Rules (1-2 arc second per pixel) – and when to break them!

Astrophotography is by its nature a complex subject, so several ‘rules’ have developed that reduce some of this complexity to a simple guide. I would like to take the opportunity to talk about one of the most commonly used.

Rule : Your image scale should be between 1 and 2 arc sec per pixel

Let’s start by describing what this means, why we might wish to do this, how we achieve it, and why we might like to break the rule.

What we are describing with the arc sec per pixel figure is the image scale. It’s an amount of sky which will cove one pixel on your cameras sensor. To get a sense of scale the moon is approximately half a degree wide. You can also gauge one degree by holding your arm out with your palm facing away from you raise your little finger, the width of this finger is about 1 degree. You should be able to completely hide the moon behind your little finger with your arm out stretched. Angles are traditionally split into minutes and seconds. In this case we are not talking about time but a fraction of an angle. 1 arc minute is 1/60th of a degree. While 1 arc second is 1/60th of an arc minute. To imagine this (which is not easy!) think of a small coin at a distance of 3-4 miles (km). It’s small.

The reason that we astronomers are interested is arc seconds is that the earth’s atmosphere limits the resolution we can achieve in our images. For most locations on a good still night the ‘seeing’ will be about 2 arc seconds, i.e. objects smaller than 2 arc sec will be blurred to a size of 2 arc seconds by the atmosphere.

It’s worth mentioning here that all stars are so far away that their angular size is always much smaller than 1 arc second. However we will see them as having a size of at least 2 arc seconds due to the blurring effect of the atmosphere.

The telescope and camera combination will give us the arc seconds per pixel. The formulae is
(Pixel Size (μm) of camera / Focal length of telescope) * 206.3 = angular resolution (arcseconds/pixel)

The longer the focal length of the telescope the smaller the arc seconds per pixel. Conversely the shorter the focal length the larger the number of arc seconds covering each pixel. The pixel size also plays a role. The smaller the pixel the less arc seconds cover each pixel and larger pixels have more arc seconds.

So why the 1-2 arc seconds per pixels rule?

If you choose a camera telescope combination that gives a small number of arc seconds per pixel (think long focal length telescope and small pixels) stars will cover many pixels and appear large or ‘bloated’. As you are spreading out the light from the star over many pixels the sensitivity of your imaging will decrease. Also any shortcomings or defects in your optical train will be magnified; for example non-round stars at corners of image or elongated stars due to imperfect tracking.

Looking at the other side, low arc seconds per pixel value. Here most of the light from a star will fall on a single pixel. The image of the star can appear blocky as not enough pixels are used to convey a round shape to a star. Also if a one shot colour camera is used the star light will need to fall on separate red green and blue pixels for a true colour to be recorded. If all the light falls on a single green pixel then you end up with a green star, which will look strange. Then sensitivity is also affected. If arc sec per pixel is very low (below 1) then more sky background is also mixed in with the light reaching the pixel. This again decreases sensitivity.

Examples of an oversampled and undersampled image.

So for reason of sensitivity, and image quality the rule of 1-2 arc seconds per pixel is a good guide. Sticking to the rule should get you the most detail and the most sensitivity.

Now let’s think about when you might want to break the rule.

First with short focal length telescopes or lenses. These will have big fields of view and allow is to take whole constellation shots. Also with “the world at night” type imaging we can place a terrestrial object in the image. Typically short focal length scopes make focusing, tracking, and guiding easier. You might not be taking the most detailed images but lots of enjoyable imaging can be had above 2 arc sec per pixel.

Personally I prefer going with longer focal lengths. This gives smaller fields of view and allows us to image smaller, less common objects. Imaging at low arc seconds per pixel values is called over sampling. These type of images can respond well to processing especially deconvolution to reveal extra detail. Planetary imagers will image at very high arc seconds per pixel and use very short exposures (fractions of a second) to ‘beat the seeing’. This type of imaging is termed ‘lucky imaging’. While its often used by amateurs for planets its use for deep sky is more limited to professionals using electron multiplication CCDs. However recently some people are trying the technique using CMOS cameras with low read noise. Imaging at low pixel per sec is challenging but when it all comes right the images can be spectacular. If the seeing is bad on a particular night or your tracking is not working well you can always using binning to increase the pixel size and bring your image scale back towards 1.

So to conclude. It is easier to capture great images by sticking to the 1-2 arc seconds per pixel rule. However a lot of fun and enjoyment, along with some frustration, can be had by breaking this rule.

When calculating what image scale a particular telescope and camera combination will have, a field of view calculator can be useful. The Atik versions works on iOS devices available in the app store. Or you can try the following on line versions.

Sky at night magazine
Bintel
Astronomy tools