Triangle?

The ET is an interesting and elegant concept in my opinion, you simply have a different opinion and that's fine.
In partial mitigation, the lensrentals blog article does not waste too many words trying to explain how to use the exposure triangle in a quantitative manner, and the use of arrow heads is limited to only five.

There are no numbers on this version of the exposure triangle, which greatly limits the scope for confusion. If you take it to say:
  • There are 3 parameters to consider.
  • Each affects image quality and image brightness in different ways.
  • Here is a simple visual reminder. Don't stress over the details.
then there is not much of substance to argue about.

Matters get more contentious when the ET has numbers attached, which give the impression that it might offer consistent and quantitative guidance on how to manage exposure and image brightness.

You may not agree, so I leave you with an observation.

If you construct an exposure triangle in which the sides corresponding to aperture, shutter speed and ISO sensitivity are labelled from low to high values, there are 8 different ways to construct the triangle. There are 4 ways of joining the first two sides, according to whether the first vertex corresponds to low values of both aperture and shutter speed (low/low), or the alternate low/high, high/low and high/high connections. For each of these 4 combination there are 2 different ways to attach the ISO range (high ISO to aperture side, or high ISO to shutter side).

This does not distinguish between simple rotations and reflections which do not change the basic connectivity.

Is there an obvious and logical way to construct the ET, so that the interactions and quantitative relationships between aperture, shutter speed and sensitivity are clear, intuitive and mathematically sound?

Do proponents of the exposure triangle agree on its construction?

Apparently not. Search Google images, and you will find that all 8 possible triangle constructions are in use.

--
Alan Robinson
 
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The ET is an interesting and elegant concept in my opinion, you simply have a different opinion and that's fine.
In partial mitigation, the lensrentals blog article does not waste too many words trying to explain how to use the exposure triangle in a quantitative manner, and the use of arrow heads is limited to only five.

There are no numbers on this version of the exposure triangle, which greatly limits the scope for confusion. If you take it to say:
  • There are 3 parameters to consider.
  • Each affects image quality and image brightness in different ways.
  • Here is a simple visual reminder. Don't stress over the details.
then there is not much of substance to argue about.

Matters get more contentious when the ET has numbers attached, which give the impression that it might offer consistent and quantitative guidance on how to manage exposure and image brightness.
Personnally, I have never seen somebody using it as a guidance.. It is more an illustration of a concept. The illustration is spot on, could not find better than using a triangle in my opinion, see below.
You may not agree, so I leave you with an observation.

If you construct an exposure triangle in which the sides corresponding to aperture, shutter speed and ISO sensitivity are labelled from low to high values, there are 8 different ways to construct the triangle. There are 4 ways of joining the first two sides, according to whether the first vertex corresponds to low values of both aperture and shutter speed (low/low), or the alternate low/high, high/low and high/high connections. For each of these 4 combination there are 2 different ways to attach the ISO range (high ISO to aperture side, or high ISO to shutter side).

This does not distinguish between simple rotations and reflections which do not change the basic connectivity.

Is there an obvious and logical way to construct the ET, so that the interactions and quantitative relationships between aperture, shutter speed and sensitivity are clear, intuitive and mathematically sound?

Do proponents of the exposure triangle agree on its construction?
I don't understand your point.

Very simply said, the exposure is the representation of 3 variables whose sum must remain the same. It is a plane but with limits it becomes a triangle (see JACS representation).

I had posted a demo:

https://www.dpreview.com/forums/post/63947823

And the relation is illustrated by JACS:

https://www.dpreview.com/forums/post/63944383

The real numbers do not really matter because nobody uses as a guidance. What is really elegant is that it shows that only some combinations are possible and are often a matter of compromise.

What is even more elegant is that people get the idea even if this is not a detailed triangle. This is intuitive that these variables are linked, these are not 3 independant axes. 3 variables but only 2 degrees of liberties.

If some people do not like it, this is simply their opinion, nothing else, but I have a different opinion.
 
The real numbers do not really matter because nobody uses as a guidance. What is really elegant is that it shows that only some combinations are possible and are often a matter of compromise.
What makes the other combinations not “possible”?
 
