Crop sensor effect on apertures

[Great Bustard]

Ya have to admit, though, that "Great Bustard" is a classic nick! It would be a shame if that one got capped, too.

But you would also have the option of coming back as Otis ( http://en.wikipedia.org/wiki/Great_Bustard ).

The problem is that people would associate "Otis" with "Great Bustard", but not with the "typo" of my current nick.

 

[mattr]

A Mathematician, a Biologist and a Physicist are sitting in a street cafe
watching people going in and coming out of the house on the other side
of the street.

First they see two people going into the house. Time passes.
After a while they notice three persons coming out of the house.

The Physicist: "The measurement wasn't accurate.".
The Biologists conclusion: "They have reproduced".
The Mathematician: "If now exactly 1 person enters the house then it will be
empty again."

 

[iljai]

But it's not that uncommon to look at pictures taken by cell phone on it's screen while pictures taken by dslr usually printed or transfered to computer and watched on big screen. As soon as you ask what picture looks better you're doing exactly this - comparing images of different sizes taken with different systems.

...what conclusion would you make comparing the photos at the different sizes?

I allows me to find out what causes the difference I saw and make me better understand processes involved instead of remembering another rule of thumb.
http://forums.dpreview.com/forums/read.asp?forum=1029&message=37459152

For me its more convenient when I understand what I'm doing. For others more convenient may be to follow written recipes.

So, does cropped body differ only by FOV? And doesn't the dof, effective FL and effective aperture are the consequences of the way we decided is convenient to compare them?

http://forums.dpreview.com/forums/read.asp?forum=1029&message=37453545

Carlk's take is not incorrect, it is simply a different perspective on the issue which I, personally, find less useful. That is, I think it's more useful to say that, for example, 200mm f/2 on 1.6x is equivalent to 320mm f/3.2 on FF than it is to say that 200mm f/2 on 1.6x has a framing that is 1.6x tighter than on FF.

And here we are back to convenience. For experienced photographer who shot a lot with film or own both bodies its convenient to remember that aps-c increases FL and stops aperture (in dof terms). For new photographer with single body this equivalent FL and aperture may be confusing like the OP showed and it may be more convenient to think about cropped body in terms of reduced fov. He can't compare pictures directly anyway so it becomes very theoretical matter for him.

 

[Great Bustard]

...what conclusion would you make comparing the photos at the different sizes?

I allows me to find out what causes the difference I saw and make me better understand processes involved instead of remembering another rule of thumb.
http://forums.dpreview.com/forums/read.asp?forum=1029&message=37459152

For me its more convenient when I understand what I'm doing. For others more convenient may be to follow written recipes.

I think it's a lot easier to understand the differences when photos are compared at the same dimensions. For example, I wouldn't compare a 100% crop to a resized-for-web photo fret over the 100% crop being softer.

That is, it's easier to understand the differences between the performance of two cars on the same track, rather than on different tracks.

So, does cropped body differ only by FOV? And doesn't the dof, effective FL and effective aperture are the consequences of the way we decided is convenient to compare them?

http://forums.dpreview.com/forums/read.asp?forum=1029&message=37453545

Carlk's take is not incorrect, it is simply a different perspective on the issue which I, personally, find less useful. That is, I think it's more useful to say that, for example, 200mm f/2 on 1.6x is equivalent to 320mm f/3.2 on FF than it is to say that 200mm f/2 on 1.6x has a framing that is 1.6x tighter than on FF.

And here we are back to convenience. For experienced photographer who shot a lot with film or own both bodies its convenient to remember that aps-c increases FL and stops aperture (in dof terms). For new photographer with single body this equivalent FL and aperture may be confusing like the OP showed and it may be more convenient to think about cropped body in terms of reduced fov. He can't compare pictures directly anyway so it becomes very theoretical matter for him.

