Curved grating spectrometer with very high wavelength resolution

A method for analyzing a spectra composition of an optical beam, the method comprising:

• a. adjusting a location of an entrance slit in order to have best performance at a particular design goal, the optical beam entering a spectrometer through the entrance slit;
• b. adjusting a location of a detector in order to have best performance at a particular design goal, the spectra composition of the optical beam being detected by the detector;
• c. using a compact curved grating in order to analyze the spectra composition of the optical beam, the compact curved grating comprising a plurality of grooves, the step of using the compact curved grating further comprising the step of:
• i. calculating initial groove spacing using the information relating to location of the entrance slit and the detector, center of the operation wavelength, refractive index of the medium and the diffraction order;
• and
• ii. determining the positions of other grooves, the positions being determined by ensuring that path difference between adjacent grooves is an integral multiple of the wavelength in the medium, according to the following mathematical expression:
• [d1(θ1,S1,Xi)+d2(θ2,S2,Xi)]−[d1(θ1, S1, Xi−1)+d2(θ2,S2,Xi−1)]=mλ/n
• wherein d1(θ1, S1, Xi) is a distance from one of the plurality of grooves located at Xi from the entrance slit, d2(θ2,S2,Xi) is a distance from one of the plurality of grooves from the detector, m is a diffraction order and n is a refractive index of the medium, and further wherein an arc length of each of the grooves is the same;
• and
• d. adjusting the initial groove spacing and the positions of other grooves according to the calculating and determining steps.