Background blur and its relationship to sensor size

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

  • f  is the focal length (the actual focal length, not the 35mm equivalent),
  • N is the aperture or f-number,
  • w2 is the sensor width,
  • w1 is the subject height in portrait orientation or picture width in landscape orientation and
  • ms = w2/w1 is the subject magnification of the lens. 

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

  • the more you zoom (i.e. increase the focal length f),
  • the more you open the aperture (i.e. smaller f-numbers) and
  • the smaller the subject is.

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

  • As expected the iPhone (as well as every other phone on the market) is not capable to produce any kind of background blur for portrait photos. The subjects will have to be fairly small and you have to move very close in order to be able to finally get some kind of background blur (see. e.g. iPhoto 5 example)
  • Normal compact cameras are only slightly better than phone cameras and in practice they will not be able to produce significant background blur.
  • Cameras using a 1/7" sensor like the Canon S110 and Canon G12, which also have a slow lens at telephoto are also very much limited in their ability to create background blur. This might come as a surprise to some people, as the cameras are clearly targeted at the more serious photographers having lots of manual controls. Those manual controls are however close to worthless, when it comes to taking portrait photos.
  • The Nikon 1 cameras combined with their standard lens, does not look very promising either. The small zoom range and the slow lens seriously limit the ability to create background blur.

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

  • Cameras like the Panasonic LX7 or the Olympus XZ-2 (and XZ-1), are better designed as they make use of faster lenses at telephoto.
  • The Sony RX100 unfortunately lacks a faster lens, but compensates this with a larger sensor providing similar capabilities like the LX7 and XZ-2.
  • The Canon G15 now got a faster lens compared to the G12. With respect to background blur it is not much different from the Canon G1 X, which has a larger sensor, but a slower lens. The Nikon P7700 is very similar to the Canon G15, having a slower lens but also a longer zoom range.
  • FourThirds cameras using standard kit lenses are somewhat limited in their ability to create background blur, but the system offers a variety of faster lenses and longer zooms, which improves the situation signifcantly (like e.g. the 45mm 1:1.8)
  • Cameras using APS-C sized sensors are a bit better than FourThirds, but also here the standard kit lenses are a bit short on the telephoto side and too slow. Taking the next bigger zoom range is usually a better option, providing much more photographic freedom.
  • And finally it's clear that a 35mm full frame camera like the Canon EOS 6D, combined with a fast portrait lens, provides all the freedom you want. Even the Sony DSC-RX1 that uses a 35mm focal length can produce 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.

The views and opinions expressed in this article are those of the author and do not necessarily reflect the views and opinions held by dpreview.com or any affiliated companies.

Comments

Total comments: 16
mishikoff
By mishikoff (3 weeks ago)

Great stuff, thanks !

0 upvotes
CarstenKostrzewa
By CarstenKostrzewa (6 months ago)

I shortend the article a bit in the theoretical background section in order to focus on the main effects and make it easier to read.

0 upvotes
Rudy Leos
By Rudy Leos (6 months ago)

Hi,

The formula shows that if we use 2x crop sensor, compared to FF sensor, shooting the same Field Of View (same equivalent focal length and same subject framing) and the same aperture, we will eventually lose a total of 4 stops equivalent background blur, which 2 stops come from DOF, plus 2 stops come from Circle of Confusion size (related to magnification or sensor size).

Can we find any sample of real images showing the comparison of background blur of Full Frame vs MicroFourThird, with the same Field of View (same equivalent focal length) and same DOF ? For example sample photos of EM-5 40mm f2.0 vs 6D 80mm f4.0 (same FOV, same subject framing and same DOF).

It will prove whether shooting same subject framing and same subject size, 3 factors which are focal length, aperture and subject size are enough to determine strength of background blur. Or there should be 4 factors which sensor size must be included to determine the strength of background blur.

0 upvotes
CarstenKostrzewa
By CarstenKostrzewa (6 months ago)

I guess this is the same issue I mentioned below, i.e. absolute circle of confusion b vs. what you see in the photo which is the relative size of the circle of confusion B = b / w2. The absolute circle of confusion is in fact 4 times smaller for the "same filed of view" scenario. However the sensor is 2 times smaller, so the strength of the background blur is only 4/2 = 2 times smaller in the "same filed of view scenario".
Unfortunately I don't have a FF and a MFT to test, but could do so using an APS-C DSLR and a 1/1.7" compact.
I know, it sounds counter intuitive, that the sensor size is not included, but indirectly it is by using the real focal length of the lens which is e.g. 2 times smaller for a crop factor of 2. Trust me, it's really only focal length, aperture and subject size ;-)

0 upvotes
Rudy Leos
By Rudy Leos (5 months ago)

Quote:
"The absolute circle of confusion is in fact 4 times smaller for the "same filed of view" scenario. However the sensor is 2 times smaller"

That explains everything. Thank you very much for the explanation.

