# DOF and Cropping take 2

Started Feb 11, 2014 | Discussions thread
Equivalence.

Ian Stuart Forsyth wrote:

http://www.dpreview.com/forums/post/53084843

continued from the post above

Just a highlight key points I would like to address

red is Ian

Green is GossCTP

and Black awaldram

But I see it as equivalent please see below

Do you really believe this website above , I mean really ?

How accurate is the information they provide ?

I haven’t read over the whole page so I will trust you when you say with everything you have provided here as true. But what if I can prove that they are wrong (if I rely on what you have said above that cropping has no effect on DOF)

What if I crop my k5 shot with 300mmF2.8 by a factor of 1.8

K5 shot with the 300mm F2.8 Cropped by 1.8 will have a resulting image that would share the same DOF and FOV as a k5 shot with a 540mm lens at F5

Below is a screen grab using the DOF calculator of a trusted site that I used more than once & that I believe to be true

As you can see that it calculates the same equivalent of lens and F stop as I had calc’d

Here is a quote from the site

“As sensor size increases, the depth of field will decrease for a given aperture (when filling the frame with a subject of the same size and distance). This is because larger sensors require one to get closer to their subject, or to use a longer focal length in order to fill the frame with that subject. This means that one has to use progressively smaller aperture sizes in order to maintain the same depth of field on larger sensors. The following calculator predicts the required aperture and focal length in order to achieve the same depth of field (while maintaining perspective).

As an example calculation, if one wanted to reproduce the same perspective and depth of field on a full frame sensor as that attained using a 10 mm lens at f/11 on a camera with a 1.6X crop factor, one would need to use a 16 mm lens and an aperture of roughly f/18. Alternatively, if one used a 50 mm f/1.4 lens on a full frame sensor, this would produce a depth of field so shallow it would require an aperture of 0.9 on a camera with a 1.6X crop factor — not possible with consumer lenses!”

And a reminder that whether you crop an image in the camera or in post with PS you are altering the size of the format, just as many do with a D7100 or a D800 in camera or during post

Now which site do I believe yours or mine?

Here we are:

http://www.josephjamesphotography.com/equivalence/#quick

Neither the focal length nor the f-ratio of a lens change as a function of sensor (for example, a 50mm f/1.4 lens is a 50mm f/1.4 lens, regardless of the sensor behind the lens). However, the effect of both the focal length and the f-ratio on the visual properties of the photo very much depend on the sensor, and scale in direct proportion to the size of the sensor:

25mm f/1.4 on mFT (4/3) is equivalent to 31mm f/1.8 on 1.6x (Canon APS-C), 33mm f/1.9 on 1.5x (APS-C for everyone else), and 50mm f/2.8 on FF (FX), where "equivalent to" means:

• The photos all have the same diagonal angle of view (25mm x 2 = 31mm x 1.6 = 33mm x 1.5 = 50mm) and aperture diameter (25mm / 1.4 = 31mm / 1.8 = 33mm / 1.9 = 50mm / 2.8 = 18mm).
• The photos all have the same perspective when taken from the same position.
• The photos all have the same DOF (as well as diffraction softening) when they are taken from the same position with the same focal point and have the same display size.
• The photos all have the same motion blur for the same shutter speed (regardless of pixel count).
• The same total amount of light falls on the sensor for the same DOF and shutter speed.
• The same total light falling on the larger sensor will result in a lower exposure than the smaller sensor (the same total light over a larger area results in a lower density of light on the sensor).
• The larger sensor system will use a concomitantly higher ISO setting for a given brightness of the LCD playback and/or OOC (out-of-the-camera) jpg due to the lower exposure.
• The same total light will result in the same noise for equally efficient sensors (regardless of pixel count and regardless of the ISO setting).
• If the 25mm lens at f/1.4 has twice the resolution as the 50mm lens at f/2.8 on FF, 1.33x the resolution of the 33mm lens at f/1.8 on 1.5x, and 1.25x the resolution of the 31mm at f/1.8 on 1.6x, the sensors have the same pixel count and same AA filter strength, then all systems will also resolve the same detail.
• Other elements of IQ, such as bokeh, color, distortion, etc., as well as elements of operation, such as AF speed/accuracy, size, weight, etc., are not covered in this use of the term "equivalent".
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