Depth of field

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Control over the sharp and unsharp parts of the image can be of considerable importance for the success of a photograph. Traditionally, the depth of field (DOF) is a great source of confusion among photographers. To blur or not to blur, that is the question. The latter is a matter of DOF, the former not per se.

Depth of field is defined as the range of object distances within which objects are imaged with acceptable sharpness. [1]

A whole series of definitions can be found at Don Fleming's site, where a casual glance suffices to conclude that they all amount to the same thing. That is a welcome observation, because it means that there is consensus of opinion regarding the definition of DOF.


The concept of DOF

Depth of field can be treated in a theoretical framework that I will refer to as a concept. This concept is very useful because it enables extensive calculations and comparisons within the relatively simple theory of Gaussian optics. For this purpose it is assumed that the lenses are free of aberrations and that diffraction is nonexistent. The film (or digital sensor) is supposed a grainless recorder of the finest details, so that the image can be freely enlarged without loss of definition. All this is not true, but as long as we restrict ourselves to 'normal' photographic scenarios, the concept can be equated to practice with some confidence. The theory is on a separate page to preserve readability, but I will occasionally refer to an equation.


Viewing conditions

There is a difference between calculated sharpness and perceived sharpness. For the perceived or apparent depth of field, the lighting conditions are important, as a well-illuminated print will more easily reveal imperfections than the same print in a dim room. Further, an observer with a high visual acuity may reject a print that satisfies another observer with poor vision. A very important factor is the viewing distance in relation to the size of the photograph. Obviously, a large print viewed from close is much more demanding than a small print viewed from a large distance. Within the concept of DOF it is usually assumed that the print viewing distance does not depend on the picture taking lens. There is a good reason for this, for most people do not change seats during a slide presentation and at an exposition they examine the various photographs from similar distances. The concept of DOF is adapted to these habits, since the DOF scales imprinted on lenses are based on a sharpness criterion that does not depend on the focal length. Likewise, a typical DOF calculator will suggest—or may even impose—a sharpness criterion based on the film format, independent of the lens focal length. Bear in mind, however, that many of the conclusions reached in the remainder of this article would be different if we had assumed 'perspectively correct' viewing, i.e. a viewing distance in proportion to the focal length [2].


Circle of confusion

To calculate the depth of field, one needs a sharpness criterion. This criterion is taken as the so-called circle of confusion (COC). A COC value corresponds to the blur spot diameter, measured on the film/sensor, of an unsharply imaged point in object space. In DOF calculations it is customary to use the designation COC for the largest permissible circle of confusion. The blur disk diameter is zero for points in the plane of sharp focus and progressively grows as we move forward or backward from this plane in object space. However, as long as the blur disk is smaller than the acceptable COC it is considered sufficiently sharp and part of the DOF range. The appropriate value for the permissible COC is influenced by a variety of factors, including film format, print size, viewing distance, etc. In practice however a fixed COC is usually considered for a given format. Lens manufacturers cannot know what the viewing habits of their customers are and adhere to a certain standard. For example, the DOF scales imprinted on lenses for the 35-mm format are based on COC values between 25 and 35 µm. A comparison of such scales might suggest that the former (C=25 µm) lens gives less depth of field than the latter (C=35 µm), but this is not true. It's just that the sharpness criteria are different. For critical work the existing COC standards are superseded anyway and field photographers are better off with printed DOF tables based on preferred COC values or with a simple rule of thumb to overrule the lens DOF scale. Indeed, photographers should evaluate their own applications and demands to arrive at a satisfactory sharpness criterion, if necessary by trial and error.


A circle?

The designation circle of confusion is widely used, but it is rarely correct in the strict sense of the word. For the blur spot will be a circle only in the image center, and that only for a lens used at full aperture. Towards the image periphery, at full aperture, the shape is more like a cat's eye. When a lens is stopped down the blur takes on the shape of the diaphragm opening. A lens with a six-sided diaphragm, for example, comes with a hexagon of confusion. Fortunately, the depth of field does not noticeably depend upon the shape of the aperture. Whether the aperture is triangular, hexagonal, octagonal, ... the depth of field will not really depart from that of a truly circular aperture at the same F-number, although one may expect an influence on the rendering of out-of-focus areas. The deviant mirror lens design, which is associated with doughnuts of confusion, however, requires special attention in DOF calculations.


