M4 3 Dof Comparison Essay

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c_henry wrote:

m43 is a x2 crop factor for full frame, APS-C is roughly x1.6. I read that APS-C / m43 crop factor is 1.25, is that right?

I ask as when chatting to a few friends, one said he wouldn't go for anything smaller than APS-C as he likes shallow DoF, but if I'm right the difference between APS-C and M43 is 1/3 - 1/2 stops. Which would be barely noticeable?

Because they have different aspect ratios, there's no single crop factor that can describe the difference.

M43: 17.3x13mm, 225mm²

Canon APS-C: 22.2x14.8mm, 329mm²

  • Horizontal crop factor: 22.2/17.3 = 1.28
  • Vertical crop factor: 14.8/13 = 1.14
  • Diagonal crop factor: 28.3/21.6 = 1.23
  • By area: log₂(329/225) = 0.55 stops

Regular APS-C: 23.6x15.7mm, 370mm²

  • Horizontal crop factor: 23.6/17.3 = 1.36
  • Vertical crop factor: 15.7/13 = 1.21
  • Diagonal crop factor: 28.3/21.6 = 1.31
  • By area: log₂(370/225) = 0.72 stops

The diagonal crop factor is a sort of average crop factor, and it's what is usually used when comparing depth of field. If you're interested in how much noise* images will have when taken with equal exposure, area is more accurate.

Having said all that, the sensor size isn't what's important, it's the lens you put in front of it. If your friend is shooting with an f/3.5 or f/4 lens on APS-C, he'd be better off with an f/2 (or f/0.95!) on M43. For depth-of-field purposes, you can compare f-numbers between formats by dividing by the crop factor. All else being equal, an f/4 on APS-C will give the same DoF as an f/3.1 on M43 (since 4/1.28 = 3.1).

*The only kind of noise you can compare between formats without knowing the specific sensors in question is photon shot noise.

With smaller than 35mm sized sensors, you will often hear talk of a camera’s or lens’ “full frame equivalent” focal length or aperture. This can often be a source of great confusion among new shooters, and it can also be a point of disturbingly odd derision for other people, especially with regards to ‘aperture equivalence’. I’m going to try and give a clear view of what is truly meant when someone is talking about full frame equivalence, as well as dispel several myths about it, and ultimately tell you why, if you shoot with a smaller format, it mostly doesn’t matter.

Author’s Notes:  This article has been up for a while now, and from several comments I’m seeing with some regularity, I feel the need to make a few points.

  • This is not intended to show or imply superiority of any format over another.  At all.  I am not debating or arguing in any way that full frame cameras don’t have a better image quality baseline that crop cameras…they do as a general rule (same generation, etc). 
  • I fully believe that using ‘equivalence’ calculations makes perfect sense if you ‘think’ in 35mm terms, and thus it is useful in your mind to do the math to compare focal lengths, or even for depth of field calculations.  This is not an argument about using ‘equivalence’ as a point of reference.
  • This is about the use of full frame equivalence for people who have no reason to reference a format they don’t use, and against the far too often seen use of ‘aperture equivalence’ and how it relates to minimum depth of field as an absolute in determining the quality of a lens.
  • I have made some minor edits to the text in order to clarify some of the above.

What does “Full Frame Equivalent” mean?

First off, what does it mean when someone talks about a sensor or lens in terms of 35mm or ‘full frame’ equivalence? Well, quite simply, it is a way to compare angle of view, and more recently, the look you’ll get with respect to depth of field, between a full frame sensor and a ‘crop’ sensor. A few important terms to know:

  • Full Frame: A full frame camera has a sensor that is the same physical size as that of a frame of 35mm film. That is, 36mm wide x 24mm high.
  • Crop Sensor: A crop sensor camera, like on many DSLRs (which use the APS-C size) or the Four Thirds sensor (used in Four Thirds DSLRs and Micro 4/3 mirrorless cameras), is simply a sensor that is smaller in physical size than a full frame sensor.
  • APS-C: APS-C stands for “Advanced Photo System – Classic” (a reference to APS film), and means a sensor (or camera with that sensor) with a physical size between 22.2mm x 14.8mm and 23.6mm x 15.7mm.
  • Four-Thirds or 4/3: The sensor size used in Olympus and Panasonic DSLRs and mirrorless cameras (those of the 4/3 or Micro 4/3 system). The standard sensor size is in a 4:3 aspect ratio and is 17.3mm x 13mm
  • Field of View or Angle of View: The angle of view that the sensor will record for a specific camera and lens combination. For instance, a 24mm lens on Full Frame has a diagonal angle of view of 84°. This is the angle between the upper left of what’s captured by the lens and sensor and the bottom right (or vice versa).

