What is Field of View?
Have you noticed that you see a larger section of the sky through binoculars or a finder scope than through a telescope?
Maybe you’ve noticed how binoculars, finder scopes and telescopes all show you a smaller portion of the sky than your naked eye.
Knowing the field of view of your instrument is important because it indicates how much of the the sky will be visible. This means you can compare your view with that of star charts (important for star hopping) and more easily identify what you are seeing.
Why It’s Important for You to Know Your Field of View
This picture, courtesy of SkySafari shows the dramatic impact of different fields of view.
Impact of different fields of view on how much of Andromeda Galaxy (M31) you can see
The three rings show fields of view of 0.5° (smallest), 1.0° and 1.5° (largest), all at the same magnification and all centered on the heart of Andromeda Galaxy (learn where to find Andromeda Galaxy).
How much of the galaxy you can see in one eyepiece view differs dramatically, and is a bit of a clue as to why astronomers spend so much money on eyepieces that will give a wider field of view (see some typical examples on Amazon).
Now you understand how the field of view can make a significant difference to your astronomy (or night sky photography), let’s take a look at how we work it out.
How Astronomers Calculate Field of View
Telescope eyepieces have specifications describing their lens configuration, focal length, and apparent field of view (AFOV).
Apparent Field of View
The apparent field of view is the angular measurement describing how much of the sky we can see when looking through the tube of the eyepiece when it’s not attached to your telescope.
For example, a manufacturer states that a Plössl eyepiece has a 25 mm focal length and 50 degree (50°) field of view. This is its apparent field of view, and not the field of view you’ll have when the eyepiece is in your telescope, which is called the true field of view.
A 50° AFOV means that if you look through the eyepiece without putting it in your scope, the circle of sky seen through it has a diameter of 50°. Attaching it to your telescope significantly reduces that, and you’ll see how shortly.
True Field of View
The true field of view (TFOV) is how much of the sky you can see when looking through your telescope with any particular eyepiece in place.
You can calculate the true field of view of a telescope + eyepiece combination using the following formula:
True field of view = Apparent field of view / magnification
Where magnification is calculated by dividing your telescope’s focal length by the focal length of your eyepiece.
That’s a lot to take in, so let’s work through some examples to make it clearer.
Field of View Examples
Field of View Example 1
Assume our Plössl eyepiece has a 25 mm focal length and a 50° apparent field of view. We’re going to use it in a telescope which has a focal length of 1000 mm.
Begin by working out the magnification, i.e. divide the focal length of the telescope by the focal length of the eyepiece.
In this example, our magnification = 1000 mm / 25 mm = 40x
Now we have out magnification, we can calculate our true field of view, using the equation above, i.e. TFOV = AFOV / Magnification
TFOV = 50 [AFOV] / 40 [magnification]
So, in this example our TFOV = 1.25°
Which means that when we use this Plössl with our 1000mm telescope, we’ll see a circle of sky with a diameter of 1.25°.
Field of View Example 2
This time we’re using a different Plössl. It still has a 50° apparent field of view but only has a 10 mm focal length. We’ll pair it with the same 1000mm focal length telescope we used above.
As always, calculate magnification first.
Magnification = 1000mm / 10 mm = 100x
Then you can work out the true field of view:
TFOV = 50 / 100 = 0.5°
This shows that a higher magnification with the same focal length results in a smaller field of view, just half a degree in this example.
Field of View Example 3
In our third example, we’ll change the same eyepiece to a 20mm focal length Plössl with a 50° AFOV, but we’ll swap our telescope for one with a focal length 700mm.
The first impact of this change is to alter the magnification to 35x (700 / 20) from the 100x we got above.
This impacts the TFOV, changing it to 1.4° (50 / 35)
If you’d like more examples, see the video at the end of this article which explains true field of view and telescopic field of view (aka true field of view) and includes some examples of the different eyepiece+telescope combinations.
Field of View Example 4
Let’s look at one last example so we’ve seen all options.
This time we’ll return to our 1000mm telescope which we used in examples 1 and 2. We’ll also use a 10mm focal length eyepiece like the Plössl in example 2.
The difference this time is we’ve spent a chunk of cash on an ultra wide field of view eyepiece which has an AFOV of 100°.
Our magnification is no different, because we still have a 1000mm telescope and a 10mm eyepiece, giving us 100x magnification (i.e. 1000 / 10).
We work out the true field of view by dividing the apparent field of view by the magnification. In this example we end up with a TFOV of 1° (i.e. 100x / AFOV of 100°).
In summary, this is exactly the same as example 2 except we’ve double the AFOV of the eyepiece. What we’ve ended up with is the same magnification (100x) but we can see double the diameter of sky, i.e. 1.0° instead of 0.5°.
If we revisit the picture from above:
You can see what a difference the eyepiece in example 4 would make compared to using the one from example 2.
With example 2 you’d see just the core of Andromeda, but invest in a wide field of view eyepiece and you’ll now see the core AND a good portion of the galaxy’s arms without making any sacrifices to magnification.
That is why many of us consider a few hundred dollars spent on a wide field of view eyepiece a good investment in our astronomy.
How Does Field of View Change What We See?
Let’s compare the hypothetical results from our examples to some commonly seen celestial objects.
Venus may appear as large as 1.05 arcminutes, the full moon is 0.5° or 30 arcminutes across and Orion’s belt is about 2.7° long.
