diff --git "a/FNE3T4oBgHgl3EQfVgrM/content/tmp_files/load_file.txt" "b/FNE3T4oBgHgl3EQfVgrM/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/FNE3T4oBgHgl3EQfVgrM/content/tmp_files/load_file.txt" @@ -0,0 +1,760 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf,len=759 +page_content='Threading light through dynamic complex media Chaitanya K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Mididoddi,1, ∗ Christina Sharp,1 Philipp del Hougne,2 Simon A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Horsley,1 and David B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Phillips1, † 1Physics and Astronomy, University of Exeter, Exeter, EX4 4QL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' UK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' 2Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Rennes, CNRS, IETR – UMR 6164, F-35000 Rennes, France.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The scattering of light impacts sensing and communication technologies throughout the electromagnetic spec- trum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Overcoming the effects of time-varying scattering media is particularly challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' In this article we introduce a new way to control the propagation of light through dynamic complex media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Our strategy is based on the observation that many dynamic scattering systems exhibit a range of decorrelation times – meaning that over a given timescale, some parts of the medium may essentially remain static.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We experimentally demonstrate a suite of new techniques to identify and guide light through these networks of static channels – threading op- tical fields around multiple dynamic pockets hidden at unknown locations inside opaque media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We first show how a single stable light field propagating through a partially dynamic medium can be found by optimising the wavefront of the incident field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Next, we demonstrate how this procedure can be accelerated by 2 orders of magnitude using a physically realised form of adjoint gradient descent optimisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Finally, we describe how the search for stable light modes can be posed as an eigenvalue problem: we introduce a new matrix operator, the time-averaged transmission matrix, and show how it reveals a basis of fluctuation-eigenchannels that can be used for stable beam shaping through time-varying media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' These methods rely only on external camera measurements recording scattered light, require no prior knowledge about the medium, and are independent of the rate at which dynamic regions move.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Our work has potential future applications to a wide variety of technologies reliant on general wave phenomena subject to dynamic conditions, from optics to acoustics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Introduction Optical scattering randomly redirects the flow of light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' It is a ubiquitous phenomenon that has wide-ranging effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Since imaging relies on light travelling in straight lines from a scene to a camera, scattering prevents image formation through fog, and precludes high-resolution microscopy inside biological tissue [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Scattering also impairs optical communications through air and water, and disrupts the transmission of mi- crowave and radio signals [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Overcoming the adverse effects of light scattering is an extremely challenging problem [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Nonetheless, due to its prominence, substantial progress has been made over the last decades [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' When light propagates through a strongly scattering medium (also known as a ‘complex’ medium [1]), the wave- front of the incident optical field is distorted, corrupting the spatial information it carries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Elastic scattering from a static medium is deterministic, meaning that the precise way in which light has been perturbed can be characterised and sub- sequently corrected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' By sending a series of probe measure- ments through the medium, a digital model of its effect on light can be created: represented by a linear matrix operator known as a transmission matrix (TM) [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Once measured, the linearity of Maxwell’s equations means that the TM describes how any linear combination of the probe fields will be trans- formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The TM reveals how to best undo the distortion im- parted to a scattered field emerging from a complex medium, and the time-reverse: how to pre-distort an input optical field so that it evolves into a user-defined state at the output – a technique known as wavefront shaping [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Using modern high-resolution spatial light modulators (SLMs), it is possible to precisely measure and control the ∗ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='mididoddi@exeter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='uk † d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='phillips@exeter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='uk relative intensity, phase and polarization of thousands of inde- pendent optical spatial modes as they undergo many scattering events inside a highly turbid medium [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Thus, wavefront shaping, and the closely related technique of optical phase conjugation [9], have been used to image up to a depth of sev- eral hundred microns into fixed biological tissue [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' TM- based approaches have also inspired new forms of ultra-thin micro-endoscopy through rigidly-held strands multimode op- tical fibre (MMF) [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Despite these successes, control of light through time- varying complex media remains a largely open problem [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Evidently, wavefront shaping can only be successfully applied if the medium in question remains predominantly stationary for the time taken to make probe measurements and apply a wavefront correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Yet many application scenarios feature complex media that rapidly fluctuate on a timescale of mil- liseconds or faster – rendering wavefront shaping approaches exceedingly difficult [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Overcoming this challenge offers a stepping stone to a potent array of new technologies, in- cluding the ability to look directly inside living biological tis- sue, to see through fog, and to increase the data-rate of optical communications through the turbulent atmosphere