ar ti c l es doi: 10.1255/nirn.1038 Practical limits of spatial resolution in diffuse reﬂectance NIR chemical imaging Suzanne J. Hudak, Kenneth Haber, Gerald Sando, Linda H. Kidder and E. Neil Lewis Malvern Instruments, Columbia, MD 21046, USA. E-mail: firstname.lastname@example.org Near infrared chemical imaging (NIR-CI) IR-CI, a technique already widely used in industry for a range of chemical analyses, is a rapid, non-destructive method that combines rugged, flexible NIR spectroscopy with digital imaging.1 A single measurement enables the identification and spatial localisation of chemical species that can be correlated with a variety of sample performance measurements. Because most NIR-CI measurements are made in diffuse reflectance, a fundamental area of debate is the practical limitations of high magnification optics with regard to actual spatial resolution. Two factors impact on spatial resolution—the diffraction limit imposed by the wavelength of the probing radiation, and the effective pathlength of that radiation within the sample, a property which is determined in part by the mode of measurement (transmittance or reflectance). Depending on the particular experimental configuration, either one of these can be the limiting factor. For NIR wavelengths, penetration of the radiation into the sample is substantial, whereas the wavelength of light is comparatively short. Therefore, the penetration of NIR light into the sample, not the diffraction limit, becomes the limiting factor for determining spatial resolution in a diffuse reflectance imaging experiment. While the diffraction limit is a simple function of the wavelength of light and the numerical aperture of the focusing optics employed, it is less straightforward to determine the penetration depth of NIR radiation into a sample in diffuse reflectance mode. Although this question has been looked at previously,2,3 this study attempts to clarify some of the underlying issues and presents a relatively simple model to determine a limit for the maximum spatial resolution of diffuse reflectance in the NIR spectral region. This model is determined by first estimating the effective pathlength of the diffusely-reflected NIR radiation. The schematic in Figure 1 shows photons entering a sample with a finite penetration N 6 Vol. 18 No. 6 September 2007 Incident Photons Diffusely Reflected Photons Penetration Depth Figure 1. Diffuse reflectance. depth. Upon exiting the sample, the photons will have interacted with the entire sampling volume represented by the shaded area. The spectral signature of the resulting NIR radiation will be characteristic of the NIR absorbances due to interactions with all of the chemical species contained in this sample volume. As the contrast in NIR chemical images is based on NIR spectral signatures, it therefore implies that the depth of penetration, which translates to a sampling volume, will limit the highest useful lateral magnification. In other words, for high magnifications, photons emerging from an area on the sample surface will have interacted with a larger volume than indicated by the area actually imaged by a single detector. This is observed as spectral mixing, so that as magnification is increased, the observed differences in adjacent spectra become smaller, resulting in no real gain in spatial resolution. This is true for all instrumental implementations—array-based two-dimensional imaging, as well as line and single point mapping. Determining effective pathlength as a function of wavelength According to Beer’s law, absorbance is directly proportional to pathlength: A = εcl where A is the absorbance, ε is the extinction coefficient, c is the concentration, and l is the pathlength. In order to estimate the effective pathlength sampled in a typical diffuse reflect- ance experiment, polystyrene was chemically imaged (SyNIRgi, Malvern Instruments) in two different forms. In the first experiment, polystyrene was measured in diffuse reflectance by finely milling the bulk material and compressing it into a pellet of similar dimensions to that of a pharmaceutical tablet. In the second experiment, the same sample was measured, but an additional polystyrene window of the same material and of known thickness was placed in the same optical path. This has the effect of adding a known pathlength of polystyrene to the second diffuse reflectance spectrum. The contribution of the transmittance spectrum to the total spectrum can be calculated from the difference of the two. Here, we have made the assumption that the density (concentration) is approximately the same for both the transmission and diffuse reflectance samples. Since the window has a known thickness of 1.01 mm, the effective pathlength as a function of wavelength can be calculated for the purely diffuse reflectance measurements using the following equation: ⎤ ⎡ ADR lDR ( λ ) = ⎢ ⎥ ( λ ) × lT ⎢⎣ A TDR − ADR ⎥⎦ where lDR and lT are the diffuse reflectance and the transmission pathlengths, respectively, and ADR and ATDR are the diffuse reflectance and the combined transmission/ diffuse reflectance measurement absorbance values, respectively. Multiple absorption bands (spectra shown in Figure 2) were measured relative to a baseline offset at 1310 nm and used to determine the effective pathlength as a function of wavelength. As expected, the results, shown in Figure 3 illustrate a trend of decreasing pathlength with increasing wavelength from ~1.7 mm at 1210 nm to ~0.52 mm at 2360 nm. Converting effective pathlength to sampling volume The next step is to