Understanding Your Lens (Part 3)

In this third instalment of understanding your lens series, we will be concentrating on f-stops.

First, we need to clarify the word f-stop which a lot of photographers (including myself) refer to as aperture. Although f-stop and aperture are related, they are different. Aperture refers to the actual opening of the lens which is usually measured by the diameter of the opening. F-stop, on the other hand, is the ratio of the focal length and the diameter of the aperture of the lens. This is a very important distinction between the two and we will look into that in detail later on.

Every photographer should be familiar with the common f-stop numbers. They are as follows:

f22, f16, f11, f8, f5.6, f4, f2.8, f2, f1.4

Memorize those numbers because they are very important especially when you start using manual exposure mode. You should also know by now that the smaller the f-stop number, the bigger the lens opening. That is, f16 is a smaller opening compared to f8 on the same lens. The photo below shows the huge difference between f1.4 (left) and f16 (right).

Image

(Photo taken from Wikipedia)

Notice that I emphasized on the same lens. Different lenses have different opening sizes. On a telephoto lens, f8 will have a larger opening compared to a normal lens at f2.8. Let’s see why …

Consider a 300mm telephoto lens and a 50mm normal lens. Recall that f-stop is the ratio of focal length and aperture diameter or mathematically:

f-stop = ( focal length / aperture diameter)

or

aperture diameter = (focal length / f-stop)

So for the 300mm lens at f8 the opening is:

300mm / 8 = 37.50mm

and for the 50mm at f2.8:

50mm / 2.8 = 17.85mm

As you can see in the above example, there is a huge difference in the diameter of the lens openings. You can actually see this for yourself if you have a zoom lens. Look through the front element of your zoom lens and then zoom in and out without changing the aperture. You will notice how the opening increases in size as you zoom to a longer focal length.

Understanding this very basic concept is important because f-stops control exposure. F-stops regulate the amount of light that hits the camera’s sensor. It is quite obvious that the larger the opening the more light comes in. The problem is that it is not enough that you know the size of your lens opening. Back to the 300mm vs 50mm example above, 37.50mm is obviously larger than 17.85mm but we also mentioned that f8 is smaller than f2.8 so what gives?!

Well there is another factor that affects the amount of light hitting the sensor and that is distance from the light source. The farther the light source, the lesser the amount of light and that’s why stars look much fainter than our sun. In photography, this distance is the focal length of your lens. The longer the focal length, the farther the rear end of the lens is from the sensor. Another thing that you should understand is that the intensity of light varies as the square of the distance. What this means is that given the same lens opening, light coming from a 50mm lens has four times the amount of light coming from a 100mm lens. Mathematically,

light intensity = (100mm / 50mm)2 = 4

It follows that for the 100mm lens to get the same amount of light as the 50mm lens, it needs to have a larger lens opening. The immediate question is, by how much larger of an opening? This is why knowing your lens opening is not enough to control light. You should also keep track of your focal length. This makes photography so much more complicated than it should be.

And so they “invented” the f-stop. Again, recall that f-stop is a ratio of the focal length and the lens opening diameter. It is very clever because it calculates the light intensity for you automatically no matter what your focal length and your lens opening are. So given this information let’s calculate the lens opening diameter for both 100mm and 50mm at the same f-stop, say, f8:

100mm / 8 = 12.5mm

and

50mm / 8 = 6.25mm

So double the focal length requires double the lens opening diameter for the same amount of light hitting the sensor. Imagine having to change your lens opening every time you zoom in and out. Instead, you just set your f-stop to, say, f5.6 and let the lens handle the opening according to your focal length of choice. And that is exactly what you see when you keep a constant f-stop and look through the front element as you zoom in and out. Easy!

How does f-stop relate to the amount of light hitting the sensor? Each stop of difference is double the amount of light. For example, going from f5.6 to f4 is twice the light intensity and going from f4 to f2.8 is also double the intensity. So going from f5.6 to f2.8 is four times the amount of light and so on.

Let’s summarize what we have discussed so far:

1. The amount of light hitting the sensor is affected by the lens opening (aperture).

2. The amount of light is also affected by the distance of the light source to the sensor (lens focal length).

3. A f-stop is the ratio of #2 and #1. This allows us to easily calculate light intensity because the lens automatically adjusts the aperture as focal length changes. We only have to worry about one parameter instead of two.

From this, it is easy to see why fast lenses, those with wide apertures such as f1.4, are much larger than slower lenses of f4. For the same focal length, the faster lens needs to have a wider opening diameter. This also explains why some zoom lenses have varying apertures and others have constant apertures. Lenses with varying apertures, say, f4 on their widest to f5.6 on maximum zoom, are cheaper because the aperture does not change much going from wide to telephoto and are therefore smaller in terms of diameter and only need smaller glasses. Constant aperture zooms are not only more expensive but also bigger and heavier because they have to open up much wider as the focal length increases. Wider, bigger and more glass. Finally, this also explains why m43 lenses are much smaller than their full frame counterparts. The smaller m43 sensors require shorter focal lengths to cover the entire sensor area and therefore have smaller lens opening diameters.

Before I end this post, let me address a very common misconception. A lot of photographers think that full frame sensors are better than m43 sensors at capturing light because they have larger surface areas. This is not true simply because a sensor without a lens in front of it is useless. Now with a lens in front, we know that an f-stop is the same for any sensor size. A full frame camera requires a longer focal length and therefore a lesser amount of light hits the sensor compared to a m43 camera that requires a shorter focal length because of the smaller sensor. A f-stop of f5.6 in a full frame camera allows exactly the same amount of light per unit area as f5.6 in a m43 camera.

I hope you learned something in this post. There will be more next time.

Keep shooting.