Visual acuity

Under good viewing conditions, many observers can resolve objects of a size equal to 1/3000 of the viewing distance [3]. Born and Wolf, and many other sources for that matter, mention an angular resolution of one minute of arc for a normal human eye [4]. This translates to 1/3400 of the viewing distance. For a photograph viewed from a distance of 30 cm, the maximum permissible blur diameter on the print would therefore correspond to ≈ 0.1 mm. This is a small number that is at the basis of many disappointing DOF findings. For the 35-mm format, a 10×15 cm print viewed from 30 cm thus requires a permissible COC on the film of 20 µm. For a 20×30 cm print viewed from the same distance, it is a shivery 10 µm. If one relies on the lens DOF scales, which are based on a permissible COC of ~30 µm (for the 35-mm format) the 10×15 cm might just pass a casual look, but the 20×30 cm print will certainly fall short of expectation. When the viewing conditions deteriorate, for instance by dimming the illumination, the visual acuity drops and matters become less critical. The eye even becomes color blind at very low light levels.


DOF versus distance

Quite generally, the depth of field depends on the object distance, the focal length, the F-number, and on the perceptivity of the observer. Scrutiny requires a smaller permissible COC value than a casual glance. In the macro regime the lens symmetry also plays a role, but I will ignore this unless specifically mentioned. A scheme for the circle of confusion versus object distance is plotted in Fig. 1—for a given focal length and F-number. Colors are used as a third dimension to indicate the size of the blur disk. For the 35-mm format, a typical value for the acceptable COC is 30 µm. So, for this format the DOF range is bounded by the yellow color. Upon focussing on a subject at 10 meters, the DOF thus ranges from 6 m to 30 m. In other words, the front DOF amounts to 4 meters and the rear DOF to 20 meters. When the object approaches the camera, or vice versa, the DOF progressively decreases and it would become truly shallow in the macro regime.


COC versus distance

Figure 1. The circle of confusion versus distance for a range of object distances. Focal length = 50 mm; F-number = 5.6.

For the 6×4.5 cm format we might follow the light blue color and conclude that the DOF is larger than for the smaller 35-mm format, at the same focal length, F-number and object distance. However, under these conditions the field of view is larger for the larger format and the images are not really comparable. When the composition is kept the same, the conclusion would be opposite. The rear DOF rapidly increases with the object distance and at an object distance known as the hyperfocal distance it becomes infinite.

There is a persistent misconception among photographers that the rear DOF equals twice the front DOF. Although the rear DOF is never smaller than the front DOF, this statement is silly and misleading. From Fig. 1 it appears that there is exactly one object distance v for which this is true (e.g. v=5 m at a 30-µm COC) and an infinite number of scenarios for which it is not true. In the macro regime the DOF distribution (front:rear) is 1:1 and a landscape captured at hyperfocus has a distribution of 1:∞. So where does the holy 1:2 fit in?


DOF versus focal length

The phrase "a wideangle lens has more DOF than a tele lens" is frequently heard. Is it true? Sometimes it is, often it is not. It all depends on the comparison. We may assume that the lenses are compared for the same format and at the same F-number, but what about the object distance? If the object distance is kept the same the wideangle image will indeed show a greater DOF, but also a Whenever the depth of field is compared between lenses, formats, or whatever, a complete framework must be sketched within which the comparison takes place. If not, the comparison is meaningless. larger field and, consequently, a smaller subject. On the contrary, if the subject is framed the same way we have an entirely different situation. Now the depths of fields may be comparable or even identical. However, in both cases the photographs are not the same and the comparison is one between two different pictures. The former case concerns a comparison with preservation of the perspective (viewpoint) but with different magnifications, the latter preserves the magnification (the size of the subject on the film) but not the perspective. Ironically, the only case where the images are the same is also the only case where the depth of field is of no importance: the reproduction of a flat object like a stamp or a painting. For such a subject has no depth.


