Equivalence: Crop factors, sensor sizes, and apertures

Capturing
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This is a discussion thread for an article (series, possibly) I plan to write about the concept of equivalence, with respect to focal lengths, crop factors, apertures, entrance pupil size, sensitivities, and more.

Based on the discussion, I will edit the first post (this one) so as so have the latest version easy to find.

#Defining Equivalence
“Equivalent” is used in photography to refer to systems of camera plus lens which can produce the same photo when used in the same situation, with respect to angle of view and background blur.

I will begin my discussion of the concept by explaining what is .what does not affect equivalence, and then explaining what does affect equivalence.

Then, I will explain the advantages of different points along the equivalence spectrum.

Finally, I will try to head off common misconceptions about what isn’t equivalent but sometimes is argued to be.

##What doesn’t matter for equivalence
I argue that some parameters don’t matter because even lenses and sensors with identical numerical parameters (not equivalent, but the same) can have these vary.

  • Vignetting
  • Geometric distortion
  • Aspect ratio, within limits.

The following are usually aren’t relevant when discussing equivalence, but they are affected in general by what system you choose to buy. These will be mentioned later.

  • Sensor resolution: we assume that it’s adequate.
  • Sensor noise performance: we assume a fixed level of technology
  • Minimum focus distance: we assume that it’s close enough
  • Lens sharpness: for now we can assume the lenses are perfect.

##What does matter directly for equivalence
These conditions must all be true for systems to be equivalent.

  • The angle of view of the lens/sensor combination is the same.
  • The maximum entrance pupil diameter of the lens at the given angle of view must be the same size.

The angle of view is dependent on the sensor size and the focal length, while the entrance pupil diameter is equal to the focal length divided by the f/ number.

If you want equivalent systems with differently sized sensors, the focal lengths must scale precisely with the sensor diagonal, while the f-number scales inversely.

Here are some examples of real lenses that form equivalent pairs:

  • A 25/0.95 lens on M4/3 is approximately equivalent to a full-frame sensor with a 50/2 lens.
  • An 85/1.2 lens on a 1.6x crop APS-C sensor is approximately equivalent to a 135/2 lens on a full-frame sensor.
  • A 23/1.4 lens on a 1.5x crop APS-C sensor is approximately equivalent to a 35/2 lens on a full-frame sensor.
  • A 35-100/2 lens on M4/3 is equivalent to a 70-200/4 lens on a full-frame sensor.

On the other hand, there are some lens/sensor combinations (mostly fast lens plus large sensor) which are only equivalent with nonexistent lenses on smaller sensors.

  • Competing with a 50/1 lens on full-frame requires a nearly impossibly-fast f/0.7 lens on APS-C or f/0.5 on M4/3.
  • A 70-200/2.8 lens on full-frame is equivalent to a 35-100/1.4 on M4/3, which would offer no size advantage…

##What’s the significance?
The concept of equivalence is important in that you can trade off sensor size and lens speed in order to get the best system for your own purposes.

In general, the smaller sensors are significantly cheaper, and the
Speedboosters and teleconverters also come into play.

Some compromises are good: if you never need background blur, why get a full frame?

###Possible equivalence versus actual equivalence: m4/3 has no depth of field advantage if you don’t hit the minimum aperture on FF, same is true the other way

###Big fast lenses for small formats versus small slow lenses for large formats?

###Quality tradeoff: at a given entrance pupil size, longer focal length performs better, but you see sensor dust more…

###What’s actually available to buy?

##Myths about equivalence
###My phone can do plenty of blur, check out this macro shot!

###“f/2.8 is f/2.8”

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Do you want to make the post a wiki to let everyone edit, or just in responses?

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I’d prefer responses so I can see a linear progression, kinda.

I didn’t know about the possibility of making it a wiki, how does that work?

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Not sure if it’s something a normal account can do, but check the bottom of
the post for options. One of them may be “make wiki”.

If not, just poke me when you want it changed and I can do it for you.

[edit]
I just checked, and it appears you can’t change it to a wiki post. If/when you want the post turned into a wiki, just flag the post and one of the mods/admins can do it for you.

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Coming up with a coherent message is very difficult.

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The funny thing in your equivalences is that the equivalent lenses must have roughly the same weight (because they also have the same size of the front lens). So whatever the sensor size, at equivalent DOF depths the bag weighs the same.

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Just a couple of thoughts from a high-level perspective.

State the premise

Can you state simply, in one sentence, what your premise is for the article? (The statement of equivalence probably).

Why?

Why would a reader care about the equivalence?
Is there something important that an average user needs to know about that might affect their workflow?
Is there an important clarification that needs to be made?

I know that often there’s some question regarding DoF and bokeh rendering differences - is that addressed in what you’re going to write? It might be a good hook for a reader to relate to!

This is really a good place to consider the practical reason and considerations a person may care about this.

More technical stuff

I’d start at a higher level overall and slowly begin adding the technical requirements to address your ideas as they come up. That is, start high level and move more technical stuff lower as needed.

Or, if it helps, consider approaching it from a practical shooting level to address things a person may actually care about while shooting images, and move to more technical theory later. Many people care only about the handling and ability to capture what they envision without worrying too much about the theory behind the scenes (not everyone, but many folks might work this way).

(Good) Images, Images, Images!

We’re a photo site, so examples and images are key. Great big pretty interesting images are always preferred if possible. Poke the community for help! (For instance, I’d be happy to diagram anything you need - just tell me what you want and I’ll try to get you an inkscape svg or raster image to suit).

(more as I get a chance to sit down and write).

