When images are measured in reflectance, the observed structure is not necessarily just that of the sample surface. The two-dimensional
(2D) images produced by near-infrared (NIR) and mid-IR imaging are representations of three-dimensional (3D) objects. In reflectance
images the effective spatial resolution is affected by how far the radiation penetrates into the sample as well as by diffraction
and the pixel size. NIR images are typically dominated by diffuse reflection with the result that in practice spatial resolution
is limited by the penetration depth. Mid-IR reflectance images may contain both specular and diffuse components. These have
different spatial resolutions as the specular component shows purely surface structure. In attenuated total reflectance (ATR)
images the resolution has a component that depends on the distribution of components within a surface layer corresponding
to the penetration depth, which is proportional to wavelength. We illustrate these different contributions to the observed
resolution with images of materials with known 2D and 3D structures.
What do we measure in reflection? For the majority of samples, transmission measurements are not possible so spectra have
to be obtained by reflectance. This involves either external reflection, often divided into specular and diffuse reflection,
or attenuated total reflection (ATR). What you see in external reflection is the sum of what is reflected from the surface
(specular or Fresnel reflection) and what penetrates into the sample before emerging (diffuse reflection). You see only surface
reflection from a continuous uniform material where radiation that penetrates is not scattered back to the surface. Very strongly
absorbing materials also show only surface reflection as the radiation that penetrates is all absorbed. With scattering materials
some radiation that penetrates the material returns to the surface by encountering interfaces where there is a change of refractive
index. The relative amounts of surface and diffuse reflection depend on the absorptivity and particle sizes of the sample
and are wavelength dependent. Small particle size and weak absorption increase the amount of diffuse reflection. In practice,
diffuse reflection dominates in the near infrared (NIR) whereas spectra in the mid-IR often show significant contributions
from both surface and diffuse reflection.
How does this affect spatial resolution? In an imaging experiment, separate spectra are measured for each pixel while the
incident radiation covers the whole area. If reflection comes only from the surface, the spatial resolution should depend
simply on diffraction and the pixel size. However, any radiation that penetrates a scattering sample takes a random path through
the material and will not all return to the point at which it entered the sample. Thus, the radiation contributing to any
pixel in the image is a combination of rays from some volume underneath the point on the surface that is being observed. The
deeper the radiation can penetrate into the sample and return without being absorbed, the larger this volume will be. If we
assume isotropic scattering, the average lateral displacement from the point of incidence to where the radiation emerges will
be similar to the average depth to which the radiation penetrates. This will cause blurring of the image by an amount that
depends on the average penetration depth. There have been several attempts to estimate the depth that the radiation penetrates
(1,2). These suggest average values in the range of 50–100 Ám for NIR observations of materials such as pharmaceutical tablets.
As a result, the spatial resolution achieved in NIR reflection images is likely to be in this range. This is in contrast to
what is observed with the metal-on-glass reflection targets normally used where diffraction limited spatial resolution is
better at the shorter wavelengths of the NIR region than in the mid-IR.
Figure 1: Diffuse reflection and transmission.
Penetration Depth in Diffuse Reflection
One way to estimate the penetration depth is by comparing the band intensities in transmission and reflection for a scattering
sample. The absorbance is proportional to the distance traveled inside the sample. In transmission, this distance is proportional
to the thickness of the sample, but in reflection it is proportional to twice the average penetration depth (Figure 1). One
sample used was an acetaminophen tablet ground down to a thickness of 1.1 mm. The ratio of the absorbances at 8800 cm-1 measured in transmission and reflection is 18:1. From this, the average penetration depth is calculated as 30 Ám (Figure
2). Similar measurements on pressed pellets of other materials give average depths of 40 Ám to 60 Ám (Table I). Because these
are average depths we can conclude that some rays must penetrate significantly further. This will produce blurring of 50–100
Figure 2: Spectra of an acetaminophen tablet.
Measuring Spatial Resolution in Scattering Materials
We prepared a sample by pressing a pellet of microcrystalline cellulose on top of a pressed pellet of polyethylene, giving
a flat boundary between the two materials. Microtoming one edge of the pellet in a direction parallel to the interface gave
a flat sample with the boundary perpendicular to the surface. Images were obtained with a PerkinElmer Spotlight system with
a pixel size of 6.25 Ám over the 6000–1400 cm-1 range (Figure 3). The spectra include dispersive features characteristic of Fresnel surface reflection such as the polyethylene
CH2 absorptions around 2900 cm-1, strong absorptions such as the broad cellulose OH band at 3500 cm-1, and weak NIR absorptions.
Table I: Estimated NIR penetration depths
As expected, an image based on the polyethylene CH2 feature at 2864 cm-1 (Fresnel reflection) has a sharp boundary. In addition, it reveals an anomaly on the surface of the polyethylene layer at
a distance of about 50 Ám from the interface. An image of the strong cellulose OH absorption at 3600–3400 cm-1 shows a similar sharp boundary and indicates that the anomaly results from a flake of cellulose, something that is confirmed
from the individual spectra. The sharp boundary illustrates how the strong absorption limits radiation that penetrates the
sample returning to the surface. In contrast, the weak absorptions of the NIR region lead to much more diffuse images with
features from one layer visible up to 100 Ám away from the boundary. The polyethylene layer has significantly less scattering
than the cellulose layer, which probably explains why the cellulose features appear to extend farther beyond the boundary.
Figure 3: Images from a two-layer sample.