In a day picture, particularly one with diffuse lighting (dull sky), the use of light propagation laws (absorption and diffusion) sometimes allows, from mensuration or estimation of apparent luminance based on pixel levels, estimation of a possible distance range between an object observed on the picture and the camera. Some main equations on which this approach is based will be presented later.
Atmospheric diffusion effects on sharpness
Depending on weather conditions, atmospheric diffusion effects on apparent sharpness of contours may be brought out and compared between various reference objects and the analyzed object, which leads to derive a range of possible distances between that object and the camera.
On a picture taken by night, if an object appears lit by the flash, its distance from the camera cannot be larger than the flash range.
Luminance of an object
Luminance associated with a photographed object is homogeneous with an emitted power per surface unit and per solid angle unit, in the direction of the lens. It is measured in lm/sr/m2 (lumens per steradian per square meter), while correspondence between lumens and watts depends, for each wavelength, on the luminous efficiency of the radiation.
This observed luminance may be due to the object’s own luminous emission, to transmission (transparent or translucent object) or to reflection of light coming from somewhere else, in particular from the sun.
In the case of a non-luminous object, one may assess its albedo: this is the fraction of received luminous flux reflected by the object, the value of which extends from 0, for a theoretical black body, to 1, for a white body. Evaluation of albedo will sometimes, through comparisons, provide indications on the material which makes up or covers the object under study.
The luminous flux F (expressed in lumens) – emitted, transmitted or reflected by the object – is simultaneously modified in two ways by the surrounding atmosphere:
- Atmospheric propagation, between object and camera, leads to attenuation due to atmospheric absorption by air molecules, along a Bouguer line:
F = F0 10-αx
where α is the extinction coefficient and x the thickness of the crossed atmospheric layer.
α value depends on weather conditions and on the wavelength, whereas αx represents the optical density of the considered atmospheric layer.
For light sources located beyond the atmosphere (such as astronomical objects and satellites), the atmospheric total thickness is crossed, the value of which only depends on the zenital distance of the source. The source intensity then varies according to that zenital distance, following a « Bouguer line ».
- In the case of day photos, the proper luminance L of an object located in the low atmosphere, at a distance x from the lens, is attenuated by atmospheric absorption as previously indicated, thus adding a contribution of atmospheric diffusion of daylight.
If LH represents sky luminance on the horizon (x -> ∞), apparent luminance L’ of the object is given by the relation:
L’ = 10-αx L + (1 - 10-αx) LH
...where the first term represents the extinction of light coming from the object, and the second one the contribution of atmospheric diffusion.
If it is a black object (or very dark), the formula simplifies as follows:
L’ = (1-10-αx) LH
In the particular case of an object of albedo R, under a uniformly dull sky, we have:
[align=center]L’ = [1 – (1 – R/2) 10-αx ] LH[/align]
Directly measurable data that quantify light received by a given pixel in the digital image are its gray level (along the black to white axis) and its respective luminance levels in the 3 primary colors axes (red, green, blue). Those values characterize the apparent luminance of corresponding points of the scene. In silver photography, as well as in digital in the case of the RAW format, one may sometimes establish a correspondence formula – more or less empirical – between luminance and gray level, through luminance calculations. Unfortunately this becomes practically impossible with JPEG format, because of all the optimization real-time processing performed inside the camera before storing the image (RGB demastering, delinearization with application of gamma factor, compression, accentuation, etc.).
For lack of means to estimate absolute luminance values, only relative calculations are possible, taking advantage reading across to monotonic level variation according to apparent luminance.
Nevertheless, these empirical interpolations or extrapolations are invaluable in many cases, for they allow definition of a range of possible distances of an object, by comparison with other elements of the scene that are located at known distances.