What is equivalence and why should I care?
And it's not just depth-of-field
|Here we show the light being cast by a lens onto a Full Frame sensor. If you roll your mouse over the APS-C tab, above, you'll see what happens if you mount that same lens on a smaller format:
1) The first thing you'll notice is that the sensor 'sees' a narrower angle-of-view (which is why a 50mm lens on an APS-C sensor is considered to be 'equivalent' to a 75mm lens on Full Frame).
2) You are no longer capturing all the light that the lens is projecting. The light intensity on the sensor remains the same, but the amount of light you can capture has dropped. (Because you're now only capturing the inner, bronze colored cone of light, rather than the more yellow one).
The equivalent aperture not only tells you how much depth-of-field you get, on a different system, it also tells you how much total light you'll get. And, because the more light you capture, the less noisy your image, this is key to why large sensors generally give better image quality than small ones. This, as we said at the beginning of this article, was just as true when dealing with film formats: that's why people shot medium- and large-format film.
But surely F1.2=F1.2=F1.2?
Yes, it is. But F1.2 is not equivalent to F1.2 across different formats.
The F-number itself doesn't change with sensor size, just as actual focal length doesn't change with sensor size. However, the situation is essentially the same as with equivalent focal lengths: put a 50mm lens in front of a smaller-than-full-frame sensor and it's still a 50mm lens, but you get a narrower angle-of-view, because you're not capturing the full extent of the circle-of-light the lens is projecting. So we might say the lens is now 'acting as a 100mm equivalent' lens.
In a similar way, the actual F-number always tells you the intensity of the light on each square mm of the sensor - this doesn't change with sensor size. By comparison, the equivalent aperture takes into account how many square mm of sensor you've put behind the lens.
Really appreciating the difference in total light is made a bit more complicated, though, because of ISO.
|This Micro Four Thirds camera is pictured here with a 42.5mm F1.2 lens.
Its field of view is equivalent to an 85mm lens on Full Frame, so it can be thought of as an 85mm equivalent F1.2 lens.
However, it can also be useful to understand the depth-of-field it can offer. As we've seen, it can also be thought of as an 85mm F2.4 equivalent lens.
|However, while its F1.2 aperture isn't equivalent to F1.2 on a Full Frame camera, if you roll your mouse over this box, you'll see that it's a lot smaller and easier to carry around.|
ISO and its role in clarifying and confusing
The thing that complicates matters is ISO. ISO ensures that, if you expose a sensor to a given light intensity for a given amount of time, then you will get a certain brightness in your final (JPEG) image. Because it's based on intensity of light, it means that ISO depends on F-number, not equivalent aperture. This means that, a Four Thirds camera with a 50mm f/2 lens at ISO100 should produce a JPEG of the same brightness as a Full frame camera with a 100mm f/2 lens at ISO100 and, set to the same F-number and shutter speed, even though its smaller sensor means it is receiving 1/4 as much total light.
ISO is useful, in that it means that the same set of exposures work across all cameras (and frankly, it'd get confusing, otherwise). However, it ends up disguising how much total light each system gets. Since the light intensity is the same (per square mm), the Full Frame camera will receive four times as much light as the Four Thirds camera, during those exposures, because it has four times the sensor area, all experiencing that same intensity.
And this means that, for the same shutter speed, F-number and ISO, the camera with the largest sensor will have more total light to measure. And, unless the large sensor is significantly worse than the smaller one, it will produce a cleaner, less noisy image. It's likely that the large sensor camera will be bigger, heavier and more expensive, but it should provide cleaner images.
The flip-side of this is that, if you can fit a faster lens to a smaller format sensor or use a slower shutter speed then you can match the total light available to the larger system and gain similar image quality. However, this only really works in low light, where you're limited by the availability of light. In bright lighting conditions, where you're more worried about highlights clipping than you are about noise swamping the shadows, you can't simply open the aperture up to match a larger sensor's total light - you'll just end up over-exposing.
So can't you have equivalent sensitivities?
So, if the sensor area affects how much total light a camera is exposed to, doesn't that mean you can say this ISO on camera A is equivalent to that ISO on camera B?
Yes, and no. In theory you can work out how much total light one system is receiving, relative to another, and calculate 'equivalent sensitivities' - the ISO settings that would provide an image from the same amount of total light (and hence have similar noise properties). However, there are enough differences in sensor performance that, without knowing a lot more about the specific sensors you're comparing, you can't assume, for instance, that twice the total light means twice the overall low-light performance.
• Multiply the actual focal length by the crop factor and you get the equivalent focal length.
• Multiply the F-number by the crop factor and you get the equivalent aperture.
• The equivalent aperture tells you what aperture on a full frame lens would give the same depth-of-field and the same total light as the one you're assessing.
• F-numbers tell you about light intensity (how much light each square mm of the sensor sees). A larger sensor has more square mm collecting light.
• F-numbers and ISO are sensor-size independent. Knowing the F-number is useful - but you need to remember that ISO100 on a small sensor won't be the same quality as ISO 100 on a larger sensor.
And, while we're summing these things up: different formats cannot have a 'depth of field advantage' over another. Although diffraction depends on F-number, its impact on the image is proportional to sensor size. This means diffraction will have the same impact on two images shot at equivalent apertures. As a result, if an aperture is small enough to give the desired amount of depth-of-field, it'll show the same amount of diffraction, regardless of sensor size.
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