About Focal Length, Aperture, and Depth of Field for Different Sensor Sizes

Introduction | Sensor Size and Crop Factor | Angle of View, Focal Length, and Sensor Size | Depth of Field, Aperture, and Sensor Size | Using Depth of Field Markers | Summary | References

On this page, I want to touch the topic "focal length, aperture, and depth of field (DOF) for different sensor sizes." Specifically, I will discuss (1) which focal lengths produce the same angle of view on cameras using different sensor sizes, (2) what a nominally identical aperture value means for cameras using different sensor sizes, and (3) what the DOF markers on a lens mean for you if you use the lens with a camera that has a sensor of a different size than that for which the lens was designed.

 

Introduction

As users of digital cameras, we know that cameras using a small sensor have a much greater depth of field than those with a larger sensor - and as one is used from film cameras. This is apparent in many shooting situations, but particularly when shooting macros. The larger depth of field makes the shooting, at least the focusing, much easier especially for beginners, but also for street photographers, as an example. On the other hand, photos with large depth of field - ideally, going from front to back - often look boring. Therefore, advanced amateur and professional photographers like to discuss just the opposite: how to get the lowest possible depth of field to separate the photographed object from the background? This is often associated with a "bokeh" discussion (how "pleasantly" the blurred region are shown). Often, these photographers are not satisfied with the depth of field that can be achieved with APS-C cameras. For them, only so-called full-frame cameras (corresponding to the 35 mm film format) are sufficient. At best, one can achieve a shallow depth of field using APS-C cameras, when approaching the object to be photographed closely and opening aperture as wide as possible (if the quality of the lens will allow this).

Since cell phone cameras make life difficult for simple and cheap digital cameras, many camera manufacturers have started, to launch "advanced" compact cameras on the market, which, while still having compact dimensions, are distinguished by especially two features: (1) larger sensor and (2) bright optics (frequently only on the wide end). Prospects for such cameras, but, of course, other photographers as well therefore face questions such as: What does a maximum aperture of, for example, f/1.8 mean at such a camera compared with a full-frame camera with the same maximum aperture? As announced above, I will address these and other questions below.

 

Sensor Size and Crop Factor

First, a few comments on sensors of different sizes. For historical reasons, different types of names are used, which often tell little about the actual sensor size. Most important for the following is a number that is called "crop factor." It indicates the ratio between the diagonal of the full-format sensor and the diagonal of a sensor of a certain format (or the ratio of the respective angles of view, see below). This number will always accompany us in the discussion below. The following table lists dimensions and crop factors for important sensor types:

Format Full-frame Format APS-C (DX) APS-C (Canon) Foveon (Sigma) MFT MFT multi-aspect 1" 2/3" 1/1.7" 1/1.8" 1/2.3"
Dimensions (mm) 36 x 24 23.7 x 15.6 22.3 x 14.9 20.7 x 13.8 17.3 x 13.0 variable 13.2 x 8.8
12.8 x 9.3
8.8 x 6.6 7.6 x 5.7 7.2 x 5.4 6.2 x 4.62
Area (mm2) 864 370 329 286 225 variable 116
119
58 43 39 29
Diagonal (mm) 43.3 28.4 27.1 24.9 21.3 20? 16 11 9.5 8.9 7.7
Crop Factor 1.0 1.5 1.6 1.7 2.0 2.2 2.7 4 4.5 4.9 5.6

The values for the dimensions of the various sensor types differ slightly in the various sources. Here, I essentially follow Wikipedia Wikipedia (Formatfaktor). Many of the values are rounded.

Below are two diagrams from Wikipedia on this topic:

    

 

Angle of View, Focal Length, and Sensor Size

The angle of view determines how much of a photographed scene is projected onto the sensor and thus appears on the photo (for the usual rectangular image format, this is usually the the value for the image diagonal). Lenses that create different viewing angles differ in their focal lengths and thus allow you to capture a "normal" viewing impression (normal lenses), large parts of the scene (wide angle lenses), or just a small section of it (telephoto lenses). Since the 35 mm film format dominated photography in the past, people usually do not speak of viewing angles, but of focal lengths instead (wide angle, normal, telephoto focal length) to describe the behavior of lenses.