DOF at constant magnification I

There are many applications where the perspective is made subordinate to the image magnification. For instance, when we take a macro photograph of a butterfly or a product photograph, the main objective is often to render the subject at a certain size on the film. The question may then be asked: "How does the depth of field depend on the choice of focal length?" To a first approximation, on the assumption that the F-number is kept the same, the DOF will not depend on the focal length. However, a closer examination reveals that this is too simple a statement which does not always hold. The general scenario is illustrated in Fig. 2. At a fixed magnification M=0.0025 and F-number N=2.8, we notice that the shorter focal length has more rear DOF and the longer focal length more front DOF. For example, for the 24×36 mm format we may follow the yellow lines (30-µm COC) to conclude that a 100-mm lens comes with 10 m of front DOF and ~ 20 m of rear DOF, whereas a 35-mm lens has 7 m of DOF in front of the subject and several hundreds of meters in rear.


COC versus distance for a fixed magnification

Figure 2. The circle of confusion versus distance at a fixed image magnification for a range of focal lengths.

Generally, when two lenses are compared at the same image magnification and F-number one must discern between two cases. When for both lenses the object distance is much smaller than the hyperfocal distance, the depths of field are essentially the same. On the other hand, when one or both object distances is not small with respect to the hyperfocal distance, the lens with the shorter focal length brings more depth of field. The latter case is illustrated in Fig. 2, the former case occurs in the macro regime, cf. Fig. 7. (To complicate matters, a more sophisticated treatment adds a third case.)

One way to effectively increase the hyperfocal distance is to look more scrutinously at the photographs. This translates to the use of a smaller COC value. If we inspect the 10-µm bright red color in Fig. 2 we notice that the difference in DOF between the focal lengths is much smaller than at a 30-µm COC.


Background blur

A common source of confusion in DOF-related discussions is the issue of background blur. To illustrate the relation between DOF and background blur, or the lack of it, two photographs are presented in Fig. 3. Here, Gromit was captured with a 100-mm lens and a 28-mm lens on a 35-mm camera. The image magnification is approximately the same at M=0.12, and the F-number is f/4 in both cases. Despite the fact that Gromit appears at the same height, the two pictures are very different. First, the perspective differs as I needed to come closer to my subject with the 28-mm lens. Second, the 28-mm lens shows more of the background because of the wider field of view. Third, the 100-mm lens seems to yield more background blur. (Does it?)



Gromit faces a 100-mm lens @ f/4 Gromit faces a 28-mm lens @ f/4

Figure 3. A: Gromit photographed with a 100-mm lens at f/4. B: Gromit photographed with a 28-mm lens at f/4. DOF is the same.


Let us first discuss the depth of field and then the background blur. For the depth of field we need to ask the question: "What is rendered sharply?" The answer is that Gromit is completely sharp, from his hand and right foot up to the knapsack behind his head. Apart from the quick-release plate supporting the sympathetic dog, nothing else is sharp. Everything in the background is clearly unsharp and thus outside the DOF range. So, as far as we can tell from Fig. 3 the DOF is sufficiently large that it covers the entire subject. Both at 100 and 28 mm. We cannot say that the DOF differs between the two cases because there are no clues to support this. (A calculation shows that the DOF is basically the same here; an accurate reading from photographs would require a boring subject like a slanted ruler instead of our yellow friend.)

As to the matter of the background blur, one must be careful with hasty conclusions. At first sight the background in the 100-mm image seems more blurred than the background in the 28-mm image. This is true when we speak of the absolute blur. The absolute blur is given by the blur disk diameter of a point in the background, such as the highlight reflections off the cars in the street. However, when we speak of the relative blur we must relate the blur disk size to the "image magnification" of the background. And that magnification is larger with the 100-mm lens too. As a matter of fact, the relative blur of the backgrounds is identical. Fig. 4 shows a background detail, taken from both photographs, and enlarged to the same size on the screen. It appears that the blur degree of the red car and the highlights is the same. The question what F-number we need to be able to decipher the license plate of the car would yield the same answer for both lenses. Indeed, this aspect of blur, the question to what degree the various elements in the background are individually recognizable, does not depend on the focal length.

Background in the 100-mm image @ f/4 Background in the 28-mm image @ f/4

Figure 4. Background crop from the photographs in Fig. 3. A: 100-mm lens. B: 28-mm lens.

Although Fig. 3 and Fig. 4 show an example of two photographs with identical DOF and identical relative background blur, this is not a relationship that always holds. The equality of the relative blur of a distant background always holds (on the usual condition of identical subject framing and F-numbers), but the equality of the DOF breaks down when the object distances are no longer small with respect to the hyperfocal distance.