and flexi- ble fibre-optics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' So far, the main strategies to control light through mov- ing complex media have focused on achieving the task of wavefront shaping as quickly as possible [13–17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' In the op- tical regime, beam shaping at kiloHertz rates can be imple- mented with digital micro-mirror devices (DMDs) [18–20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The need for yet higher switching rates has spawned the de- velopment of ultra-fast SLMs capable of wavefront shaping at hundreds of kiloHertz [21, 22] while megaHertz to giga- Hertz modulation-rate SLMs hold future promise [23, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Spectral multiplexing enables many probe measurements to be made simultaneously, speeding up the data gathering part of the wavefront shaping process [22, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' In addition, the arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='04461v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='optics] 11 Jan 2023 2 number of probe measurements needed to reconstruct a us- able TM can be reduced by exploiting prior knowledge about the medium itself – such as correlations between elements of the TM (known as memory effects), predictions about how the power is distributed over the TM elements, or a recent but slightly degraded TM measurement [26–33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Fast optical focusing inside biological tissue can be achieved with opti- cal phase conjugation guided by ultrasonic guide-stars – re- lying on the lower levels of scattering experienced by ultra- sound [34–37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' A variety of other methods relying on correla- tions between the object of interest and externally measurable signals offer alternative routes to image through moving com- plex media [38, 39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Here we introduce a new way to control the propagation of light through dynamic scattering media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Our approach is complementary to existing techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We begin by classify- ing complex media into three categories, based on the level and type of motion exhibited over the timescale required for wavefront shaping, denoted by τws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Class 1 represents static complex media that remain completely fixed over time τws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Established TM-based methods can be applied to determin- istically control scattered light in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Class 2 repre- sents moving complex media, which undergo substantial mo- tion everywhere over time τws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' This class of media eludes current wavefront shaping approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' However, there is an opportunity to make progress by considering a third class – representing an edge-case between classes 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Class 3 comprises partially moving scattering media, which, over the timescale τws, exhibit localised pockets with time-varying properties embedded within a static medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Any dynamic complex medium possessing a range of decorrelation rates has the potential to be classified in this way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' For example, this sit- uation describes: tissue in which small capillaries conducting blood flow represent faster moving regions surrounded by a matrix of more slowly changing scattering material;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' pockets of turbulent air above hot chimneys within calmer air over a city skyline;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' and the movement of people modifying the scat- tering of microwaves only at floor level throughout a building.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' In this article we focus on how to identify light fields that predominantly stay within the static regions of such partially moving complex media (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' class 3 complex media).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We experimentally demonstrate three new techniques that excite largely stable modes within these environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We show how these optimised modes scatter almost entirely around all moving pockets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' These methods do not rely on prior knowl- edge of the location of dynamic regions and only require measurements external to the medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' These measurements can be made on the same timescale or more slowly than the medium is fluctuating – crucial for the practical application of these techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Our work expands the toolkit of methods to overcome dynamic scattering, pointing to a range of future applications in the fields of imaging, optical communications, and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Results When a light field u is incident on a time-varying medium, the time-dependent transmitted field is given by v(t) = T(t)u, (1) where T(t) is the time-dependent transmission matrix of the medium, and here u and v are represented as column vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Our aim is to find an input u that scatters around dynamic regions within the medium, thus minimising the fluctuations in the output field v(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' To experimentally investigate this new form of light con- trol, we emulate a three-dimensional time-varying scattering medium using a cascade of three computer controlled diffrac- tive optical elements, each separated by a free-space distance of δz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Cascades of phase planes can emulate atmospheric turbulence [40, 41] and have also been shown to mimic the complicated optical scrambling effects of a multiple scattering sample [42, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' In practice this set-up is implemented using multiple reflections from a single liquid crystal SLM, allow- ing the phase profiles to be arbitrarily digitally reconfigured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We choose this test-bed as it is a versatile way to control the degree of scattering, and the number and location of dynamic regions for proof-of-principle experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' 1(e), top row, we display a static random phase pattern on each phase screen, spatially distorting optical signals flowing through the optical system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' On each plane we also define an area within which the phase profile is programmed to randomly fluctuate in time – these patches represent the ‘pockets’ of dynamic material embedded inside the scattering sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' A second SLM is used to shape the light incident onto the