The Unbearable Lightness of Mystic "Exposure" Triangle

Correct lightness ≠ correct exposure

We should begin by saying that the point of all of this is not to criticize one of the most repeated photographic myths out there – that's just a tool. The goal is to show how, by rejecting this myth, you (the now-enlightened user) will be able to more fully utilize the capabilities that your camera has, as well as to improve the quality of your photographs.

It is necessary to note at the very beginning that in this article, we will be talking about raw; we will address some JPEG considerations as well, but the primary object of this article is raw.

For those who would prefer to move immediately to the practical implications and skip the detailed analysis:

* 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.

And now, let’s start deconstructing the myth...

You won’t find very many photographic websites, blogs, or publications in general where, for the purposes of explaining exposure in photography, a model that uses as its basis the so-called exposure triangle, unifying in itself shutter speed, aperture, and ISO is not brought to bear. Texts about the exposure triangle demonstrate varying levels of authorial understanding of the roles and photographic effects of each of the component parts; however, all of these authors emphatically and categorically maintain that exposure is determined by a combination of all three parameters, and changing the three parameters (shutter / aperture / ISO) in some concordant way will cause the exposure to remain the same.

Let us note briefly that the first “triangle”, consisting of film (later to become ISO), aperture, and shutter speed was initially concocted by Bryan Peterson. In his 1990 book “Understanding Exposure,” intended for a wide array of photographers, he termed this heady brew the “photographic triangle.”

In the process of replication and “improvement” in the internet-publication supply chain, this photographic triangle somehow changed both its meaning and its name, transforming into the fetishistic “exposure triangle,” which, as makes sense with fetishes, is not just unnecessary and not just incorrect – it is, in point of fact, extremely harmful, especially when shooting raw images for maximum quality (with JPEGs, one can also do better if he discards the triangle, read on to see why and how). An incorrect understanding of the way that exposure and ISO work, as well as their roles during the shooting process, leads to a falloff in the quality of shots that photographers get.

Definitions and Facts

To start with, let’s lay out a few basic definitions and empirically verifiable (and indeed verified) facts that have to do with exposure and ISO:

• Exposure time: this is the time during which light hits the photosensitive material in your camera; when the shutter closes, exposure ends.
• Photographic exposure is only about two things: the light intensity and the exposure time: the light, coming from the scene, hitting the front element of the lens, reduced by the aperture opening, and acting during the exposure time.
• By definition, photographic exposure is calculated as the product of the illuminance of the photosensitive material and the exposure time, and is measured in lux-seconds; photographic exposure is the product of luminous flux per unit area by time.
• The elements that have direct control over exposure in the camera are the shutter and the aperture (not counting built-in neutral or other filters).
• As such, ISO cannot be an element of exposure; it’s determined through the exposure (see standard ISO 12232:2019, "Photography — Digital still cameras — Determination of exposure index, ISO speed ratings, standard output sensitivity, and recommended exposure index" and the wiki), and is “applied” after exposure.

Standard ISO 12232:2019, section 3, p. 3.7 (page.2)

