VISIBLE ABSORPTION SPECTROMETRY continued
Dispersion In the grating stack, we employ surface relief transmission gratings
(SRTGs). Each grating is in intimate contact with its predecessor, so the grating(s) closer to the light source set up diffraction patterns that are rediffracted by grating(s) closer to the camera. The position of each blue intensity peak corresponds to diffraction of the peak LED emission at 450 nm, so to the extent that dispersion is proportional to order number and λ(r) = 450 nm + kn (λ – 450 nm), determination of k for a single order calibrates every order, provided n can be identified. In fact, measuring r (450 nm) implies n for each order. However, dispersion varies by about 6% between 400 nm and 700 nm for the gratings we use (as with any grating, dλ/dx = d cos β/nf where f is the instrument focal length and β the diffraction angle for λ. Saying dispersion is constant can only be true in the absence of dispersion). With a camera field of view less than ±30°, cos β changes by less than 17%. For many applications, that is not negligible. Figure 2 illustrates that the first grating in the stack disperses several orders, the second redisperses those orders, and so on for as many gratings as one wishes. We find that three double-dispersion gratings are more than enough to generate the desired spectral richness.
Order overlap One can readily see in a SpectroBurst that orders diffracted along a
cardinal direction (parallel to one axis of the double dispersion gratings) overlap just as would multiple orders in an ordinary spectrometer. What’s different is that cross-dispersion generates numerous overlap-free orders. Part of the art being developed is automating the identification of clean, nonoverlapped orders. A second level of sophistication will be to add
chemometrics to exploit overlapped orders and to determine where such use improves measurement precision.
Intensity calibration What signal comes from a particular pixel? It is a sum of offset, dark current,
and the sum, over relevant wavelengths, of photon flux times quantum efficiency. Dark current can be easily measured as a function of exposure time (at fixed temperature) and subtracted from raw signal. However, the slope response depends on both the detector and the optical throughput. To exploit the SpectroBurst, the relative response for each pixel must be normalized. Figure 3 shows four hypothetical pixels, each linear (solid line) or nonlinear (dashed line) in response. For high throughput, I = S (the true exposure I and the pixel readout signal S are the same) up to the point that the detector saturates. For weaker orders, I = 2S, I = 4S, or I = 8S. Clearly, such integer scaling is fanciful, but the cartoon of how varied throughput allows wide dynamic range from low range cameras is real.
Interorder information The space between the orders contains useful information. Unlike almost
all absorbance spectrometers, light is not refocused and recollimated after going through the cuvette. Fluorescence or light scattering will flood the field of view with uncollimated light. The bad news is that this will compromise dynamic range. The good news is that we can directly observe the phenomenon and, at low levels, subtract the stray light in real time. Unlike ordinary spectrometers, the instruments described here can detect when scattering or luminescence occurs.
Computation speed With all the manipulations involved in turning a SpectroBurst into a
spectrum, the algorithms must be fast or the improved data density of the image cannot be turned into chemically relevant information quickly
Figure 2 – How the stacked gratings generate hundreds of orders. The first double-dispersion grating generates 40+ orders (here we look side-on and show only two of these orders, pointed to by horizontal arrows). The second grating redisperses each order, some to greater distance from the optical axis, some to less, as identified by the vertical arrows. The result is the many families of orders seen in Figure 1.
Figure 3 – Possible responses of pixels to exposure. Normalization for linear differences in response is simple; normalization for nonlinear response requires linearization as well as rescaling.
AMERICAN LABORATORY • 38 • SEPTEMBER 2014
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