About Tracker and wavelength measurement

Tracker is a video analyzer and modelling software created by Douglas Brown^4,5 (Brown, 2008; Brown & Cox, 2009) and is a project of the Open Source Physics⁶. This software is frequently used for motion studies in mechanics, but also optics as recently reported⁷.

Tracker software has a tool called Line Profile that allows users to measure the intensity of the image pixels along a straight line with length defined by the user. One can increase the line width changing the spread value; image pixels above and below the line are averaged in order to reduce noise and/or increase sensitivity. So we can detect the maximum and minimum intensity of light along a line in an image and the distance between them, in pixels or, after calibration, in meters. This means that we can use this tool to identify the peak of intensity of each color line in a light spectrum, with more accuracy than the human eyes!

Spectrometer construction

The spectroscope can be built using a commercial transmission diffraction grating (the typical setup for a pocket spectroscope), replacing the eye with the camera (figure 2). The most simple is placing a grating in front of the camera lens (with some adhesive tape), and then make a thin slit to put it in front of the source light in order to create a thin line spectrum. In our case we used two razor blades close to each other. This setup usually requires a darkened room.

Figure 2.

Experimental setup. C - digital camera; TG - transmission grating; S - screen; SL - spectral lamp; A - aperture.

The slit aperture must be narrow enough to resolve the spectral lines detected by the camera. The width of the lines is important in determining the correct wavelength of each line.

The positions of the colors on the screen, as seen from the camera, correspond to the different wavelengths within the light beam. These wavelengths can be computed using Tracker tools, after calibration of the device (shown in the following). The transmission grating needs to be chosen according to the camera lens: a high number of lines/mm increases the spectral resolution, but it also increases the diffracting angle which can be a problem if the spectral lines go out of the optical field of view.

The novelty in our work is that with very simple, common and affordable materials such as a camera and a diffraction grating, we can build a spectrometer with very good resolution (accuracy of about 2 nm/pixel in our case, but it depends on the quality of the image). This can be calibrated using only a well-known light source.

So far we have considered the ideal situation when all spectral lines are aligned in the plane of the screen. However this may not be entirely true because of the lens distortion.

Spectrometer calibration

The calibration is done using a light source with a well-known spectrum (a sodium lamp or an economizer lamp).

The calibration must be done before measuring the spectra of any light source, because it depends on the experimental conditions of the setup – usually a simple shot with a calibrating light is enough.

In schools, teachers can also use any available spectral lights from sodium or Helium lamps, but we do not recommend Hydrogen lamp due to the complex spectrum of H₂. Teachers can also use other available light sources, such as a commercial He-Ne laser. We recommend not pointing the laser directly to the camera lens because this can damage the camera CCD; instead point it to a white background (e.g. a white sheet of paper) behind the slit.

After capturing an image of the laser spectrum, Tracker can be used to calibrate the image dimensions as described in Rodrigues & Carvalho⁷.

Experimental measurements

The first thing to implement is the experimental setup. We can place the camera with the grating in front of the aperture from which light comes from the spectral lamp, as represented in figure 2. The relative positions of the camera and screen must not move along all the experiment (otherwise, calibration must be restarted). Using the opaque tube setup we avoid this problem. Photo resolution must also be fixed for all the photos.

We then need to control the light intensity coming into the camera and the shutter speed: high light intensity creates bright spectral lines but can blur the spectra; however with very low light intensity, some lines can become “masked” in darkness. Therefore some photos must be taken in order to identify the best experimental shooting conditions and the spectral lines. The photos can be taken in normal room light or in a dark room for more beautiful spectrum photos. The more dark the image background the more visible are the intensity peaks of the spectrum lines.

Starting with the simplest spectra, the Sodium, the yellow spectral line (which, in fact, are two) at 590 nm corresponds in figure 3 to an average displacement x from the central line of about 330.4 pixels. The average displacement was used to minimize the misalignment between the camera, the grating and the plane of the slit. From equation (2), we can calculate the effective distance D in pixels, which will be fixed for the whole experiment and corresponds to our most important calibration parameter.

Figure 3.

Plot of Tracker main view showing the central and the yellow spectral lines of Sodium, and the corresponding light profiles. In the photo (left side), the distance is measured in pixels; in the plot (right side), the distance is converted to wavelength via equation (2).

The conversion from pixels to wavelength can be done using an Excel sheet, but in a more easy way it can be done with Tracker, using equation (2) in the Data Builder tool. This way allows students to analyze spectrum light directly in the Tracker’s plot as shown in figure 3.

Tests of this setup were made with Mercury, Helium and economizer lamps, with a grating of 530 lines/mm (distance between rulings, d = 1/530 mm).

The maxima for each spectrum were measured by Tracker’s measuring tool Line Profile.

The average distances from the central line to each line of the first constructive interference pattern in all lamps are presented in Table 1, together with the corresponding values referred in literature.

Table 1:

Wavelengths of spectral lines of helium and mercury bulbs, after calibration with the sodium lamp. The accuracy is about 2 nm. The experimental values are compared with those found in literature.

Results above confirm that the major Mercury lines are easily identified on its spectrum. Therefore we can use commercial economizer lamps to calibrate the low-cost spectrometer.