DOF for Digital Cameras



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The Great Depth-of-Field of Digital Cameras
The blurring that we lost
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In my previous article about The Charms and Myths of the Medium Format it was shown that the comparison of different formats should be based on the analysis of the degree of blurring in the final prints of equal size. The amount of blurring is proportional to the ratio of

f / N

where
f stands for the focal length of a lens;
N stands for the f-number (1.4; 2; 2.8; 4, 5.6; 8; … ).

This ratio allows us not only to compare various film formats with each other but also compare film frames with digital sensors.

Most digital sensors are smaller than a 35mm frame. Therefore digital cameras have to employ lenses of smaller focal distances for the equivalent angles of view. As a result, photographers have to open apertures of their lenses wider to maintain the same the degree of blurring in the final prints (maintaining the f / N ratio constant).

Unfortunately, many affordable digital cameras do not allow photographers to open the aperture wide enough to compensate for the shorter focal distances. Because of this, many people (especially those who have considerable experience in film photography) have to complain about too large depth-of-field of their digital gear.

The subtlety of the physical essence

It is very important to understand that different initial conditions lead to different conclusions. In our case it means there may be assumptions that will lead us to the conclusion that digital cameras provide smaller depth of field. Is it possible? Yes, it is. :-)

For example, let us consider the case when the same lens is used on both film and digital SLR cameras. In the article that has already been mentioned it is shown that the degree of blurriness in the final print is proportional to

(K f) (f / N),

where
K stands for the enlargement factor;
f is the focal length of a lens;
N is f-number (1.4; 2; 2.8; 4, 5.6; 8; … ).

Since in our case the lens is the same, the focal length is constant (f = const). Therefore the blurriness is proportional to the ratio of K / N. When we work with digital cameras, we have to enlarge our frame to a greater degree to obtain the final picture of the equal size. Thus, blurriness will be greater on a picture from a digital camera. It means depth of field will be smaller. It is not a paradox. It is the result of different initial conditions.

When our digital sensor is 1.5 times smaller than a negative of the 35mm photography (which is true for many modern digital SLR cameras), we will have to stop down our lens by 1.5 times (i.e. switch to the next larger f–number) to have the same depth of field. Without stopping down, a digital image of the equal size will demonstrate smaller depth of field.

However, it is more correct to compare systems with the same angles of view, which leads to the condition: (K f) = const. When we deal with digital and film cameras, we had better compare systems with lenses of different focal lengths. It is this approach that is used throughout the main text of this article.

That is what the theory shows. Now let us consider some good examples.

Compact digital cameras

To begin with, let us consider the following edifying case:

Suppose we want to substitute the lens of the CANON Digital IXUS i camera with some other lens that will provide us with the same degree of blurring as the PENTAX 43mm/1.9 Limited lens on the 35mm frame. It is easy to calculate that the aperture of our new lens should be f / 0.28!!! (6.4 / 0.28 approximately equals 43 / 1.9).

Alas! Such an aperture is not within the limits of feasibility. The aperture of a photo lens cannot be wider than f / 0.5. Therefore, no lens will do the job for us! Under no circumstances, CANON Digital IXUS i would blur the background of our pictures similar to the PENTAX 43mm/1.9 Limited lens.

To be more accurate, I must say that in this case PENTAX 43mm/1.9 Limited is actually similar to a lens with the focal distance of 7mm (not 6.4mm). To provide the equivalent degree of blurring, it must have an aperture of f / 0.3. But the conclusions remain the same. Such an aperture is not physically feasible.

Now lets consider another group of cameras: Sony Cyber-shot DSC-V1, Nikon CoolPix 5400, Canon PowerShot G5, and Konica KD-410Z. To be on par with PENTAX 43mm/1.9 Limited in terms of blurriness, their lenses must have an aperture of f / 0.39 (@ f = 8.9mm, which is equivalent to f = 43mm in the 35mm photography). Again, this aperture is unfeasible.

Let us make our requirements not so strict. Let us take for comparison the old good Industar 50-2 lens (50mm/3.5), which is not that fast as PENTAX 43mm/1.9 Limited. Now for the cameras from our set, we can obtain the equivalent aperture of f / 0.72. The feasibility barrier is broken down! However, it is not the time to celebrate the victory. The problem remains unsolved, because the aperture of f / 0.72 is still too wide for a lens with photographic quality. Thus, we must admit that there are no lenses for our compact photo cameras that can be as blurry as even the modest 50mm/3.5 lenses in 35mm photography.

Please do not think the compact cameras that were selected for this article are simply not good enough. Most cameras of this type are almost the same in terms of blurring. Feel free to analyze any other models on the basis of our formula. You may obtain slightly different figures, but the final conclusion will remain unchanged.

Digital SLR cameras

Digital SLR cameras are better performers in terms of blurriness. The explanation is simple: their sensors are considerably larger. Most modern digital sensors for SLR cameras are only 1.5 times smaller than 35mm frames.
Mention should be made that there are larger sensors on the market. For example, Canon EOS-1D Mark II has a sensor with diagonal of 34.5mm, which is only 1.25 times smaller than traditional 35mm frame.

Now let us find peers of PENTAX 43mm/1.9 Limited and Industar 50-2 (50mm/3.5) in this class. For cameras, whose sensors are 1.5 times smaller than the traditional frame, it is easy to derive the following equivalents: 28.7mm/1.3 and 33.3mm/2.3 correspondingly. Both lenses are quite fast (and, therefore, expensive!), but feasible.

Physical meaning of the f / N ratio

The f / N ratio is nothing else but the working diameter of a lens. Some people (especially those who like Harold M. Merklinger’s theory) prefer to operate with this term. However, in this article I chose to talk about the f / N ratio. The main reasons are as following:

First, when we compare digital and film cameras we always talk about lenses with different focal distances. Under such circumstances, the f / N ratio helps us to assess feasibility (or availability) of equivalent lenses (similar to the examples described above).

Second, the working diameter is often misunderstood by those who are not quite familiar with the optical theory. For example, some people think that the working diameter is the diameter of the first element of a lens, which is, generally speaking, not true.

Third, the information about f and N is always explicitly indicated. Thus, there are no misunderstandings.

Conclusion

The comparatively larger depth-of-field of digital cameras is due to the fact that their sensors are smaller than the 35mm frame.

Digital SLRs typically outperform digital compact cameras in terms of blurriness, since their sensors are significantly larger.

Links

1. Igor Yefremov. The Charms and Myths of the Medium Format. The article explains why the degree of fuzziness is proportional to f/N, when different formats are compared to each other.

2. Digital Camera. Photo & Video. This magazine provided me with the information about the specifications of digital cameras available on the market. (Attention! The title in English is misleading. The magazine is in the Russian language.)

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