Step 1: Choose the geometry
The first step is to choose between the Czerny-Turner or LGL type geometry. For the Czerny Turner a typical value for Θ is around 30° wheras transmission gratings are generally used in the Littrow configuration and –1st order where α = -β => Θ = 0°.
Step 2: Choose grating
The second step is to choose a diffraction grating. Most grating vendors have an on-line catalog where you can find one or more grating options to try in your design. You should choose a grating that has high diffraction efficiency in your wavelength. The important parameter that you shall use for the design in the next steps is the groove density G.
Step 3: Calculate diffraction angle
The angle of incidence α on the grating and the diffraction angle β for the center wavelength λc are key parameters in the spectrometer design. These angles can be calculated once the grating groove density G and the total deflection Θ are chosen.
Step 4: Choose detector
The purpose of the spectrometer design is to disperse the wavelength range across the width of the detector array LD. There is a large range of diode array detectors specifically designed for spectrometers. In general, if you need a compact spectrometer you should aim for a short detector (typically 1/4” or 6.4 mm). However, if you require a broad spectral range and/or a high resolution you should aim for a wide detector (typically 1/1” or 25.8 mm).
Step 5: Calculate focal length of focus lens
Once the width of the detector is known you can calculate the focal length of the focusing mirror or lens.
Step 6: Choose a magnification
As mentioned earlier, the spectrometer is imaging the input slit to the detector and we generally want to have the slit as wide as possible to collect as much light through the input slit as possible. Therefore, the magnification in the system Μ should preferably be close to 1 which means that the width of the input slit ideally is imaged 1:1 onto the detector array.
Step 7: Calculate focal length of collimation lens
As in any imaging system, the magnification is determined by the ratio between the focal lengths of the two lenses in the system. For a spectrometer, this ratio has to be slightly modified due to the deflection along the beam path in the grating. However, once the magnification is chosen the focal length of the collimation mirror or lens can easily be calculated.
Step 8: Calculate input slit width
The input slit width ωslit is determined by the required optical resolution Dl and the magnification. Once you know your input slit width you are ready to evaluate if your spectrometer design is viable or you have to go back and change some of your choices for grating, detector, or magnification for instance.