In partial mitigation, the lensrentals blog article does not waste too many words trying to explain how to use the exposure triangle in a quantitative manner, and the use of arrow heads is limited to only five.

There are no numbers on this version of the exposure triangle, which greatly limits the scope for confusion. If you take it to say:
  • There are 3 parameters to consider.
  • Each affects image quality and image brightness in different ways.
  • Here is a simple visual reminder. Don't stress over the details.
then there is not much of substance to argue about.
The problem is that sometimes the text accompanying the exposure triangle implies incorrectly that the ISO setting is part of the definition of exposure. I didn't notice any such text in this article. For what it's worth, I don't see that the exposure triangle has much relation to the rest of the article, except for incidentally mentioning exposure. It could just as easily have been omitted.
 
The ET is an interesting and elegant concept in my opinion, you simply have a different opinion and that's fine.
In partial mitigation, the lensrentals blog article does not waste too many words trying to explain how to use the exposure triangle in a quantitative manner, and the use of arrow heads is limited to only five.

There are no numbers on this version of the exposure triangle, which greatly limits the scope for confusion. If you take it to say:
  • There are 3 parameters to consider.
  • Each affects image quality and image brightness in different ways.
  • Here is a simple visual reminder. Don't stress over the details.
then there is not much of substance to argue about.

Matters get more contentious when the ET has numbers attached, which give the impression that it might offer consistent and quantitative guidance on how to manage exposure and image brightness.
Personnally, I have never seen somebody using it as a guidance.. It is more an illustration of a concept. The illustration is spot on, could not find better than using a triangle in my opinion, see below.
You may not agree, so I leave you with an observation.

If you construct an exposure triangle in which the sides corresponding to aperture, shutter speed and ISO sensitivity are labelled from low to high values, there are 8 different ways to construct the triangle. There are 4 ways of joining the first two sides, according to whether the first vertex corresponds to low values of both aperture and shutter speed (low/low), or the alternate low/high, high/low and high/high connections. For each of these 4 combination there are 2 different ways to attach the ISO range (high ISO to aperture side, or high ISO to shutter side).

This does not distinguish between simple rotations and reflections which do not change the basic connectivity.

Is there an obvious and logical way to construct the ET, so that the interactions and quantitative relationships between aperture, shutter speed and sensitivity are clear, intuitive and mathematically sound?

Do proponents of the exposure triangle agree on its construction?
I don't understand your point.
Most of the exposure triangles I have encountered are seriously lacking in clarity and soundness, and I do not find them intuitive.
Very simply said, the exposure is the representation of 3 variables whose sum must remain the same. It is a plane but with limits it becomes a triangle (see JACS representation).
The variables shown are usually f-number, exposure time and ISO sensitivity. More precisely a combination of sums and differences of their logarithms remains the same, but that does make some kind of sense.
What J A C S illustration makes clear to me is that the quantities, aperture, exposure time and ISO sensitivity, are measured normal to one of the adjacent sides, not parallel to the side of the triangle where the quantitative markings are usually labelled.

Similarly, the colour-coding of your diagram eliminates that potential ambiguity.

What I find confusing are diagrams like this which show brightness increasing monotonically as one follows triangular contours around the exposure triangle.

Or this, which shows increasing ISO sensitivity corresponding to "more light", when the converse is generally the case. Arguably one could make a case for "brighter" rather than "more light", but it still conflicts with the "plane of constant brightness" concept.

In contrast, in your diagram it is clear that all points on the plane of the triangle have the same brightness, with the constant ISO lines also contours of constant exposure.
The real numbers do not really matter because nobody uses as a guidance. What is really elegant is that it shows that only some combinations are possible and are often a matter of compromise.

What is even more elegant is that people get the idea even if this is not a detailed triangle. This is intuitive that these variables are linked, these are not 3 independant axes. 3 variables but only 2 degrees of liberties.
I see where you are coming from, but I find it much more intuitive to think along the lines that brightness, subject luminance, exposure time, sensitivity and aperture are linked via the simple proportionality relationship:

Brightness ~ L T S / N²

One could visualise this as slices through a tetrahedron, but I find counting stops rather easier. YMMV.
If some people do not like it, this is simply their opinion, nothing else, but I have a different opinion.
 
