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Diffraction grating calculator12/18/2023 Incident light angles from 0 to 90 degrees can be inputted although practically an instrument should operate near the blaze angle for best efficiency. The incident angle of the light from the input slit to the grating perpendicular can be adjusted. The calculator provides parameters to customize the grating, spectrometer, and the detector array used. Expected spectrometer performance can then be plotted, including dispersion, wavelength calibration, and line width at the grating output. The calculator then models the average spectral intensity response of the grating using a scalar diffraction theory 1. These properties are needed to estimate the resolution of the device. Once the grating parameters including blaze angle are selected, the spectrometer physical properties need to be inputted. A message is displayed indicating which design element is limiting the grating resolution. It also calculates the resolution set by the pixel size on the output arm of the spectrometer. The calculator attempts to estimate the resolution of the grating spectrometer by calculating the diffraction of light from the entrance slide through the input arm to determine the illuminated portion of the grating. This is the maximum resolution of the device, in practical terms the entrance and exit slit size and arm length, aberrations in grating and optics manufacture and étendue (light transmission through the spectrometer) will limit the resolving power of the instrument. Where λ is the wavelength of the central peak, dλ is the width to the first minima, k is the ruling period, n is the order, W g is the illuminated width of the grating and N is the number of illuminated rulings. The number of illuminated grating rulings determines the resolving power of the grating. Light enters through an input slit and expands through diffraction to fill the grating. The LightMachinery grating model is based upon a Czerny-Taylor monochromator or spectrometer with input and output legs of equal length, Figure 3. This technique allows the light in one order to be maximize while suppressing the residual power in other orders. The efficiency that the grating diverts light into a particular order can be modified by varying the angle of the ruling surface to the grating perpendicular. Where ∝ is the angle between the incident light and a perpendicular to the plane of the grating, β is the angle between the diffracted light and a perpendicular to the plane of the grating, k is the period (mm/line), n is the diffraction order and λ is the wavelength. The angle of dispersion for a given wavelength of incident light is determined by the period of the rulings according to: As such the dispersion equation must include both incident and diffracted angles. The model chosen for this calculator estimates the performance of a reflection grating with regular ruled lines. A specific wavelength of light is diffracted into multiple angles which correspond to constructive interference. Where Ɵ is the diffracted angle, d is the slit spacing, n is the order and λ is the wavelength of the diffracted light. The equation for double slit diffraction is: As with a pair of slits, the diffraction of light from a grating occurs as a result of constructive and destructive interference of light.įigure 1, Diffraction Orders from a Double Slit This structure can be regular slits or index variations in transmission or ruled lines in a mirror surface in reflection. Reference papers used in the development of this calculator can be found in the Bibliography at the end of this note.Īn optical grating acts as a wavelength dispersive element by diffracting or refracting light from a periodic structure. The tool calculates grating performance using a scalar theory of diffraction 1. The LightMachinery Grating calculator is a simple design tool for determining the approximate performance of a grating, taking into account basic grating parameters like blaze angle, ruling period, and length. Grating based spectrometers and monochromators are industry staples for spectral analysis.
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