On Equivalence and Assumption

Until you know for sure, it’s confusing to know who to believe. Is a 50mm f1.4 lens equivalent to a 75mm f1.8 on APS-C? Are Micro FourThirds sensors two stops noisier than full frame sensors? Can you get the ‘medium format drop-focus look’ on APS-C by using a two stop faster lens?

If you want to know badly enough, may I recommend Joseph James’ excellent dive into the subject found here, which there’s no need to rehash here. The important takeaways are:

  1. etc

Queries like the above (frustratingly) tend to make certain assumptions that demand clear definition before meaningful answers can be given. Let’s consider some common assumptions and practical outcomes.

Assumption 1: Speed and Noise

Theory aside, an important assumption is your personal threshold of acceptability for noise. In practice – more than advances in hardware – refinements in post-production have raised the bar on this gradually over the last decade. Most sensors on the market in 2024 are only incrementally better than their 2014 counterparts, but in-camera and RAW processing algorithms are much smarter.

But let’s imagine we own a camera of each format, and define our primary goal as ‘acceptable’ noise levels in an 8000px wide image. A M43 or APS-C camera of 24MP will require noise-amplifying upsampling. A 40MP ‘full-frame’ camera is already at the target resolution, and a 100MP Fujfilm GFX will benefit from noise-shrinking downsampling. Let’s assume the native performance of each sensor sets the bar at an acceptable threshold (for instance) of ISO 3200 for the M43; ISO 4000 for the APS-C, ISO 6400 for the FF, and ISO 12,800 for the GFX. However, upsampling of the smaller image to 8000px will ‘cost’ us (for example) a stop of noise, and the downsampling of the larger image will gain us a stop. The M43 camera then needs to be limited to ISO 1600, and the APS-C to ISO 3200 – whereas we can safely shoot at ISO 25,600 on the GFX. 

Let’s go further and make a second assumption – a common necessity when shooting in low light – that the shutter speed must be kept above 1/30. If a correct exposure can be gained in ambient light with the full frame at f2.0 / ISO 6400, the GFX ‘equivalent’ in terms of succesfully acquiring an image of 8000px at 1/30s is an aperture of f4.0. This is not at all to comment on the equivalence of depth of field, diffraction, or any other aspec of ‘the look’ – simply the temporal and practical mechanics of getting the shot. On APS-C, an aperture of f1.4 would be required. On M43, aperture of f1.0 would be required.

Practically, then, we might imagine the full-frame sensor as ‘one stop better at light-gathering’ than APS-C, two stops ahead of M43, and two stops behind the GFX format – even though formulating it in this way is incorrect. But if we set the bar at 8000px and demand a shutter speed of 1/30, it’s true enough.

What if we set the bar at a 1200px-wide destined for use on Instagram? In that case, it’s not necessary to make an adjustment for pixel-level noise: its effect on an image so hugely downsampled (from 24MP, 47MP or 100MP) is negligible. In fact, M43 is just as good as GFX, and all can safely be shot at ISO 25,600 or higher.

Of course noise isn’t the only issue: colour accuracy and dynamic range suffer at higher sensitivities – both will be visible at 1200px. Here we begin to make other assumptions on other quality criteria. Each new piece on the board increases the complexity of what we can fairly define as ‘equivalent’, and shifts the parameters of the conversation. For instance . . .

Assumption 2: Depth of Field

Operating on an entirely different assumption, let’s assume that the goal – independent of image size – is the apparent depth of field generated by a 50mm f2.0 lens. Crucially, this is not a fixed assumption: there’s no standardised benchmark of 50/2-ness.

Lenses of the same nominal specification vary widely with regard to the gradient of their focus transition and bokeh character – including the size and shape of defocused specular highlights in various sectors in the image circle. When placing a subject centrally, lenses with stronger aberrations in their outer image circle present as ‘faster’ than they are – inasmuch as they blur even in-focus subjects in Zones B and C. Field curvature – which is rarely linear – also weaves in and out of the theoretical focal plane to add its own signature – sometimes, for instance, bringing into sharper focus distant objects in the frame corners. Not all 50mm f2.0 lenses are equal, or even equivalent, with regard to apparent depth of field.

Having said that, in principle, a similar ‘look’ to 50/2.0 on full frame is achieved on APS-C with a 33.3mm f1.4, a 25mm f1.0 and a 75mm f2.8 on GFX.

Assumption 3: Bulk and Cost

Switching priorities again, let’s assume a different, but common, objective: distant action-stopping – sport, wildlife, etc – with a target size of 6,000px and shutter speed of at least 1/250s. The equivalence we’re seeking here is not that of aperture or image size, but speed – and the priority is likely mobility and reach. 

If we take an ideal zoom lens for such purposes – on full-frame, 100-500mm – the GFX equivalent would be 150-750mm with a XXmm image circle – a monster. On APS-C, it’s a more manageable 65-330mm (rounded), and on Micro FourThirds, a positively pocketable 50-250mm. Smaller lenses for smaller formats with smaller image circles are decidely not equivalent in terms of price and size, and that endows them with real-world advantages.

In such situations, rapid autofocus tends to be a high secondary priority. It’s easier to make smaller lenses more responsive than larger ones, which again privileges smaller formats. Even the smallest is comfortably able to deliver 6,000px images with room to crop.

But what about the aperture disadvantage? In terms of depth of field, the ‘look’ of a 300mm f4 on full frame can be achieved by a 150/2 on M43, a 200/2.8 on APS-C and a 450/5.6 on GFX. A 300/4 lens for full frame (ie, Nikon FX) mounted on APS-C (ie, Nikon DX) remains a 300/4, but it will deliver the framing of a 450mm lens on full-frame, and a similar depth-of-field to a f5.6 lens on full-frame. However, because it is an f4 lens, it retains the action-stopping potential of an f4 lens – the shutter speed will be unchanged. A 135mm f2 lens designed for full frame becomes a much more useful combination of speed and reach when mounted on APS-C – with the motion-freezing potential of an f2 lens and the framing of a 200mm full-frame lens.

But what of noise? Assuming similar levels of technology and a similar pixel count (ie, a full-frame 24MP camera v APS-C 24MP camera), the larger format of course claws back its apparent one stop deficit by being able to shoot at higher ISO. But – in practice – with a requirement for ‘only’ 6000px and 1/250, the difference may not matter at all: in good light, it may be negligible: the difference between 1/500s and 1/1000s, or a difference in terms of colour and noise that is trivial. Similarly, at 400mm, the difference between the look of f5.6 and f4.0 may not be field-significant: both settings create heavily blurred backgrounds with excellent subject isolation.

We might imagine different assumptions, and each would change the ground rules. If you demand 8000px+ captures (for whatever reason*), or regularly crop hard, or work in low light, or demand an ultra-shallow DoF, or shoot only from a fixed position on a tripod, or have unlimited budget – all favour a larger format. And of course for some assignments there is no zoom too long or lens too fast. However, in most real-world scenarios, for most shooters, there are real advantages to smaller formats like APS-C and M43 when working with remote fast moving subjects.


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