Is my thinking about equivalence right?

Started 3 months ago | Questions thread
bobn2 Forum Pro • Posts: 69,811
Re: Is my thinking about equivalence right?

Muster Mark wrote:

Hi all, I realize this is NOT the topic everyone loves to discuss and I totally understand. I hope no-one feels annoyed by this post. That said, after some investigation I have come to the conclusion that "traditional" equivalence math is only useful as a rough heuristic to get a sense of what DOF will be and NOT a reasonable way to compare individual lenses or judge cost/performance of lenses in different systems. I wanted to see what other geeky 4/3 sensor users think and if I am missing something in my calculations. I should add I fully understand the traditional argument that total light is 4x on FF camera (for example) at the same aperture since we need to multiply (integrate, actually) brightness by the sensor size to calculate S/N. This idea only works if you have an IDEAL lens and an ideal sensor. Lenses are never ideal though, so I wanted to dig deeper.

OK, a thoughtful, detailed post which deserves a detailed response. So here it is.

For the sake of simplicity let's limit ourselves to looking at "normal" lenses: e.g. fov roughly 1 radian. This FoV tends to "favor" larger formats as far as I can tell especially if the goal is to maximize bokeh-ball size/$. Furthermore, to limit permutations I only looked at examples of lenses for m43 and Sony E mount, specifically trying to find an "equivalent" lens to the M.Zuiko 25mm f1.2

My analysis boils down to 2 points:

1: No two lenses are actually "equivalent". This seems obvious. There is more to evaluating a lens than pupil diameter and FoV. People seem to forget this when comparing between systems.

That's what is called a 'semantic argument'. Before you argue about whether things are, or are not equivalent, you need to agree on what the word 'equivalent' is going to mean. This is a very common practice in science and engineering, we give every day word very precise definition so as to avoid that kind of lack of clarity. For photographic equivalence, the word 'equivalent' is defined with respect to 'equivalent photographs' which are defined to have the:

Same Perspective
Same Framing
Same Exposure Time
Same DOF / Diffraction / Total Amount of Light Projected on the Sensor
Same Lightness
Same Display Dimensions.

That's it. There's no point arguing with whether or not that's the right definition. In the context of the discussion, the is the definition. Choose a different definition, and you end up with a different discussion.

2: Talking about "total light" without accounting for vingetting is either lazy or disingenuous. I am guessing this is 100% laziness as calculus is annoying. However FF lenses have much worse vingetting than m43 lenses for obvious reasons. Is this a hugely important aspect to image quality? No not really, IMHO, it's pretty easy to correct in post if you have the lens profile, but you are losing some of the signal to noise ratio advantage in the process. How much? that's what I wanted to figure out. By my calculation (of course it depends on lens a huge deal) FF lenses at 50mm lose about half a stop of light to vingetting MORE than the 25 f1.2. Specifically, the Sony GM 50mm 1.2 at 1.2 gathers about 2.9x the total light gathered by the olympus 25mm 1.2 (at 1.2). Is this a huge deal? No probably not, but it's not quite as impressive as the 4x factor everyone is repeating is it? I just thought it was interesting, mainly.

It's no more 'lazy' or 'disingenuous' that talking about exposure without accounting for vignetting.

Calculating total light (for point 2): This is pretty handwavey, but after squinting at the data on, and specifically the level curves for brightness I thought it looked remarkably parabolic. Thus I approximated the brightness function of a lens wide open as a decreasing parabaloid -(x^2+y^2)K, where K is a constant that depends on the specific lens (I compared contour plots of these functions to the level curves provided by lens tip and they are remarkably close). When comparing between lenses of different aperture, there is a shift applied: e.g. approximating 1.4 as half a stop slower than 1.2, we would shift by -1/2. We then exponentiate and integrate over the frame. For these calculations I am assuming Fstop equals Tstop. Which is not correct, though lenses with similar numbers of elements will not have much difference in T stop I don't think (am no expert!). I couldn't find information on T stops for a lot of lenses which is why I left it out of consideration. I also couldn't find information on how it's measured (are they integrating total lite or measuring intensity at the center of the frame?) which further complicated trying to incorporate it.

