There are various ways to define wavelength resolution, for there are various demands about wavelength information. The most important are:
- Rayleigh Criterion
- Full Width Half Max(imum)
- Sub-Pixel Resolution
The potential spectral resolution is mainly given by two components of a spectrometer: the grating and the detector array. Assuming the resolving power of a grating and the imaging quality of a spectrometer are fine, the potential resolution is given by the detector array. Here the key parameter is the pixel dispersion = bandwidth per pixel. This is easily calculated by the overall spectral range covered by the number of pixels:
ΔλPixel = (λEnd – λStart)/ NPixel
Note: Due to non-linear dispersion of a spectrograph the pixel dispersion nor the resolution are constant over the entire spectral range covered, but above equation is a good assumption.
|1. Rayleigh Criterion:||λRayleigh = 2.5 … 3 x λPixel|
|2. Full Width Half Maximum:||λFWHM = 2.5 … 3 x λPixel|
|3. Sub-pixel Resolution (Accuracy)||λSPR = λPixel / (5 … 10)|
Rayleigh resolution: specifies the wavelength resolution of two lines at equal intensity. These two broadened lines are considered resolved if the dip between the two maxima is 19%. It is appropriate for spectral analysis which requires the separation of individual lines within a spectrum.
Simulation of two approaching equal lines
FullWidthatHalfMaximum: describes the broadening of a single line, the value given is the spectral width at the 50% level. The resulting value is about 90% of the Rayleigh value. It is much easier to determine than the Rayleigh one. Directly useful if line width, e.g. LEDs, is measured.
Sub-Pixel Resolution: describes the capability to determine the position of a spectral feature e.g. a monochromatic line with much higher accuracy compared to resolution. Since even monochromatic light gets broadened by a spectrometer, more than 1 pixel is illuminated. When more than 2 pixels receive illumination the “center of gravity” of the such broadened line can be determined (e.g. by a parabolic fit). The accuracy is given by the stability of the spectrometer, i.e. how stable a performed calibration persists (please see that page for details). It can be about 10 times lower than the classical resolution values.” The value is important when it comes to the determination of peak positions, e.g. laser emission or filter cutoff positions, without the requirement to resolve any spectral structure.
The entrance slit width is selected so at least 2, better 3 to 4 pixels are illuminated. The slit height should not be forgotten, for the imaging quality in the slit direction is degrading with the distance from the spectrometer’s main plain, i.e. the larger the entrance slit height the more broadening at the detector area, the worse the resolution. Here are the main differences in quality of manufacturers.
A small entrance slit also limits the light throughput and thus the sensitivity. Typical considerations: to find the best trade-off between wavelength resolution and sensitivity!
A technical mean to boost the throughput of a spectrometer is a cross-section converter. A fiber-optical bundle can transfer e.g. a round image to a linear slit shaped one. Depending on the slit shape required, an order of magnitude of throughput can be gained. A permanently fixed fiber-optic input freezes the optical axis of the spectrometer and such improves calibration stability (see Accuracy/ Reproducibility).