Gotcha covered:

http://www.josephjamesphotography.com/equivalence/#introduction

• Equivalence is only relevant when comparing different formats. For example, if we are comparing the performance of a 50mm lens designed for 135 (35mm FF) to a 50mm lens designed for APS-C or 4/3, both lenses being used on the same camera, Equivalence does not come into play.

 

[Great Bustard]

Let's describe the "logic" that we often see on DPR:

A stats professor plans to travel to a conference by plane. When he passes the security check, they discover a bomb in his carry-on-baggage. Of course, he is hauled off immediately for interrogation.

"I don't understand it!" the interrogating officer exclaims. "You're an accomplished professional, a caring family man, a pillar of your parish - and now you want to destroy that all by blowing up an airplane!"

"Sorry", the professor interrupts him. "I had never intended to blow up the plane."

"So, for what reason else did you try to bring a bomb on board?!"

"Let me explain. Statistics shows that the probability of a bomb being on an airplane is 1/1000. That's quite high if you think about it - so high that I wouldn't have any peace of mind on a flight."

"And what does this have to do with you bringing a bomb on board of a plane?"

"You see, since the probability of one bomb being on my plane is 1/1000, the chance that there are two bombs is 1/1000000. If I already bring one, the chance of another bomb being around is actually 1/1000000, and I am much safer.

 

[mattr]

Let's describe the "logic" that we often see on DPR:

A stats professor plans to travel to a conference by plane. When he passes the security check, they discover a bomb in his carry-on-baggage. Of course, he is hauled off immediately for interrogation.

"I don't understand it!" the interrogating officer exclaims. "You're an accomplished professional, a caring family man, a pillar of your parish - and now you want to destroy that all by blowing up an airplane!"

"Sorry", the professor interrupts him. "I had never intended to blow up the plane."

"So, for what reason else did you try to bring a bomb on board?!"

"Let me explain. Statistics shows that the probability of a bomb being on an airplane is 1/1000. That's quite high if you think about it - so high that I wouldn't have any peace of mind on a flight."

"And what does this have to do with you bringing a bomb on board of a plane?"

"You see, since the probability of one bomb being on my plane is 1/1000, the chance that there are two bombs is 1/1000000. If I already bring one, the chance of another bomb being around is actually 1/1000000, and I am much safer.

This professor has his basic concepts totally confused. He should google "conditional probability". Or even better he should stop posting and go out to take some pictures.

 

[dsjtecserv]

Ya have to admit, though, that "Great Bustard" is a classic nick! It would be a shame if that one got capped, too.

But you would also have the option of coming back as Otis ( http://en.wikipedia.org/wiki/Great_Bustard ).

The problem is that people would associate "Otis" with "Great Bustard", but not with the "typo" of my current nick.

We could always find you on Facebook: http://on.fb.me/fSrb58

Dave
--
http://www.pbase.com/dsjtecserv

 

[Great Bustard]

Ya have to admit, though, that "Great Bustard" is a classic nick! It would be a shame if that one got capped, too.

But you would also have the option of coming back as Otis ( http://en.wikipedia.org/wiki/Great_Bustard ).

The problem is that people would associate "Otis" with "Great Bustard", but not with the "typo" of my current nick.

We could always find you on Facebook: http://on.fb.me/fSrb58

I guess I should get a Facebook account!

 

[Great Bustard]

No : because the DOF is only a matter of aperture, focal and distance to the subject. From the compact camera to the big format, these rules never changes.

By "aperture", do you mean "f-ratio" or the actual aperture diameter? No worries either way -- DOF has more variables than aperture, focal length, and distance to subject:

http://www.josephjamesphotography.com/equivalence/#dof

Yes, because at equal framing, when you want to shot a portrait at 10 feets (or whatever distance) you will have to use a 100 mm with an APS C camera, and a 160 mm with the FF.

But what if you just used 100mm on both and got closer with FF? These scenarios, and more, are described in the box at the above link (scroll down a bit).

