What is equivalence and why should I care?

Smaller pixels always get less light, for any given exposure (same light per unit area but less area) and hence are noisier. However, if you consider the entire image by viewing or printing at the same size, this stops being the case.

This example compares some of the smallest with some of the largest pixels you can currently get on a full frame sensor and the results are essentially identical, except the higher pixel count camera captures more detail.

It's not a 100% like-for-like comparison, since the D850 has a BSI sensor, but BSI doesn't have much of a noise impact in chips/pixels this big (see Fujifilm X-T2 and X-T3 as an example). BSI's main advantage for large sensors is its ability to receive light at oblique angles at the corners of the sensor (since the photosensitive part of each pixel is nearer the surface).

For reference, a7R III is BSI, not Stacked (multi-level).

There are ways of trying to address and work around the lower per-image light capture of small sensors (such as taking multiple exposures, as you say), but this is addressing the very basic 'how much light does your sensor get to create an image' and that's not inherently changed.

They don't explain that clearly; "F1.2 is not equivalent to F1.2 across different formats" should mention that it only really applies to full-frame lenses used on cropped formats with no focal reducer. A MFT lens at f/1.8 delivers f/1.8 worth of light to the sensor, end of story. A FF lens at f/1.8 on a MFT body delivers the equivalent of f/3.6 worth of light to the area covered by the cropped sensor. There are a number of things in the article that could use such clarification.

You're mistaken. An F1.8 lens delivers the same light per unit area to a sensor, regardless of sensor size or which format the lens was designed for.

But total light is more relevant than light per unit area, if you view or print the images at the same size. So an F1.8 lens delivers F1.8's worth light to an MFT's sensor, regardless of whether it's an MFT or FF lens. Let's call that light per unit area x photons per square mm, for, say a 1/100th exposure time. So "F1.8's worth of light" for an MFT sensor is 224x, since it's getting x photons per sq mm across its 224 square mm of sensor.

If you find a lens with the same angle of view for FF and set it to F3.6, you'll get 1/4 as much light during your exposure (F3.6 is 2 stops slower). In other words, 1/4x per square mm. But a FF sensor has a capture area of 864mm, so you capture 864 * 1/4x. In other words 216x in total. Hence your image is made from essentially the same number of photons, despite different F-numbers.

What is your source for these claims?

Which aspect are you querying?

So far as I can see, it all follows, so long as you're happy that f-numbers normalize illuminance (light per unit area). That seemed pretty uncontentious.

A 25mm f/1.8 MFT lens will gather the same amount of light as a 50mm f/1.8 MFT lens pointed at the same thing framed identically, assuming all other factors are identical. Crop factor does not apply to the light-gathering ability of the aperture; that is what the f-number loosely specifies. It's technically an approximation and is only correct for infinity focus, so closer objects have a lower working f-number; in that regard, the same focal length and aperture lens on MFT and full-frame will gather more light on MFT because the camera must be twice as far away for identical framing.

Using your logic, my Panasonic LX3 4.3x crop should gather 1/(4.3^2) or 0.054x the light of a f/2.0 FF lens. Tonight I took photos under an awning during late sunset with no direct sunlight. -2/3 EV, ISO 125-160, f/2, 1/30 sec; with 0.05x (4.3 stops less) light, why isn't it black? Would a FF cam have gotten away with 1/250 sec instead? Why do I have similar historic results on APS-C in similar lighting?

Because, like F-numbers, ISO is based around light per unit area.

Please read this article before responding.

The point is: you can either fixate on ISO and conclude that different formats have different depths of field and noise levels or you can consider the image-level as well as per unit area perspective and understand why.

You're comparing apples to oranges. I've gone farther than reading your article; 25mm MFT = 50mm FF with the same aperture in light-gathering. Are you going to tell me that doubling one side (the focal length -> field of view) when the other is halved does not equal one?

ISO is a loose standardization of camera gain and has nothing to do with raw light-gathering of the optical system that puts down the image circle to be captured. Sensor size *does not* affect light-gathering capability. Fundamental physics says so and so does the rest of the internet that isn't Tony Northrup and PetaPixel. Both assume crops of adapted FF lenses and that assumption is objectively erroneous. 50mm FF adapted -> 100mm, not 25 -> 50. Apples =/= oranges.

https://www.becomingintermediate.com/travel/2018/2/22/does-crop-factor-effect-focal-length-aperture-and-light-gathering
https://photo.stackexchange.com/a/32383/60340
https://digital-photography-school.com/making-sense-lens-optics-crop-sensor-cameras/

Sorry, I don't understand the point you're trying to make.

Those links all focus, either explicitly or by omission, on illuminance/light per unit area. So they overlook the per-image perspective.

I've provided examples and explanations, and you can test it for yourself (no need for adapting anything).

My point simple: light-gathering doesn't drop by sensor size for identical 35mm equivalent focal lengths, aperture, and framing.

A lens for MFT that's half the focal length and the same aperture as an equivalent FF lens will put down an image circle with the exact same amount of light. Both sensors get the same light. The mistake is assuming the same non-equivalent focal length is in use and has cropped framing on the cropped sensor as a result. Yes, that's less light gathered, but the "equivalence" then goes the other way.

