#### [tutorial] multispectral imaging, a case study

Without signal processing courses, the following equation should be awfully familiar to astronomers of photometry and handling data:

$$c_k=\int_\Lambda l(\lambda) r(\lambda) f_k(\lambda) \alpha(\lambda) d\lambda +n_k$$

Terms are in order, camera response (c_k), light source (l), spectral radiance by l (r), filter (f), sensitivity (α), and noise (n_k), where Λ indicates the range of the spectrum in which the camera is sensitive.

Or simplified to $$c_k=\int_\Lambda \phi_k (\lambda) r(\lambda) d\lambda +n_k$$

where φ denotes the combined illuminant and the spectral sensitivity of the k-th channel, which goes by augmented spectral sensitivity. Well, we can skip spectral radiance r, though. Unfortunately, the sensitivity α has multiple layers, not a simple closed function of λ in astronomical photometry.

Or $$c_k=\Theta r +n$$

Inverting Θ and finding a reconstruction operator such that r=inv(Θ)c_k leads spectral reconstruction although Θ is, in general, not a square matrix. Otherwise, approach from indirect reconstruction. Continue reading ‘[tutorial] multispectral imaging, a case study’ »