Two design strategies were recently described for compressive Raman detection, in which filter functions are applied to either a digital micromirror array device (DMD) [1
] or analog-based liquid crystal [2
] spatial light modulators (LC-SLM). DMDs provide binary states, as each mirror pixel can be programmed to be either “on” or “off”, corresponding to a mirror tilt of ±12°. LC-SLMs, on the other hand, use light polarization to produce either phase or amplitude modulated variable analog filters [18
]. Each pixel on LC-SLMs is a separately addressable optical phase modulator, which is used to rotate the polarization of the detected light between 0 (p
-polarized) and 90 (s-polarized). The filter functions on liquid crystal cell control the degree to which, for example, the input p
-polarized signal is rotated to s-polarization and thus reflected into the detection optical path. In this way, the spectral component that became s-polarized by means of the liquid crystal cell is entirely transmitted to the single channel detector while no p
-polarized light reaches the detector. Earlier applications using transmissive LC-SLMs in compressive spectroscopy suffered from low light throughput of ~20% [6
]. Recent developments in reflectance LC-SLM with higher light throughput (~80%) and fill factor [19
] made possible for better performing spectrometers [2
The data obtained in CD technology is fundamentally photon counts, which essentially corresponds to the dot product of filter functions and the spectra vectors. The filter functions are simply the combination of wavelengths specifically designed to regenerate the eigenvectors (often referred to principal component) obtained from chemometric algorithms. Multivariate techniques like PLS and PCA are appropriate to use to generate the optimal eigenvectors for a given experiment when the components are known [21
]. These techniques use pure component samples as a built-in calibration set [23
]. However, if components are not known then techniques like MCR may be more valuable to extract component information [26
]. The amplitude of the measured signal is proportional to the amplitude of the eigenvectors, and thus to the amount of the corresponding compound.
The present review is focused primarily on recent developments in DMD-based CD systems.
Digital Micromirror Device (DMD)-Based Compressive Raman Detection
DMD is a micro-electronic mechanical system (MEMS) which consists of thousands of individually addressable moving micromirrors controlled by underlying electronics. DMD is also an SLM as the mirrors are highly reflective and are used to modulate light; to rotate the light to either a +12 degree or −12 degree position relative to the flat state of the array depending on the binary state of the cell below each pixel. These two positions determine the direction that light is deflected. Each tiltable mirror-pixel can be moved to reflect light to, or away from an intended target [29
In DMD-based Raman detection systems the micromirrors on DMDs are horizontally binned (x mirrors/pixels) and vertically fully binned. That is, all mirrors in each column of the array are set to the same angle of either −12 or +12 and mirrors in each row are divided into adjacent groupings. Bins are defined by bands of photon energy, then groups of x adjacent columns are set in unison. The filter functions on DMD, then tells which columns of pixels are turned “on”, sending those selected photons to the detector and which columns are turned “off”, directing those photons away from the detector. More specifically, while photons with certain energy levels corresponding to “on” columns are collected in a single-channel detector and recorded, photons with wavelengths reaching “off” columns are disposed.
The first reported use of DMD SLMs in spectrometry dates back to 1995 by Wagner et al. [33
]. In this early work the contrast ratio of the DMD was only about 60:1; today it goes as high as 2000:1 with a higher fill factor, allowing the design of better performing compressive Raman systems. Two approaches were reported recently to construct binary filters for DMD based-Raman systems [15
]. The filter design developed by Scotte et al. is based on maximizing the precision of the components proportion estimates [15
] using a new Cramer-Rao lower bound based algorithm. Buzzard and Lucier’s approach was to minimize the error in estimating photon emission rates of the chemical species investigated [34
]. Both approaches based their theory on the fact that the photons transmitted through filter functions are modeled by Poisson random variables when the measurements are photon-noise limited [1
]. Here, optimized binary compressive detection (OBCD) procedures based on Buzzard and Lucier’s approach is overviewed.
OBCD design: The recently-developed optimized binary compressive detection (OBCD) method relies on binary filters, which provides optimal measurement settings. Input data to be modeled to generate filter functions are photon counts, modeled by Poisson random variables whose variances equal to their means. Photon emission rates are correlated to the concentration of components of interest. In other words, concentrations are not directly measured, rather photon emission rates of each compound are estimated and the concentrations are calculated from this estimation. Objective is to minimize the mean square error between estimated and true emission rates.
