Complex Coherence Factor Research Articles

Passive 3D Imaging Method Based on Photonics Integrated Interference Computational Imaging System

Planetary, lunar, and deep space exploration has become the frontier of remote sensing science, and three-dimensional (3D) positioning imaging technology is an important part of lunar and deep space exploration. This paper presents a novel passive 3D imaging method based on the photonics integrated interference computational imaging system. This method uses a photonics integrated interference imaging system with a complex lens array. The midpoints of the interference baselines formed by these lenses are not completely overlapped. The distance between the optical axis and the two lenses of the interference baseline are not equal. The system is used to obtain the complex coherence factor of the object space at a limited working distance, and the image evaluation optimization algorithm is used to obtain the clear images and 3D information of the targets of interest. The simulation results show that this method is effective for the working scenes with targets located at single or multiple limited working distances. The sharpness evaluation function of the target presents a good unimodality near its actual distance. The experimental results of the interference of broad-spectrum light show that the theoretical basis of this method is feasible.

Decorrelation and anti-correlation from defocus indigital holographic interferometry.

This paper presents a theoretical modeling of the speckle noise decorrelation in digital Fresnel holographic interferometry in out-of-focus reconstructed images. The complex coherence factor is derived by taking into account the focus mismatch, which depends on both the sensor-to-object distance and the reconstruction distance. The theory is confirmed by both simulated data and experimental results. The very good agreement between data demonstrates the high relevance of the proposed modeling. The particular phenomenon of anti-correlation in phase data from holographic interferometry is highlighted and discussed.

Influence of measurement errors of the complex coherence factor on reconstructed image quality of integrated optical interferometric imagers

Interferometric imagers need to measure the phase, modulus, and spatial frequency coordinates of the complex coherence factor to reconstruct images. However, these three measurement parameters are accompanied by certain measurement errors in the actual imaging process, thereby affecting the quality of the reconstructed image. Based on the checkerboard integrated optical imaging system, we simulate the influence of measurement errors of the complex coherence factor on the imaging performance of the integrated optical interferometric imager. The simulation results show that, on the premise that measurement errors follow the normal distribution, the modulus measurement error does not significantly reduce the quality of the reconstructed image, whereas the phase and spatial frequency coordinate measurement errors have a great impact. When the mean value of the phase measurement error is 0, the standard deviation must be <0.18π to ensure the high quality of the reconstructed image. For the measurement error of the spatial frequency coordinates, when the standard deviation of the lenslet position errors is <0.075 times the shortest baseline length, its influence on the quality of the reconstructed image is acceptable. The simulation results are of great help to the engineering, manufacturing, and application of integrated optical interferometric imaging technology.

Melt pool monitoring in laser beam melting with two-wavelength holographic imaging

Over the past two decades, laser beam melting has emerged as the leading metal additive manufacturing process for producing small- and medium-size structures. However, a key obstacle for the application of this technique in industry is the lack of reliability and qualification mainly because of melt pool instabilities during the laser-powder interaction, which degrade the quality of the manufactured components. In this paper, we propose multi-wavelength digital holography as a proof of concept for in situ real-time investigation of the melt pool morphology. A two-wavelength digital holographic setup was co-axially implemented in a laser beam melting facility. The solidified aluminum tracks and melt pools during the manufacturing of 316L were obtained with full-field one-shot acquisitions at short exposure times and various scanning velocities. The evaluation of the complex coherence factor of digital holograms allowed the quality assessment of the phase reconstruction. The motion blur was analyzed by scanning the dynamic melt pool.

Modeling of speckle decorrelation in digital Fresnel holographic interferometry.

This paper presents analytical modeling of the speckle decorrelation noise in digital Fresnel holographic interferometry. The theoretical analysis is carried out by considering the complex coherence factor between two speckled images from two digitally reconstructed holograms at two different instants. The expression giving the modulus of the coherence factor is established and depends on the local surface deformation and parameters from the holographic setup. The analysis is supported by realistic simulations and experiments. Both simulations and experimental results exhibit a very good agreement with the theoretical prediction.

The study of pixelated sampling and its influences on the 2nd-order spatial coherence measurement

Since the measurement of spatial coherence requires multiple sampling to acquire the complex coherence factor of a wavefield, it is convenient to accomplish such dynamic work by a non-redundant multi-slit through a programmable device such as spatial light modulator (SLM). In this study, we examined the influence of SLM-like pixelated structure, parameterized by whose fill factor, on both intensity distribution (first-order statistics) and complex coherence factor (second-order statistics). Based on the generalized Van Cittert–Zernike theorem that as the source satisfied the quasi-homogeneous condition, the coherence factor of the wavefield was irrelevant to the pixelated sampling structure. The inference was validated by a SLM-based experiment from a pseudothermal light source. We expected this work to be useful for future dynamic coherence measurement.