You're trying to make the case that a FF sensor will receive 4x the light of an MFT sensor with lenses at identical 35mm equivalent focal lengths and apertures, and that is an objectively false assertion. Your first page 4 test demonstrates the assertion is false.

Now, do smaller sensors have more noise at the same settings? Yes, obviously; physics says they must due to simple photon randomness. That's not the same thing as how much light hits the sensor.

You need to be more specific about what you mean by 'same amount of light.' An F2 lens will project the same number of photons onto a Four Thirds sensor as a full frame F2 projects onto the central 224sqmm of its sensor, during the same exposure time. (Hence there's no difference between using a full frame 25mm F2 and an Micro Four Thirds 25/2 on the same sensor).

I'm not saying the same focal length gives 4x the light (it would, but would only make sense if you were shooting a uniformly lit plain surface, which isn't really how photos work). I'm saying that a 50mm F2 on full frame will give the same angle of view as a 25mm F2 but, because it's projecting the same light per unit area, and your sensor is 4x larger, you'll get 4x as much light.

And you're absolutely right to say that the difference is down to photon shot noise. Since shot noise is the square root of the signal, increasing the signal by 4x means noise only increases 2x, which means you get a 2x improvement in SNR.

Though in a convoluted way, I think we've come to an understanding. I greatly respect your willingness to tolerate my arguments. Thank you. You're a gentleman if nothing else.

Very kind of you to take the time to respond.

Wow, that ended well!

Disagreements need not be disrespectful ;-)

The whole idea of equivalence is to take a "whole image" view, rather than worrying too much about individual pixels. Doing so doesn't mean that you're treating the whole sensor as if it were a solar cell: where each photon of light hits still matters, it just doesn't matter too much how much resolution you sample it in.

So, getting to the point you made on the other article, about aperture not changing and therefore exposure not changing. If by 'aperture' you mean f-number, then yes, sensor size does not change f-number.

However, sensor size changes the effect of the aperture, just as it changes the effect of the focal length.

So: a 50mm F1.4 is always a 50mm F1.4.

However, the field of view of a lens is changed by sensor size, as is the proportion of the projected light that you can capture: per the diagram at the top of page 2 of this article.

The exposure system, which used F-number and ISO, is specifically designed to work across formats, so masks what's happening.

So: no one is saying sensor size changes the spec of a lens, nor are they questioning that the standard exposure model works. Instead, we're suggesting you also consider the total amount of light you're capturing, rather than just the light per sq mm.

It shouldn't be controversial to suggest that an 85mm lens on full frame will give the same field of view as a 42.5mm lens on a Four Thirds sensor.

That's a completely reasonable thing to compare, since they're the lenses you'd need to shoot the same images from the same position.

So you can ignore equivalence, just worry about standard exposure and conclude that if both lenses were set to F2.4, you'd get same light per sq mm and hence 'require' the same ISO setting. Which would mean you had two images with different depths-of-field, different noise levels, different diffraction effects but the same exposure settings written in the EXIF field.

Which is fine. Not very enlightening, but fine.

So every square mm on both sensors got the same amount of light but each scene element is projected over four times as many square mm on the full frame sensor.

Now consider the whole image, rather than sq mm of sensor (this means putting the standard exposure model to one side for a moment).

If you set the two lenses to have the same absolute aperture size (let's say 34.5mm diameter). This way both sensors are seeing the same scene through the same sized hole.

This is an F1.2 aperture in the Four Thirds sensor's 42.5mm lens and it's an F2.4 aperture in the Full Frame camera's 85mm lens.

Now take the photos with the same shutter speed. The light intensity on the Four Thirds sensor is 4x higher but again, each element of the scene is being projected on 1/4 of the area, relative to the full frame chip.

In other words, the same number of photons describe each element of the scene. In which case, assuming both cameras' sensors are similarly efficient, both will capture roughly the same amount of light to describe each element in the scene, despite the 'exposures' being different.

I tried to explain the effect at the pixel level about four posts ago. I absolutely am not saying that you only need care about the value of the sum total of all light, but point two cameras at the same scene and what matters is how much light describes each object in the scene (however many pixels they're captured by).

For whatever reason, that's just words to me. I guess there's too much implicit that isn't obvious to me.

If you don't understand the relationship between focal length, framing, and sensor size, please start a thread on it in the Beginners Forum, and, with any luck, you'll not only get in depth explanations, but also a few examples.

I came up with that work-around thought experiment I included in my question, thanks. If there's no simpler way to understand it than that, I'm not interested. And maybe I'll accept the formula as obviously true going forward, having thought it through once. I thought it was worth posting though, since this is supposed to be an explanation for beginners, and for me it didn't quite work. I suppose the authors might tweak it, or tweak the next update, if they get enough complaints like this. Then again, maybe I'm uniquely obtuse.

Well, also there is this historical precedence where lens focal length was not list as a function 8x10, 4x5 or MF, or FF, etc film sizes...
Because these old film fogies knew a thing about focal length and aperture and things like that.