OBCD design has been shown to enable high-speed chemical classification, quantitation, imaging [1
], as well as facilitating Raman classification in the presence of fluorescence background [8
]. The design of an OBCD Raman spectrometer with 785 nm laser excitation whose schematic is shown in Figure 1
A is described in detail in reference [1
]. This design is configured to collect backscattered Raman photons with the same objective lens used to focus the excitation laser onto the sample. After separating Rayleigh photons using dichroic and notch filters, then Raman light is directed to the spectrometer module. It is then dispersed onto the DMD ((Texas Instruments, DLP D4000, 1920 × 1080 aluminum mirror array with 10.8 μm mirror pitch) after passing through volume holographic grating (VHG). In this design, 15 columns of adjacent mirrors are binned to yield a total of 128 bins, each bin corresponding to ~30 cm−1
and the whole spectral window being ~200–1700 cm−1
. The Raman light transmitted by the “on” mirrors (corresponding to +12 degree tilt of mirrors) is then sent to the low-noise photon-counting avalanche photodiode (APD) module (dark count rate of ~200 photons/s and no read noise). The input binary optical filters tell which mirrors will point toward (assigned value of one) or point away (assigned value of zero) the detector. Authors have demonstrated that the OBCD with 785 nm excitation can be used to rapidly quantify binary and tertiary liquid mixtures with known components, and also to generate chemical images of mixed powders as well as generating filter functions using the MCR algorithm to facilitate high speed chemical imaging of samples for which pure components spectra are not available. [37
]. They reported that with the OBCD strategy, a mixture of glucose and fructose is discriminated with as low as ~10 photons per pixel, corresponding to pixel dwell time of ~ 30 μs.
In order to demonstrate the accuracy of the OBCD detection mode, pairs of liquid mixtures with various degrees of spectral overlap were tested. Classification error was found to vary both with the degree of overlap and acquisition time. Low to moderately overlapping spectra (benzene/acetone with a correlation coefficient of 0.12, and n-hexane/methylcyclohexane with a correlation coefficient of 0.71) were accurately classified with as few as 10–25 photons per measurement in tens to hundreds of microseconds. The highly overlapped case of n-heptane/n-octane mixture with a correlation coefficient of 0.99, correct classification was achieved with ~200 photons in a few milliseconds. These acquisition times obtained using OBCD strategy were not accessible using comparative CCD-based Raman spectroscopy.
Another OBCD Raman spectrometer prototype with 514 nm laser excitation with similar design to the 785 nm system mentioned above was also prototyped in Ben-Amotz’s lab [8
]. For this design, a DMD chip of 608 × 684 mirror array with 10.8 μm mirror pitch was used. Two columns of adjacent mirrors were binned to give a total of 342 bins with each bin corresponding to 12 cm−1
and yielding a spectrometer with a ~200–4100 cm−1
spectral window. As a single channel detector, a photomultiplier tube (PMT) with a dark count rate of ~500 photons/s was used in this design. In this work [8
] the feasibility of the OBCD strategy for Raman imaging of moderately fluorescing samples was demonstrated. A strategy for fitting a fluorescence background to the third-degree Bernstein polynomials was adopted to train OBCD filters, which were then used to quantitatively separate Raman signals from the fluorescence background, facilitating Raman imaging of chemicals in the presence of a fluorescence background.
OBCD2 design: In the OBCD detection strategy only a fraction of Raman photons, which were transmitted by “on” (+12 degrees) stage of micromirrors, were read by the detector. Raman light reaching to “off” (−12 degrees) micromirrors on DMD was disposed. A new strategy, termed as OBCD2, was proposed to increase the efficiency of Raman detection, wherein binary filters were generated in pairs [7
]. Two detectors were used to count all Raman photons transmitted by two complimentary OB filters. OBCD2 is considered a derivative of OBCD, accordingly many of the assumption made in formulating the OBCD strategy [1
] remain valid for OBCD2 strategy, as well.
A schematic of this technique is shown in Figure 1
B. In the OBCD2 strategy, when one OBCD filter is generated corresponding to the “on” mirrors on DMD, the exact complement of that filter is also generated for implementation to “off” mirrors. To describe a system with n
components a minimum of 2(n
− 1) filters, which constitutes to n −
1 pairs of complementary filters, are required. Photons of different wavelengths are selectively reflected by micromirrors either positive 12 degrees or negative 12 degrees to the surface of the DMD and are directed to either one or the other PMT detector (dark count of ~500 photons/s) shown in Figure 1
B. With OBCD2 filtering strategy all Raman photons are detected. As a result, Raman scattering rates recovered using OBCD2 filters have lower variance than those using OBCD filters [7
]. In order to quantify the performance advantage of the OBCD2 over OBCD strategy, a ternary system of benzene, hexane, and methylcyclohexane were analyzed in [7
]. For this system there were three OBCD filters and 2 × (3 − 1) = 4 OBCD2 filters (or two complementary pairs). The standard deviations of the estimated recovered Raman scattering rates are shown to improve ~63%, ~23%, and ~24% for benzene, hexane, and methylcyclohexane, respectively.