How to compare two measurement datas from 2 different devices?

Hallo,

I have two different csv measurements(xyz) from 2 different devices. One is a device doing spiral scanning and other is an interferometer. Since both of the devices will give different xyz. I am scanning the same workpiece in both devices. In order to do better comparison, i believe i need xyz almost close to each other for the devices,so how can i do it? Is the interpolation over common grid (x,y) works or is there any other better options?

Answer 1

[Star Strider]

It would help to have the data, or at least a representative sample of it.

Without knowing more, I would create a grid over the dimensions of the (x,y) plane that included all those data, so the minimum of both the x-coordinates to the maximum of the both x-coordinates, and the same of the y-coordinates. You can create those grids using the ndgrid funciton. Then create surfaces of the data using the scatteredInterpolant function, and then use the ndgrid results to plot them.

That might go something like this --

x1 = linspace(1, 2, 10);
y1 = linspace(2, 3, 11);
z1 = randn(numel(x1), numel(y1));

x2 = linspace(2, 4, 12);
y2 = linspace(1, 5, 10);
z2 = randn(numel(x2), numel(y2));

[X1,Y1] = ndgrid(x1, y1);

figure
stem3(X1, Y1, z1, 'filled')
grid on
xlabel('X_1')
ylabel('Y_1')
zlabel('Z_1')
title('Data Set #1')

[X2,Y2] = ndgrid(x2, y2);

figure
stem3(X2, Y2, z2, 'filled')
grid on
xlabel('X_2')
ylabel('Y_2')
zlabel('Z_2')
title('Data Set #2')

●

FZ1 = scatteredInterpolant(X1(:), Y1(:), z1(:), 'nearest', 'none');
FZ2 = scatteredInterpolant(X2(:), Y2(:), z2(:), 'nearest', 'none');

x3 = linspace(min(min(x1),min(x2)), max(max(x1),max(x2)), 20);
y3 = linspace(min(min(y1),min(y2)), max(max(y1),max(y2)), 20);;

[X3,Y3] = ndgrid(x3, y3);

Z1i = FZ1(X3, Y3);
Z2i = FZ2(X3, Y3);

figure
stem3(X3, Y3, Z1i, 'filled', DisplayName='Z1i')
hold on
stem3(X3, Y3, Z2i, 'filled', DisplayName='Z2i')
hold off
grid on
legend(Location='best')
xlabel('X_3')
ylabel('Y_3')
zlabel('Z_3')
title('Data Sets Combined')

Much depends on your data and the result you want.

.

[Jes]

Is it ok, if i share 5 csv files?. but it is from same device. I did this thing to check the repeatability. Since these csv files have different xyz values.

[Star Strider]

Sure!

This takes a while to run.

t appears to work --

tic

files = dir('*.csv')

files = 5×1 struct array with fields:
    name
    folder
    date
    bytes
    isdir
    datenum

x1 = zeros(numel(files),1);
x2 = zeros(numel(files),1);
y1 = zeros(numel(files),1);
y1 = zeros(numel(files),1);

for k = 1:numel(files)
    A{k,:} = readmatrix(files(k).name);
    [x1(k,:),x2(k,:)] = bounds(A{k}(:,1));
    [y1(k,:),y2(k,:)] = bounds(A{k}(:,2));
    SzA = size(A{k})
    
    FZ{k} = scatteredInterpolant(A{k}(:,1), A{k}(:,2), A{k}(:,3), 'nearest', 'none');
    
    vn{k} = extractBefore(files(k).name, '.');
    
    figure
    % stem3(A{k}(:,1), A{k}(:,2), A{k}(:,3), '.')
    scatter3(A{k}(:,1), A{k}(:,2), A{k}(:,3), '.')
    xlabel('X')
    ylabel('Y')
    zlabel('Z')
    title(files(k).name)
end

SzA = 1×2

23691 3

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SzA = 1×2

23693 3

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SzA = 1×2

23690 3

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SzA = 1×2

23690 3

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SzA = 1×2

23690 3

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●

% [x1 x2]
% [y1 y2]

toc

Elapsed time is 4.123727 seconds.

xc = linspace(min(x1), max(x2), 2.5E+2);                % Reduce Interpolation Matrix Size
yc = linspace(min(y1), max(y2), 2.5E+2);                % Reduce Interpolation Matrix Size