Neither the absolute nor the relative background blur should be used as a criterion to judge the depth of field. Much of the confusion in DOF discussions arises because people base their judgment on out-of-focus parts of the image. DOF should not be judged from background blur. A shallow DOF is not synonymous with a generously blurred background. A shallow DOF implies that there is a shallow region in object space that is rendered acceptably sharp, regardless of whether the background is just not sharp or completely blurred. The luminous landscape puts considerable effort into examination of background blur, but to no avail. The definition of DOF is clear. It concerns the sharp parts of the image, not the blurred parts.


DOF at constant magnification II

If we were to decrease the size of the photographs in Fig. 3, or increase the viewing distance, there is a point where the 28-mm image would start to show more DOF than the 100-mm image. The same would occur if we were to increase the F-number. When the display size is made smaller we effectively increase the permissible COC value, which in turn lowers the hyperfocal distance. If the F-number is increased, the hyperfocal distance decreases too. When the hyperfocal distance is sufficiently small the 28-mm starts to yield noticeably more DOF as its object distance is no longer small compared to the hyperfocal distance. In fact, when the display size is small enough (or the F-number large enough), there is a point where the 28-mm photograph will appear completely in focus with infinite DOF whereas the 100-mm image would still exhibit a noticeably unsharp background. Fig. 5 illustrates just this. Two Gromit photographs are shown again, this time taken at f/22 and displayed at a smaller size. The backgrounds are markedly less blurred than in Fig. 3, but the 100-mm image still has a background that is not really sharp. On the other hand, in the wideangle picture the background does look sharp (if we are not too critical) and the DOF is now obviously larger at 28 mm than at 100 mm because it includes the cars in the background. We could blow up the red car again, to discover that the relative blur is still identical (and the license plate still undecipherable), but for the DOF all that matters is that the car is sufficiently small in the 28-mm photograph that it is not noticeably unsharp. In other words, it is acceptably sharp and thus, by definition, part of the depth of field.

100-mm lens @ f/22 28-mm lens @ f/22

Figure 5. A: 100-mm lens at f/22. B: 28-mm lens at f/22. B shows more depth of field as the DOF now includes the background.

Conversely, any change from Fig. 3 that increases the hyperfocal distances leads to depths of field that approach one another. The smaller the F-number, the larger the size of the photographs, or the closer the viewing distance, the more similar the depths of field. In other words, the more critical we look at our photographs the more apparent it becomes that there is only one plane that is really sharp. Nonetheless the whole concept of DOF in terms of a region of acceptable sharpness is perfectly valid. As we have just seen, the print size and viewing distance are of considerable importance in any DOF assessment; in a calculation these parameters must be taken into account via a suitable COC choice. For the scenarios in Fig. 3 and Fig. 5 the calculation is ~ as follows:


                    3A         3B         5A         5B
  VWDOF 2.1---------input-------------------------------------
  Format            24x36 mm   24x36 mm   24x36 mm   24x36 mm 
  COC               0.12 mm    0.12 mm    0.2 mm     0.2 mm   
  Focal length      100 mm     28 mm      100 mm     28 mm    
  F-number          4          4          22         22       
  Magnification     0.12       0.12       0.12       0.12     
  ------------------output------------------------------------
  Object dist       0.933 m    0.261 m    0.933 m    0.261 m  
  Hyperfocal dist   20.9 m     1.66 m     2.37 m     0.206 m  
  Front DOF         35.9 mm    32.7 mm    0.250 m    0.148 m  
  Rear DOF          38.9 mm    43.6 mm    0.540 m    Inf      
  Depth of field    74.8 mm    76.2 mm    0.791 m    Inf      

Here, the COC values are larger than usual because of the relatively small display size of the photographs and the poor resolution of a monitor compared to print paper. Another way to phrase this would be that large COC values may be used when we are not inspecting a photograph critically. At any rate the COC must be larger for Fig. 5 than for Fig. 3 because the picture size is smaller while it is assumed that the viewing distance remains the same. Hopefully the idea is clear: in Fig. 3 the depths of field are nearly the same, in Fig.5 they are not.