The problem is that sometimes the text accompanying the exposure triangle implies incorrectly that the ISO setting is part of the definition of exposure. I didn't notice any such text in this article. For what it's worth, I don't see that the exposure triangle has much relation to the rest of the article, except for incidentally mentioning exposure. It could just as easily have been omitted.
He is walking a very fine line there.

Properly exposing an image will always come down to three main settings – Shutter Speed, Aperture, and ISO.

Well, ISO does not change the exposure (if you force the other two parameters to be the same) but proper exposure does depend on the ISO. If your ISO is too high, for example, you will get basically a white frame, which would not be "proper". Also, "come down" is too vague.

These three settings are known as the exposure triangle.

True, like it or not.

To put it very simply, the exposure of an image will be the same if you adjust these settings in correlation with each other.

A bit too simple and vague. What correlation? If only two are correlated, would that be enough? Keeping the ISO fixed - is that correlation?

For example, if you need to increase your shutter speed, you can adjust it by two 2/3 stops (so two clicks on your dial) to something faster, and open up your aperture by two clicks of the wheel to match the exposure from the previous shot.

Fortunately, ISO is missing in this example.

While each of these settings will alter the image’s exposure [...]

Well, ISO will not (unless you are in some auto mode). This is wrong unless you accept zero altering as altering.
 
The ET is an interesting and elegant concept in my opinion, you simply have a different opinion and that's fine.
In partial mitigation, the lensrentals blog article does not waste too many words trying to explain how to use the exposure triangle in a quantitative manner, and the use of arrow heads is limited to only five.

There are no numbers on this version of the exposure triangle, which greatly limits the scope for confusion. If you take it to say:
  • There are 3 parameters to consider.
  • Each affects image quality and image brightness in different ways.
  • Here is a simple visual reminder. Don't stress over the details.
then there is not much of substance to argue about.

Matters get more contentious when the ET has numbers attached, which give the impression that it might offer consistent and quantitative guidance on how to manage exposure and image brightness.
Personnally, I have never seen somebody using it as a guidance.. It is more an illustration of a concept. The illustration is spot on, could not find better than using a triangle in my opinion, see below.
You may not agree, so I leave you with an observation.

If you construct an exposure triangle in which the sides corresponding to aperture, shutter speed and ISO sensitivity are labelled from low to high values, there are 8 different ways to construct the triangle. There are 4 ways of joining the first two sides, according to whether the first vertex corresponds to low values of both aperture and shutter speed (low/low), or the alternate low/high, high/low and high/high connections. For each of these 4 combination there are 2 different ways to attach the ISO range (high ISO to aperture side, or high ISO to shutter side).

This does not distinguish between simple rotations and reflections which do not change the basic connectivity.

Is there an obvious and logical way to construct the ET, so that the interactions and quantitative relationships between aperture, shutter speed and sensitivity are clear, intuitive and mathematically sound?

Do proponents of the exposure triangle agree on its construction?
I don't understand your point.
Most of the exposure triangles I have encountered are seriously lacking in clarity and soundness, and I do not find them intuitive.
Very simply said, the exposure is the representation of 3 variables whose sum must remain the same. It is a plane but with limits it becomes a triangle (see JACS representation).
The variables shown are usually f-number, exposure time and ISO sensitivity. More precisely a combination of sums and differences of their logarithms remains the same, but that does make some kind of sense.
What J A C S illustration makes clear to me is that the quantities, aperture, exposure time and ISO sensitivity, are measured normal to one of the adjacent sides, not parallel to the side of the triangle where the quantitative markings are usually labelled.
Very true.

But the 2 demos show that the graphical representation of 3 variables whose sum is constant is a triangle, that is the important point.
Similarly, the colour-coding of your diagram eliminates that potential ambiguity.

What I find confusing are diagrams like this which show brightness increasing monotonically as one follows triangular contours around the exposure triangle.

Or this, which shows increasing ISO sensitivity corresponding to "more light", when the converse is generally the case. Arguably one could make a case for "brighter" rather than "more light", but it still conflicts with the "plane of constant brightness" concept.

