What is Fresnel diffraction: Definition and 20 Discussions

In optics, the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation of waves in the near field. It is used to calculate the diffraction pattern created by waves passing through an aperture or around an object, when viewed from relatively close to the object. In contrast the diffraction pattern in the far field region is given by the Fraunhofer diffraction equation.
The near field can be specified by the Fresnel number, F, of the optical arrangement. When



{\displaystyle F\gg 1}
the diffracted wave is considered to be in the near field. However, the validity of the Fresnel diffraction integral is deduced by the approximations derived below. Specifically, the phase terms of third order and higher must be negligible, a condition that may be written as






{\displaystyle {\frac {F\theta ^{2}}{4}}\ll 1,}


{\displaystyle \theta }
is the maximal angle described by





{\displaystyle \theta \approx a/L}
, a and L the same as in the definition of the Fresnel number.

The multiple Fresnel diffraction at closely spaced periodical ridges (ridged mirror) causes the specular reflection; this effect can be used for atomic mirrors.

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  1. K

    A Diffraction theory, power density and angle of incidence

    Hello everybody I am currently looking at diffraction through a rectangular aperture. I am looking at an aperture which is large compared to wavelength, and am looking at diffraction at all angles behind the aperture in a distance which is approx equal to the size of the aperture. I am...
  2. Douglas-Stinson

    A Calculating Fresnel Diffraction Pattern from Circular Apertures

    I am attempting to calculate the Fresnel difraction pattern from different diameter circular apertures for specific source to aperture and aperture to sensor distances. I'm generally following the procedure given in Klaus D. Mielenz "Algorithms for Fresnel Diffraction at Rectabngual and Circular...
  3. ergospherical

    Fresnel diffraction from square: on axis intensity

    I'd appreciate if someone could check whether my work is correct. The ##x##-##y## symmetry of the aperture separates the Fresnel integral:\begin{align*} a_p \propto \int_{-a/2}^{a/2} \mathrm{exp}\left(\frac{ikx^2}{2R} \right) dx \int_{-a/2}^{a/2} \mathrm{exp}\left(\frac{iky^2}{2R} \right) dy...
  4. J

    I Using Diffraction (i.e., Fresnel Zone Plate) to defocus/diverge light

    I am wondering if it is possible to use principals of diffraction to cause a collimated beam of light (laser) to become divergent. I see that zone plates are most always used for focusing the light from a source, unless they are used in reverse. This is why zone plates are seemingly always...
  5. K

    Real Fresnel diffraction experiment

    I'm wondering if I can perform an actual experiment to observe Fresnel diffraction. I would like to do it with a rectangular aperture and of course, visible light. What should its dimensions be? And from which distance from it can I expect to start seeing a decent diffraction pattern? I know I...
  6. Vipanj

    I How can we visualise a half period zone inside a zone plate?

    how can we consider/ visualise a half period zone inside blackened portion of +ve zone plate ?
  7. F

    A Fresnel Diffraction - Opaque Barrier Question

    Hello! I'm very interested in knowing your opinion on how close my model is to the Fresnel Diffraction by an opaque barrier, as seen here: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/difopa.html#c1 My model: Sorry for the low quality image.
  8. C

    MATLAB FFT problem for Fresnel simulation

    Hi all, I'm trying to simulate the Fresnel diffraction by using this expersion : $$ A(x')=\frac{1}{j\lambda z}e^{jk(z+\frac{x'^2}{2z})}F(A^{trans}(x)e^{jk\frac{x^2}{2z}})_{u=\frac{x'}{\lambda z}} $$ So when I use this formula my problem is that I don't know how to take the good frequency, here...
  9. Vaibhav DixiT

    Fresnel Diffraction through a straight edge

    I read in texts that when a rays of light are diffracted from a straight edge, the phenomenon can be explained using the half period zones. The things that is confusing me is this: "Odd number of half period zones, if exposed, lead to a bright fringe. Even number of half period zones exposed...
  10. E

    Code of the Angular Spectrum Method

    I constructed my code of the Angular Spectrum Method. However, as the distance between the object and the plane of interest increases, the diffraction pattern never disappears; there is still some sort of a diffraction pattern, and I am expecting that it disappears as distance increases. Here...
  11. E

    MATLAB Implementation of Fresnel Diffraction in MatLab

    I'm trying to simulate the Fresnel Diffraction in MatLab using the Fast Fourier Transform syntax. But I'm not getting really good diffraction patterns. Here is the code: %% Fourier Transform for G(p, q) g = layer.*exp(((1i*pi)/(lambda*z))*(r_obj)); G = fftshift(fft2(g)); %% Fourier Transform...
  12. E

    Computer Simulation of Fresnel Diffraction

    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}##...
  13. J

    How to observe Fresnel diffraction at home?

    I would like to see the difference between Fraunhofer and Fresnel diffraction with a homemade setup. Has anyone achieved this? In this example, it seems that the main components are a He-Ne laser, a short-focal lens, a pinhole and an adjustable aperture. I have some doubts about the possible...
  14. K

    Deriving F=a2/λL in Fresnel Diffraction

    Hi guys, I can't find my notes on Fresnel diffraction and I have my Optics exam on Monday... Does anyone know how to derive F=a2/λL where L=1/z+1/z' I've googled it to death, checked here and tried in Optics 4th edition by Hecht with no luck... I'd really appreciate any help...
  15. T

    Circular Aperture Fresnel Diffraction

    Homework Statement A circular aperture, with diameter 3.1 mm, is illuminated by a monochromatic plain wave. On the screen, which lays 1m ahead, we observe that the center of the diffraction pattern is dark. When we start to move the screen gradually backwards, the center becomes bright, then...
  16. R

    Fresnel Diffraction Simulation Troubleshooting

    Hi Everyone, I am having trouble with my Fourier optics. I am trying to simulate Fresnel diffraction using the following form of the equations: Li(xi, yi) = K * magnitude ( FT{ P(xp, yp)E(xp, yp) } p= xi/ld ;q= yi/ld ) ^2 K = 1/(ld)^2 E(xp, yp) = e^(i*(PI/ld)*(xp^2+yp^2)) P is the...
  17. A

    Fresnel Diffraction Homework: Sun 45°, 10m Wall, 500nm Lambda

    Homework Statement The sun is 45 [deg] above the horizon. A wall, 10 [m] height is penpandicular to the line sun-earth. Compute the luminous flux, under the following conditions: 1. The geometric shadow, while the sun angular dimension is 0.5 [deg]. 2. Fernsel diffraction- the sun as a...
  18. J

    Maple Plotting Fresnel Diffraction Pattern with Maple

    Help with printing a string I have a theoretical plot for the fresnel diffration pattern, however i want maple to show the values plotted on the x and y cordinates. How do i do this. Please explain in simple terms heres my code > fresdi:= proc(a,b) (FresnelC(a) - FresnelC(b))^2 +...
  19. J

    Fresnel diffraction; geometrical shadow

    What is geometrical shadow qualitatively? please don't refer me to hyper physics
  20. B

    Fresnel Diffraction: Explaining Zero Intensity at Center

    Hey people... This isn't really a homewrok question, I am asking it to try and improve my understanding, but if i still have posted it in the wrong place i sincerely apologise if i upset anyone. I am going over some notes before my exam in 4 days and have encountered a problem... the...