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Background blur and its relationship to sensor size

CarstenKostrzewa | Technology | Published Sep 21, 2012

Most experienced photographers know that they can modify the amount of background blur by adjusting the aperture of a camera. A typical use case is a portrait of a person, in which the person is in focus and the background is blurred in order to visually isolate the person from the background. But also the sensor size plays a critical role in determining how much background blur the photo will have at a certain aperture and focal length setting. Today's market offers a wide variety of cameras, using all sorts of different sensor sizes, maximum aperture setting and zoom ranges, making it virtually impossible for the user to estimate how much they will be able to adjust the background blur with a certain camera. This article tries to provide a practical guide on how to estimate the maximum strength of background blur for a given camera / sensor type.

Theoretical background

In order to be able to say whether a camera is capable to create background blur, we first need to define the term "strength of the background blur". The Depth of field and Lens (optics) Wikipedia articles are good references for the basic formulas that I will use.

Most explanations about background blur start with the term Depth of Field (DoF). While Depth of Field is good, when defining the area of subject sharpness, it can be somewhat misleading if you try to translate the characteristics to the strength of background blur.  If you e.g. caluculate the Depth of Field with a DoF calulator first for a subject distance of 1m using a 50mm focal length and then another time moving to a distance of 2m and increasing the focal length to 100mm to reach the same subject framing, you will notice, that the Depth of Field is the same in both situations. This is however not true for the amount of backgrund blur. The further you move away from the subject and compensate this by a stronger zoom, the stronger the background blur will get. The reason for this is, that the stronger zoom results in a narrower angle of view, which will capture less of the background compared to the shorter focal length. This smaller part of the background is however "stretched" to the same frame size, leading to a larger amount of background blur. In the example above moving from 50mm to 100mm will roughly double the strength of background blur, as you can see from the calculations below. So Depth of Field is not the same as strength of background blur.

How strong the background of a photo is defocused can best be seen when taking a look at photos that have spot highlights in the back. Those spots will appear as “blurred discs” in the shape of the aperture when getting defocused, as can be seen in the picture below.

Photo with strong background blur, with clearly visible blur discs in the back

The blur disc size b is approximately equal to (please refer to the DoF Wikipedia article):

         b = f ·ms / N = (f ·w2) / (N ·w1),

in which

Please note, that the equation above is only valid, if the background is sufficiently distant from the subject.

The absolute value of b does not tell much by itself, when comparing cameras with different sensor sizes. If we however compare b to the sensor size w2 we can estimate how big the blur disc size is compared to the total picture height (please refer to the photo above) and thus come to a definition of the strength of the background blur B: 

         B = b / w

Example: if the blur disc is 1/1000th (i.e. 0.1%) of the sensor width, the background is almost as sharp as the focused area. If on the other hand the blur disc is only 1/10th (i.e. 10%) of the sensor width, then the background is significantly blurred, as the blur disc covers 10% of the entire picture.

Merging the formulas above yields the following equation for the strength of the background blur

         B = f / (N ·w1)

From this equation, you can already see the basic dependencies. The background blur increases

For a typical portrait of a person the photo should probably cover the head, the shoulders and a part of the upper body. A rough estimation is, that the value will be around w1 = 0.6m. This will of course depend on the size of the person and obviously on how much of the person you want to cover in the portrait.

As you can see, estimating the maximum strength of background blur can easily be done by using data that is right away available in the camera specifications. In fact you can even estimate it from data that is available on the lens. Just take the maximum zoom (the actual value, not the 35mm equivalent), divide it by the maximum aperture for the maximum zoom, and then divide this by a typical portrait height of w1 = 0.6m. In the next section I will explain how to interpret the resulting value for B.

Examples pictures that help to understand the values of B

The photos below were taken with a Nikon D7000 using a 18-200mm lens using a variety of aperture and focal length settings in order to be able to create a wide variety of background blur values (please have a look at the next page to see more steps). Please note that although I used the focal length setting equal to 200mm on the lens itself, the actual focal length for a distance of s1 = 2,2m is rather around 145mm. My assumption is that there is a variation in the field of view due to the internal focusing mechanics of the lens and that the actual focal length varies with the subject distance. I tested this and a focal length of 200mm can only be reached for subject distance well beyond 10m. This effect needs to be taken into account when calculating the maximum blur.

