Back to Basics by Ctein

Ctein (it's pronounced "kuh-TINE" and it's his entire legal name) was a longtime regular columnist on TOP. This is a somewhat shortened version of a recent recent column from his newsletter, which you can subscribe to here.

Ctein is the author, with John Sandford, of the sci-fi thriller Saturn Run. Recently he has collaborated with David Gerrold on a new sci-fi book called Ripple Effect which you can start reading for free. All the information you need is here.

Guest post by Ctein

One of the things you discover pretty quickly if you're a regular writer of articles and columns for magazines is that you have to repeat yourself. There are two reasons for that: the first is that they are always new readers coming in who haven't read what's been written before. The second is that—remarkably—people don't remember every single word you've ever written.

What inspired me to do this was, in part, the business of posting my old TOP columns (over 300!), wherein I was reminded of this bit of wisdom. Along with the fact that I didn't remember everything I'd written...so how can I expect you to do so?!

Should you find yourself having questions about any of these assertions, please read the linked articles before girding for battle. You might find that I've already addressed your concerns.

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1. Photography Isn't Math...or Physics...

This first one's a bit meta: most of the fallacies (and stupid assertions) that I read online are due to people who think that photography and optics are simple things, amenable to easy calculation. They are not. It's not just that the devil is in the details; the devil frequently dominates! A good rule of thumb is that any time you see someone making an assertion that they back with the phrase "it's simply a matter of physics (or mathematics)"...they will not know what they're talking about. They are appealing to an authority that is nonexistent.

Related to that: Even when something is a matter of physics, it doesn't mean that physical law is limiting the technology. I can state as a matter of physics that rocket engineers can't build spacecraft that will travel faster than the speed of light. At our current levels of engineering, this is not particularly restricting their endeavors!

You may enjoy reading the following for expansion on these points.

—> Further Reading: "Reality Is Not Arithmetic" and "NOT Off-topic: Mathematics vs. Science"

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2. It Doesn't Take 10,000 Hours to Master a Craft

Also kinda meta...

Malcolm Gladwell inserted this dubious notion into the public consciousness with such success that people took it on face value. It was a most definite case of jumping way beyond the available data to a facile conclusion, but its very facilety (yeah, I know—not a word) made it so appealing.

Too bad that it's wrong, and that it has inhibited so many people from pursuing their passions, people who internalize that and say to themselves, "OMG, if I spent an hour a day on this every single day of my life, it would still take me three decades to get really good!"

I will present the counter-example that I happen to be most familiar with…me. (In case you're wondering this is by no means the only counter-example I know of, but it's the one I can document with authority.)

I am universally considered by my peers to have been one of the grand masters of dye transfer printing, although whether anybody truly masters this arcane art is another matter. I keep pretty good records of my time in the darkroom (see the citation below). By the time I hit 1,500 hours of practicing that craft, I was already recognized as one of the best printers in the business. Most certainly before I hit 3,000 hours I had learnt everything about dye transfer printing that I was ever going to.

It's also true that some people will spend their entire lifetime and never master their craft. Not everyone gets to be really good.

I don't think this is a matter of "innate talent" to anywhere near the extent that most people do. I feel people give way more weight to it than they should. I assert this without much evidence, I admit, but I think an awful lot of what people attribute to talent is entirely teachable: It's got a lot more with how you approach the task than what you bring to it.

—>Further Reading: "How Many Hours?"

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3. Focal Lengths Have Equivalents, Apertures Don't

To be sure, there are major advantages to being able to democratize the dialogue, but there were certain advantages to having professional gatekeepers. This particular bit of weirdness never showed up until online conversations took over the discourse.

Focal lengths have equivalents for different formats. For example, my Micro 4/3 format is almost exactly half the size of 35mm AKA "full-frame" format. There are modest differences in the proportions, but not enough to matter. Focal length determines the angle of coverage in a photograph, so it's correct to say that my Olympus M.Zuiko 75mm ƒ/1.8 lens is the equivalent of a full-frame 150mm lens. Both would convey about the same field of view in the photograph.

What is not correct is to claim that this ƒ/1.7 lens is the equivalent of a full-frame 150mm ƒ/3.5 lens! There is a technical term for that—"utter nonsense."

