how to plot frequency vs distance surface plot from frequency vs wave-vector surface plot?

This type of dispersion plot I have. I want to convert it to f vs distance plot.

Answer 1

[Charu]

Hello Amrit,

From my perspective you are trying to plot a frequency v/s distance surface plot from a frequency v/s wave-vector surface plot.

You might consider using the relation (\lambda = \frac{v}{f}) if the speed of propagation (v) is known, which could help in determining the distance under specific conditions. If the data is not readily available, another approach could be to extract it from the graph using MATLAB functions of image processing toolbox. Here is how you can do it:

1. Load and preprocess the image using “imread” to load the image and “rgb2gray” to convert it into greyscale.
2. Enhance the image using “imadjust” and then apply edge detection function “edge”.
3. Use “bwlabel” and “regionprops” to identify and extract the centroids of the plot lines.
4. Convert pixel to data coordinates by mapping the pixel coordinates to actual data coordinates using known axis scales.

Here is a code snippet for that:

img = imread('plot_image.png'); 
grayImg = rgb2gray(img); 
enhancedImg = imadjust(grayImg); 
edges = edge(enhancedImg, 'Canny'); 
[labeledImage, numObjects] = bwlabel(edges); 
stats = regionprops(labeledImage, 'Centroid'); 
centroids = cat(1, stats.Centroid); 

After extracting the data convert the wave-vector data to distance with the relation (\lambda = \frac{2\pi}{k}). To create a surface plot in MATLAB for a function f versus distance, you can use the ‘surf’ function as shown below:

surf(d, f, Z);  
%where d is distance, f is frequency 
% You can replace the function Z with your specific data or function to visualize.

To know more about the functions used you can refer to these documentation links given below:

‘surf’: https://www.mathworks.com/help/matlab/ref/surf.html

‘edge’:https://www.mathworks.com/help/images/ref/edge.html

‘bwlabel’: https://www.mathworks.com/help/images/ref/bwlabel.html

‘rgb2gray’:https://www.mathworks.com/help/matlab/ref/rgb2gray.html