The sensitivity of a high-resolution Raman imaging system is crucial to the quality of the acquired information. The spectral
and spatial resolutions are among the primary factors that influence the obtainable results. The limits of resolution are
defined theoretically by the laws of physics, but are experimentally determined by the instrument parameters. In this article,
the theoretical background and the possibilities in practical applications are discussed.
Confocal Raman microscopes are the instruments of choice for many Raman measurements in a wide variety of applications ranging
from geosciences (1–3), biology (4–6), nanocarbon materials (7–9) to pharmaceutical compounds (10,11), just to name a few.
This article sheds light on the possibilities and, in part, the origins in terms of spectral and spatial resolution for confocal
Raman systems in general.
Any confocal Raman system will have a spectral resolution which is mainly determined by the following parameters:
- the focal length of the spectrometer (the longer the focal length, the higher the spectral resolution)
- the grating (the higher the groove density, the higher the spectral resolution)
- the pixel size on the charge-coupled device (CCD) camera (the smaller the pixels, the higher the spectral resolution)
- the entrance slit or pinhole (the smaller the slit or pinhole the higher the spectral resolution)
- the line shape preservation (equals imaging quality) of the spectrometer.
In some cases, one of the parameters can put limitations on the spectral resolution. If, for example, the projection of the
pinhole onto the CCD is already large compared to the pixel size on the CCD camera, then a further reduction of pixel size
will not increase the spectral resolution.
Please note that the microscope components such as the objective used for collection of the signal should not influence the
spectral resolution if the entrance slit or pinhole is the limiting element. This is preferential with confocal Raman microscopes.
The determination of the spectral resolution is often a point of debate. First, one should clearly differentiate the spectral
resolution from the sensitivity of the system to detect shifts of individual peaks. Relative peak shifts can be detected with
a much higher accuracy using fitting algorithms as has been demonstrated with a sensitivity down to 0.02 rel. 1/cm standard
deviation of the peak shift of a Si peak (12). The maximum achievable fit accuracy depends heavily on the number of detected
photons and the width of the peak that is fitted. This shift analysis is especially relevant for examining stress within a
sample, but may not be taken as a measurement for the spectral resolution.
The spectral resolution, which determines how the system can measure (that is, full width at half maximum [FWHM] of a narrow
peak or how well overlapping peaks can be differentiated), needs to be addressed separately from the peak shift sensitivity.
There are various ways to state the spectral resolution, and some of the most common ones are outlined below.
The pixel resolution is the difference in wavenumbers when moving from one pixel on the CCD camera to the next and is independent of factors such
as slit width or peak width of the detected peak. This can only be seen as the true resolution limit if the pixel size and
not the size of the entrance slit or pinhole is the limiting factor. For example, if the image of the slit or pinhole on the
CCD camera is 100 Ám in diameter and the pixel size on the CCD camera is 26 Ám, then the resolution would be significantly
worse than the distance (in wavenumbers) between two pixels. Since wavenumbers are measured in reciprocal space, it also needs
to be noted that the pixel resolution will differ depending on the spectral position where it is determined. The resolution
close to the Rayleigh line can, in this way, differ by almost a factor of two from the pixel resolution near 3500 rel. 1/cm
in the case of 532-nm excitation.
For this criterion two times the pixel resolution is taken. The logic behind this is that to discriminate two neighboring
peaks one needs to have one pixel on one peak, one in the minimum between the peaks, and a third one on the next peak. This
criterion is analogous to the Nyquist theorem in signal processing. The same limitations as outlined for the pixel resolution
criterion apply in this case.
Full Width at Half Maximum of Atomic Emission Lines
Atomic emission lines are typically much narrower than any Raman line. Their narrow width makes them a good probe to check
the resolution. Figure 1 shows an atomic emission line of mercury near 579.07 nm. The x-axis is given in units of rel. 1/cm assuming a 532.00-nm excitation laser. The spectrum was recorded using a mercury and
argon calibration lamp coupled via a 10-Ám core diameter multimode fiber to a UHTS300 spectrograph (WITec GmbH) equipped with
both 1800- and 2400 grooves/mm gratings (BLZ at 500 nm) and a Newton electron multiplying charge coupled device (EMCCD) camera
with a pixel size of 16 Ám. The integration time was 0.1 and 0.24 s, respectively, for the spectra. The FWHM derived through
this approach is a good measure of the resolution, but care must be taken to ensure that enough points are available within
the curve to ensure a good fit to the curve.
Figure 1: Spectra of the mercury atomic emission line at 579.066 nm plotted as a function of wavenumber assuming a 532.00-nm
excitation. The red line is the fitted curve (pseudo voight function) and the blue diamonds are the measured data points for
the 1800-grooves/mm grating. The green triangles and the purple curve show the results obtained using the 2400-grooves/mm
Measurement of Peak Resolution on Known Reference Samples
There are a few samples that are established standards to demonstrate spectral resolution. The most prominent is probably
CCl4. Figure 2 shows two spectra of this substance recorded with different spectral resolutions. It can clearly be seen, that
the peaks are nicely separated in the red spectrum whereas the separation is not as clear for the purple spectrum.
Figure 2: Raman spectrum of CCl4 with 532-nm excitation at different spectral resolutions.
Therefore, spectral resolution can be defined in many different ways and, thus, it is advisable to specify exactly how a spectral
resolution was or should be determined. Comparing actual measurement results under identical measurement conditions is certainly
one of the best ways to illustrate this. It should also be noted that with few exceptions the natural linewidths of Raman
lines are typically larger than 3 rel. 1/cm. Taking the Nyquist criterion into consideration, a resolution in the range of
1 rel. 1/cm should be sufficient for the majority of samples.