Reconstruction of longitudinal distributed incoherent 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.

Nonuniform coherence sampling for fields produced by incoherent three-dimensional sources

A nonuniform sampling scheme is described for measuring the mutual intensity of the wave field produced in a plane a distance z from a spatially incoherent, three-dimensional source object. Both uniform and nonuniform sampling are analyzed and discussed in detail, and comparisons of the two schemes are made. It is shown that nonuniform sampling requires fewer measurements than uniform sampling to specify the coherence function. Additionally, the smallest separation required between measurement points is larger for the nonuniform case.

Multiplex sensors and the constant radiance theorem

Coherent mode representation of the cross-spectral density is used to derive a modal analog of the constant radiance theorem with general applicability to linear optical systems. The theorem is used to consider the relationship between spatial detector geometry and multiplexing capacity.

Cone-beam tomography with a digital camera

We show that x-ray computer tomography algorithms can be applied with minimal alteration to the three-dimensional reconstruction of visible sources. Diffraction and opacity affect visible systems more severely than x-ray systems. For camera-based tomography, diffraction can be neglected for objects within the depth of field. We show that, for convex objects, opacity has the effect of windowing the angular observation range and thus blurring the reconstruction. For concave objects, opacity leads to nonlinearity in the transformation from object to reconstruction and may cause multiple objects to map to the same reconstruction. In x-ray tomography, the contribution of an object point to a line integral is independent of the orientation of the line. In optical tomography, however, a Lambertian assumption may be more realistic. We derive an expression for the blur function (the patch response) for a Lambertian source. We present experimental results showing cone-beam reconstruction of an incoherently illuminated opaque object.

Astigmatic coherence sensor for digital imaging

We present a novel sensor that measures the entire spatial coherence function within an aperture by use of a variable astigmatic lens. This sensor permits digital capture and processing of partially coherent fields. We demonstrate the sensor by sampling and computing the coherent modes of a three-dimensional incoherent source.

Visible cone-beam tomography with a lensless interferometric camera

Digital processing of optical coherence functions can reconstruct three-dimensional objects illuminated by incoherent light. It is shown that Fourier analysis of the mutual intensity of the field produces projections that are mathematically identical to the projections of x-ray cone-beam tomography. A lensless interferometric camera that captures planes of mutual intensity data is described and used to reconstruct an incoherently illuminated visible object in three dimensions.

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.