# Resolution of Monochromators and Spectrographs

### Grating Groove Density, Resolution and Dispersion

Diffraction gratings are available in various groove densities (i.e. lines/mm). Higher groove densities give higher reciprocal dispersion and therefore higher resolution. The grating dispersion is similar for gratings with the same groove density. The exact dispersion is dependent upon other physical characteristics of the grating in addition to the groove density.

The resolution is the ability to separate wavelengths. It is usually expressed as the Full Width Half Maximum (FWHM). The resolution can be theoretically determined by multiplying the reciprocal dispersion of the grating by the slit width. The monochromator bandpass with a 1200 lines/mm grating is half that of the same arrangement with a 600 lines/mm grating. Note that this simple relationship is not accurate for slit widths below 50 µm, as the optical aberrations begin to play a role in the resolution.

Using a grating with a high groove density may increase resolution, but the spectral range narrows. The dispersion of a grating changes inversely with the groove density. If the groove density is halved, the dispersion is doubled. When performing a scan, to save time it is important to consider the resolution when determining the interval wavelength (i.e. the step size) of the scan. For example, if the resolution with a particular grating and slit is 5 nm, it is not necessary or practical to perform a scan every 1 nm.

### Spectral Resolution

The resolution is the ability to separate wavelengths. It is usually expressed as the Full Width Half Maximum (FWHM). The resolution can be theoretically determined by multiplying the reciprocal dispersion of the grating by the slit width. The bandpass with a 1200 lines/mm grating is half that of the same arrangement with a 600 lines/mm grating. Note that this simple relationship is not accurate for slit widths at or below 120 µm, as the optical aberrations begin to play a role in the resolution.

Figure 1. Typical output power and resolution of various Oriel Tunable Light Sources, which utilize a Cornerstone 130 monochromator with extended range gratings. The slit width is set to 120 µm in the left illustration, and 760 µm in the right illustration.

The entrance slit width generally determines the spectral resolution of a spectrograph. However, the limiting resolution is reached when the entrance slit is reduced to the width of a single pixel in the detector array. Nyquist Sampling Theory requires the resolution to be calculated over two pixels. Thus, the limiting resolution for Oriel’s MS257 Spectrograph with a diode array and 25 µm pixels would be about 0.2 nm. This is twice the 0.1 nm limit possible with the same instrument used as a scanning monochromator with 25 µm slits.

Figure 2. Comparing the output of these otherwise identical systems, the wider slit results in increased power and the inability to distinguish the finer Xenon lines. The relationship between slit width and resolution also apply to spectrographs.

Although some improvement can be achieved using arrays with very small pixels, such as Oriel’s LineSpec CCD, most instruments reach their aberration-limited resolution with 10 to 25 µm input slits. Beyond this point, narrower slits and/or pixels only reduce system throughput.

### Spatial Resolution

Spatial resolution is the ability of an imaging spectrograph to distinguish between two features perpendicular to the spectral axis. There is no standard measurement. Some manufacturers refer to the number of independent fiber sources that can be resolved, but this is only meaningful for specific fiber diameters and does not describe the signal leakage from one channel to its neighbor. The most significant measurement is the aberration limited spatial resolution. This value is defined as the Full Width Half Maximum (FWHM) of the smallest feature that can be resolved.