Fourier_Optics_1 Flashcards
What is the principle of Fourier optics?
Fourier optics is a method of analyzing light propagation by representing it as a superposition of plane waves, useful in describing signals and systems in many fields.
What is the wave equation for the electric field in a sourceless medium?
The wave equation is ∇²E - (n²/c²) ∂²E/∂t² = 0.
How is the Helmholtz equation derived from the wave equation for a monochromatic wave?
Assuming the polarization is approximately independent of space, we extract the Helmholtz equation: ∇²U + k²U = 0, where k = nω/c.
What is the spatial Fourier transform in the context of plane wave propagation?
The spatial Fourier transform is V(kx, ky, z) = ∫∫ U(x, y, z) e^(i(kx x + ky y)) dx dy, a 2-D Fourier transform in space.
What is the Fresnel approximation?
The Fresnel approximation simplifies the transfer function by assuming small spatial frequencies or small angles, resulting in a quadratic phase function.
What is a Gaussian beam and why is it important in laser physics?
A Gaussian beam is a solution to the paraxial Helmholtz equation, characterized by parameters such as the waist radius, Rayleigh range, and divergence angle, crucial for understanding beam propagation.
What is the Fraunhofer limit or far-field approximation?
The Fraunhofer limit is the condition where the Fresnel number is much smaller than 1, leading to the far-field approximation where the field output is a Fourier transform of the input field.
How does the rectangular aperture affect the diffraction pattern?
The diffraction pattern of a rectangular aperture is described by the sinc function, resulting in a product of two orthogonal sinc functions in Fourier space.
What is the Airy pattern?
The Airy pattern is the diffraction pattern from a circular aperture, characterized by a central bright spot surrounded by concentric rings, with the first minimum occurring at 1.22λd/D.
What is the significance of the phase masks and lenses in Fourier optics?
Phase masks and lenses affect the phase of the light wave, which can be used to control the propagation of light, such as focusing or modifying the wavefront.
