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depth of field - detailed information

see depth of field examples using the C8080



WARNING: traditional DOF calculations such as those below and lens markings only apply to 4-8x enlargements which is OK for film, but for small digital sensors when we are often looking to make enlargements of A4 and larger, these DOF calculations will give increasingly soft images as enlargement size increases, and nothing impacts more on an image than lack of sharpness when you want it.

There is a lot of mis-information and misunderstanding on the internet when it comes to depth of field, hopefully, I won't be contributing to it. Firstly, many people state that DOF is purely a function of the lens - its native focal length (not its 35mm equivalent focal length), camera to subject distance and aperture and if that lens is used on a full frame camera you will have the same DOF as when it is used on a cropped sensor. This would be true if you used the same subject distance, native focal length and aperture AND you printed an enlargement with the SAME amount of magnification AND viewed it from the same distance - ie. the cropped sensor print would have a cropped print size, so the prints would look pretty much identical other than the cropped sensor print being smaller with the outer parts of the image missing.

In reality, when one uses a cropped sensor, one usually would print to the same size as if it were not cropped and thus the magnification of the print becomes greater and when viewed at the same distance, the amount of acceptable depth of field becomes shallower.

It is complicated further by what people mean - many people concentrate on the degree and quality of background blurring so that the subject is then emphasised and has more impact, but this is actually due to a mix of different factors:

  • depth of field
    • how sharp the region proximal and distant to the focus plane is rendered in a final print or image that is viewed from a given distance.
    • dependent on magnification (subject distance and focal length), aperture, circle of confusion size & intended degree of enlargement and viewing distance.
  • degree of background blurring (convolution)
    • for the same subject magnification (ie. change subject distance when change focal length) with same subject to background distance, degree of background burring is inversely proportional to aperture alone.
  • quality (aesthetics) of background blurring (bokeh)
    • this is primarily dependent on the shape of the aperture with a circular aperture usually giving the best bokeh, but additional factors include potential clipping of the cone of light by the mirror compartment at wide apertures, vignetting & lens aberrations affecting out of focus areas which may be corrected for in-focus areas. Mirror lenses in particular give donut-shaped out-of-focus highlights of double contours which generally are not aesthetic.

Depth of field:

