四个部分相干点源的完全相消干涉特性

使用部分相干光的干涉定律,对部分相干光照明呈正方形对称四孔干涉仪的干涉场做了研究.结果表明,一定条件下,可出现完全相消干涉,并存在光强和光谱相干度的相位奇点.与二个、三个部分相干点源的干涉做了比较.对所得结果物理上可解释为：虽然四个点源是部分相干的,但从两个点源出射场之和与从另外两个点源出射场之和却可能是完全相关的. 关键词： 相关奇点光学 完全相消干涉 部分相干光 刃型位错线     

Correlation-induced spectral changes dependent upon spatiotemporal interference effects

A wave-front folded interferometer consisting of a Kösters prism and an image forming lens provides an excellent way to make a precision measurement of correlation-induced spectral changes. Experiments are successfully made by incorporating a primary spectral source of super-luminescent diodes. The diode emits a Gaussian-like spectrum. Theoretical background for the measurement is given in the framework of geometric optics. It is shown theoretically and experimentally that the spectral changes are induced by two causes: one is the complex degree of spectral coherence of the secondary source, and the other the time delay between the interfering optical waves. No spectral change takes place if the secondary source satisfies a spatially incoherent condition at particular optical frequency, whereas the spectrum changes most clearly if a spatially coherent condition is satisfied.     

Zone-plate interferometry at 13 nm wavelength

We report on interferometry using a two-zone-plate common-path interferometer operating at a wavelength of 13 nm. The interferometer was set up with a laser-driven high-harmonic source emitting radiation with the high degree of spatial and temporal coherence necessary for interferometry. The interferometer is suited for investigations of the coherence properties of the light source employed, as well as for simultaneous measurements of the real and imaginary part of the complex index of refraction in the 100 eV regime. This is demonstrated in a proof of principle experiment with a piece of Zr-foil as the phase-shifting and absorbing sample. PACS 41.50.+h; 42.65.Ky; 42.87.Bg; 07.60.Ly     

Determination of the angular separation and the spectra of two-point sources from spectral coherence measurements

We present a novel method not only for determining the angular separation of unknown two-point spectral sources but also for obtaining each of their spectral profiles from measurements of both their complex degree of spectral coherence and their spectra across an observation area in the space-frequency domain. The theoretical predictions are fully proved by an experimental demonstration with a pair of uncorrelated two-point spectral sources.     

Polarization properties of partially coherent electromagnetic elegant Laguerre–Gaussian beams in turbulent atmosphere

Based on the extended Huygens–Fresnel Principle and the unified theory of coherence and polarization, the analytical formulas for the polarization degree and spectral coherence degree of partially coherent electromagnetic elegant Laguerre–Gaussian (PCEELG) beams through turbulent atmosphere are obtained theoretically in detail. It is found that the polarization degree of PCEELG beams tends to the value of its source plane after a sufficiently long propagation distance in turbulent atmosphere. Furthermore, this value is independent of the beam orders, the correlation length in the source plane and the structure constant of the turbulent atmosphere ( $C_{n}^{2}$ ). The polarization degree of PCEELG beams also acquires a particular value at a certain distance in free space, which is different from the value in the source plane. The spectral coherence degree of PCEELG beams has an oscillatory behavior for different propagation distance, beam orders and  $C_{n}^{2}$ .     

Measurement of angular distributions by use of low-coherence interferometry for light-scattering spectroscopy

We present a novel interferometer for measuring angular distributions of backscattered light. The new system exploits a low-coherence source in a modified Michelson interferometer to provide depth resolution, as in optical coherence tomography, but includes an imaging system that permits the angle of the reference field to be varied in the detector plane by simple translation of an optical element. We employ this system to examine the angular distribution of light scattered by polystyrene microspheres. The measured data indicate that size information can be recovered from angular-scattering distributions and that the coherence length of the source influences the applicability of Mie theory.     

Slanting propagation of stochastic electromagnetic twist anisotropic Gaussian–Schell model beams in turbulent atmosphere

Based on the extended Huygens–Fresnel diffraction integral and the unified theory of coherence and polarization, the slanting propagation properties of stochastic electromagnetic twist anisotropic Gaussian–Schell model (ETAGSM) beams in turbulent atmosphere have been investigated. Both numerical calculation and physical interpretation are obtained. The influence of the atmospheric turbulence and the source parameters on the polarization distribution, intensity distribution and coherence distribution has been studied in great detail. The investigation reveals that slanting propagation can weaken the influence of atmospheric turbulence on the spectral properties of stochastic ETAGSM beams more obviously. It is also shown that we can modulate the spectral degree of polarization in the output plane especially in the far field by simply controlling the coherence, the spot width or the twisty properties of the source beams. The distribution of the spectral degree of polarization and cross-polarization of the beams in the output plane is also given out.     