@ GEONYC

The reason is because the focal length (and actual relative aperture) that are written on the lens are the *actual* focal length (and relative aperture). It's the *effect* the focal length (and relative aperture) have on the photo that changes as a function of the sensor behind the lens, not the focal length (and relative aperture) itself.

So, if the industry wished to choose a particular format as an industry standard (and that standard need not be FF), they could *choose* to label the box the lens comes in with a list of the equivalent focal lengths (and relative apertures). the lens will have on all the different formats it is designed to be used with.

But isn't it simpler and easier just to multiply the actual focal length (and relative aperture) by the equivalence ratio (crop factor) if you want to know what the lens is equivalent to in another format?

Of course, for sensor other than FF is valid other size of circle-of-confusion (CoC), just D/C as writen in formula, but not emphasized in text, sorry. Always, standard size of CoC is 1/1440 of sensor resp. image diagonal. Image diagonal is assumed as standard view distance. CoC circle is seen so from about 2.4 angle minute, near of human eye resolution, in sense that all out of depth-of-field is sure in bokeh.

@minoltatron:

Re: "No, circle-of-confusion is based on pixel size, not sensor size."

Sorry, but you are mistaken -- this is not the case:

https://en.wikipedia.org/wiki/Circle_of_confusion

If you disagree, please feel free to start a thread on the matter in the Photographic Science and Technology forum, and there are many there who will be happy to explain in more detail.

@ minoltatron

You are still mistaken, but you clearly don't wish to understand why. That's far from unusual, especially in discussions that involve Equivalence.

まあいい。俺に関係ないでしょ。

oh arr!

:D

Oddly enough, I'm not going to re-write the entire article in an response clarifying a single point.

Yes, aspect ratios play a role: you can't actually take the same photo with a 4:3 camera and a 3:2 one (not without cropping one or the other). But that sounds a lot like trying to find threads to pull on, rather than acknowledging the bigger picture.

There is no such thing as equivalent speed. There may be equivalent DOF or equivalent FOV or even equivalent exposure.
Nikon 1 with f/1.2 is not going to result as good as FF (in terms of noise), even if there was a CX f/1.2 lens, because, to get the same "total light", it needs to be exposed for the same duration, in which case, Nikon 1 would be rather over exposed.
The "Equivalence" explains how the FF image may be made to look as bad as Nikon 1 image but not the other way round.
This is not about how FF is always better, however, as if you took J5 and D810 at ISO 160 and printed 4x6 size, it would be hard to tell apart. If you printed to 11x14, I think most can tell the difference, though. Then, there is J5 with CX 70-300mm combination to be compared to D810 with FX 70-300mm combination that puts more pixels on the darn duck...

DPR calls equivalent aperture in the chart to show equivalent F#; however, not quite the same thing. Aperture = Focal Length / F#. Actually, F# = FL/Aperture (diameter) but the mathematical equivalence actually works here.
So, 100mm f/4 and 50mm f/2 has equivalent aperture (equal) of 25mm; does that make f/4 equivalent to f/2?
I've been advocating to understand that the smaller sensor cameras have shorter FL lens that account for the difference in DOF calculation, rather than equivalent FL and F#. For example, DPR list equivalent FL and equivalent F# in their chart rather than emphasizing the FL of the lens on the camera.
BTW, F# are called "relative aperture" but I realize "equivalent relative aperture" seems rather cumbersome already.

F# = FL / Aperture diameter

eF# = eFL / Aperture diameter

Nothing about that suggests that f/2 is equivalent to f/4. You cannot make a statement about equivalence without context. F2 on one system can be equivalent to F4 on another system, but that's no more or less true (or more or less ambiguous) than equivalent focal lengths. The majority of people are comfortable with the ideal that, in one context, 23mm can be equivalent to 35mm, so they don't repeatedly ignore the context and say it's confusing.

And yes, the shorter focal length absolutely plays a role, just as resizing/magnification does, if you view all formats at the same size. But it's a multi-dimensional puzzle [focal length, aperture diameter, sensor size, shooting distance, output size, etc] so you have to decide which you're going to treat at fixed and which you're going to move, otherwise no one can make sense of anything.

If you think 30mph is equivalent to 60mph if you go half the distance, not sure what the context would be.
My point is that if one understood how FL, F# and sensor size (crop factor) affect FOV, DOF and noise, one will have better understanding than understanding FOV/DOF/noise as equivalence to FF. I'll shut up if you say I am wrong.
However, if I may add, F2 and F4 are not equivalent even if both result the same for different system. It's that the different systems becomes equivalent if it's parameters are set so that the result looks the same.
So FF and mFT are equivalent if different FL, F# and ISO result in the very similar (equivalent) image when viewed at the same size.
I realize we are arguing the semantics but I think the semantics have consequences.
FWIW, I appreciate your willingness to engage.

It's primarily about defining terms, in order to being able to use them without long-winded explanations from then on. I see this article as defining the term "equivalence" for systems with different sensor sizes (I don't mind if it defines it for the first time, it's nicely compact and illustrative).