  • traditional depth of field (DOF) is the distance ranges from the camera within which a subject will appear acceptably sharp when enlarged to a 8“x10” print and viewed from 15“ and thus a dot produces a dot no larger than 250micron on the print.
    • this 250 micron dot when represented on the film or sensor (= 250micron/magnification to print) is the circle of confusion (COC) for that film or sensor
      • COC values: 35mm film = 29.5micron; Olympus C8080 digital = 8 micron;
    • note that at small apertures, the diffraction limit may be larger than the COC and thus the estimated COC no longer applies. The diffraction limited spot size is 6 microns at f4.5, 8.45 microns at f6.3 and 10.7 microns at f/8.
    • NB. the COC may not really be a circle but the shape of the lens diaphragm and this impacts on bokeh - the nature of out of focus areas in the image.
  • for a given lens and focus position, there is really only one plane which will be in focus (in most lenses apart from special flat-field macro lenses, this plane is usually a curve with all points equidistant to the camera). Everything else closer or further away than this plane will be out of focus, but the amount of out of focus will determine whether we will perceive it as being acceptably sharp or not, hence the depth of field concept.
  • some rules of thumb:
    • for the same subject image magnification, DOF is dependent on f ratio and NOT on focal length as you must alter subject distance when you change focal length.
    • different sensor sizes of the same number of pixels will give equivalent DOF if:
      • f/ratio is multiplied by the ratio of the pixel sizes, and,
      • focal length used is multiplied by the ratio of the pixel sizes to give the same effective focal length, and,
      • camera to subject distance is kept constant
      • obviously, for the same exposure, either shutter speed must be changed, or if kept constant, the ISO must be multiplied by the square of the ratio of the pixel sizes, which according to Clark should give equivalent S/N ratios.
      • in other words, a larger sensor CAN give the same DOF as a smaller sensor at the same shutter speed and image noise by increasing ISO to allow the f/ratio to be increased.
    • the zone of acceptable sharpness is equal closer and more distant to the focused subject NOT 1/3 : 2/3 as usually stated.
    • stopping down the lens 1 stop gives 40% more DOF, while opening it up 1 stop gives 30% less DOF.
    • stopping down the lens 2 stops gives twice the DOF, while opening it up 2 stops gives 50% less DOF.
    • stopping down the lens 7 stops gives 10x the DOF
    • DOF scales linearly with focus distance for a given focal length, thus DOF at 10m will be twice that when focused at 5m.
    • if you want everything 5mm and larger to be resolved, then you must use an effective lens diameter of 5mm (ie. f/10 on a 50mm lens) or smaller AND focus no closer than half the distance to the most distant object you wish to be sharp.
    • when photographing people more than 3m away with a focal length < 50mm (in 35mm terms), then:
      • for best resolution of distant subjects such as landscapes, acceptable results may be possible by focusing on infinity as long as effective lens diameter is less than 5-6mm (eg. f/10 or more on 50mm lens).
      • if resolution of distant objects is not so important, consider focusing at the hyperfocal length as long as it is less than 6m.
      • if you want the subjects eyes to be the key and the rest of the scene is not important, focus on the eyes.
  • everything sharp:
    • sometimes, we want everything to be as sharp as possible including distant objects, in which case we should set the focus position of the lens on the hyperfocal distance for that focal length/aperture combination, and then everything from half the hyperfocal distance to infinity will be acceptably sharp. In fact, I suspect the designers of the Olympus 8080 do this by default when auto-focus fails - the only problem is that your subject may be closer than the DOF allows and thus appear blurry.
    • on the other hand, Merklinger suggests that:
      • if you want anything at infinity to be sharp, then it is be best to focus on infinity assuming you have a good lens and technique, as to do so means you would lose a factor of two in the subject resolution at near limit of depth of field, but gain a factor of six in the subject resolution for distant subjects. (ref: page 32 of his pdf)
    • the closest hyperfocal distance is usually achieved by using a small aperture and wide angle lens with a small sensor or film, examples:
      • f/5.6 f/8 f/16 35mm with 28mm lens 4.7m 3.3m 1.6m 35mm with 50mm lens 14.9m 10.6m 5.2m 35mm with 90mm lens 48m 34m 17m Oly8080 with 28mm 1.1m 0.8m n/a Oly8080 with 55mm 4.4m 3.1m n/a Oly8080 with 90mm 14m 9.8m n/a
  • blur the background (convolution):
    • at other times we wish to render the foreground and background out of focus and blurred so that the viewer will be drawn to the subject rather than distracted by the background. In this situation, we need to minimise the depth of field to just enough to cover the depth of the subject.
    • this is one of the reasons a portrait lens is a medium telephoto with wide aperture
    • however, depth of field is NOT directly related to degree of background blur. Depth of field equations tell you over what range of distances objects will appear to be acceptably sharp (or at least not unacceptably unsharp). It tells you nothing about how much blur there will be of objects well outside the depth of field. That's governed by different physical parameters and determined using totally different equations:
      • background blur of infinity point source = focal length x image magnification / f-stop
    • in addition, modern lenses are often over-corrected for spherical aberration to produce a more pleasing blurred background (bokeh) at the expense of quality of foreground blurring.
    • Merklinger uses the concept of disk-of-confusion to help determine what will be in focus (see page 32 of his pdf):
      • the disk-of-confusion is the hypothetical diameter of the cone of light from the film projected onto an object
      • disk-of-confusion at distance of the object =
        • (focus distance - lens to object distance) x focal length / (focus distance x f ratio)
        • THUS, at the same subject and background distance, a 100mm lens should have about the same degree of background blurring at f/2.8 as a 50mm lens would have at f/1.4 but of course, the subject will be twice as large as well.