• At the same time, ISO is not the sensitivity of the sensor (see the datasheets on sensors): the sensitivity of the sensor doesn’t change when altering ISO, the only thing that is changed is the scaling coefficient applied to the signal / data obtained as a result of exposure.
• Purely analog ISO increases do not cause more noise (easily enough tested empirically), because amplifier noise is minuscule compared to the other components of noise.
• The increases in noise in a shot is almost entirely caused by lowering the exposure and can only be slowed down by boosting the ISO (again, easily tested in the right experiment), because transport noise (the noise that goes along with passing a signal from a pixel to an analog-to-digital converter) and the noise from the analog-to-digital converter itself become less noticeable when the signal from the source is amplified.
• The actual photodetectors in the sensor are photodiodes. Their properties, including sensitivity / responsivity, are fixed at the time of design. No setting available in the camera can change photodiode sensitivity, and ISO is included under "no setting". ISO job starts after the photodiode job is done.
• Everywhere except the deepest shadows, the main part of noise is caused by the fundamental property of light, photons being quantum particles. This most important component of noise is called (photon) shot noise, and it is intrinsic to the light and light measurement process. What we see as noise here is the effect of the fluctuations of the number of photons detected, photon arrival events being random and independent of one another.
• The amount of shot noise inherent in the signal depends on the amount of signal — the higher the exposure, the more signal you have, therefore a smaller fraction of the signal consists of shot noise, and the higher the signal-to-noise ratio (SNR), which, in turn, translates into less perceivable noise.
• Usually it is laid out this way: shot noise SNR is equal to the square root of the signal. This means that decreasing exposure by 2 EV (4x) causes 1 EV drop in SNR (1 EV is 2x, square root of 4x).
• The main source of (excessive) noise is (insufficient) exposure, and you can control that noise, to a point. Increase the exposure, and shot noise fraction goes down. Decrease the exposure, and shot noise fraction goes up.
• If you are shooting in raw, that's the justification for setting the hottest exposure you can afford, and setting ISO only after that.
• If you are shooting JPEGs, that's the justification for setting exposure to the maximum, manually, and letting the camera set the ISO (using Auto ISO); if the camera indicates overexposure already at base ISO, start decreasing exposure.
• By setting ISO you are telling the metering system what is the target average exposure. The metering system will calculate exposure based on this, and will not suggest a higher exposure even if it is photographically possible.
• Thus, if ISO is set first, and the exposure is guided by the metering system, the intrinsic noisiness coming from shot noise is predetermined; if ISO is higher than possible, noisiness is also higher than possible. That's why it is beneficiary to start with base ISO and raise it after the exposure is set to practical maximum, or to use Auto ISO.

A few more facts, now no longer from the field of physics, but rather from the fields of standards and practices:

• The standard explicitly does not recommend and even forbids applying ISO speed criteria to raw (see below excerpts from the standard). ISO speed is defined for a “ready” shot (out-of-camera TIFF or JPEG), and as a result camera (DSC), or system, sensitivity (that is, output, not input sensitivity) is discussed in the standard, and nothing is mentioned as to the sensitivity of the sensor itself

Standard ISO 12232:2019, section 6, p. 6.1 (page.6)

Standard ISO 12232:2019, section 7, (page.11)

• The standard says that the magnitude of ISO might not play any role at all in the exposure calculation process…

Standard ISO 12232:2019, section 3, p. 3.7 (page.2)

• ... and even in the process of forming JPEGs or TIFFs in the camera.

Standard ISO 12232:2019, Introduction

• The standard in no way specifies and in no way limits the methods of implementing ISO speed or EI in the camera, leaving that to the judgment of the manufacturer.
• This ambiguity is convenient for camera manufacturers.
• As a result, the roundabout approach of the standard with respect to defining photographic sensitivity allows camera manufacturers to flagrantly disregard the very natural demands of transparency and consistency (even for different camera models released by the same manufacturer, interpretations and implementations of the positions of the standard may differ):
• advanced measuring systems (highlight priority, for example) are oriented towards the dynamic range of the scene and the dynamic range of the camera, and may not try to find the midtone at all;
• the Fujifilm DR, Sony S-Log, Panasonic V-Log modes use the ISO that the user set while calculating exposure, but when actually capturing the image will invoke a different ISO, which will be a stop or more below what the user set (when displaying the image back to you, it will use some processing to bring the midtone up to where the standard expects it to be);
• turning on Nikon Active-D Lightening may simply cause a decrease in exposure by increasing the shutter speed by a stop or more; and later, at JPEG conversion, force a different tone curve that raises the middle point to put the midtone back where it "belongs" while compressing highlights by forming a longer and more gentle shoulder (roll-off in highlights);
• etc.

Here’s our private opinion of ISO:

• really, there’s no objective reason to not extend the definition of ISO speed to raw, we would just have to answer the question of why the ISO speed ratings for raw and for JPEGs are different.

