Display of spatial coherence

The mutual-intensity function plays a major role in characterizing quasi-monochromatic, partially coherent optical signals. We demonstrate an optical system for displaying the mutual intensity of a one-dimensional input beam. The experimental system is based on the fact that the mutual intensity of a signal can be expressed as the ensemble averaging of a cross-correlation operation between two related optical signals. The setup consists of a Sagnac interferometer followed by an optoelectronic joint transform correlator. Experimental results demonstrate the capabilities of the mutual-intensity analyzer.     

部分相干光学成像系统的光学传递函数和像质评价准则

根据光学成像理论，建立了部分相干成像光学系统的光学传递函数。该函数与非相干成像光学系统传递函数相同，因而部分相干成像和非相干成像两者的光学系统波面像差公差标准也是相同的。这一点解释了显微镜光学系统的光学设计惯用法则：镜头像差公差标准的选择，并不因为采用成像照明方式的不同而有所差异。     

Partially coherent Fresnel diffraction by a slit aperture. IV. Effect of the phase term in the coherence function

A formula was derived in paper 1 of the this series for investigating the Fresnel diffraction field of a slit aperture when the mutual coherence function of the illumination contains a quadratic phase term. That formula is applied to study the intensity distribution in the Fresnel diffraction field of a slit aperture illuminated by a quasi-monochromatic incoherent slit source. The phase term has a big effect on the features of Fresnel diffraction.     

Is the Van Cittert-Zernike Theorem Applicable to Spatially Incoherent Broadband Spectral Source?

This paper deals with the propagation law of mutual intensity and cross-spectral density of the light emitted from an extended broadband spectral source that is spatially incoherent. The mutual intensity of light does not obey the same mathematical formalism as the Van Cittert-Zernike theorem applicable to quasi-monochromatic light, although the cross-spectral density of light does in the propagation zone of the Fresnel diffraction region.     

All-incoherent dispersion-compensated optical correlator

We report on a simple, spatially incoherent, wavelength-independent imaging system that, in contrast to the conventional case, exhibits a dispersion-compensated point-spread function. Our hybrid (diffractive-refractive) three-lens imaging configuration thus acts as an all-incoherent dispersion-compensated optical irradiance correlator. So the optical arrangement is well adapted to processing color information (both spatially and temporally incoherent) under natural illumination.     

Optical security and encryption with totally incoherent light

We present a method for securing and encrypting information optically by use of totally incoherent illumination. Encryption is performed with a multichannel optical processor working under natural (both temporal and spatially incoherent) light. In this way, the information that is to be secured can be codified by use of color signals and self-luminous displays. The encryption key is a phase-only mask, providing high security from counterfeiting. Output encrypted information is recorded as an intensity image that can be easily stored and transmitted optically or electrically. Decryption or authentication can also be performed optically or digitally. Experimental results are presented.     

Spatially incoherent illumination as a mechanism for cross-talk suppression in wide-field optical coherence tomography

Comparison of two illumination modes for wide-field optical coherence tomography has revealed that spatially coherent illumination generates coherent cross talk, causing significant image degradation, and that spatially incoherent illumination, with an adequate interferometer design, provides an efficient mechanism for suppression of coherent cross talk. This is shown by comparison of a pulsed laser with a thermal light source for a U.S. Air Force resolution target covered with a scattering solution made from microbeads as well as for an ex vivo tooth.     

Optical image encryption with Hartley transforms

We propose a new method for image encryption based on Hartley transforms that is a real transform and can be realized by spatially incoherent or coherent illumination. The proposed optical implementation is based on a Michelson-type interferometer in which the pure random intensity is distributed at the Hartley plane in encryption. Computer simulations prove it is possible. A Hartley hologram method is also given and described to resolve the sign ambiguity problem that would be encountered in image reconstruction.     

Optical filtering

This contribution deals with phase and amplitude filters used in coherent, partially coherent and incoherent illumination both for improvement of optical images and for detection of similarities (correlation). Other types of filters such as intensity filters, phase only filters etc. will be also discussed where appropriate. Most of the space, however, will be devoted to optical filtering in coherent illumination.     

Optical fibre excitation by polychromatic partially coherent sources

The general formalism describing modal fields excited in optical fibres by partially coherent sources is given. The limiting cases of spectrally pure, quasi-monochromatic, coherent and totally incoherent sources are discussed.     

Visible regime application of zone plate coded incoherent holography

Unlike conventional optical holography which requires coherent radiation, zone plate coded holography (ZPCH) offers the possibility of encoding 3D information of an incoherent radiation source. But ZPCH with its coherent optical reconstruction (COR) is unsuitable to be used in the visible regime. However, proposed digital ZPCH scheme for visible regime uses digital decoding instead of COR and overcomes this limitation. This paper discusses the issues of visible regime ZPCH and presents experimental results of applying the modified scheme to encode and successfully decode a visible source, for the first time, to our knowledge. In addition to imaging of incoherent radiation sources, visible regime incoherent holography may find use in constructing holograms of live cells or objects, like retina, where coherent illumination can be detrimental.     