The f-number, along with the shutter speed, controls exposure. If your light meter is telling you that the exposure should be, oh, say, 1/100th of a second at ƒ/4, it's going to be 1/100th of a second at ƒ/4 no matter what format or focal length lens you are using. Assuming all the cameras have the same sensitivity/ISO setting, of course.

The know-it-(not-at)-all's will argue, "Yes, but the full-frame ƒ/1.8 lens collects four times as many photons." Sure, but then it's distributing those little buggers over four times the area, so the flux per square millimeter on the film/sensor remains the same. That's why the exposure doesn't change!

Having failed on that challenge, they will bring up the shallower depth of field in larger formats. The problem with that argument is that the relationship is highly dependent upon the distance to the subject, the focal length of the lens, the f-aperture, and the resolution of the camera. There is no simple equivalency.

Let's put a stake through the heart of this one if we can.

(Caveat for the uber-geeks: absolute aperture—diameter—rather than f-ratio matters when you're photographing point sources, like stars. This is why telescope/lenses intended for astrophotography include both the f-ratio and the aperture of the scope in their specs. The former will matter for photographing extended objects—e.g., the moon, planets, and nebulae—but the latter will matter for photographing isolated stars.)

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4. Zoom Lenses are Not Optically Worse than Prime Lenses

OK, this is one that I believed up until about a dozen years ago—that zoom lenses wouldn't perform as well, optically, as prime lenses. There were just too many design compromises that had to be made to get good performance over a range of focal lengths.

(If size, weight, and maximum aperture are concerns, then primes still hold the advantage. No question of that. I'm only talking about image quality.)

That was old wisdom, and by old I mean it was something I learned very early on. It probably remained true through the 20th century.

As I got more invested in the Olympus system, I found myself with a couple of zooms in my lens kit, along with some primo prime lenses. The zooms filled in the holes in my focal length choices, but I wondered how much I was compromising my picture quality by using them. Time to run tests!

You can read the detailed results in the citations below, but my overall conclusion was that the zoom lenses performed, on average, as well as the primes—in some cases better than the equivalent primes, in others not so much.

In conversations with other photographers, who also know their technical chops, I've heard the same thing. Lens design techniques and materials have advanced immensely in the past 50 years, and zooms have especially benefited from that.

I hope it's understood that I'm talking about averages here. Will any particular zoom beat out any particular prime lens? Who knows...until you run the tests. Some lenses are so spectacularly good that nothing can compare. Others? Meh.

—>Further Reading: "Zooms vs. Primes, Part I and Part II"

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Well, I think that's enough for this time. That's plenty to chew on, especially if you dive into the citations. In future columns you can expect me to attack many more prevalent myths…and more controversial ones; if you want to make sure you don't miss any of these, subscribe to my newsletter.

Ctein

Original contents copyright 2024 by Ctein. All Rights Reserved. Links in this post may be to our affiliates; sales through affiliate links may benefit this site. As an Amazon Associate I (Mike) earn from qualifying purchases. (To see all the comments, click on the "Comments" link below or on the title of this post.)

Featured Comments from:

Comments

[JOHN B GILLOOLY]

Somewhat related to the 10,000 hours topic. I have done much thinking about the idea of the point of diminishing returns as it relates to skills and hours. I have a friend years ago that referred to me as "80% guy." He meant it as both a compliment and an insult and I took it as both.

For example, for 30 years I have hovered between a 3-7 handicap in golf. I don't play very much - maybe 15 actual rounds per year with another 10-15 partial rounds. People will say, "man, if you actually played a lot, you could be really good!"

OK, but at what cost? I can play very little and just view golf as a fun hobby and be around a 5 handicap. To most, that is very good. To really good players, that's not very good. But to get from a 5 handicap to a 1 would require a huge effort - probably practicing/playing intentionally 5 days per week. And if I was a 1 handicap, most people would still think I was "really good" and really great players would think I was "ok." Not much different, but at a huge cost.

If I had unlimited time and loved playing and practicing - great. But all else equal, I'd rather be at my son's baseball game or my daughters swim meet. Or roaming around Boston taking pictures. I don't care that much about being a great golfer and I am sort of already at the point of diminishing returns.

For me, the same applies to my fitness regiment. My nutrition profile. I'm sort of 80% guy. I'm sort of an anti-extremist and for me, the next step beyond "80%" is down a rabbit hole of diminishing returns.

[Kodachromeguy]

Oh, oh, Ctein, now you have done it. The equivalence "experts" will pummel you with their pseudo-physics and new math to prove that their rantings and endless arguments really proved the stuff about f-stops and photons. To battle!