Foreground blur

The behavior of the foreground blur is similar to that of the background blur. It increases with a decreasing F-number and when the object distance is kept the same it also increases with the focal length. By contrast, in a situation where the image magnification and F-number are kept the same, a wideangle lens will give rise to more (absolute) foreground blur.

When there is a barrier like a wire mesh in between the photographer and the subject, sufficient foreground blur may render the wire mesh completely invisible in the image. This is demonstrated in Fig. 6, which shows two photographs taken with a 50/1.4 lens pressed against a thick wire mesh. In photo A the lens was employed at f/16 and two mesh wires present themselves as dark bands across the frame. Photo B was taken at the lens full aperture of f/1.4. The mesh is now completely invisible, even though the wires are still there, right in front of the lens. The gradual corner darkening that is manifest at f/1.4 is not due to the mesh but must be ascribed to vignetting.

Photo through wire mesh @ f/16 Photo through wire mesh @ f/1.4

Figure 6. Photograph taken through a wire mesh with a 50-mm lens at f/16 (A) and at f/1.4 (B).

With knowledge of the distance between the mesh and the lens front principal plane H it is possible to quantify the amount of foreground blur in such cases—if someone would desire such knowledge. For now, I will content myself with the outcome. At f/16 each point of the wire mesh is smeared out over a 3-mm disk (on the film), which is obviously not enough to make the wires disappear. At f/1.4 the blur is 35 mm, which implies that the wires are smeared out over an area comparable to the entire 24×36 mm frame. So, at f/1.4 the wires can no longer be discerned and just act as a neutral-density filter because they still do block some light. The chance of blurring a wire mesh beyond the noticeable is larger for large apertures and also increases with the focal length—on the presumption that the lens-to-subject distance is the same. With the wire mesh dictating the viewpoint, this condition is always fulfilled. Also note that thin wires, or minute objects such as dust particles on the front element or on a filter, are less troublesome than the thick wires of the fence in Fig. 5.


Macro depth of field

Depth of field is small in the world of macro photography and although the subjects are small too, it is often difficult to attain sufficient DOF. So long as we use lenses of similar optical design the depth of field will not depend on the lens focal length, on the assumption of the same magnification and F-number (Eq. 13). This is illustrated in the left graph Fig. 7. The growth of the COC away from the plane of the sharpest focus is the same for all focal lengths between 35 and 100 mm, and it would still be if the range were extended to extreme short and long-focus lenses (still on the condition of similar optical design). By contrast, the blur size of a faraway background (right graph) is proportional to the focal length (Eq. 15), regardless of the design.

Macro DOF

Figure 7. The COC at unit magnification and f/11. The DOF is independent of the focal length (left), but the absolute background blur increases progressively with the focal length (right).


A photograph of a fungus with a height of a few centimeters illustrates the shallow DOF of the macro regime: Fig. 8. Upon focussing on the front part of the cap, the stem is already out of focus and the (rear) depth of field covers only a few millimeters.

Macro photograph

Figure 8. A fungus immortalized with a 100-mm macro lens at f/16.


DOF at constant magnification III

So far, so good. Fig. 7 showed that, in the macro regime, the DOF is not affected by the choice of focal length. This is only true, however, when lenses of symmetrical design are compared. For magnifications smaller than, say, 0.1 the (a)symmetry of the lens design must be taken into account. This can be done via the pupil magnification P (Eq. 1). As a rule of thumb, P equals one for symmetrical designs, is larger than one for retrofocus lenses and smaller than one for telephoto lenses. The below calculation shows the depth of field at unit magnification calculated for two existing macro lenses, the Carl Zeiss Makro Planars 2.8/60 and 2.8/100. The former is a nearly symmetrical design (P=1), the latter departs somewhat towards a telephoto design (P=0.7). Consequently, the 100-mm lens offers more DOF than the 60-mm lens. At f/8 the difference is a mere 0.2 mm, which is a small number, but at the same time it is as much as a 20% difference.


