Digital Camera Lenses

1. Basic Design Concepts. 

Focal Lengths, Fields of View, & Depth of Field

With the advent of digital cameras many aspects involving the use of them has changed in comparison to that of film. One particular area where this is seen is with the lenses that they use. It isn't that they look or work much differently to the optical designs used with film cameras, although technological changes and advances have occurred as happens with most items, but rather that in most cases their descriptions have altered, or have stayed the same but mean something different, as in the case of 35mm SLR film camera lenses used on a small sensor DSLR. 

To understand and appreciate these differences, and what they mean in terms of actual use of a digital camera it is necessary to look several factors, the first of which is the actual size of the sensors used in digital cameras.

Sensor size

One of the biggest changes to have occurred is in the size of the sensors that are used in place of film. Sensors are expensive to make, and as one of the perceived advantages of the move to digital was the ability to make smaller cameras, sensors much smaller than the normal 35mm film size are used in most digital cameras. And not just one size, there are a range of them. The table below illustrates the main sizes currently in use, some of which are just a fraction of the size of 35mm and seem incredibly small by comparison.

The use of sensors this small has both disadvantages as well as advantages as you will discover. We would also suggest you refer to our  Sensors  pages for full details of camera sensors and some other factors surrounding their use

Camera Lenses

One result of the smaller sensors is that camera lenses, particularly those used by digicams, use much shorter focal lengths than hitherto encountered for the fields of view [FOV] they provide. This has led to some confusion amongst those familiar with cameras and used to the normal 35mm designations regarding the focal length of lenses, and the fields of view obtained using them, standard, wide-angle, telephoto. 

Further confusion also occurs with the use of current 35mm designed SLR lenses with the new types of Digital SLR's with their smaller than normal sensors, for this also results in the effective focal length of the lens used  changing, or rather the actual field of view that results.

So the convention has arisen whereby digital camera lenses are often referred to in equivalent 35mm terms. Whilst this is helpful in many ways, giving users a benchmark with which to make judgments, it also adds to the confusion because the actual focal length of a camera lens has direct implications as regards depth of field [DOF].

Depth of Field is an extremely important factor in images. It determines how much of the image appears sharp. Whether it is shallow to isolate a subject from it's background, or deep to depict as much detail as possible, its effect on image quality and the type of image obtained cannot be overstated, and adds to the advantages and disadvantages each camera sensor format has over the other. For there are marked depth of field differences between the different sensor formats in general, and particularly between digicams and DSLR's. And the reason for this is quite simple. DOF is related to both focal length and aperture setting, but not sensor size. 

The Standard Camera lens

In order to understand the differences arising from the use of lenses with different focal lengths, and the implications of the various sensor sizes, perhaps it is best to start with some basic information on camera lenses.

Like most high precision optical instruments camera lenses use circular optical elements. This means they produce a circular image view. It is from this circular image that the rectangular image format that a camera produces is taken. In order for this to occur the image circle that the lens makes must cover or exceed the diagonal of the rectangular sensor being used. The focal length required to accomplish this is determined by the size of the image circle. 

So what is focal length? It's the distance behind a lens that the image is brought to focus when the lens is set to infinity. This point is known as the focal plane, and this is where the film or sensor is placed to record the image.  So for example a 50mm lens set to focus to infinity produces a circular image focused 50mm behind it and with a diagonal of 50mm. It results in an image giving a field of view similar to that of the naked eye. Around 53°. 

In the above illustrations the lens is shown as single element for simplicity. A camera lens comprises a number of elements arranged in groups and because of this is known as a compound lens. The number of elements and groups varies depending on the type and quality of lens. A lens that is designed to produce a flat field of view, in other words one where straight lines appear straight, is known as a rectilinear lens. Most camera lenses are thus categorized as compound rectilinear types.

Determining the standard focal length lens for any film or sensor size is therefore just a matter of finding the diagonal of the respective film or sensor format size. We have compiled a table below listing the standard lens focal length for most digital sensor sizes, and for comparison some film formats. The table also lists the field of view, which you will see is exactly the same for all lenses. 

The first thing most photographers with any knowledge of 35mm may spot is that the standard for this size is not that which is normally associated with it. A 50mm lens is. It has an field of view of 47°. Why this has occurred no one seems to know, but it has been the convention for many years. But it is not correct. 43mm is the 'real' standard lens for 35mm because 43mm is the diagonal measurement of the 35mm film format. 

You may also notice that the field of view is the same whatever focal length is involved. This is because field of view is not tied to a specific focal length alone. There is a relationship regarding field of view and focal length, but it is dependent on image size.

The important point is that for each sensor/film size there is a 'standard' focal length, or field of view, and any focal length shorter than this figure can be regarded as 'wide-angle', and any focal length longer as 'telephoto'. For field of view should really be associated and measured in degrees. Lenses with focal lengths different to that of the standard required for the sensor size and format are optically designed so that the image circle they provide matches that of the standard focal length.

