By Swapan K. Saha
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Extra resources for Diffraction-limited Imaging With Large and Moderate Telescopes
The irradiance of the spherical wave is proportional to the square of the amplitude a(r, ν)/r at a distance r. The complex amplitude is a constant phasor in the monochromatic case, therefore, the Fourier transform (FT) of the complex representation of the 9 Monochromatic radiation is the radiation of single precise energy; the energy is related with its wavelength which is often used to specify the color of the visible radiation. 10 A function is analytic if its components are harmonic conjugates.
134) turns out to be, ∇ × E0 (r, ω) = −iω B0 (r, ω). 138) ∇ · J0 (r, ω) = −iω ρ(r, ω). 139) These are the Maxwell’s equations for the Fourier transform of the electromagnetic fields, E0 (r, ω), B0 (r, ω), etc. Let the integral of the complex Poynting vector be examined, 2 π ∞ n · [Sc (r, ω)]dω = 0 ∞ 2 π n· 0 c 8π E0 (r, ω) × H0∗ (r, ω) dω. 140) By using Parseval’s theorem (see appendix II), one finds, ∞ ∞ c [E(r, t) × H(r, t)]dt 4π 2 ∞ c E0 (r, ω) × H0∗ (r, ω) = n· π 0 8π 2 ∞ = n· Sc (r, ω) dω.
Thus the Poynting vector is directly proportional to the first Stokes parameter. 2 Harmonic time dependence and the Fourier transform The Maxwell’s equations for an electromagnetic field with time dependence are simplified by specifying a field with harmonic dependence (Smith, 1997). 111) where aj (r, ω) is the amplitude of the electric wave, κ the propagation vector, and j = 1, 2, 3. Directi on of p r opoga tio n λ Fig. 3 Propagation of a plane electromagnetic wave; the solid and dashed lines represent respectively the electric and magnetic fields.
Diffraction-limited Imaging With Large and Moderate Telescopes by Swapan K. Saha