# DOF and Cropping take 2

Started Feb 11, 2014 | Discussions thread
Re: Equivalence.

Great Bustard wrote:

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".

Good work agree 100% with this , wish I'd written it

Covers off the areas that break the 'equivalence' model nicely.

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