By H. A. Buchdahl
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1 Black Body Radiation and Gas-Discharge Lamps 33 Fig. 1. Logarithm of black-body radiation power Lf per cm2 steradian and 1 Hz bandwidth for various temperatures, as indicated in K The graphs in Fig. 1 are typical emission characteristics for glowing solids like tungsten ﬁlaments. Tungsten-ﬁlament lamps are particularly useful as light sources in the visible and near IR spectral range if a broad-band emission is required. To increase the lifetime of high-power lamps small amounts of halogen gases are often added to the low-pressure noble gas ﬁlling.
4 polar coordinates have been used. The direction of particle propagation is the polar axis. The ﬁgure demonstrates the characteristic diﬀerence for the two types of radiation. For a relativistic particle nearly all radiation is emitted forward whereas for a nonrelativistic particle forward and backward emission are almost the same. Note that the diagram does not have rotational symmetry any more. Symmetry is only retained with respect to the plane of the storage ring and the sagittal plane normal to it.
Spatial coherence is relevant for interference experiments with light from extended sources. Since this will not be discussed in the frame of this book, we will restrict ourselves to temporal coherence. 54). 54) the temporal coherence function or autocorrelation function explicitly 1 T →∞ 2T T G(τ ) = lim E ∗ (t)E(t + τ )dt . 55) −T The autocorrelation function is maximum for τ = 0 and may go to zero for τ → ∞. The autocorrelation function for a partially or highly stochastic light ﬁeld vanishes for τ → ∞ since eventually E(t) and E(t + τ ) become random in phase and all contributions cancel due to the time averaging.
An Introduction to Hamiltonian Optics by H. A. Buchdahl