Effect of cross-polarization of electromagnetic source on the degree of polarization of generated beam

In this paper we study the degree of cross-polarization of a beam-like field whose cross-spectral density matrix is symmetric with respect to the permutation of its spatial arguments. Formulas were derived expressing the degree of cross-polarization in terms of the generalized Stokes parameters. With the help of an uniformly polarized quasi-homogeneous model source, the effect of degree of cross-polarization of a source on the degree of polarization of the radiated beam was demonstrated, that, two sources with same spectral degrees of coherence and polarization but with different degrees of cross-polarization can generate beams that have different spectral degrees of polarization in the far field.     

Condition for invariant spectral degree of coherence of an electromagnetic plane wave on scattering

Within the accuracy of the first-order Born approximation, the condition for invariant spectral degree of coherence of an electromagnetic plane wave scattered from random media is presented. The condition for the electromagnetic plane wave is different from the one for the scalar plane wave. Results also indicate that, different polarizations of the incident plane wave would have essential effects on analytical forms of the condition. These effects may be due to the correlation-induced changes in the scattered spectral degree of coherence.     

孪生光束干涉法测量光源的空间相干性

定量测定光源空间相干性在部分相干光成像, 非相干全息术及光信息处理领域具有重要的研究价值. 本文基于三角全息干涉光路提出了一种测量光源空间相干性的新方法. 利用三角干涉全息光路系统中分束镜产生的孪生光束进行干涉获得干涉图, 通过调整光源中心位置在写入平面内偏离光轴的量, 改变两孪生光束空间分离量的大小, 采集对应的一系列干涉图, 计算干涉图样的对比度, 从而对光源照明空间的波前上一系列不同距离的点对之间的空间复相干度进行测量. 实验系统光路配置较为简单且不需要使用特殊加工的光学元件. 针对一个准单色的扩展光源设计并进行实验, 结果表明利用文中提出的方法可以准确的测量光源的空间相干性, 实验结果相对于理论计算值的误差仅为3.8%. 关键词： 相干性 全息干涉 干涉仪 光学应用     

Scintillation index of a stochastic electromagnetic beam propagating in random media

We study the behavior of the scintillation index (the normalized variance of fluctuating intensity) of a wide-sense statistically stationary, quasi-monochromatic, electromagnetic beam propagating in a homogeneous isotropic medium. In particular, we show that in the case when the beam is treated electromagnetically apart from the correlation properties of the medium in which the beam travels not only its degree of coherence but also its degree of polarization in the source plane can affect the values of the scintillation index along the propagation path. We find that, generally, beams generated by unpolarized sources have reduced level of scintillation, compared with beams generated by fully polarized sources, provided they have the same intensity distribution and the same state of coherence in the source plane. An example illustrating the theory is considered which examines how the scintillation index of an electromagnetic Gaussian Schell-model beam propagates in the turbulent atmosphere. These results may find applications in optical communications through random media and in remote sensing.     

Spatial coherence measurements through turbulent atmosphere using a computer-aided interferometer

The complex degree of coherence over a telescope aperture is measured by processing instantaneous values of the complex degree of coherence fluctuated by turbulent atmosphere. Fringe patterns produced by a computer-controlled wave-front folding interferometer are analyzed in a short time by a photodiode array to calculate the instantaneous values of the complex degree of coherence. The system is applied to one-dimensional simulation experiments.     

Laboratory demonstration of an infrared-to-visible up-conversion interferometer for spatial coherence analysis

We experimentally demonstrate the possibility of retrieving the spatial coherence of an infrared source by using an up-conversion interferometer. Sum-frequency generation in Ti-diffused periodically poled lithium-niobate waveguides in both arms of the interferometer is used to convert the infrared into the visible domain. The fringe contrast of the interference pattern in the visible domain permits us to resolve the spatial separation of two uncorrelated pointlike infrared sources, which simulate a binary star. The validity of these measurements is confirmed through a simultaneous comparison with a reference interferometer working in the infrared domain.     

Modal expansion for spherical homogeneous sources

The modal expansion of a class of stochastic spherical scalar sources is studied. At the surface of these sources the cross-spectral density is assumed to be homogeneous, in the sense that the power spectrum is position-independent and the spectral degree of coherence depends on the angular distance between points only. It is shown that for any such source the modes are given by the spherical harmonics and the associated eigenvalues can be evaluated by solving simple integrals. Three examples of the spectral degree of coherence for this type of sources are given for which the eigenvalues can be found in closed form.     

