2k + 1 positions, one Step Size apart. It measures the Star Size at each, fits a curve to the results and sets focus at its bottom. With too small a step, every point sits near the bottom of the curve. With too large a step, focus can fall between two points. The tool picks the step that puts the outermost points at about 3¼ times the in-focus Star Size. Since a run starts within half a step of focus, the largest star size usually ends up between 3 and 4 times the smallest.

Out of focus, a star spreads into a disc whose diameter is the defocus ÷ N, where N is the focal ratio. At each point, the tool combines that disc’s half-flux radius with the in-focus Star Size. Until you enter a measured value, the in-focus size is estimated from the seeing, the pixel scale and diffraction.

The Critical Focus Zone is the depth over which focus is as good as perfect. It is 4.88 · λ · N² in µm, with λ = 0.55 µm. The simulated run starts up to half a step off focus and takes 2k + 1 samples, each with 5% random noise. It fits them the way the program does, with a hyperbolic, parabolic or V-curve fit, and tells you whether the chosen focus lands inside the zone.

Treat the answer as a starting value. The simulation ignores backlash, and for ASIAIR, ToupTek StellaVita and Astro Photography Tool the point count and the fit are assumptions. Once you have the number, check it with one real run.

Formula

Step Size = round[ 2√2 · N · h · √(3.25² − 1) ÷ (k · t) ]

N is the focal ratio after any Barlow or reducer. h is the in-focus half-flux radius in µm, which is the star size in pixels times the pixel size in µm. k is the number of points on either side of the centre one. t is the travel per motor step in µm: the travel per turn in mm times 1000, divided by the steps per turn. The result comes out in motor steps.

Worked example

Take a Telescope with 100 mm of aperture and 500 mm of focal length, so N = 5. A Camera with 3.76 µm pixels in Average seeing (3″) gives an estimated star size of 1.797 px, so h = 1.797 × 3.76 = 6.76 µm. Put a ZWO EAF (5760 steps per turn) on a focuser that travels 20 mm per turn, and t = 20 × 1000 ÷ 5760 = 3.47 µm. N.I.N.A. uses k = 4, which gives 2√2 × 5 × 6.76 × √(3.25² − 1) ÷ (4 × 3.47) = 295.6 ÷ 13.9 = 21.3, so the Step Size rounds to 21 motor steps. The Critical Focus Zone is 4.88 × 0.55 × 5² = 67 µm, or 19 motor steps.

Common questions

How do I choose an autofocus step size?

Aim for the step that puts the outermost points of the run at about 3¼ times the in-focus Star Size. That depends on the focal ratio, the Star Size and how far the drawtube travels per motor step. Enter those and read the Step size.

How many steps should autofocus take?

Each program has its own point count. N.I.N.A. and most others use 9, KStars / Ekos uses 11, and Voyager and FocusMax use 15. If yours differs, type another odd number from 3 to 99 in Points and the Step Size follows.

What is the critical focus zone?

It is the depth over which focus is as good as perfect, 4.88 · λ · N². That comes to 67 µm at f/5 and 268 µm at f/10. A motor step bigger than a quarter of it is too coarse to land inside reliably, and the tool warns you.

How accurate is the step size?

It is only as good as the Star Size behind it. Until you enter a measured one, that is an estimate, and real stars can differ. Run autofocus once, enter the lowest Star Size it measured, and every Step Size updates to match.

Focus Step Calculator