Nikon's FX cameras are sold with a kit lens 24-85mm f/3.5-4.5. The equivalent CX kit lens would be 9-31mm f/1.3-1.7, not 10-30mm f/3.5-5.6. It would make no sense anymore to compare ISO 3200 on FX with ISO 3200 on CX; compare with ISO 440 on CX instead.

My point is that it is a pity if a promising system like Nikon 1 possibly dies, just because people don't understand (or don't respect) equivalence.

Regarding APS-C sized DX, people just seem to be waking up since Sigma released their f/1.8 zoom lenses that enable results equivalent to using f/2.8 zoom lenses for full frame.

If we're going to be pedantic about semantics (not something I'm necessarily against), then yes, 'F2' cannot be equivalent to 'F4.' However, a specific F2 lens on a specified system can be equivalent to another lens that's F4 on another system.

@mostlyboringphotog - almost everybody uses, and most people understand equivalent focal lengths. And I'd be happy to include in the 'understand' group those who are unclear on the subtlety between a crop changing the focal length and a crop changing the effect of a focal length.

That's something that it's too late to push back against. Every manufacturer discusses and promotes equivalent focal lengths, usually on compact cameras.

So it's already commonplace to say that a 50mm lens behaves like a 135mm lens on CX format.

Adding equivalent apertures/equivalent f-numbers is no different, beyond a more pressing need to know that (because exposure is built on actual F-numbers) its the effect that changes, not the underlying property.

However, since your proposed 50mm F2 lens, mounted CX, would offer the same angle of view, depth of field, diffraction and total light for the same shutter speed as a 135mm F5.3 on full frame (and the only way in which they're different is in terms exposure terminology), then it seems entirely legitimate to say they are equivalent.

Equivalent doesn't mean 'identical to' but, since a 50mm F2 on CX will have more in common with a 135mm F5.6 than a 135mm F2, it's the more comparable referent point.

Conversely, saying 'it's still a 50mm F2 and you just have to learn what that means on CX' is unhelpful to the point of perversity, when in so many respects it behaves like an F5.6 version of the 135mm lens (on full frame) that most people would already compare it to.

So long as people are clear when they're using equivalent F-numbers and are clear that they can't be used in the conventional exposure model, it's a useful means of understanding the performance envelopes of different systems.

OMG years later and it's still this same confusion. It is EXACTLY in terms of "conventional exposure model" where a 50mm f2 on CX is equivalent to a 135mm f2 on FX.
Shooting a 50mm f1.4 on a CX body is EXACTLY like shooting a 50mm f1.4 on FX cropped by 2.7x.

It doesn't behave like a 135mm f5.6 because when you say something like that you end up with the kind of idiocy spouted by Tony Northrup that you cannot possibly shoot sports with the FZ200 because the lens is "equivalent to" a f16 lens and how can you possibly stop action with a F16 lens?

The DoF changes based on the crop as well but that's also a function of the crop and not because the aperture itself changed.

The reason I show those ones is to illustrate the effect of scaling to the same resolution (and hence the benefit of using the extra sensor area and its captured light).

Still here's a comparison between the 24MP APS-C sensor of the Nikon D5300 and the 24MP full frame sensor of the Nikon D750. The difference in sensor size should leave the D750 around one and a third EV better-off than the D5300. And, the results do appear to show its results are slightly better than when the D5300 is set 1EV lower.

As you'd expect, larger pixels usually give better pixel-level nois. But they play less of a role if you consider the whole image by comparing at a common viewing size.

And, as it says on the last page of the article (which covers noise):

"Differences in sensor... characteristics mean that, while it gives a very good guide, equivalence doesn't give a precise prediction of performance."

I'm not saying all sensors of the same size are the same, it's just that the differences in performance are (usually) smaller than the differences made by sensor size. A good Four Thirds chip may be better than a poor APS-C one. Equivalence shows the potential.

Richard, if you have to raise ISO under the circumstances you mention, that means you're gathering less light and need to compensate that loss through one of the exposure variables, so you're not really "capturing the same amount of light". You're trying to impose false notions on the readers. The 'equivalent aperture' theory is false.
Please circumscribe your ideas to the 'field of view' dominion - even if that is also debatable.

Two lenses of the same F-number project the same amount of light per unit area (this is easiest to recognise if you imagine them all being pointed at the same, evenly illuminated panel).

So, if you reduce the F-number by two stops, you get 1/4 as much light per unit area. However, if you then use a sensor with 4x the area, then you end up capturing the same amount of light in total.

Yes, the ISO rating is different but that's because the ISO number, by definition relates light per unit area to final image brightness. This disguises the reason that the two images, taken with equivalent apertures and the same shutter speed, will have the same depth-of-field, the same amount of diffraction and very similar noise levels, when viewed at the same size. (Because both sensors had access to the same amount of light).

The article has real-world examples showing this to be the case.

My BS detector has just overloaded.

In which case, I'd recommend recalibrating it. Perhaps by testing the principles explained here.