To help illustrate this here is another table. We have listed a zoom lens in each of the sensor sizes that it is common to find. There is the field of view coverage, and to help understand the relationships we have also included the convention of stating the lens focal length equivalents in 35mm terms.

 To obtain comparable focal length sizes in relation to 35mm we have used the following Lens Multiplication Factors. LMF. 1.2/7" - 6.560 ; 1.1/8" - 4.865 ; 2/3" - 3.936 ; 4/3rds - 1.92 ; APS-C - 1.535 .

Some figures we have used might be different to those you have seen used elsewhere. For example 2x is usually quoted as the LMF for the 4/3rds system. There are several reasons why this may be so. Often figures given in respect of products for consumer use are rounded up to whole numbers for ease of understanding where they are just for general information, which is all that is generally required. Most don't want information to 3 decimal places, 1 is usually sufficient when appropriate. Besides this, edge pixels around sensors are used to collect additional data and makers often use slightly differing numbers to do this, altering the sensor collection size as a result. 

For the APS-C sensor we have used the Pentax/Minolta/Nikon type with 1.5x LMF. Canon uses a slightly smaller sensor size at 1.6x, and Sigma a smaller size still at 1.7x. You can assume that any figures for the 1.5x APS-C size will be increased for the Canon and Sigma types. The focal lengths will be slightly longer, angles of view narrower, depth of field greater. The Sigma is almost halfway in size between the largest APS-C 1.5x sensor and the 4/3rds. 

Again please refer to  Sensors

Depth of Field

Although each sensor size has different focal lengths in relation to field of view, there is one constant factor that is applicable to lens focal length irrespective of sensor size - Depth of field. 

When a lens is focused on a subject there is an area both in front of the focused point, and behind it, that will appear sharp in the image. This is the depth of focus, or as it is more commonly called, depth of field. To put it another way, it's the distance between the nearest and furthest points from the camera lens at which everything appears sharp. However objects outside this depth do not suddenly become un-sharp, it's a gradual and proportional effect. So depth of field is an area of sharpness within an image which progressively becomes less sharp. 

Depth of Field relies on circles of confusion. These are the smallest circles in an image the eye perceives as points. As an image is enlarged beyond a certain magnification, these points begin to be seen as circles, and as this happens the image appears less sharp.  A very high magnification of an image requires that it is viewed from a greater distance. This is why extreme magnification of an image on a computer screen is not a good idea. Viewed close up, any image magnified beyond a reasonable level for its image format size will look un-sharp and quite good enough images when viewed at normal distance are often discarded or classed as poor because of this, which is a mistake.

The circle of confusion figures we have used in our calculations assume production of an image at roughly 8"x 10". These are ; 1.2/7" :- 0.005mm ; 1.1/8" :- 0.006mm ; 2/3" :- 0.008mm ; 4/3rds :- 0.015mm ; APS-C :- 0.020mm ;   35mm :- 0.030mm . These are the standard figures used with these format sizes.

So depth of field is governed by four factors. The actual focal length of a lens, irrespective of field of view. The distance it is focused to. The aperture used. And the circles of confusion figure applicable to each sensor or film format.

Focused Distance

Depth of field is proportional to subject distance. The largest or maximum amount of depth of field a lens produces is when it is focused at infinity. This is when its elements are closest to the film plane. As the focused distance is reduced, and sharp focus is maintained by moving the lens elements farther away from the focal plane, so the depth of field reduces. At the minimum distance the lens is able to be focused at, the depth of field is at it's least, or minimum. It is for this reason that macro lenses, which focus closer than normal lenses, are often called 'long throw' lenses because the lens elements are moved away from the focal plane much farther than with normal lenses. It also accounts for these lenses having very shallow depth of field at the high magnifications they produce, and the reason why they often have minimum apertures of F32 and sometimes F45.

Focal Length

As well being proportional to subject distance depth of field is relative to focal length, as the shorter the focal length the nearer the lens elements will be to the focal plane, and the longer the focal length the further away they are.  Within each film format or sensor size the depth of field will thus be deeper for a wide angle lens and shallower for a telephoto, but in relation to other sizes the truism is that the smaller the format the larger the general depth of field. 

Aperture

Depth of field at any focused distance can be increase proportionally by reducing the size of the lens aperture, called 'stopping down'.  As the aperture is reduced the depth of field increases. Normally when looking at a scene through a cameras viewfinder or on it's LCD screen, the lens aperture will be at it's maximum - wide open - to give as bright an image as possible, essential in low light levels. This means however that the least amount of depth of field is visible.

Determining Depth of Field

Depth of Field is usually determined visually, using the depth of field preview facility found on many DSLR's,  or on a digicams rear LCD screen - many show the view at the set aperture prior to taking the shot. In the past many camera lenses, mainly of the prime manual focus type, had depth of field scales etched on them. This made finding the depth of field easy and also helped in the use of hyperfocal distance focusing. This is a method using a combination of focused distance and aperture to obtained the greatest possible depth of field in an image. Unfortunately the advent of zoom lenses and autofocus has meant depth of field scales have disappeared from lenses and hyperfocal distance focusing is thus much more difficult. It can also be calculated using equations. Whilst this has many uses, it's not perhaps the best method to use when out taking images. 

