Spectral Imaging: Methods, Design, and Applications - Biomedical Optical Imaging Technologies: Design and Applications - page 140

Fig. 4.17 Fourier transform analysis for Fourier spectroscopy. a A delta-function spectrum.
b Its interferogram. c A spectrum of two Gaussian-like peaks. d Its measured interferogram.
e The analyzed spectrum without apodization ( blue ) and with apodization ( red ). f The apodized
interferogram of the spectrum shown in c
Figure 4.17 shows interferograms of two typical spectra and the effect of the
image processing as described above. Figure 4.17 a shows a delta function of
quasi-monochromatic spectrum and Fig. 4.17 b shows its cosine-like interferogram.
Figure 4.17 c shows a spectrum with two Gaussian-like peaks and Fig. 4.17 dshows
its interferogram. Figure 4.17 f shows the apodized interferogram using a Blackman-
Harris window. Figure 4.17 e shows the resulted calculated spectrum by applying the
inverse Fourier transformation without apodization (blue) and with the Blackman-
Harris-type apodization. The dramatic effect of the apodization is clear.
Another method that is related to time-scanning methods is based on the
Hadamard transform [ 45 ]. This method uses an imaging spectrometer equipped with
a CCD and special optics. A spatial light modulator (SLM) compresses the whole
2D image onto the slit of the imaging spectrometer and allows blocking any set of
points from the image. By measuring many 2D images, each of which contains
a superposition of spatial and spectral information and performing a Hadamard
transformation, the spectral imaging information can be retrieved.