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# Is my thinking about equivalence right?

Started 2 months ago | Questions thread
Re: Is my thinking about equivalence right?
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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.

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.

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.

Calculating total light (for point 2): This is pretty handwavey, but after squinting at the data on lenstip.com, 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.

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.
--
Cheers,
-Ian

Lets say you have a 50mm F4 lens on FF.

To achieve 50mm equiv on MFT, as far as similar DOF, it takes a 25mm F2 lens, so 2 stops. IE a wider lens has a larger DOF so you need a faster lens by about 2 stops to roughly match the DOF.

As far as light gathering of FF vs MFT, I dont buy all the blanket equiv nonsense because it depends on FF chip mp, and how large are the individual sensors.

For instance, assuming the chip design is the same, IE BSI etc. if you are compare a 20mp FF chip (with larger sensor sites) to a 20mp MFT chip (smaller sites) then yes the FF chip would gather more light.

However, again with the same type of chip, if you are comparing a FF 80 mp image chip to a 20mp MFT chip then the light gathering would be roughly the same.

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