In contrast, in your diagram it is clear that all points on the plane of the triangle have the same brightness, with the constant ISO lines also contours of constant exposure.
I agree, this is funny to see the various interpretation of the triangle !!! It is not close....

But one important thing remains. It shows that these 3 parameters are the pillars for exposure (in fact brightness). But good triangles should illustrate at least the fact that each combination is a compromise, which is not the case for all of them.

The real numbers do not really matter because nobody uses as a guidance. What is really elegant is that it shows that only some combinations are possible and are often a matter of compromise.

What is even more elegant is that people get the idea even if this is not a detailed triangle. This is intuitive that these variables are linked, these are not 3 independant axes. 3 variables but only 2 degrees of liberties.
I see where you are coming from, but I find it much more intuitive to think along the lines that brightness, subject luminance, exposure time, sensitivity and aperture are linked via the simple proportionality relationship:

Brightness ~ L T S / N²

One could visualise this as slices through a tetrahedron, but I find counting stops rather easier. YMMV.
I find the triangle intuitive.

I agree that it can be a bit misleading for beginners, so it is important for a good teacher to explai that the ET applies in a given context (jPG). It is important for instance to explain that higher ISO does not increase noise per see, the ET is not contradictory with this as it shows an indirect relation.

Without a triangle, it is true that you can also simply explain that if you increase a parameter, you have to decrease one of the other parameter. Do we really need a triangle ? A triangle make things certainly easier to remember.

BTW, I appreciate the tone of your answer. When I had posted the demo of the triangle, i received very agressive answers, I had not insulted anybody. We are in the PST forum, everybody can post his arguments and challenge them. So thank you for this !
If some people do not like it, this is simply their opinion, nothing else, but I have a different opinion.
 
Personnally, I have never seen somebody using it as a guidance.. It is more an illustration of a concept. The illustration is spot on, could not find better than using a triangle in my opinion, see below.

----

I don't understand your point.

Very simply said, the exposure is the representation of 3 variables whose sum must remain the same. It is a plane but with limits it becomes a triangle (see JACS representation).

...

The real numbers do not really matter because nobody uses as a guidance. What is really elegant is that it shows that only some combinations are possible and are often a matter of compromise.

What is even more elegant is that people get the idea even if this is not a detailed triangle. This is intuitive that these variables are linked, these are not 3 independant axes. 3 variables but only 2 degrees of liberties.

If some people do not like it, this is simply their opinion, nothing else, but I have a different opinion.
Nice opinions [plural as self contradicting], no facts
 
But one important thing remains. It shows that these 3 parameters are the pillars for exposure (in fact brightness).
Causing user confusion between brightness and exposure seems to be a major problem with the "exposure triangle" notion.
 
A “larger plane” is for sure an interesting concept.
That is the correct term—it's a concise, more easily understood way of saying "range of image plane distances z' with an acceptable level of defocusing."
If I know what a plane is, but I don’t know anything about optics or photography, how do I know that someone who talks about a “larger plane” knows that planes extend infinitely in two dimensions, and that thus, by “larger”, they mean “deeper” and not “wider”? After all, when you stop down, the edges tend to become sharper. “Is that what the author means?” I could legitimately wonder.

It’s “easily understood” if you already know the information.
 
But one important thing remains. It shows that these 3 parameters are the pillars for exposure (in fact brightness).
Causing user confusion between brightness and exposure seems to be a major problem with the "exposure triangle" notion.
Not to mention it's not even brightness.
 
Causing user confusion between brightness and exposure seems to be a major problem with the "exposure triangle" notion.
Not to mention it's not even brightness.
Are you referring to this? https://www.fastrawviewer.com/blog/mystic-exposure-triangle
We are using the term "lightness" while referring to digital values, like it is used in Lab color space; reserving the term "brightness" for where the actual reflected or emitted light is present. Lightness is more like filter transparency, a relative value determining what percentage of light will pass through, and not how bright the image will appear - that depends on the brightness of the light. Lightness is data, while brightness is a visual perception which you can change by simply rotating a knob on your monitor.
 