In a physical point of vue, the 160 mm at equal distance from the subject, as smaller DOF than the 100 mm, hence, the 1,3 stop difference in term of DOF.

The 1 1/3 stop differential is because the diameter of the aperture is 1.6x larger on FF for the same perspective and framing, assuming the photos are displayed at the same size.

 

[iljai]

...what conclusion would you make comparing the photos at the different sizes?

I allows me to find out what causes the difference I saw and make me better understand processes involved instead of remembering another rule of thumb.
http://forums.dpreview.com/forums/read.asp?forum=1029&message=37459152

For me its more convenient when I understand what I'm doing. For others more convenient may be to follow written recipes.

I think it's a lot easier to understand the differences when photos are compared at the same dimensions.

To saw the difference - yes. To understand what caused it no.

And how you'll figure by what caused difference in dof when you compare different system with requerment for same result size, same perspective, same framing? All of those affect dof. To make it even more interesting requerment for same size and same perspective/fov both affect dof but in oposite way. To separate which requrement causes what effect you do this, compare at different fov, compare at different sizes, etc.

For example, I wouldn't compare a 100% crop to a resized-for-web photo fret over the 100% crop being softer.

If you'll do you would find that scaling down image increase dof. Or requirement to compare at the same size of image from cropped body and ff causes change in dof not "cropped" body itself.

That is, it's easier to understand the differences between the performance of two cars on the same track, rather than on different tracks.

And those cars have different tires, engines, aerodynamic, fuel, finally they're driven by different drivers. Can you be sure that this car definitely better than another. So distant analogies causes much more confusion than resolve.

So, does cropped body differ only by FOV? And doesn't the dof, effective FL and effective aperture are the consequences of the way we decided is convenient to compare them?

http://forums.dpreview.com/forums/read.asp?forum=1029&message=37453545

Carlk's take is not incorrect, it is simply a different perspective on the issue which I, personally, find less useful. That is, I think it's more useful to say that, for example, 200mm f/2 on 1.6x is equivalent to 320mm f/3.2 on FF than it is to say that 200mm f/2 on 1.6x has a framing that is 1.6x tighter than on FF.

And here we are back to convenience. For experienced photographer who shot a lot with film or own both bodies its convenient to remember that aps-c increases FL and stops aperture (in dof terms). For new photographer with single body this equivalent FL and aperture may be confusing like the OP showed and it may be more convenient to think about cropped body in terms of reduced fov. He can't compare pictures directly anyway so it becomes very theoretical matter for him.

Gotcha covered:

http://www.josephjamesphotography.com/equivalence/#introduction

• Equivalence is only relevant when comparing different formats. For example, if we are comparing the performance of a 50mm lens designed for 135 (35mm FF) to a 50mm lens designed for APS-C or 4/3, both lenses being used on the same camera, Equivalence does not come into play.

An't we compareing different formats? When we state that 200/2 on aps-c behave like 320/3.2 on ff aren't we talking about equivalence?
Or what was that about?

 

[Great Bustard]

I think it's a lot easier to understand the differences when photos are compared at the same dimensions.

To saw the difference - yes. To understand what caused it no.

Sure. The understanding is in the math and physics, the verification is in the seeing.

That is, it's easier to understand the differences between the performance of two cars on the same track, rather than on different tracks.

And those cars have different tires, engines, aerodynamic, fuel, finally they're driven by different drivers. Can you be sure that this car definitely better than another. So distant analogies causes much more confusion than resolve.

If we are comparing two systems based on the IQ of the photos, then there are a huge number of variables that need to be considered, not the least of which are the scene and the skill of the photographer in not only capturing the scene, but in processing the capture into a photo.

However, I wouldn't intentionally compare two photos with different perspectives, different framing, different DOF, different shutter speeds, and with different display sizes unless I specified a reason for doing so.