[Jeff]

Even the researcher Gladwell cites as a basis for his 10,000 hour rule finds fault with his interpretation..

https://www.6seconds.org/2022/06/20/10000-hour-rule/

[Tom Passin]

About the 10,000 hours. That was only a guide or summary of a lot of research into different areas of endeavor - and varied a lot depending partly on the kind of activity - and it was never supposed to stand on its own. The work needed to include *thoughtful*, diligent study and practice, under the guidance or mentoring of a skilled teacher.

[Albert Smith]

Regarding item 3, the conversion of the aperture is not about the exposure part of the f-stop when people state the "equivalent" thing, but rather the effect on DOF. A 50mm f/2 lens on a full frame and a 35mm f/2 on an APSC will have roughly the same angle of view, the same shutter speed for the f/2 aperture (assuming the same ISO), but they will not have the same selective focus for the same subject.

The APSC camera with have DOF of a full frame camera shot at f/3. When people talk equivalent this is what they mean. Of course an f-stop is an f-stop regardless of the format, or else hand-held exposure meters wouldn't work for any size capture... and they do.

[Arg]

While not disagreeing with what Ctein *did* say about aperture in item 3, what he *didn’t* say is the real reason that there *is* such a thing as aperture equivalence. Namely, a 50mm f/4 photo taken on APS-C will have the same ‘look’ as a 75mm f/6 photo on FF, taken from the same position. Same framing, same DOF.

That’s why there *is* such a thing as aperture equivalence. What Ctein is quite rightly reminding us, though is that there are wrong ways to try and use it, such as exposure calculations. Those ways don’t work.

Cheers

[ctein]

Dear Jeff,

Thank you for the link to that article! Very entertaining – I especially liked the variation in chess masters' hours. Talk about extremes!

_________

Dear Albert and Arg,

[[ FYI, I am planning to tackle nonsensical notions about depth of field in one of my future Back to Basics columns. In the meantime you could wade through this to get you started (including the comments) :

https://theonlinephotographer.typepad.com/the_online_photographer/2009/06/depthoffield-hell.html

https://theonlinephotographer.typepad.com/the_online_photographer/2009/06/depth-of-field-hellthe-sequel.html

https://theonlinephotographer.typepad.com/the_online_photographer/2013/08/the-practical-side-of-depth-of-field.html ]]

I am replying to you collectively, because you're both quoting the same relative ratios for apertures. This leads me to suspect you're getting that information from the same source. My response?

Show me the math. Seriously. I'm 99% certain I can prove it wrong or show that it's based on some arbitrary assumptions.

I'm pretty sure that whatever math you show me isn't going to work for all distances. If it's good for close-ups, it's going to fail for distant objects. If it's good for distant scenes, it's going to fail for close-ups. In between? It'll fail at both ends.

For that matter, are you talking the same number of pixels in both formats or the same size pixel?

It is a broadly true that the larger the format, the shallower the depth of field... but that's all you can say. I assert that a simple equivalency does not exist.

I'd be happy to be shown the error of my ways — I like to learn new things! Honest and truly! But ya gotta show me.

pax / Ctein

(please excuse any word-salad. Apple Dictate's fault)

[ctein]

P.S. Maths aside...

As I explain in the linked columns, real-world lenses do not have a mathematically ideal depth of field. Two different designs of lenses, of the same focal length and at the same aperture, can have very different depths of field, as well as different distributions of that depth in front of and behind the plane of focus.

That's physical reality. Even if the maths worked (and they don't) the real world wouldn't conform.

[Moose]

"Having failed on that challenge, they will bring up the shallower depth of field in larger formats. The problem with that argument is that the relationship is highly dependent upon the distance to the subject, the focal length of the lens, the f-aperture, and the resolution of the camera. There is no simple equivalency."

He's right, of course, And I like theory. I also like pragmatic tests. I had a friend who always did the math for DoF, and lived by the results — until I posted actual photos, on the actual cameras and lenses we used. There was clearly no visible diffraction softness at more than a stop over his calculated limit. I've had other examples.

And here is an example, fairly close focus, wildly different lenses, a very recent design, 19 elements in 14 groups, special elements 3 HR, 2 ED, 1 E-HR, 1 HR, 1 Super-ED, vs an early 1950s design, 7 elements in 5 groups.

