Extract wavelength from an image using FFT

I'm doing some experiments to study the effects of acoustics on an oil-in-water emulsion. The emulsion forms patterns like shown in the attached image and I'm trying to extract the wavelength from this image using 1D FFT.

I think I have to invert the image data and apply fft then plot it to find the peak which should be the wavelength.

I'm sharing some of the work I've done.

clear all;

close all;

clc;

warning off;

% [file,path] = uigetfile;

%

% filename = [path file];

filename = 'image.jpg';

Z = imread(filename);

% process image

Z = imboxfilt(Z); % apply filter to reduce noise

Zeq = imadjust(Z); % enhance constrast

Zinv = max(max(Zeq))-Zeq; % invert color scheme

% pixel scale

% formula: 0.1553374 microns * (60/obj) *(bin/mag)

pscale = 0.1553374*(60/4)*(1/1);

%pscale = 1;

Zavg = mean(Zinv); % average intensities

X = pscale*[1:1:length(Zavg)];

Ts = mean(diff(X));

Fs = 1/Ts;

% Sampling frequency

Fs = 1/(X(2)-X(1));

% Calculate fft

ydft = fft(Zavg);

% Only take one side of the Fourier transform

ydft = 2*ydft(1:ceil((length(Zavg)+1)/2));

% Calculate the frequencies

f = 0:Fs/length(Zavg):Fs/2;

% Normalise according to length of signal

ydft = ydft'/(2*length(f'));

P1 = abs(ydft);

figure(1)

semilogx(1./f,P1), xlabel('wavelength [um]');

I would really appreciate if anyone can please check this and see if its right or has a better and simpler code for it.

Answer 1

[Akash]

Hi Diwakar,

I understand that you are conducting experiments to study the effects of acoustics on an oil-in-water emulsion and have implemented the code to plot the spectrum to identify the peak corresponding to the wavelength.

In the code you provided, the inverse of the frequency "(1./f)" is used as an approximation of the wavelength, assuming a linear relationship between frequency and wavelength. However, it's important to note that the relationship between frequency and wavelength in an image "FFT" is not always straightforward.

To accurately determine the wavelength from an image "FFT", I recommend referring to the below mentioned MATLAB Answer discussion:-

https://www.mathworks.com/matlabcentral/answers/80537-how-do-i-convert-the-x-axis-of-an-fft-from-frequency-to-wavelength?s_tid=srchtitle

This discussion provides insights and guidance on converting the "FFT" results from frequency to wavelength, enabling you to extract more accurate wavelength information from the image.

Hope it helps.

Thanks,

Akash.