[Xc,Yc] = ndgrid(xc, yc);

figure
hold on
for k = 1:numel(A)
    Z{k} = FZ{k}(Xc, Yc);
    % stem3(Xc, Yc, Z{k}, '.', DisplayName=vn{k})
    % stem3(Xc, Yc, Z{k}, '.', DisplayName=vn{k}, BaseValue=-4)
    hs = scatter3(Xc, Yc, Z{k}, '.', DisplayName=vn{k});
    hsc{k,:} = hs(1);
end
hold off
xlabel('X')
ylabel('Y')
zlabel('Z')
% title('Interpolated ''stem3'' Plots')
title('Interpolated ''scatter3'' Plots')
legend([hsc{:}], Location='best')
% axis('equal')
daspect([5 5 1])
view(-27,30)
grid on

toc

Elapsed time is 10.426519 seconds.

Zcat = cat(3,Z{:});

Zmean = mean(Zcat, 3, 'omitnan');
t95 = tinv([0.025 0.975],numel(Z)-1)

t95 = 1×2

-2.7764 2.7764

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Zsem = std(Zcat, [], 3, 'omitnan')/sqrt(numel(Z));

Zci025 = t95(1) * Zsem + Zmean;
Zci975 = t95(2) * Zsem + Zmean;

Summary_Stats = [mean(Zci025,'all','omitnan'); mean(Zmean,'all','omitnan'); mean(Zci975,'all','omitnan')]

Summary_Stats = 3×1

-1.4262 -1.4245 -1.4229

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figure
surf(Xc, Yc, Zmean, EdgeColor='interp')
% hold on
% surf(Xc, Yc, Zci025, EdgeColor='interp', FaceAlpha=0.5, EdgeAlpha=0.5)
% surf(Xc, Yc, Zci975, EdgeColor='interp', FaceAlpha=0.5, EdgeAlpha=0.5)
% hold off
colormap(turbo)
colorbar
xlabel('X')
ylabel('Y')
zlabel('Z')
% title('Mean of ''Z'' Data & 95% Confidence Intervals')
title('Mean of ''Z'' Data')

toc

Elapsed time is 16.147413 seconds.

% figure
% surf(Xc, Yc, Zci025, EdgeColor='interp', FaceAlpha=0.75, EdgeAlpha=0.75)
% hold on
% surf(Xc, Yc, Zci975, EdgeColor='interp', FaceAlpha=0.25, EdgeAlpha=0.25)
% hold off
% colormap(turbo)
% colorbar
% xlabel('X')
% ylabel('Y')
% zlabel('Z')
% title('Separate Confidence Intervals of ''Z'' Data')
% 
% 
% toc

% figure
% hold on
% for k = 1:numel(A)
%     surf(Xc, Yc, Z{k}, DisplayName=vn{k}, EdgeColor='interp')
% end
% hold off
% colormap(turbo)
% colorbar
% xlabel('X')
% ylabel('Y')
% zlabel('Z')
% title('Interpolated ''surf'' Plot')
% % legend(Location='best')
% % axis('equal')
% daspect([2,2,1])
% view(-27,30)
% grid on

toc

Elapsed time is 16.149665 seconds.

I reduced the sizes of the interpolation matrices to about 1% of their original sizes, in the interests of both memory usage and time. Change them as necessary.

Make appropriate changes to get the result you want.

EDIT -- (26 Sep 2025 at 17:03)

Added mean and coinfidence interval plots. However the confidence intervals are not easily visible (their differences from the mean are quite small), so I commented-out the plots of them.

EDIT -- (27 Sep 2025 at 15:24)

Converted stem3 plots to scatter3 plots to make them clearer,and because I could not get the 'BaseValue' name-value pair to work with the last stem3 plots. With the last one, it simply produced a completely black figure window.

.

[Jes]

Is it possible to get the final interpolated files with new XYZ into one csv? I would like to ask, if i have 10 csv files in one folder, where can i use it in the script? can i load the folder in the script?

[Star Strider]

Yes.

First, create the individual vectors for the concatenated 'X', 'Y', and 'Z' data, save them to a matrix or table (I chose a table here), then save the table to a .csv file.