Olympus 25/1.2 vs. Canon LTM 50/1.2

Yes, some differences, my framing is imperfect, as I did it just for me. But the results pretty closely follow the two stop idea for DoF eq. So, for me, with my gear, it's simple. YMMV

[DaveB]

Ctein….welcome back! If any two guys should be Bloggers it’s you and the Guy who runs this one.

[Sean]

As someone who grew up in an inner city neighbourhood with a fair share of broken windows, it didn’t take 10,000 hours to figure out the inferential leaps Gladwell made in The Tipping Point were unjustified. But in coming to strong conclusions from weak evidence, Gladwell was just replicating the social sciences from which he gathered his material.

[Lothar Adler]

I'm probably getting on Ctein's nerves, but a few years ago I took test shots to determine the "equivalent focal lengths and apertures".
From the same camera point of view, I used Nikkor 1.4 / 85 mm at f/1.4 and Pentax 67 2.8 / 165 mm, f/2.8.
On visual inspection, the two images were practically identical in terms of depth of field and the representation of space.
Of course, the exposure times were different, but the image effect was the same.

[Robert Roaldi]

I shoot m4/3s and never spent a minute thinking about f-stop vs DOF equivalence. I take photos with the camera in my hands, not some other model I might have bought. People are just fixated on "full-frame", presumably because of its dominance in 35 mm film days.

I enjoyed the forum posts from 10-15 years ago when people asserted that "full-frame" sensors will never form the mainstream.

[Daniel Homan]

Ctein wrote: "The know-it-(not-at)-all's will argue..." As a professional Astrophysicist who works with Astronomical data every day from some of the best telescopes on Earth (and Space), and a Physics and Astronomy professor who has taught this stuff for more than two decades, I feel a certified know-it-(not-at)-all should perhaps have a chance to respond. If it matters, I've also been an amateur photographer for 30 years and regularly use both micro-four-thirds and full-frame cameras, so I have daily practical experience with the notion of 'equivalence'.

First, Ctein's point that total light only matters for unresolved point sources is simply false. I work almost exclusively with resolved images, and I can assure you, Astronomers care very much about total light. It is the number one and most important reason for making telescopes larger and larger. It is true that larger telescopes have more resolution, and that is also very important (especially in my field), but signal-to-noise is king and to say that the size of your aperture somehow doesn't matter if you image is resolved is false. You only don't care about about SNR if you have tons of "S", which is not true in all genres of photography.

Second, Ctein says that light-density doesn't change with f-ratio, which is true by definition of the f-ratio. It is also true by the definition of ISO that exposure will remain exactly the same for a given f-ratio and ISO. What is misleading here is that ISO in digital sensors is calibrated by the area of the photo well (and sensitivity of the detector material). The gain must be increased for small area photo wells, which is what makes the per pixel noise higher in those images. The noise in the 1600 iso images in my 20 MP micro-four-thirds camera was very, very similar to the noise in my 6400 iso images in my (same generation) 24 MP full-frame camera. This is simple Physics playing itself out. It is true that newer generation full-frame cameras have more pixels, so the per pixel noise is closer to even now, but the per image noise is not... which is what we care about in the final image that goes on the wall.

Third, depth of field. Imagine we take a full frame camera + subject and scale every distance down by a factor of two: including each dimension of the sensor, lens dimensions, subject distance, subject size, etc... In that case, nothing changes in terms of the depth of field. The focal length has changed, but the f-ratio has not. The signal is even higher by a factor of four because the object is closer. In short, the image you make is equivalent in every way using geometrical optics.

Of course, in the real world we cannot shrink the size of our subject and often cannot change its location. To make the 'equivalent' image with the 2x smaller-in-every-dimension camera we need to keep all the geometrical relationships the same, but we cannot. The now shorter focal length will still bring the focus plane rays to the sensor as before, and your subject will still fill the frame as it did before thanks to the shorter focal length. The front-back relationships at the edges of the frame have changed, which leads to increased depth of field at the same aperture. In fact, to a very good approximation, the depth of field has changed such that the image looks virtually identical to one taken by a full frame camera/lens with twice the focal length and the aperture stopped down two stops.