Example | Mag | TFoV | Celestial Bodies |
---|---|---|---|
Example 1 1000mm Telescope + 25mm Plössl with 50° AFoV | 40x | 1.25° | Venus:Small & bright Moon: See the entire disc Orion’s Belt: See half of it |
Example 2 1000mm Telescope + 10mm Plössl with 50° AFoV | 100x | 0.50° | Venus:Larger & brighter. Easy to see phases Moon: Fills the field of view Orion’s Belt: Only see one star at a time |
Example 3 700mm Telescope + 20mm Plössl with 50° AFoV | 35x | 1.42° | Venus:Disc appears small Moon: See the entire disc, but smaller Orion’s Belt: See more than half of it |
Example 4 1000mm Telescope + 10mm eyepiece with 100° AFoV | 100x | 1.00° | Exactly the same magnification as example 2, but 2x the diameter of sky |
You can see from this that to get the whole of Orion’s belt in a single eyepiece view is going to be almost impossible. Whereas venus may be lost in a wide field of view and you’d be better examining it with a higher magnification and smaller field of view.
When doing backyard astronomy, you don’t just have magnification to think about, but the amount of sky you can see too. Many deep space objects are large but faint, Andromeda Galaxy (M31), for example, is 6 times wider than the full moon, but very faint.
Andromeda is wide and faint, you need good magnification and a wide field of view (source)
To see Andromeda most effectively we need a higher magnification and as wide a field of view as we can muster.
Field Stops and Field of View
If your telescope manufacturer provided the diameter of your eyepiece’s field stop instead of the apparent field of view, use the following formula to approximate the true field of view:
True field of view = (57.3 x field stop diameter) / telescope focal length
Field stop and focal length measurements must be in mm for this formula to work.
Using the Drift Method to Calculate Field of View
If you only know the focal length of your eyepiece or want to know the true field of your finder scope or mounted binoculars (where magnification and diameter of the objective are known) true field of view can be measured using the drift method.
The drift method makes use of the fact that stars appear to travel westward across the sky at a rate of one revolution of earth every 23 hours 56 minutes, which is 86,160 seconds.
To complete measurements with the drift method you’ll need a telescope mounted on an equatorial mount (or where you can accurately set declination).
You will also need a star atlas or software to look up declinations of stars, a stopwatch and a scientific calculator.
The Drift Method
- Select a bright star near the celestial equator and look up it’s declination. Some examples of bright stars near the celestial equator are in the below table
- Set up your telescope-eyepiece combination so that your chosen star is visible
- Turn off your motor drive (if using one) and check that the star drifts west through the center of the eyepiece – if it is off to one side you will not get a true measure of the diameter of your field of view. Adjust your telescope as needed to get the star passing through the center of your view
- When you’re happy with the set-up, it’s time to take some measurements. Adjust your telescope’s right-ascension so that the star is just out of view on the eastern edge on the eyepiece
- Use your stopwatch to measure the length of time it takes for the star to first appear in the eyepiece, drift across the field of view and then disappear from view. This must be recorded in seconds
- Repeat this measurement 2 more times and take the average of your three separate timings to get a number to use in the formula below
Now, here comes the math which you’ll need that scientific calculator for:
TFOV° = (Drift Time * (cos(star’s declination)) * 360°) / 86,160
That is perhaps the most complex formula on this whole website, so let’s work through an example to make it clearer:
Drift Method Worked Example
We’re going to use an example originally produced on this website.
Aldebaran is one of the brightest stars in the night sky and can be found shining at magnitude 1 in the constellation of Taurus.
Aldebaran is near the center of this map of Taurus (source)
It’s not too clear from the picture, but the declination (vertical axis) of Aldebaran 16°30″. It’s easiest to begin our calculation by working out the cos of this number, which is 0.9588.
Let’s assume we followed the drift method three times for Aldebaran and got an average drift time of 120 seconds. We now have enough information to use that complex formula and work out our true field of view.
TFOV° = (Drift Time * (cos(star’s declination)) * 360°) / 86,160
= (120 * 0.9588 * 360) / 86,160
= 41,420.16 / 86,160
TFOV = 0.481°
To measure the true field of view of a finderscope or eyepiece with crosshairs is a little easier. You can save time by centering the star on the crosshairs and letting it drift out of view.
The total drift time is twice the measured time.
Bright Stars Near the Celestial Equator
Because these stars are near the celestial equator, they make a great choice for the drift method.
Constellation | Star | Declination |
Orion | Mintaka | 0° 18′ |
Virgo | Porrima | 1° 29′ |
Aquarius | Sadalmelik | -0° 17′ |
Serpens | a-Serpens | 1° 00′ |
Taurus | Aldebaran | 16° 30′ |
Field of View Summary
True field of view is the amount of sky (measured in angular degrees) that you can see with any given telescope-eyepiece combination.
If you know the apparent field of your eye piece you can calculate the true field of view using the formula:
True field of view = Apparent field of view / magnification
We’ve seen that if you don’t know the apparent field of view of your eyepiece, then it can be worked out by using the drift method.
Field of view is an important concept for astronomers because we need to know how much of the sky we can see when looking through the eyepiece.
For larger areas of sky, especially for DSOs like nebulae and galaxies, we need to invest in large field of view eyepieces with shorter focal lengths. They will allow us to see more of the sky under higher magnification… but will (sadly) cost us more money.
To understand more about fields of view, check out the video below from David Fuller at Eyes on the Sky.