Infinite depth of field

[Tom Axford]

I was rather taken aback to see that probably a majority of voters in another thread think that "the depth of field is infinite" means that everything is in sharp focus.

As far as I can see this seems to be based upon a non-mathematical definition of "infinite" as meaning "everywhere" as well as "going on forever".

I cannot recall encountering the word infinite being used in this way, it was quite a surprise to me. Presumably those who interpret an infinite DoF in this way have little familiarity with the mathematical concept of infinity.

What do others think? Have you encountered the terms infinity or infinite being used in this sense? Or do you think I have misinterpreted what is going on here?

 

[J A C S]

As I said in the other thread, it depends - infinite what? Some view DOF as a number (a value of a function, if you wish), like the DOF is 1m; some view it as a range, like from 1m to 2m, some view it as the physical space between two planes; and most have no clear idea. Some want to have objects in focus in the shot, sharp or not, some do not. The wikipedia definition is sloppy, misquotes a book, and the definition in the book is not great either. The wiki definition defines DOF as a number.

Now, about infinity/infinite in math:

• As a number (a possible numerical value of a function to be more precise), it is just a limit. Nothing exotic, and infinity per se is just a figure of speech.
• An infinite set is a set with infinitely many elements. The interval [0,1], considered as a subset of the real numbers is infinite, for example. It is bounded however.
• An infinite physical space - that is not math, but it could be if the question is posed properly. This has little to do with DOF though. It is relevant in cosmology, for example. A space (manifold) can be "infinite" ("bounded" is a better term) in some directions but can have a finite volume, etc.
• Infinity arises in some other contexts in math, CS, etc., but AFAIK, each such occurrence is just a specific flavor of what I listed above.

I have never seen infinite meaning filling all. The term "maximal" comes to mind for that.

 

[JimKasson]

I was rather taken aback to see that probably a majority of voters in another thread think that "the depth of field is infinite" means that everything is in sharp focus.

As far as I can see this seems to be based upon a non-mathematical definition of "infinite" as meaning "everywhere" as well as "going on forever".

I cannot recall encountering the word infinite being used in this way, it was quite a surprise to me. Presumably those who interpret an infinite DoF in this way have little familiarity with the mathematical concept of infinity.

What do others think? Have you encountered the terms infinity or infinite being used in this sense? Or do you think I have misinterpreted what is going on here?

In geometric derivations, DOF, a scalar, is infinite when the lens is focused to the hyperfocal distance or beyond.

 

[Tom Axford]

I was rather taken aback to see that probably a majority of voters in another thread think that "the depth of field is infinite" means that everything is in sharp focus.

As far as I can see this seems to be based upon a non-mathematical definition of "infinite" as meaning "everywhere" as well as "going on forever".

I cannot recall encountering the word infinite being used in this way, it was quite a surprise to me. Presumably those who interpret an infinite DoF in this way have little familiarity with the mathematical concept of infinity.

What do others think? Have you encountered the terms infinity or infinite being used in this sense? Or do you think I have misinterpreted what is going on here?

In geometric derivations, DOF, a scalar, is infinite when the lens is focused to the hyperfocal distance or beyond.

Try telling that to the people who say that focussing at infinity does not produce infinite DoF.

For example, in this post which has 30 likes! :-O

 

[JimKasson]

I was rather taken aback to see that probably a majority of voters in another thread think that "the depth of field is infinite" means that everything is in sharp focus.

As far as I can see this seems to be based upon a non-mathematical definition of "infinite" as meaning "everywhere" as well as "going on forever".

I cannot recall encountering the word infinite being used in this way, it was quite a surprise to me. Presumably those who interpret an infinite DoF in this way have little familiarity with the mathematical concept of infinity.

What do others think? Have you encountered the terms infinity or infinite being used in this sense? Or do you think I have misinterpreted what is going on here?

In geometric derivations, DOF, a scalar, is infinite when the lens is focused to the hyperfocal distance or beyond.

Try telling that to the people who say that focussing at infinity does not produce infinite DoF.

For example, in this post which has 30 likes! :-O

Well, if you focus on the moon and Andromeda is in focus, that's near enough to infinity for me. You could argue that the universe is not infinite, though, but now we're getting close to angels dancing on pinheads.

 

[Tom Axford]

I was rather taken aback to see that probably a majority of voters in another thread think that "the depth of field is infinite" means that everything is in sharp focus.

As far as I can see this seems to be based upon a non-mathematical definition of "infinite" as meaning "everywhere" as well as "going on forever".

I cannot recall encountering the word infinite being used in this way, it was quite a surprise to me. Presumably those who interpret an infinite DoF in this way have little familiarity with the mathematical concept of infinity.

What do others think? Have you encountered the terms infinity or infinite being used in this sense? Or do you think I have misinterpreted what is going on here?

In geometric derivations, DOF, a scalar, is infinite when the lens is focused to the hyperfocal distance or beyond.

Try telling that to the people who say that focussing at infinity does not produce infinite DoF.

