A beginner's guide to "is equal to" vs "is equivalent to".

[Paul B Jones]

Because of physics yer 300mm lens is going to be the equivalent of a 480mm lens when you switch it from a Canon camera with a full frame sensor to a Canon camera with a smaller APS-C (crop) sensor.

Formula works on any lens.1.6 is the magic multiplication number (300mm X 1.6 = 480mm).

So ... wide angles lenses get less wide angle going from full frame to crop. Telephotos get more telephoto.

That's pretty much all you need to know.

 

[kiwi2]

Compare that to lenses with the same F-stop. They can have widely different sizes, weights, DOF, and resolution. Saying a F/2.8 lens on a cell phone has any resemblance to F/2.8 on a crop, medium format, or a telescope is a joke. The only thing they have that is similar is exposure--which has nothing to do with photographic quality or properties.

The difference between a cell phone and a FF camera is the 50 times difference in sensor area. It collects 50 times more light with the same exposure of the same scene.

They would both have the same light intensity per unit area. The same exposure.

This concept is pretty handy in photography. It's why my Canon Rebel kit lens will expose just the same at f/8 as my 6" f/8 telescope would in the same light...


55mm f/8, 1/250 sec, ISO 100


1200mm f/8, 1/250 sec, ISO 100

Remember, the F-stop is itself a parameter that has been normalized to the sensor size as an aid to set exposure manually. Aside from that, it's useless. Equivalence theory really de-normalizes the F-stop so that you can compare the true properties of a lens.

f/ratio has nothing to do with sensor size. It is solely the relationship of the aperture size to the focal length. A property of the lens regardless of what you put behind it.

You can see here as we change the area of sensor behind the lens that it always stays at f/8 in this particular case...







--

1 year with Fuji

Explore this photo album by Pete Oliver on Flickr!

flic.kr

 

[Great Bustard]

Because of physics yer 300mm lens is going to be the equivalent of a 480mm lens when you switch it from a Canon camera with a full frame sensor to a Canon camera with a smaller APS-C (crop) sensor.

Formula works on any lens.1.6 is the magic multiplication number (300mm X 1.6 = 480mm).

So ... wide angles lenses get less wide angle going from full frame to crop. Telephotos get more telephoto.

That's pretty much all you need to know.

Some don't even need to know that. But, inasmuch as one might also care about the aperture of a lens, then the equivalence for the relative aperture is worth knowing.

 

[kiwi2]

Sure, people can express mathematical equations to explain something.

It doesn't mean other people have to think it's that terribly important to the outcome of their photography work.

Sure. You don't need to understand gravity to enjoy (and be good at) skydiving. But you wouldn't argue against gravity would you? And you wouldn't say that someone computing how much time you have before you hit the ground in the event of a chute malfunction is full of it, would you?

www.dpreview.com/forums/post/62048291

You don't understand the f/ratio of a lens but still manage to take photos don't you?

 

[Great Bustard]

Sure, people can express mathematical equations to explain something.

It doesn't mean other people have to think it's that terribly important to the outcome of their photography work.

Sure. You don't need to understand gravity to enjoy (and be good at) skydiving. But you wouldn't argue against gravity would you? And you wouldn't say that someone computing how much time you have before you hit the ground in the event of a chute malfunction is full of it, would you?

www.dpreview.com/forums/post/62048291

Oh man -- you posted that link? That didn't end well for you.

You don't understand the f/ratio of a lens...

In fact I do. You link and quote *anything* I've said that you feel supports that bogus assertion, and I'll link and quote where I've showed you to be mistaken about that. Deal?

...but still manage to take photos don't you?

I typically shoot in Av or M mode and manually select the f-number -- you know, the think you claim I don't understand. Are you saying I'd be no better off than shooting in P mode and letting the camera choose?

 

[J A C S]

68,484 and counting...

 

[Great Bustard]

68,484 and counting...

And so many still don't understand it. Well, that's not a crime -- it's more those that are willfully ignorant of what it says and misrepresent it after it's explained to them over and over, which is probably the bulk of those posts.

 

[kiwi2]

Sure, people can express mathematical equations to explain something.

It doesn't mean other people have to think it's that terribly important to the outcome of their photography work.

