This trade is concerned with the two properties, spectral resolution and fringe frequency. Spectral resolution is the ability to distinguish between different wavelength intervals. Fringe frequency, on the other hand, is an intrinsic property of the diffraction grating that describes the number of fringes that occupies the number of fringes per mm. The spectral resolution can be broken down into the sensor spectral resolution and the optical spatial resolution. The optical spatial resolution is the one that is dependent on the fringe frequency, which directly affects the resolvance.
There is no set requirement for fringe frequency, though the spectral resolution must be at least 10 nm (less is better).
The key factors that must be taken into consideration are the upper and lower wavelengths (for sensor spectral resolution),the beam diameter and the target wavelength (for optical spectral resolution).
Tinkering around with all of the aforementioned parameters yield similar exponential plots regardless of the values imputed.
The plot above was created with the following values:
Based on the results, we can conclude that the spectral resolution is not something that we need to necessarily worry about when choosing the fringe frequency. When the upper and lower wavelengths were expanded to 900 nm and 1700 nm, respectively, a similar plot was created. There were only minor changes when beam diameter was adjusted to be smaller. The cutoff for meeting the requirement for most of the beam diameter values (>7) was a fringe frequency of 20 mm^-1. When the beam diameter was lower than 7, a larger fringe frequency was necessary to meet the requirement.
Provide recommendation(s) and next steps based on the findings of the tradeoff analysis. This might include a recommendation for a preferred option.
To account for the uncertainty in the beam diameter, we recommend that a fringe frequency of at least 50-60 mm^-1 is used to be sure that the spectral resolution fits within the requirements that are set for the FINCH Eye.