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6 thoughts on “Understanding Your Lens (Part 3)”

  1. Interesting blog. Your second to last paragraph is partly true, partly misleading and partly unclear.

    It is true that for a given ideal f-stop and shutter speed, Exposure (what you call the amount of light per unit area and which I prefer to think of as photons per unit area) is the same independently of sensor format.

    However it is misleading to imply that Full Frame sensors do not capture more ‘light’ than smaller formats most other things including Exposure being equal: they do, as you say, because they have relatively more surface area and therefore capture more photons overall (or ‘light’ if you prefer).

    And it is not clear whether you meant to include concepts of equivalence in the relative discussion. Many are quite counter-intuitive and need to be discussed individually and explicitly for clarity.

    Cheers,
    Jack

    1. While FF gathers more light, that light is spread across a wider area. Light gathering in photography is all about exposure, that is, light per unit area and NEVER about total light. The unit area in a sensor is the individual pixel.

      What confuses a lot of people is that they are comparing a sensor to a solar panel. While individual solar panel cells contribute to the total energy produced, camera sensor pixels are totally independent of each other in capturing light. This is pretty obvious — the shadow parts of an image are way more noisy than the bright parts. Thinking only about total light captured is photographically very wrong. It’s light intensity that matters.

  2. That may very well be but as far as Image Quality is concerned (specifically SNR and DR) what confuses a lot of people is not realizing that digital photography is all about the image of the scene projected by the lens onto the sensing plane – which in current applications is mostly independent of sampling frequency (pixel pitch/area).

    To see this, for example, take pixel pitch out of the equation by assuming that sensors of both formats have the same number of pixels. The FF pixel will therefore be 1.5×1.5=2.25 times as big as the APS-C’s. For a given Exposure (shutter speed and f-stop) and image captured the FF pixel will therefore receive 2.25x the number of photons as the APS-C’s, resulting in a higher signal and correspondingly lower SNR both in the highlights and shadows of the raw captured data.

    Within limits of current typical applications, this works even when you do not control for the number of pixels in the sensor. So sensor size does matter in terms of the SNR and DR of the displayed photograph. Pixel pitch/area matters as well but it is instead mostly related to a different IQ parameter, namely the maximum spatial resolution captured.

    1. I think that argument is fundamentally wrong in the sense that the basic light gathering unit of a sensor is the sensel. Each sensel has SNR and DR INDEPENDENT of other sensels. It’s not the sensor that captures light but the individual sensels. In film photography that’s equivalent to the individual film granules. A sensel that happens to capture a shadow area will have noise while those that are in bright areas will look clean. They are independent of each other. While the TOTAL light gathered may be greater in FF, an APS-C sensor does not need half of that light (that’s why it’s called a crop sensor).

      Have a look at film. The same emulsion is available in different sizes but you expose them in EXACTLY the same way. The same sunny f/16 rule applies whether it is 35mm or 8×10 sheets although the 8×10 film has captured way more light. It simply means that total light gathered has ansolutely got nothing to do with photographic exposure. It has always been LIGHT PER UNIT AREA. Full frame has more gathered light but dispersed in a larger area so SNR and DR remains constant.

  3. I am glad we agree that what counts is the image on the sensing plane and not the sensing medium. I would leave Sensitivity out of the equation for now not to complicate things (Sunny 16).

    On the other hand I am not sure what you mean when you say that ‘total light gathered [total number of photons captured] has absolutely got nothing to do with photographic exposure’: in fact the number of photons captured for a given image and Exposure is proportional to Exposure times Sensing Area – independently of sensing medium.

    I am also not sure I understand what you mean by ‘Full frame has more gathered light but dispersed in a larger area so SNR and DR remains constant’. That’s definitely not the case when displaying a photograph of the same image captured at the same Exposure (shutter speed and f-stop) by two different sensing formats. As I showed in the example in the previous post in such a situation the FF sensor (or its sensels if you prefer) receives more than twice the number of photons than its APS-C counterpart. This results in a higher Signal recorded which produces lower SNR and DR in the larger format aotbe.

    I think you may be referring to a different situation which needs to be better flushed out.

    Cheers,
    Jack

    1. Hmmm…let me try to explain one more time. I’ll quote one of my articles. See how you go with this one:

      “Supposing that you have a D800 sensor under any lens. Keep the same lens but now cover one half of the sensor with a completely opaque material therefore exposing only half of it. Do not cover the lens; just the sensor. If the myth is true, then it follows that this sensor half (a crop) will now gather less light and therefore produce more noise. Now uncover this half and cover the other half. Again, if the myth is true then this second half would also gather less light and, just like the other half, will produce more noise. It follows that if you fully uncover the full frame sensor, it’s really just a combination of two more noisy halves! The myth is telling us that two noisy half-sensors will produce one clean full frame sensor?! This is absurd!

      This thought experiment is not just a thought experiment. It actually happens every time you click your shutter. At fast shutter speeds, the shutter curtain does not actually fully open and close. Instead, the shutter curtain behaves like a very small slit that glides over the sensor. Therefore, the sensor is not exposed as a whole at the same time but in chunks defined by the curtain slit size. This slit is way smaller than half a sensor. Since this slit exposes only a part of the sensor at any given time, your full frame is really acting like a combination of multiple smaller sensors! If the myth is true then a full frame sensor is really just a combination of multiple very small noisy sensors!!!

      We can continue this experiment by further subdividing the sensor until we come to a point where all we have left is just one sensel. If the myth holds then this sensel will be hopelessly noisy. It follows that a full frame sensor is composed of individual hopelessly noisy sensels!

      The only conclusion is that sensor size does NOT matter! Note that half of a full frame is your APS-C sensor. Therefore full frame and APS-C have the same light gathering capacity and therefore exhibit the same noise profile!”

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