[Photographic] Equivalence -- what it is and isn't.

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[Photographic] Equivalence -- what it is and isn't.
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The recent DPR articles on the new Olympus f/1.2 primes have resulted in quite a few comments about Equivalence in the comments section.

On the one hand, we have people disparaging the new lenses because they are "only" f/2.4 FF equivalent and thus don't warrant their price. Well, DOF options on the wide end and light gathering, while two important aspects to a lens, are, still, only two aspects of a lens. One rarely hears of Leica lenses being disparaged because they charge so much for their lenses when much less expensive equivalents exist.

On the other hand, we have tons of ignorant comments saying that Equivalence is bogus and/or useless, where many of the comments clearly show that the people making them don't even know what Equivalence actually says.

So, to that end, let's clear matters up a bit. First of all, what is Equivalence? Here's the definition of Equivalence:

Equivalent photos are photos of a given scene that have the:

As a corollary, Equivalent lenses are lenses that produce Equivalent photos on the format they are used on which means they will have the same AOV (angle of view) and the same aperture diameter.

Here it's fleshed out a bit more in ten bullets:

Equivalence relates the visual properties of photos from different formats based on the focal length and aperture of the lens. Neither the focal length nor the relative aperture 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 relative aperture 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 (all others' APS-C), 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 f/1.8 = 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 exposure time (regardless of pixel count).
  • The same total amount of light falls on the sensor for the same scene, DOF, exposure time, lens transmission (e.g. if the 25mm lens is t/1.6 at f/1.4, the 31mm lens is t/2 at f/1.8, the 33mm lens is t/2.1 at f/1.9, and the 50mm lens is t/3.2 at f/2.8), and vignetting.
  • 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 on the LCD playback and/or for the OOC (out-of-the-camera) jpg due to the lower exposure (keeping in mind that the ISO setting affects noise only inasmuch as higher ISO settings result in less electronic noise than lower ISO settings -- e.g. a photo "properly exposed" at f/2.8 1/100 ISO 1600 will have less noise than a photo of the same scene at f/2.8 1/100 ISO 200 pushed to the same brightness).
  • Elements of IQ, such as bokeh, color, flare handling, 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". For example, the Canon 50 / 1.4 on the Canon 5D (13 MP FF) is equivalent to the Sigma 50 / 1.4A on the Nikon D810 (36 MP FF) despite the fact that the latter system will have significantly higher resolution, lower noise, better bokeh, etc., etc..
  • However, the same total light will result in the same noise if the sensors record the same proportion of light falling on them (same QE) and add in the same electronic noise (the noise from the sensor and supporting hardware), regardless of pixel count and ISO setting. It should be noted that sensors of the same, or nearly the same, generation typically record very nearly the same proportion of light falling on them regardless of brand, size, or pixel count (a notable exception would be BSI tech which records a third to half a stop more light for a given exposure than non-BSI tech) and that the electronic noise matters only for the portions of the photo made with very little light.
  • In addition, if the 25mm lens at f/1.4 in the example above is twice as sharp (lp/mm), the 31mm lens is 1.6x as sharp at f/1.8, and the 33mm lens is 1.5x as sharp at f/1.9 as the 50mm lens at f/2.8 (or any equivalent relative apertures), the sensors have the same number of pixels, and the AA filter introduces the same blur, then all systems will also resolve the same detail (lw/ph).

OK, so what's the point of Equivalence? Here's a little on that:

A common criticism of Equivalence is that some people say that it does nothing to help them to take better pictures. However, Equivalence is simply a framework by which to compare the IQ of different formats on the basis of six visual properties that are independent of the technology -- the same perspective, framing, DOF / diffraction / total amount of light on the sensor, exposure time (motion blur), brightness, and display dimensions. Equivalence is not an "instruction manual" for how to take a photo, but rather a comparison point for photographs from different systems.

If one system can take a photo that another system cannot, and that results in a "better" photo, then, of course, we would do so. For example, if low noise meant more than a deeper DOF in a scene where motion blur were a factor, then we would compare both systems wide open with the same shutter speed, as that would maximize the amount of light falling on the sensor and thus minimize the noise. Equivalence tells us, however, that this would *necessarily* result in a more shallow DOF for the system using a wider aperture, and thus most likely result in softer corners. So, we surely would not criticize the larger sensor system for having softer corners on the basis of a *choice* the photographer made.

