Raman Images from Raman Maps - Spatial Resolution, Mapping Speed, and Multivariate Techniques for Constructing the Image - - Spectroscopy
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Raman Images from Raman Maps - Spatial Resolution, Mapping Speed, and Multivariate Techniques for Constructing the Image


Spectroscopy
Volume 23, Issue 10, pp. 14-21

The spatial resolution of any imaging tool is determined by diffraction theory. In an optical microscope, it is assumed that a microscope objective is illuminated uniformly by light and the focal area is described by the Airy disk as

ωo = 1.22 (λ/NA)

where NA stands for the numerical aperture of the objective. When the same objective is used to focus a laser beam, the beam profile is not uniform (it is very often Gaussian), nor does it fill the objective aperture. However, the minimum beam spot is described by a similar expression:

ωo = K (λ/NA)


Fran Adar
with the constant K not very different from 1. That means that for laser lines in the visible part of the spectrum (approximately 0.5 μm) and for high-magnification objectives (for example 90 with NA = 0.9), the minimum spot size is near 0.68 μm. The question, of course, is how to measure the spot. One method has been to perform a line profile across a silicon–metal interface: Follow the silicon signal as the sample is moved so that the metal masking the silicon falls under the laser-illuminated spot, then take the derivative of the intensity profile of the silicon, and measure the full width at half maximum (FWHM). We will show results of polysilicon lines on silicon done at several laser wavelengths, but first we want to show a Raman image of particles with submicrometer dimensions.


Figure 1
A sample that was known to have particles of diamond with diameters of 0.2 μm (200 nm) or larger was mapped with the HeNe laser (632.8 nm). For this sample, Raman maps should be acquired with steps of about 40 nm (five points per particle), but a stage with only 100-nm (0.1-μm) steps was available. The result, shown in Figure 1, was an image of a particle whose FWHM was no greater than 0.4 μm! Because this quantity represents a convolution of the beam profile and the particle size, which was 0.2 μm, the beam profile must be somewhere in the range of 0.2 to 0.3 μm, considerably smaller than the prediction from diffraction theory.


Figure 2
Additional experiments were done on polymer particles. First we systematically compared the images obtained by varying the step size between data points for a given particle. Figure 2 shows the results obtained from maps of a 6-μm bead of polystyrene obtained with 1.0-, 0.5-, and 0.1-μm steps. Clearly, 1-μm steps are far from adequate to map out a particle 6 μm in diameter.


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