Full length articleShock-wave distortion cancellation using numerical recalculated intensity propagation phase holography
Introduction
Digital holography is a non-intrusive optical technique that enables three-dimensional (3D) analysis of a wide range of systems. This is accomplished by numerically refocusing diffraction patterns generated by objects that absorb, refract, or delay light propagation [1], [2], [3], [4]. Digital in-line holography (DIH) has been successfully applied in the study of several multi-phase flow systems [3] including liquid breakup systems [5], [6], [7], aluminum particle combustion in solid propellants [8], [9], [10], and velocimetry in complex flows [11], [12], [13].
As experimental conditions become more extreme, shock-waves [14], [15], flames [16], [17], high-speed flows [18], and other phenomena that generate density gradients produce optical distortions in digital in-line holograms, as demonstrated in Fig. 1(a). These distortions make locating the true edge of an absorbing feature more difficult, greatly limiting the ability to characterize quantities such as particle sizes and positions. One new experimental technique, phase conjugate digital in-line holography (PCDIH) [19], [20], [21], [22], was recently developed to remove a large portion of the phase-distortions associated with shock-waves. PCDIH passes a laser beam over a region of interest containing both objects and distortions. Then, the light is passed into a phase conjugate mirror, which inverts the phase [23]. When the reflected beam passes through the distortion a second time, the forward and inverted phases cancel to remove distortions. While PCDIH is an effective in-situ method that has been demonstrated at up to 5 million-frames-per-second [22], it does have several drawbacks. First, the technique requires nonlinear four-wave mixing to generate the phase conjugate signals. This requires high laser pulse energies, scales poorly at ultra-high-speeds, and double-passes light through the object and distortion field [22]. By double-passing the light through the phase distortion, additional imaging artifacts due to object or shock-wave motion during the laser light time-of-flight are generated. Outside of PCDIH, there are currently no alternative techniques or examples in the literature that demonstrate shock-wave distortion removal for particle tracking applications.
Phase measurement techniques, on the other hand, have been explored in other microscopy-related application areas. This includes electric field propagation (EFP) techniques such as two-step phase measurement [24], [25], [26] and parallel phase shifting [27], [28], [29], [30], [31], [32], [33]. In these techniques, the amplitude and phase information is separated using iterative numerical post-processing. This includes phase estimation using trained neural networks [34] and iterative phase retrieval (IPR) [35] methods. Because phase measurement techniques focus on accurately determining phase, the algorithms can be more computationally intensive, requiring iterative processing and the application of phase unwrapping algorithms [36].
Rather than cancelling the phase distortions in-situ or iteratively determining phase, we propose removal of the phase distortion contributions numerically in a single post-processing step. Numerical phase distortion cancellation has not been previously explored in the literature. Additionally, electric field hologram, phase measurement, and numerical distortion cancellation methods have not been applied previously in the literature for tracking particles in high speed flows. To remove shock-wave distortions, we propose an innovative recalculated intensity propagation phase holography (RIP phase holography or RIPPH) method for numerical phase distortion cancellation. The first step of the technique is to capture the electric field of the hologram using a single camera and exposure. Then, the electric field is propagated to the center of the phase distortion source. At this point, the intensity is calculated to generate a RIPPH image, effectively removing phase contributions in a simple, elegant, and computationally efficient fashion. Further propagation of the intensity hologram to other planes, as illustrated in Fig. 1(b), show that phase distortions are successfully cancelled.
The RIPPH technique has several important advantages over existing methods like DIH, EFP, PCDIH and IPR. Traditional EFP and DIH experiments do not implement phase cancellation and cannot be used quantitatively in distorted environments with both amplitude and phase objects. Iterative phase retrieval methods require repetitive processing to separate phase objects from amplitude objects. With RIPPH, no quantitative phase information is needed; therefore the numerical correction algorithms are significantly simpler, computationally efficient, and more practical to apply than IPR methods. Only the approximate -location of the distortion is required and phase distortions are automatically removed during intensity calculation. After correction with RIPPH, quantitative image segmentation can be completed with the same algorithms as traditional DIH techniques. Because scattering processes are linear, RIPPH does not require high power lasers, nonlinear optical methods, or four-wave mixing. Therefore RIPPH is significantly simpler to experimentally implement than PCDIH and scales well to higher repetition rates. In addition, light only needs to pass once through the object field and imaging artifacts associated laser light time-of-flight effects no longer need to be considered.
In this paper, we explore the RIPPH technique in several different scenarios where refractive index gradients cause optical distortions. To evaluate the effectiveness of the technique, the theory behind RIPPH is first discussed followed by simulation and numerical distortion cancellation methodologies. RIPPH is then compared to DIH, EFP, and IPR techniques. Several different experimental systems are then studied using both DIH and RIPPH, ranging from low Reynolds number flows driven by thermal gradients to extreme supersonic and explosive environments. Results illustrate how RIPPH can be successfully applied in several systems with phase distortions that were previously difficult to study using DIH. In this paper, we demonstrate successful numerical phase distortion cancellation for the first time for digital holograms. This work is also the first to apply the technique to environments with shock-waves, blast-waves, and density gradients, which are of increasing importance to fields ranging from fluid dynamics to hypersonics to energetic materials.
Section snippets
Digital in-line holography
Because of its relative simplicity and robustness, DIH is a commonly used diagnostics for studying multiphase flows [3]. DIH captures 3D particle field information using a single two-dimensional sensor and a single laser beam. Experimental implementations propagate a coherent light source with a reference electric field of through a 3D space containing distributed objects. Here, is the wave number, is the wavelength, and is the frequency. Objects in the
Simulations
In order to study the performance of the distortion correction concept, simulations were created to test the RIPPH methodology. First, a 532 nm laser light source is simulated and propagated through a purely absorptive 100 m radius vertical wire and a 1.2 mm radius spherical shock-wave produced by a laser spark. Fig. 3(a) illustrates the geometry of the simulation. Here, the shock-wave distortion is simulated as a planar object with uniform phase equivalent to a 3D spherical distortion
Experimental results and discussion
Three separate systems were experimentally studied with the RIPPH technique: a supersonic air jet, a spherically expanding shock-wave laden with particles, and a convectively-driven thermal gradient. In addition to demonstrating different distortion conditions, each of these experiments also exhibits different configurations between the phase distortion and the objects of interest. Distorted DIH and distortion-cancelled RIPPH measurements are made in each of these systems for comparison.
Conclusion
In this paper, we propose a new recalculated intensity propagation phase holography (RIPPH) technique for numerically cancelling phase distortions in 3D holographic images. In RIPPH, amplitude and phase information is numerically constructed from four interferograms captured at different polarizations. Numerical phase distortion correction is then implemented by propagating the electric field to the center of the phase distortion and then calculating the intensity to remove phase data. By
CRediT authorship contribution statement
Andrew W. Marsh: Methodology, Software, Resources, Investigation, Visualization, Writing - original draft. Tyrus M. Evans: Conceptualization, Methodology, Software, Resources. Benjamin C. Musci: Investigation, Resources. Jaylon Uzodima: Conceptualization, Resources. Sean P. Kearney: Methodology, Funding acquisition, Writing - review & editing. Daniel R. Guildenbecher: Methodology, Funding acquisition, Writing - review & editing. Yi Chen Mazumdar: Conceptualization, Methodology, Software,
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
Support from the Sandia National Laboratories Academic Alliance Laboratory Directed Research and Development (LDRD) program is gratefully acknowledged. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. The funding source had no involvement
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