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But one important thing remains. It shows that these 3 parameters are the pillars for exposure (in fact brightness).
Causing user confusion between brightness and exposure seems to be a major problem with the "exposure triangle" notion.
Not to mention it's not even brightness.
I think you simple omit, again, the context of the ET which is for JPG.
You think wrong. For brightness to appear, it needs a light source. Light source, contrary to the data in a captured image, is a variable. You can change it with a turn of the brightness knob on monitors.

Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light.

 
Causing user confusion between brightness and exposure seems to be a major problem with the "exposure triangle" notion.
Not to mention it's not even brightness.
Are you referring to this? https://www.fastrawviewer.com/blog/mystic-exposure-triangle
We are using the term "lightness" while referring to digital values, like it is used in Lab color space; reserving the term "brightness" for where the actual reflected or emitted light is present. Lightness is more like filter transparency, a relative value determining what percentage of light will pass through, and not how bright the image will appear - that depends on the brightness of the light. Lightness is data, while brightness is a visual perception which you can change by simply rotating a knob on your monitor.
Ah! Thanks for that link and quote; I was wondering about Iliah's comment, and that clarifies matters--an interesting and useful distinction I'll try to keep in mind.

Info like this is why I read PS&T.
 
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But one important thing remains. It shows that these 3 parameters are the pillars for exposure (in fact brightness).
Causing user confusion between brightness and exposure seems to be a major problem with the "exposure triangle" notion.
Not to mention it's not even brightness.
I think you simple omit, again, the context of the ET which is for JPG.
You think wrong. For brightness to appear, it needs a light source. Light source, contrary to the data in a captured image, is a variable. You can change it with a turn of the brightness knob on monitors.

Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light.

https://www.its.bldrdoc.gov/fs-1037/dir-005/_0719.htm
 
But one important thing remains. It shows that these 3 parameters are the pillars for exposure (in fact brightness).
Causing user confusion between brightness and exposure seems to be a major problem with the "exposure triangle" notion.
Not to mention it's not even brightness.
I think you simple omit, again, the context of the ET which is for JPG.
You think wrong. For brightness to appear, it needs a light source. Light source, contrary to the data in a captured image, is a variable. You can change it with a turn of the brightness knob on monitors.

Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light.

https://www.its.bldrdoc.gov/fs-1037/dir-005/_0719.htm
Ok, this was not at all the question, off topic
LOL
If this is not a brightness triangle, what is it then ?
A wrong model of exposure.

Ciao.


--
 
But one important thing remains. It shows that these 3 parameters are the pillars for exposure (in fact brightness).
Causing user confusion between brightness and exposure seems to be a major problem with the "exposure triangle" notion.
Not to mention it's not even brightness.
I think you simple omit, again, the context of the ET which is for JPG.
You think wrong. For brightness to appear, it needs a light source. Light source, contrary to the data in a captured image, is a variable. You can change it with a turn of the brightness knob on monitors.

Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light.

https://www.its.bldrdoc.gov/fs-1037/dir-005/_0719.htm
Ok, this was not at all the question, off topic
LOL
If this is not a brightness triangle, what is it then ?
A wrong model of exposure.
Strange, i had removed the term exposure.

You say that this is not brightness but you are not able to say what it is !!!

I know the ET is evil for you but you have not prooven anything, unless you deliberately decide to misinterpret the ET.
 
Causing user confusion between brightness and exposure seems to be a major problem with the "exposure triangle" notion.
Not to mention it's not even brightness.
Are you referring to this? https://www.fastrawviewer.com/blog/mystic-exposure-triangle
We are using the term "lightness" while referring to digital values, like it is used in Lab color space; reserving the term "brightness" for where the actual reflected or emitted light is present. Lightness is more like filter transparency, a relative value determining what percentage of light will pass through, and not how bright the image will appear - that depends on the brightness of the light. Lightness is data, while brightness is a visual perception which you can change by simply rotating a knob on your monitor.
Yes. In the words of Dr. Fairchild , brightness is an absolute perceptional value, while lightness is a relative value:

"Brightness - The perceived quantity of light emanating from a stimulus."

"Lightness - The brightness of a stimulus relative to the brightness of a stimulus that appears white under similar viewing situations."

 
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