Hadamard transform Raman imagery with a digital micro-mirror array
Introduction
The imaging of heterogeneous samples in the visible, near-infrared or mid-infrared spectral regions can be done either with a two-dimensional (2D) multichannel detector array or with a single detector. With the 2D detector array the sample is globally illuminated, and all spatial resolution elements are observed simultaneously during the entire period of data acquisition. With the single detector, the individual spatial resolution elements are observed consecutively via a raster scan so that each one is observed for a small fraction of the period of data acquisition. The 2D detector array may be the better choice if cost is not a consideration. For the visible spectral region silicon based charge-coupled devices (CCDs) and charge-injection devices (CIDs) are readily available at reasonable cost. For the near-infrared and mid-infrared spectral regions, 2D detector arrays based on indium antimonide (InSb), mercury–cadmium–telluride (MCT), and related materials may be cost prohibitive and difficult to obtain. The single detector is cost-effective but its performance for imaging purposes cannot approach that of the 2D detector arrays. A possible compromise is Hadamard transform imaging where a single detector is used but there can be a multiplex advantage compared to raster scanning with a single detector. Hadamard transform imaging is best introduced by starting with a description of Hadamard transform spectrometry.
In a conventional dispersive spectrometer, the radiation from a source is collected and separated into its individual spectral resolution elements by a spectral separator, and then is collected and focused for spatial presentation on a focal plane. The dispersive spectrometer uses a single exit slit to select one spectral resolution element of N spectral resolution elements for measurement by the detector. The Hadamard transform spectrometer (HTS) uses a multi-slit array (i.e., a mask) at the focal plane to select one more than half, (N+1)/2, of the spectral resolution elements at the focal plane for measurement by the detector. This arrangement allows for the simultaneous measurement of a multitude of spectral resolution elements at a single detector, which results in a multiplexing spectrometer. The recovery of N spectral resolution elements requires measuring the detector response for N different encodements of (N+1)/2 open mask elements. The raw data is recorded as the detector response vs. encodement number and is called an encodegram. Hadamard transformation of the encodegram yields the spectrum 1, 2.
Hadamard encoding of spectral resolution elements at a focal plane of a spectrometer employs a one dimensional (1D) encoding mask. If this mask were to be divided and the sections folded or stacked in some manner, the result would be a two-dimensional (2D) mask that can be used for spatial encoding 3, 4. For example, a 1D mask of 1 row of 15 columns can be folded into a 2D mask of 3 rows of 5 columns (3×5 array) with rows 1, 2, and 3 of the 2D mask containing column 1–5, 6–10, and 11–15 of the 1D mask, respectively. The corresponding Hadamard encoding matrices are folded in the same manner when constructing 2D Hadamard encoding masks.
Section snippets
Background
Over a decade of investigation by the Hammaker–Fateley group at Kansas State University into the use of stationary Hadamard encoding masks for the application of Hadamard transform techniques in spectrometry, depth profiling and surface mapping has involved liquid crystal technology 2, 5, 6, 7. The nature of liquid crystal devices limited their utility as Hadamard encoding masks. The liquid crystal masks that were constructed could only be used in the visible and near-infrared spectral regions.
