MATLAB Code for Plotting Optical Transfer Function (MTF) of Optical Systems

Below is MATLAB code for calculating the Optical Transfer Function (MTF) of optical systems. This program generates an MTF curve plot that displays the resolution performance of optical systems. The implementation utilizes Fourier transform techniques, which convert the system's Point Spread Function (PSF) into MTF values. MTF serves as a valuable tool for evaluating optical system performance and optimizing optical design parameters.

```Matlab

% MTF calculation program for optical systems

% This program uses Fourier transform to convert point spread function to MTF

% Author: [Your Name]

% Define input parameters

f_number = 4; % F-number (aperture setting)

focal_length = 50; % Focal length in millimeters

exit_pupil_diameter = 12.5; % Exit pupil diameter in millimeters

wavelength = 550; % Wavelength in nanometers

image_size = 20; % Image size parameter

pixel_size = 10; % Pixel size in micrometers

% Calculate spatial frequency range

Nyquist_frequency = 1 / (2 * pixel_size); % Maximum resolvable frequency

frequencies = linspace(0, Nyquist_frequency, image_size / 2); % Frequency sampling points

% Compute MTF values across frequency spectrum

MTF = zeros(size(frequencies)); % Initialize MTF array

for i = 1:length(frequencies)

frequency = frequencies(i);

MTF(i) = compute_MTF(f_number, focal_length, exit_pupil_diameter, wavelength, frequency);

end

% Plot MTF curve with proper labeling

plot(frequencies, MTF);

xlabel('Spatial Frequency (cycles/mm)');

ylabel('MTF Value');

title('Optical System MTF Curve');

function MTF = compute_MTF(f_number, focal_length, exit_pupil_diameter, wavelength, frequency)

% Calculate point spread function using diffraction theory

delta = wavelength / (2 * f_number); % Characteristic diffraction length

x = linspace(-exit_pupil_diameter/2, exit_pupil_diameter/2, 1000); % Spatial coordinate array

PSF = sinc(x / delta).^2; % Squared sinc function representing Airy pattern

% Compute MTF through Fourier transformation

MTF = abs(fft(PSF)); % Fast Fourier Transform of PSF

MTF = MTF(1:length(MTF)/2); % Take positive frequency components

MTF = MTF / MTF(1); % Normalize to DC component

MTF = interp1(linspace(0, 1, length(MTF)), MTF, frequency); % Interpolate at specific frequency

end

```