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interval (in which case, the system sensitivity S varies for each sensor), or the light
sources employed show a very narrow emission spectrum. In both cases, the value
a obtained from an acquisition can be interpreted as the value of function
E(λ)R(λ)S(λ) at a specific wavelength, so that, by changing sensors or light
sources, different values of this function can be estimated on the whole visible
light spectrum. For a given wavelength λi, Equation 1 then becomes
(2) ai = E(λi)R(λi)S(λi) ,
and if the properties of the illuminant and sensor(s) are known or can be measured,
then the values E(λi) and S(λi) are known and R(λi) can be computed. As an
alternative, the output values ai can be compared with the corresponding values
previously obtained from the acquisition of a reference physical sample whose
reflectance is known. If the result of this previous acquisition is indicated with ai´,
then it is
(3)
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ai
E
=
a′
E
i
( λi
) R(
λi
) S(
λi
)
( λ ) R′
( λ ) S(
λ )
i
i
i
R
=
R
( λi
)
′ ( λ )
i
,
where R´ is the (known) reflectance of the reference sample. The value of R(λi)
can then be computed using the following equation:
i
(4) R( λ ) R′
( λ )
i
a
= i .
a′
i
If necessary, the model can be further complicated to cope with such phenomena
as internal light scattering and re-emission. Also, appropriate steps can be taken to
account for any fluorescence, if needed.
Multispectral acquisition systems that use this approach can be extremely precise;
however, they also often suffer from drawbacks including expensiveness, need of
specialized personnel for the operation, bulky and unwieldy machinery, and
misalignment problems.
3. ‘Wide-band’ multispectral imaging
The second approach to multispectral acquisition is based on wide-band sensors. In
this case, each sensor is sensitive to light energy in a sufficiently large wavelength
interval, and the emission of the light source considered has a sufficiently broad
spectrum, so that the values ai obtained from the acquisition cannot be associated
to specific wavelengths. The relationship between these values and the actual
reflectance values must then be somehow established to estimate the reflectance