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1.
Cryst Growth Des ; 24(9): 3589-3594, 2024 May 01.
Article in English | MEDLINE | ID: mdl-38708370

ABSTRACT

Laser-induced crystallization is a novel alternative to classical methods for crystallizing organic molecules but requires a judicious choice of experimental parameters for the onset of crystallization to be predictable. This study investigated the impact of the laser repetition rate on the time delay from the start of the pulsed laser illumination to the initiation of crystallization, the so-called induction time. A supersaturated urea solution was irradiated with near-infrared (λ = 1030 nm) laser pulses of pulse duration τ = 5 ps at a pulse energy of approximately E = 340 µJ while varying the repetition rate from 10 to 20,000 Hz. The optimal rate discovered ranged from 500 Hz to 1 kHz, quantified by the measured induction time (median 2-5 s) and the mean probability of inducing a successful crystallization event (5 × 10-2%). For higher repetition rates (5-20 kHz), the mean probability dropped to 3 × 10-3%. The reduced efficiency at high repetition rates is likely due to an interaction between an existing thermocavitation bubble and subsequent pulses. These results suggest that an optimized pulse repetition rate can be a means to gain further control over the laser-induced crystallization process.

2.
J Epidemiol Popul Health ; 72(1): 202195, 2024 Feb.
Article in English | MEDLINE | ID: mdl-38477476

ABSTRACT

The cluster randomized trial allows a randomized evaluation when it is either not possible to randomize the individual or randomizing individuals would put the trial at high risk of contamination across treatment arms. There are many variations of the cluster randomized design, including the parallel design with or without baseline measures, the cluster randomized cross-over design, the stepped-wedge cluster randomized design, and more recently-developed variants such as the batched stepped-wedge design and the staircase design. Once it has been clearly established that there is a need for cluster randomization, one ever important question is which form the cluster design should take. If a design in which time is split into multiple trial periods is to be adopted (e.g. as in a stepped-wedge), researchers must decide whether the same participants should be measured in multiple trial periods (cohort sampling); or if different participants should be measured in each period (continual recruitment or cross-sectional sampling). Here we outline the different possible options and weigh up the pros and cons of the different design choices, which revolve around statistical efficiency, study logistics and the assumptions required.


Subject(s)
Randomized Controlled Trials as Topic , Research Design , Humans , Cross-Sectional Studies , Longitudinal Studies
3.
J Epidemiol Popul Health ; 72(1): 202196, 2024 Feb.
Article in English | MEDLINE | ID: mdl-38477477

ABSTRACT

In cluster randomized trials, individuals from the same cluster tend to have more similar outcomes than individuals from different clusters. This correlation must be taken into account in the analysis of every cluster trial to avoid incorrect inferences. In this paper, we describe the principles guiding the analysis of cluster trials including how to correctly account for intra-cluster correlations as well as how to analyze more advanced designs such as stepped-wedge and cluster cross-over trials. We then describe how to handle specific issues such as small sample sizes and missing data.


Subject(s)
Randomized Controlled Trials as Topic , Research Design , Humans , Cluster Analysis , Cross-Over Studies , Sample Size
4.
Int J Eat Disord ; 2024 Mar 12.
Article in English | MEDLINE | ID: mdl-38469971

ABSTRACT

Randomized controlled trials can be used to generate evidence on the efficacy and safety of new treatments in eating disorders research. Many of the trials previously conducted in this area have been deemed to be of low quality, in part due to a number of practical constraints. This article provides an overview of established and more innovative clinical trial designs, accompanied by pertinent examples, to highlight how design choices can enhance flexibility and improve efficiency of both resource allocation and participant involvement. Trial designs include individually randomized, cluster randomized, and designs with randomizations at multiple time points and/or addressing several research questions (master protocol studies). Design features include the use of adaptations and considerations for pragmatic or registry-based trials. The appropriate choice of trial design, together with rigorous trial conduct, reporting and analysis, can establish high-quality evidence to advance knowledge in the field. It is anticipated that this article will provide a broad and contemporary introduction to trial designs and will help researchers make informed trial design choices for improved testing of new interventions in eating disorders. PUBLIC SIGNIFICANCE: There is a paucity of high quality randomized controlled trials that have been conducted in eating disorders, highlighting the need to identify where efficiency gains in trial design may be possible to advance the eating disorder research field. We provide an overview of some key trial designs and features which may offer solutions to practical constraints and increase trial efficiency.

