Rectangular Aperture: Angular Widths of the Main Lobe Angular width of main lobe in horizontal direction is governed by the function: ( ) (( )) sin' 2 sin sin ' 2 2 sin 2 φ φ x x x x x x kL kL k L k L = The angular half-width is determined by when the term inside the sine function becomes ±π x x null kL L π λ φ =± =± 2 sin ' k x =k sin (θ)cos φ=k sin φ' For: 2 π θ= ' 2.
- Rectangular Aperture Diffraction Pattern
- Fraunhofer Diffraction Rectangular Aperture
- Fraunhofer Diffraction Rectangular Aperture
Optics: Fraunhofer diffraction - rectangular apertureInstructor: Shaoul EzekielView the complete course: Creative Com. Engineering Physics I by Prof. Rajdeep Chatterjee,Department of physics,IIT Roorkee.For more det. Rectangular aperture Computer simulation of Fraunhofer diffraction by a rectangular aperture When a slit of width W and height H is illuminated normally by a monochromatic plane wave of wavelength λ, the complex amplitude can be found using similar analyses to those in the previous section, applied over two independent dimensions as: 14 15. Light rays passing through a small aperture will begin to diverge. Some cameras have pixels which are slightly rectangular, in which case diffraction.
The equations listed below use the following symbols: Rectangular Aperture Diffraction Pattern
$lambda$ | Wavelength | $z$ | Aperture To Image/Observation Distance |
$U_1$ | Aperture Field | $U_2$ | Image/Observation Field |
$x_1,y_1$ | Aperture Plane Coordinates | $x_2,y_2$ | Image/Observation Plane Coordinates |
$Im$ | Fourier Transform Operator | $Im ^{-1}$ | Inverse Fourier Transform Operator |
Fraunhofer Diffraction
Exact Analytic Solution
The Fraunhofer diffraction pattern of a rectangular aperture using the exact analytic solution is given by $$I(x,y) propto sinc^{2} left ( frac{pi Wx}{lambda z} right ) sinc^{2} left ( frac{pi Hy}{lambda z} right )$$ where $W$ is the rectangle width, $H$ is the rectangle height, $lambda$ is the wavelength, $z$ is the aperture-to-image distance, and $x$ and $y$ are the observation plane coordinates.
Fourier Transform
The Fraunhofer diffraction pattern is calculated using the Fourier transform method $$U_2(x_2,y_2) = left | Imleft ( U_1left ( x_1,y_1right )right ) hleft ( x_2,y_2right ) right |^2$$ where $h$ is the impulse response $$h(x,y) = frac{e^{ikz}}{i lambda z}e^{frac{ik}{2z}(x^2+y^2)}$$
Fresnel Diffraction
Transfer Function Method
The Fresnel diffraction pattern is calculated using the transfer function method $$U_2(x,y) = left | Im ^{-1}left ( Im left ( U_1(x,y) right )H(x,y) right ) right |^2$$ where $H$ is the transfer function $$H(x,y) = e^{ikz}e^{-i pi lambda z (x^2 + y^2)}$$
Impulse Response Method
The Fresnel diffraction pattern of is calculated using the impulse response method $$U_2(x,y) = left | Im ^{-1}left ( Im left ( U_1left (x,yright ) right )Im left ( hleft (x,yright ) right ) right ) right |^2$$ where $h$ is the impulse response $$h(x,y) = frac{e^{ikz}}{i lambda z}e^{frac{ik}{2z}(x^2+y^2)}$$
Diffraction Limited Imaging
Coherent Imaging
A diffraction-limited coherent camera system with the specified aperture produces an image based on the equation $$U_2(x_2,y_2) = Im ^{-1}left (H(x_2,y_2) Im left (I_g(x_2,y_2) right ) right)$$ where $I_g(x_2,y_2)$ is the ideal image field and $H(x_2,y_2)$ is the transfer function $$H(x_2,y_2)=P(-lambda z x_2,-lambda z y_2)$$ where $P$ is the pupil function
Incoherent Imaging
Fraunhofer Diffraction Rectangular Aperture
A diffraction-limited incoherent camera system with the specified aperture produces an image based on the equation $$U_2(x_2,y_2) = Im ^{-1}left (Im(|H(x_2,y_2)|^2) Im left (I_g(x_2,y_2) right ) right)$$ where $I_g(x_2,y_2)$ is the ideal image field and $H(x_2,y_2)$ is the transfer function $$H(x_2,y_2)=P(-lambda z x_2,-lambda z y_2)$$ normalized by the area of the transfer function, where $P$ is the pupil function
1. Computational Fourier Optics by David Voelz, SPIE Press, 20112. Numerical Simulation of Optical Wave Propagation with Examples in MATLAB by Jason D. Schmidt, SPIE Press, 2010
Fraunhofer Diffraction Rectangular Aperture
Большой англо-русский и русско-английский словарь. 2001.