correlate the effective pathlength of the NIR radiation to a sampling volume. A random walk model is used a r ti c le s 1 Diffuse Reflectance + Transmission Diffuse Reflectance Absorbance 0.8 0.6 0.4 0.2 0 1200 1400 1600 1800 2000 2200 2400 Wavelength (nm) Figure 2. NIR absorption spectra of polystyrene. to estimate the volume sampled by a typical photon.4 This model assumes that an object, here a photon, travels a set distance and then changes directions randomly. This process is repeated many times before the photon ultimately leaves the sample and is measured by the detector. The following equation is used to calculate the standard deviation, σ, of the displacement of the photon from the origin: σ2 = t 2 ε δt where t is the time elapsed since the start of the random walk, ε is the size of each step taken before a change in direction, and δt is the time elapsed between two successive steps. In this model, the step size is assumed to be equal to the wavelength of light. This is likely to be an underestimation of the scattering length, leading to an overestimation for the highest attainable spatial resolution predicted resolution > actual resolution). The pathlength calculated from Beer’s law and the transmission results along with the speed of light provide the value for t, the time it takes the photon to enter, interact and leave the sample. The wavelength of light, along with the speed of light provide the value for δt, as discussed earlier. For the polystyrene “tablet” the calculated σ values vary as a function of wavelength from 46 µm at 1210 nm to 31 µm at 2360 nm. Since these numbers correspond to a sampling radius from which ~68% of the measured spectral intensity imaged onto a single detector pixel originates, it therefore suggests that the upper limit of the spatial Figure 3. Effective diffuse reflectance pathlength as a function of wavelength. resolution is a sphere with minimum diameters between 92 µm and 62 µm. The Nyquist criterion states that the sampling interval should be at least two measurements (2 pixels) for each spatial resolution element probed. Therefore, using the lower limit of 62 µm, it implies that an appropriate sampling frequency (magnification) for a NIR chemical imaging system should not be significantly less than 31 µm. Determining effective pathlength in a pharmaceutical tablet Pharmaceutical products such as tablets are typically imaged in diffuse reflectance and in order to estimate the spatial resolution attainable for this type of sample, a similar experiment was repeated. In this case, the polystyrene tablet was replaced with a commercial aspirin tablet. The rationale for this was that both polystyrene and aspirin contain similar aromatic groups, and for the purposes of these calculations we have assumed that the extinction coefficients and “concentrations” for the two samples are the same. For polystyrene, the overtone of the aromatic CH stretch is observed at 1680 nm compared to 1660 nm for aspirin. The transmission experiment absorbance value for the polystyrene plastic was calculated by taking the difference between the Figure 4. Aspirin (red) and Aspirin + polystyrene (black) NIR spectra. Vol. 18 No. 6 September 2007 7 ar ti c l es absorbance values at 1680 nm in the diffuse reflectance and the diffuse reflectance/ transmission experiments. The calculated absorbance intensity values at 1680 nm for polystyrene and at 1660 nm for aspirin are 0.54 and 0.42, respectively. Assuming ε to be the same, an effective pathlength of 780 µm is calculated for aspirin at 1660 nm, resulting in a predicted sampling volume equivalent to a sphere of 72 µm in diameter. Within the limits of the assumptions made in this article, the results are similar to those obtained for the polystyrene samples. Effect on spatial resolution What this means in terms of practical spatial resolution is that, depending on wavelength, ~70% of the photons exiting the sample at any given point in a “typical” diffuse reflectance measurement will have interacted with 8 Vol. 18 No. 6 September 2007 a spherical region with a diameter of ~90– 60 µm. Several factors such as the selected scattering lengths and the use of a single standard deviation suggests that mixture spectra will be observed over areas and volumes significantly larger than this, and spatial resolution is degraded accordingly. Further, while optics can be constructed resulting in magnifications of 10 µm/pixel or less, the usefulness of this is questionable due to the optical scattering effects described above. Increasing the magnification beyond the inherent spatial resolution only accomplishes a decrease in the area sampled in any given time. The values calculated in this study are relatively consistent with previous estimates.2,3 References 1. E.N. Lewis, J.W. Schoppelrei, E. Lee and L.H. Kidder, “NIR Chemical Imaging as a Process Analytical Tool”, in Process Analytical Technology, Ed by K. Bakeev. Blackwell Publishing, Ch. 7, p. 187 (2005). 2. F.C. Clarke, S.V. Hammond, R.D. Jei and A.C. Moffat, “Determination of the Information Depth and Sample Size for the Analysis of Pharmaceutical Materials Using Reflectance Near-Infrared Microscopy”, Appl. Spectrosc. 56(11), 1475 (2002). 3. R. Spragg, T. Locke, R. Hoult and J. Sellors, “Microscopic Chemical Imaging in the NIR Region”, in Proceedings of the 11th International Conference NIR Near Infrared Spectroscopy, Ed by A.M.C. Davies and A. Garrido-Varo. NIR Publications, Chichester, UK (2003). 4. B.D. Hughes, Random Walks and Random Environments. Oxford University Press (1996).