Tomographic microscopy of three-dimensional phase objects in spatially incoherent light

The use of spatially incoherent light is proposed for raising the quality of interference projection data in tomographic microscopy of phase objects. The optical scheme of the tomographic microscope is based on the scheme of a Linnik microinterferometer with an extended source of quasi-monochromatic light. Characteristic features of the tomography of phase objects positioned near flat reflecting surfaces are considered.     

Influence of Partially Spatially Coherent Illumination on the Measurement of Two-dimensional Correlation Function

A coherent optical filtering is often applied to the measurement of correlation function of two-dimensional patterns. The present report treats the influence of spatial coherence on such an optical filtering. A general formula for optical filtering with partially spatially coherent illumination is obtained. The intensity distribution of correlation in the output image plane for several special cases is calculated, where different kinds of coherence conditions of illumination in the process of holographic recording of a filter, or of filtering are assumed. An experiment is performed to verify the theory.     

Fiber coupling efficiency for random light and its applications to lidar

Employing the van Cittert-Zernike theorem of classical coherence theory, we derive a general expression for the efficiency with which quasi-monochromatic random light can be coupled to an optical fiber by means of a lens. For the important case of a source with Gaussian intensity distribution, we obtain and discuss the dependence of the coupling efficiency to single-mode fibers on the lens-to-fiber coupling geometry as well as on the ratio of lens size to speckle size. A specialization to the emerging fields of both incoherent and coherent fiber-based lidar applications shows that a maximum coupling efficiency of ~42% can be obtained for a monostatic system.     

Partially coherent multiple-beam interference

The general formula for multiple-beam interference due to regular slit arrays illuminated with partially coherent quasi-monochromatic light is derived. The correlation functions chosen for partially coherent light assume Gaussian, sinc and besinc forms of correlation. The intensity distribution in the interference patterns is presented and discussed as a function of the spatial coherence condition. It is shown that spatial coherence of the illumination largely affects the features of multiple-beam interference patterns.     

Spatial coherence properties of light from optical fibres

The mutual intensity of the optical field in the Fraunhofer diffraction region produced from the end of an optical fibre under illumination of a coherent beam, is theoretically analysed by using an optical fibre-end source model. In this source model, the optical field at the end of the fibre is expressed as an aggregation of independent plane waves with random directions and phases, because the guided modes propagating through the fibre may be regarded as a stochastic process. It is found that the optical field in the diffraction region from the multimode optical fibre is not homogeneous butquasi homogeneous in a statistical sense. The spatial coherence properties in the field are discussed in connection with theV number (the normalized frequency) of the fibre and in comparison with those in the field produced from an incoherent source obeying the van Cittert-Zernike theorem.     

Entangled-photon imaging of a pure phase object

We demonstrate experimentally and theoretically that a coherent image of a pure phase object [implemented by a microelectromechanical system (MEMS) micromirror array] may be obtained by use of a spatially incoherent illumination beam. This is accomplished by employing a two-beam source of entangled photons generated by spontaneous parametric down-conversion. One of the beams probes the phase object while the other is scanned. Though each of the beams is, in and of itself, spatially incoherent, the pair of beams exhibits higher-order interbeam coherence.     

Comparative analysis of the resolving power of optoelectronic imaging systems upon incoherent and coherent illumination of objects

Results of calculations of the resolving power (according to Foucault) of optoelectronic imaging systems with incoherent and coherent illumination under the conditions of atmospheric phase distortions are presented. It is suggested that incoherent optical images are formed in the case of incoherent illumination and speckle images are formed in the case of coherent illumination. The shape of objects observed is estimated from these images. The resolving powers are shown to be practically the same in the formation of incoherent optical images and speckle images in the case of strong phase distortions and smoothing of images by a matrix photodetector. At the same time, the limiting resolving power in the formation of incoherent optical images is twice as large as in the formation of speckle images.     

Space-time analogy for partially coherent plane-wave-type pulses

In this Letter we extend the well-known space-time duality to partially coherent wave fields and, as a limit case, to incoherent sources. We show that there is a general analogy between the paraxial diffraction of quasi-monochromatic beams of limited spatial coherence and the temporal distortion of partially coherent plane-wave pulses in parabolic dispersive media. Next, coherence-dependent effects in the propagation of Gaussian Schell-model pulses are retrieved from that of their spatial counterpart, the Gaussian Schell-model beam. Finally, the last result allows us to present a source linewidth analysis in an optical fiber communication system operating around the 1.55 microm wavelength window.