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Depth of Field

 

Selective focus (depth of field control) is just one of many creative techniques used in practical photography. To a standard observer, the depth of field is that zone of a photograph (from foreground to background) in acceptably sharp focus. However, the boundary from sharp to unsharp focus is not a discontinuity but a uniform gradation.
To select the optimal camera settings for a particular photo - opportunity, some appreciation of the concept of depth of field is necessary. Though most cameras feature a depth of field preview, because the viewfinder darkens as the lens is closed, to gauge the sharpness of an image is easier said than done. Furthermore, most modern lenses have no depth of field scale. On a digital camera the LCD screen allows images to be reviewed, (select an area of the image and zoom - in), even so, to estimate the depth of field is not straightforward.


Hyperfocal distance (HD) is a photographic measure that is closely related to depth of field (DOF). Focus at infinity and the nearest distance in acceptably sharp focus is
the hyperfocal distance. To maximise the available depth of field: refocus at the hyperfocal distance and the zone of acceptably sharp focus extends from half the hyperfocal distance to infinity.
                                            


Hyperfocal focusing is an effective technique that is relevant to many photographic disciplines (particularly landscape photography). However, to apply the principles to real scenes (without consideration) may not guarantee the desired visual effect,
you may prefer to trade the
sharpness in featureless regions for more sharpness elsewhere. Hyperfocal distances may vary from a few metres for a wide angle lens (typical is the 17 - 35 mm zoom) to many metres for a telephoto lens (typical is the 70 - 300 mm zoom). In practice you can estimate the hyperfocal distance, precise focusing is unnecessary, focus further than the hyperfocal distance and close the lens (one stop). Most scene features are rendered in acceptably sharp focus, but how is acceptably sharp defined.

A camera lens can focus in only one plane. For a three dimensional scene (a typical scene has spatial depth), objects in front and behind the point of focus are imaged
at the focal plane as a blur circle. The blur circle is the surface generated by a converging (object in front of the point of optimum focus) or diverging (object
behind the point of optimum focus) cone of light that intersects the focal plane
(see Depth of Field Calculation). The so - called circle of confusion is the maximum circle of light (blur circle) that is unresolved (perceived as a point) by the unaided eye, the resolving power of the human eye is limited. The criterion for 'acceptably sharp' is based on the visual examination of a photograph, traditionally this is an
8 x 10 inch print, viewed at a distance of about 10 inches (distance of most distinct vision). That the human eye can just resolve spatial detail of 0.01 inches at this distance is rooted in the photographic (film) technology of former times. In fact,
the normal eye can resolve about one minute of arc, 20/20 vision, that corresponds to spatial detail of 0.003 inches, nonetheless, the accepted standard used by optics manufacturers is 0.01 inches (0.25 mm).
Spatial detail of 0.25 mm in the print corresponds to spatial detail of 0.03 mm
in the image (0.25/8), since a magnification of about 8x (aspect ratios may differ)
is necessary to produce an 8 x 10 inch photo enlargement from a 35 mm format image. Hence, the diameter of the circle of confusion is 0.03 mm.
For the advanced photographic system (APS) format, the diameter of the circle of confusion is less than 0.03 mm, since a higher magnification is necessary to produce an 8 x 10 inch photo enlargement, for the medium and large formats, the diameter
of the circle of confusion is more than 0.03 mm, since a lower magnification is necessary to produce an 8 x 10 inch photo enlargement.
                                     
Since the resolving power of the normal eye varies with luminance and retinal location (under ideal conditions the human eye can resolve about thirty seconds of arc, 20/10 vision), at the depth of field limits the focus is not exceptionally sharp. However, some blurring of the image is not necessarily ruinous and may even be desirable for aesthetic effects. Even t
hough 0.03 mm (or thereabouts) is the accepted standard that is used by optics manufacturers for depth of field tables and lens markings, depth of field is a subjective property (related to the physiology and psychology of visual perception), the circle of confusion is an arbitrary limit that may be changed to suit the desired sharpness (within the limitations of diffraction effects) or particular style of photography.   

To recap, depth of field is not a fundamental (lens - film/image sensor) parameter that is measurable. The circle of confusion, our criterion for acceptably sharp focus determines the near and far focus limits and the extent of the depth of field.
The circle of confusion is related to the viewing geometry (the print size and the viewing distance) and the resolving power (the reciprocal of the visual acuity) of the human eye. Change the viewing geometry, the circle of confusion changes and the depth of field changes.