Looking at photography in terms of total light, rather than the light per unit area approach (that is necessary for the same exposure rules to work across different film formats/sensor sizes), may seem antithetical and alien, but that doesn't mean it's untrue.

Nobody is proposing that 'total light' be used to set exposure, however, it does provide a useful way to compare the performance evelopes of different formats.

Look at the examples in the examples in the article, try for yourself. It may not 'feel' right, but it stands up to scrutiny, both logically amd practically.

Thanks for the apology, it's appreciated.

As I say, the way we think about exposure (F-numbers and ISO, specifically) is designed to ensure that you don't notice any difference in exposure between your two systems. I'm not arguing against that or proposing that equivalence should be used in its place.

However, when you shoot at F22 on a Micro Four Thirds camera, you are shooting not at F44 but at the equivalent of F44. You'll get the same depth-of-field, and diffraction and very similar noise characteristics as shooting F44 on your full frame camera.

Let's, assume you're talking about a 100mm lens. F22 would be a 4.5mm aperture diameter. If you set up your full frame camera in the same spot, then you'd need a 200mm lens to give the same framing (putting to one side the 3:2/4:3 aspect ratio difference).

A 4.5mm aperture diameter in that 200mm lens would be an F44 aperture. It would project one quart as much light over every square mm of sensor but you are capturing/measuring light on 4x the number of square mm.

Consequently, you can look at it two ways:

You could increase the exposure time on the full frame camera and conclude the full frame camera is less noisy at the same ISO.

Or you could keep the shutter speed the same, use a higher ISO and note that you've got two images which are virtually identical (D-O-F, diffraction, noise), except for the ISO rating.

If you're not satisfied with the examples in the article and you have access to both a full frame and a Micro Four Thirds camera, then send me a private message and we can discuss ways for you to test this to your own satisfaction.

Just to be clear, I'm not suggesting that, day-to-day, you change the way you shoot either camera, I'm just saying that it helps you understand their relative strengths.

Ok, let's take it back to brass tacks:

Just as equivalent focal lengths tell you the angle of view of one system relative to another, equivalent f-numbers tell you about the effect of the aperture size, relative to another system.

However, because F-numbers and ISO are based around light-per-unit area, not total light, equivalence is not necessarily helpful for setting exposure.

So you can either ignore equivalence and just think that larger sensor cameras are somehow less noisy and can offer shallower depth-of-field, or you can try thinking in terms of equivalent apertures and understand how much of a difference there is between systems, so that you can fully understand the size/price/IQ balance each one strikes.

I get your point Richard. Sometimes I forget how clean high ISO adds another dimension to exposure.

For m4/3 you have only two options to try to compete in low light with FF. First, you can simply drop ISO by several stops. This requires slower shutter and/or faster lenses, and if subjects are moving at all only faster lenses will do.

But you can do that for FF too, and so it is never a fair fight. But for those who want to shoot only m4/3 you just live with these limitations. This is why, after living with m4/3 only for years, I have just acquired a D600. Sometimes you get tired of bringing knives to gun fights.

Most m4/3 cameras have more problems acquiring focus in low light than FX cameras, thus the fight would be lost before it began!

I would like to add to the above, that you can focus m43 cameras in rooms so dark you have to use a one second long or longer shutter speed. They focus fast and accurately in these conditions. The 5-axis in-body image stabilization is so good, you can do this hand held with no problem. Very few ASP-C or FF cameras can do this without a tripod. The images turn out clear and sharp. I have good images taken wiht m43 cameras at ISO 25,000 as an example of focusing in low light. Had no problem doing this. If you look around, you can find a lots of examples of street shooting at night with these cameras at night. You can find low light comparisons with ASP-C and FF cameras. How could you compare them in low light if the M43 camera didn't focus? There would be nothing to compare.

The only reason APSC appears to have more depth of field is because for the same angle of view an APSC camera uses a shorter focal length lens. But the APSC image needs to be enlarged more in post than the FF. That also enlarges the out of focus circles of confusion of the APSC image more than the FF image. So typically, FF has better resolution than APSC. But in real life use they are now both so good that it's hard to see the difference unless extreme enlargement is made. The easiest way to avoid diffraction is to avoid apertures between 11 and 22 with almost any lens, especially shorter focal length lenses that crop sensor cameras typically require. That is because the thickness of the diaphragm blades become more of an issue with smaller diameter openings. If you require more depth of field just put up with some loss of definition or use a tilt shift lens and enable maybe f5.6. As a rule of thumb 5.6 is the sweet point for resolution with most lenses. It's not that complicated.

Shoot a scene through the same aperture size (let's say 25mm diameter) with two cameras with the same view of the scene.

On one sensor this is with a 100mm lens (so it considered F4), on the other, with a smaller sensor, a 50mm lens gives the same angle of view (so is an F2).

Let's assume they're the same pixel count (though it matters less than you might assume), and view them at 100%, on your monitor.

Both will have the same perceptual depth of field.

Almost as if a 25mm aperture in a 100mm equivalent lens does a very similar thing to a 25mm aperture in an actual 100mm lens.

