%Simulation

lambda = 0.6*10^-6; %wavelength, m

delta = 10*lambda; %samling period, m

z = 0.07; %propagation distance, m

M = 512; %space size

%object

c = 1:M;

r = 1:M;

[C, R] = meshgrid(c,r);

THOR = ((R-M/2-1).^2 + (C-M/2-1).^2).^0.5;

RR = THOR.*delta;

OB = zeros(M);

for a = 1:M

for b = 1:M

if RR(a,b) <= 5*10^-4; %aperture radius, m

           OB(a,b) = 1;

end

end

end

%diffraction

QP = exp(1i*pi/lambda/z.*(RR.^2)); %k0 = 2*pi/lambda

FD = abs(fftshift(fft2(fftshift(OB.*QP))));

FD = FD/max(max(FD));

figure;

subplot(121); imshow(OB);

title('Circular aperture (transparency function)');

subplot(122); imshow(FD);

title('Modulus of the Fresnel diffraction pattern');

Diffraction Limit (Excerpt from Optical Design Fundamentals for Infrared Systems, Second Edition)

An ideal optical system would image an object point perfectly as a point. However, due to the wave nature of radiation, diffraction occurs, caused by the limiting edges of the system’s aperture stop. The result is that the image of a point is a blur, no matter how well the lens is corrected. This is the diffraction blur or Airy disk, named in honor of Lord George Biddel Airy, a British mathematician (1801–1892). Its cross section and its appearance are shown in the figure below.

Airy disk, energy distribution and appearance.

Since this blur size is proportional to the wavelength, as indicated in Eq. (3.74), the diffraction effect can often become the limiting factor for infrared systems. If the aperture of the lens is circular, approximately 84% of the energy from the energy from an imaged point is spread over the central disk surrounded by the first dark ring of the Airy pattern. The diameter of this central disk is

For a LWIR system operating at a wavelength of 10 μm and an f-number of 2, the diffraction blur with 84% of the energy is 48.8 μm (approximately 0.002 in.) in diameter. The trend to decrease the pixel sizes in focal plane arrays to increase the system's resolution requires awareness of this limit set by nature. Including the energy of a diffraction blur twice in diameter of the central disk (the measure of the second dark ring) increases the total encircled by only 7%. The spread of the energy outside the central disk can cause disturbing crosstalk into adjacent detector elements in an array.

References:

www2.engr.arizona.edu/~dial/ece425/notes9.pdf

https://spie.org/publications/tt48_38_diffractive_limit?SSO=1