F-sin(&thgr;) lens system and method of use of same

Abstract

An optical system for focusing an incident light so as to obtain a linear output (as a function of the wavelength, or of the order of diffraction, or of the grating spacial frequency or of the inverse of the index of refraction) comprises a diffraction grating and a lens, or a group of lenses, having a f-Sin(&thgr;) characteristic, where f is the effective focal length of the lens, or group of lenses, and &thgr; is an output angle of the light exiting from the diffraction grating. Therefore, a light incident on the diffraction grating reaches the lens, or the group of lenses, and results in a linear output. Using the present invention in a spectrometer reduces the time consuming calibration process required and renders it easier because of the linear output between wavelength and pixels positions. The lens, or group of lenses, has a diffractive, refractive or reflective property, or any combination thereof. The incident light can be a collimated, converging or diverging beam. The diffraction grating can be a plane, concave or convex grating.