This is why people harp on 'equivalence', not because it is strictly true in the exact details, but because it is approximately true (to a very good approximation in many situations) for three things:

1) noise -- stopping down the full frame lens by two stops changes the SNR by the same factor as the smaller sensor size

2) focal length -- the subject fills the frame in the same way

3) depth of field -- stopping down the full frame lens by two stops very nearly changes the depth of field to match the smaller sensor for the same subject and distance and fraction of the frame filled.

If you don't believe any of this, you can test it yourself with a full frame camera. Try cropping your images by a factor of two in each dimension. This is like using a micro-four thirds camera: you have less total SNR and your depth of field is greater because you are near the center of the imaging area.

Look, "equivalence" is not a bad thing. I use it to decide what camera and lens to take with me for different excursions. I think it is fantastic that for many, many purposes a small camera can capture virtually the same image as a much larger, heavier setup. Why bother with that if you don't need to?

[ASW]

Based on a quick calculation, I have spent 10,000 hours in bed for every 3.4 years of my life, with my (conservative) total bed time around 131,000 hours now. Somehow, I'm still a horrible sleeper...

[Daniel Homan]

Correction. I wrote:
"Try cropping your images by a factor of two in each dimension." and I should have said, "Try cropping your images by a factor of two in each dimension, and comparing to the same image taken with a longer focal length from the same position".

It is actually easier to do this test if you have both a micro-four thirds camera and a full frame camera, then it the effect is obvious. I recommend trying it if you haven't.

[Jnny]

A lot of folks miss the point completely about Gladwell's contention. It wasn't about the hours, it was about the support required to reach that number of hours. It requires amazing support systems for anyone to reach the number hours required for mastery of an art whether it is 1000 hours or 10,000 hours.

[Bill S.]

It seems to me the debate over f number equivalence is largely semantic. Strictly speaking FOV on 35mm on m43 is not "equal" to 70mm on ff, but it's close enough no one objects to miss use of the word. Comparing f number is much more complex, so equivalence is much more debatable. It is also a debate between "old school" photographers who are judging an image based on a print and young whippersnappers who are judging an image by pixel peeping. The older photographers are likely to consider the younger photographers idiots, but both may fully understand the craft and be able to create excellent images.

[Craig Yuill]

Aperture equivalence became a way for well-heeled camera owners to put down those with tight budgets who couldn’t justify buying expensive full-frame cameras and premium fast lenses. I left one of the early popular photo forum sites after one frequent poster admonished another to get a better-paying job so that they could afford the full-frame camera and fast lenses that they (supposedly) really wanted to own. What crap! (This was during a time when photos with super-thin depth of field were in vogue, which (as far as I’m concerned) was just a way for some to show off their expensive gear and put down others that didn’t have some.)

The funny thing about it all was that I would use tilts and small apertures to maximize depth of field during my large format 4x5 film phase, back in the day. I am glad the super-thin-depth-of-field fad has gone away. Nowadays I go back and forth between using APS-C and 1-inch sensor cameras. I somehow manage to get photos that please my eyes. No equivalence considered.

[ctein]

Dear Lothar & Moose,

Hey, Lothar, that's my favorite film camera! You may not know, but the Pentax 67 was my standard camera for over four decades – I got one of the very first ones that came into the US back in 1970, when I was in college. A wonderful camera!

I also used the two-stop rule, but that's because most of my work with landscape work. It happens that the f-ratio does scale exactly with the format size at the hyperfocal distance. If all your photography is distant work, that "equivalency" applies.

The problem is that it becomes increasingly wrong as the image magnification increases. At 1:1 photography, the "equivalent" f-number scales as approximately the square root of the format size. In other words, if you're comparing micro 4/3 to full frame where there's almost exactly a factor of two difference in size, the equivalent aperture is only one stop smaller.

Moose, that's a fabulous illustration (I looooove rollovers!), but it isn't showing a two-stop equivalency. It's only a little over one stop. You didn't specify what image magnification was involved for the full frame camera, but it was probably less than 1:1 (unless those are REALLY small figurines), so that's what I would expect for close-but-not-really-close photography.

A more subtle difference is that the depth of field isn't equally distributed between the foreground and the background in the two sets of photos. Part of that is very likely due to the radical difference in lens designs, but part of it is because varying the focal length also varies the proportion of foreground to background depth of field (which most people don't know—I went into that in detail in the "Depth of Field Hell—The Sequel" column). Even if you match apertures, the DoF's are not going to be equivalent.