The digital micro-mirror array (DMA)
Fig. 1 provides the details of a typical DMA. This DMA incorporates 480,000 micro-mirrors in a (600×800) array that is 10.2 mm by 13.6 mm. The dimensions of the DMA are similar to commercially available 2D detector arrays mentioned previously. An individual micro-mirror is 16 um2 and adjacent micro-mirrors are separated by 1 um. The micro-mirrors are built using standard conventional metal oxide semi-conductor (CMOS) construction techniques on top of the integrated circuits that are used to
Experimental
The experimental configuration used is shown in Fig. 2. The source employed was a Coherent Radiation model 52 argon ion laser producing 7.59 W of continuous power at 514.5 nm. The output beam of the laser was expanded and directed onto the DMA at a particular angle to allow the source irradiance illuminating any mirror in the `on' or +10° state to be directed through the projection optics and impinge upon the conjugate image location at the sample plane. The change in source intensity over the
Results
Two different heterogeneous samples were examined in this experiment using Hadamard transform Raman imaging. The first sample was three layers of immiscible liquids in a standard 1 cm path length rectangular parallelepiped cuvette. The second sample was a layer of solid benzoic acid stuck to a piece of double sided tape with a 1.0 mm2 chip of naphthalene pressed into the layer of benzoic acid and near one corner of the benzoic acid layer. Time to generate an image was dependent upon the number
Conclusions
Chemical imaging of various liquid and solid heterogeneous samples where the different constituents are distributed over a 2D sample plane can be accomplished using Hadamard transform imaging techniques. The results of this and previous investigations into using 2D Hadamard encoding masks and a single detector have shown that this technique can be applied to imaging samples in the visible 2, 4, 5, 6, 7, near-infrared [10]and mid-infrared [10]spectral regions. The employment of a moving 2D
Future plans
We are planning additional experiments to fully explore the potential of the DMA to provide improved spatial resolution and speed in image acquisition. There is no advantage in using a Hadamard scan compared to a raster scan when the detection system is operating in the shot-noise limit expected for a cooled photomultiplier tube. The experiments described in this contribution were chosen to demonstrate that the DMA functions well as a Hadamard encoding mask. Our unpublished experiments in
Acknowledgements
The technical assistance of the following individuals is gratefully acknowledged: Dr. D.B. Chase (DuPont, Wilmington, DE), Mr. A.N. Mortensen (Kansas State University, Salina Campus, Salina, KS), Dr. C.M. Sorensen (Department of Physics, Kansas State University, Manhattan, KS), and Dr. J.D. Tate (Dow Chemical, Freeport, TX) Financial assistance from D.O.M. Associates (Manhattan, KS) and Dow Chemical (Midland, MI) is also gratefully acknowledged.
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Research on Dispersive Detection Technology Based on Digital Micromirror Device by Atomic Fluorescence Spectrometry
2018, Chinese Journal of Analytical ChemistryThe processing method of spectral data in Hadamard transforms spectral imager based on DMD
2014, Optics CommunicationsCitation Excerpt :Many scholars have done a lot of research work in utilizing DMD to modulate the dispersed spectrum and design DMD-based Hadamard transform spectral imager [2–7]. The physical models of this type of spectral imager have been proposed and experimentally demonstrated [8–12]. Although the spectral imager is feasible in principle, the actual encoding process of the dispersive spectrum on DMD does not strictly conform Hadamard transform [4].
Applications of Hadamard transform-gas chromatography/mass spectrometry to the detection of acetone in healthy human and diabetes mellitus patient breath
2014, TalantaCitation Excerpt :Each method mentioned above has a unique advantage and disadvantage regarding sensitivity, precision and simplicity of use. The Hadamard transform (HT) technique has been applied to many fields, including time-of-flight mass spectrometry [12–15], Raman spectrometry [16–18], fluorescence imaging [19–22], ion mobility spectrometry [23,24], NMR [25,26] and capillary electrophoretic separations [27–31]. The application of a multiplexing technique such as a Hadamard transformation has also been demonstrated to be useful in GC [32–35] and liquid chromatography [36–41].
Applications of Hadamard transform-gas chromatography/mass spectrometry for the detection of hexamethyldisiloxane in a wafer cleanroom
2012, Journal of Chromatography ACitation Excerpt :Consequently, a novel and more sensitive method for detecting and quantifying this class of compounds would be highly desirable. The Hadamard transform (HT) technique has been applied to many fields, including time-of-flight mass spectrometry [15–18], Raman spectrometry [19–21], fluorescence imaging [22–25], ion mobility spectrometry [26,27], NMR [28,29] and capillary electrophoretic separations [30–34]. The application of a multiplexing technique such as a Hadamard transformation has also been demonstrated to be useful in GC [35–40] and liquid chromatography [41–46].