FX vs DX at the same eq focal length. In term of DoF ?

Started Dec 16, 2016 | Questions thread
beatboxa Senior Member • Posts: 5,047
Re: FX vs DX at the same eq focal length. In term of DoF ?

kaktusdarock wrote:

Hello everybody,

I ve seen a lot of topic that are almost the same at this one but I ve never seen the exact comparison.

Here is a side-by-side comparison of a 50mm FX (D750) vs a 35mm DX (D7000) from a tripod in the same spot at the same settings.

Will the DoF of 300mm 2.8 on a DX body be the same of a 400mm 2.8 on a FX body ? (from the same standing point, you can't get closer in order to compensate)

No. Even though the F-number is the same, the aperture is different.

  • The 300mm has a 107mm aperture, while
  • The 400mm has a 143mm aperture.

Easy to calculate: F number = Focal length / F-number. 300mm / 2.8 = 107mm.

If the 400mm also had a 107mm aperture (= @ F/3.74), then the two would have the same DoF.

Also worth considering:  100mm F/2 has the same aperture as 200mm F/4.

I know the 300mm on a DX is about 450mm on a FX but lets say there is no difference between 400 and 450mm.

If I understood everything correctly the 300 2.8 on a DX will not have the same DoF of a 400 2.8 on a FX. The 300 2.8 on a DX will more likely have a Depth of Field of an aperture F4 eq on a FX body ?

Close. 4.2 @ 450mm. An easy way to remember this : Multiply the F-number by the crop factor as well as the focal length. For example:

  • 300mm F/2.8 on DX = 450mm F/4.2 on FX
  • 50mm F/2 on DX = 75mm F/3 on FX
  • 100mm F/4 on DX = 150mm F/6 on FX
  • etc.

Am I right ?

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“Photography is a love affair with life.”

Right about the overall effects, see above for the actual numbers. That's the mathematical explanation.

If you want to know why, the physical / optical explanation is due to the angles of light hitting the sensor plane. There are 3 main things that affect Depth of Field...together:

  • Aperture
  • Focal distance
  • Subject distance

Note: that "sensor size" is not one of them.  A DX ("crop") camera just crops--this means that the same lens has the same DoF at the same apertures & distance on an FX or DX. However, since the field of view is different, in order to fit everything into the same frame, on a DX, you'd typically have to move much further away from the subject--increasing the depth of field.  This is why in practice, FX images often have a shallower DoF than DX images.

The sensor plane is flat, and the lens curves light. Some light that travels in a straight line from the subject will not be angled by the lens. In theory, this only happens at the very center of the aperture of the lens. This is a great image to describe this (pasted below). Notice how the center line is straight, but the two on the outside 'bend'. This site also seems to have some good pictures. I'll use some of these.

(the light at the center of the lens travels straight through.

Light that is further from the center of the lens bends more. As such, it travels a different distance to the focal plane. So as aperture increases (the lens gets 'bigger'), more light comes from even further outside of the lens, bends further, and is further out of focus. There's aperture's effects.

Focal distance & subject distance also plays an integral role in depth of field. The focal distance marked on your lens (eg. 300mm) is the focal distance for a subject at infinity. When you focus your lens on anything closer than infinity, you effectively either:

  • increase the focal distance (move the lens closer to the subject & further from the sensor), or
  • increase the optical power of the lens (make lens bend light more sharply).

In either of the above, you are making light rays bend at a greater angle.

This is a good image to illustrate this.

(Subject on the left, sensor on the right). To get the 'green subject' in focus, you can either move the lens to the left (closer to the subject & further from the sensor, increasing focal distance) or increase the optical power (keep the lens in place, but make the lens bend the light more sharply).

When you do this, the red & blue images on the right will also be affected, but not as much as the green. The effect decreases as the subject is further away. ie. the difference between getting the red and blue image in focus is smaller than the difference between blue and green, even though the red subject is infinitely far away--much further than blue is from green.

Another way to think about this: Imagine a red object at infinity (as far to the left as possible). The light rays from this object (red, above) are coming all coming in 'straight lines' at the lens--they coming from so far away, that they're not angled. Now imagine a red object a mile away. Still pretty straight. Now, a football field away to the left. Still pretty straight.

As you get closer, this angle quickly starts to change--the effect increases. The green object might only be an inch away from the blue above, but the difference in angles is sharper for green and blue vs. blue and red object(s), even though we know the difference in distance between 1 football field and 1 mile is more than the difference between 1 inch and 2 inches.

This is also how you could calculate, for example, hyperfocal distance : the focus point with the deepest depth of field (AKA, where the far end of the 'depth of field' first touches infinity).

Anyways, that's how depth of field works.  If you want to get a shallower depth of field, you've got a few options:

  1. Get closer to your subject.
  2. "Open up" the lens.  Get a bigger aperture.
  3. A bigger sensor allows you to use a longer 
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