Davide Pierangeli
email: davide.pierangeli@roma1.infn.it.

Giulia Marcucci
email: giulia.marcucci@uniroma1.it

Daniel Brunner
email: daniel.brunner@femto-st.fr

Claudio Conti
email: claudio.conti@uniroma1.it

Keywords: Ising machines, optical computing, optimization problems, spatial light modulation

Ising machines are novel computing devices for the energy minimization of Ising models. These combinatorial optimization problems are of paramount importance for science and technology, but remain difficult to tackle on large scale by conventional electronics. Recently, various photonics-based Ising machines demonstrated fast computing of a Ising ground state by data processing through multiple temporal or spatial optical channels. Experimental noise acts as a detrimental effect in many of these devices. On the contrary, here we demonstrate that an optimal noise level enhances the performance of spatial-photonic Ising machines on frustrated spin problems. By controlling the error rate at the detection, we introduce a noisy-feedback mechanism in an Ising machine based on spatial light modulation. We investigate the device performance on systems with hundreds of individually-addressable spins with all-to-all couplings and we found an increased success probability at a specific noise level. The optimal noise amplitude depends on graph properties and size, thus indicating an additional tunable parameter helpful in exploring complex energy landscapes and in avoiding getting stuck in local minima. Our experimental results identify noise as a potentially valuable resource for optical computing. This concept, which also holds in different nanophotonic neural networks, may be crucial in developing novel hardware with optics-enabled parallel architecture for large-scale optimizations.

Introduction

Solving large combinatorial problems is crucial for widespread applications in fields such as artificial intelligence, cryptography, biophysics, and complex networks. However, finding the optimal solution to many of these tasks causes the required resources to grow exponentially with the problem size, a reason why such problems are considered as computationally intractable for traditional computing architectures [START_REF] Hromkoviĉ | Algorithmics for Hard Problems: Introduction to Combinatorial Optimization, Randomization, Approximation, and Heuristics[END_REF]. A promising approach to efficiently solve these problems is to recast them in terms of an Ising model [START_REF] Barahona | On the computational complexity of Ising spin glass models[END_REF][START_REF] Lucas | Ising formulations of many NP problems[END_REF], which describes a system of classical interacting spins, and searching its ground state by an artificial network of spins evolving according to an Ising Hamiltonian. Ising machines are physical platforms made of electronic or photonic elements that can be programmed to encode Ising problems with known coupling values, and the ground state obtained after the system's relaxation provides the optimal solution. They have been realized in a variety of quantum and classical systems including cold atoms [START_REF] Kim | Quantum simulation of frustrated Ising spins with trapped ions[END_REF][START_REF] Simon | Quantum simulation of antiferromagnetic spin chains in an optical lattice[END_REF], single photons [START_REF] Ma | Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems[END_REF][START_REF] Pitsios | Photonic simulation of entanglement growth and engineering after a spin chain quench[END_REF], superconducting [START_REF] Johnson | Quantum annealing with manufactured spins[END_REF][START_REF] Boixo | Evidence for quantum annealing with more than one hundred qubits[END_REF] and magnetic junctions [START_REF] Borders | Integer factorization using stochastic magnetic tunnel junctions[END_REF], electromechanical [START_REF] Mahboob | An electromechanical Ising Hamiltonian[END_REF] and CMOS circuits [START_REF] Yamaoka | A 20k-spin Ising chip to solve combinatorial optimization problems with CMOS annealing[END_REF], polariton and photon condensates [START_REF] Berloff | Realizing the classical XY Hamiltonian in polariton simulators[END_REF][START_REF] Dung | Variable potentials for thermalized light and coupled condensates[END_REF], or lasers and nonlinear waves [START_REF] Ghofraniha | Experimental evidence of replica symmetry breaking in random lasers[END_REF][START_REF] Nixon | Observing geometric frustration with thousands of coupled lasers[END_REF][START_REF] Pierangeli | Observation of replica symmetry breaking in disordered nonlinear wave propagation[END_REF], but with practical difficulties in scalability, connectivity, or in engineering the spin interaction.

