## Depth of field and digital sensors

**Christophe Métairie** is an image professional who specializes in screen calibrations,photography equipment and printers. His website is full of information for professionals or anyone passionate about photography. Christophe loves to share his experiences and the results of the numerous tests he has conducted. His articles are precise, without any marketing language or jargon. Each of his articles includes a practical test that is often publicized. He recently wrote a particularly interesting article about depth of field with digital cameras. He has agreed to let us share it with you here.

**What is so important about this subject?**

All photographers who have worked with film are used to using the depth of field scale on their cameras. This allows them to know the precise limits of the depth of field zone in the photograph they are going to take. The arrival of digital cameras changed things. Sensors are much more definitive than film and the transition from clear to blurry is very different. I have observed this with my photographs and here Christophe explains it to us in detail.

### Depth of field and digital sensors

### Introduction

Digital camera users make the same observation: **depth of field in digital is not the same as it is using film.** It is easy enough to verify this phenomone. The digital depth of field seems less important than when using film,especially since the lack of grain and perfect clarity of digital images accentuates the perception of this difference. For anyone who has tried to use the depth of field tables on a digital camera, it is clear that they are based on the critiea for film and they do not allow you to accurately predict the depth of field for digital images.

**From a purely theoritical point of view, the depth of field doesn’t exist**: everything that is in front of or behind the plane of focus is blurred.In practice, we see that there is a range of distance in front of and behind the plane of focus that seems clear. I purposely said ‘seems’ clear because **this notion of sharpness is subjective** since the sharpness decreases gradually in front of and behind the plane of focus.To define depth of field, it is therefore necessary to define at what level of clarity will we consider a detail clear or blurry. **We define this tolerance under the concept of “circle of confusion”** that is included in the calculations.

The below formula gives us the calculation of the depth of field for a distance much greater than the focal length (this formula is not valid in macro). This calculation takes three steps: calculation of the hyperfocus, then the calculation of the sharpness of close and far away distances, then the final depth of field of view which is the difference between the in-focus spaces that are close and those far away.

There are two variables that exist in these formulas:

– The ones which are directly dependant on the conditions of the lens: diaphragm, focus, distance from the focal point and

– The variable which is not dependant on the condition of the lens, but the circle of confusion which arbitrarily determines the tolerance of the minimum allowable sharpness for a detail to be considered perfectly in-focus.

*Circle of confusion (Wikipedia)*

Historically with film, the value of the circle of confusion was chosen in relationship to the format of the film used (24x36mm, average format, plan-film), or the size of the prints (in relation to the enlargement). In fact, a negative enlarged 5 times its size does not need the same level of sharpness as a negative enlarged 20 times its size. The smaller the film’s format, the smaller the value of the circle of confusion. In 24x36mm film, for example, Japanese opticiens define the size of the circle of confusion as 0.030mm (30µm), but Leica’s definition of the depth of field tables were calculated with a more restrictive value (0.025mm or 25µm).It is true that the variation of this value didn’t change the real depth of field in the lens, but it did change ones ability to calculate the depth of field tables in relation to reality.

In the digital era, the problem is different: the size of the sensor is no longer directly in relation to its definition, there are APS-C of 24 million pixels and 24×36 of 12 million pixel sensors. **It is, therefore, no longer possible to base the circle of confusion simply on the size of the sensor.**

### The tests

The tests were done with two very different types of cameras:

– an average model digital camera, Pentax 645D (6.6 µm photosites) and

– an old compact digital Canon S80 (4.7µm photosites).

The extreme differences between the focal lengths and sensors between the way these systems capture images will validate the results: if the values found on a 33x44mm sensor are valid on the tiny S80 sensor, then these values will work in a wide range of cases.

*one of the patterns used for this test*

A first series of shots was performed on a test chart with 5mm stairs, the focus being made on a specific marker of the pattern, we measured the actual depth of field of the shot by looking at the images at 100% on the screen. This made it easy to find the value C of the circle of confusion in order to calculate the depth of field.

It is interesting to compare the value of the size of a photosite with the value of the circle of confusion resulting from this calculation (called Factor in the table):

– The Canon s80 has 4.7µm photosites and a resulting value of the circle of confusion calculated at 6.9µm, for the focal length of 20.7mm and 7.01μm for the focal length 7mm, respectively 1.46 times and 1.49 times the size of a photosite (factor x1.46 and x1.49).