5.
Res Synth Methods ; 2024 Feb 05.
Article in English | MEDLINE | ID: mdl-38316613

ABSTRACT

We aimed to explore, in a sample of systematic reviews (SRs) with meta-analyses of the association between food/diet and health-related outcomes, whether systematic reviewers selectively included study effect estimates in meta-analyses when multiple effect estimates were available. We randomly selected SRs of food/diet and health-related outcomes published between January 2018 and June 2019. We selected the first presented meta-analysis in each review (index meta-analysis), and extracted from study reports all study effect estimates that were eligible for inclusion in the meta-analysis. We calculated the Potential Bias Index (PBI) to quantify and test for evidence of selective inclusion. The PBI ranges from 0 to 1; values above or below 0.5 suggest selective inclusion of effect estimates more or less favourable to the intervention, respectively. We also compared the index meta-analytic estimate to the median of a randomly constructed distribution of meta-analytic estimates (i.e., the estimate expected when there is no selective inclusion). Thirty-nine SRs with 312 studies were included. The estimated PBI was 0.49 (95% CI 0.42-0.55), suggesting that the selection of study effect estimates from those reported was consistent with a process of random selection. In addition, the index meta-analytic effect estimates were similar, on average, to what we would expect to see in meta-analyses generated when there was no selective inclusion. Despite this, we recommend that systematic reviewers report the methods used to select effect estimates to include in meta-analyses, which can help readers understand the risk of selective inclusion bias in the SRs.

6.
BMC Med Res Methodol ; 24(1): 31, 2024 Feb 10.
Article in English | MEDLINE | ID: mdl-38341540

ABSTRACT

BACKGROUND: The Interrupted Time Series (ITS) is a robust design for evaluating public health and policy interventions or exposures when randomisation may be infeasible. Several statistical methods are available for the analysis and meta-analysis of ITS studies. We sought to empirically compare available methods when applied to real-world ITS data. METHODS: We sourced ITS data from published meta-analyses to create an online data repository. Each dataset was re-analysed using two ITS estimation methods. The level- and slope-change effect estimates (and standard errors) were calculated and combined using fixed-effect and four random-effects meta-analysis methods. We examined differences in meta-analytic level- and slope-change estimates, their 95% confidence intervals, p-values, and estimates of heterogeneity across the statistical methods. RESULTS: Of 40 eligible meta-analyses, data from 17 meta-analyses including 282 ITS studies were obtained (predominantly investigating the effects of public health interruptions (88%)) and analysed. We found that on average, the meta-analytic effect estimates, their standard errors and between-study variances were not sensitive to meta-analysis method choice, irrespective of the ITS analysis method. However, across ITS analysis methods, for any given meta-analysis, there could be small to moderate differences in meta-analytic effect estimates, and important differences in the meta-analytic standard errors. Furthermore, the confidence interval widths and p-values for the meta-analytic effect estimates varied depending on the choice of confidence interval method and ITS analysis method. CONCLUSIONS: Our empirical study showed that meta-analysis effect estimates, their standard errors, confidence interval widths and p-values can be affected by statistical method choice. These differences may importantly impact interpretations and conclusions of a meta-analysis and suggest that the statistical methods are not interchangeable in practice.


Subject(s)
Public Health , Humans , Interrupted Time Series Analysis
7.
Phys Rev Lett ; 132(6): 063801, 2024 Feb 09.
Article in English | MEDLINE | ID: mdl-38394585

ABSTRACT

Structured light offers wider bandwidths and higher security for communication. However, propagation through complex random media, such as the Earth's atmosphere, typically induces intermodal crosstalk. We show numerically and experimentally that coupling of photonic orbital angular momentum modes is governed by a universal function of a single parameter: the ratio between the random medium's and the beam's transverse correlation lengths, even in the regime of pronounced intensity fluctuations.