        • IF you adjust your subject magnification to be constant by moving in closer or further from subject depending on lens focal length, but keep distance of subject to background constant and aperture constant, then theoretically, the degree of blurring remains constant irrespective of lens focal length, but the width of the background will get smaller in proportion to the effective focal length (ie. perspective changes).
          • the longer the focal length, the bigger and more expensive it is to make a lens of the same aperture, this is why a 85mm f/1.2 or f/1.4 lens is often the sweet spot in portrait lenses
      • if you wish to make letters on a sign in the background unreadable:
        • the disk of confusion of the sign must be equal to or larger than the letter height
        • NB. it will be readable if disk-of-confusion is less than 1/5th of letter height
        • NB. between 1/5th of letter height and letter height, readability will depend on style of letter, shape of lens diaphragm (bokeh effect), orientation of diaphragm shape to letter, contrast of letter, and characteristics of lens itself.
        • unfortunately we may run into the problem that at the f ratio needed to blur the background letters will result in insufficient depth of field for our primary subject. Changing focal length will not help this, as to keep the same subject size, we need to alter our camera-subject distance and thus while the actual relative size of the letters in the background may change due to the change in perspective, the degree of readability is only dependent on f ratio.
  • DOF is inversely proportional to size of sensor or film if both f/ratio and effective focal length in 35mm terms are constant
    • this is why digital cameras with small sensors make good point and shoot cameras as they have large DOF, but tend to be hard to adequately blur the background.
    • conversely, large format cameras such as 6”x7“ film or larger have very shallow DOF, often requiring special lens tilting to enable adequate DOF to be attained.
    • an 8”x10“ film (7x larger than 35mm) requires f/64 for reasonable DOF for landscapes (ie. 35mm DOF equiv. of f/9)
    • Let's look at a quick DOF comparison assuming portrait at 2m from camera using a 100mm focal length (35mm equiv.):
      • Olympus E330 + Leica 14-50mm lens at f/3.5 = DOF range = 17cm
        • Olympus E330 + 50mm f2 macro or 35-100mm f2 ⇒ DOF range = 10cm
      • Canon 350D + EFS 17-85mm at f/5.6 ⇒ DOF range = 21cm
        • moving back to 2.7m and use 135mm equiv. focal length gives same DOF but you would get more perspective control with its wider zoom range
      • Canon 5D full frame + 70-200mm L series at f/2.8 ⇒ DOF range = 6cm
        • now that is what I am talking about! even at f/8 it beats the Canon 350D with a DOF range of 18cm.
      • 6”x6“ medium format film camera at f/3.5 ⇒ DOF range of 6cm
  • DOF and focal length at same subject distance and f/ratio:
    • DOF is narrower as you increase the focal length of your lens and keep the subject distance and f-stop the same because you are increasing the subject's magnification.
    • total DOF is dependent on image magnification than on focal length for relatively close subjects such as macro & portrait subjects:
      • DOF is proportional to coc x effective f-stop / magnification2
    • THUS for the same f-stop and film/sensor size, if you keep the subject the same magnification (ie. the same size in the viewfinder by adjusting the distance to the subject), the total DOF actually remains approximately constant with changing focal length.
    • thus when choosing a focal length to use for a subject where you can adjust camera position to maintain a constant magnification, the total DOF will be constant but the following will change:
      • the shorter focal length lens will have less front depth of field and more rear depth of field at the same effective f-stop but the same total DOF.
      • the perspective changes as the background becomes more magnified as you increase the focal length.
      • distant background points will be rendered more blurry in proportion to the focal length chosen as their image circles = focal length x magnification / f-stop, this is part of the reason why longer focal length lenses at wide apertures are used for portraits to ensure distracting backgrounds are adequately blurred - in addition the quality of this blurring becomes important “bokeh” and this is dependent on the lens design, in particular, the construction of the iris, hence the new Olympus lenses have circular irises to give better bokeh.
      • for action photos with a moving subject coming towards you, a longer focal length at the same image magnification actually makes focusing easier as the lens will not need to move through as much of its focus range and thus auto-focus should be quicker.
  • DOF equation:
    • The near and far distance values of depth of field can be calculated as d = s/[1 ± ac(s-f)/f²] with plus in the denominator used for the near, and minus — for the far value. The notation is:
      • s — the subject distance (measured from the lens entrance pupil)
      • f — lens focal length
      • a — aperture (or F-stop), like e.g., 2.8
      • c — the diameter of the acceptable circle of confusion.
    • Negative results for the far limit (i.e., with a '-' in the denominator) mean that it reaches the infinity. The value of c is often set to the 1/1440 of the diagonal of the film frame or light sensor: 0.03 mm for 35 mm cameras, 0.0061 mm for the C-3000/3030Z, and 0.0077 mm for the E-10.
    • for a really in depth look at DOF equations see
      • total DOF = 2 x f-stop x coc x (1 + image magnification/pupil magnification) / [image magnification2 - (coc2 x f-stop2/focal length2)]
      • and if coc x f-stop / focal length is much smaller than image magnification as occurs when subject distance is much smaller than the hyperfocal distance, then the denominator can be simplified to just the square of image magnification.
  • hyperfocal distance equation:
    • Have a look at the formula above again. The far DOF limit (with a '-' sign used) becomes infinity for a single value of the subject distance, s, which is sh = (f²/ac) + f (many sources skip the final f, as it is usually much smaller than f²/ac). This is the so-called hyperfocal distance, and, as you can see, for any given focal length f it depends on the used aperture, a. Also note, that when we use s=sh in the previous formula to compute the near DOF limit, the result will be sh/2.