dynamic medium, and a camera records the level of intensity fluctuations in transmitted light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Unguided optimisation: We first explore a straight-forward optimisation method: iterative modification of input field u to suppress intensity fluctuations at the output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Figure 1(a) shows a schematic of this approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Supplementary Informa- tion (SI) §1 shows a full diagram of the optical set-up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The op- timisation commences by transmitting an initial trial field u0 through the sample, and recording the intensity fluctuations on the camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We sample 20 realisations of the fluctuating speckle pattern, and the level of fluctuations over these frames is quantified by the objective function F = ¯σI/¯I, where ¯σI denotes the standard deviation of the fluctuating intensity, av- eraged over all illuminated camera pixels, and ¯I is the aver- age transmitted intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' This choice of objective function ensures that fluctuations are normalised with respect to trans- mitted power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The input SLM used to generate the incident fields is sub- divided into 1200 super-pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The phase delays imparted by these super-pixels represents the independent degrees-of- freedom we aim to optimise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We begin by setting each super- pixel to a random phase value, creating incident field u0, and measure the level of output fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Next, two new test fields are sequentially transmitted through the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' These are generated by randomly selecting half of the input SLM super-pixels used to create u0, and adding/subtracting a small constant phase offset δθ from these pixels, yielding inputs 3 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Unguided optimisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' (a) Schematic of experimental set-up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' An input wavefront is iteratively modified to reduce the intensity fluctuations in transmitted light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' (b) A plot of fluctuation level as a function of iteration number throughout the optimisation procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Convergence is reached after several thousand iterations: the fluctuation level does not fall to zero, but plateaus when the residual fluctuations fall below the experimental noise floor, indicated (approximately) in pink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' (c) Fluctuations in the output field for a randomly chosen input field used as the starting point of the optimisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Upper heat maps show the mean intensity of transmitted light at the output plane, and lower heat maps show the fluctuation level around the mean, represented as a standard deviation around the mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The line-plots show line-profiles through the output field along the lines marked with white hatched lines, with mean intensity (red line) and fluctuations about the mean (gray shading).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' (d) Equivalent plot to (c) but now showing the optimised transmitted field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We see the fluctuations have been strongly suppressed in (d) compared to (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' (e) Measured shape of the optimised field inside the dynamic scattering sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The top row shows the 3 phase planes that form the scattering system, with a fluctuating region on each plane highlighted by a red box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The middle and bottom rows show the optical field (middle row) and intensity pattern (absolute square of the field – bottom row) incident on each plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We see that the optimised field arriving at each plane has a low intensity region corresponding to the location of the fluctuating region – highlighted by white arrows – thus ‘avoids’ these regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' u±δθ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We measure the corresponding level of output fluctua- tions for these two new trial inputs, and if either exhibit lower fluctuations than u0, the optimised input field is updated ac- cordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' This process is repeated until the output fluctuation level no longer improves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' This algorithm relies on accurately capturing the output fluctuations on each iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' However, even in the absence of any other sources of noise, there is an uncertainty in the mea- surement of ¯σI and ¯I due to the finite number of realisations of the dynamic medium sampled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' To enhance the algorithm’s robustness to this source of noise, on each new iteration we re-test the optimum input field from the last iteration and com- pare this to the new trial fields – doing so increases the optimi- sation time, but crucially prevents a single measurement with an erroneously low value of F from blocking the optimiser from taking steps in subsequent iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Figure 1(b) shows a typical optimisation curve throughout our experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The noise floor is governed by the uncertainty in real fluctuations detailed above, along with small variations in the intensity of the laser source, camera noise and uncontrolled fluctuations in light reflecting from the liquid crystal SLM as it is updated, which all add to the apparent level of measured fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Figures 1(c) and 1(d) show examples of the output fluctua- tions of an initial trial field (c) and an optimised field (d) using this approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' See also Supplementary Movie 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We see that fluctuations of the output field are heavily suppressed after optimisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' As we have full control over the test scattering medium, we are able to digitally ‘peel back’ the outer scat- tering layers to look inside and directly observe the evolution of the optimised field as it propagates through the cascade of phase planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Experimentally this is achieved by switching- off the aberrating effect of the second and third phase planes, and imaging the optimised field that is incident on plane 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We recover the phase of this optical field using digital holog- raphy, and reconstruct the fields at planes 1 and 3 by numeri- cally propagating the field at plane 2 (see SI §2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We see the optimised field scatters through the medium to form a speckle pattern that evolves to exhibit near-zero intensity at the loca- Fluctuating regions 2元 (a) (b) (e) Phase masks 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='25 Lens Optimisation 2 3 Fluctuation level Camera Phase masks Phase (rad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=') Shaped input wavefront Noise floor Intensity fluctuations Dynamic scatterer 0 0 0 3000 Iteration number Feedback 2元 (c) Optical field Initial transmitted field (p) Optimised transmitted field (pet) Phase ( Intensity Intensity 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='5 Amp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' 0 0 Mean Intensity (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=') Intensity intensity Std.