“If the triangles made a god, they would give him three sides”

Let’s return to that same “exposure triangle” and take a look at a few of the major contradictions that flow out of the model it offers.

OK, we’ve set an exposure, and then for some reason (maybe we zoomed in) we increased the shutter speed by a stop and compensated for this by opening the lens aperture by a stop. Obviously, the exposure stayed the same (see above the definition of photographic exposure).

Now, let’s imagine that we were not able to compensate for the increased shutter speed by further opening the aperture, and, instead of that, we increased the ISO. What happens to the exposure? Would it, as with the previous situation, stay the same? Based on the definition of photographic exposure, obviously not. So, what do we do with the exposure triangle, from which it follows that the exposure doesn’t change in the second situation the same way that it doesn’t change in the first?

Let’s set up the question a bit differently. Suppose we made two shots that differed only in the ISO setting. If we follow the triangle, these two shots have different exposures. However, this is obviously false: going off of the definition of photographic exposure, both shots were taken with the exact same exposure. How do they differ then, well, other than in ISO? The answer: they differ in lightness.

Accordingly, a change in ISO leads to a change in the lightness of the image as processed by a converter, and not to a change in the exposure of the shot, which, for a given scene under given light, is determined only by the shutter speed and the aperture, which are set during the shooting process. So what is ISO doing in the “exposure triangle”?

Take a good, close look at the two shots, equalizing the lightness between them. Do you see it? The one that’s shot at a higher ISO has a bit less noise (well, for some cameras and some ISO ranges, they’ll actually be virtually identical) – meanwhile, the triangle leads one to think that something completely different should be going on; according to the triangle, raising the ISO should raise the noise. But, the highlights on the shot with the higher ISO are also clipped a bit more, and the triangle didn’t even have the courtesy of warning us about that.

If you would like to check this for cameras that you don’t have, you can do this using an application on DPReview.

On the application page, select a characteristic area of the target for study

... and then pick out a camera and ISO from the list

As you can see, for the 4 cameras selected for this example, the shots at ISO 3200 are less noisy than equally exposed shots at ISO 200. Contrary to popular opinion, raising ISO helped reduce the noisiness.

In general, there are a lot of riddles in this triangle, which, really, seems to be common for triangles: for some reason, it has substituted the meaning of “lightness” for the meaning of “exposure”, while the strange markings on the sides call to mind the words of the school math teacher trying to gently explain why it is not (to put it mildly) correct to add together lightbulbs and oranges…

Let’s take a closer (mental) look at the sides of the triangle (we are consciously not showing an image of the exposure triangle here, but those who would like to refresh their memory of it can easily find dozens of publications dedicated to it online, all with the same triangle in them, the only difference being the artistic preferences of the graphic designer and the graphics packages that they’re used to).

On two sides, corresponding to the elements of setting exposure, we have comprehensible, simple, and practical photographic goals – more DoF, less blur, … In the triangle, DoF is tied to the aperture, which is accurate (we won’t nitpick “small details” like the fact that diffraction is not mentioned, let alone illustrated, at all, and diffraction, starting from a certain aperture number, significantly reduces sharpness). Blur is tied to the shutter speed which is, again, generally accurate.

The problems start with attempts to grasp the mystery of the third side on offer, “ISO”:

• The triangle ties the level of noise to ISO instead of tying it directly to exposure.
• If some publication doesn't clearly state the above, the author doesn't understand what photographic exposure is. Further, connecting the perceived noise level with ISO is a terrible mistake, with far-reaching consequences. According to the triangle, f/5.6 1/200 sec ISO 200 is the exact same exposure as f/5.6 1/3200 sec ISO 3200, the second is just “noisier” due to the “noise that is inherent to high ISOs.” In actuality, in the second case the exposure is, by definition, 16x, or four stops lower.
• Exactly this, this quite significant difference in exposure, is primarily responsible for the difference in the perceived noise level, while raising the ISO, contrary to the teachings of the triangle and the pronouncements made by its adepts, not only does not amplify this difference, but in fact smooths it out. It is quite easy to check and convince oneself of the fact that a shot with the same exposure as for the one at ISO 3200 (f/5.6 1/3200 sec), but taken at ISO 200, after equalizing its lightness with the shot taken at ISO 3200, is just as “noisy” or even more so than the one at ISO 3200, and furthermore might not entirely hold the neutrality (or white balance, if you prefer to put it this way) in the shadows.
• And here’s the next bit of foolishness: raising ISO is somehow tied to amplifying the amount of light falling on the sensor, or speeding up its “collection” and measurement.
• Which light, falling where, amplified how, and measured by what? Raising ISO is amplifying/multiplying the signal we already got. ISO is just an after-the-fact thing. By the time ISO kicks in (which is done only at the stage of converting the already accumulated during exposure photo-charge with the goal of getting an image with the lightness in the midtone that was determined by that ISO), the exposure is already over, the light has been collected and measured. Meanwhile, the analogy of how the ISO level regulates the number of bees in your bonnet (oh, pardon me, your camera), well that’s just straight out of the theater of the absurd, no matter what "The Book" may state.
• Why is it that ISO has an equal leg (with aperture and shutter speed) to stand on in the “exposure triangle,” so equal in fact that the triangle is equilateral?
• ISO, by definition, plays no role in and of itself in exposure. The only way that it can affect exposure is indirectly, by causing the user to change the shutter speed and/or aperture settings.

A Few Other Sharp Questions

Let’s start with the main question. Why is it that this triangle is necessary at all, and what exactly does the graphic allow for in terms of easier and better explanation?

1. Where did this “exposure triangle” name come from, when the object of this triangle is lightness (something that is much less significant than exposure, by the way)?
2. What is the point in unifying the parameters for setting the exposure (shutter speed and aperture) with parameters for regulating lightness (ISO) in the triangle?
3. The only result of this combination is that it creates a perverse and incorrect perception that both exposure and lightness are selected once and for all at the moment when the shutter release is pressed. Of course, the exposure is set before the shutter opens (except for the scenes where the light itself changes during exposure: light painting, flash photography, etc.) and cannot be changed after the shutter is closed, but what does lightness have to do with any of this? Lightness is a separate and independent parameter, which is set through and regulated while processing and editing the image. The lightness of the image that you get out of a shot can be changed any number of times.
4. Thom Hogan gives a story of sorts that applies here - Ansel Adams:
5. "If you were to go to an Ansel Adams gallery or retrospective and look at his work over time, you'd notice something: the prints changed. Earlier in his career, the prints were lighter, brighter, and somewhat less contrasty; over time he often re-worked and re-printed work darker and with more contrast subtleties. Quite obviously, his "exposure" wasn't changing, because the negatives that he was printing from were already processed and fixed. What was changing was what he did with the exposure he had captured. It's not a coincidence that he split his books up into ones that individually covered the capture, the processing, and the printing. He was separating exposure from artistic interpretation."

3. Is the triangle really needed to understand the basic (and let’s note, not always applicable at this point in time) principle of how light measurement and exposure calculation systems in the camera work, which consists of “with this scene (il)luminance and with this ISO setting, to get standard lightness in the midtone of the image you need this exposure” or “with this scene (il)luminance and with this exposure setting, to get the standard lightness in the midtone of the image you need this ISO”? (Let’s note that not even Bryan Peterson, in any of the five editions of his book “Understanding Exposure” that we have, uses any triangles in any of his illustrations.)
4. Does the triangle help us understand that it is precisely exposure that we need to raise in order to reduce noise?
5. Does the triangle help us understand that after the exposure has been raised to the limit, the next resource for lowering noise is raising the ISO (for those cameras and those ranges of ISO where the ISO controller affects something - apart from lightness) - at all, which is not all cameras and not all ranges of ISO)?
6. This is to say nothing of the fact that the triangle prevents one from understanding the standard mechanism for working with autoexposure – when raising ISO, the exposure falls (and, to repeat, it is precisely because of the decrease in exposure that the amount of noise rises; writing under the ISO side that “more exposure, less noise – less exposure, more noise” is forbidden by the dogma of The Triangle).
7. Because the triangle mistakenly includes ISO into exposure, it contradicts even the basic principle of the zero click sum to hold exposure constant:
   • Each click that increases the shutter speed is balanced by an aperture click, opening it more
   • Each click that decreases the shutter speed is balanced by an aperture click, closing it more
8. The triangle performs a bait-and-switch in terms of goals – instead of optimizing exposure with the goal of raising the quality of the image, the emphasis is placed on maintaining the lightness, which has no real connection to the quality of the image.
9. The length of the texts that inevitably accompany and decode the triangle do not inspire confidence in the explanatory benefits of the model.
10. And so on and so forth...