Photonic Ising machines encode the spin state in the phase or amplitude of the optical field. Realized photonically, such Ising machines hold the prospect of processing data in parallel at high speed through active optical components and hence be much faster than those based on other encoding schemes [START_REF] Brunner | Parallel photonic information processing at gigabyte per second data rates using transient states[END_REF]. Various prototypes have recently been realized with sizes spanning from few to thousands of spins. In the class of photonic optimizers known as coherent Ising machines (CIMs), the nonlinear dynamics of time-multiplexed optical parametric oscillators [START_REF] Marandi | Network of time-multiplexed optical parametric oscillators as coherent Ising machine[END_REF][START_REF] Mcmahon | A fullyprogrammable 100-spin coherent Ising machine with all-to-all connections[END_REF][START_REF] Inagaki | A coherent Ising machine for 2000-node optimization problems[END_REF][START_REF] Inagaki | Large-scale Ising spin network based on degenerate optical parametric oscillators[END_REF][START_REF] Takeda | Boltzmann sampling for an XY model using a non-degenerate optical parametric oscillator network[END_REF], fiber lasers [START_REF] Babaeian | A single shot coherent Ising machine based on a network of injection-locked multicore fiber lasers[END_REF], or simple opto-electronic oscillators [START_REF] Böhm | A poor man's coherent Ising machine based on opto-electronic feedback systems for solving optimization problems[END_REF], is exploited to solve NP-hard optimization problems with notable performance [START_REF] Hamerly | Experimental investigation of performance differences between coherent Ising machines and a quantum annealer[END_REF]. CIMs are dissipative optical networks in which the ground-state search is performed in reverse direction by slowly raising the gain, according to a general non-equilibrium bifurcation mechanism that currently inspires novel algorithms and settings [START_REF] Goto | Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems[END_REF][START_REF] Kalinin | Global optimization of spin Hamiltonians with gain-dissipative systems[END_REF][START_REF] Puri | Quantum annealing with all-to-all connected nonlinear oscillators[END_REF][START_REF] Tiunov | Annealing by simulating the coherent Ising machine[END_REF][START_REF] Clements | Gaussian optical Ising machines[END_REF][START_REF] Böhm | Understanding dynamics of coherent Ising machines through simulation of large-scale 2D Ising models[END_REF][START_REF] Kalinin | Simulating Ising and n-state planar potts models and external fields with nonequilibrium condensates[END_REF][START_REF] Leleu | Destabilization of local minima in analog spin systems by correction of amplitude heterogeneity[END_REF][START_REF] Bello | Persistent coherent beating in coupled parametric oscillators[END_REF][START_REF] Chou | Analog coupled oscillator based weighted Ising machine[END_REF][START_REF] Tradonsky | Rapid laser solver for the phase retrieval problem[END_REF]. On the other hand, optimization platforms based on waveguides circuits [START_REF] Wu | An optical fiber network oracle for NP-complete problems[END_REF][START_REF] Vázquez | Optical NP problem solver on laser-written waveguide platform[END_REF] and integrated nanophotonic processors [START_REF] Roques-Carmes | Heuristic recurrent algorithms for photonic Ising machines[END_REF][START_REF] Prabhu | A recurrent Ising machine in a photonic integrated circuit[END_REF][START_REF] Shen | Deep learning with coherent nanophotonic circuits[END_REF][START_REF] Harris | Linear programmable nanophotonic processors[END_REF] operate as optical recurrent neural networks [START_REF] Bueno | Reinforcement learning in a large-scale photonic recurrent neural network[END_REF] converging to Ising energy minima.