How is that more complicated than thinking about enlargement (which requires you knowing the size of the individual pixels in your camera)?

F16 on a 50mm lens on Four Thirds will experience the same amount of diffraction as F21 on a 67mm lens on APS-C and F32 on a 100mm lens on full frame, so I'm not sure your "between 11 and 22" advice works well across formats.

Absolutely true: there's no difference between shooting with an APS-C camera and shooting with the APS-C region of a larger sensor. I've not ever said otherwise.

However, a full frame camera in APS-C mode produces a noisier image with less depth-of-field than it would shooting using its whole sensor with a lens with the same F number and the same field of view.

Equivalence doesn't have anything to do with full frame.

The 35mm film format is used as a reference point because it was the de facto standard of the film era, so it became near-universally adopted when the digital age brought a proliferation of formats to the mass market.

Equivalence doesn't favour any format over another.

Physics says that larger formats can produce better IQ because they can capture more light, but that shouldn't be surprising or controversial.

Well I use both FF and APSC cameras. I sometimes use a cellphone camera too. One is not better than the other. They are each different in some ways. Just like a carpenter uses different saws. Rip saws or crosscut etc.
And a FF sensor only "gathers" more light because it has a bigger frame to fill. Each corresponding square mm of a FF sensor will receive exactly the same amount of light as an APSC sensor. ( in the same conditions)

It's important because it makes clear that the amount of light is what gives you the same amount of noise (because, in most tones and for most regular photography, shot noise from the amount of light is the main cause of noise).

The point being that, yes, if you want your JPEG to be the same brightness, you'll need to increase the ISO setting, but that this in and of itself isn't adding noise (which is a widely held misunderstanding).

If you're in a situation where you can increase the shutter speed, then you'll be able to produce a cleaner image with the FF camera, because you'll be giving it more light.

My point would be that total light (which takes sensor size into account) is the primary determinant of noise.

(It actually works pretty much irrespective of pixel count, but it's easiest to think about with the same pixel count).

The S/N of the sensor is a function of the the individual pixel size not the sensor size. A FF sensor with the same size pixels as a 1" sensor will have the same S/N as a the 1" sensor.
Averaging pixels when printing will yield an advantage in S/N of the larger sensor.

Total light reaching the larger sensor vs the smaller sensor is nonsense when discussing S/N of the sensor. DPreview should know better.

The entire article is intentionally written without reference to pixel size, to avoid reinforcing the widely-held misconception about the importance of pixel size.

If the larger sensor has the same number of pixels, then its image is cleaner. The light per unit area is the same and each pixel has a larger area. However, hold onto that thought before concluding that pixel size is the root cause of the difference.

If the larger sensor has the same sized pixels, then as soon as you view or print the images at the same size, you end up combining pixels from the larger sensor and it's still better (broadly speaking, by around the same amount).

In both cases, irrespective of pixel size, the image quality of the larger sensor is better in direct proportion to how much bigger the sensor is. At which point, rather than ascribing the difference to 'pixel size' in one example and 'averaging' in the other, doesn't it make sense to recognise the total light available is the underlying cause?

No problem.

Ultimately all of this is background theory - differences between sensor technology can and will have an impact. For instance, I'm not saying that four smaller pixels combined will be better than one large one, just that the contribution from shot noise will be essentially the same and the differences made by read (electronic) noise will be small, such that the final result will be very similar.

Ultimately this article should (I hope) make it clearer why the total amount of light captured makes so much difference (because most of the noise in your images is from the light you captured).

Thank you for devoting so much time to this and for giving me the benefit of the doubt. It does run counter to the way 'exposure' is usually discussed, so does seem to contradict what many people have been taught. Keep pulling the threads and you get to see another perspective, I think.

Light is both a wave and a particle but that's not being contradicted by anything here. You're complaining about counting photons? The photon's wavelength is relevant when the aperture's physical dimensions restrict resolution or the photo-sites are smaller than the waveform aka diffraction. Wave effects arrive in diffraction, which is another equivalence that equivalent aperture can highlight using the crop ratio squared. Within the diffraction limit, referring to light in it's particle sense is the most straightforward.

I think maybe this would be a way to explain it to more physics inclined folks: The diffraction resolution limit of the light is proportional only to the physical aperture (equivalent f-stop calcualted by crop^2*fstop), not the ratio of aperture to it's focal length (fstop). The information projected from the lens on the sensor is related to the aperture not the size of the projection (sensor size). Larger sensors can extract more information proportionally by size.

Let’s use your argument but instead of digital we use film
I have 2 cameras, one is the 35mm and the other is 6x7 and I load the same film(same generation of sensor) into both.
I select the same DOF & FOV for both cameras and in doing so the larger format camera I have to select a slower shutter speed to accommodate the more light I am able to put on to that film. This is the opportunity.
Now if I want to put the same amount of light into the 35mm camera to do this I have toselect a slower shutter speed the same as what I used in the 6x7 camera, what will happen to the image in the 35mm camera.
The opportunity arises for the larger camera if you cannot find a slower film to accommodate that longer shutter speed of the larger format

@kpaddler - The reason I wrote 'opportunity' is precisely because there are differences in sensor performance. These tend to be small, compared to the differences between common sensor sizes (especially if you're comparing sensors of a similar vintage).

