A picture of the output of my program can be seen below. The basic set-up of the spectrometer consists of a beam of light hitting a focusing mirror. After reflecting off the mirror, the beam hits a diffraction grating, where the light is diffracted different angles depending on the wavelength. The diffracted light hits a microchannel plate, which is a plate that basically emits electrons when a photon hits it. The electrons from the microchannel plate hit a phosphor plate that is positioned behind it. When the electrons hit the phosphor plate, the phosphor plate fluoresces, which creates a mark on the plate in the visible portion of the electromagnetic spectrum.
A model of the experimental set-up. A beam of light hits a focusing mirror, hits a diffraction grating and the light diffracts based upon its wavelengths. Only the zero, first, and second order diffraction are shown in this picture.
In the program, all positions and angles are variables. Thus, all these variables are changed in order to find the effect each component has on the width, positions and separation of the spectral lines that are shown on the phosphor plate.
In order to make sure my focusing mirror was working correctly I generated this picture.
This is a picture of parallel beams of light hitting a spherical mirror with a radius of convergence of 3 meters. According to this picture, the light focuses at the point 1.5 m, which agrees with theory. Thus, I was convinced the mirror I modelled was working correctly.
From this model, the positions and the widths of each harmonic can be determined on the MCP. An example plot of the intensity of each harmonic on the MCP can be seen below. The position is given in meters, the intensity is given in arbitrary units.
From this data, and calculating the respective horizontal widths of each spectral line, a picture that shows the theoretical positions and widths of each spectral peak can be generated. The picture shown below is a theoretical representation of data that should be generated on the phosphor plate in the lab. This picture was made using Mathematica.
A theoretical spectrum of the 11th – 29th harmonic as it would be seen on the phosphor plate.
An example of a spectrum generated during an experiment can be seen below. The white mark in the center of this photo is a burn mark on the camera. Note: the phosphor plate used is burned in the center, so the spectral lines will be a lot less intense in the center due to the decreased efficiency of the phosphor plate.