THz Imaging Compressive sensing Hadamard spectroscopy THz Laser DMD Hadamard matrices Experimental model v1.0 Experimental model v2.0 Experimental model v3.0
THz spectroscopy
With IR spectroscopy a sample can be probed, in terms of vibration and rotation modes, and information about molecular structure and bonding achieved. This technique has the major advantage of simultaneously detecting a large variety of chemical specimens with minimum expenses.
In THz spectroscopy two methods are predominantly used, namely:
  • Fourier Transform THz Spectroscopy
  • THz Time-Domain Spectroscopy
Fourier Transform THz Spectroscopy (THz-FTS), is the most common technique used to study molecular resonances [RD06]. This method encompasses an interferometric system to investigate a given material. The sample to be analyzed is placed in one of the interferometer optical paths. Usually with such a technique, a helium cooled bolometer is used as detector and a thermal source as THz generator.
The main disadvantages of the THz-FTS method are:
  • limited spectral resolution
  • only amplitude information from the recorded spectra
  • essential moving parts
THz Time-Domain Spectroscopy (THz-TDS), technique is recent and uses a special radiation generation/detection scheme in order to investigate a given sample. Thus, a pulsed laser is used for generation/detection of THz radiation and photoconductive antennae are used as emitter and receiver. The main advantage of such a method is the sensitivity to both amplitude and phase of the THz radiation. Sub-picosecond pulses of THz radiation are detected after propagating through a sample and an identical length of a free space. A comparison of Fourier transforms of these pulse shapes gives the spectra of absorption and dispersion of the sample under investigation. Such measurements can be successfully performed for investigation of gases and organic materials.
Hadamard spectroscopy
Generally, in Hadamard spectroscopy the spectral components (e.g. obtained after passing through a dispersive/or diffracting element) are modulated by a series of masks (i.e. performed at the DMD). The spectral information is obtained applying an inverse Hadamard transform. Note, such a technique has the major advantage of using no slits (as in classical spectrometers) and thus, it has a better signal-to-noise ratio.
The optical layout of spectroscopy for our experiment is presented in the image bellow.

Hadamard spectroscopy with 7 samples
The resolution of the spectrum measured by Hadamard spectrometry depends on the matrix size. For a 7 samples spectrum, the Cyclic S matrix must be of size 7 × 7. Each row corresponds to a mask with 7 binary elements.
In the image bellow we have the graphical representation of a 1D Hadamard matrix, with white and black stripes (i.e. slits or elements) representing a binary system of 1s (i.e. light is passing) and 0s (i.e. light does not pass). Each consecutive mask is obtained by shifting the window to the right, by one element.
The corresponding sliding strip consists of 7 + 6 elements configured according to the binary sequence (1110100111010). This configuration is used in obtaining the mechanical mask.
The mechanical mask is obtained by cutting slits in a sheet of metal, according to the sequence mentioned above and a slit is 20mm × 2mm in dimension. In order to select a group of 7 elements, a rectangular window of 20mm × 14mm is cut on a second sheet of brass. These components and the assembled mechanical Hadamard mask are shown bellow.

The window is fixed while the sequence of slits slide behind it and configures, one by one, the rows of the Cyclic S matrix. These configurations correspond to the following sequences: (1110100), (1101001), (1010011), (0100111), (1001110), (0011101) and respectively (0111010). For each configuration, the detector records a voltage value that corresponds to samples ci, i=1,…,7. The mask components are made from brass sheets, each with a thickness of 1 mm. For the experiments we used a He lamp as the light source, more precisely, the red and yellow components of its spectrum (as shown in the image bellow) with wavelengths λred = 7065.71 Å and respectively λyellow = 5875.97 Å.

The image bellow shows the result of a first measurement and the recovered spectrum with equation Sc-1 = (2 ⁄ (N+1))(2ScT−IN). Because the Hadamard transform is implemented to the signal when applying the mechanical mask, this inverse transformation is needed to reconstruct the spectrum.
Although the plot has only 7 points, two peaks corresponding to the red and yellow spectral lines, mentioned above, are visible. The experiment was repeated three times.

These measured spectra have slightly different shapes due to measuring and mechanical errors. More precisely, the masks were commuted manually and small variations in the position of the slits with respect to the window may cause differences in the recorded voltage values at the detector. The measured intensities also vary with the focal length of the focusing lens on the detector. Thus, the further from the focus the detector is placed the lower the intensity value, recorded as voltage on the detector. This is because the energy of the incident beam is concentrated in a smaller focal spot (i.e. at focus) or in a larger focal spot (i.e. away from focus).
  1. C. Fernandez et. al., Longwave infrared (LWIR) codedaperture dispersive spectrometer, Optics Express 15 (9), 5742-5753 (2007).
  2. W.Wang, Z-Y. Wen, Z-H. Zhang and X-X. Mo, Realization of Hadamard transform encoding mask using programmable digital micro-mirror device, Key Engineering Materials 483, 497-502 (2011).
  3. E. D. NELSON, Hadamard Spectroscopy, JOURNAL OF THE OPTICAL SOCIETY OF AMERICA, VOLUME 60, NUMBER 12, 1664-1669 (1970).
  4. M. Hangyo, M. Tani and T. Nagashima, Terahertz time-domain spectroscopy of solids: A review, Int. J.Infra. Mill. Waves, Vol. 26 (12), pp. 1661–1690 (2005).
∴ Facts
Title: Compressive THz Imaging and Hadamard Spectroscopy for Space Applications
Project No: 17/19.11.2012
Project type: CDI STAR Project
Starting date: Nov 2012
Duration: 36 months
Partners: 2
INFLPR - Coordinator
CEO Space Tech - Partner
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