However, I didn't want to make any assumptions about sensor performance, so merely stated that the extra light is there, giving the sensor the opportunity to capture it, rather than stating that the larger sensor will capture the extra light.

This is precisely why I wrote, at the end:

"Differences in sensor and lens characteristics mean that, while it gives a very good guide, equivalence doesn't give a precise prediction of performance."

And why we talk about the images being equivalent, rather than identical.

@Richard.

I think I understand what you mean. But not sure if the article actually clarify anything, I actually think there is more than one aspect to clarify. One of the reasons I picked at your article is that, after decades of playing with the toys of all formats, I thought replacing one of my older dslr bodies with a low end medium format, maybe. But I have not any one simple reason or rule that would tell me inherently the bigger sensor will win the highest total score.

And that's why I don't agree with a generalization of the larger sensor makes life easier to get the better quality....years ago while on a personal photo shoot in the Badlands I learned my $400 olympus c4040 took much better pictures than my 15k Linhof outfit, because the Linhof served better as sail in the wind than a steady camera in the wind. So, every format has its straighten but not everything sums up to positive value.

Equivalence can only tell you the potential for each camera or format, it can't possibly tell you whether it fits your needs.

As soon as the Fujifilm GFX 50S becomes available, we'll be closely comparing that to cameras such as the D810 and a7R II to see what you do and don't gain from that larger sensor, given that all the lenses are F2 or slower (F1.58 equiv, in 35mm terms).

The article tries to make clear that equivalence tells you the depth of field difference but that in terms of quality it only provides a framework for understanding the magnitude of difference that can exist, not the precise difference that does.

"Total light" is a misleading statement in terms of noise performance.

If you have two sensors with the same exact performance and pixel density, but different sizes, then a lens with a T-Stop of say something like a 1.2 should yield the exact same exposure and noise performance. The photosites on the smaller sensor are not individually influenced by the extra photosites of the larger sensor

For example, if you have a 3x3 grid of photosites with the exact same noise performance, a lens with a T-Stop of 1.2 will yield a certain level of performance on this 3x3 grid for each individual photosite. If you then have a 9x9 grid of photosites with each photosite having the exact same performance as the individual photosites of the 3x3 grid, then a lens with a T-Stop of 1.2 will yield the exact same level of performance on the 9x9 grid for each photosite. Adding more total photosites does not improve the performance of each individual photosite. For both sensors, the noise performance is at the photosite level, hence "total light" (i.e. a larger grid of photosites) does nothing to increase performance.

Now, if you have two sensors of the same pixel density and and noise performance, but they are different sizes, then the larger sensor will have more resolution. When you downsample the larger format image to be the same resolution as the smaller sensor, the appearance of noise is reduced because the individual samples of noise are downscaled. This is why when all things are equal, the larger sensor produces apparent cleaner images when downscaled to the cropped sensor.

Again, I don't believe total light has anything to do with noise performance, because each photosite is independent of each other photosite.

rfsIII - larger sensors (of the same pixel count) do place lower demands on lenses but I'm struggling to see any reason why sensor size requires any change of distance for a given field of view.

Jared Caldwell - The entire article is intentionally written to be independent of pixel size or count, since this makes very little difference.

Imagine two sensors of the same pixel count. One is bigger than the other. Print both images at the same size and you could say the larger sensor has better noise because its pixels are bigger.

Now imaging two sensors with the same pixel size. One bigger than the other. Print them both at the same size and you combine the captures of multiple pixels such that the effective pixel count is the same. You could attribute the better quality of the larger sensor camera to having captured more samples.

It should be apparent that the underlying cause in both instance is the additional light.

I'm not suggesting that photodiode design scales perfectly or that all sensors have the same performance (the the difference may be smaller than you think).

The difference in size between most sensor classes, 1/2.3"-type, 1"-type, Four Thirds-type, APS-C, Full Frame or 44 x 33 medium format tends to be much greater than the differences in overall sensor performance between sensors of a similar vintage.

This article only claims the images will be similar (hence equivalent, not equal).

You can't disprove the idea of total light by taking a per-pixel perspective (by its very nature, total light requires you to consider the entire image).

So, in your 3x3 vs 9x9 pixel example, you need to fit a different lens to the 9x9 grid so that both sensors 'see' the same image.

At which point, although each pixel gives the same performance, one camera is concentrating nine pixels on a part of the scene, for each 1 pixel the other camera is. As soon as you view or print the image at the same size, you'll combine the samples from multiple pixels in the larger sensor and get a cleaner image.

Downscale an image and you combine pixels and no, they don't combine to create brighter pixels, but you essentially average-out the error in each pixel. It's the same effect (but to a lesser extent) of shooting the same frame multiple times and combining them. You don't necessarily create a brighter image, but you do create a cleaner one.