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I think there’s usually a middle ground: going large format, the camera dominates over the lenses, while for a point-and-shoot, you’d end up needing to go crazy for an absurd f/0.2 lens…

Somewhere in the middle, you may find something good. Both price-wise and size-wise.

It also depends on the focal length in question.

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##The premise…

would probably be:

Use equivalence when choosing what camera brand and system to buy, so that you can balance size and cost against the system capabilities.

I guess that’s the root argument: FF is not always better (“Should I go FF?” is a really, really common question on /r/photography); staying with APS-C can be perfectly fine, and M4/3 has its advantages.

Is it going to be just a guide to specs-based buying, with technical analysis? Maybe that’s what I should aim for.

##Case studies

Maybe I need to have a few ‘case studies’ as a motivator/hook, that demonstrate the above principles, with general analyses I can back up later…

###When you want to push the equivalence limits

  • Bokeh addict, no holds barred: Go full frame, because there’s simply no comparison.
  • Reach addict, size/cost limited: FF or APS-C, trading off portability against light-gathering power and reach. Nikon 1 can be interesting here…
  • Smallest size possible: prime lens compacts, m4/3, pancakes on various systems.

###When you are fine in the middle, but want zooms

  • Not many decent light FF zooms; for casuals you’re limited to primes
  • APS-C has a nice selection: Canon’s budget STMs on both mirrorless and DSLR; 17-50/2.8 type lenses are good.
  • M4/3 is also good; the best lenses are a bit more expensive though.

###When you’re fine in the middle, but want primes

  • FF you can adapt old ones to Sony for dirt cheap; decent quality moderate-priced ones are available for Nikon and Canon (pentax??).
  • APS-C: if you want wide, you can get compacts (GR, Coolpix A, X100) to augment your system for SLR users. For mirrorless, Fuji has great selection (bit pricey) and Samsung too.
  • M4/3 has tons of primes from the tiny to the chunky, from slow to fast, cheap to expensive, and you can adapt as well. Loads of fun.

###Best quality; don’t care about blur

  • FF or medium format all the way. You can’t do better.

##Technical stuff
I may end up leaving out resolution and noise…

##Images

I can make some diagrams myself, and I do want to rent a 5Ds to see if it’s really that awesome, giving me a chance to do controlled APS-C vs. FF comparison shots to demonstrate that equivalence works.

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[quote=“Ofnuts, post:6, topic:431, full:true”]
The funny thing in your equivalences is that the equivalent lenses must have roughly the same weight (because they also have the same size of the front lens). So whatever the sensor size, at equivalent DOF depths the bag weighs the same.
[/quote]Making the (possibly unjustified) assumption that a lens is a cylinder, the length of which is the focal length and the base of which is the entrance pupil, and it’s weight is proportional to it’s volume, it looks like the crop factor a factor in weight too:

1109×339 24.2 KB

But I just got out of bed. :smiley:

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Focal length cubed over F-stop squared? That’s not constant equivalence; with equivalence they move in exact proportion: f/1.4 25mm on m4/3 is equivalent to f/2.8 50mm on FF.

Of course, your weight assumption is very…idealistic; a symmetrical f/2.8 lens can have miniscule amounts of glass while an f/1.4 is pretty involved. That’s why there’s a middle ground.

Your weight assumption may be more correct for zooms, though.

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[quote=“CarVac, post:11, topic:431”]
Focal length cubed over F-stop squared? That’s not constant equivalence;
[/quote]Umh yeah, it’s not a constant factor. I was … sleepy, fixed that. o_o
It obviously ignores a lot, most likely way too much :wink:

In the end I think the best advice is look at the actual camera+lens combinations one is interested in and compare those. The equivalence can help to determine the candidates for that.

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I think in the end that’s what the article will be mainly focused on: all the systems have their uses somewhere along the capabilities versus size and cost spectrum.

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Tony Northrup has a fairly comprehensive set of videos on crop factor vs depth of field vs angle of view vs image quality. Here’s the first one:

There’s also a bunch of replies and replies-to-replies if you’d like to go deeper:

https://www.youtube.com/results?search_query=tony+northrup+crop+factor

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That’s a really good summary.

Maybe it’d be better to go into the technicals? With entrance pupil size and light gathering and stuff.

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I’ve been thinking it might be fun/helpful to create a short animation video that might demonstrate some of these ideas. Did you have any thoughts on what might be best to cover?

As a first step, I was thinking it might be helpful to show how a smaller sensor covers a smaller area of the image circle from a lens (more of a general look at what it means to be a crop sensor in general). Something to show a lens, the imaging circle it creates, and then visualizing how different sensor sizes capture different portions of that circle.

I was thinking it might be a neat segue into the equivalency stuff you’re looking at? Just thinking out loud here…

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I came upon this link on reddit: http://comparelenses.info

It gives full equivalency calculations for actual lens/body combinations.

And in the discussion, I realized that there is another key part of equivalence: iso equivalence.

When you multiply the aperture by the crop factor, you must also multiply the iso by the square of the crop factor.

You can think of it as full frame cameras having more iso range on the low end: a micro 4/3 camera can’t go to full frame equivalent iso 100.

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So, I’m resurrecting this topic because just today I got in a debate of sorts on reddit about this very topic.

It appears that the common misunderstanding is about the definition of the word “equivalent”.

For me, ‘equivalent’ means: equal angle of view, equal blur, equal diffraction, equal exposure duration, equal noise.

For other people, ‘equivalent’ means: equal angle of view, equal f-number, equal ISO. f/1.4=f/1.4=f/1.4. The distinction is that this sort of false equivalence does not result in equivalent photos.