The N-times-F rule for digital cameras:

  • as an approximation, the DOF of a digital camera with 35mm film focal length multiplier of N will be the same as that for the equivalent lens on a 35mm camera stopped down to an aperture of N times the f/ratio of the digital camera.
  • thus the Olympus C8080 sensor has a 35mm focal length multiplier of 3.6 (a 7.1mm focal length lens is equivalent to a 28mm lens on a 35mm camera), and thus at 7.1mm lens at f/4 it has the same depth of field as a 28mm lens at f/14.
  • ie:
    • a camera with a CCD 1/N the size of a 35mm frame has the same depth of field at Fx as the 35mm camera a F N*x, where x is the F-number.
    • to make an example, the 5050 has a CCD with a crop factor of approx. 5. At F1.8 the 5050 will have the same DOF as a full-frame camera at F9 (= 1.8 * 5). The D70 with its 1.5 crop factor will have the same DOF at F6 as a full frame camera at F9. Of course all this at the same 35mm equivalent focal length.

A comparison of calculated depth of fields:

  • DOF range at largest lens aperture when focused at 3m (courtesy of Jens Birch):
  • Camera / EFL 28mm 35mm 50mm 80mm max. telephoto Nikon D70 with Nikon 18-70/F3.5 - 4.5 f/3.5 6.4m f/3.6 3.8m f/4.0 1.6m f/4.0 0.6 m 112mm f/4.5 0.32m Nikon D70 with Sigma 18-50/F3.5 - 5.6 f/3.5 6.4 m f/3.8 4.0 m f/4.5 1.8 m f/5.6 0.8 m 80mm f/5.6 0.8 m Olympus C5050 n/a f/1.8 6.8m f/2.0 2.5m f/2.2 1.0m 105mm f/2.8 0.7m Olympus C5060 f/2.8 infinite f/2.9 infinite f/3.2 5.1m f/3.6 1.6m 114mm f/4.6 0.9m Olympus C8080 f/2.4 infinite f/2.5 10m f/2.8 3.1m f/3.2 1.2m 140mm f/3.5 0.9m Olympus E-1 with Digital Zuiko 14-54/F2.8 - 3.5 f/2.8 6.7m f/2.9 3.1m f/3.2 1.4m f/3.4 0.6m 108mm f/3.5 0.3m Olympus E-300 with Digital Zuiko 14-45/F3.5 - 5.6 f/3.5 12.9m f/3.6 4.5m f/4.0 1.9m f/4.5 0.76m 90mm f/5.6 0.75m
  • if you need large DOF and you have low light levels (eg. indoors or macro) then consider the Olympus C5050:
    • if you can shoot f/1.8 at ISO64 on the Olympus C5050, to get the same DOF at the same effective focal length on a Nikon D70, you would need to shoot at f/6 at ISO 880 which would be more noisey.
    • but if you need to shoot action photos, don't bother with the C5050.
  • if you need small DOF at telephoto (eg. portraits) at low light levels then consider the Olympus E series with the 14-54 lens:
    • at 108mm, DOF of the E-1 at f/3.5 is comparable to the D70 at f/4.5 but you can use lower ISO with the E1 as it is f/3.5.

Depth of field in view camera scenarios:

  • N = D/(2c)

    Where 'N' is the admissable aperture, 'D' is the focus spread between focus at the furthest point to be recorded sharply and focus at the nearest point to be recorded sharply and 'c' is the circle of confusion for the print size and viewing distance that you require.
  • circle of confusion for an 11×14 print at minimum viewing distance:
    • 4×5 film = 0.066
    • 5×7 film = 0.1
    • 8×10 film = 0.133
    • NB. coc used for calculating DOF marks on lenses for 35mm is for 5”x7“ print while medium format it is 8”x10“ print.
  • Finely check the focus at the furthest element in the scene which you want to render as sharp. Mark this point on the focus track. Now, focus on the nearest point in the scene which you want to render as sharp. Mark it also and subtract determine how many millimetres separate the two points (let's say the focus spread is 4 mm) Focus the camera at a point half way between those two points - that is 2 mm away from other end point.
    • 'D' in the equation becomes 4 and for a 4×5 the C. of C is 0.066.
    • The admissable aperture becomes 4/(2 x 0.066) which is 30.3 and so a working aperture of f32 will render the range in the scene acceptable sharp in an 11 x 14 print.

Image resolution:

  • image resolution is dependent upon:
    • film or sensor resolution
    • optical resolution - aperture size vs optical aberrations of the lens vs wavelength of light
      • resolving power of a telescope:
        • Dawe's limit of telescope resolving power in arc seconds = 116 / telescope lens diameter in mm
          • actually, in arc seconds = 2270000 x wavelength of light / telescope lens diameter in mm
    • optical diffraction effects at small apertures
    • focus accuracy
    • lens flare
    • atmospheric aberrations of light (”seeing“)
  • in general, the following is what limits image resolution assuming same contrast/detail subject, good photographic technique, minimal flare, high quality lens, etc:
    • large format film: ability to keep the film flat to ensure accurate focus
    • medium format film: lens optical resolution
    • 35mm film or digital sensor: film or image resolution
    • consumer size digital sensor: sensor resolution, or at small f-stops, diffraction limits (hence cannot usually use smaller than f/8)

Image magnification:

  • a bit of physics - let So = front principal point to subject distance, Si = rear principal point to image (eg. film) distance and f = focal length
  • 1/f = 1/So + 1/Si and as magnification (M) = Si/So, then M = f/(So-f) = (Si-f)/f
photo/dof_details.txt · Last modified: 2017/05/25 23:03 by gary1

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