Sure. You don't need to understand gravity to enjoy (and be good at) skydiving. But you wouldn't argue against gravity would you? And you wouldn't say that someone computing how much time you have before you hit the ground in the event of a chute malfunction is full of it, would you?

www.dpreview.com/forums/post/62048291

Oh man -- you posted that link? That didn't end well for you.

You don't understand the f/ratio of a lens...

In fact I do. You link and quote *anything* I've said that you feel supports that bogus assertion, and I'll link and quote where I've showed you to be mistaken about that. Deal?

Sure.... www.dpreview.com/forums/post/62129091

 

[Michael Fryd]

Compare that to lenses with the same F-stop. They can have widely different sizes, weights, DOF, and resolution. Saying a F/2.8 lens on a cell phone has any resemblance to F/2.8 on a crop, medium format, or a telescope is a joke. The only thing they have that is similar is exposure--which has nothing to do with photographic quality or properties.

The difference between a cell phone and a FF camera is the 50 times difference in sensor area. It collects 50 times more light with the same exposure of the same scene....

But if you stop down your larger camera, you will find that at the same angle of view, and same depth of field, the larger sensor collects the same total number of photons.

For instance, the iPhone 6 has a crop factor of 7.21, focal length of 4.15mm and a f/2.2 maximum aperture.

A full frame body with a 30mm lens at f/16 will have the same depth of field and collect the same light per unit area as that iPhone.

The sensor on the full frame has about 50 times the area of the iPhone sensor. However, at f/16, it gets about 1/50 the light per unit area as the iPhone sensor.

Both the iPhone with a 4.15mm at f/2.2 and the full frame with a 30mm at f/16 have an aperture diameter of about 1.9 mm.

The advantage of the full frame, is that you can open up wider that a 1.9mm aperture diameter. With the iPhone, that 1.9mm is your maximum aperture.

It really does boil down to aperture diameter and angle of view.

 

[stevo23]

Sure, people can express mathematical equations to explain something.

It doesn't mean other people have to think it's that terribly important to the outcome of their photography work.

Sure. You don't need to understand gravity to enjoy (and be good at) skydiving. But you wouldn't argue against gravity would you? And you wouldn't say that someone computing how much time you have before you hit the ground in the event of a chute malfunction is full of it, would you?

www.dpreview.com/forums/post/62048291

Oh man -- you posted that link? That didn't end well for you.

You don't understand the f/ratio of a lens...

In fact I do. You link and quote *anything* I've said that you feel supports that bogus assertion, and I'll link and quote where I've showed you to be mistaken about that. Deal?

Sure.... www.dpreview.com/forums/post/62129091

Huh? I don't see GB even contributing to that thread. Are you seriously posting links to links to that same thread where you were repeatedly thrashed? You're not planning to crash and burn on purpose are you?

 

[Bob A L]

There are certainly plenty that don't understand - this thread just reinforces that for sure.

 

[stevo23]

Compare that to lenses with the same F-stop. They can have widely different sizes, weights, DOF, and resolution. Saying a F/2.8 lens on a cell phone has any resemblance to F/2.8 on a crop, medium format, or a telescope is a joke. The only thing they have that is similar is exposure--which has nothing to do with photographic quality or properties.

The difference between a cell phone and a FF camera is the 50 times difference in sensor area. It collects 50 times more light with the same exposure of the same scene....

But if you stop down your larger camera, you will find that at the same angle of view, and same depth of field, the larger sensor collects the same total number of photons.

For instance, the iPhone 6 has a crop factor of 7.21, focal length of 4.15mm and a f/2.2 maximum aperture.

A full frame body with a 30mm lens at f/16 will have the same depth of field and collect the same light per unit area as that iPhone.

The sensor on the full frame has about 50 times the area of the iPhone sensor. However, at f/16, it gets about 1/50 the light per unit area as the iPhone sensor.

Both the iPhone with a 4.15mm at f/2.2 and the full frame with a 30mm at f/16 have an aperture diameter of about 1.9 mm.

The advantage of the full frame, is that you can open up wider that a 1.9mm aperture diameter. With the iPhone, that 1.9mm is your maximum aperture.

It really does boil down to aperture diameter and angle of view.

Where are you fitting noise into that?

 

[Great Bustard]

Sure, people can express mathematical equations to explain something.

It doesn't mean other people have to think it's that terribly important to the outcome of their photography work.

