physical description |
colorSpec type |
infinite
dimensional |
vector |
finite dimensional description |
---|---|---|---|---|
a
light source, |
light |
the space of absolutely integrable functions on an interval of wavelengths, e.g. [380,780] nm. For simplicity, we denote this space L1[380,780] by L (for light). |
L |
row vectors |
a
light responder, |
responsivity.light |
the space of continuous functionals on L, which is the dual space L*. This dual of L1[380,780] is isomorphic to L∞[380,780] = the essentially bounded functions on [380,780]. All such functionals are given by an inner product with a function in L∞[380,780] |
L* |
column vectors |
a
diffuse reflector, |
material |
the space of multiplication operators on L , which is denoted by M (for material or multiplier) and is isomorphic to L∞[380,780]. |
M |
diagonal matrices |
a material responder |
responsivity.material |
the space of continuous functionals on M , which is the dual space M*. It is not isomorphic to L1[380,780]; M* is bigger. |
M* |
diagonal matrices |
Table C.1 The 4 types of spectra and their corresponding vector spaces