0 upvotes
Rudy Leos
By Rudy Leos (6 months ago)

Nice article.

You formula shows Blur = B = f · ms / N
while ms (magnification) = sensor width (size) / subject width (size)

But, When you calculate B for the comparison table, why do you omit the magnification (ms)?

Let's say sensor size of Full Frame is "1" and microFourThird is "0.5" (due to 2x crop size, to achieve the same framing). Subject size is 0.6m = 600mm

If on 6D 85mm f1.8 = 85 x (1/600) / 1.8 = 7.87% (agree).
Then on OMD EM-5 42.5mm f1.8 = 42.5 x (0.5/600) / 1.8 = 1.97% (not 3.94%).
Using Blur Calculator (by Bob Atkins) also shows similar result.

Do I miss something? Please advise.

0 upvotes
CarstenKostrzewa
By CarstenKostrzewa (6 months ago)

I have to admit that using small and capital letters b and B may have been a bit confusing. b (= f · ms / N) is the blur disc in absolute terms projected onto the sensor. You need to relate this to the sensor size in order to come to a meaningful metric for the strength of the blur, i.e. relate b to sensor width w2 (please have a look at the first photo above to see what I mean). So B = b / w2 which results in:
B = b /w2 = f ·ms / N / w2 = (f ·w2) / (N ·w1) / w2 = f / (N ·w1)
You find this towards the end of "Theoretical background" section. This means that the strength of the blur is independent of the magnification, but of course only if you use the real focal length that the lens has and not the equivalent. So for the OMD EM-5 42.5mm f1.8 you really only need to calculate 42.5 / 600 / 1.8 = 3.94%
I hope this explains.

0 upvotes
Johann3s
By Johann3s (Feb 23, 2013)

Nice article! However, you discard one very important effect, which is the distance between the subject and the background. Your simplified equations are only valid for when this distance is substantially far away.

There is a nice tool to show graphs of the amount of background blur for different sensor sizes and lenses. It can be found at http://howmuchblur.com

You will see that sometimes a certain lens is in the advantage for nearer backgrounds, but loses that advantage for backgrounds which are further away. It is important to also mention this effect.

Comment edited 2 times, last edit 31 seconds after posting
0 upvotes
CarstenKostrzewa
By CarstenKostrzewa (Mar 5, 2013)

Indeed you are right. The simplified calculation is only valid, when the background is far away. I personally would consider the estimation to be good enough, once the background distance is let's say 5 times the subject distance (so for a normal portrait maybe larger than 10m), but there is of course no right or wrong. And you also raise a good point, that the behavior of the background blur changes from camera/lens/sensor size combination to combination, as the closer the background gets, the more similar the behavior gets to the DoF definition.
Also many thanks for the link. I had not this before. Looks very interesting.

0 upvotes
mishikoff
By mishikoff (3 weeks ago)

Thanks for the link, very helpful !

0 upvotes
CarstenKostrzewa
By CarstenKostrzewa (Oct 15, 2012)

Thanks to all of you. I am happy to hear, that you think the article is helpful.

1 upvote
Peksu
By Peksu (Oct 11, 2012)

Absolutely brilliant stuff, I never knew how to exactly take the difference in magnification into account when comparing subject separation, but now I know. This makes comparing lenses so much clearer.

I have your blog in a prime place in my bookmarks because it was the only source I had previously found that even touched the interesting subject, but now the formulas are here in full. Thank you!

1 upvote
NiallM
By NiallM (Oct 4, 2012)

Great work Carsten; it also shows one advantage of all that zoooom in the Nikon P7700, regarding purchasing one of the latest compacts, with out-of-focus stuff in mind..

0 upvotes
J D Tranquil
By J D Tranquil (Oct 4, 2012)

I followed the link and found this very interesting article. It answered some questions that I had. Thank you very much, Carsten.

0 upvotes
Michael_13
By Michael_13 (Oct 2, 2012)

Very interesting, thank you, Carsten!

Your results also show an often overlooked disadvantage of FF sensors like in Sony's RX1: Even at 35mm you have to deal with almost 3% blur. This means that indoors, when taking pics of people, you need to use F4.0 or higher and push up ISO.
Compacts like XZ-1/2 can use open apertures an still provide enough DOF.

Regards,
Michael

1 upvote
CarstenKostrzewa
By CarstenKostrzewa (Oct 3, 2012)

Thanks, Michael!
And the additional point you added is indeed a very interesting aspect, I have never thought about before. Thanks.
Carsten

0 upvotes
Total comments: 16