The situation is made even worse by the fact that the adepts of the triangle not only do not understand what “sensitivity of DSC as per ISO” means, but make a series of monstrously absurd statements in their articles, which fails to inspire confidence in any technical texts that seep out of their quills. Here are a few examples:

• ... "we can control the sensitivity of the digital sensor on the fly";
• ... "increased ISOs result in increased noise and less detail";
• ... "basically, the lower the ISO number, the less light is hitting your sensor";
• ... "the aperture is the hole inside your lens, which acts as the ‘iris’ similar to your eyes. A wide or low-number aperture, such as f.2/8 will have a very small focal length";
• ... "a typical range would be f/1.4, f/2.8, f/4, f/5.6, f/8, f/16 and f/22. The numbers almost double every time. For the ones that don’t (f/4 and f/22), they are usually the previous two numbers added together (or thereabouts)";
• ... "you need to add two more stops of light into your settings for a correct exposure. You could add it using ISO, changing it from 100 to 400".

Once More into the Negatives of the “Exposure Triangle” Dear Friends, Abridged Version:

• The triangle model states that noise rises as a result of ISO being increased.
• This is tosh, it’s worse than saying that “well, the wind is blowing because the trees are swaying” (in that case, all that’s happened is a mix-up of cause and effect), it’s like saying that the sea is salty because of all of the lox swimming in it (which goes beyond just confusing cause and effect, because here the “cause” is an absolute invention – a salmon swimming in the sea isn’t salty, while lox, a product of brining salmon fillets, doesn’t swim in the sea. It doesn’t swim at all).
• The model warns against raising ISO “because of increases in noise”.
• Another lie – everything is exactly the opposite; when the exposure is fixed, not only will raising ISO not worsen the signal-to-noise ratio, it may noticeably improve it.
• The model says, right in the name, that ISO is a part of exposure, which is absolute balderdash.
• The model presents ISO as a part equal to exposure itself (highlighted by the fact that the sides of the triangle are equilateral), which is, again, absolute nonsense.
• The model does not at all underscore the leading role of exposure in controlling noise and dynamic range. In fact, the model hides it.
• Exposure is much more important, and it needs to be set first so as to be as high as possible, while ISO is set afterwards so as to reach the desired lightness, but without clipping the elements in the highlights that are important to the composition of the scene. In this case, even the simple in-camera histogram isn’t unhelpful, because a mistake towards insufficiently high ISO leads to less, if any, additional noise than a mistake with the exposure due to a premature clipping indication taken “from the JPEG”.
• The model suggests that one consider the goal of exposure to be lightness.
• Absolute hokum. Lightness only appears as a result of rendering and processing, and all of that happens after exposure. Exposure and lightness are different physical quantities, with different units of measurement – how can they be interchanged?

When it is written honestly under the triangle that in auto-exposure mode raising the ISO causes a decrease in exposure, and lowering exposure causes the very increase in the noise level that they now attribute to ISO, then and only then can we start at least discussing said geometric shape as a triangle of lightness (but lightness, not exposure!) for JPEG.

