A filter-lens combination in conjunction with partially coherent light is used to produce a secondary source that violates a certain scaling law. The spectral shifts observed have been found to be dependent on the complex degree of spectral coherence, filter peak transmission wavelength, and half-band-width of the filter.
Statistical correlations of the light emitted by a partially coherent source can produce frequency shifts in the spectrum observed in the far field if the correlation function of the emitted radiation does not satisfy a certain scaling law. A Fourier achromat is used to generate a secondary source in which the degree of spectral coherence is independent of wavelength; i.e., it violates the scaling law. The spectrum detected in the far zone of the secondary source is, in general, found to be displaced in frequency and distorted relative to the spectrum measured at the secondary source. The displacement can be toward the higher frequencies or the lower frequencies depending on the direction of observation.
It is generally taken for granted that the spectrum of light does not change on propagation. This belief is implicit in all spectroscopy. In the last few years it was discovered that while such spectral invariance holds for radiation from commonly used sources it does not hold, in general, because the spectrum of emitted radiation depends not only on the source spectrum but also on the coherence properties of the source. It was found that in some cases the induced changes may be appreciable, possibly resulting in frequency shifts of spectral lines. It has also been demonstrated that similar spectral changes may be produced by scattering on media whose dielectric susceptibility is appropriately correlated.
Recent developments in coherence theory have shown that the spectrum of the field produced by a partially coherent source depends not only on the source spectrum but also on the spatial correlations of the source fluctuations.1 In particular, it has been found that some correlations may give rise to frequency shifts of spectral lines.2 Questions have been raised concerning energy conservation in such situations. In this paper we first discuss energy conservation laws pertaining to fields generated by sources of any state of coherence, and we use these fields to demonstrate that conservation laws are not violated when source correlations produce spectral changes in the emitted radiation. We also show that spectral shifts may be generated by isotropic sources, without violating energy conservation.