aliasz said:
I observed a photograph taken with my telephone, and it has depth of field. foreground blurring
of an metal grid mesh. yet some objects in the background are visible troughout the total blur of the mesh. marked with green circles.
the depth of field or focal blur, almost makes the metal mesh somewhat trancelucent.
how can this phenomena be explained?
Unfortunately, this concept (depth of field) is not so simple to quantify because it fundamentally is a quality of the *perceived* image, not a property of the optical system. One particular metric that *is* worth knowing is the 'hyperfocal distance'.
First, some 'official' definitions:
Defocus: in ray optics, when the image plane is not located where the sensor is, the detected image is 'defocused'. In ray optics, this is not considered an aberration because the designer simply either moves the sensor to the image plane or moves the entire lens assembly to place the image plane onto the sensor plane. (Field curvature, on the other hand, is a lens abberation). Strictly speaking, an object is in focus at the image plane and out-of-focus everywhere else.
Depth of focus: the tolerance of sensor placement such that the image is judged to be 'in focus' (who judges this? read on...). Depth of focus generally has meaning when applied to manufacturing tolerances, as opposed to design criteria.
Depth of field: the range of object distances that are judged to simultaneously be imaged 'in focus'. This also is not really a design criterion, because the depth of focus is a conglomeration of many parameters: focal length, numerical aperture, and distance to 'best focus'. The hyperfocal distance 'H' is the focus distance, set at the lens, that results in everything from a distance H/2 to infinity being judged 'in focus'- landscape photographers really need to pay attention to the hyperfocal distance.
A ray optics diagram of depth of focus can be found here:
http://www.cambridgeincolour.com/tutorials/depth-of-field.htm
Note the phrase 'circle of confusion'. This is the largest blob on the final displayed/printed image that is
visually indistinguishable from an actual point. That is, since points are not imaged as points but rather as smeared blobs ('blur circle' is fine, call it an 'Airy disc', if you must), finite-sized blobs below a certain size threshold will be perceived as identical Airy discs.
What is this size threshold? This question was studied by the major lens and film companies in the 1950s and 1960s (Zeiss, Polaroid, etc) and the consensus decision was that when 35mm film is printed at 8x10 and held at a comfortable distance, a 30 micron diameter disc is the cutoff size for a circle of confusion (CoC). Then, to translate that back to the exposed film, it was a simple consideration about enlargement: how much was the 35mm film image enlarged to produce that 8x10 print? The enlargement factor is one reason why the CoC (and depth of focus) varies for differently-sized sensors.
Practically speaking, there are online calculators that will determine the depth of field (based on the above diagram) for you. Most interchangeable lenses have markings to indicate depth-of-focus range as well.
Now, the second part: why can you 'see through' the blurry bits? It's simply due to image contrast- there is a reduction in image contrast due to the blurred wire, but the high-contrast features located in the distance are still able to produce enough contrast, even after being attenuated.
Defocus is not easier to describe in terms of wave optics, unfortunately. In some simple cases it can be analyzed and one result is the existence of 'contrast reversal' (see Goodman's book on Fourier Optics), but again, it's a subjective measure of image quality.
Bokeh is another attempt to describe depth of focus, it's sort of the derivative of 'defocus'; as it describes how the blur circle changes as defocus changes.
