Calculates histogram of facet slopes in atomic force microscopy (AFM) images. See Surface and Interface Analysis 25 (1997) 74.

//Calculates a histogram of slopes of facets in AFM images.  See Chatelier et al. in Surface and Interface Analysis 25 (1997) 741.
//Similar to the output of Gwyddion image analysis software after selecting Data Process-->Statistics -->Slope Distribution --> Inclination (theta)
//Assumes that the AFM image has been plane filtered, is loaded into a 2D wave, and has heights in nanometers
Function slope_freq(w1) 
	wave w1
	variable X_index, Y_index, totalcycles=0, array_size, mini_wave_scaling=1
	Prompt mini_wave_scaling, "Enter nm/point value: " // Set prompt for x-y scaling (example:  this should be ~9.78 nm/point for a 512  x 512 pixel image that is 5 microns on a side)
	DoPrompt "nm/point", mini_wave_scaling
	if (V_Flag)
		return -1 // User canceled
	endif
	RemoveFromTable slopes, mini_x, mini_y	//probably could comment out all of the remove/kill statements, but they can be useful.  They will cause errors the first time the function is used.
	Killwaves slopes, mini_x, mini_y
	make/N=3 mini_x
	make/N=3 mini_y
	SetScale/P x 0,(mini_wave_scaling),"", mini_x
	SetScale/P x 0,(mini_wave_scaling),"", mini_y
	wavestats/Q w1
	array_size=V_npnts
	make/N=((array_size^0.5-2)^2) slopes
	for (X_index=1; X_index<(array_size^0.5-1); X_index+=1)
			for (Y_index=1; Y_index<(array_size^0.5-1); Y_index+=1)
				mini_x=w1[Y_index][(p+X_index-1)]
				curvefit/Q line mini_x
				variable dzdx=k1
				mini_y=w1[(p+Y_index-1)][X_index]
				curvefit/Q line mini_y
				variable dzdy=k1
				slopes[totalcycles]=(atan((dzdx^2+dzdy^2)^0.5)/(2*pi))*360  //slopes in degrees are between the normal of the facet and the nominal sample normal
				totalcycles+=1
			endfor
	endfor
	AppendToTable slopes
	Histogram/B={0,0.1,900} slopes,slopes_Hist	 //Bin slopes of 0-90 degrees into histogram.  Typically need to duplicate slopes and slopes_Hist waves into other wavenames to save results
End