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Both increasing the sensor size and increasing the aperture size (in terms of f-stop) increases low light performance and decreases depth of field.

Given, say, an equivalent of a full frame and f/1.8 level of low light performance and depth of field, would it be better to have a larger sensor with smaller f-number or a smaller sensor with larger f-number? (which would be more cost-effective, compact, sharp etc)

closed as primarily opinion-based by Philip Kendall, mattdm, scottbb, Itai, Michael C Nov 30 '16 at 5:27

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    I'm voting to close this as primarily opinion-based. There are various tradeoffs and each has its advantages and disadvantages for different situations and preferences. If that weren't the case, there naturally would not be any options on the market — just the one best thing. Perhaps you could reword to focus on the more objective question of what situations would be preferred over the other. – mattdm Nov 29 '16 at 17:56
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    Except technically, increasing sensor size requires less enlargement, which increases permissible Circle of Confusion, which increases depth of field. We get the notion of the opposite effect because the larger sensor requires a shorter focal length lens just to see the same view size, and it is only the shorter focal length that decreases depth of field. But all things equal, the larger sensor technically is the opposite. – WayneF Nov 29 '16 at 23:36
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    comparing the same f-numbers is unfair, because the bigger camera automatically gets bigger aperture and therefore more light. taking two cameras only differing by sensor size but having equal aperture might be more interesting! – szulat Nov 30 '16 at 0:08
  • @szulat Please explain how the bigger camera "...automatically gets bigger aperture?" – Michael C Nov 30 '16 at 5:16
  • @WayneF I think it is more the idea that one must shoot closer with the same focal length to get the same framing that leads to the often correct assumption (depending on all of the variable that are normally implied, rather than made explicit) that the DoF will be thinner with the same lens at the same aperture on a larger sensor. – Michael C Nov 30 '16 at 5:19
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[W]ould it be better to have a larger sensor with smaller f-number or a smaller sensor with larger f-number?

In theory, both options are equivalent in every way - the low-light performance, the amount of background blur, the angle of view, and everything else.

First, let's clarify what we mean by aperture size. The absolute aperture size of a lens is the diameter of the opening in the lens's diaphragm - for example 30mm. The relative aperture size, or f-number, is defined as the focal length of the lens divided by the absolute aperture size. For example, a 50mm lens with a 30mm aperture has an f-number of 50÷30 = 1.667. The lens is labeled as f/1.667, which makes sense because if we substitute the focal length of 50mm as f, then f/1.667 = 50mm ÷ 1.667 = 30mm, which is precisely the size of the absolute aperture.

Spoiler: It turns out that if you have two sensors of different sizes, and two lenses that have the same absolute aperture but different focal lengths to produce the same angle of view on its respective sensor, then the resulting image will be the same in every way.

Suppose we have a full-frame sensor and a 64mm lens with a 32mm absolute aperture. The lens's relative aperture is f/2.0. The horizontal field of view is 31.4°. The rate of light gathered by the lens (per unit of time) is dictated by the diameter of the absolute aperture. It doesn't matter what components or sensor is behind the lens. Assuming an ideal lens with perfect transmission, all of the light is deposited on the sensor.

Now suppose we have a 1.6× crop APS-C sensor and a 37.5mm lens with a 32mm absolute aperture. The lens's relative aperture is f/1.17. The horizontal field of view is still 31.4° because of the new shorter focal length we selected. But again, the rate of light gathered by the lens is controlled by the 32mm physical opening of the aperture. And assuming no losses in the optics, all of that light gets deposited on the smaller sensor.

In our example, if both the full-frame and APS-C sensors have the same number of pixels, then each pixel will receive the same amount of light - 64mm f/2.0 full-frame vs. 37.5mm f/1.17 APS-C.


In practice however, there are some problems with using small sensor formats. The main one is that small f-numbers (in other words, the aperture size approaching or exceeding the focal length) become increasingly hard to manufacture - they are expensive and require extensive optical elements to correct for aberrations.

To put it in another way, if a 50mm f/4 lens is designed for a 4× crop sensor, then a 200mm f/4 lens can for a full-frame sensor can be produced by simply scaling up the design without internal changes. But taking a 200mm f/4 lens, keeping the absolute aperture size the same, and producing a 50mm f/1 lens is incredibly difficult.

Another concern is that even if the lens is perfect, it can be difficult for a small sensor to accept a high density of photos. In our example we designed the situation so that regardless of the sensor size, the total light energy deposited on the sensor remained constant. If the sensor is small, then a lot of energy is received on small pixels, which means they must have very "deep" wells or else they will overflow. It is safe to say that it is easier to design pixels with more surface area to accept the same amount of light energy.

All in all, there are engineering reasons for why large sensors are tool of choice for gathering more light and making more bokeh. Now you know why.

I have an article on this topic on my web site: https://www.nayuki.io/page/absolute-and-relative-lens-apertures

  • Isn't Absolute aperture size only relevant with a simple thin lens? For any compound lens the entrance pupil size is the denominator in the focal length/diameter calculation used to get the f-number. – Michael C Nov 30 '16 at 5:31
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Increasing pixel size (or rather well size) will reduce stochastic noise at low light levels. Large pixel size equates to larger sensor size only if pixel density remains constant. A reduction in stochastic noise improves low light performance.

That's not quite the same thing as a larger aperture because a larger aperture increases the amount of light reaching the sensor. A larger aperture boosts absolute signal by increasing the total number of photons available.

Generally, the cost benefit ratio appears to favor investment in the optics over the sensor. High end medium format cameras don't have 4x6 sensors and camera phones have small sensors with wide (short focal length) lenses.

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