Sure. You don't need to understand gravity to enjoy (and be good at) skydiving. But you wouldn't argue against gravity would you? And you wouldn't say that someone computing how much time you have before you hit the ground in the event of a chute malfunction is full of it, would you?

www.dpreview.com/forums/post/62048291

Oh man -- you posted that link? That didn't end well for you.

You don't understand the f/ratio of a lens...

In fact I do. You link and quote *anything* I've said that you feel supports that bogus assertion, and I'll link and quote where I've showed you to be mistaken about that. Deal?

Sure.... www.dpreview.com/forums/post/62129091

Everything I was quoted on in that link is 100% correct and was pointed out to you before by someone more than a little competent in these matters. However, you're not the type to let the facts get in the way of your misunderstanding.

My suggestion to you: start a thread in the PST forum quoting what I wrote in that link and, more importantly, the source of all of those quotes. Ask if I was mistaken on *any* of it. Hint: it won't go the way you are hoping. Then again, how'd that work out for you last time? And there's no reason to think anything has changed.

 

[Michael Fryd]

Compare that to lenses with the same F-stop. They can have widely different sizes, weights, DOF, and resolution. Saying a F/2.8 lens on a cell phone has any resemblance to F/2.8 on a crop, medium format, or a telescope is a joke. The only thing they have that is similar is exposure--which has nothing to do with photographic quality or properties.

The difference between a cell phone and a FF camera is the 50 times difference in sensor area. It collects 50 times more light with the same exposure of the same scene....

But if you stop down your larger camera, you will find that at the same angle of view, and same depth of field, the larger sensor collects the same total number of photons.

For instance, the iPhone 6 has a crop factor of 7.21, focal length of 4.15mm and a f/2.2 maximum aperture.

A full frame body with a 30mm lens at f/16 will have the same depth of field and collect the same light per unit area as that iPhone.

The sensor on the full frame has about 50 times the area of the iPhone sensor. However, at f/16, it gets about 1/50 the light per unit area as the iPhone sensor.

Both the iPhone with a 4.15mm at f/2.2 and the full frame with a 30mm at f/16 have an aperture diameter of about 1.9 mm.

The advantage of the full frame, is that you can open up wider that a 1.9mm aperture diameter. With the iPhone, that 1.9mm is your maximum aperture.

It really does boil down to aperture diameter and angle of view.

Where are you fitting noise into that?

If the shutter speeds are the same, the iPhone at f/2.2 will have about the same shot noise as the full frame at f/16. (Both sensors are seeing the same total amount of light).

Obviously, the full frame will need to be set to a higher ISO in order to get the same image lightness as the iPhone photo.

I don't have a comparison of the sensor technologies, so I won't comment on how other factors contribute to the noise. I will say that my impression is that the iPhone uses a more aggressive noise reduction algorithm.

My guess is that the image noise from the iPhone at f/2.2 will be in the same ballpark as the image noise from the full frame at f/16 (assuming the same shutter speed).

 

[Great Bustard]

There are certainly plenty that don't understand - this thread just reinforces that for sure.

Not understanding is not a sin. Not caring is not a sin. But willful ignorance most certainly is.

 

[Great Bustard]

Sure, people can express mathematical equations to explain something.

It doesn't mean other people have to think it's that terribly important to the outcome of their photography work.

Sure. You don't need to understand gravity to enjoy (and be good at) skydiving. But you wouldn't argue against gravity would you? And you wouldn't say that someone computing how much time you have before you hit the ground in the event of a chute malfunction is full of it, would you?

www.dpreview.com/forums/post/62048291

Oh man -- you posted that link? That didn't end well for you.

You don't understand the f/ratio of a lens...

In fact I do. You link and quote *anything* I've said that you feel supports that bogus assertion, and I'll link and quote where I've showed you to be mistaken about that. Deal?

Sure.... www.dpreview.com/forums/post/62129091

Huh? I don't see GB even contributing to that thread. Are you seriously posting links to links to that same thread where you were repeatedly thrashed? You're not planning to crash and burn on purpose are you?

Some people feel that because they can [repeatedly] block a punch with their face, often by their own hand, that they've won the fight.

 

[mamallama]

You're wasting your effort. Mr. Llama doesn't believe in a spherical earth...eh...equivalency.

Oh please.

So anybody that doesn't swallow hook line and sinker all of the nonsense the self

appointed experts spout in these forums must be a flat-earther...???

What does any of that have to do with the subject at hand? This is about equivalence. You don't "believe in" equivalence?