For a given sharpness criterion that is characterised by the diameter of the
circle of confusion
, Depth of Field is dependent on

                                               f - number of the lens (relative aperture)
                                               focal length of the lens

                                               
focus distance (camera to subject distance)

The highlighted quantities are lens parameters, closing or opening the lens aperture 
(f - number increasing or decreasing) changes the hyperfocal distance and the depth of field.
The effect of aperture (f/#) on the depth of field (the focal length and focus distance are constant) is illustrated (the focus point is the nearest golf ball).
 
 

             F/5.6                   F/16                   F/32
             
                                     
      
                                

         

            

Since the hyperfocal distance and depth of field are influenced by the same lens parameters, depth of field may be recast in terms of the hyperfocal distance and focus distance.

Show the way, build a
Hyperfocal Distance/Depth of Field Calculator
for your general photography.
The simple Hyperfocal Distance/Depth of Field Calculator operates thus, determine the hyperfocal distance from the focal length and f - number of the lens, then determine the depth of field from the hyperfocal distance and focus distance. 
 
The Hyperfocal Distance (H) and Depth of Field (DOF) are given by                   

where f, f/# are the focal length and f - number of the lens, c is the diameter of the circle of confusion (0.03 mm for the 35 mm format) and u is the focus distance.
To understand the detailed derivation of hyperfocal distance and depth of field is
unnecessary (some algebraic manipulation is used), for the mathematically minded,
(see Depth of Field Calculation).

Procedures based on this simplified formulation are ideal for programmable handheld devices, use separate memory areas to store the hyperfocal distance and depth of field procedures.
Please read your calculator/palmtop manual to code the procedures. Units must be consistent throughout (feet or metres or ...), enter the focal length of the lens in millimetres.
 
In the field, to calculate the
Hyperfocal Distance and Depth of Field takes less than one minute. So that unforeseen photo - opportunities are not missed, you may prefer to create a Depth of Field/Hyperfocal Distance chart for the most useful camera settings.

For Digital Cameras that use image sensors of different size and type (aspect ratios may differ), calculate the diagonal
(width2 + height2 = diagonal2) of the image sensor active area (the effective pixels that contribute to each image). Consult your digital camera handbook for the active area of the image sensor.
The Focal Length Multiplier (FLM) or crop factor is the ratio of the 35 mm format 
diagonal to the image format (film gate/image sensor) diagonal.
                       


The focal length multiplier for most digital compacts is typically between 2x and 8x and for most DSLRs is typically between 1.3x and 2x, (see Digital Cameras).
Because there are many digital camera types (compact and SLR), image formats differ, hence for the same field of view the focal length must change proportionally. In order to avoid confusion, most manufacturers of digital cameras quote the
35 mm equivalent focal length
, the combination of 35 mm (film) format and
focal length that gives the same field of view.

A lens of focal length f mounted on a digital body (focal length multiplier, FLM) gives the same field of view as a lens of focal length (f x FLM) mounted on a 35 mm body, where (f x FLM) is the 35 mm equivalent focal length.


For digital cameras, the diameter of the circle of confusion is (0.03/FLM).
You can obtain FLM from the image format diagonal or from the ratio of the
35 mm equivalent focal length to the real focal length.

Use the calculator for general photography (not close - up photography) to determine Hyperfocal Distance and Depth of Field, note the approximation used (H >> u >> f). Enter the REAL FOCAL LENGTH of the lens and for the diameter of the circle of confusion, enter (0.03/FLM). For 35 mm film
(full frame digital), FLM = 1. You can compare the depths of field of film cameras, digital cameras, any camera, however, image quality may not be the same (see
Digital Cameras).


Notice the depth of field is directly proportional to the focal length multiplier.
The smaller the image format, the larger the focal length multiplier and the greater
the depth of field. My Nikon D80 has 1.5x more depth of field than a 35 mm format camera (for the same field of view). For digital cameras that use even smaller image sensors (1/3", 2/3", ...) and short focal length lenses, the hyperfocal distance is
very small and the depth of field is very large. Users of digital compacts may
find that selective focusing to isolate subject matter from the background can be
especially challenging.

