Spectral Imaging: Methods, Design, and Applications - Biomedical Optical Imaging Technologies: Design and Applications - page 143

Fig. 4.19 A typical image acquired with a CTIS system. The center shows the zero order of
the diffraction, which is the original image. The color is only shown for emphasizing how the
dispersion looks on the camera, but it is usually a gray-level detector. The higher orders ˙2

around it show a dispersed image. By analyzing this information, which is clearly well organized,
the spectral image can be extracted (Image courtesy of Greg Bearman, Snapshot Spectra, USA)

˙1 and

using a fiber connected to a monochromator and illuminating different wavelengths
from different points in the image, while measuring the diffraction pattern for each
illumination, I.x; y; /. Because the holographic dispersion element provides a
linear response, a relatively small number of points can be measured. Having the
series of these patterns provides the system transfer function [ 49 ].
The performance of a CTIS depends on the spectral distribution along the image.
The most extreme cases would be a single point with a certain spectrum or a uniform
image with the same spectrum. A single point can be analyzed with a CTIS with a
relatively high spectral resolution while it gets worse with a uniform field.
Other methods that are based on a spectral-spatial projection of the spectral
image onto an array detector were also developed and demonstrated based on
compressed sensing [ 50 ]. In these methods, a more complex set of two dispersive
elements are used together with a coding aperture. A similar method based on
regular array detector and a prism was also demonstrated lately [ 51 ]. The principle
is conceptually similar. Let us assume that a certain optical system with some
kind of dispersion element causes the spectral information to be convolved on the
image plane in a systematic manner. If we also assume that the spectral convolution
function can be calculated or measured, then it means that the spectral image can
be deconvolved by using the appropriate algorithm. The quality of the deconvolved
spectral image depends on many parameters of the system, as well as the type of
spectral image, and it is a subject that must be treated for each system separately.