I'm saying that not believing in equivalence, which can be tested and proven, is not very dignified. It's like being a flat earther - foolishness in the face of proof.

What is your definition of equivalence that can be tested and proved. Is your proof mathematical or intuitive?

So you're saying you don't buy it, is that it? I seem to recall that you scoff at these explanations.

I don't know what it is that you think I'm not buying.

You do think equivalency works?

According to Richard Butler, "Equivalence, at its most simple, is a way of comparing different formats (sensor sizes) on a common basis".

Of course that works. It is just a way of comparing different formats on a common basis.

How some of these comparisons are used to draw certain conclusions is what is debatable.

Specifically which is debatable?

Why total noise in an image, which the equivalency advocates keep emphasizing, is a more useful metric than the signal-to-noise ratio?

I am asking you about your statement that equivalence can be tested and proved. What is proved and where is it proved?

You don't know?

I don't know what you mean that equivalence has been tested and proved.

 

[Great Bustard]

You're wasting your effort. Mr. Llama doesn't believe in a spherical earth...eh...equivalency.

Oh please.

So anybody that doesn't swallow hook line and sinker all of the nonsense the self

appointed experts spout in these forums must be a flat-earther...???

What does any of that have to do with the subject at hand? This is about equivalence. You don't "believe in" equivalence?

I'm saying that not believing in equivalence, which can be tested and proven, is not very dignified. It's like being a flat earther - foolishness in the face of proof.

What is your definition of equivalence that can be tested and proved. Is your proof mathematical or intuitive?

So you're saying you don't buy it, is that it? I seem to recall that you scoff at these explanations.

I don't know what it is that you think I'm not buying.

You do think equivalency works?

According to Richard Butler, "Equivalence, at its most simple, is a way of comparing different formats (sensor sizes) on a common basis".

Of course that works. It is just a way of comparing different formats on a common basis.

How some of these comparisons are used to draw certain conclusions is what is debatable.

Specifically which is debatable?

Why total noise in an image, which the equivalency advocates keep emphasizing, is a more useful metric than the signal-to-noise.

"Total Noise" is simply about comparing the noise over the same proportion of the photo, rather than one pixel on one photo to one pixel on another photo when the pixels cover different portions of the photo.

So, "Total Noise" simply represents the average SNR for corresponding portions of the photo.

 

[mjc1]

Thanks for the write up. Probably most people here have seen similar posts before, or have a good enough understanding of this concept, however I am sure there are many that don't and this is a nice, concise simple guide.

I have a comment/question.... you wrote:

"The effect of the crop factor is the same as if you used the same lens and settings on a FF camera and cropped out the middle 1.5x (or 1.6x) of the photo."

Someone just looking for simple information, which this post provides, that helps them understand this topic may not really understand the statement. They may not really understand what "the middle 1.5x of the photo" means so they may get confused. Probably most of us posting to this topic know what you are saying, but this information isn't really geared to those that do.

Thanks again for taking the time to help beginners.

 

[Great Bustard]

Thanks for the write up. Probably most people here have seen similar posts before, or have a good enough understanding of this concept, however I am sure there are many that don't and this is a nice, concise simple guide.

Glad you liked it!

"The effect of the crop factor is the same as if you used the same lens and settings on a FF camera and cropped out the middle 1.5x (or 1.6x) of the photo."

Someone just looking for simple information, which this post provides, that helps them understand this topic may not really understand the statement. They may not really understand what "the middle 1.5x of the photo" means so they may get confused. Probably most of us posting to this topic know what you are saying, but this information isn't really geared to those that do.

It's funny you mention it, 'cause I was thinking that when I wrote it, but decided against explaining what I meant in more detail to keep the length of the post down. That's the whole problem with these kinds of posts -- keep it succinct, and someone points out an omission; make it more complete, and someone says it's too verbose. ;-)

OK, to add some clarity to that point, the middle 1.5x (or 1.6x) of the photo is the central 44% (or 39% for 1.6x) of the photo. For example, if the photo were 6000 x 4000 pixels, we would crop out the central 6000 / 1.5 x 4000 / 1.5 = 4000 x 2667 pixel (or 6000 / 1.6 x 4000 / 1.6 = 3750 x 2500 pixel for 1.6x) portion.

Thanks again for taking the time to help beginners.

Kind of you to say!