Provided that focus distance and focal length are changed proportionally (to maintain the magnification), the total depth of field (for a given format) is effectively constant. Though the total depth of field is effectively constant, the front and rear depths of field are not evenly divided. For long focal length lenses, the front and rear depths of field are similar, for short focal length lenses, there is less front depth of field and more rear depth of field. Zooming (in or out) from a set location changes the focal length (the magnification) and the depth of field (see Depth of Field Calculation).


Diffraction and Depth of Field

DIFFRACTION places a fundamental limit on image quality, the lens aperture cannot be progressively closed to extend the depth of field (zone of acceptably sharp focus).

A perfect imaging system maps object points to corresponding image points, consistent with the rectilinear propagation of light and the laws of geometrical optics. In the real world a point in object space is mapped to a blur circle (a diffuse patch of light) in image space due to DIFFRACTION a fundamental property of the wave nature of light. Fraunhofer (far - field) diffraction phenomena relate to collimated (parallel) light, where the effects are observed in the image plane. The image is just the superposition of the blur circles that correspond to all object points. Diffraction describes the spreading of waves (into a region of geometrical shadow) as they pass through a finite aperture or the edge of an obstacle. This is illustrated for light of wavelength λ.      

Diffraction phenomena are not restricted to light, all waves diffract, matter (electron, neutron, ...), radio, sound, water, .... . Familiar examples of light diffraction are the haloes that encircle street lights and the stripes of colour on the surface of a CD. According to the Huygens - Fresnel principle, points on a wavefront are a source of diverging secondary waves (wavelets) that can interfere constructively or destructively, dependent on their phase relationship. Since the lateral extent of the wavefront is bounded, no optical system (camera) can be diffraction free.
Though aberrations, (spherical aberration, coma, astigmatism, field curvature, distortion and chromatic aberration), diffraction and defocus all contribute to the image blur, diffraction sets the upper limit on spatial resolution. For an ideal lens
at best focus, the diffraction pattern of a point source has the form of a circular core of light, the Airy disc (after G Airy, 1801 - 1892) surrounded by fainter concentric
rings of light that gradually fade. For a non ideal lens that has residual aberrations,
light is redistributed to the rings (decreasing the contrast) and can form irregular
shaped patterns (aberrated Airy pattern).

                                             

The onset of noticeable diffraction blur can be estimated from the diameter of the Airy disc, the bright circular core of the diffraction pattern that contains about 84% of the light energy. For a uniform intensity distribution, the diameter of the Airy disc in the focal plane (Φ) is given by
                                           

Φ = 2.44 λ f/#


where, λ is the wavelength of the light and f/# is the f - number of the lens,
the ratio of the focal length to the entrance pupil diameter (lens aperture).
Notice that
Φ is wavelength dependent, different for each of the primary colours,
Φ
R > ΦG > ΦB. Longer wavelengths red light are diffracted more than shorter wavelengths blue light, and hence the diffraction blur (measured by the Full - Width at Half - Maximum (FWHM) of the Airy disc) decreases from red to blue.

Call to mind the circle of confusion, our criterion for acceptably sharp focus or tolerable blur. It is instructive to compare the diameters of the Airy disc and 
circle of confusion. For light at the centre wavelength (λ = 0.555 μm) of the visible spectrum, there is increasing image degradation due to diffraction at f - numbers (f/#)
≥ (circle of confusion (mm)/0.0014). The corresponding f - numbers for
red light and blue light are lower and higher.
For any image format, the diameter of the circle of confusion is
0.03/FLM (mm), where FLM is the focal length multiplier. Of course, the pixel size must not limit the resolution, provided that several pixels are used to sample the circle of confusion,
the conclusions should be plausible. 
 

  • For the (full frame) 35 mm format, the simple analysis demonstrates that blurring due to diffraction becomes the dominant factor at about f/22. Beyond f/22 the diameter of the Airy disc exceeds the diameter of the circle of confusion and the camera performance is degraded more by diffraction.
     
  • For the (sub full frame) digital formats, the simple analysis demonstrates that blurring due to diffraction becomes the dominant factor at about f/# (see table, FLM and f/# are rounded). Beyond f/# the diameter of the Airy disc exceeds
    the diameter of the circle of confusion and
    the camera performance is degraded more by diffraction. For (sub full frame) digital compacts a limiting aperture
    of f/8 is typical.  
     