And, though I could be wrong on this, I believe light fall-off is assessed from the light source to the film plane. As such, the distance from the lens to the film plane is a tiny fraction of that distance, such that small differences between cameras make essentially no difference.

@Jared - the root cause is the amount of light. The point is, that it doesn't matter whether you have a large sensor with more (but smaller) pixels or the same number of pixels. When you downscale a digital image, you merge the data from different pixels into a new superpixel, whose SNR is better than the SNR of the separate pixels and is usually very similar to the result from originally capturing with a single, larger pixel.

Shot noise is the primary source of noise in most photography and shot noise is a function of the amount of light you captured. The examples in the article I linked to illustrate this fairly well.

@kpaddler - That's a different topic. I was purely responding to your comment about light fall off, not all possible optical considerations of different flange distances. Nothing I've written diminishes the importance of good lens design though thankfully the precision nature of sensor fabrication eliminates the concerns about capture plane uniformity*.

Richard, I still don't see how total light affects the noise characteristics of an image based on your argument. The affects of apparent noise reduction due to downsampling is a property of resolution, not total light.

If you took a smaller sensor with higher resolution and a larger sensor with lower resolution, and they both had similar noise handling (maybe a newer small format sensor vs an older large format sensor), then the image with the highest resolution would downscale and have less apparent noise. By your logic, the larger sensor captured more total light because it has a greater surface area, therefore should render a cleaner image when shown at the same size as a smaller sensor that captured less total light.

Regardless, I've made my points, so I'm excited to just read and see how the thread continues. No need for me to keep repeating myself. Thanks so much for the responses!

Jared - the root cause of why downsampling imprives noise is that signal rises faster than noise, when you do. Which itself comes from the amount if signal (light) you captured in the first place.

In your proposed example, the larger sensor would look better (broadly in proportion to the size difference). Downscaling the high res small sensor would improve its apparent noise performance, but not beyond the result that you'd get from shooting natively at the resultion you've downscaled to.

Kpaddler - everything I can find about depth-of-focus suggests it's a question of tolerance to misalignment elsewhere in the optical path. As I say, since digital sensors are much more uniformly flat than film, the remaining causes of misalignment would appear to be 'manufacturing tolerances in terms of sensor alignment, lens mount alignment or lens construction.'

Note i did not say lens quality.

If the images are printed viewed at same size and DPI/PPI, using a good resampling algorithm, the pixel density of the sensor module will be equalized to the same pixel density.
The effect/benefit of more light collected by a larger sensor module is same as the larger films size not being enlarged as much as the smaller film size,
If the viewing images are enlarged by the same factor, the noisiness of the viewing image will be about the same.
Also, the dominant noise source is the shot noise, and the image noisiness increases with the decrease in exposure.

"Also, the dominant noise source is the shot noise, and the image noisiness increases with the decrease in exposure."

To avoid confusion, it's more accurate to say that image noiseiness increased with a decrease in total light (since you can shoot at a lower exposure on a larger sensor and get the same amount of total light, and hence shot noise).

As you point out, shot noise is directly related to the total number of photons which is what total light is telling you.

If thinking in terms of maginification works for you, that's fine but the total amount of light is clearly the fundamental cause.

Thanks for the reply, and great read with that link, but I think I am more confused but I think I am starting to understand what you are saying. If we take a picture in low light with a cell phone, and we 'standardize' the same picture with a SLR by lowering the f-stop and increasing shutter speed to match the cell phone, we are then going to have essentially the same picture even though the sensors are of different size and pixel size/density may be different because at the end, the single most important factor is the amount of light hitting the sensor, and everything else essentially does not matter?

The amount of light hitting the sensor is by far the most significant factor.

Consequently, if, on a larger sensor, you can open up the aperture more, then you can probably capture more light and get better image quality.

Yes but that is not how people use it and misuse on these forums. Surely you must be aware of that.

Thanks for the quick reply! So it seems my misunderstanding has come in believing the 50 & 100mm equivalents would be placed at different distances from the model to achieve the same shot size due to their focal length, when in fact, due to their field of view, they would be placed in exactly the same spot. In their natural field of view (ie. inequivalent - both shot full frame) they would be at different distances to achieve the same shot size, and thus "feel" different, but not in their equivalent. Which means the "feel" is more determined by field of view, not focal length. (Of course other things influence feel - subject, light etc - I am just trying to understand the role of the lens in it).

Ah, I see.

The statement isn't inherently wrong. Since a 100mm equiv field of view will be the same as a 100mm on 35mm, then to get the same framing, you must be in the standing in the same place (and hence get the same perspective).

It's been a while since I wrote this but I was actually trying to dismiss the common misunderstanding that perspective is connected to focal length (there are still a lot of people who think a 50mm lens has a specific 'look' and level of perspective distortion).

I'll see if I can make it less ambiguous.

I did also try to make clear that equivalence is primarily a means of understanding one system relative to another - not for day-to-day shooting. Personally I find it most useful when trying to explain the differences in capabilities between enthusiast compacts, many of which have F1.8-something lenses but are built around a variety of sensor sizes.