Spatial coherence measurements of the EUV emission from laser-plasma source based on xenon/helium gas puff target

In this paper, we present the first measurements of the partial spatial coherence of the EUV emission from xenon plasma in laser-plasma source, based on a double stream gas puff target. The Young double slit approach was employed to measure complex coherence factor of the EUV Xe emission at 13.5-nm wavelength in two orthogonal directions. The radius of coherence of ~60 μm was estimated at the distance of 2.1 m from the source. The number of coherently emitted photons was sufficient to demonstrate coherent imaging. Using partially coherent radiation from such source Gabor EUV holography was successfully demonstrated.

Gaussian-Schell analysis of the transverse spatial properties of high-harmonic beams.

High harmonic generation (HHG) is an established means of producing coherent, short wavelength, ultrafast pulses from a compact set-up. Table-top high-harmonic sources are increasingly being used to image physical and biological systems using emerging techniques such as coherent diffraction imaging and ptychography. These novel imaging methods require coherent illumination, and it is therefore important to both characterize the spatial coherence of high-harmonic beams and understand the processes which limit this property. Here we investigate the near- and far-field spatial properties of high-harmonic radiation generated in a gas cell. The variation with harmonic order of the intensity profile, wavefront curvature, and complex coherence factor is measured in the far-field by the SCIMITAR technique. Using the Gaussian-Schell model, the properties of the harmonic beam in the plane of generation are deduced. Our results show that the order-dependence of the harmonic spatial coherence is consistent with partial coherence induced by both variation of the intensity-dependent dipole phase as well as finite spatial coherence of the driving radiation. These findings are used to suggest ways in which the coherence of harmonic beams could be increased further, which would have direct benefits to imaging with high-harmonic radiation.

Circular grating interferometer for mapping transverse coherence area of X-ray beams

A circular grating interferometer was used to map the transverse coherence area of an X-ray beam. Due to the radial symmetry of the circular grating, coherence lengths along all transverse directions were obtained simultaneously by measuring the visibility decay of interferograms recorded at different distances behind a single circular π/2 phase grating. The technique is model-free and provides direct measurement of the complex coherence factor of the beam. The use of a circular grating also enables the unique capability of measuring the source shape profile. Sensitivity of this technique was demonstrated by detecting the small source tilt of a few degrees.

Digital in-line holography with a rectangular complex coherence factor

We propose in this paper the study of a particular spatially partially coherent source applied to digital in-line holography of dense particle flow. A source with a rectangular complex coherence factor is implemented. The effects of such a source on the intensity distribution of the diffraction pattern are described. In particular, we show that this type of source allows us to eliminate the diffraction pattern along one axis while all the information about the dimension of the particle is kept along the other perpendicular axis. So particle images can be well reconstructed along one direction and the speckle can be largely limited.

Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry

A study of the coherence and wavefront properties of a pseudo-channel-cut monochromator in comparison with a double-crystal monochromator is presented. Using a double-grating interferometer designed for the hard X-ray regime, the complex coherence factor was measured and the wavefront distortions at the sample position were analyzed. A transverse coherence length was found in the vertical direction that was a factor of two larger for the channel-cut monochromator owing to its higher mechanical stability. The wavefront distortions after different optical elements in the beam, such as monochromators and mirrors, were also quantified. This work is particularly relevant for coherent diffraction imaging experiments with synchrotron sources.

Speckle noise suppression in measurement by phase-shifting digital holography

A new algorithm for fringe phase analysis is proposed for shape and deformation measurement of diffusely reflecting surfaces by digital holography. It derives the phase of the averaged conjugate product of complex amplitudes before and after wavelength change or object deformation, corresponding to the complex coherence factor, and is consistent with a theory on fringe formation in holographic interferometry. By experiments and computer simulations, it is demonstrated that the algorithm is much more immune to speckle noise in phase analysis and unwrapping than conventional methods.

Measurement of Surface Shape and Position by Phase‐Shifting Digital Holography

Abstract: Phase‐shifting digital holography is applied to measure the shapes and positions of rough surfaces from the averaged conjugate product of the reconstructed complex amplitudes, named complex coherence factor, corresponding to dual wavelengths. The phase of the averaged product at the object plane provides the shape of the surface, whereas the peak position of the modulus with respect to reconstruction distance provides the position of the surface. The phase is almost free from speckle noise and easy to be unwrapped. The resultant resolution of surface shape amounts to a few tens of micrometres. The sensitivity of the position measurement that requires no marking on the object is several per cent of object distance from a charge‐coupled device (CCD). The method corresponds to the detection of the position of maximum contrast of the fringes to be observed in conventional holographic interferometry. It makes use of fringe phase for shape measurement and fringe contrast for position measurement. Both the theory explaining the principle and experimental results are presented.

