A1 - Digital Scanning

I obtained this plot from Canadian Journal of Physics dated 1953.

The following table shows the pixel locations of the tick marks for both X and Y axes of the digitally scanned plot.

along x
points	px	py
0	140	1129
0.2	271	1129
0.4	401	1129
0.6	531	1129
0.8	661	1129
1	791	1129
along y
points	px	py
0	140	1129
4	140	994
8	140	859
12	140	724
16	140	589
20	140	457
24	140	324
28	140	190
32	140	60

To obtain a conversion factor (pixel/unit) for each axis, simply count the number of pixels that lie within each tick mark. For cases wherein the number of pixels within tick marks of one axis ( Y-axis in my case) varies, average the values to obtain a general conversion factor. The values I obtained are the following:

x-axis: 130.2 pixels/unit (unit in this case, means, within one tick mark)
y-axis: 133.625 pixels/unit

These values are then used to obtain physical values of the points on the graph. The next step is to get the pixel values of the points the graph. I obtained the following for the scanned plot shown above.

px	py
203	998
267	936
331	879
398	824
461	773
528	722
591	665
658	602
721	459
780	58

Using the conversion factor (pixel/unit) for both axes, I obtained the following physicals values by dividing the pixel values with the conversion factor. (i.e. px/130.2 for x location values)

x	y
1.559139785	7.468662301
2.050691244	7.004677268
2.542242704	6.578110384
3.056835637	6.166510758
3.540706605	5.78484565
4.055299539	5.403180543
4.539170507	4.976613658
5.053763441	4.505144995
5.537634409	3.434985968
5.99078341	0.434050514

I then used Excel to plot these values and see if the same trend as the scanned plot will be observed. (Note: Image origin is different from Excel. Image origin is on the upper left corner of the image while Excel is on the lower left. For comparison, in plotting the physical values in Excel, plot values in reverse order.) This is how the plot in Excel looks The trend is much obvious with the original image superimposed on the plot. ...
Rating 10 - The trend I obtained in re-plotting the scanned copy was similar to the original plot.
...
Thanks to...
...Benj Palmares for helping with the Excel, especially with superimposing the original image. ...Jeric Tugaff for pointers in paint. _________________________________________________________________________________

A1 - Digital Scanning EDITED VERSION: posted June 19, 2008

I obtained this plot from Canadian Journal of Physics dated 1953.

The following table shows the pixel locations of the tick marks for both X and Y axes of the digitally scanned plot.

along x
points	px	py		pixel values included within each tick mark
0	136	1126		135
0.2	271	1126		130
0.4	401	1126		131
0.6	532	1126		131
0.8	663	1126		131
1	794	1126	average	131.6

along y
points	px	py		pixel values included within each tick mark
0	136	1126		134
4	136	992		133
8	136	859		135
12	136	724		135
16	136	589		132
20	136	457		134
24	136	323		133
28	136	190		131
32	136	59	average	133.375

To obtain a conversion factor (pixel/unit) for each axis, simply count the number of pixels that lie within each tick mark. Then, average the values to obtain a general conversion factor. The values I obtained are the following:

x-axis: 131.6 pixels/one tick mark
y-axis: 133.375 pixels/one tick mark

These are then used to obtain physical values of the points on the graph. The next step is to get the pixel values of the points the graph. I obtained the following for the scanned plot shown above.

px	py
203	998
267	936
331	879
398	824
461	772
528	721
590	665
658	602
721	458
780	58

Using the conversion factor for both axes, I obtained the following physicals values by dividing the pixel values with the conversion factor. (i.e. px/131.6 for x location values). These physical values, however, should be biased in order to properly correlate the points with those present in the image. Therefore, for both x and y, I subtracted the physical value of the origin from x physical values and y physical values (i.e. x biased = x-(136/131.6) and y biased = y-(1126/133.375)).

x	y
1.542553191	7.482661668
2.02887538	7.017806935
2.515197568	6.590440487
3.024316109	6.178069353
3.503039514	5.78819119
4.012158055	5.405810684
4.483282675	4.985941893
5	4.513589503
5.478723404	3.433926898
5.927051672	0.434864105

x biased	y biased
0.509118541	-0.959700094
0.995440729	-1.424554827
1.481762918	-1.851921275
1.990881459	-2.264292409
2.469604863	-2.654170572
2.978723404	-3.036551078
3.449848024	-3.456419869
3.96656535	-3.928772259
4.445288754	-5.008434864
4.893617021	-8.007497657

I then used Excel to plot these values and see if the same trend as the scanned plot will be observed. This can be done because the points which are now biased according to the origin can be plotted in a manner that will coincide with your scanned image given that you overlay a properly cropped image, that is cropped at the pixel value of the origin. One should also be careful in overlaying the image to your Excel plot, therefore check the limits of both your x and y axes to see if proper correlation with your cropped image is observed. The following shows the Excel plot.

The following shows the Excel plot with an overlay of the cropped image.

---
Thanks to...
... Dr. Maricor Soriano for pointing out my mistake, giving tips on how to correct that mistake and for giving me a second chance at a 10. :)