In the end, if we apply your argument to exposure, what you're saying is that f/2 ≠ f/2 ≠ f/2. Well, fine. Things are more accurate if we use T-stops, and more accurate still if we abandon T-stops and use some kind if exposure map for each individual lens. And when you said 'For these calculations I am assuming Fstop equals Tstop' you rather undercut the whole point you were making, because you applied exactly the 'lazy' or 'disingenuous' thinking as you were arguing against.

Comparing lenses holistically: When more is taken into account than just pupil diameter, it seems to me at least, m43 lenses are not overpriced. For example the 25mm1.2 is optically pretty amazing when it comes to corner to corner sharpness, longitudinal CA correction (which is hard to correct in post, if my understanding is correct) and bokeh quality (not size).

For half the price one could use the Sony 50mm 2.5. This amounts to being about half a stop dimmer due to vingetting, the bokeh while the same size is much busier. Longitudinal CA is only a smidge worse though. Oh and yeah if you want a sharp full frame you need to stop down to f4 (the 50mm 1.8 by sony is not really worth looking at if optical performance is something you care about).

The Sony GM 50mm 1.2 lens performs very well when stopped down (and is pretty good wide open), but now we are back to being much heavier and costlier than the olympus. I am NOT saying it's a rip off, but I also don't think the lens needs defending as no one seems to doubt it.

The Zeiss 55mm 1.8 has lovely bokeh, but bad Long. CA and needs to be stopped down to 2.8 to be sharp.

Sigma ART lenses start to really shine honestly. Generally very well corrected optically, much less vingetting on FF than other lenses when wide open, and even slightly cheaper priced to the olympus. They are significantly bigger though (the 50mm 1.4 is 815g, versus 410g for the oly).

So what do we make of all this? My take away is that there is no free lunch. All lenses are compromises and on a system-wide level nobody is scamming anyone. If size of the bokeh balls is not your biggest concern, and you care about system size/weight and optical performance, m43 makes a lot of sense. I guess you already know that

I personally am shopping around at the moment (trying to decide if I want to adapt old 4/3 glass to m4/3 bodies, or buy new lenses and potentially change systems or buy new m4/3 lenses) and thus did this analysis to try to compare systems more accurately. Hopefully it was moderately interesting?

If there is anything I should be accounting for that I am not (and you know how I might, e.g. t stops) I'd be curious to hear.

This has now stopped being a careful and precise argument, and has diverged in to a randomised set of views, some of which cannot be sustained with evidence, about different cherry-picked lenses. Mostly it is irrelevant to the issue of Equivalence, because that has nothing to say at all about image quality, bokeh quality and such like. Sometimes well done testing doesn't produce the results you would think. For instance, here is the Lens Rentals test of the Olympus 25mm f/1.2 which you say is 'pretty amazing'.

And here is the smaller, cheaper, lighter Sony ZA 55mm f/1.8, which gives a larger entrance pupil.

We can see that the Sony is as sharp, and at the centre sharper than the Olympus. And remember that these are absolute resolution tests. Considering that the Olympus has to produce double the resolution of the Sony just to match it in a final image, due to being magnified twice as much, then there's not much of a comparison. You have to compare the Olympus lines with the lined for half the lp/mm on the Sony. On FF 10 lp/mm corresponds to 215 lp/ph, whilst on FF that final resolution is given by 20 lp/mm, so if we compare the two at the same final resolution, we find that the Sony gives an MTF of 0.93 in the centre and 0.85 at the edge, whilst the Olympus gives 0.77 in the centre and 0.69 at the edge.

The Sony lens costs $700, and is 65x71mm and weighs 281g. The Olympus costs $1100, and is 70x87mm and weighs 410g. The Olympus costs a lot more, is bigger, weighs a lot more, delivers less light to the sensor and produces a less sharp final image across the field.

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