8.
Br J Anaesth ; 2024 Jan 24.
Article in English | MEDLINE | ID: mdl-38267338

ABSTRACT

BACKGROUND: Dexamethasone has been shown to reduce acute pain after surgery, but there is uncertainty as to its effects on chronic postsurgical pain (CPSP). We hypothesised that in patients undergoing major noncardiac surgery, a single intraoperative dose of dexamethasone increases the incidence of CPSP. METHODS: We devised a propensity score-matched analysis of the ENIGMA-II trial CPSP dataset, aiming to compare the incidence of CPSP in patients who had received dexamethasone or not 12 months after major noncardiac surgery. The primary outcome was the incidence of CPSP. We used propensity score matching and inverse probability weighting to balance baseline variables to estimate the average marginal effect of dexamethasone on patient outcomes, accounting for confounding to estimate the average treatment effect on those treated with dexamethasone. RESULTS: We analysed 2999 patients, of whom 116 of 973 (11.9%) receiving dexamethasone reported CPSP, and 380 of 2026 (18.8%) not receiving dexamethasone reported CPSP, unadjusted odds ratio 0.76 (95% confidence interval 0.78-1.00), P=0.052. After propensity score matching, CPSP occurred in 116 of 973 patients (12.2%) receiving dexamethasone and 380 of 2026 patients (13.8%) not receiving dexamethasone, adjusted risk ratio 0.88 (95% confidence interval 0.61-1.27), P=0.493. There was no difference between groups in quality of life or pain interference with daily activities, but 'least pain' (P=0.033) and 'pain right now' (P=0.034) were higher in the dexamethasone group. CONCLUSIONS: Dexamethasone does not increase the risk of chronic postsurgical pain after major noncardiac surgery. CLINICAL TRIAL REGISTRATION: Open Science Framework Registration DOI https://doi.org/10.17605/OSF.IO/ZDVB5.

9.
Stat Methods Med Res ; 33(1): 24-41, 2024 Jan.
Article in English | MEDLINE | ID: mdl-38031417

ABSTRACT

This article introduces the 'staircase' design, derived from the zigzag pattern of steps along the diagonal of a stepped wedge design schematic where clusters switch from control to intervention conditions. Unlike a complete stepped wedge design where all participating clusters must collect and provide data for the entire trial duration, clusters in a staircase design are only required to be involved and collect data for a limited number of pre- and post-switch periods. This could alleviate some of the burden on participating clusters, encouraging involvement in the trial and reducing the likelihood of attrition. Staircase designs are already being implemented, although in the absence of a dedicated methodology, approaches to sample size and power calculations have been inconsistent. We provide expressions for the variance of the treatment effect estimator when a linear mixed model for an outcome is assumed for the analysis of staircase designs in order to enable appropriate sample size and power calculations. These include explicit variance expressions for basic staircase designs with one pre- and one post-switch measurement period. We show how the variance of the treatment effect estimator is related to key design parameters and demonstrate power calculations for examples based on a real trial.


Subject(s)
Randomized Controlled Trials as Topic , Research Design , Cluster Analysis , Linear Models , Probability , Sample Size
10.
Evolution ; 78(1): 174-187, 2024 Jan 04.
Article in English | MEDLINE | ID: mdl-37943790

ABSTRACT

Host shifts to new plant species can drive speciation for plant-feeding insects, but how commonly do host shifts also drive diversification for the parasites of those same insects? Oak gall wasps induce galls on oak trees and shifts to novel tree hosts and new tree organs have been implicated as drivers of oak gall wasp speciation. Gall wasps are themselves attacked by many insect parasites, which must find their hosts on the correct tree species and organ, but also must navigate the morphologically variable galls with which they interact. Thus, we ask whether host shifts to new trees, organs, or gall morphologies correlate with gall parasite diversification. We delimit species and infer phylogenies for two genera of gall kleptoparasites, Synergus and Ceroptres, reared from a variety of North American oak galls. We find that most species were reared from galls induced by just one gall wasp species, and no parasite species was reared from galls of more than four species. Most kleptoparasite divergence events correlate with shifts to non-ancestral galls. These shifts often involved changes in tree habitat, gall location, and gall morphology. Host shifts are thus implicated in driving diversification for both oak gall wasps and their kleptoparasitic associates.