For example, let's say we are comparing the IQ of two systems for landscapes. Why would I need to use the same DOF on both systems when the entire scene is likely within the DOF even wide open? I'd select the sharpest aperture for both. Furthermore, why would I be concerned with shutter speed if the light is good and/or using a tripod? Motion blur is rarely an issue for landscapes.

But, I would have to acknowledge that my conclusions were only valid for that particular scenario.

And here we are back to convenience. For experienced photographer who shot a lot with film or own both bodies its convenient to remember that aps-c increases FL and stops aperture (in dof terms). For new photographer with single body this equivalent FL and aperture may be confusing like the OP showed and it may be more convenient to think about cropped body in terms of reduced fov. He can't compare pictures directly anyway so it becomes very theoretical matter for him.

Gotcha covered:

http://www.josephjamesphotography.com/equivalence/#introduction

• Equivalence is only relevant when comparing different formats. For example, if we are comparing the performance of a 50mm lens designed for 135 (35mm FF) to a 50mm lens designed for APS-C or 4/3, both lenses being used on the same camera, Equivalence does not come into play.

An't we compareing different formats? When we state that 200/2 on aps-c behave like 320/3.2 on ff aren't we talking about equivalence?
Or what was that about?

I was discussing your comment above about a "new photographer with single body". When I used a 20D (1.6x), I didn't think in terms of FF. But, when I wanted something with more IQ (5D), I compared them in terms of equivalent settings to see what the 5D would give me that the 20D would not.

 

[iljai]

If I scale them to the same size it's different story but again it's not because of bodies but of what I did to images.

But that means you have different sized final images, whether on paper or on screen.

Sorry, I misunderstood you previous statement. Yes final image on screen or paper is different but what image size has to do with body? Its screen or paper - i.e. parameter of final image, but my statement was that croped body differs from ff body only in FOV. How "image size" could be characteristic of the body?
And difference if FOV exist even before you get any image at all.

Compensating FOV while keeping perspective, framing and resulting image size are the way photographers use different systems so it makes it practical to compare that way. But it is what it is - the way to compare not characteristic of system itself. And result depends of both characteristics of the systems and the way comparison made.

And doesn't the dof, effective FL and effective aperture are the consequences of the way we decided is convenient to compare them?

Not convenient - realistic. In reality, I don't choose my final print size based on the size of the sensor used to capture the image.

May be it's exactly in reverse? Knowing what size of image you'll require (for publishing or work, etc) you choose the body?

Usually not. For example, I shoot weddings with a 5D and a 20D. The client doesn't know which was used for any particular shot, and their selections of print sizes are not in any way based on the sizes of the sensor in the camera.

But you didn't took neither phone nor compact (there's both with 8 mp sensors).

Because both dslrs capable to produce good images of required sizes and cell phone and compact don't. Yes I agree usually printing size doesn't choosen by sensor size. But it's not that impossible too.

I'm sorry I forgot to put smile in the previous post. It was partially a joke and I didnt' intend to direct conversation away from the main topic by it.

 

[Lee Jay]

Compensating FOV while keeping perspective, framing and resulting image size are the way photographers use different systems so it makes it practical to compare that way.

Exactly.

But it is what it is - the way to compare not characteristic of system itself. And result depends of both characteristics of the systems and the way comparison made.

Right, but it's also the way things get used.

Usually not. For example, I shoot weddings with a 5D and a 20D. The client doesn't know which was used for any particular shot, and their selections of print sizes are not in any way based on the sizes of the sensor in the camera.

But you didn't took neither phone nor compact (there's both with 8 mp sensors).

Because both dslrs capable to produce good images of required sizes and cell phone and compact don't. Yes I agree usually printing size doesn't choosen by sensor size. But it's not that impossible too.

The sensor size mainly affects the amount of light needed to capture an acceptable image, not the acceptability of the image itself. There are other reasons to choose a dSLR including physical properties, lens interchangeability, focusing performance, compatibility with accessories etc. that have nothing to do with sensor size.