See the diagram below. You’ll see arcs showing the diagonal, horizontal and vertical angles of view. In this diagram, the green rectangle represents the image captured by a full frame camera. If the same lens is used, the red rectangle represents the image captured by a crop sensor camera. It simply takes the center area of the image circle projected by the lens, resulting in a narrower angle of view.

A diagram showing angle of view and the effect a crop sensor has on a lens’ angle of view

Crop Factor

One term that has been around since DSLRs made their entrance is ‘crop factor,’ which details the difference in focal length required for the same field of view between a smaller sensor camera and a full frame camera. This term was coined to help visualize that when you use lenses designed for full frame cameras on a crop sensor camera, the field of view is narrower…like cropping the photo in camera.

The first DSLRs used APS-C sized sensors because making viable full frame digital sensors at the time was cost prohibitive and very difficult. As the industry progressed, the APS-C sized sensors became somewhat of a sweet spot for high image quality with lower production cost.

The Crop Factor for an APS-C sensor is either 1.6x (Canon) or 1.5x (most others). What this means is that if you use a 50mm lens on an APS-C camera, it will have the same Field of View as a 75mm lens (50 x 1.5) on a full frame camera. The crop factor on 4/3 sensors is 2x, so a 25mm lens on a 4/3 or Micro 4/3 camera will have the same field of view as a 50mm lens will on a full frame sensor.

You will often hear people say “well, you have a crop sensor camera, so your 50mm lens becomes a 75mm lens on that camera.” This is WRONG. Focal length is a property of the LENS and the LENS ONLY, and it does not change in any way regardless of what camera you mount it on. What is true is that on an APS-C DSLR or CSC, a 50mm lens will have the same FIELD OF VIEW as a 75mm lens on a full frame camera. I’ll get more into this in a bit.

Digital Sensor Sizes and their “Crop Factors” – image by MarcusGR, Wikimedia Commons

The key point to remember about crop factor is that it is ONLY a reference point. That is, if you are used to shooting 35mm film or a full frame DSLR, using the crop factor will help you select a lens focal length that will give you the same look that you expect from your experience with a full frame lens. If you know what a 50mm lens looks like through your camera, you now know you need about a 33mm lens on APS-C or a 25mm lens on 4/3 to get the same field of view. That’s IT. It serves no other purpose. More on that later.

Aperture ‘equivalence’

This is a new one. In the past few years, people have also been using the crop factor to relate so called ‘aperture equivalence.’ That is, they’ll multiply the F-stop of a lens by the crop factor to get the ‘equivalent aperture’ of a lens. This has some basis in reality, but it is a pretty major fallacy, in my opinion, and it really skews people’s perceptions. I’ve gotten angry and rude comments on this blog about how I’m delusional about Micro 4/3 because of aperture equivalence. Interestingly enough, this term really only started to be thrown around when Micro 4/3 started getting popular…it was almost never brought up with regards to APS-C DSLRs. There’s a little bit of fanboyism going on quite often with this. Anyway, let’s delve a little deeper:

A few things regarding aperture:

  • The maximum aperture of a lens is the size of the light opening of a lens when the blades of the aperture diaphram (the blades that open and close to let more or less light in) are wide open. More specifically, it’s the effective size of the opening that determines the cone angle of the light rays entering the lens. Aperture size is generally given as a ratio of the effective aperture size to a lens focal length. This is called the f-stop. If a 50mm lens has a maximum aperture of 25mm, it would be an f/2 lens. (Focal length/aperture = 50/25 = 2). The reason there is a division sign is because f/2 means the aperture size is the Focal Length / 2. (in this case, 25mm.)
  • The f-stop is one of the key components in exposure. The intensity of light hitting the film or sensor will be the same for the same f-stop, regardless of the focal length or actual physical aperture size. If you have a 200mm lens at f/2.8 and an 18mm lens at f/2.8, they both will have the exact same intensity of light hitting the sensor…the same number of photons per unit area. This, combined with ISO and shutter speed, helps determine how bright or dark your picture is. A larger number in f-stop means a smaller aperture (remember, it’s division: f/8 means the aperture is 1/8 the size of the focal length), which means less light hits the sensor.
  • A ‘full stop’ means the exposure is doubled or halved. With aperture and f-stops, a difference of the square root of 2 is one full stop. (1.4 is a good approximation to use). So, f/1.4 to f/2 is one full stop, as is f/5.6 to f/8 (5.6 x 1.4 = 7.9, or approx. 8).
  • Depth of Field: Depth of Field (DOF) is the depth of an image that appears to be in focus. Depth of field depends on three things: Focal Length, F-stop and Focus Distance (distance to your subject). These are all directly related. In fact, it is such that if you FRAME your subject the same way, all lenses will have the same depth of field for the same f-stop on the same format. To visualize this, consider a portrait where your subject is framed with the tops of the shoulders at the bottom of the frame, and the top of the head right at the top. If you frame your subject with a 50mm lens at f/2, then move BACK twice the distance you originally stood and use a 100mm lens at f/2, the depth of field, or amount that subject is in focus, will be the same.
  • Background Blur: The amount that the area behind your subject is blurred. Using really wide-aperture