Example --

tic

files = dir('*.csv');

NrFiles = numel(files)

NrFiles = 5

x1 = zeros(numel(files),1);
x2 = zeros(numel(files),1);
y1 = zeros(numel(files),1);
y2 = zeros(numel(files),1);

for k = 1:NrFiles
    A = readmatrix(files(k).name);
    [x1(k,:),x2(k,:)] = bounds(A(:,1));
    [y1(k,:),y2(k,:)] = bounds(A(:,2));
    FZ{k} = scatteredInterpolant(A(:,1), A(:,2), A(:,3), 'nearest', 'none');
    vn{k} = extractBefore(files(k).name, '.');
    fprintf('\nFile %d: %s', k, files(k).name)
end

File 1: Export5.csv
File 2: Export6.csv
File 3: Export7.csv
File 4: Export8.csv
File 5: Export9.csv

fprintf('\n\n')

toc

Elapsed time is 0.645423 seconds.

xcyclen = 2.5E+2;                                       % Vector Lengths Of 'xc' and 'yc' 
xc = linspace(min(x1), max(x2), xcyclen);               % Reduce Interpolation Matrix Size
yc = linspace(min(y1), max(y2), xcyclen);               % Reduce Interpolation Matrix Size

[Xc,Yc] = ndgrid(xc, yc);

figure
hold on
for k = 1:NrFiles
    Z{k} = FZ{k}(Xc, Yc);
    hs = scatter3(Xc, Yc, Z{k}, '.', DisplayName=vn{k});
    hsc{k,:} = hs(1);
end
hold off
xlabel('X')
ylabel('Y')
zlabel('Z')
title('Interpolated ''scatter3'' Plots')
legend([hsc{:}], Location='best')
daspect([5 5 1])
view(-27,30)
grid on

toc

Elapsed time is 6.791245 seconds.

Zcat = cat(3,[Z{:}]);
Xcr = repmat(Xc, 1, numel(Z));
Ycr = repmat(Yc, 1, numel(Z));

% Sizes = [size(Xcr); size(Ycr); size(Zcat)]

figure
scatter3(Xcr(:), Ycr(:), Zcat(:), '.')
xlabel('X')
ylabel('Y')
zlabel('Z')
title('Combined (Concatenated) Interpolated ''scatter3'' Plots')

figure
surf(Xcr, Ycr, Zcat, EdgeColor='interp')
colormap(turbo)
colorbar
xlabel('X')
ylabel('Y')
zlabel('Z')
title('''surf'' Plot of ''Z'' Data')

toc

Elapsed time is 13.943905 seconds.

Xcrv = Xcr(:);                                          % Create Vectors For 'table'
Ycrv = Ycr(:);                                          % Create Vectors For 'table'
Zcatv = Zcat(:);                                        % Create Vectors For 'table'

Concatenated_Data = table(Xcrv, Ycrv, Zcatv, VariableNames={'X','Y','Z'})

Concatenated_Data = 312500×3 table
       X          Y        Z 
    _______    _______    ___

     -10.95    -10.975    NaN
    -10.862    -10.975    NaN
    -10.774    -10.975    NaN
    -10.686    -10.975    NaN
    -10.598    -10.975    NaN
     -10.51    -10.975    NaN
    -10.422    -10.975    NaN
    -10.334    -10.975    NaN
    -10.246    -10.975    NaN
    -10.158    -10.975    NaN
     -10.07    -10.975    NaN
    -9.9825    -10.975    NaN
    -9.8946    -10.975    NaN
    -9.8066    -10.975    NaN
    -9.7187    -10.975    NaN
    -9.6307    -10.975    NaN

writetable(Concatenated_Data, 'Concatenated_Data.csv')

Check = readtable('Concatenated_Data.csv')

Check = 312500×3 table
       X          Y        Z 
    _______    _______    ___

     -10.95    -10.975    NaN
    -10.862    -10.975    NaN
    -10.774    -10.975    NaN
    -10.686    -10.975    NaN
    -10.598    -10.975    NaN
     -10.51    -10.975    NaN
    -10.422    -10.975    NaN
    -10.334    -10.975    NaN
    -10.246    -10.975    NaN
    -10.158    -10.975    NaN
     -10.07    -10.975    NaN
    -9.9825    -10.975    NaN
    -9.8946    -10.975    NaN
    -9.8066    -10.975    NaN
    -9.7187    -10.975    NaN
    -9.6307    -10.975    NaN

figure
scatter3(Check{:,1}, Check{:,2}, Check{:,3}, 15, Check{:,3}, '.')
colormap(turbo)
colorbar
xlabel('X')
ylabel('Y')
zlabel('Z')
title('''scatter3'' Plot of ''X'', ''Y'', ''Z'' Data From ''.csv'' File')

toc

Elapsed time is 16.038273 seconds.