--
Lee Jay
(see profile for equipment)

 

[x-vision]

People usually have difficulty with paradigm shifts. In this case, changing the old paradigm of f-ratio and exposure with a new paradigm based on aperture and total light:

http://www.josephjamesphotography.com/equivalence/#exposure

Look, you seem to think that I don’t understand your essay and/or I disagree with it – and hence you seem to be dismissing everything I say as a misunderstanding and/or a disagreement.
Please don’t insult my intelligence with such assumptions.

Your essay is establishing a very good framework for comparing different formats – and I agree with basically all points in it. It’s an extensive effort, which gets my respect.

Having said that, I discovered some blatantly incorrect statements in it and this is what I’m arguing about her5e - not with the essay in general.

Here’s one such statement (emphasis is yours):

For the same perspective and framing, the total light depends only on the aperture diameter and shutter speed (as opposed to the f-ratio and shutter speed for exposure).

This is incorrect. You assume that at the sensor plane you have at your disposal the same amount of light that entered the lens trough its aperture.

This is an incorrect assumption, so trying to explain how a sensor with an 85mm lens @2.8 somehow collects more light that sensor with a 50mm lens @2.8 is flawed.

What happens in practice is that for the same f-ratio, a larger sensor will collect more light energy than a smaller sensor simply because of its larger area.

This in turn means that to collect the same light energy, a smaller aperture needs to be used. Ergo, the same ‘apparent exposure’ on the larger sensor is achieved with a smaller aperture.

Your concept of ‘apparent exposure’ is valid by itself. It is just not explained correctly.

If you really understand how things work, you should also understand why I used the term ‘amount of light energy’ above and not 'amount of light'.

Your essay will actually benefit if you switch your explanations to use light energy rather than amount of light. You know why, right ().
Take care.

 

[Great Bustard]

People usually have difficulty with paradigm shifts. In this case, changing the old paradigm of f-ratio and exposure with a new paradigm based on aperture and total light:

http://www.josephjamesphotography.com/equivalence/#exposure

Look, you seem to think that I don’t understand your essay and/or I disagree with it – and hence you seem to be dismissing everything I say as a misunderstanding and/or a disagreement.
Please don’t insult my intelligence with such assumptions.

Your essay is establishing a very good framework for comparing different formats – and I agree with basically all points in it. It’s an extensive effort, which gets my respect.

Having said that, I discovered some blatantly incorrect statements in it and this is what I’m arguing about her5e - not with the essay in general.

Here’s one such statement (emphasis is yours):

For the same perspective and framing, the total light depends only on the aperture diameter and shutter speed (as opposed to the f-ratio and shutter speed for exposure).

This is incorrect. You assume that at the sensor plane you have at your disposal the same amount of light that entered the lens trough its aperture.

It is quite correct. For a given scene, perspective, and framing, the total light depends only on the aperture diameter (as opposed to f-ratio) and shutter speed, just as stated.

For example, consider the following two scenarios:

7D: 50mm f/2.8 1/100
5D: 80mm f/4.5 1/100

I'm sure you'll agree that, from the same position (persepctive), they'll both result in the same framing (50mm x 1.6 = 80mm). I'm sure you'll also agree that the aperture diameters are the same (50mm / 2.8 = 80mm / 4.5 = 17.9mm).

Thus, with the same shutter speed, the same amount of light (the same number of photons) will fall on each sensor.

"But wait!" you exclaim, "The shutter speeds can't be the same for the same exposure!" Exactly correct. The exposures will be different. However, exposure, when comparing different formats, is irrelevant -- the total amount of light, not the density of the light (exposure), is the relevant measure:

http://www.josephjamesphotography.com/equivalence/#exposure

"But wait!" you exclaim again, "The 5D will have to use a higher ISO to keep the same shutter speed!" Well, no, it doesn't require a higher ISO -- the apparent exposure can be boosted in post instead. But, for some sensors (such as the 7D and 5D sensor), a higher exposure makes the sensor more efficient, so it's a good idea to use the higher ISO rather than push in post (if low noise matters more than blown highlights, depending on the DR of the scene). See here for more details:

http://www.josephjamesphotography.com/equivalence/#iso

This is an incorrect assumption, so trying to explain how a sensor with an 85mm lens @2.8 somehow collects more light that sensor with a 50mm lens @2.8 is flawed.