Measurement of hard X-ray coherence in the presence of a rotating random-phase-screen diffuser

A suitably large coherence area is important in coherent X-ray optics, when using techniques such as interferometry or phase contrast imaging (PCI). The work done by Suzuki using a prism interferometer to measure X-ray coherence at 12.4 keV [1] is here extended to consider the use of a diffuser at the bio-medical imaging energy of 25 keV. In order to achieve a broader, more even X-ray field and eliminate speckle, a spinning piece of paper may be used as a rotating random-phase screen to diffuse the hard X-ray beam, but this will concomitantly decrease the magnitude of the complex degree of second-order coherence. We also study the effect of source size and source-to-sample distance on coherence, where imaging area and required flux must be considered. Coherence measurements at the 20XU beamline at the SPring-8 synchrotron are compared to results from wave-optical computer modelling. These show that while the diffuser will decrease the magnitude of the complex degree of coherence, further free-space propagation will lessen this effect. In the design of an experiment, the collimating slit size and use of a diffuser must therefore be balanced with distance from the source, in order to maximise coherence while maintaining the desired field of view and exposure time.     

Interpretation of the recipe for synthesizing genuine cross-spectral density matrices

A physical interpretation of the recipe for synthesizing genuine 2 × 2 cross-spectral density matrices that characterize stochastic electromagnetic sources and beams is described. In this interpretation, the synthesized field is regarded as an incoherent superposition of spatially coherent fields originating from a partially polarized, spatially incoherent virtual source. The coherence and the polarization properties of the synthesized field are also examined in view of this interpretation. As a result, we found that the spectral degree of coherence and that of polarization of the synthesized field are generally different from those of the virtual source by the effect of the superposition. We also found, however, that there are some situations in which the spectral degree of polarization of the synthesized field remains unchanged even though the superposition takes place.     

Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence

We formulate and evaluate in terms of graphical outputs, source and receiver plane expressions, the complex degree of coherence, beam size variation and power in bucket performance for higher order partially coherent dark hollow beams propagating in turbulent atmosphere. Our formulation is able to cover square, rectangular, circular, elliptical geometries for dark hollow and flat-topped beams in one single expression. From the graphical outputs of the receiver plane, it is observed that higher order partially coherent dark hollow beams will initially develop an outer ring around a central lobe, but will eventually evolve towards a Gaussian shape as the propagation distance is extended. It is further observed that stronger turbulence levels and greater partial coherence have similar effects on beam profile. During propagation, modulus of complex degree of coherence of partially coherent dark hollow beams appears to rise above that of the source plane values, reaching as high as near unity. Beam size analysis shows that, among the types examined, (nearly) flat-topped beam experiences the least beam expansion. Power in bucket analysis indicates that lowest order square fully coherent dark beam offers the best power capturing.     

Spatial correlation properties and the spectral intensity distributions of focused Gaussian Schell-model array beams

The spatial correlation properties and the spectral intensity distributions of focused Gaussian Schell-model (GSM) array beams are studied in detail. The closed-form expressions for the spectral degree of coherence and the spectral intensity of focused GSM array beams are derived. It is shown that the spectral degree of coherence of focused GSM array beams is the same as that of focused GSM beams in the focal plane. On the other hand, it is found that, in the focal plane the spectral intensity distribution of focused GSM array beams is the fringe pattern when the value of the coherence length is small. However, it becomes one peak located at the center as the value of the coherence length is large enough. In the focal plane, the spectral intensity maximum increases and the width of the normalized spectral intensity distribution decreases as the beam number increases. In general, for GSM array beams, the width of the modulus of the spectral degree of coherence in the focal plane always exceeds that of the normalized spectral intensity distribution, which is different from the behavior of focused GSM beams. In addition, the power in the bucket (PIB) and the beam propagation factor (M² factor) are also discussed. The main results are explained physically.     

Effects of Spatial Coherence and Dispersive Diffraction on a Change in Optical Spectrum

This paper describes a change in optical spectrum on propagation in free space for a particular class of spatially partially coherent fields emanating from a polychromatic secondary source. A rectangular opening aperture in an opaque screen, illuminated with an extended incoherent polychromatic primary source, works as the secondary source. The spectral change is explored in detail theoretically and experimentally in association with spatial coherence in the secondary source as well as dispersive diffraction by the secondary source. The peak shift of the spectrum is associated with the coherence area for characterizing the secondary source. The peak shift becomes maximum if the secondary source is spatially coherent, but no shift occurs if the secondary source is spatially incoherent.     

Polarimetric and spectral changes in random electromagnetic fields

Beginning with a recently formulated unified theory of coherence and polarization for random electromagnetic fields, we show how partially polarized light can be generated through correlation of unpolarized components. The effect is demonstrated by use of a Mach-Zehnder interferometer, showing the possibility of producing light with adjustable spectral density and an adjustable degree of polarization.