The spectral estiraates 

 The spectral estimates U(r, s) are shown in figures 11.9, 11.10, and 

 11.11. Figure 11.11 is the average of figures 11.9 and 11,10, The values 



plotted at the grid intersections should be divided by 1000 to put them in units 



2 2 



of (ft) . The contours are correctly labeled in units of (ft) . As described in 



Part 8, the spectra have the property that the same value is obtained at U('»r,'=-s) 

 as was obtained at Ufrps). If these figures are cut in half by a line through the 

 origin, the sum of the Ufrss) values on one side of the line will equal the vari- 

 ance of the spot height data. 



The contours do not give a true representation of the shape of the spectrum. 

 As drawn, they represent an estimate of the volume under the true spectrum 

 when integrated over a square of the size shown in the figure and centered at the 

 contour position. Thus steep slopes in the spectral surface teiid to be smoothed 

 out. 



These spectra due to the errors hinted at above also have errors in them. 



The region of analysis should be exactly square. The area shown is rectangular 



and in actuality the area a.nalyzed should be as high as it is wide. Seven rows 



of numbers have been omitted from the top and bottom of the figures. At the 



top of the figure above the dash dot line and at the bottom of the figure below 



the dash dot line the omitted numbers were all slightly negative. Near the 



bottom and top edges they were of the order of •»002 (ft)^ Moreover, near the 



left and right edges along the r axis of the figures there are considerable areas 



of negative values with some values of -0.024 (ft) , 



161 