Subject(s)
Quercus , Wasps , Animals , Wasps/genetics , Trees , Phylogeny , Ecosystem
11.
Sci Rep ; 13(1): 21701, 2023 Dec 07.
Article in English | MEDLINE | ID: mdl-38066083

ABSTRACT

Uncertainty relations are core to both classical and quantum physics, and lend themselves to tests across many degrees of freedom, with structured light emerging as a vibrant tool to harness these degrees of freedom. Here, we test Popper's conjecture by replacing the traditional spatial and momentum states with angular position and orbital angular momentum (OAM) states of photons, showing that the OAM spectrum for an entangled photon passing through a virtual slit differs from that of a photon passing through a physical slit. To achieve this, we produce two OAM entangled photons, one of which is sent to a slit encoded as a digital hologram, thereby localising its angular position, all the while measuring the OAM of the other. We show that the measured OAM spectrum is limited to that of the initial SPDC photons, independent of the OAM encoded into the slit, consistent with Popper's viewpoint. Our approach allows us to overcome prior limitations imposed by physical slits and linear momentum, and offers a versatile toolbox for further probes of quantum systems.

12.
Nat Commun ; 14(1): 8243, 2023 Dec 13.
Article in English | MEDLINE | ID: mdl-38092724

ABSTRACT

Information exchange between two distant parties, where information is shared without physically transporting it, is a crucial resource in future quantum networks. Doing so with high-dimensional states offers the promise of higher information capacity and improved resilience to noise, but progress to date has been limited. Here we demonstrate how a nonlinear parametric process allows for arbitrary high-dimensional state projections in the spatial degree of freedom, where a strong coherent field enhances the probability of the process. This allows us to experimentally realise quantum transport of high-dimensional spatial information facilitated by a quantum channel with a single entangled pair and a nonlinear spatial mode detector. Using sum frequency generation we upconvert one of the photons from an entangled pair resulting in high-dimensional spatial information transported to the other. We realise a d = 15 quantum channel for arbitrary photonic spatial modes which we demonstrate by faithfully transferring information encoded into orbital angular momentum, Hermite-Gaussian and arbitrary spatial mode superpositions, without requiring knowledge of the state to be sent. Our demonstration merges the nascent fields of nonlinear control of structured light with quantum processes, offering a new approach to harnessing high-dimensional quantum states, and may be extended to other degrees of freedom too.

13.
Vet J ; 300-302: 106042, 2023.
Article in English | MEDLINE | ID: mdl-37939997
14.
BJA Open ; 8: 100235, 2023 Dec.
Article in English | MEDLINE | ID: mdl-37927381

ABSTRACT

Background: Clinical research in perioperative medicine requires the perspectives of patients and caregivers to increase its relevance and quality, benefiting both researchers and the community. Identifying these priorities will enable researchers, funders, and governing bodies to efficiently use scarce funding and resources. We aim to identify the top 10 research priorities in perioperative medical research in Australia. Methods: A mixed-methods, exploratory-sequential design will be conducted. The study will include five phases. Initially, a published open-ended survey gathered responses from the population (researchers, healthcare workers, and consumers) regarding uncertainties/questions relevant to the population about perioperative medical research. We collected 544 questions and quantitatively analysed and grouped them according to the Standardised Endpoints in Perioperative Medicine-Core Outcomes Measures in Perioperative and Anaesthetic Care (StEP-COMPAC) endpoints. Using multicriteria decision-making software, workshops combining the population will be conducted to determine the top 10 priorities for perioperative medicine research for the Australian population. Ethics and dissemination: Ethical approval to conduct the study was obtained from the Alfred Health (Australia) Human Research Ethics Committee (ID: 171/19). The findings will be disseminated in peer review publications, conferences, and dissemination across perioperative research networks. The top 10 priorities will be available to inform research funders, grant submissions, guidelines, and the population.