Again, if people want to say "Hey, you have to stop down more with a larger format to get comparable depth of field," I'm fine with that. When they declare a format–proportional equivalency, they're wrong.

Except for hyperfocal-landscape photography.

Which is mostly what I do... but it's not all about me (grin)!

(please excuse any word-salad. Apple Dictate's fault)
pax / Ctein
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[ctein]

Dear Daniel,

Hey, let's not get too deep into the weeds on astronomy. I did solar astronomy at Big Bear Observatory, and I agree with some of what you said, but not other parts of it—mostly not as it applies to photographers as opposed to astrophotographers.

(Sidenote for the amusement of lay-people. Solar astronomers have as much trouble capturing enough photons as nighttime photographers. You would think not, but we're taking 0.01 nm slices out of the spectrum. That's not a whole lotta light!)

For regular photographers, doubling the aperture while keeping the f-number the same means doubling the focal length. So, no, the counting statistics don't get any better for extended objects.

Scientific/astronomical instruments are different, but "consumer" cameras—and I'm including "pro" gear in that—are almost never photon-counting-statistic limited. Other sources of noise (and insensitivity) dominate. You happened to hit upon a case where they did scale nicely, but I could find as many or more where it doesn't, especially as the technology continues to change.

Some years ago, I was able to run comparison photographs between my "all in one" Fuji Finepix and a Nikon D200. The Fuji was only a factor of two worse in low-light performance than the Nikon, although the pixels were 1/6 the size. The Fuji was three years newer than the Nikon, so I'm not relating this to diss Nikon. It just goes to how poorly scaling factors operate in the real world of ever-changing technology, comparing apples to oranges.

I've run the depth of field comparisons you talk about. They don't produce the results you think they do (nor does the math). Moose just posted a great comparison example of that and in my response to him I explain why.

(please excuse any word-salad. Apple Dictate's fault)
pax / Ctein
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-- Ctein's Online Gallery http://ctein.com
-- Digital Restorations http://photo-repair.com
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[Walfredo Cirne]

Thanks for helping dispelling the myth of aperture equivalence, Ctein.

[Moose]

"Moose, that's a fabulous illustration (I looooove rollovers!) "

Easy HTML. I love them too. I originally did this one just for myself, to see stuff more easily than in PS or LR.

", but it isn't showing a two-stop equivalency. It's only a little over one stop. "

Seemed to me closer to two, but now, looking again, it seems that the ratio depends, as you say, somewhat on focal distance, even within this limited range. (And the lenses really are wildly different.)

" You didn't specify what image magnification was involved for the full frame camera, but it was probably less than 1:1 (unless those are REALLY small figurines), so that's what I would expect for close-but-not-really-close photography. "

I didn't specify 'cause I didn't know. \;~)>

Most of the figurines are pens, from gift shops, etc. The two front left are, I believe, meant to be Arthur and Merlin, bought in the ticket station for Tintagel last year; couldn't resist.

Measurement indicates about 1:6.7 mag. Possibly closer than possible on the cameras it was designed for, but not much, as my adapter has extension.

[Daniel Homan]

For regular photographers, doubling the aperture while keeping the f-number the same means doubling the focal length. So, no, the counting statistics don't get any better for extended objects.

Of course the counting statistics are better, with a full frame lens you've doubled the focal length to frame the object the same way, so at the same f-number you have four times as many photons entering your lens from that object. A factor of four is two stops in sensitivity. It is true that your imaging area at the focal plane is larger by the same factor, so the photon density is the same at image plane, but we don't show images scaled by their sensor size. We show images based on the size of the frame we pick for the wall. For the final image on the wall, a micro-four thirds camera will have the four times less photons contributing to each square-centimeter on the image *unless* you open up your aperture by two stops when you take the photo.

I've tested this with my own equipment extensively and for both SNR and depth-of-field for the range of use cases I have, the two stop rule is just about spot-on.

I actually sold my first full-frame camera and lenses after doing this test when I realized that I very rarely took a photograph at less than f/4 with that kit. My Olympus could do the same job with a few primes, so I was good to go. Then a few years later my kids joined night-time Marching Band, and I finally had a case where a bit more light helped.

[Robert]

“ In fact, to a very good approximation, the depth of field has changed such that the image looks virtually identical to one taken by a full frame camera/lens with twice the focal length and the aperture stopped down two stops.