  VWDOF 2.1---------input---------------------
  Format            24x36 mm     24x36 mm     
  COC               0.030 mm     0.030 mm   
  Focal length      60 mm        100 mm       
  Pupil factor      1.0          0.7          
  F-number          8            8            
  Magnification     1            1            
  ------------------output--------------------
  Depth of field    0.960 mm     1.17 mm      

The idea that a lens with a longer focal length yields more DOF than one with a shorter focal length may sound controversial, but the effect really is due to the design, not the focal length. Macro lenses exist with a focal length of ~ 200 mm, and these presumably have a pupil magnification that is even smaller than 0.7. Then, provided that the subject is framed the same way, a telephoto macro lens for many applications offers three potential advantages over its more symmetrical competitor of shorter focal length: an increased working distance, an increased depth of field, and a narrower field of view that comes with a more (absolutely) blurred and less obtrusive background. Of course, for those macro applications where a close perspective, a narrow DOF or a large FOV is desirable the shorter focal length will be a better choice.

A final wrap-up of the issue of a depth of field comparison at a constant image magnification and F-number is the following:

  1. When for both lenses the object distance is much smaller than the hyperfocal distance, the depths of field are essentially the same.
  2. When one or both object distances are not small with respect to the hyperfocal distance, the lens with the shorter focal length brings more depth of field.
  3. If the lens designs are the same, points 1 and 2 are the whole story. If the lens designs (pupil magnifications) differ, point 2 still holds but point 1 must be reconsidered. Depending on their design either one of the lenses in the comparison can yield more DOF.

In case you wonder what the pupil magnification P is for a certain lens, you should look at the sizes of the entrance and exit pupil as specified in the lens information sheet. If this information is not available, you may estimate P by inspection of the lens. Close down the lens by a few stops, estimate the size of the diaphragm opening when you look into the lens from the front (entrance pupil) and from the rear (exit pupil), and apply the definition of P (Eq. 1). Finally, you may want to enter the value in a DOF calculator to find out whether or not it matters for your application.


Digital depth of field

Photography with digital cameras is subject to the same DOF rules as chemical photography. Nonetheless there is a subset of digital cameras that deserve special attention. This concerns the consumer cameras with very small sensor sizes. To achieve a reasonable field of view, the focal length must be very short for such cameras and this has important consequences for the depth of field.
Let's make a comparison between two photographs, one taken with a 35-mm camera and one with a digital camera equipped with a miniature sensor. I will consider a (hypothetical) sensor size of 6×9 mm, which may not exist but which has the same aspect ratio as a 24×36 mm frame. The idea is clear. A fair comparison requires 'identical' pictures, i.e. the object distance (perspective) and field of view (FOV) must be the same in both cases. The following calculation does just that. For the 35-mm format a focal length of 50 mm is considered, an F-number of 4 and an object distance of 3 m. To achieve the same field of view with the digital camera, its lens must have a focal length of one fourth of the 50-m lens, which is 12.5 mm. Now this equivalence is exactly true at infinity focus, but as the FOV changes with the object distance there is a slight difference in the FOV when the subject is at 3 m. The focal lengths might be finetuned to achieve exactly the same FOV at an object distance of 3 m, but this would not change the conclusions so we'll just stick with the nice value of 12.5 mm. In the light of a fair comparison we also want to consider eventual prints or screen displays of the same size, which implies that the digital image needs a linear magnification four times as high as that of the 35-mm image. Therefore, the allowed circle of confusion must be four times as small. For the 35-mm scenario we adopt the conventional 30-µm COC, for the smaller sensor we thus take 7.5 µm.


   VWDOF 2.1---------input---------------------------------
   Format            6.0x9.0 mm   24x36 mm     24x36 mm    
   COC               0.0075 mm    0.030 mm     0.030 mm    
   Focal length      12.5 mm      50 mm        50 mm       
   F-number          4            4            16          
   Object dist       3 m          3 m          3 m         
   ------------------output--------------------------------
   Field of view     46.6 deg     46.1 deg     46.1 deg    
   Hyperfocal dist   5.22 m       20.9 m       5.26 m      
   Depth of field    5.13 m       0.867 m      5.00 m      
   Infinity blur     13.1 mu      0.212 mm     53.0 mu     

Although the perspective, composition and F-number are the same, the depths of field differ greatly. The digital image has 5 meters of DOF, the 35-mm image barely 1 meter. This is due to the very short focal length of the digital camera, which outweighs the smaller COC criterion. The infinity blur in the above table denotes the blur disk diameter, on the film/sensor, of a distant point. So, in addition to the larger DOF, the digital image also has less background blur. (Both absolute and relative.) On a 20×30 cm print, the blur disks would measure 0.43 and 1.8 mm, respectively. These characteristics of miniature-sensor digital cameras are considered an advantage in landscape photography, which often requires a large DOF, but it becomes a nuisance in portraiture when the photographer tries to blur the background. This is often just not possible.
An interesting observation is made in the third column of the calculation, in which the 35-mm photograph is taken at f/16. The calculated quantities are now remarkably similar to the outcome of the first column, including the infinity blur once the images are blown up to the same size.