For example, in this post which has 30 likes! :-O

Well, if you focus on the moon and Andromeda is in focus, that's near enough to infinity for me. You could argue that the universe is not infinite, though, but now we're getting close to angels dancing on pinheads.

I agree entirely, Jim, but it seems that there are a lot of people who do not and who are very unwilling to change their minds.

 

[Pixel Pooper]

I agree entirely, Jim, but it seems that there are a lot of people who do not and who are very unwilling to change their minds.

I was one of them, but I did change my mind thanks to your explanation. Unfortunately most people will not, or at least will not admit they were wrong. I wouldn't lose any sleep over it.

 

[Pixel Pooper]

Some view DOF as a number (a value of a function, if you wish), like the DOF is 1m; some view it as a range, like from 1m to 2m, some view it as the physical space between two planes; and most have no clear idea.

The other thread filled up before I got a chance to reply, but I found this part odd because the definition is right there in the name. It's called depth of field, so it refers to the depth, which is a distance. If it were a range it would be called range of field.

 

[kenw]

I was rather taken aback to see that probably a majority of voters in another thread think that "the depth of field is infinite" means that everything is in sharp focus.

As far as I can see this seems to be based upon a non-mathematical definition of "infinite" as meaning "everywhere" as well as "going on forever".

I’m disappointed that the linked thread didn’t also include an argument about denumerabiliy…

 

[J A C S]

I was rather taken aback to see that probably a majority of voters in another thread think that "the depth of field is infinite" means that everything is in sharp focus.

As far as I can see this seems to be based upon a non-mathematical definition of "infinite" as meaning "everywhere" as well as "going on forever".

I’m disappointed that the linked thread didn’t also include an argument about denumerabiliy…

This must be French for countability?

The other thread mentioned cardinality though:

Semi-infinite: Open Talk Forum: Digital Photography Review (dpreview.com)

I even cracked a relativity joke:

zero: Open Talk Forum: Digital Photography Review (dpreview.com)

It was a pretty high level discussion...

 

[D Cox]

I was rather taken aback to see that probably a majority of voters in another thread think that "the depth of field is infinite" means that everything is in sharp focus.

As far as I can see this seems to be based upon a non-mathematical definition of "infinite" as meaning "everywhere" as well as "going on forever".

I cannot recall encountering the word infinite being used in this way, it was quite a surprise to me. Presumably those who interpret an infinite DoF in this way have little familiarity with the mathematical concept of infinity.

What do others think? Have you encountered the terms infinity or infinite being used in this sense? Or do you think I have misinterpreted what is going on here?

In geometric derivations, DOF, a scalar, is infinite when the lens is focused to the hyperfocal distance or beyond.

Try telling that to the people who say that focussing at infinity does not produce infinite DoF.

For example, in this post which has 30 likes! :-O

Well, if you focus on the moon and Andromeda is in focus, that's near enough to infinity for me. You could argue that the universe is not infinite, though, but now we're getting close to angels dancing on pinheads.

Red shift presumably limits the distance of stars that can be photographed with visible light.

Don Cox

 

[J A C S]

I was rather taken aback to see that probably a majority of voters in another thread think that "the depth of field is infinite" means that everything is in sharp focus.

As far as I can see this seems to be based upon a non-mathematical definition of "infinite" as meaning "everywhere" as well as "going on forever".

I cannot recall encountering the word infinite being used in this way, it was quite a surprise to me. Presumably those who interpret an infinite DoF in this way have little familiarity with the mathematical concept of infinity.

What do others think? Have you encountered the terms infinity or infinite being used in this sense? Or do you think I have misinterpreted what is going on here?

In geometric derivations, DOF, a scalar, is infinite when the lens is focused to the hyperfocal distance or beyond.

Try telling that to the people who say that focussing at infinity does not produce infinite DoF.

For example, in this post which has 30 likes! :-O

Well, if you focus on the moon and Andromeda is in focus, that's near enough to infinity for me. You could argue that the universe is not infinite, though, but now we're getting close to angels dancing on pinheads.

Red shift presumably limits the distance of stars that can be photographed with visible light.

Red shift is just evidence of an expanding galaxy. EDIT: I missed the point of visible light.

BTW, the distance (considering the points in time-space) to any star we see is zero.

 

[ThrillaMozilla]

It's odd, but most people seem to have missed the point that the far depth of field is infinite, but the near depth of field is not.

And by the way, as an aside, please note that infinity is not a number. The total depth of field is the sum of the near depth of field and the far depth of field, but it's undefined in this case. Expressed as a range, the depth of field is bounded on the near side but unbounded on the far side.

I don't understand why this has caused such a conundrum, or why anyone is even commenting on it.

 

[J A C S]

It's odd, but most people seem to have missed the point that the far depth of field is infinite, but the near depth of field is not.

As far as I remember, nobody did.

And by the way, as an aside, please note that infinity is not a number.

It does not have to be (but it is part of the extended real line).

Measure (mathematics) - Wikipedia

The total depth of field is the sum of the near depth of field and the far depth of field, but it's undefined in this case.

It is, it is infinite by definition.

 

[kenw]

Red shift presumably limits the distance of stars that can be photographed with visible light.