Ths 'xcyclen' vslue (that determines the lengths of those vectors and therefore the size of the interpolation matrix) can be whatever you want. I chose a smaller value here to conserve memory and shorten processing time. This value is about 1% of the matrix sizes.

EDIT -- (30 Sep 2025 at 13:54)

There are several overlapping points, so calculaitng the mean of them (and the 95% confidence interval) simply requires one accumarray call for each metric (mean and standard error of the mean).

Example --

[G,Xs,Ys] = findgroups(Xcrv, Ycrv);
Zmean = accumarray(G,Zcatv, [], @(x)mean(x,'omitnan'));                 % Regional 'mean'

Zmeanm = reshape(Zmean, numel(xc), numel(yc));                          % Reshape Vector To Matrix

t95 = tinv([0.025 0.975],NrFiles-1)

t95 = 1×2

-2.7764 2.7764

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Zsem = accumarray(G, Zcatv, [], @(x)std(x,'omitnan')/sqrt(NrFiles));   % Regional SEM
Zsemm = reshape(Zsem, numel(xc), numel(yc));                            % Reshape Vector To Matrix
Zci95{1} = Zmean + t95(1) * Zsem;                                       % Lower 95% CI Bound Matrix
Zci95{2} = Zmean + t95(2) * Zsem;                                       % Upper 95% CI Bound Matrix

[Zmax,idx] = max(Zmean(:));
Ex_CI95 = [Zci95{1}(idx); Zmax; Zci95{2}(idx)]

Ex_CI95 = 3×1

-0.0022 -0.0019 -0.0016

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figure
surf(Xc, Yc, Zmeanm, EdgeColor='interp')
colormap(turbo)
colorbar
xlabel('X')
ylabel('Y')
zlabel('Z')
title('''surf'' Plot Of Mean ''Z'' Data')

toc

Elapsed time is 17.293416 seconds.

I did not plot the 95% confidence interval surfaces, since they are likely would not be visible. They are also extremely close to the mean surface, each separated from it by 0.0003.

EDIT -- (30 Sep 2025 at 15:54)

Saving the averages to a file is similarly straightforward, although recovering the matrices requires reshape calls --

Concatenated_Mean = table(Xc(:), Yc(:), Zmean(:), [Zci95{1}], [Zci95{2}], VariableNames={'Xc','Yc','Zmean','CI025','CI975'})

Concatenated_Mean = 62500×5 table
      Xc         Yc       Zmean    CI025    CI975
    _______    _______    _____    _____    _____

     -10.95    -10.975     NaN      NaN      NaN 
    -10.862    -10.975     NaN      NaN      NaN 
    -10.774    -10.975     NaN      NaN      NaN 
    -10.686    -10.975     NaN      NaN      NaN 
    -10.598    -10.975     NaN      NaN      NaN 
     -10.51    -10.975     NaN      NaN      NaN 
    -10.422    -10.975     NaN      NaN      NaN 
    -10.334    -10.975     NaN      NaN      NaN 
    -10.246    -10.975     NaN      NaN      NaN 
    -10.158    -10.975     NaN      NaN      NaN 
     -10.07    -10.975     NaN      NaN      NaN 
    -9.9825    -10.975     NaN      NaN      NaN 
    -9.8946    -10.975     NaN      NaN      NaN 
    -9.8066    -10.975     NaN      NaN      NaN 
    -9.7187    -10.975     NaN      NaN      NaN 
    -9.6307    -10.975     NaN      NaN      NaN 

Xv = Concatenated_Mean{:,1};
Yv = Concatenated_Mean{:,2};
Zv = Concatenated_Mean{:,3};

Xvu = unique(Xv);
Xdim = numel(Xvu)

Xdim = 250

Xmtx = reshape(Xv,Xdim,[]);
Ymtx = reshape(Yv,Xdim,[]);
Zmtx = reshape(Zv,Xdim,[]);

figure
surf(Xmtx, Ymtx, Zmtx, EdgeColor='interp')
colormap(turbo)
colorbar
xlabel('X')
ylabel('Y')
zlabel('Z')
title('''surf'' Plot Of Mean ''Z'' Data Read From Table')

toc

Elapsed time is 17.779619 seconds.