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' intensity 8z fluctuations Sz 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='12 Speckle evolution Std.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' intensity fluctuations4 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Physical adjoint optimisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' (a) Schematic of experimental set-up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' On iteration i an input field u(i) is transmitted through the dynamic medium from the left-hand-side (LHS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The output field is time-averaged on the right-hand-side (RHS) – the schematic shows output fields recorded at individual times v(t1), v(t2) · · · v(tN) (where N is the total number of recorded output fields).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' These are averaged to yield ⟨v⟩t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Digital optical phase conjugation (DOPC) is carried out to transmit the phase conjugate of ⟨v⟩t back through the medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The resulting field emerging on the LHS is then time-averaged, and used to calculate δu, such that the input of the next iteration (i + 1) is given by u(i+1) = u(i) + δu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' (b) A plot of fluctuation level as a function of iteration number throughout the optimisation procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' In this scheme, convergence is reached after ∼ 15 iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' (c) The experimentally recorded intensity of the optimised field arriving at the three phase planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The maximum intensity at each plane is normalised to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' The white squares indicated the location of the moving region on each plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We see that, once again, the optimised field avoids these moving regions of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' tions of the fluctuating regions on each plane (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' 1(e), bot- tom row) – thus avoiding these dynamically changing regions and minimising fluctuations in the transmitted field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' This is an encouraging result, however this form of undirected optimisation is a relatively slow process – in this case requiring several thousand iterations to converge (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' 1(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Therefore, we next ask: is there a way to find optimised fields more rapidly?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Physical adjoint optimisation: In our first strategy, on each iteration we directly measure how one randomly chosen spa- tial component of the input field should be adjusted to re- duce the fluctuations in the output field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' We now describe a more sophisticated technique to simultaneously obtain how all spatial components composing the input field should be adjusted in parallel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' This strategy converges to an optimised input beam in far fewer iterations than unguided optimisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Our approach can be understood as gradient descent optimi- sation using fast adjoint methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Adjoint optimisation refers to the efficient computation of the gradient of a function for use in numerical optimisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Here, we lack sufficient in- formation to numerically perform this adjoint operation, but instead we show how it is possible to physically realise it by passing light in both directions through the dynamic scattering medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' SI §3 gives a detailed derivation of this method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' In sum- mary, to suppress output fluctuations we aim to maximise the correlation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' overlap integral) between all output fields over time, given by the real positive scalar objective function F = ����� T � t=1 T � t′=1 � v†(t) · v(t′) � ����� 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' (2) To increase F, at each iteration we incrementally adjust the complex field of all elements of the input field u, so that the input field at iteration i + 1 is given by u(i+1) = u(i) + δu, where u(i) is the input field of iteration i, and column vector δu = δAeiθ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Here δA is the optimisation step size: a small real positive constant, and we find (see SI §3) that column vector θ is given by θ = − arg � TT · ⟨v∗⟩t � , (3) where ⟨v∗⟩t is the phase conjugate of the time-averaged out- put field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Our adjoint optimisation scheme is shown schematically in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' 2(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Iteration i commences by illuminating the dynamic scattering medium from the left-hand-side (LHS) with trial field u(i), and time-averaging the transmitted optical field on the right-hand-side (RHS), yielding ⟨v⟩t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Equation 3 specifies that ⟨v⟩t should be phase conjugated, and transmitted in the reverse direction through the dynamic media, from the RHS back to the LHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' Measuring the phase of the resulting field on (a) Physical adjoint optimisiation scheme (b) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content='4 2元 Coherent reference Fluctuation Phase (rad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=') v(ti) level u(i+1) Camera Noise floor Shaped input 0 v(t2) Amp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' 0 field u(i) 0 30 Su Iteration number Time-average (c) optical field LHS Dynamic scatterer RHS Evolution Time-average optical field of optimised field .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FNE3T4oBgHgl3EQfVgrM/content/2301.04461v1.pdf'} +page_content=' v(tn) Return field Sz DOPC Camera Sz