SHARPNESS  in all details

The sharpness comes from many factors which are:
  • the shape of the objects
  • the contrast
  • the color
  • the gradation of outlines
  • the nature of backing
  • the characteristics of human vision
The purpose of this paper is to better understand this phenomenon, its various applications in photography and infography through the three fundamentals concepts :
¤  visual acuity
¤  circle of confusion
¤  resolution and resolving power
It shows some common applications.









The visual acuity is the smallest discrimination between an object and its background.
There are different types of acuity:
  • The detection acuity  which is the smallest discernable dimension, for example a star in the sky. Very small, it is less than half a second of arc.  Á    Á
  • The resolution acuity  which is the minimum space to see apart two dots, or two lines. It is about one minute of arc for two dots, and half a minute for two lines. Á ÁÁ  Á ÁÁ
  • The recognition acuity which is the average size of different shapes that are discriminated, as a square, a disk, a triangle or a letter. It is about 4 minutes of arc. ª  £ ¢ Á  ª  £ ¢ Á
  • The localization acuity  defined as the smallest offset of abutting lines. It is about 10 seconds of arc. {__---{
> The visual acuity is an angle which international unit is the radian.
>  The standard visual acuity  is equal to 0.0003 radians, or 1 minute of arc.
>  The binocular acuity , as used in stereoscopy is better up to 25% than the monocular acuity.
>  A vision de 10/10 (scale used in France) is the angular vision of optotypes (lettres, shapes) of 0,001 radians, or 4 minutes.
>  Vision changes with age; weak 0,1/10 for infant, (which can only see figures) it reaches 10/10 after 5 years old, peaks to 15 to 20/10 at 20 years old, is maintained at 10/10 between 50 and 70 years, and decreases to 5/10 over 80 years old.
> The eye has a focal length of 16mm.


Common values of acuity:
  The visual standard acuity is 0,0003 rd (radian).
The value 0,0003 suits well to the neat and well contrasted optotypes in ophtalmology.
In photography, this value is sometimes applied, often 0,00035 and 0,0004 and seldom 0,0005.
Radian, rd:
The radian is a mathematical angle unit which is such that the full angle of a 360° circle is p (pi) radians. The relation is:
1 rd = 180° / 3,14116
The advantage of radian is that for the small angles, there is only to multiply it by a distance to get the size at this distance.


Already, in the first half of the XXth century, the great specialist of photographic techniques, L.P. Clerc deplored that many technical documents didn't indicated the reference value of their calculations.
For my own, I take the a = 0,0004 radians value which seems to me better corresponding to the present applications in infography, photography, and cinematography. It must be considered the contrasts of colors, the retinal persistencefor the electronic screens. Another more pragmatic reason is explained further hereunder.




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The circle of confusion is on an image the offset at which two dots cannot be differentiated by the eye.
The circle of confusion is a physiologic quantity
with a=0,0004 the circle of confusion is equal to 1/1000 of the viewing distance, for example 5mm to 5m.


The value of the circle of confusion, or c.o.c, is calculated from the visual acuity by the formula:
c = 2,5 x a x D
a  = visual acuity
D = distance from eye to object.
Conventional viewing:

The conventional viewing distance is 25cm, or 250mm.



The circle of confusion to the conventional distance of 25cm is equal to 0,25mm with acuity of 0,0004




Some authors are speaking of circle of diffusion instead of circle of confusion. In no way it is a phenomenon of diffusion, and this wording is not correct..





The resolution is the size of the smallest detail that an imager can show.
The resolution is a physical quantity
Note also that it is a linear value.


Measuring resolution is done on a test pattern drawn with lines of equal thickness alternatively white and black, as the keys of a piano.
The resolution is equal to the step of the target lines, which is the width of a pair of lines, a white and a black one.


Opposite, a typical target of a test pattern.
 Modulation transfer function:
The measurements of resolution have been improved to take in account the complexity of phenomenon such as acutance, spacial interferences, and contrast of colors. The measures of the Modulation Transfer Function, or MTF, also based on test patterns of alternating lines are now commonly used.

 Resolving power:

The resolving power is the inverse of the resolution for a unit of length. Therefore, it is the number of pairs of lines in the unit of length.


The resolving power is usually given in number of pairs of lines per mm [pl/mm] or cycles per mm [cy/mm]. It is the same than counting the black lines only.
A resolving power of 80 pl/mm is equivalent to a resolution of 0,0125mm.
Relation resolution <?> circle of confusion:
Most of the time, the photographers get the habit to apply résolution = circle of confusion. But it is not equal.
Have two dots which are the width of a line of the pattern. To discriminate them, it must be offset of half the width according to the circle of confusion definition, whilst with the resolution it could be guessed that it would be sufficient to place them side by side. Moreover, on a film it is possible to offset of half a value, but on digital patterns, it will be necessarily of an entire value.
To make it short, use the resolution as equivalent to the circle of confusion, is like saying that  c = 2,5 ~ 2 on a film, and c=2,5 ~ 3 in digital.
The theoretical error when assimilating the resolution to the circle of confusion is 25% on a film and 50% for digital.
Above, I mentioned that I use the 0,0004 for visual acuity rather than the ophtalmologist value of 0,0003. The difference is 33% which is between the errors percentage. Therefore, the 0,0004 value is between the correct values of film and digital.
The equivalence circle of confusion = resolution is acceptable with a visual acuity a=0,0004
c = 1.25 r
The resolution of a lens is limited by the diffraction of the light. By diffraction, the image of a dot is becoming concentric circles named Airy disc.
The diameter is calculated by the Raleigh formula:
D = 1,22 l n  in which:
l  wave length of light
n   aperture value
The Airy disc and the Raleigh formula explain why when closing the aperture, the optical resolution of the lens is increased, and the images so got are of better clearness.
With a good lens, the resolution is sufficient to achieve photographs of good quality at any aperture. When at great aperture, an enlargement is not enough sharp, the lens is poor quality.


The resolving power of a lens is given in pairs of discernable lines in its focal plan.
For 35mm films, 24x36mm size, the resolving power of a lens more or less:
# over 80 for a good lens of reflex camera and some P&S ones.
# 50 to 80 for many zooms and most of the P&S cameras.
# below 50 for simple cameras and disposable cameras.
In digital photography, there are few datas now. The reason is that the camera must be dismounted, and the sensor separated to do measures on the lens.

the resolution of a film is:

    r = 0.012mm for high resolution films
    r = 0.015mm for films 100 to 400 ISO
    r = 0.018mm for films 800 ISO and more.


Express in resolving power for comparison with lenses, the correspondances are:
0,012mm   => 83 pl/mm
0,015mm   => 67 pl/mm
0,018mm   => 55 pl/mm
Digital cameras:
The resolution of the sensor of a digital camera is easy (normally) to determine because the pixel lines are doing the alternating white and black lines. It needs only to know the number of pixels and the size of the sensor.
For example, the size of pixel of  a sensor 1/1,8" of 4Mpx is 3,125 microns or 0,00031mm.


The resolution is given by the formula:
r = 2U / I in which
i number of pixels
U width of sensor in mm
The resolution of  a sensor 1/1,8" of 4Mpx (2272x1704 pixels) is r = 2 x 7,2 / 2272 = 0,0063mm
It is often named "resolution" datas given in pl/mm but it deals obviously with resolving power.



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