Warning: Hardware-accelerated graphics is unavailable. Displaying fewer markers to preserve interactivity.

Writing it to a .csv file and reading it would work similarly to the previous example.

EDIT -- (01 Oct 2025 at 00:26)

Improved code created in previous EDIT.

.

[Jes]

Hallo, I would like to ask you one doubt. If i have spirally scanned data from a sensor and a an interferometer data, both have different x,y and z, Due to high resolution of interferometer, it has high number of data points and spiral scanning have less number of data points. In this case, the biggest problem will be aligning both interferometer and sensor measurements in X and Y. So is there any ways to do the alignment?

[Star Strider]

I am not certain what you intend by 'alignment'. My code generates a common grid that is defined by the maximum and minimum of all the data (so it includes all the possible data points), and then interpolates the data from the various files onto that grid, in order to do statistics on tthem.

In that sense, they are 'aligned' onto the common grid. That result is plotted in the scatter3 plot titled 'Interpolated ''scatter3'' Plots'. The interpolated points from each file are plotted in different colours.

The grid can be made to have whatever resolution you want, providing that it meets the memory size constraints, and runs in the appropriate time limits that you find acceptable. Grids with greater resolution -- more points -- require more memory and require longer to run.

.

[Jes]

Hallo, thank you for your answer. Actually, my intention is to compare both the datas. The interferometer dara is reliable and i need to know, how much close the both datas to each other.Please ask me if you need more info.

[Star Strider]

My plesure.

It is not possible for me to determine what data comes from what instrument.

files = dir('*.csv');

for k = 1:numel(files)
    fprintf('\n====================\n%s --\n\n', files(k).name)
    T = readtable(files(k).name)
end

====================
Export5.csv --

T = 23691×3 table
     Var1       Var2       Var3  
    _______    _______    _______

    -0.4308    -10.967    -2.9385
    0.20761    -10.973    -2.9381
     0.8452    -10.941    -2.9377
     1.4798    -10.873    -2.9373
     2.1094    -10.767    -2.9369
     2.7316    -10.625    -2.9365
     3.3446    -10.448     -2.936
     3.9461    -10.235    -2.9356
     4.5342    -9.9871    -2.9351
     5.1068    -9.7057    -2.9346
      5.662    -9.3915    -2.9341
      6.198    -9.0456    -2.9335
      6.713    -8.6692    -2.9329
     7.2051    -8.2635    -2.9323
     7.6728    -7.8298    -2.9317
     8.1144    -7.3698     -2.931

====================
Export6.csv --

T = 23693×3 table
      Var1       Var2       Var3  
    ________    _______    _______

     -1.2266    -10.908     -2.939
    -0.59027     -10.96    -2.9386
    0.047999    -10.975    -2.9383
     0.68599    -10.953    -2.9379
      1.3216    -10.893    -2.9376
      1.9526    -10.797    -2.9372
      2.5769    -10.664    -2.9368
      3.1923    -10.495    -2.9364
      3.7969    -10.291    -2.9359
      4.3885    -10.052    -2.9354
      4.9652    -9.7791    -2.9349
      5.5249    -9.4731    -2.9344
      6.0659     -9.135    -2.9338
      6.5863    -8.7661    -2.9332
      7.0843    -8.3675    -2.9326
      7.5582    -7.9408     -2.932

====================
Export7.csv --

T = 23690×3 table
      Var1       Var2       Var3  
    ________    _______    _______

    -0.94065    -10.936     -2.939
    -0.30316    -10.971    -2.9387
     0.33526    -10.969    -2.9383
     0.97243     -10.93    -2.9379
      1.6062    -10.854    -2.9375
      2.2344    -10.742    -2.9371
       2.855    -10.593    -2.9367
      3.4659    -10.408    -2.9363
      4.0648    -10.188    -2.9358
        4.65    -9.9335    -2.9353
      5.2193    -9.6454    -2.9348
      5.7708    -9.3248    -2.9343
      6.3028    -8.9727    -2.9337
      6.8133    -8.5903    -2.9331
      7.3007    -8.1789    -2.9325
      7.7633    -7.7399    -2.9319