Generally, when two formats are compared with the purpose of taking the same picture, the larger format requires a focal length that is R times as large as the lens focal length for the smaller format, where R is the ratio of the format dimensions. The above observation may then be generalized into a rule of thumb: The smaller format employed at an F-number N yields the same DOF as the larger format at an F-number of R × N. Please note that this rule of thumb is just a rule of thumb, not a mathematically exact relationship. It should only be applied at intermediate and long object distances, because at close range the equivalence breaks down. When the F-numbers are the same, the smaller format brings inherently more DOF and less background blur.

In the above example it is questionable whether a consumer digital camera has a receptor grid fine enough to allow a COC of 7.5 µm in the calculations. However, this is more an issue for the practicability of this example than it is for the validity. The concept of DOF doesn't mind.


Flashlight and ghosts

Another striking feature that received attention with the emergence of small-sensor digital cameras is the appearance of white or grayish disks in flash photography. Fig. 9 illustrates this phenomenon. Several ghost spots scattered across the image add to the spookiness of the graveyard.

The orb effect

Figure 9. Ghost spots typical of flash photography with small-sensor digital cameras. (Sony Cybershot, picture by Brandy Rolin.)

Fantastic theories are going the rounds on the internet as to the origin of this effect. Ghost hunters speak of orbs and consider them as evidence of the paranormal. No surprise, the orb theory is not adopted by rationally thinking people. The ghosts are in actual fact small particles (dust, smoke) in the air illuminated by the camera flash. From the stain sizes it can be derived that the dust is within a distance of a few cm of the lens. At this distance the particles experience a flash intensity that is larger by orders of magnitude than the intensity received by the subject. Although they are well outside the DOF range and considerably blurred, the high illumination level nonetheless renders them visible against darker parts of the background.
In theory dust ghosts can occur with any camera, but there is a combination of two factors which make them more apparent with miniature digital cameras. First, the flash is usually very close to the lens, which increases the illumination level difference between the particles and the subject. Remember that the flashlight is subject to the inverse square law of intensity versus distance. Second, the short focal length of the digital camera comes with a reduced foreground blur. With a larger-format camera a particle close to the lens would be blurred more because the lens has a longer focal length, thereby degenerating into a kind of veiling glare. To obtain ghosts with similar sizes with the larger format, the dust must be further from the lens. In that case however they get hit by much less flash light and the intensity of the ghosts will consequently be much smaller too. Conventional formats are more likely to attract orbs such as in Fig. 9 with raindrops or snowflakes than with dust particles.


Hyperfocal distance

The hyperfocal distance H (Eq. 10) is an unavoidable part of any DOF treatment. When a lens is used at its hyperfocal setting the maximum depth of field is obtained, ranging from H/2 up to infinity. As such, it is of paramount importance for landscape photographers who want everything from some nearby object to infinity in sharp focus. It is this very application that confronts photographers with the limitations of the conventional depth of field scales on lenses. Insufficient depth of field is today's number one customer complaint at Carl Zeiss [6]. The origin harks back to the early days of photography, when film quality was poor. The sharpness criterion appropriate to pre-war emulsions is still used by lens manufacturers today, but since films have dramatically improved over the years they now reveal the inappropriateness of the DOF scales on our lenses.

For hyperfocal photography a solution is to overrule the lens DOF scale. For example, when the aperture is set at f/11, the DOF markings for f/8, f/5.6, or even f/4 may be used—depending on the demand. For a 20×30 cm print viewed from 30 cm, a three-stop difference is required for the photograph to pass a critical examination. Merklinger discusses an alternative approach [7]. Here, the idea is to simply focus at infinity. In this case all of the faraway subject matter, which often forms the largest part of the image, will be genuinely sharp and foreground details will suffer only by a little. The advantage of this approach is that the photographer is less likely to stop down the lens too much, which might result in an overall lack of sharpness due to diffraction.