Spatial-photonic Ising machines are a different class of optical devices for Ising problems that have been demonstrated very recently [START_REF] Pierangeli | Large-scale photonic Ising machine by spatial light modulation[END_REF]. They make use of spatial light modulation for encoding an unprecedented number of spins [START_REF] Roques-Carmes | Photonic Ising machines go big[END_REF] and the programmed Hamiltonian is optically evaluated by measuring the intensity distribution after propagation in free-space [START_REF] Pierangeli | Large-scale photonic Ising machine by spatial light modulation[END_REF] or through nonlinear media [START_REF] Kumar | Large-scale Ising emulation with four-body interaction and all-to-all connection[END_REF]. These devices take advantage of optical vector-matrix multiplications and by the large pixel density of spatial light modulators (SLMs), thus enabling the implementation of large-scale neuromorphic computing [START_REF] Hamerly | Large-scale optical neural networks based on photoelectric multiplication[END_REF][START_REF] Zuo | All-optical neural network with nonlinear activation functions[END_REF][START_REF] Saade | Random projections through multiple optical scattering: Approximating kernels at the speed of light[END_REF][START_REF] Dong | Optical reservoir computing using multiple light scattering for chaotic systems prediction[END_REF][START_REF] Del Hougne | Leveraging chaos for wave-based analog computation: Demonstration with indoor wireless communication signals[END_REF][START_REF] Matthès | Optical complex media as universal reconfigurable linear operators[END_REF].

Noise is an unavoidable ingredient in any hardware. In CIMs it represents one of the main error sources and can induce dynamics beyond the regime of Ising spins [START_REF] Strinati | Theory of coupled parametric oscillators beyond coupled Ising spins[END_REF]. On the contrary, in recurrent algorithms and artificial neural networks for Ising problems, noise furnishes a finite effective temperature, and it is expected to facilitate and speed up convergence to the ground state if noise amplitude is adequately leveraged [START_REF] Roques-Carmes | Heuristic recurrent algorithms for photonic Ising machines[END_REF][START_REF] Cai | Harnessing intrinsic noise in memristor hopfield neural networks for combinatorial optimization[END_REF]. The effect has been recently observed in a platform with few photonic spins and various competing interactions [START_REF] Prabhu | A recurrent Ising machine in a photonic integrated circuit[END_REF]. Noise-tolerant settings are especially important when scaling the device to solve systems with many units. Nevertheless, the impact of noise in large-scale photonic Ising machines remains mainly unexplored.

In the present article, we investigate the effect of experimental noise on a spatial-photonic Ising machine with hundreds of spins, proving the existence of an optimal noise level. The precise impact of noise depends on each problem's particular features. Specifically, we found that it enhances the machine's success probability on problems with both positive and negative interactions, while it is detrimental for models having only positive couplings. By providing a mechanism to escape from local minima, noise represents an additional parameter with beneficial properties for our optical computing device. Our findings demonstrate noise as a valuable resource in large-scale photonic computing.

Ising machine by spatial light modulation

In our Ising machine the spin variables are encoded on a coherent laser wavefront via binary values of the optical phase and processed by spatial light modulation [START_REF] Pierangeli | Large-scale photonic Ising machine by spatial light modulation[END_REF]. As schematically illustrated in Figure 1(a), our optical setting employs an optical path in which an SLM encodes spins σ i ±1 by 0, π phase delays over an amplitude-modulated beam. Linear interaction between spins occurs by interference on the detection plane and its strength is controlled by spatial modulation of the input intensity. The optical machine works via a measurement and feedback scheme. Once initialized to a given problem, feedback from the detected intensity allows the phase distribution on the SLM to converge towards a state minimizing an Ising Hamiltonian

H -∑ ij J ij σ i σ j (1)
with couplings J ij ξ i ξ j ĨT , where ξ i is the amplitude illuminating the ith spin [START_REF] Pierangeli | Large-scale photonic Ising machine by spatial light modulation[END_REF]. ĨT is the Fourier transform of a predetermined target image, and the difference between I T and the image detected on the camera is the cost function. At each machine iteration, we measure the intensity on the CCD modes [Figure 1(b)] and the spins are updated in order to minimize the cost function. Importantly, and other than for CIMs [START_REF] Mcmahon | A fullyprogrammable 100-spin coherent Ising machine with all-to-all connections[END_REF][START_REF] Inagaki | A coherent Ising machine for 2000-node optimization problems[END_REF][START_REF] Böhm | A poor man's coherent Ising machine based on opto-electronic feedback systems for solving optimization problems[END_REF], our machine avoids electronically computing the energy as well as the field acting on each spin. Due to the intrinsic noise of each experimental setup, the machine always behaves as coupled to a thermal bath. Noise therefore provides an effective temperature for the final spin ground state, as reported in Ref. [START_REF] Pierangeli | Large-scale photonic Ising machine by spatial light modulation[END_REF]. Sources of noise come from intensity discretization and processing in each CCD mode, as well as from the imperfect spatial light modulation. As detailed below, we here control the noise level by means of a tunable error rate in the machine's measurement and feedback scheme.