If you would like to find out more about depth of field in greater detail - which is outside the general scope of this page - how hyperfocal distance focusing works, how to use it, and how you can download small free software applications with which to make scales and charts to use, we suggest you visit a very good website dealing with all of this -  www.dofmaster.com 

Depth of Field comparisons

Because there are an endless number of permutations of focal length, aperture and focused distance that can be calculated, and as the general purpose is just to give some illustration of the scale of difference that applies between the different focal lengths and the implications that can be drawn from this in regard of digital cameras, we have restricted ourselves to using just a few focal lengths and distances for the tables and charts that follow. These were all taken from the hyperfocal charts that can be generated using the software available from the website mentioned previously. 

The fields of view, and the resultant focal lengths along with the focused distance, have been chosen to help illustrated where we feel important differences lie in respect of depth of field. 

NB. If you get confused looking at these tables just remember the 35mm size is at the bottom. The sensor type focal length given for that size is equal to the 35mm focal length in field of view terms.

All figures in the charts and tables are in millimeters.

Standard Lens

The first chart/table shows the depth of field at a focused distance of  0.5 metre/19.5" using the 'standard' focal length at f 2.8, f 4.0, f 5.6 and f 8.0 for the small digicams, with f 11, f 16 and f 22 added for the larger sizes. We chose these figures because most camera lenses can focus this close without using 'macro' mode - which is another matter altogether -  and the focal length is available to all, usually as part of a zoom lens focal range. 

The reason f 8.0 is the maximum figure used for the digicams in these tables is that most don't have apertures smaller than this, while f 11, f 16 and f 22 have been added for the larger sizes because their depth of field is so small at the wider apertures and the comparison at these apertures with the performance of the digicams at the wider one's is very revealing.

Being able to get close to an object when taking a shot of it is often important in photography. The closer you get, the larger the object will be in the shot, whatever focal length lens you use, up to the minimum focusing distance for that particular lens. For most general close up shots - which some call macro shots, but which is not strictly true - a lens with an field of view which does not cause distortion of the image but gives 'normal' perspective is normally involved. A standard focal length lens is quite good for this. At the close distances needed to take shots of small objects, depth of field becomes quite important, being minimal, so the table above gives some interesting results. 

The most outstanding figures, and those which illustrate just how large the differences that exist are, concern the very first, and the very last. At an aperture of f 2.8, a digicam using the smallest sensor size, can provide a depth of field that a 35mm sensor camera, a DSLR, cannot equal until it uses an aperture of f 22  -  7stops difference. This is  highly significant. Even the more common APS-C DSLR's need to use f 11-f 16 to obtain similar depth of field. Although the larger digicams don't offer quite the same advantage, they are still much better, offering between 2-4 times the depth of field at any given aperture, compared to the DSLR's from the 4/3rds system up. 

Short Telephoto

For this next table we have chosen a field of view considered to give a natural look for portraiture, 24.5 degrees, equivalent to 100mm focal length in 35mm terms. At this angle a full face shot needs to be taken from around 2½ - 3 metres. We have used 3 metres/ 9'.9" as the measurement. Only two apertures are featured. f 2.8 and f 5.6. This is because with portraiture the need usually exists to blur the background by using a wide aperture, yet at the telephoto end most standard SLR zoom lenses maximum aperture is f 5.6. However the results are interesting.

Once again the figures show the huge depth of field the small sensor digicams can deliver at wide apertures. But with portraiture this is often not what is required. The ability to isolate a subject from the background by using shallow depth of field is widely used, as we have said, yet with the small digicams that is not really possible, even at the widest aperture. Despite their relatively slow maximum apertures of f 5.6, even the standard SLR zoom lenses are better in this respect.

Longer Telephoto's

The next tables concern much narrower fields of view. There are increasing number of digicams that have zooms with quite long focal lengths, with 35mm equivalents of between 200-400mm. So we have compiled three tables. A 12.5 degree field of view at 5 metres. 8.2 degree field of view at 10 metres. And finally, 6.2 degrees at 20 metres. These fields of view are equivalent to 200mm, 300mm, and 400mm focal lengths in 35mm terms.

Two aperture sizes are used, f 4.0 and f 5.6. The smallest sensor size has been omitted because fields of view/focal lengths of this nature do not feature in cameras using these sensors.

  200mm                                                         300mm

400mm

As with the previous tables these show just what an advantage in depth of field the small sensor digicams have over the larger sensor cameras. Of particular note to us was that the APS-C sensor DSLR's hold a significant advantage over the 35mm size with the very long focal lengths. At f 4.0, greater depth of field is available than the 35mm can produce at f 5.6. A whole stop of light difference at these focal lengths and distances is crucially important and can mean the difference between getting a shot and not.

More significantly, although they retain an advantage as regards depth of field, the small sensor digicams ratio of advantage is much less. They have lost their advantage of faster apertures, the apertures available being much the same.

The next page deals with some practical examples