To achieve the same visual impression with cameras using sensors of different sizes, lenses with different viewing angles / focal lengths have to be used. For a very small sensor, for example, a focal length that would result in a wide-angle lens at full frame format, already represents a telephoto lens. Therefore, people use to convert focal lengths of all digital cameras to "35 mm equivalent" values in order to compare them. And not surprisingly, the crop factor comes into play here:

Camera Examples

The following table lists data of some cameras, particularly of those that my wife or I own(ed) or that I find interesting:

     
Maximum Aperture
Camera Sensor Size Crop Factor short
actual
short
35 mm equivalent
long
actual
long
35 mm equivalent
Any... Full-frame format 1   identical
with actual
  identical
with actual
Leica X Vario APS-C (DX) 1.5 18 mm 28 mm 46 mm 70 mm
Ricoh GR APS-C (DX) 1.5 18.3 mm 28 mm --- ---
Ricoh GXR A16 APS-C (DX) 1.5 15.7 mm 24 mm 55.5 mm 85 mm (83.5 mm)
Panasonic GM5 (Kit) MFT 2 12 mm 24 mm 32 mm 64 mm
Panasonic LX100
Leica Digilux 109
MFT multi-aspect 2.2 10.9 mm 24 mm 34 mm 75 mm
Sony RX100 M1 1" 2.7 10.4 mm 28 mm 37.1 mm 100 mm
Sony RX100 M3 1" 2.7 8.8 mm 24mm 25.7 mm 70 mm
Panasonic LX1000
Leica VLux 114
1" 2.7 9.1 mm 25 mm 146 mm 400 mm
Ricoh GX100/200
Ricoh GXR S10
1/1.7" 4.5 5.1 mm 24 mm 15.3 mm 72 mm
Ricoh CX4
Ricoh GXR P10
1/2.3" 5.6 4.9 mm 28 mm 52.5 mm 300 mm

 

Depth of Field, Aperture, and Sensor Size

Now I want to return to my question that I asked at the beginning, here in a somewhat generalized form: What does the same aperture value mean in a camera with a smaller sensor and in a full-frame camera? There are two answers to this:

Since full aperture steps are graded with a factor of √2 (1.414 ...), one can state that the depth of field of an APS-C camera corresponds to about a full-frame camera that has been dimmed by a full f-stop compared with the APS-C camera. For the MFT format, this will already be two full stops.

In the article entitled Sensorgröße und Schärfentiefe, the following advantages and disadvantages are mentioned:

Camera Examples

The following table lists aperture-related data for the cameras above:

     
Initial Aperture
Camera Sensor Size Crop Factor wide
nominal
wide
for DOF
Tele
nominal
Tele
for DOF
Any... Full format 1   identical with
nominal
  identical with
nominal
Leica X Vario APS-C (DX) 1.5 3.5 (28 mm) 5.6 (28 mm) 6.4 (70 mm) 9.6 (70 mm)
Ricoh GR APS-C (DX) 1.5 2.8 (28 mm) 4.2 (28 mm) --- ---
Ricoh GXR A16 APS-C (DX) 1.5 3.5 (24 mm) 5.6 (24 mm) 5.5 (85 mm) 8.25 (85 mm)
Panasonic GM5 (Kit) MFT 2 3.5 (24 mm) 7 (24 mm) 5.6 (64 mm) 11.2 (64 mm)
Panasonic LX100
Leica Digilux 109
MFT multi-aspect 2.2 1.7 (28 mm) 3.74 (28 mm) 2.8 (75 mm) 6.16 (75 mm)
Sony RX100 M1 1" 2.7 1.8 (28 mm) 4.86 (28 mm) 4.9 (100 mm) 13.23 (100 mm)
Sony RX100 M3 1" 2.7 1.8 (24 mm) 4.86 (24mm) 2.8 (70 mm) 7.56 (70 mm)
Panasonic LX1000
Leica VLux
1" 2.7 2.8 (25 mm) 7.56 (25 mm) 4 (400 mm) 10.8 (400 mm)
Ricoh GX100/200
Ricoh GXR S10
1/1.7" 4.5 2.5 (24 mm) 11.25 (24 mm) 4.4 (72 mm) 19.8 (72 mm)
Ricoh CX4
Ricoh GXR P10
1/2.3" 5.6 3.5 (28 mm) 19.6 (28 mm) 5.6 (300 mm) 31.36 (300 mm)

*) All focal lengths are given as 35 mm equivalent values.

