The Field Of View Equivalency Factor: Degrees and Angles Of View

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The Field Of View Equivalency Factor "The FOV Thing"
Degrees and Angles Of View December 26, 2004
FOVEF: Introduction • FOVEF: Image Circles FOVEF: Olympus Four-Thirds Lenses • FOVEF: Nikon DX Lenses • FOVEF: How Do You Get That Number? FOVEF: Degrees and Angles Of View • FOVEF: Conclusion
So Many Terms, So Much Confusion
Since Olympus and Nikon have introduced lenses which are matched to their cameras imager size (Sigma is also making lenses specific to imager sizes), we now have another complication when discussing FOV Crops. Since the lenses are matched to the sensor, there is no FOV Crop. As stated earlier in the discussion, an FOV crop only occurs when a lens is larger than the sensor it was designed for. Now that we have Nikon DX lenses and Olympus 4/3 lenses, there is no crop, but there is...a Field Of View Equivalency Factor (FOVEF). You're probably scratching your head asking, Soooo, if there's no physical crop and no crop factor, then how do you come up with the 2x factor? Good question indeed, and let's take a look at something we haven't discussed yet: Degrees and Angles of View.
Lens Angles and AOV
All 300mm lenses are not necessarily the same. The physical focal length is still the same (this is why a 300mm is still branded a 300mm on all lenses, no matter what brand or size), but the Angle Of View, can change. And it does change when you see the following examples.
Olympus 300mm lens with an AOV of about 4°
35mm 300mm lens with an AOV of about 8°
What you are seeing above, is FOVEF (Field Of View Equivalency Factor) at work. The physical focal length of the lenses do not change, but the perceived field of view, or Angle Of View, does change.
Why Does The AOV Change?
Since the imager on the Olympus is almost exaclty 1/2 the size of a 35mm imager (we measure the differences by the diagonals, remember, not by the width or the height exclusively), a smaller image circle can be made. Since a smaller image circle can be made, the AOV of the lens changes. Why? Because you don't need the same coverage of a 35mm anymore. Since the imager is only half the diagonal of a 35mm imager, the AOV of the lens can now be half the size as well.
Where do you get the 4° and 8° spec of the lens?
Almost all lenses have an AOV spec, or put more simply, the degree of coverage. If you look on the E-1 Olympus website, and look at the 300mm specifications, you see an AOV of about 4°. It's actually 4.2°. Now, go to Canon's website or Nikon's website, and look up the AOV of their 300mm prime lenses. You will see an AOV spec of about 8°.
Where does Olympus get the 600mm equivalency?
Do me a favor and guess what the AOV of a Canon or Nikon 600mm prime is. Since Olympus is saying their 300mm has the same equivalency as a 600mm, I wonder what a 35mm 600mm lens AOV could be. Hmmmm. Can you guess? It's actually too obvious, and you might have overlooked it. I know I did at first. Let's take a look at a 600mm prime lens, and it's AOV.
35mm 600mm lens with an AOV of about 4°
Ahah! Notice anything similar to the above illustrations? Yes indeed, a 35mm 600mm prime lens has an AOV which is the same as the Olympus 300mm. This is why Olympus says their 300mm lens behaves the same way as a 600mm. It has the same Angle Of View or Field Of View, of a lens twice its focal length. Given this fact, we can hypothetically make our own lenses and figure out what the 35mm equivalent would be.
A Little Exercise
Imagine if DigitalDingus Optics made a 300mm lens and said it behaved as a 1200mm lens. Wow! This is an awesome lens! Now, from this information alone, can you tell me roughly what the AOV of this 300mm lens would be? Remember, DigitalDingus Optics made this lens to have the same 35mm equivalency (FOVEF) as a 1200mm lens. All the information you need to get the AOV of the DigitalDingus Optics 300mm lens, is on this page.