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My understanding of ISO is that it is electronic gain from recorded light in a sensor, ie it doesn't actually change the sensitivity of the sensor (because that is dictated by the quantum efficiency of the sensor), rather it just amplifies the light more or less by reducing the dynamic range. As such, it doesn't actually influence exposure.

This being said, most sites/ books I have read on the topic refer to the 'exposure triangle' being f/ratio, shutter speed and ISO. If it is true that ISO doesn't actually change the exposure, why is it counted as part of this graphic? The only reason I could think of, is that exposure is defined in these cases, as the point at which the image is closest to middle grey, rather than the actual amount of light collected, and therefore signal from the sensor.

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You're both right and wrong.

Yes, technically the "ISO setting" is merely an amplification of sensor data. However the quantization (feeding the analog signal into the analog-digital converter) happens after the amplification. So, from the sensor (as in photosensitive die alone) point of view, the amplification doesn't change the actual light sensitivity. But for the rest of the camera, "sensor" is the whole package: photosensitive silicon, amplifier and DAC. So, from the point of the camera, the effective sensitivity is changed.

Bonus: RAW is what comes straight from DAC. So even if you're dealing in RAWs, the "ISO setting" has already affected exposure.

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We control the sensitivity of the digital sensor or technically speaking controlling the post-image gain applied to the signal, but for all intents and purposes, we can think of it as sensitivity.

It is part of the exposure triangle because when using an automatic or semi-automatic exposure mode the ISO setting influences the selected shutter speed or aperture. It's part of the equation, just like the two other parts.

ISO changes, does change exposure.

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Because the gain you set affects the image.

The higher the gain, the brighter the resulting image from the sensor. While it may not specifically be the sensitivity of the sensor hardware to light that's affected, the sensitivity of the final image data to the light is affected by the iso setting you choose.

Whether or not you use a gain setting of iso 100 or iso 1600 still makes a very large (four-stop) difference on the shutter speed/aperture setting combinations you can use to make a good exposure.

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ISO (International Organization for Standardization) specifies how photographic films are to be tested to determine their sensitivity to light. The ISO of any film is one of the key elements needed to calculate the camera exposure settings.

Technically the ISO value is specific for films however digital photography embraces ISO thus the ISO settings of the digital camera mimic the ISO settings of the film camera.

You are debating the accuracy of the ISO setting of the digital camera. Consider: You are a film photographer with a camera loaded with 100 ISO film. On a sunny day the “Sunny 16” rule of thumb is applicable. Set aperture to f/16 – set shutter to 1 over ISO = 1/100. Such a setting will likely deliver a reasonable image. Note that the three ingredients are ISO – f/number – shutter speed.

Now suppose this film photographer chooses to artificially elevate the sensitivity of the film he/she is using. This is possible (routinely preformed) by changing the method used in the film chemical development process. One can “push process” and double of triple the rated ISO of the film. Say the film speed is doubled by aggressive development. Now the film preforms as a 200 ISO film. Using the “Sonny 16 Rule”, the revised exposure is f/16 @ 1/200 of a second shutter speed.

My message is, don’t let details of how the digital camera manipulates the sensitivity of the imaging chip. What is important is, what is the ending ISO as this value is one of the three pieces to the puzzle of the exposure.

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