Three-dimensional imaging of random radiation sources

Incoherent Diffractive Imaging via Intensity Correlations of Hard X Rays

Established x-ray diffraction methods allow for high-resolution structure determination of crystals, crystallized protein structures, or even single molecules. While these techniques rely on coherent scattering, incoherent processes like fluorescence emission-often the predominant scattering mechanism-are generally considered detrimental for imaging applications. Here, we show that intensity correlations of incoherently scattered x-ray radiation can be used to image the full 3D arrangement of the scattering atoms with significantly higher resolution compared to conventional coherent diffraction imaging and crystallography, including additional three-dimensional information in Fourier space for a single sample orientation. We present a number of properties of incoherent diffractive imaging that are conceptually superior to those of coherent methods.

Passive quasi-monochromatic depth discrimination using a coherence imager with volume holographic pupil

We present a new passive depth detection method for quasi-monochromatic and spatially incoherent objects. We utilize the wavefront discrimination properties of a volume holographic pupil combined with a measurement of the degree of coherence of the diffracted field. Depth detection is posed as the Bayesian hypothesis testing on the outcome of the coherence measurement. We present the analysis of our proposed optical system and experimental results confirming binary depth discrimination with high confidence for featureless objects.

Integral three-dimensional imaging with digital reconstruction

A computed three-dimensional (3-D) display system based on integral imaging is presented. The 3-D image is reconstructed by numerical processing of an optically observed image array formed by a microlens array. The algorithm for reconstructing 3-D images is robust, and it enables us to obtain the images viewed from arbitrary directions. This computer-based image retrieval makes it possible to improve qualities of the image such as contrast, brightness, and resolution by numerical techniques. Also, this method eliminates the need for special purpose optical equipment such as high-quality liquid-crystal display and micro-optics components to display the 3-D images. We present experimental results of 3-D image reconstruction to test and verify the performance of the algorithms and the imaging system.

Three-dimensional coherence imaging in the Fresnel domain

We show that three-dimensional incoherent primary sources can be reconstructed from finite-aperture Fresnel-zone mutual intensity measurements by means of coordinate and Fourier transformation. The spatial bandpass and impulse response for three-dimensional imaging that result from use of this approach are derived. The transverse and longitudinal resolutions are evaluated as functions of aperture size and source distance. The longitudinal resolution of three-dimensional coherence imaging falls inversely with the square of the source distance in both the Fresnel and Fraunhofer zones. We experimentally measure the three-dimensional point-spread function by using a rotational shear interferometer.

Evaluation of three-dimensional convolutions by use of two-dimensional filtering

A three-dimensional to two-dimensional mapping is proposed that permits the reduction of three-dimensional convolutions-correlations to two-dimensional ones and thereby lays a theoretical foundation for their optical implementation.

Three-dimensional optical Fourier transform and correlation

Optical implementation of a three-dimensional (3-D) Fourier transform is proposed and demonstrated. A spatial 3-D object, as seen from the paraxial zone, is transformed to the 3-D spatial frequency space. Based on the new procedure, a 3-D joint transform correlator is described that is capable of recognizing targets in the 3-D space.

Reconstruction of longitudinal distributed incoherent sources

We describe measurement of the degree of coherence induced by a random light source distributed along the longitudinal z axis. If this degree of coherence is measured only between all the in-plane pairs of points placed along the radial lines it is proportional to the Fourier transform of the source's three-dimensional intensity distribution as seen from the paraxial far zone. A reconstruction of the source shape from the measured degree of coherence is also demonstrated.