Final Design Details

There are two accessible methods to disperse light and study its spectrum: dispersion using a diffraction grating and dispersion using a prism. There are certain advantages and disadvantages to both methods. The diffraction grating produces a wider angle of dispersion (the resulting spectrum is much wider than that of a prism, making it easier to work with), but produces several orders of the spectrum. These orders do not usually interfere with each other, unless they are of a higher order, but the unwanted orders still need to be considered. The diffraction grating dissipates the light a lot more than the prism and costs slightly more. The prism on the other hand is less expensive, produces only one diffraction pattern, and does not dissipate the light much. The only drawback is that the spectrum is narrow compared to that of a diffraction grating.

There are two methods to acquire the spectrum. One is to physically move a photodiode across the entire spectrum. The other is to arrange many diodes in an array and capture the spectrum all at once. The advantage of using the array is that it performs the acquisition very fast, and there are no mechanical errors due to motion. The disadvantage is that the resolution will be low, since the number of diodes is limited. The number is limited by cost, and also by the difficulty of placing two diodes very close together.

The spectrometer design which was chosen uses a prism to disperse visible light. The refractive index of the prism depends on the wavelength of light: red light will have a smaller refractive index than violet light. Since the light will leave the prism at different angles depending on the wavelength, it will be possible to use physical geometry to monitor the refracted light, and record a spectrum. The proposed design consists of three stages:

Stage 1: Collection Stage

The light from an LED will fall onto a slit, which is made out of aluminum foil. The width of the slit is less than 1mm, and ideally the emerging light will act as many point sources emanating along the slit. Only a part of the LED’s intensity passes through the slit, and one way to improve this would be to focus the incoming light onto the slit. However, this idea was not used because an appropriate lens was not available. After the light emerges the slit, light is focused onto an image plane using a convex lens.

Stage 2: Dispersion Stage

The prism will be kept fixed with the triangular face parallel to the horizontal surface, which will be the operating plane. The angle of incidence will be chosen by varying it and observing the best results. There are theoretical considerations for the best angle, which will be discussed later. The prism used is a SF18 uncoated equilateral prism. The refractive index for red light (650nm) is 1.71492 and the refractive index for violet light (400nm) is 1.76917.

Below an angle of incidence of 50o total internal reflection occurs. The largest angular distance between the two spectral lines is achieved right after 50o, but ideally the operating angle of incidence should be around 70o. The reason is that a small change in the angle of incidence will not cause a drastic change in the angle of dispersion.

During the first stage the image of the slit was projected onto an image plane, and so the refracted light will still form an image of a slit at a different angle. Of course, if the light source has many wavelengths present then the image of the slit will be blurred in different colors.

Stage 3: Detection Stage

A regular silicon diode was chosen, because it is inexpensive and covers the visible spectrum. The diode will be mechanically moved across the whole spectrum, and will provide information about position vs intensity. The position can then be converted to wavelength. A microcontroller will be used to move the diode and read the data.

Electrical Design