Смотреть что такое 'diffraction by aperture' в других словарях:
- Aperture masking interferometry — is a form of speckle interferometry, allowing diffraction limited imaging from ground based telescopes. This technique allows ground based telescopes to reach the maximum possible resolution, allowing ground based telescopes with large diameters… … Wikipedia
- diffraction — ► NOUN Physics ▪ the process by which a beam of light or other system of waves is spread out as a result of passing through a narrow aperture or across an edge. DERIVATIVES diffract verb diffractive adjective. ORIGIN Latin, from diffringere break … English terms dictionary
- Diffraction — Computer generated intensity pattern formed on a screen by diffraction from a square aperture … Wikipedia
- Diffraction-limited system — Memorial to Ernst Karl Abbe, who approximated the diffraction limit of a microscope as , where d is the resolvable feature size, λ is the wavelength of light, n is the index of refraction of the medium being imaged in, and θ (depicted as α in the … Wikipedia
- diffraction by a circular aperture — difrakcija per apskritą angą statusas T sritis fizika atitikmenys: angl. diffraction by a circular aperture vok. Beugung an kreisförmiger Öffnung, f rus. дифракция на круглом отверстии, f pranc. diffraction par une fente circulaire, f;… … Fizikos terminų žodynas
- diffraction par une fente circulaire — difrakcija per apskritą angą statusas T sritis fizika atitikmenys: angl. diffraction by a circular aperture vok. Beugung an kreisförmiger Öffnung, f rus. дифракция на круглом отверстии, f pranc. diffraction par une fente circulaire, f;… … Fizikos terminų žodynas
- diffraction par une ouverture circulaire — difrakcija per apskritą angą statusas T sritis fizika atitikmenys: angl. diffraction by a circular aperture vok. Beugung an kreisförmiger Öffnung, f rus. дифракция на круглом отверстии, f pranc. diffraction par une fente circulaire, f;… … Fizikos terminų žodynas
- diffraction — noun Physics the process by which a beam of light or other system of waves is spread out as a result of passing through a narrow aperture or across an edge … English new terms dictionary
- Fraunhofer diffraction — In optics, Fraunhofer diffraction is a form of wave diffraction, which occurs when field waves are passed through an aperture or slit, causing only the size of an observed aperture image to change Hecht, E. (1987) , p396 Definition of Fraunhofer… … Wikipedia
- Fresnel diffraction — In optics, the Fresnel diffraction equation for near field diffraction, is an approximation of Kirchhoff Fresnel diffraction that can be applied to the propagation of waves in the near field.[1] The near field can be specified by the Fresnel… … Wikipedia
- Selected area diffraction — Selected area (electron) diffraction, abbreviated as SAD (SAED), is a crystallographic experimental technique that can be performed inside a transmission electron microscope (TEM).In a TEM, a thin crystalline specimen is subjected to a parallel… … Wikipedia
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