What happens in practice is that for the same f-ratio, a larger sensor will collect more light energy than a smaller sensor simply because of its larger area.

This in turn means that to collect the same light energy, a smaller aperture needs to be used. Ergo, the same ‘apparent exposure’ on the larger sensor is achieved with a smaller aperture.

Your concept of ‘apparent exposure’ is valid by itself. It is just not explained correctly.

If you really understand how things work, you should also understand why I used the term ‘amount of light energy’ above and not 'amount of light'.

Your essay will actually benefit if you switch your explanations to use light energy rather than amount of light. You know why, right ().

You need to differentiate between the total amount of light, and the density of the light (exposure). As for "light energy", well, that's proportional to the total amount of light. For example, one trillion green photos have half the "light energy" of two trillion green photons.

The only reason to distinguish between the total amount of light and the "light energy" is when comparing different colors (two trillion photons of red light have basically the same "light energy" as one trillion photons of blue light), but this is completely irrelevant to the matter at hand.

You are coming at this the wrong way -- you are presuming you are correct, and I am wrong, when it is quite the other way around. This thread is short, but when it fills, I'll be happy to explain point-by-point. I appreciate how you quoted what you felt to be in error, and gave me the opportunity to explain why there was no error. If you are not satisfied with the explanation, please explain why, and we can go from there. But, in the end, two and two will add to four, it's just a matter of me finding the right way to explain it to you.

Take care.

That's my line.

 

[iljai]

But it is what it is - the way to compare not characteristic of system itself. And result depends of both characteristics of the systems and the way comparison made.

Right, but it's also the way things get used.

And causes a lot of confusion as this topic shows.

May be separating characteristics of system from characteristics of the scene on which they're tested and the way test is perfomed would cause a little less confusion.

Usually not. For example, I shoot weddings with a 5D and a 20D. The client doesn't know which was used for any particular shot, and their selections of print sizes are not in any way based on the sizes of the sensor in the camera.

But you didn't took neither phone nor compact (there's both with 8 mp sensors).

Because both dslrs capable to produce good images of required sizes and cell phone and compact don't. Yes I agree usually printing size doesn't choosen by sensor size. But it's not that impossible too.

The sensor size mainly affects the amount of light needed to capture an acceptable image, not the acceptability of the image itself.

I think both. You don't want all you wedding pictures to be flat too.

There are other reasons to choose a dSLR including physical properties, lens interchangeability, focusing performance, compatibility with accessories etc. that have nothing to do with sensor size.

Yes, but many of those say toward compact. For example physical properties of weight and size is a huge advantage of compacts and phone to the point when lens interchangeability could be replaced with camera interchageability and it still be lighter and smaller. And this do has a lot to do with sensor size. As you perfectly aware many accessories like flashed, auxilery wide, tele, macro lenses, even fisheye converter could be used with compact. I even saw teleconverter for iphone.

So why did you shoot that wedding with too dslr instead of one compact and on dslr? It would be able capture acceptable image at any amount of light and use another reasons, especially physical ones.

 

[Lee Jay]

There are other reasons to choose a dSLR including physical properties, lens interchangeability, focusing performance, compatibility with accessories etc. that have nothing to do with sensor size.

Yes, but many of those say toward compact. For example physical properties of weight and size is a huge advantage of compacts and phone to the point when lens interchangeability could be replaced with camera interchageability and it still be lighter and smaller.

I don't want it lighter and smaller for the same reason I can type faster on a full-size keyboard than I can on my phone - ergonomics.