    A candid with noticeable background blur due to a large aperture lens – in this case the Olympus 75mm f/1.8 on the OM-D E-M5.

    lenses, like f/1.4, can yield very blurry backgrounds, while your subject remains sharp. While background blur is related to depth of field, they are NOT the same thing. Background blur is dependent on the same three things as depth of field, but in a different way. While depth of field relations depend on focus distance, f-stop and focal length, background blur can be simplified from that: It is wholly dependent of focus distance and physical aperture size. The mathematicians here are having a field day saying that since physical aperture size can be determined via focal length and f-stop that they are they same…but the relationship is different. Let’s look at that example from the previous bullet point. While a 50mm shot at f/2 and a 100mm shot at f/2 that’s taken from double the distance as the 50mm shot will have the same depth of field, the 100mm shot will have a BLURRIER background. Why? While the f-stop is the same between a 50mm lens at f/2 and a 100mm lens at f/2, the 100mm lens has a physically larger aperture (50mm vs 25mm). We can get into the reasons why this works (mainly, you are enlarging the area behind the focus point more with the longer focal length), but the big rule of thumb is, for the same focus distance, lenses with the same physical aperture size will yield similar amounts of background blur.

So, after all that drivel, what’s this aperture equivalence speak? Well, it refers entirely to the comparison of depth of field for a given sensor/lens combination. That is…you can multiply the f-stop by the crop factor to determine the aperture on a full frame camera that will give you the same depth of field.

So, if I shoot a portrait with a Micro 4/3 camera and a 25mm f/1.4 lens, and I shoot it at f/1.4. The field of view, depth of field and amount of background blur will be the same as if I’d shot the image at the same spot with a full frame camera, and a 50mm lens at f/2.8. Since Micro 4/3 has a crop factor of 2: 25mm x 2 = 50mm lens for the same field of view, and f/(1.4 x 2)= f/2.8 for the same depth of field. Similarly, 25mm/1.4 = 17.9mm aperture size and 50mm/2.8 = 17.9mm aperture size (so same amount of background blur at the same focus distance).

This means that, all things being equal, a smaller format will generally have DEEPER depth of field and less background blur than a larger format. This makes sense because smaller format cameras use shorter focal lengths for the same field of view, and therefore similar f-stops mean a smaller physical aperture size: less blur.

Total Light

One final nitpick that people like to point out on aperture equivalence is that it also shows you the settings that not only yield a similar image, but also allow for the same total amount of light used to make an image. For instance, a full frame sensor is four times larger in area than a Micro 4/3 sensor. Therefore, if the f-stops are the same, and thus the intensity of the light is the same (and the exposure is the same), then the full frame camera will be using four times the total amount of light to make the image because it’s got four times the total area. For the smaller sensor to have the same total amount of light, they need two stops faster aperture or two stops lower ISO with a longer shutter speed. This is why, often, it’s said that full frame sensors will have two stops better ISO performance over a Micro 4/3 sensor.

Noise comparison – OM-D E-M5, Canon 5D and 5D Mark II, Courtesy, DxO, Click to Visit DxO Labs Comparison Tool

However, this doesn’t work completely linearly in the real world, as smaller sensors are more light efficient than larger ones, and it is also dependent on sensor technology being identical. If you look at the DxO Mark sensor comparison, you will see that if you compare the Olympus OM-D E-M5 with the Nikon D600 and the Canon 5D Mark III (both of which are full frame sensors), they measure roughly 1 2/3 stops better in ISO performance. Not two like you’d expect.  You may be thinking ‘that’s close enough, but it speaks to the further point:

Compare different sensor generations and everything breaks down, though advocates of this equivalence never use the equivalence when comparing full frame sensors of different generations. The OM-D E-M5 is only about a half a stop behind the Canon 5D and just over one stop behind the 5D Mark II…a camera that was current only 9 months ago. (See chart above).

My whole point here is that the total light argument implies a direct 2x or 4x improvement in image quality with ISO. However, this is really only true for approximating how one sensor design may scale with size, but is terrible as a blanket equivalence based on sensor size alone due to the changing of technologies over time and differnent sensor construction even among cameras of the same generation.

Now, let me tell you why none of this matters: Next Page

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