Activity 2 - Digital Scanning

For today's activity, we first obtained a scanned image of a handwritten plot. I took mine from a paper from the Proceedings of the 4th National Physics Congress, 1985 (exact paper and authors to follow!). The task is to reproduce the plot by obtaining the conversion factor between the number of pixels in the scanned image to the physical variable that the plot represents.

The plot I chose shows the graph of impulse squared (in million K/m^2) versus the distance (in cm) of a glider that moves in an airtrack before colliding with a bumper. The exact methodology is described in the paper. The graph is supposed to reflect the relationship of energy, impulse and momentum.

First, I tabulated the pixel values for each tick mark on the x-axis, which corresponds to the distance in centimeters. I did the same for each tick mark on the y-axis. However, it can be seen from the graph that there are two trials recorded (because there are two sets of data points). I obtain two conversion factors: one for cm-to-pixel and another for impulse-to-pixel. 

0.076488 cm per pixel

0.309547 million K/m^2 per pixel

Next, I selected the first few points in the graph and obtained the coordinates in pixels. Using the above conversion factors I was able to plot the pixel values in their corresponding physical values. Also, since it can clearly be seen that the graph is linear, it is only a simple matter to interpolate and obtain the remaining points for the graph.

Lastly, to check if I was able to satisfactorily reproduce the graph, I overlaid the original scanned plot (cropped to show only the plot itself) and the tabulated data. The result is shown below.

I think this is a very satisfactorily reproduced plot, as it can clearly be seen that the plot points correspond. In my reproduced plot, I assigned different colors for the two trials to differentiate them. The trend line is from the original plot, and from that I can see that the original and replotted points coincide well.

While doing this activity, I was thinking that most of the tasks here are mechanical, that is, one should be very careful in doing the experiments. No skill level needed, actually, you just have to know how to read pixel values. We've been doing this method in previous courses already. We used to have photographs of our oscilloscope data (mostly in Electronics lab class) and then we read the pixel values to reproduce the plots that we obtained. It's a very handy yet still crude way to collect raw data from photographs. Our only problem was the accuracy of the method. However, as long as the trend is preserved, we generally prefer to do this rather than to painstakingly record each data point on paper. The rest is manipulation through a spreadsheet program.

Grade I give myself: 12/10. Aside from being able to reproduce my graph, I was able to do the bonus task of overlaying the original picture onto the reproduced graph.