No blur, B = 0.3%, N = 32, s1 = 1.1m, w1 = 0.52m , f = 50mm
Very limited blur, B = 0.6%, N = 16, s1 = 1.1m, w1 = 0.52m , f = 50mm
Limited blur, B = 1.2%, N = 8, s1 = 1.1m, w1 = 0.52m , f = 50mm
Reasonable blur, B = 2.2%, N = 16, s1 = 2.6m, w1 = 0.42m , f = 146mm
Strong blur, B = 4.4%, N = 7.1, s1 = 2.6m, w1 = 0.42m , f = 146mm
Very strong blur, B = 11.6%, N = 5.6, s1 = 1.1m, w1 = 0.2m , f = 130mm

 In order to categorize the strength of the background blur I used the following definition for B

 BDescription
0,00%  < 0,375% No blur 
0,375% < 0,75% Very limited blur
0,75% < 1,50% Limited blur
1,50% < 3,00% Reasonable blur
3,00% < 6,00% Strong blur
> 6,00% Very strong blur

Of course there is no such thing as a fixed definition for the strength of background blur and your taste may vary. It's also clear that a camera that is capable to produce B = 1.4 is not much different from a camera with B = 1.6. The idea is just to give an approximate sense to the numerical value.

Camera comparison

In order to be able to compare various cameras, we need to define a common scenario. As said above, the smaller the subject the easier it is to create decent background blur. So it does not make sense to compare photos of very small subjects, as basically all cameras will be able to create some kind of background blur. If on the other hand the subject is very far away, you are most likely taking a picture of a landscape for which the background is supposed to be sharp all the way through. Hence the most interesting scenario is to evaluate the before mentioned portrait situation with w1 = 0.6m (head, shoulders and a part of the upper body). I will compare the cameras in two different ways:

  1. using the maximum zoom, resulting in a maximum achievable background blur for a given camera.
  2. using a 85mm equivalent focal length setting (which most cameras and standard kit lenses are able to achieve), so that all photo will have the same field of view (subject distance s1 = 1.5m for w1 = 0.6m)

Comparison using maximum zoom

The table below shows a comparison of the background blur B utilizing the maximum zoom available on the respective camera.

Comparison of the maximum achievable background blur B for a portrait height of w1 = 0.6m

Comparison for 85mm equivalent

The table below shows a comparison of the background blur B utilizing the 85mm equivalent zoom.

Comparison of the background blur B for a portrait height of w1 = 0.6m, using 85mm equivalent zoom, i.e. the subject distance s1 is around 1.5m. Please note, that for reasons of simplicity I used the aperture for the maximum zoom, as I did not have the exact aperture for 85mm equivalent. In most cases this will be close enough, as 85mm equivalent is close to the end of the zoom range (maybe except for the Nikon P7700)

Discussion of the results

Limited background blur

Cameras which at least provide some capabilities to create decent background blur

Conclusion

As shown above, estimating the maximum strength of background blur is very easy. Just take the maximum zoom (the real value, not the 35mm equivalent), divide it by the maximum aperture at maximum zoom and then divide this by a typical size of the subject you want to take photo of (as said above 0.6m - 0.7m are good reference points for portraits). On the next page you will find additional pictures, that may help you to find define your own reference point.

Reference pictures for the strength of background blur B

B=0.31%, Aperture 32 B=0.34%, Aperture 29
B=0.39%, Aperture 25 B=0.45%, Aperture 22
B=0.49%, Aperture 20 B=0.55%,Aperture 18
B=0.61%, Aperture 16 B=0.70%,Aperture 14
B=0.76%, Aperture 13 B=0.89%,Aperture 11
B=0.98%, Aperture 10 B=1.09%, Aperture 9
B=1.23%, Aperture 8 B=1.38%, Aperture 7.1
B=1.56%, Aperture 6.3 B=1.76%, Aperture 5.6
B=0.97%, Aperture 36 B=1.09%, Aperture 32
B=1.20%, Aperture 29 B=1.40%, Aperture 25
B=1.59%, Aperture 22 B=1.75%, Aperture 20
B=1.94%, Aperture 18 B=2.18%, Aperture 16
B=2.5%, Aperture 14 B=2.69%, Aperture 13
B=3.18%, Aperture 11 B=3.49%, Aperture 10
B=3.88%, Aperture 9 B=4.37%, Aperture 8
B=4.92%, Aperture 7.1 B=5.54%, Aperture 6.3
B=6.24%, Aperture 5.6