When, in their commentaries on the triangle graphic, the publicists indicate that in order to increase the DoF, they closed the aperture; and to decrease blurriness they increased the shutter speed; and thus exposure fell, while the ISO increase did not compensate for this drop in exposure except by raising the lightness, then, maybe, the flood of plaintive prayers about “noise and stripes caused by high ISO” might abate somewhat.

Right now, this “exposure triangle” only confuses photographers, and then one has to do serious battle with these confusions that have grown like mushrooms in a dark corner of the internet. Right now, this triangle can only be laughed at as a product of absolute illiteracy, while the articles that “explain” it must be mocked as malicious disinformation.

So, maybe, just maybe, stop advertising it and citing it, especially considering that much of it (starting from its name) is incorrect, while the complete lightness triangle diagram is complicated and not very useful in practice? Maybe it would be better to begin learning the right way from the start?

Summarizing Key Facts

• Analog amplification and increasing the pixel gain are here to decrease the noise, that's their raison d'être, not the purposes of compensating for "under-exposure" or raising lightness.
• Lightness is a question of scale. If the analog amplification does not give you enough advantage in the signal-noise ratio, then in practice this amplification doesn’t need to be there and only the negative and harmful effects of it remain (for example, in scenes with high dynamic range it could lead to abrupt “cut-offs” in the highlights). The contribution of analog amplification to noise reduction differs from camera to camera, and can often differ for different modes and ISO settings in the same camera, so each individual photographer ought to spend some time with their own camera to experiment, the same way that back in the days of film, each purchased batch of film was subjected to individual testing.
• The ISO controller in the camera ought to be looked at as a scale multiplier (analog, digital, hybrid) with the function of a noise reducer, and used depending on the effectiveness of noise reduction in the current handle position, taking into account the highlight clipping as the coefficient rises. (The terms “multiplier” and “scaling” are fairly stably used in the analog world, as a search for “analog multiplier” and “scaling amplifier” will show.)
• The practical effect here is precisely noise reduction, while the fact that this is reached via an amplifier and / or through increasing pixel gain is an implementation detail, the method of noise reduction. Scaling the raw value in the camera carries no useful function in and of itself. We could, with the same result, increase the lightness in the raw conversion process.
• For a shot with acceptable lightness, you can treat ISO setting used for the shot as an indicator of "underexposure" on the shot (relative to the full exposure the sensor can tolerate); and expect the noisiness that comes with this amount of underexposure.
• Raising the exposure decreases the perceived noise more than raising the ISO.
• The exceptions to this are generally at very low ISO, close to the base: there are a fair amount of Canons for which, from ISO 100 to ISO 200, the character of the noise becomes subjectively less irritating, sometimes noticeable less irritating, while objectively the other parameters of quality do not suffer; Sony DSLR-A900 also has our preferred ISO a bit higher than the base, and a handful of other models by various manufacturers exist where the base ISO is noisier or the noise is more irritating than at ISOs a bit higher than the base. This is mainly because the amplification is necessary after all, and a 14-bit ADC isn’t always enough at the base ISO.
• Raw has no lightness in and of itself;
• Raw is the result of measuring the illuminance of the sensor, which is done by the pixels, or photodiodes, though the optical filters at the time of exposure. Just as the reading on a voltmeter won’t shock you, raw will not blind you.
• The goal of exposure isn’t lightness; it’s recording as much data as possible about elements of the scene that are important to the composition.
• Overexposure in RAW is not a shot that’s “too light”, it’s the loss of details that are important to the composition of the scene in the highlights. Lightness is set according to taste during conversion.
• Underexposure in raw is not a shot that’s “too dark”, it’s an excess of noise in shadows that are important to the composition of the scene.

We'll repeat again:

Many thanks to Thom Hogan and Andrew Rodney for reviewing a draft of this article.

For specific information on ADC noise, please see an article by Analog Devices "ADC Input Noise: The Good, The Bad, and The Ugly. Is No Noise Good Noise?"