And this do has a lot to do with sensor size. As you perfectly aware many accessories like flashed, auxilery wide, tele, macro lenses, even fisheye converter could be used with compact. I even saw teleconverter for iphone.

Most of those accessories are of poor quality, and further ruin the already-horrible ergonomics of those devices, plus they don't solve the inherent problem that small sensors collect very little light at the same f-stop as larger sensors.

--
Lee Jay
(see profile for equipment)

 

[iljai]

I was discussing your comment above about a "new photographer with single body". When I used a 20D (1.6x), I didn't think in terms of FF. But, when I wanted something with more IQ (5D), I compared them in terms of equivalent settings to see what the 5D would give me that the 20D would not.

But he read that this lens is equivalent to something else on the different body. So there's comparison but theoretical. Another body is in his head. And the statement "that it's equal" could be very confusing especially when FL, zoom and "reach" used in the same meaning. Read smi's original post. With "reduced fov statement" there's no such confusion.

 

[Great Bustard]

I was discussing your comment above about a "new photographer with single body". When I used a 20D (1.6x), I didn't think in terms of FF. But, when I wanted something with more IQ (5D), I compared them in terms of equivalent settings to see what the 5D would give me that the 20D would not.

But he read that this lens is equivalent to something else on the different body. So there's comparison but theoretical. Another body is in his head. And the statement "that it's equal" could be very confusing especially when FL, zoom and "reach" used in the same meaning. Read smi's original post. With "reduced fov statement" there's no such confusion.

I believe I already linked to my response:

http://forums.dpreview.com/forums/read.asp?forum=1029&message=37453545

Carlk's take is not incorrect, it is simply a different perspective on the issue which I, personally, find less useful. That is, I think it's more useful to say that, for example, 200mm f/2 on 1.6x is equivalent to 320mm f/3.2 on FF than it is to say that 200mm f/2 on 1.6x has a framing that is 1.6x tighter than on FF.

In other words, a 1.6x shooter contemplating purchasing a 200 / 2L IS for $5400 might do well to consider a 300 / 2.8L IS for $4500 and a FF body which will result in photos that have higher IQ.

It is not so useful for the photographer to think, "Huh -- the 200 / 2L IS on my 1.6x DSLR will crop out most of the image circle".

 

[x-vision]

For example, consider the following two scenarios:

7D: 50mm f/2.8 1/100
5D: 80mm f/4.5 1/100

I'm sure you'll agree that, from the same position (persepctive), they'll both result in the same framing (50mm x 1.6 = 80mm). I'm sure you'll also agree that the aperture diameters are the same (50mm / 2.8 = 80mm / 4.5 = 17.9mm).

That's right.

Thus, with the same shutter speed, the same amount of light ( the same number of photons) will fall on each sensor.

Nope. This is where you get confused. You assume that if 100 photons enter each lens, all 100 photons fall on each sensor. This is incorrect.

"But wait!" you exclaim, "The shutter speeds can't be the same for the same exposure!" Exactly correct. The exposures will be different.

So far so good.

However, exposure, when comparing different formats, is irrelevant -- the total amount of light, not the density of the light (exposure), is the relevant measure:

Nope. Again, you are assuming that if 100 photons enter each lens, all 100 of them will fall on each sensors.

"But wait!" you exclaim again, "The 5D will have to use a higher ISO to keep the same shutter speed!" Well, no, it doesn't require a higher ISO -- the apparent exposure can be boosted in post instead.

I get it. This is your 'apparent exposure' concept.

You are coming at this the wrong way -- you are presuming you are correct, and I am wrong, when it is quite the other way around.

Like I pointed out - please verify your assumption that if 100 photons enter a lens, all 100 make it to the sensor. This is very important.

And I don't mean (minor) light losses caused by the optics here. Make sure you fundametally understand how light travels through a shorter vs longer lens - and how that affects photon counts reaching the sensor.