– The Pentax 645D 75mm et 200mm lens have circle of confusion values close to 10µm et 9.5µm, compared with 6.6µm of the size of the photosite, we get a Factor of x1.51 (75mm) ou x1.43 (200mm).

As a result of these first tests in the studio, we are able to deduce a pattern: in digital a realistic circle of confusion value (calculated from specific and varied examples) would be multiplied by 1.5 the size of the photosite. In order to obtain the reliable depth of filed through calculation tables regardless of the size or resolution of the sensors.

We are able to verify that **using traditional tables based on a circle of confusion of 30µm or more would be a mistake** and that in all cases a modern digital sensor needs to take into account a circle of confusion 3 to 5 times smaller that one used on a 24×36 film camera. In the table below, you can clearly see that the depth of field in a film camera is largely superior to what is obtained with digital cameras, when pictures are taken under identical conditions.

*Comparison of the depth of field in film and digital cameras depending on the size of the circle of confusion taken into account for these calculations*

Next we look at whether this value for the circle of confusion is confirmed for photos taken of long distances outdoors. We are using excellent software “Depth of field v1.6” by Pierre Chauveau (downloadable here) pfor the theorectical calculation of the depth of field.Since the publication of this article, the software creator has in fact intergrated the possibility to choose a photosite size which is a multiplication factor, which allows the circle of confusion to be calculated accordingly.

These calculations have been made with a 6.6µm photosite and a multiplication factor of 1.5. The resulting circle of confusion being from 9.9µm (1.5 times the size of the Pentax 645D photosite).

*100% size – Pentax 645D*

The below photos were taken with a Pentax 645D, at 200mm at f/11, first focused on the boat (distance 190 meters) in the foreground and then focused on the street lamp in the middle of the trees (distance 320 meters). The facades of the buildings in the distance are a 2080 meters (determined by Google Earth).

– Focus at 190 meters: not surprisingly, the boat is perfectly clear since this is where the focus was directed. The street lamp is very clear and the facade of the buildings in the distance are blurred. The calculation of the depth of field for this distance is:

*Calculation of the depth of field for the photo at 190 meters / Pentax 645D, 200mm, f/11, CoC 9.9µmm*

The calculation gives a zone of clarity from 125 to 394 meters, which confirms the visual results: the street lamp situated a 320 meters is well in the zone of clarity so the buildings in the distance at 2080 meters are outside of this zone.

– Focus at 320 meters: the street lamp and the boat in the foreground are very clear. The facades of the buildings are perfectly clear in constrast to the photo focused at 190 meters.

*Calculation of the depth of field for a focus at 320 meters / Pentax 645D, 200mm, f/11, CoC 9.9µm*

The calculation this time gives a zone of clarity of 171 meters to 2495 meters, confirming the visual evidence: the entire photographed scene is in focus.

### Conclusion

The tests are clearly showing that the calculations of the depth of field in the digital world need to take into account the size of the circle of confusion defined not in function of the film format, but in function of the size of the photosites of the sensor of camera used multiplied by the factor of 1.5.

This factor of 1.5 can be adjusted according to your preferences, knowing that someone who is only taking photos in a small format can increase this factor without it distrubing the prints, but a exigent photographer who is taking photos in a large format can utilize this factor of 1.5 in order to predict the actual depth of field of photos.

*depth of field scale on an optical rangefinder*

**The depth of field scales engraved on the lenses are handled with care**: They are often calculated with the value of a circle of confusion which isn’t adapted to digital cameras. Leica, for example, they are calculated with a value of 25µm, completely valid in film but totally irrelevant if you put your lenses on a M8 or a M9! On a M8 or M9, the size of the photosites are 7µm, multiplied by 1.5 this gives 10.5µm for a realistic circle of confusion! The depth of field scales engraved on the lenses are therefore largely overestimated when using lenses on digital cameras.

I invite you to use the “Depth of Field v1.6” software of Pierre Chauveau (downloadable here) which will allow you to make your own tests and create your own depth of field tables for your camera and to your specifications.

*Source : http://www.cmp-color.fr/pdc.html
Reproduced with the authorization of the author: Christophe Métairie, Photographe // infos@cmp-color.fr
Date de publication : november 2011*

[small_button]English version by Danielle Harrell, English teacher for ArtFx[/small_button]