Fig. 10 illustrates the concept of the hyperfocal distance. I used the lens DOF markings for f/5.6 but set the aperture at f/11. Everything appears to be in sharp focus on this relatively small monitor display, from the foreground stones to the bushes in the distance.

Hyperfocal DOF

Figure 10. A landscape captured at hyperfocus. (21-mm lens @ f/11)

Depth of field preview

Some of the more expensive SLR camera models are equipped with a so-called DOF preview button. The function of this knob is to reduce the lens aperture to the set value. As a consequence, the viewfinder image changes and shows an increased DOF, as compared with the normal view with the lens wide open. What you see is what you get, so to speak. However, it is very difficult—if not impossible—to judge the depth of field accurately in a viewfinder. The more the lens is stopped down, the dimmer the viewfinder. At small apertures the viewfinder image is so dark that it is impossible to assess which parts of the scene are rendered sharply. Nonetheless the viewfinder may still allow an examination of whether or not the subject stands out against the background. As such, the designation blur preview would seem more appropriate.


Depth of focus

The depth of focus Eq. 14 may be regarded as the depth of field at the film side of the lens. It has a few properties in common with the depth of field, such as that it increases with the F-number, but there are also differences. Provided that the image magnification and F-number are kept the same, there is no dependence on the focal length whatsoever. The dependence on the image magnification is weak, a humble factor of two between infinity focus (M=0) and lifesize portrayal (M=1). The significance of the depth of focus is found in relation to the precision of camera alignment and film flatness. On the assumption of accurate focussing and a properly aligned camera, the depth of focus indicates the tolerance of the photographic system with respect to film displacement. In other words, if the film departs from its proper position by a distance which brings it out of the depth of focus the subject is imaged with a COC larger than the permissible value and considered out of focus. Overall the depth of focus is smaller for miniature (digital) cameras than it is for larger formats, which puts more stringent demands on manufacturing tolerances.


Sensor dust

Sensor dust is a common nuisance with digital cameras. Dust particles, or other types of matter entering the camera, can settle on the sensor and block part of the image-forming light. At small lens apertures the particles may totally eclipse light-sensitive cells, which leads to dark spots in the image. Fortunately such particles do not settle on the actual cells, but on a thin transparent filter in front of them. This implies that it is possible to mitigate the effect of particles by widening the light cone emerging from the lens exit pupil, i.e., by using larger apertures. The principle is equivalent to the wire-mesh demonstration, but on the other side of the lens. Although post-processing time can be saved by regularly cleaning the sensor, sensor dust is a valid reason for not using smaller apertures then needed.


Conclusions

Any statement along the line of 'a short-focus lens gives more DOF than a long-focus lens' is meaningless unless a complete framework is sketched within which the comparison takes place. Relevant parameters may include the object distance, image magnification, F-number, film format, print size, viewing distance, sharpness criterion (COC), etc. For all relevant parameters it must be specified which one is taken constant and which one varies for the statement to have any significance. Additionally, in the macro regime the pupil magnification must be taken into account and although it might be considered identical between lenses for the purpose of a simple comparison, it rarely is in practice.

Finally, although the depth of field is a primary discipline of the photographic craft its importance should be seen in the proper perspective. It does not require familiarity with equations to confront the world with stunning photography. IMHO, from the theory of DOF, the most important ingredients would be the quest for the true hyperfocal distance to avoid backgrounds that are just not sharp, and the art to disengage the subject from the background. The latter, however, is more a matter of blur and FOV control than DOF control.

© Paul van Walree 2002–2014



References


[1]   Leslie Stroebel et al, Basic Photographic Materials and Processes, 2nd ed., Focal Press (2000).
[2]   Rudolf Kingslake, Optics in Photography, SPIE Optical Engineering Press (1992).
[3]   Photography for the scientist, edited by Charles E. Engel, Academic Press (1968).
[4]   Born and Wolf, Principles of Optics, 7th ed., Cambridge University Press (1999).
[5]   Sidney F. Ray, Applied photographic optics, 3rd ed., Focal Press (2002).
[6]   Carl Zeiss, Camera Lens News 1 (1997).
[7]   Harold M. Merklinger, The INs and OUTs of FOCUS, v1.03e (2002).