- #1
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Considering this system (from Wikipedia),
The Fresnel Diffraction at x, y, and z is
##E \left(x, y, z\right) = \frac{z}{i \lambda} \int \int^{+\infty}_{-\infty} E \left(x', y', 0\right) \frac{e^{ikr}}{r^2} dx' dy'##
where ##r = \sqrt{\left(x - x'\right)^2 + \left(y - y'\right)^2 + z^2}##, ##E \left(x', y', 0\right)## is the aperture, and ##i## is the imaginary unit. The integration process I used to solve the integral is the Trapezoidal Rule (I don't know any good processes that is not step length dependent, and this is the one I am most familiar with).
As of now, the aperture size is infinite, so the image at ##z = 0## is unobstructed. I tried using the Fresnel Diffraction with this image:
And this was the corresponding Fresnel Diffraction at 4 meters with a wavelength of 700 nm:
Is this correct?
The Fresnel Diffraction at x, y, and z is
##E \left(x, y, z\right) = \frac{z}{i \lambda} \int \int^{+\infty}_{-\infty} E \left(x', y', 0\right) \frac{e^{ikr}}{r^2} dx' dy'##
where ##r = \sqrt{\left(x - x'\right)^2 + \left(y - y'\right)^2 + z^2}##, ##E \left(x', y', 0\right)## is the aperture, and ##i## is the imaginary unit. The integration process I used to solve the integral is the Trapezoidal Rule (I don't know any good processes that is not step length dependent, and this is the one I am most familiar with).
As of now, the aperture size is infinite, so the image at ##z = 0## is unobstructed. I tried using the Fresnel Diffraction with this image:
And this was the corresponding Fresnel Diffraction at 4 meters with a wavelength of 700 nm:
Is this correct?