1. Digital Scanning

Before the advent of Excel, MATLAB, Python, LabView and the whole arsenal of scientific computing software at our disposal, our predecessors plotted their data manually on paper and smoothing was done with the almighty french curves.

Applied Physics 186 or Instrumentation 2 is a course on Digital Image Processing. For our first activity, we searched for old hand drawn plots of scientific data. The aim of the activity is to reproduce the plot using a spreadsheet software.

Figure 1 is a plot of Butyl rubber’s continuous and intermittent stress relaxation at 130 Centigrade and 50% elongation. The y-axis is the ratio of stretched and unstretched length. The x-axis is time in hours. For this activity, the plot of interest is the continuous stress relaxation (Fig. 2).

Original hand drawn plot
Plot of continuous stress relaxation

To reproduce this plot, the numerical values of each data point was determined. As a digital image, the pixel location of each data point can be easily obtained. I used Inkscape, a vector graphics program, to determine each pixel location.

To convert each data point to numerical values, one must determine the conversion factor for the x and y axes.

conversion factor (CF) = (Nmax-Nmin)/(Pmax-Pmin)

For the y-axis,
CF = (10-0)(340.39-109.24)

where 340.39 and 109.24 are the pixel locations corresponding to 10 and 0 along the y-axis. The same procedure is done for the x-axis.

The numerical value for a data point is simply,

N = CF x (P-Pmin)

Armed with the numerical value of each data point, a reproduction of the original plot can be easily generated using the OpenOffice Calc and applying cubic spline smoothing.

Original plot and reproduction

The superposition of the reproduction and original was easily generated with David’s tip from Dr. Soriano’s blog. Thanks to Dr. Soriano for the advice and the CS Lib staff for allowing me to use the journals without finishing my registration.I give myself a 10 in this activity. I finished it on time and I like the final plot. Conversion was successful, with small deviations that can be from the image being skewed when it was photocopied or scanned. Some difficulty was encountered during the superposition of the reconstruction with the original data. One must remember to restart their OpenOffice Calc after uploading the original image as bitmap area fill.

References:
1. M. D. Stern and A. V. Tobolsky. Stress-Time-Temperature Relations in Polysulfide Rubbers. Journal of Chemical Physics. Vol. 14, No. 2. 1946.
2. E. David. Inserting Images as Background for OpenOffice Calc Graphs. 2008.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s