Don Cox

Indeed the current distance record has UV already shifted entirely below the visible band and only starts to be imaged around 1.6 um.







--
Ken W
See profile for equipment list

 

[Tom Axford]

It's odd, but most people seem to have missed the point that the far depth of field is infinite, but the near depth of field is not.

As far as I remember, nobody did.

And by the way, as an aside, please note that infinity is not a number.

It does not have to be (but it is part of the extended real line).

Measure (mathematics) - Wikipedia

The total depth of field is the sum of the near depth of field and the far depth of field, but it's undefined in this case.

It is, it is infinite by definition.

Yes,

infinity + any finite number = infinity

is a basic property of infinity.

 

[kenw]

I was rather taken aback to see that probably a majority of voters in another thread think that "the depth of field is infinite" means that everything is in sharp focus.

As far as I can see this seems to be based upon a non-mathematical definition of "infinite" as meaning "everywhere" as well as "going on forever".

I’m disappointed that the linked thread didn’t also include an argument about denumerabiliy…

This must be French for countability?

Oui.

The other thread mentioned cardinality though:

Semi-infinite: Open Talk Forum: Digital Photography Review (dpreview.com)

Oh I missed that! Well I’d say that’s close enough that it counts. (Denumerates?)

I even cracked a relativity joke:

zero: Open Talk Forum: Digital Photography Review (dpreview.com)

Lol. That was relatively funny regardless of your frame of reference.

It was a pretty high level discussion...

High on so many levels…

 

[ThrillaMozilla]

It's odd, but most people seem to have missed the point that the far depth of field is infinite, but the near depth of field is not.

As far as I remember, nobody did.

And by the way, as an aside, please note that infinity is not a number.

It does not have to be (but it is part of the extended real line).

Measure (mathematics) - Wikipedia

The total depth of field is the sum of the near depth of field and the far depth of field, but it's undefined in this case.

It is, it is infinite by definition.

Yes,

infinity + any finite number = infinity

is a basic property of infinity.

Sorry, yes I blew that part of it. It's defined, but still not a number.

 

[Bill Ferris]

I was rather taken aback to see that probably a majority of voters in another thread think that "the depth of field is infinite" means that everything is in sharp focus.

As far as I can see this seems to be based upon a non-mathematical definition of "infinite" as meaning "everywhere" as well as "going on forever".

I cannot recall encountering the word infinite being used in this way, it was quite a surprise to me. Presumably those who interpret an infinite DoF in this way have little familiarity with the mathematical concept of infinity.

What do others think? Have you encountered the terms infinity or infinite being used in this sense? Or do you think I have misinterpreted what is going on here?

In geometric derivations, DOF, a scalar, is infinite when the lens is focused to the hyperfocal distance or beyond.

Try telling that to the people who say that focussing at infinity does not produce infinite DoF.

For example, in this post which has 30 likes! :-O

Well, if you focus on the moon and Andromeda is in focus, that's near enough to infinity for me. You could argue that the universe is not infinite, though, but now we're getting close to angels dancing on pinheads.

In fairness to the respondents, the poll question does not clearly establish that the question should be considered only within the context of the meaning of photographic depth of field. All resolved and acceptably sharp objects within the frame of the photo are at a finite distance from the sensor plane. Within that context, one can accurately say the depth of the scene was finite.

That poll illustrates a fundamental problem for the person who designs a poll that will generate meaningful results. The onus is on the pollster to craft a meaningful and clear question. If the poll question doesn't pass muster, the responses won't be based on a shared or common understanding of the question. That's what happened, here.

 

[J A C S]

I was rather taken aback to see that probably a majority of voters in another thread think that "the depth of field is infinite" means that everything is in sharp focus.

As far as I can see this seems to be based upon a non-mathematical definition of "infinite" as meaning "everywhere" as well as "going on forever".

I cannot recall encountering the word infinite being used in this way, it was quite a surprise to me. Presumably those who interpret an infinite DoF in this way have little familiarity with the mathematical concept of infinity.

What do others think? Have you encountered the terms infinity or infinite being used in this sense? Or do you think I have misinterpreted what is going on here?

In geometric derivations, DOF, a scalar, is infinite when the lens is focused to the hyperfocal distance or beyond.

Try telling that to the people who say that focussing at infinity does not produce infinite DoF.

For example, in this post which has 30 likes! :-O

Well, if you focus on the moon and Andromeda is in focus, that's near enough to infinity for me. You could argue that the universe is not infinite, though, but now we're getting close to angels dancing on pinheads.

In fairness to the respondents, the poll question does not clearly establish that the question should be considered only within the context of the meaning of photographic depth of field. All resolved and acceptably sharp objects within the frame of the photo are at a finite distance from the sensor plane.

This is always the case. So the DOF is never infinite?

The DOF does not care if there are objects in the frame. It is the depth of the field, not of the objects in it.

Besides, almost everybody saying that the DOF was finite said that not because all well resolved objects were at finite distance. They said that because there was an object which was not well resolved. It is kind of the opposite of what you claim about their motivation.

Within that context, one can accurately say the depth of the scene was finite.