Experimental setup and noisy-feedback method

The experimental device follows the setup illustrated in Figure 1(a). Light from a CW laser at λ = 532 nm is expanded and polarization controlled. The beam is first spatially modulated in amplitude and then in phase by a single reflective modulator (Holoeye LC-R 720, 1280 × 768 pixels, pixel pitch 20 × 20 μm). A section of the modulator operates in amplitude mode to generate the profiles ξ i . A 4-f system then images this state on the second SLM section that performs binary phase modulation, which we realize with less than 10% residual intensity modulation. We select an active area of approximately 200 × 200 SLM pixels and divide it into N addressable optical spins by grouping several pixels. Modulated light is spatially filtered using an holographic grating and focused by a f = 500 mm lens on a CCD camera. The intensity is detected on 18 × 18 spatial modes, where the signal in each mode is obtained averaging over 10 × 10 camera pixels, a size comparable with the spatial extent of a speckle grain.

The measured intensity pattern determines the feedback signal. At each machine cycle a single spin is randomly selected and flipped; the recorded image is compared with the reference I T on the same set of modes, and the spin state is updated to minimize the difference between the two images. Due to errors at the readout, there always exists a finite probability to update the spin configuration. The rate at which readout errors occur determines the noise level, which therefore is ultimately related to the magnitude of the intensity fluctuations on the detection plane. We exert control over the noise level by tuning the camera exposure time, where shorter exposure corresponds to larger error amplitudes. Fixing the CCD settings and analyzing the machine's behavior, we map the exposure time into a normalized noise level ρ ∈ [0, 1], which indicates the probability at each iteration to measure a false decrease of the cost function and to erroneously flipping a spin. The minimum noise level available, ρ 0, corresponds to faults in the feedback loop coming from spontaneous optical fluctuations in the setup.

Optimization with spontaneous noise

We first quantify the solutions found by our Ising machine for ρ 0, a condition analogous to previously reported experiments [START_REF] Pierangeli | Large-scale photonic Ising machine by spatial light modulation[END_REF]. We optically implement two different classes of Ising systems: mean-field and Mattis spin glasses. In a mean-field Ising model, also known as infinite-range Ising model, the spins are all-to-all coupled with the same positive interaction strength. We realize such coupling using a plane wave of constant amplitude ξ i E 0 and maximizing the intensity detected on a single CCD mode, such that ĨT c, being c an arbitrary constant and J cE 2 0 . In Mattis spin glasses the pairwise interaction is given as a product of two independent variables J ij ∝ ξ i ξ j [START_REF] Mattis | Solvable spin systems with random interactions[END_REF][START_REF] Nishimori | Statistical Physics of Spin Glasses and Information Processing: An Introduction[END_REF]. In this case, since the couplings are both positive and negative, a minimal amount of noise introduces frustration [START_REF] Nishimori | Statistical Physics of Spin Glasses and Information Processing: An Introduction[END_REF]. In our spatial optical setting, pairs of negatively-coupled spins correspond to points of the optical field that give destructive interference on a fixed CCD mode [see bottom panel in Figure 2(d)]. Sparsity is implemented all-optically by decoupling a random subset of spins via amplitude modulation (i. e., ξ i 0 for blocks of spins). Since the interaction matrix is given in any case as a product of separate amplitude values, the sparse Ising Hamiltonian still maintains the form of a Mattis model.

Optical ground states found by the device for a meanfield system of N 100 spins are reported in Figure 2(a-c). The evolution of a spin configuration initialized to a random distribution is shown in Figure 2(b) for a single machine run; after thousand iterations, a low-temperature ferromagnetic state is measured. The energy probability distribution of these ground states is reported in Figure 2(c we show the graph for a Mattis spin glass instance along with the corresponding target image. In agreement with the programmed Hamiltonian [START_REF] Nishimori | Statistical Physics of Spin Glasses and Information Processing: An Introduction[END_REF], the spin evolution in Figure 2(e) exhibits the formation of two domains with opposite magnetization and equal size. However, from the ground-state energies in Figure 2(f), we observe a reduced ability of the machine in solving such frustrated models. As we demonstrate hereafter, increasing the noise level is an effective way to improve the machine performance on problems affected by trapping in local energy minima.