The point of photography is making photos. As such, one doesn't choose the particular system to get photos which are equivalent to another system. A person chooses a particular system for the best balance of the factors that matter to the them, such as price, size, weight, IQ, DOF range, AF, build, etc.. By understanding which settings on which system create equivalent images, these factors can be more evenly assessed to choose the system that provides the optimum balance of the needs and wants of a particular photographer.

Some would argue that the point of Equivalence is to say larger sensor systems are superior to smaller sensor systems. Well, for some purposes yes, for others no. In any case, no, Equivalence does not say, or imply, that at all. Here's a quick bit on that:

Q: Are bigger formats better than smaller formats?

A: For some specific purposes, yes; for others, no. The more specific the purpose the of photography, the easier it becomes to say that System A is "better than" System B for a particular photographer; the more broad the photography, the less easy it is for one system to be superior to the other.

Q: When are larger formats better than smaller formats?

A: To answer this question, we need to invoke the "all else equal" clause, because there are so many variables that may make one system better than another for any particular photographer. In short, the advantage of a larger sensor system over a smaller sensor system is that the larger sensor system will generally have lenses that have wider aperture (entrance pupil) diameters for a AOV (diagonal angle of view) than smaller sensor systems, which allows for more shallow DOFs (as an option, not a requirement) and will put more light on the sensor for a given exposure, resulting in less noise. In addition, larger sensors typically have more pixels which, when combined with a lesser enlargement factor from the recorded photo to the displayed photo, results in more detailed photos (at least for a given DOF). Whether or not these advantages are more important than the disadvantages (size, weight, cost, etc.) is another matter all together.

Q: Isn't Equivalence a vehicle for promoting the "superiority" of larger sensor systems?

A: Not by a long shot. If there is an agenda to Equivalence, it is to change the photographic paradigm based on the relative aperture (f-ratio) and exposure with a new paradigm based on the effective aperture (entrance pupil) and total amount of light falling on the sensor, at least for cross-format comparisons.

Q: So Equivalence is about the lens as opposed to the sensor?

A: That's a good way to put it -- it's the effective aperture (entrance pupil) for a given AOV that is of central importance. However, sensor size still plays a role, as larger sensors typically have more pixels and typically can absorb more light for a given exposure.

Q: Isn't Equivalence all about DOF?

A: No, Equivalence is not "all about DOF" -- it's also about the amount of light that makes up the photo. Understanding that both DOF and and the amount of light making up the photo are intimately connected to the aperture is central to Equivalence. That said, DOF, by itself, is still a critical consideration to the captured detail in the photo, since portions of the scene outside the DOF, by definition, will not be sharp, and all systems suffer diffraction softening equally at the same DOF. Likewise, the noise in the photo is primarily due to the amount of light making up the photo.

Q: Doesn't Equivalence say that we should shoot different formats at the same DOF?

A: Not at all, and, in fact, quite the opposite. That is, one does not choose one format over another to get photos Equivalent to what one would get on another format. Rather, one chooses one format over another to get photos they could not get on another format, or get better photos than they could get on another format, assuming, of course, that differences in operation, size, weight, and cost are not significant enough to be the primary consideration.

Q: Overall, then, isn't FF best the choice?

A: Again, which is best is completely subjective. While for me, personally, I prefer FF, it is my opinion that the vast majority are better served with smaller formats. As all systems continue to improve, the number of situations where FF has a significant advantage over smaller formats narrows. Of course, if size, weight, and price were not considerations, then larger is almost always better. However, since size, weight, and price not only matter, but are often (usually) the primary considerations, then it is my opinion that the advantages of FF over smaller formats are not enough to offset the disadvantages for most people in most situations.

All the above links and quotes are from the Equivalence Essay which I wrote around 10 years ago. Here are some more recent articles on Equivalence and related matters written by DPR:

https://www.dpreview.com/articles/2666934640/what-is-equivalence-and-why-should-i-care

https://www.dpreview.com/learn/2799100497/equivalence-in-a-nutshell

https://www.dpreview.com/articles/8189925268/what-s-that-noise-shedding-some-light-on-the-sources-of-noise

https://www.dpreview.com/articles/0388507676/sources-of-noise-part-two-electronic-noise

https://www.dpreview.com/articles/5365920428/the-effect-of-pixel-and-sensor-sizes-on-noise

It is my hope that the above will facilitate more productive discussions that involve Equivalence. However, we all know that there are those that will never let the facts get in the way of an opinion. Still, if it helps even a few, then mission accomplished.

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