A2 - Digital Scanning

                                   A2 - Digital Scanning

    We were tasked to recreate digitally scanned hand-drawn graphs. I used Image J to locate the pixel locations on the graph and Microsoft Excel to tabulate their coordinates. 

The original scanned image , generously donated by my classmate Justine Carpio is shown below

                        

                       Fig 1. Original image of hand-drawn graph digitally scanned and provided by Ms. Justine Carpio

     The hand-drawn graph describes the relationship between the spectral radiance L vs the wavelength of  blackbody sources at various temperatures. I chose to recreate the  plot corresponding to the blackbody source at 1895 K.  I cropped the graph from the above photo creating a new image file with dimensions 1036 x 1324. This is shown below

                                             

                              Fig 2. Cropped image of hand-drawn graph with dimensions 1036 x 1324 pixels

       I then used Image J to find the pixel locations of the tick marks in the x and y axes. The y-axis is in the logarithmic scale so tabulating the results for the pixel locations of the tick marks in  y-axis and its corresponding magnitude ( in log) I got the table below. The magnitudes are the physical variables which in this case are wavelength and spectral radiance.

     

y ticks pixels	Magnitude
1169	7
1008	8
849	9
691	10
531	11
371	12
211	13
54	14

  Table 1. Pixel location and magnitude of the physical variable ( Spectral Radiance) of the tick marks in the y-axis

Graphing it  and setting the linear trend line, I got the equation relating the pixel location a tick mark on the y-axis with its corresponding magnitude. This equation can then be used to find the magnitude on the y-axis of any point on the graph with a known y pixel location

                           

 Figure 3. Graph of Table 1 with the corresponding equation for the linear trend line giving the relationship between pixel location and radiance 

I repeated this with the tick marks on the x-axis and its magnitudes giving me the table 

x ticks pixels	Magnitude
175	0
334	1
491	2
650	3
812	4
974	5

 Table 2. Pixel location and magnitude of the physical variable ( Wavelength) of the tick marks in the x-axis

and its graph 

Figure 4. Graph of Table 2. with the corresponding equation for the linear trend line giving the relationship between pixel location wavelength

with the equation for the linear trend line, y=.0063x -1.0867 , which I used to find the x-magnitudes of points with known x pixel locations. 

   I tabulated the a and y pixel locations of 17 points on the curve corresponding to the 1895 K blackbody source  shown in the cropped image with dimensions 1036 x 1324 and applied the equations y=-.0063x + 14.332 to find the x-magnitudes and y=.0063x -1.0867 to find the y magnitudes which I tabulated. The process of using ratio and proportion is exercised by Microsoft Excel in the derivation of the trend line equation. I came up with the table shown below 

test x	test y		test x mag	test y mag
229	1170		0.356	6.961
235	1090		0.3938	7.465
243	1010		0.4442	7.969
251	927		0.4946	8.4919
259	850		0.545	8.977
270	768		0.6143	9.4936
287	690		0.7214	9.985
312	618		0.8789	10.4386
341	564		1.0616	10.7788
424	530		1.5845	10.993
494	546		2.0255	10.8922
576	566		2.5421	10.7662
657	596		3.0524	10.5772
735	624		3.5438	10.4008
818	650		4.0667	10.237
890	670		4.5203	10.111
980	688		5.0873	9.9976

 Table 3.  x and y pixel locations of 17 points chosen on the curve corresponding to the blackbody source as 1895 K and its computed magnitudes using the equations shown in Table 1 and 2.

where the columns text x and text y correspond to the pixel locations of the 17 chosen points and the columns test x mag and text y mag correspond to the magnitudes of these points in the x and y -axes. I graphed these magnitudes and made the background image of the plot a cropped image showing the curve of the blackbody source at 1895 K. The plot of the graph using the values from the table above almost matches the actual one as shown in the figure below. 

Figure 5. Final Output. Graph of the computed x and y magnitudes shown in Table 3 which is an attempted recreation of the plot shown in Figure 2 ( specifically the curve corresponding to the blackbody source at 1895 K). the recreated curve matched the actual curve. 

      Using the rubrik given in the 186 syllabus I believe I deserve a 10 in this activity because my images, text and tables are of excellent quality with captions that can definitely stand alone. My only flaw was that my recreated plot doesn't  perfectly match the original. My output however shows that I understood the lesson completely enough. Maybe I deserve 9.5 at worst but if we're rounding up then I think I get a should get a 10 :D yay.