====================
Export8.csv --

T = 23690×3 table
      Var1       Var2       Var3  
    ________    _______    _______

      -0.877    -10.941    -2.9391
    -0.23932    -10.973    -2.9388
     0.39906    -10.967    -2.9384
       1.036    -10.924     -2.938
      1.6693    -10.845    -2.9376
      2.2969    -10.728    -2.9373
      2.9166    -10.576    -2.9368
      3.5263    -10.387    -2.9364
       4.124    -10.164    -2.9359
      4.7077    -9.9062    -2.9355
      5.2753    -9.6148    -2.9349
      5.8249     -9.291    -2.9344
      6.3548    -8.9359    -2.9338
      6.8631    -8.5505    -2.9333
       7.348    -8.1362    -2.9326
      7.8081    -7.6945     -2.932

====================
Export9.csv --

T = 23690×3 table
      Var1       Var2       Var3  
    ________    _______    _______

     -1.5118    -10.873    -2.9394
      -0.877    -10.941    -2.9391
    -0.23932    -10.973    -2.9388
     0.39906    -10.967    -2.9384
       1.036    -10.924     -2.938
      1.6693    -10.845    -2.9377
      2.2969    -10.728    -2.9373
      2.9166    -10.576    -2.9369
      3.5263    -10.387    -2.9364
       4.124    -10.164     -2.936
      4.7077    -9.9062    -2.9355
      5.2753    -9.6148     -2.935
      5.8249     -9.291    -2.9344
      6.3548    -8.9358    -2.9338
      6.8631    -8.5505    -2.9332
       7.348    -8.1362    -2.9326

None of the files have any identifying information in their names or other internal data that would allow me to determine their source.

If that information were available, one method of comparing them would be to calculate the root-mean-square difference between the data from from the interferometer and the data from the spiral scan.

Another approach would be to calculate the mean of the interferometer data and then compare that to the mean of the data from the spiral scan, probably using the roor-mean-square approach.

I would calculate the means the same way I calculated 'Zmean' previously.

The easiest way would be to interpolate them to the same grid, and then do the calculations.

These are your data. How would you want to do that comparison?

.

[Jes]

Thank you so much. Actually, there is no file from Interferometer here. The interferometer data is in .dat format. I am not sure, whether that is work with MATLAB. If yes, i can share it by tomorrow.

[Star Strider]

My pleasure!

A '.dat' format file could be anything. If it is a text file, MATLAB should be able to import it, although that could require some experimentation. If it is a binary file, any information you can share about it would be helpful.

[Jes]

I think its binary file

[Star Strider]

In that instance, I need to know how best to read it.

See the documentation on the fread function for details on the information I will need in order to read it correctly (or read it at all, for that matter). The documentation for the interferometer should provide that information. Please include all those details.

I will most likely use fread to import it, since I doubt there are any other options.

If the interferometer has the option to export the data as a MATLAB .mat file or text (for example .txt or .csv) or Excel (.xlsx) file, that would make importing the information easier. The documentation should have that information.

[Jes]

I think, there is an option of csv file. but it is showing NaN when i tried to open in excel

[Jes]

I have a doubt, is the interpolation on common grid x and y of interferometer works for sensor? Means is it possible to use the x and y of the interferometer to find the corresponding z of the sensor by interpolation? if it is not possible please correct me

[Star Strider]

(1) Since .csv files are text files (or should be text files), see if you can open the .csv file in a text editor. Upload it here anyway to see if I can read it. Also, the .dat file may not be able to be uploaded here as a .dat file. Use the zip function to put it in a .zip file and then upload the .zip file. That should work. (I forgot to mention that earlier.)

(2) Interpolating to a common grid should work for any set of values from all instruments. The x and y coordinates should have the same units of measurement and approximately the same values, or a way to convert them to the same range of values. With a grid of appropriate resolution (high number of points) the interpolation should be nearly exact. It may not be as exact here because of the size and time constraints, however you will be able to use the working code to create your own high-resolution grid to get acceptable results.

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