15.
BMJ Open ; 13(10): e067243, 2023 10 29.
Article in English | MEDLINE | ID: mdl-37899157

ABSTRACT

INTRODUCTION: The use of high fraction of inspired oxygen (FiO2) intraoperatively for the prevention of surgical site infection (SSI) remains controversial. Promising results of early randomised controlled trials (RCT) have been replicated with varying success and subsequent meta-analysis are equivocal. Recent advancements in perioperative care, including the increased use of laparoscopic surgery and pneumoperitoneum and shifts in fluid and temperature management, can affect peripheral oxygen delivery and may explain the inconsistency in reproducibility. However, the published data provides insufficient detail on the participant level to test these hypotheses. The purpose of this individual participant data meta-analysis is to assess the described benefits and harms of intraoperative high FiO2compared with regular (0.21-0.40) FiO2 and its potential effect modifiers. METHODS AND ANALYSIS: Two reviewers will search medical databases and online trial registries, including MEDLINE, Embase, CENTRAL, CINAHL, ClinicalTrials.gov and WHO regional databases, for randomised and quasi-RCT comparing the effect of intraoperative high FiO2 (0.60-1.00) to regular FiO2 (0.21-0.40) on SSI within 90 days after surgery in adult patients. Secondary outcome will be all-cause mortality within the longest available follow-up. Investigators of the identified trials will be invited to collaborate. Data will be analysed with the one-step approach using the generalised linear mixed model framework and the statistical model appropriate for the type of outcome being analysed (logistic and cox regression, respectively), with a random treatment effect term to account for the clustering of patients within studies. The bias will be assessed using the Cochrane risk-of-bias tool for randomised trials V.2 and the certainty of evidence using Grading of Recommendations, Assessment, Development and Evaluation methodology. Prespecified subgroup analyses include use of mechanical ventilation, nitrous oxide, preoperative antibiotic prophylaxis, temperature (<35°C), fluid supplementation (<15 mL/kg/hour) and procedure duration (>2.5 hour). ETHICS AND DISSEMINATION: Ethics approval is not required. Investigators will deidentify individual participant data before it is shared. The results will be submitted to a peer-review journal. PROSPERO REGISTRATION NUMBER: CRD42018090261.


Subject(s)
Oxygen , Surgical Wound Infection , Adult , Humans , Surgical Wound Infection/prevention & control , Systematic Reviews as Topic , Meta-Analysis as Topic , Respiration, Artificial , Randomized Controlled Trials as Topic
16.
Res Synth Methods ; 14(6): 882-902, 2023 Nov.
Article in English | MEDLINE | ID: mdl-37731166

ABSTRACT

Interrupted time series (ITS) are often meta-analysed to inform public health and policy decisions but examination of the statistical methods for ITS analysis and meta-analysis in this context is limited. We simulated meta-analyses of ITS studies with continuous outcome data, analysed the studies using segmented linear regression with two estimation methods [ordinary least squares (OLS) and restricted maximum likelihood (REML)], and meta-analysed the immediate level- and slope-change effect estimates using fixed-effect and (multiple) random-effects meta-analysis methods. Simulation design parameters included varying series length; magnitude of lag-1 autocorrelation; magnitude of level- and slope-changes; number of included studies; and, effect size heterogeneity. All meta-analysis methods yielded unbiased estimates of the interruption effects. All random effects meta-analysis methods yielded coverage close to the nominal level, irrespective of the ITS analysis method used and other design parameters. However, heterogeneity was frequently overestimated in scenarios where the ITS study standard errors were underestimated, which occurred for short series or when the ITS analysis method did not appropriately account for autocorrelation. The performance of meta-analysis methods depends on the design and analysis of the included ITS studies. Although all random effects methods performed well in terms of coverage, irrespective of the ITS analysis method, we recommend the use of effect estimates calculated from ITS methods that adjust for autocorrelation when possible. Doing so will likely to lead to more accurate estimates of the heterogeneity variance.


Subject(s)
Public Health , Interrupted Time Series Analysis , Computer Simulation
17.
Scand Stat Theory Appl ; 50(3): 1048-1067, 2023 Sep.
Article in English | MEDLINE | ID: mdl-37601275

ABSTRACT

Stepped wedge trials are increasingly adopted because practical constraints necessitate staggered roll-out. While a complete design requires clusters to collect data in all periods, resource and patient-centered considerations may call for an incomplete stepped wedge design to minimize data collection burden. To study incomplete designs, we expand the metric of information content to discrete outcomes. We operate under a marginal model with general link and variance functions, and derive information content expressions when data elements (cells, sequences, periods) are omitted. We show that the centrosymmetric patterns of information content can hold for discrete outcomes with the variance-stabilizing link function. We perform numerical studies under the canonical link function, and find that while the patterns of information content for cells are approximately centrosymmetric for all examined underlying secular trends, the patterns of information content for sequences or periods are more sensitive to the secular trend, and may be far from centrosymmetric.

