A few words on Equivalence and comparing systems

Started Apr 2, 2013 | Discussions thread
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A few words on Equivalence and comparing systems

I was reading in another thread where the 35-100 / 2.8 on mFT was being compared to a 70-200 / 2.8 on FF, and, well, you know.

So, let's see if this post can't serve as a reference for such future "discussions".

First of all, I don't think that anyone disagrees that 35-100mm on mFT has the same [diagonal] AOV (angle of view) as 70-200mm on FF.  This will result in the same framing (plus-or-minus due to the difference in the 4:3 and 3:2 aspect ratios) for the same perspective (subject-camera distance).

Furthermore, I hope everyone understands that f/2.8 on mFT results in the same DOF (depth-of-field) as f/5.6 on FF for a given perspective and framing, or, conversely, that f/2.8 on FF results in the same DOF as f/1.4 on mFT.

In addition, I believe everyone understands that f/2.8 results in the same exposure on all systems for a given scene luminance and shutter speed (give or take for the difference between the t-stop and f-ratio of the lens).

But there are two points that do cause some amount of confusion:

  • All systems suffer the same from diffraction softening at the same DOF
  • The same total amount of light falls on the sensors for the same scene luminance, DOF, and shutter speed for all systems, which will result in the same total noise for equally efficient sensors.

Failure to understand these last two points by some people are where the vast majority of the problems come from, in my opinion (and experience), so let me flesh these points out just a bit.

Saying that all systems suffer the same from diffraction softening at the same DOF does not mean that all systems resolve the same amount of detail at the same DOF.  It simply means that the blur introduced by diffraction is the same for all systems at the same DOF.  Clearly, an otherwise sharper photo will still be sharper if the same amount of blur is applied to it as a less sharp photo (well, I hope that's clear).

Next, the primary sources of noise in a photo come from the light itself (photon noise) and the sensor and supporting hardware (read noise).  The exposure is simply the density of light falling on the sensor, whereas the total light is, well, the total amount of light falling on the sensor.  We can relate exposure and total light in the following manner:

Total Light = Exposure x Effective Sensor Area

The sensor efficiency comes in two parts.  First of all, there's the QE (Quantum Efficiency) which is simply the proportion of light falling on the sensor that is recorded.  For example, if a sensor has a QE of 50% (which is pretty much where most modern sensors are at), half the light falling on the sensor is recorded.  The second component is how much additional noise is added by the sensor and supporting hardware (read noise), which is often a function of the ISO setting (ISOless sensors, on the other hand, have the same read noise regardless of the ISO setting).

Now, no one would say that a 35-100 / 2.8 on an EP1 is not equivalent to the same 35-100 / 2.8 on an EM5, even though the EM5 will record more detail and have less noise.  So, simply because 35-100mm f/2.8 doesn't necessarily record the same detail or have the same noise as 70-200mm f/5.6 on FF does not mean that they are not equivalent:  "Equivalent" does not mean "equal".

This is an important point that cannot be understated.  When we say that 35-100mm / 2.8 on mFT is "equivalent to" 70-200mm f/5.6 on FF, what is meant is:

  • The photos all have the same AOV (diagonal angle of view) and aperture (entrance pupil) diameter: 35mm / 2.8 = 70mm / 5.6 = 12.5mm, 100mm / 2.8 = 200mm / 5.6 = 35.7mm.

  • The photos all have the same DOF (as well as diffraction softening) when they have sameperspective (subject-camera distance), AOV, aperture diameter, and display size.

  • The photos all have the same motion blur and the same total amount of light falls on the sensor when the aperture diameter and shutter speed are the same (e.g. ISO 100 on mFT and ISO 400 on FF).

  • The photos all have the same same noise when the same total amount of light falls on the sensor if the sensors are equally efficient (less noise if the sensor is more efficient, more noise if the sensor is less efficient).

  • Other elements of IQ, such as resolution, bokeh, flare resistance, 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".

Lastly, one doesn't choose a particular system to get images which are equivalent to another system.  Instead, one chooses a particular system for the best balance of the factors that matter to the them, such as price, size, weight, IQ, DOF range, available lenses, and/or operation.  By understanding which settings on which system create equivalent images, the difference in their capabilities is more easily understood.

In other words, simply because 35-100mm f/2.8 on mFT is equivalent to 70-200mm f/5.6 on FF, it doesn't make one "better than" the other.  But it may well have a great deal with why one chooses one system over the other, or, in fact, why so many seem to enjoy both.

Olympus PEN E-P1
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