Spatial Coherence Measurement of 13.9 nm Ni-like Ag Soft X-Ray Laser Pumped by a 1.5 ps, 20 J Laser

In this paper, we report the first measurement of the time-integrated spatial coherence of the Ni-like Ag X-ray laser at 13.9 nm pumped by a 1.5 ps, 20 J Nd glass laser, in which the transient collisional excitation (TCE) pumping scheme is realized. The time-integrated complex coherence factor (CCF) of the X-ray laser has been determined from partially coherent diffraction patterns of a multislit array placed 1 m away from the X-ray laser source. The transverse coherence lengths in the directions horizontal and vertical to the Ag target surface are estimated respectively to be within 110 µm to 140 µm at a position 1 m from the X-ray laser source. We tried to explain the profile of the CCF with a quasi-monochromatic incoherent source model with various profiles.

Spatial coherence property of a laser beam during acousto-optic diffraction

The spatial coherence property of a partially coherent light during the Bragg acousto-optic interaction is investigated. Starting from the wave equation, four coupled, parabolic equations that can describe the evolution and the propagation of mutual intensity functions of the diffracted light during the acousto-optic interaction are derived. A partially coherent light beam with arbitrary spatial profile and complex degree of spatial coherence is assumed to be incident on the Bragg acousto-optic cell. With the use of a statistical theory of linear systems, a general formalism of angular-correlation functions for zero-order and minus-one-order light can be derived. The corresponding mutual intensity and complex coherence factor functions are hence implemented numerically. From the solutions one can note that, through the acousto-optic interaction, the degrees of spatial coherence of the diffracted light beams are controllable by the intensity and the frequency of the sound wave.

X-ray speckles from an optical grating

We report a study of speckles produced by x rays of partial transverse coherence scattered from the surface of an optical reflection grating. This study reveals the presence of surface inhomogeneity that is undetectable with either laser (visible) light or transversely incoherent x rays. Qualitative analysis of the speckle patterns provides us with information on the surface morphology of the optical grating. The underlying order due to the periodicity of the grating enhances the detection of the x-ray speckles. The speckle patterns are obtained using a well-characterized partially transverse-coherent source (a secondary source) produced with an arrangement of slits and a focusing mirror in a synchrotron x-ray beamline. The degree of transverse coherence is measured and compared quantitatively with statistical optics predictions for the complex-coherence factor. {copyright} {ital 1998} {ital The American Physical Society}

Estimation of the squared modulus of the mutual intensity from high-light-level intensity measurements

The problem of estimating the squared modulus of the mutual intensity (or the complex coherence factor) from high-light-level intensity measurements is addressed for the situation in which the fluctuations of the complex-valued amplitude are governed by circular-Gaussian statistics and the light level is high enough that all nonclassical fluctuations of the measurements can be ignored. A lower bound on the variance of any unbiased estimator is presented, and this bound is compared with the variance of Ebstein’s polynomial estimators [ J. Opt. Soc. Am. A8, 1450 ( 1991)] along with the variance of the maximum-likelihood estimator.

Imaging in an Optical Projection System with a Laser Light Source. I: Gaussian Laser Light Illumination

Intensity distributions for a line-and-space pattern with 5 lines are calculated using a one-dimensional model. Their dependence on Gaussian laser light illumination is analyzed. The laser light travels distance z and illuminates a second light source plane for an illumination system. The complex coherence factor µ12 at the object plane has an absolute value of 1, but a change in the phase of µ12 becomes greater with increasing distance z or coherence factor σ c. Compared with imaging in incoherent light source systems, intensity distributions at the image plane are more easily varied depending on z and σ c, and focal tolerance is narrower.

Spatial coherence diagnostic for laboratory x-ray lasers (abstract)

A spatial coherence diagnostic for measuring the spatial coherence of laboratory x-ray lasers has been developed. The x-ray laser beam illuminates a uniformly redundant array of slits, producing a partially coherent diffraction pattern which can be analyzed to yield the complex coherence factor for the x-ray laser beam from a single x-ray laser pulse. Measurements using x-ray lasers at LLNL will be presented and discussed in detail. Results from experiments conducted in collaboration with the Rutherford x-ray laser consortium to improve the spatial coherence of x-ray lasers will also be discussed. A definition of a highly spatially coherent x-ray laser based on simple physical arguments will be given. This work was performed under the auspices of the U. S. Department of Energy by Lawrence Livermore National Laboratory under contract No. W-7405-ENG-48.

Complex interferometry

An efficient device using a transparent grooved screen and three detector channels is described for measuring the complex coherence factor between two optical beams. The device statically provides both in-phase and quadrature fringe components, the same signals as are customarily available in radio interferometry. The deleterious effects of a nonaplanatism in stellar interferometry are described along with a novel configuration for interferometrically combining two telescopes to provide simultaneously fringes anywhere in the field of view with the goal of optical aperture synthesis. Complex fringe detection also has certain applications in spectral interferometry, and a suitable interferometer with achromatized throughput is described. That interferometer may also be used for distance or thickness measurement.