| The spectral analysis of radiation is one of most important analytic methods in science. Implicit in its use is the assumption that the spectrum of light does not change as the radiation propagates in free space. This assumption has been called into question for past ten years. In 1986, Professor Wolf, a famous optics researcher of America, showed that only when the spectral degree of coherence of a source satisfies the so-called scaling law, does the spectrum of the radiation from the source keep the spectral invariance during its propagation. Conversely, when the source does not satisfy the scaling law, the spectrum of the radiation from the source will experience spectral change. This kind of phenomenon is termed correlation-induced spectral changes. Later it is also found that when partially coherent light whose spectral degree of coherence satisfies the scaling law is diffracted by an aperture, the spectrum of the light in the diffracted field will be changed as well. This kind of spectral changes sometimes is called the diffraction-induced spectral changes.Generally the normalized spectrum of the radiation generated by two point sources, with the same normalized spectrum, is different from the normalized spectrum of each source. The normalized spectrum of the light at the superposition of region is modulated by the correlation of the two sources. Only when the two sources are completely uncorrelated, is the normalized spectrum of the light of the superposition region equal to the normalized spectrum of each source.Quasi-homogenous sources are frequently encountered in nature and laboratory. The relation between the spectrum of the light in the far zone radiated from the source and the spectrum of the source has been derived. It is shown that the normalized spectrum of the light in the far zone is not equal to the normalized spectrum of the source, but is dependent on the spectral degree of coherence of the source and the observed direction. To ensure the normalized spectrum of the light radiated from the quasi-homogenous source be the same throughout the far zone, the spectral degree of coherence of the source should satisfy following equation:here, r' denotes the vector difference between the two points r, and r2 , i.e., r'= r2 -r1. k = ω/ c is the wave-number associated with the frequency ω . c is the light speed in vacuum.Formula (1) is just the scaling law. Based on formula (1), we can judge that the spectrum of radiation from a source changes or not. Fortunately some of most commonly occurring sources found in the nature and in laboratory satisfy formula (1).A Gaussian Schell-model (GSM) beam is one special kind of partially coherent beam. Both the intensity distribution and the coherence distribution of the GSM beam are Gaussian distribution. We have studied the spectral changes of a GSM beam during its propagation. It is shown that even when a GSM beam propagates in free space, its normalized spectrum will change. The spectral changes are dependent on the frequency dependence of the GSM source radius w0 and of the effective coherencewidth σ0 (ω) . To keep the spectral invariance of the GSM beam propagating in the free space, the effective coherence width σ0 (ω) should behere w0 is assumed to be independent of frequency ω , and y is a positive constant.Based on the ray matrix method, the generalized formulas for describing the propagation of a GSM beam through an optical system of ABCD ray matrix are derived. It is shown that in general the spectral changes also take place as the beam propagates through the optical system, and the spectral changes are not only dependent on the parameters of the GSM beam, but also on the elements of the ray matrix of the optical system. As a special example, the focusing of a GSM beam by a lens with chromatic aberration is presented. We show that suitable chromatic aberration of the lens will lead to remarkable spectral changes of the light near the focus. The spectral changes also depend on the coherence, the lower coherence of th...
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