                                       
   Format    FLM      f/#    
       1/3"       7.2        3.0       
       1/2.5"       6.0        3.6
       1/2"       5.4        4.0
       1/1.7"       4.6        4.7
       2/3"       3.9        5.4       
       1"       2.7        7.9      
       4/3"       2.0      10.7      
Cn APS - C       1.6      13.2     
Nikon DX       1.5      14.1
Cn APS - H       1.3      17.1      


The effect of diffraction on image quality is gradual, there is no step change of sharpness as the lens aperture is closed, even so, there may be 'smoothing' of the image. A lens functions as a low - pass filter (the cutoff frequency is inversely proportional to the f - number) of the scene detail, passing lower frequencies (coarse detail) and attenuating higher frequencies (fine detail). Needless to say, there are trade - offs, lower f - numbers to reduce diffraction, higher f - numbers to reduce aberrations. The lens may be aberration limited or diffraction limited. Close the lens, typically 2 - 4 stops to balance the aberration and diffraction blur, thus maximising the performance. Close the lens further and the performance is degraded more by diffraction. The depth of field (zone of acceptably sharp focus) does not continue to increase as the lens aperture is progressively closed, from the near to far focus, the image quality deteriorates. Though diffraction blur permeates the recorded scene,
the loss of sharpness (low contrast fine detail may no longer be distinguished) is most noticeable at the plane of focus.
A simple pinhole camera has a vast depth of field, however, the image is blurred, everywhere. As you reduce the hole diameter, the geometric blur decreases but the diffraction blur increases. There are many formulae for the optimal pinhole diameter, the classical formula is 1.9 f λ, where f is the focal length and λ is the centre wavelength of the visible spectrum.
For any image forming system, the resolution limit (the ability to distinguish
small angular separations) increases with decreasing aperture and with increasing wavelength. To minimise diffraction effects (reduce the diameter of the Airy disc),
so that fine detail is resolvable, telescopes use large apertures, microscopes use
short wavelength UV light.
Given that image formation is the end result of diffraction and interference, these processes must decide the achievable resolution. According to the Rayleigh criterion, two points of light A and B (for example, distant car headlights or a double star) are just resolved when the central maximum of the diffraction pattern of A falls on the first minimum of the diffraction pattern of B (linear separation ≥ 1.22 λ f/#). At the Rayleigh limit, the mid - point intensity is about 0.81 of the maximum intensity and the corresponding MTF is about 0.09 (see Modulation Transfer Function).
Be aware, this is an optical resolution limit, the diffraction resolution limit is quite apart from the film/image sensor resolution limit, set by the dye - silver grain/pixel size. The Rayleigh limit (close to the empirical Dawes' limit) is intended for visual instruments (micro, spectro, ..., scopes), nonetheless, the criterion is applicable (with some adaptation) to modern cameras. In practice, the spatial resolution of the lens, characterised by the diameter of the Airy disc must match the spatial resolution of the image sensor, characterised by the pixel pitch. This is a simplification, numerous factors contribute. For monochrome cameras, the necessary condition to avoid undersampling (aliasing) is
(2 x pixel pitch = diameter of the Airy disc).
For colour cameras that use a standard Bayer colour filter (the sampling rate is that
of the RGBG 2 x 2 array), the necessary condition to avoid undersampling (aliasing) is
(4 x pixel pitch = diameter of the Airy disc).
Bear in mind, increasing the MegaPixel count (smaller pixels for a fixed image sensor size) is not synonymous with enhanced resolution and image quality, the resolution may be imposed by the optics, and for smaller pixels, photon noise and the effects of decreasing signal to noise ratio may become performance issues.

Diffraction is a fundamental property of wave propagation that limits the resolution of an optical system. I have said that aberrations, diffraction and defocus all contribute to the image blur and that diffraction sets the upper limit on spatial resolution
(for an aberration - free optical system at best focus, the image of a point source is the Airy pattern)
. However, for practical photography, residual aberrations (modern lenses are not aberration - free), camera and subject movement, focus error and the atmospheric conditions (haze and turbulence reduce the image contrast) are often
more significant than quality limitations resulting from diffraction phenomena.

 

All images and text imajtrek