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MathGroup Archive 1996

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deconvolution programm

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4074] deconvolution programm
  • From: nik at ksc.iasnet.ru
  • Date: Fri, 31 May 1996 01:34:15 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

I would like an evaluation of the following notebook.

Nikolai Berdunov
e-mail: nik at ksc.iasnet.ru

>Do you want this posted to the Mathematica newsgroup and mailing
>list?

>Steve Christensen
> (*^
> 
> ::[     frontEndVersion = "Microsoft Windows Mathematica Notebook Front End Version 2.2";
>         microsoftWindowsStandardFontEncoding;
>         fontset = title, "Arial", 24, L0, center, nohscroll, bold;
>         fontset = subtitle, "Arial", 18, L0, center, nohscroll, bold;
>         fontset = subsubtitle, "Arial", 14, L0, center, nohscroll, bold;
>         fontset = section, "Arial", 14, L0, bold, grayBox;
>         fontset = subsection, "Arial", 12, L0, bold, blackBox;
>         fontset = subsubsection, "Arial", 10, L0, bold, whiteBox;
>         fontset = text, "Arial", 12, L0;
>         fontset = smalltext, "Arial", 10, L0;
>         fontset = input, "Courier New", 12, L0, nowordwrap, bold;
>         fontset = output, "Courier New", 12, L0, nowordwrap;
>         fontset = message, "Courier New", 10, L0, nowordwrap, R65280;
>         fontset = print, "Courier New", 10, L0, nowordwrap;
>         fontset = info, "Courier New", 10, L0, nowordwrap;
>         fontset = postscript, "Courier New", 8, L0, nowordwrap;
>         fontset = name, "Arial", 10, L0, nohscroll, italic, B65280;
>         fontset = header, "Times New Roman", 10, L0, right, nohscroll, italic;
>         fontset = footer, "Times New Roman", 10, L0, right, nohscroll, italic;
>         fontset = help, "Arial", 10, L0, nohscroll;
>         fontset = clipboard, "Arial", 12, L0, nohscroll;
>         fontset = completions, "Arial", 12, L0, nowordwrap, nohscroll;
>         fontset = graphics, "Courier New", 10, L0, nowordwrap, nohscroll;
>         fontset = special1, "Arial", 12, L0, nowordwrap, nohscroll;
>         fontset = special2, "Arial", 12, L0, center, nowordwrap, nohscroll;
>         fontset = special3, "Arial", 12, L0, right, nowordwrap, nohscroll;
>         fontset = special4, "Arial", 12, L0, nowordwrap, nohscroll;
>         fontset = special5, "Arial", 12, L0, nowordwrap, nohscroll;
>         fontset = leftheader, "Arial", 12, L0, nowordwrap, nohscroll;
>         fontset = leftfooter, "Arial", 12, L0, nowordwrap, nohscroll;
>         fontset = reserved1, "Courier New", 10, L0, nowordwrap, nohscroll;]
> :[font = subtitle; inactive; nohscroll; center; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; 
fo
> ntColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Arial"; fontSize = 18; ]
> Three-Dimensional Deconvolution Programm for Reconstraction of Atomic Force Microscopy Image
>  
> :[font = section; inactive; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fo
nt
> ColorGreen = 0; fontColorBlue = 0; bold; fontName = "Arial"; fontSize = 14; ]
> Discussion and Implementation
> 
> :[font = text; inactive; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontC
ol
> orGreen = 0; fontColorBlue = 0; plain; fontName = "Arial"; fontSize = 12; ]
> Well-knowing problem of Atomic Force Microscopy (AFM) technique is obtaining of the true surface image since AFM imag
e 
> is a surface-tip convolution. 
> Evidently that the greater is  the Tip, the greater is Image distortion and conversely. And the less is structure wic
h 
> we want observing, the less must be the Tip,It is hopeless case. We suggest the our algorithm until the problem is te
ch
> nology insoluble.
> 
> :[font = subsection; inactive; ]
> Example
> 
> :[font = text; inactive; startGroup; Cclosed; ]
> As an illustration our algorithm we use cubic structure on the plane
> 
> :[font = input; endGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorR
ed
>  = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ]
> Nt=5; Ny=40; Nx=40;
> Tip=Table[(51.+(x^2+y^2)),{x,-Nt,Nt},{y,-Nt,Nt}];
> Samp=Table[If[i>15 && j>15 && i<25 && j<25,25,0],{i,Ny},{j,Nx}];
> New=Table[0,{i,Ny-2 Nt},{j,Nx-2 Nt}];
> l2:=Table[GrayLevel[1],{i,Ny-2 Nt-1},{j,Nx-2 Nt-1}];
> q1=ListPlot3D[Samp[[Range[Nt+1,Ny-Nt],Range[Nt+1,Nx-Nt]]],
> l2,PlotRange->{All,All,{-5,40}}];
> :[font = text; inactive; startGroup; Cclosed; ]
> 
> and semispherical Tip.
> :[font = input; endGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorR
ed
>  = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ]
> Tip1=Table[(51.+(x^2+y^2)),{x,-2Nt,2Nt},{y,-2Nt,2Nt}];
> l2:=Table[GrayLevel[1],{i,4 Nt},{j,4 Nt}];
> q1=ListPlot3D[Tip1,l2,PlotRange->{All,All,{Min[Tip],140}},
> ViewPoint->{1.566,-2.890,0.803}, Boxed->False,Axes->False];
> :[font = text; inactive; startGroup; Cclosed; ]
> Then result of Tip-scaning on Surface.(It will be dependent on the cub and sphere size).
> 
> :[font = input; endGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorR
ed
>  = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ]
> Do[New[[i,j]]=Min[N[Tip-Samp[[Range[i,2 Nt+i],
> Range[j,2Nt+j]]]]],{i,Ny-2 Nt},{j,Nx-2 Nt}];
> l2:=Table[GrayLevel[1],{i,Ny-2 Nt-1},{j,Nx-2 Nt-1}];
> q1=ListPlot3D[Max[New]-New,l2,PlotRange->{All,All,{-5,40}}];
> :[font = text; inactive; startGroup; Cclosed; ]
> And new Image is obtained by using Deconvolution Algorithm.  
> This is case of no full reconstraction. It is determined by contact Tip with  Surface do not all points.
> Otherwise will be seen a full reconstruction and new Image will be identical to initial Image.
> 
> :[font = input; endGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorR
ed
>  = 0; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ]
> Table[Samp[[i,j]]=0,{i,Ny},{j,Nx}];
> Table[Samp[[i,j]]=New[[i-Nt,j-Nt]],{i,Nt+1,Ny-Nt},{j,Nt+1,Nx-Nt}];
> Do[New[[i,j]]=Min[N[Tip-Samp[[Range[i,2 Nt+i],Range[j,2Nt+j]]]]],
> {i,Ny-2 Nt},{j,Nx-2 Nt}];
> l2:=Table[GrayLevel[1],{i,Ny-2 Nt-1},{j,Nx-2 Nt-1}];
> q1=ListPlot3D[30-Max[New]+New,l2,PlotRange->{All,All,{-5,40}}];
> :[font = help; inactive; nohscroll; ]
>  For question and more information You should be adressed :
> :[font = name; inactive; nohscroll; ]
> Kazan Physical Technical Insitute
> Nikolai Berdunov
> e-mail: nik at ksc.iasnet.ru
> or        Nikolai.Berdunov at ksu.ru
> ^*)$
> 
> 


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