This is why people harp on 'equivalence', not because it is strictly true in the exact details, but because it is approximately true (to a very good approximation in many situations) for three things:

1) noise -- stopping down the full frame lens by two stops changes the SNR by the same factor as the smaller sensor size

2) focal length -- the subject fills the frame in the same way

3) depth of field -- stopping down the full frame lens by two stops very nearly changes the depth of field to match the smaller sensor for the same subject and distance and fraction of the frame filled.”

Thank you to the astrophysicist.

Yes, exactly. And this is precisely my experience, using both cropped APS -C fuji sensors and Sony full frame sensors since 2008. Equivalence is a very useful predictor of how real world depth of field works out, no matter how vehemently Ctein claims to be right, it obviously does not convince experienced photographers.

[Nick]

I had forgotten all about those m4/3 lens comparisons you did way back in the day! I would love to see how the Oly 75 mm (which, in my use, seems to actually be superior to my dearly loved 45 mm, with better microcontrast) stacks up to those zooms in your mind, and how some of the more modern zooms (like the 12-40 mm f/2.8) fare as well.

[ctein]

Dear Daniel & Robert,

I'm glad the two-stop rule works for your equipment and conditions. It does not work in the general case. Really. Math says it doesn't and experimental evidence says it doesn't.

If it's a good rule of thumb for you, great. I have no problem with that! But keep it as your personal rule of thumb and not an objective pronouncement, please?

(And, Daniel, no, we do not agree on the meaning nor significance of the counting statistics, but this is so far down in the weeds and off topic that if you want to continue the conversation, please email me.)

pax / Ctein

[ctein]

Dear Nick,

Oh, I don't even need to run those tests. The Olympus 75mm is spectacularly good in every respect, over its entire field of view. Yes, it's better than the 45mm Olympus, better than the 42.5mm Lumix (which is better than the 45mm). Its one of those utterly outstanding lenses that belong on anyone's list of "best lenses ever made."

It'll beat out the zooms because it'll beat out almost anything in that focal length.

pax / Ctein

[Daniel Homan]

Follow-up: actually the DOF math was remarkably simple and fits on one whiteboard, with explanations. The essential idea is to use the point where the circle of confusion first becomes unacceptably large. The diameter of that circle, d = the diameter of the aperture * the focal length of the lens * constant (for a fixed object and distance). I assume the object distance is >> focal length, but the definition of >> is really only a factor of a few to a good approximation, so were talking about most non-macro lenses behaving this way.

Because d depends on aperture diameter * focal length, and focal length depends on sensor size, s, to get the same framing, d/s which is the size of the confusion circle relative to your framing (which is what we care about) depends only the diameter of the aperture, not the f-stop! It was fun to see this work out.

I can share an image of my whiteboard with the math and result, but I don't see an easy way to attach an image.

[Tahir Hashmi]

Regarding equivalence, Ctein is right in highlighting that from a point of view of photometry the aperture of a lens doesn't change with sensor size. E.g. an f/1.7 lens needing 1/50 exposure at ISO 100 on FX sensor would need exactly the same parameters of exposure for m43 as it would on a larger 645 sensor (assuming all other lens characteristics are the same)

However, while there is no equivalence in exposure parameters, there is absolutely undeniably an equivalence in visual parameters, i.e. framing and depth of field. It's trivially verifiable and has been demonstrated thousands of time online.

And it is useful.

Since Mike talked about DoF equivalence being used by FX owners to show off, let's take an example from Weegee, who shot with a Kodak 127mm Ektar on a massive 127mm x 101mm (5" x 4") film "sensor". His favourite shooting apertures... f/11 (longer distance) through f/22 (close-ups). [https://archive.org/details/wgPhotoflash]

It's impractical for me to acquire a 5x4 camera today, so I must make do with my puny little 35mm sensor. Applying the equivalence math, I ought to be using a 35mm lens set to f/3 through f/6 or thereabouts. Seems plausible, looking at his published photos, I reckon those settings would fit.

If I were to ignore DoF and FoV equivalence and shoot with 127mm at f/22, I don't think I'd be doing close-ups anymore.

And, oh, getting Weegee's f/22 DoF on my humble iPhone... impossible! But somehow the iPhone gets everything in focus even at its f/1.8 aperture.

There is such a thing as DoF equivalence, and it shouldn't be denied. What's needed is clarity around where to apply aperture invariance (exposure calculations) and where to apply aperture equivalence (visual approximation).