If you look at the the aperture values in the table above, you can find some cases where cameras with smaller sensor and nominally large apertures actually "slip" behind (or show more depth of field than) cameras, which have a larger sensor, but a smaller maximum aperture. With respect to exposure times, however, larger maximum apertures are equally useful for both types of cameras.

The technical specifications of the cameras and, especially, the advertising of the camera manufacturers often list the 35 mm equivalent focal lengths instead of the actual ones, which can easily lead to misunderstandings. Sometimes, it is not easy to retrieve the actual focal lengths, but most of the time they are still written on the front of the lens ...

 

Using Depth of Field Markers

When I bought the M-mount expansion unit for my Ricoh GXR and used it with Leica M lenses, I noticed that some parts of the photo were not sharp, although they were located within the depth of field zone for the aperture value that I had used. This "zone" is marked on the lens (see the photos below) and this focusing method is therefore called "zone focusing." Only by chance, I found out that, if one uses a full-frame lens on a camera with smaller sensor, one has to take a different aperture value into account for the depth of field than the one that one has set on the lens. It is important that you do not forget this in the rush of shooting...

Basically, you have to observe the following: If you use full-format lenses on cameras with a smaller sensor, the aperture value must be divided by the crop factor to obtain the aperture value that is relevant for determining the depth of field. For APS-C cameras, the aperture value has to be opened one stop, for MFT cameras it is two stops. This difference is essential to observe when using the depth markings on the lens! For APS-C cameras, the difference between the crop factor of 1.5 and one full f-stop (√2 = 1.414...) is so small that it is sufficient in practice to use the marks of one full f-stop more open.

    

Photos: Distance scale with depth of field marks M-mount lenses - Minolta M-Rokkor 28mm f/2.8 (left) and Voigtländer Color Skopar Pancake II 35mm f/2.5 (right). The left lens is set to an aperture value of f/8, however, the f/5.6 marks have to be considered, because it is mounted to an APS-C camera module!!! For the right lens the non-existing f/2.8 marks would have to be considered if it were mounted to an APS-C camera, because it is set to an aperture value of f/4.

In the literature, I found that the exact aperture value for full-frame format lenses that are used at APS-C camerasis to be changed for about 1.3 and 1.5 f-stops (nevertheless, for simplicity reasons, to open aperture for one f-stop was recommended). Since no details were given there, I had to understand this on my own and looked at the crop factor for various APS-C sensor types in relation to changes in aperture values (if you do not take into account the circle of confusion, but it should be comparable for sensor sizes that similar). The following table illustrates this:

Sensor Type Crop Factor Factor

f-stops

    1.414213562
√2
1
APS-C (DX) 1.5 (1.51, 1.52) 1.5 < 1 1/3
    1.587401052
√2*6th √2
1 1/3
APS-C (Canon) 1.6 1.6 < 1 1/2
    1.681792831
√2*4th √2
1 1/2
Foveon (Sigma) 1.7 1.7 > 1 1/2
MFT 2 2 2

The table shows that the difference is clearly below 1 1/3-stops for "DX" sensors, such as is used in the Ricoh GXR, the Ricoh GR, and the Leica Vario X *. Here, you do not make a significant error when you use the depth markings of the next larger aperture. For APS-C Canon sensors, the difference is about 1 1/3 stops and for Foveon sensors about 1.5 stops - the differences are already more apparent here. For MFT sensors, the reading has already to be changed to two f-stops.

*) The crop factor of 1.5 is pretty much in between a full f-stop of √2 (1.414 ...) and 1 1/3 f-stop increments (1.587).

 

Summary

*) The difference is so small that, in practice, it is sufficient to open one full aperture value, at least when using the DX format.

 

References

 

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14.02.2016