Planetary Imaging Barlow Calculator: Ideal f-Ratio

For planets, the camera's pixel size decides how much focal length you need, not the telescope. Sample too coarsely and fine detail on Jupiter's belts falls between the pixels; push the f-ratio far past what the optics can resolve and you only get a dimmer, noisier image. The ideal f-ratio is roughly 3.5 to 5 times your pixel size in microns, and the Barlow's job is to get you from your telescope's native f-ratio to that number.

How the calculator works

A telescope can only pass detail down to a certain fineness, set by its aperture and the wavelength of the light. To record all of that detail the camera has to sample it at least twice per cycle, the Nyquist rule borrowed from signal processing. Put into telescope terms, the f-ratio at which a pixel of size p just meets that rule is:

f-ratio = 2 × pixel size ÷ wavelength (both in microns)

At 550 nm that works out at about 3.6 times the pixel size. The rule of thumb you will see quoted on imaging forums, "f-ratio = 5 × pixel size", is the same sum done for 400 nm light, the blue end of the spectrum, so it builds in some extra sampling. Most planetary imagers land somewhere between the two, which is why the calculator gives you both and picks a Barlow that lands in that window.

The Barlow you need is simply the target f-ratio divided by your telescope's native f-ratio. A 200mm f/6 Newtonian with a 2.9 µm camera has a Nyquist target of f/10.5 and a 5× rule target of f/14.5, so a 2x Barlow (f/12) or a 2.5x (f/15) both work.

Why going past the target doesn't help

Image brightness on the sensor falls with the square of the f-ratio. Going from f/12 to f/24 does not show more of Jupiter; it spreads the same detail over four times as many pixels and quarters the light each pixel gets. You then need four times the exposure or more gain, and both cost you: longer exposures freeze less of the seeing, and higher gain adds noise. On a night of poor seeing, dropping a step below the target is often the better call.

Things that change the real number

• Barlow spacing. The "2x" printed on a Barlow is only true at its design distance. Add a filter wheel or an ADC between the Barlow and the camera and the magnification goes up, sometimes by a lot. If you can, measure it: image Jupiter, measure its width in pixels, and compare it with the size the calculator predicts.
• Colour cameras. A one-shot-colour sensor has a Bayer filter, so red and blue are only sampled on every other pixel. Some imagers push a little past the 550 nm figure to compensate.
• Seeing. In the UK, the atmosphere often limits detail long before the optics do. The target f-ratio is the most you can use, not a figure you must hit every night.