18.
Stat Methods Med Res ; 32(11): 2123-2134, 2023 11.
Article in English | MEDLINE | ID: mdl-37589088

ABSTRACT

A frequently applied assumption in the analysis of data from cluster randomised trials is that the outcomes from all participants within a cluster are equally correlated. That is, the intracluster correlation, which describes the degree of dependence between outcomes from participants in the same cluster, is the same for each pair of participants in a cluster. However, recent work has discussed the importance of allowing for this correlation to decay as the time between the measurement of participants in a cluster increases. Incorrect omission of such a decay can lead to under-powered studies, and confidence intervals for estimated treatment effects can be too narrow or too wide, depending on the characteristics of the design. When planning studies, researchers often rely on previously reported analyses of trials to inform their choice of intracluster correlation. However, most reported analyses of clustered data do not incorporate a correlation decay. Thus, often all that is available are estimates of intracluster correlations obtained under the potentially incorrect assumption of no decay. In this article, we show that it is possible to use intracluster correlation values obtained from models that incorrectly omit a decay to inform plausible choices of decaying correlations. Our focus is on intracluster correlation estimates for continuous outcomes obtained by fitting linear mixed models with exchangeable or block-exchangeable correlation structures. We describe how plausible values for decaying correlations may be obtained given these estimated intracluster correlations. An online app is presented that allows users to obtain plausible values of the decay, which can be used at the trial planning stage to assess the sensitivity of sample size and power calculations to decaying correlation structures.


Subject(s)
Research Design , Humans , Cluster Analysis , Sample Size , Time Factors
19.
BMC Med Res Methodol ; 23(1): 160, 2023 07 06.
Article in English | MEDLINE | ID: mdl-37415140

ABSTRACT

BACKGROUND: Standard stepped wedge trials, where clusters switch from the control to the intervention condition in a staggered manner, can be costly and burdensome. Recent work has shown that the amount of information contributed by each cluster in each period differs, with some cluster-periods contributing a relatively small amount of information. We investigate the patterns of the information content of cluster-period cells upon iterative removal of low-information cells, assuming a model for continuous outcomes with constant cluster-period size, categorical time period effects, and exchangeable and discrete-time decay intracluster correlation structures. METHODS: We sequentially remove pairs of "centrosymmetric" cluster-period cells from an initially complete stepped wedge design which contribute the least amount of information to the estimation of the treatment effect. At each iteration, we update the information content of the remaining cells, determine the pair of cells with the lowest information content, and repeat this process until the treatment effect cannot be estimated. RESULTS: We demonstrate that as more cells are removed, more information is concentrated in the cells near the time of the treatment switch, and in "hot-spots" in the corners of the design. For the exchangeable correlation structure, removing the cells from these hot-spots leads to a marked reduction in study precision and power, however the impact of this is lessened for the discrete-time decay structure. CONCLUSIONS: Removing cluster-period cells distant from the time of the treatment switch may not lead to large reductions in precision or power, implying that certain incomplete designs may be almost as powerful as complete designs.


Subject(s)
Research Design , Humans , Cluster Analysis , Sample Size
20.
Opt Express ; 31(15): 24516-24536, 2023 Jul 17.
Article in English | MEDLINE | ID: mdl-37475277

ABSTRACT

Master Oscillator Power Amplifier (MOPA) systems find extensive use in laser development to increase the optical power of laser emissions from a Master Oscillator (MO). Commonly used are the cylindrical rod MOPAs that are optically excited using a multimode fiber-coupled (FC) diode laser emission in an end-pumped configuration. Current analytical 3D models that incorporate thermal effects, gain saturation, and iterative Fourier beam propagation methods, collectively, rely on static approximations of the evolution of the FC pump beam profile over the longitudinal volume of the amplifier crystal. Furthermore, in general, the spectral behavior of the FC diode emission is assumed to be static, and the thermal wavelength shift is not accounted for in the simulation. In this work, we demonstrate a novel approach for accurate modeling of the multimode FC pump beam emission as a complex field using a phase-only Gaussian to flat-top (FT) diffractive optical element, thus allowing for the inclusion of the pump beam into the iterative propagation method. Additionally, we present a method for precise calibration of the model using simple experimental measurements of the diode emission spectrum. The theoretical model is experimentally validated using an end-pumped Nd:YAG crystal rod to perform single-pass amplification of a Gaussian beam, showing excellent agreement with predicted output powers over the calibrated range of pump powers. Furthermore, we provide experimental data that exhibits a strong correlation between the Gaussian to FT phase-only transformation and the multimode FC diode evolution in free-space propagation.

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