Effect of the noise level on the Ising machine performance

To introduce controllable noise, we exploit the detection process previously described. The Ising machine is made to operate under different noise levels. To quantify the performance when the setup is initialized to different parameters, we use two distinct and complementary quantities: the success probability p s and the Hamming distance h. To evaluate the success of the computation, we consider the correlation between the measured spin configuration and the known optimal solution, being C = ±1 for the zero-temperature spin system in the lowest energy state [START_REF] Nishimori | Statistical Physics of Spin Glasses and Information Processing: An Introduction[END_REF]. A machine run is defined as successful if its final state gives |C| > a, being a any fixed accuracy; the success probability p s is the fraction of repeated experiments with random initial conditions that converged successfully. The Hamming distance is a metric used in information theory. Here, h indicates the number of units (spins) that need to be inverted to reach the minimum energy configuration [START_REF] Boixo | Evidence for quantum annealing with more than one hundred qubits[END_REF]. We would like to point out that using this quantity to characterize the quality of Ising machines is significantly more accurate than the groundstate energy. In fact, spin configurations very far from the known solution can still have energies comparable with the optimal one. Figure 3 illustrates the performance of the spatialphotonic Ising machine as we vary the noise level. For the infinite-range Ising model, we found a success probability that decays as noise increases, a behavior independent of the selected accuracy [Figure 3(a)]. The measured h in Figure 3(b) has a growing trend, thus indicating that for emulating such Hamiltonians the best performance is obtained for minimum noise. A completely different picture emerges when solving frustrated Ising models. As shown in Figure 3(c) for dense Mattis spin glass instances, the low success probability observed under spontaneous noise rapidly increases as additional fluctuations are introduced. p s has a maximum value and then decays to zero for large noise levels. Moreover, the mean Hamming distance as a function of the noise level exhibits a pronounced minimum [Figure 3(d)], which indicates an optimal noise level, ρ opt ≈ 0.05. A similar behavior is found on sparse Mattis spin glasses, as reported in Figure 3(e-f), with ρ opt ≈ 0.07. This demonstrates that an optimal noise level promotes the exploration of energy landscapes with many minima during optimization on the optical platform.

Scaling of the optimal noise level

We investigate how the noise-enhanced machine operation depends on the system size. While keeping the SLM's active area constant, we vary the total number of spins and, for each system size N, we perform the experiments at different noise levels. The results obtained on dense Mattis spin glasses are shown in Figure 4. We observe an optimal noise level that significantly depends on the spin number, with values that grow and saturate as the system size increases.

For small-scale systems (N = 16) additional noise yields only limited advantages due to finite size effects and the small number of frustrated configurations. However, a constant optimal level ρ opt ≈ 0.07 enhances the optimization for large scale Hamiltonians. This specific value is not a general recipe to improve the Ising machine, but guarantees improved performance on specific problem graphs in our setup. Ising instances with distinct properties (graph type, connection density etc.) would have diverse optimal levels, having landscapes with different features. These findings establish the noise level as a hyperparameter of the photonic computing device. Another important fact is that residual errors do not increase rapidly with N. To prove this property, Figure 4 shows the Hamming fraction h/N (i. e., the mean Hamming distance normalized to the spin number) as a function of N.

Residual errors shows a sublinear increase with minor oscillations as N varies. This preliminary evidence suggest a smooth dependence of the machine accuracy on the system size, although larger systems naturally require more machine iterations to converge to their ground state. According to thermodynamic considerations, this is consistent with the presence of an effective thermal bath for the spin state. It suggests that lowering the effective temperature of the machine by improving the experimental setup can lead to larger ground-state probabilities even for large-scale models.

Conclusions

Understanding the role of noise in optical Ising machines and neuromorphic devices is crucial for their application to large-scale computational tasks. In particular, noisetolerant settings are attractive candidates for developing unconventional computing architectures. We have reported the first evidence that spatial-photonic Ising machines can take advantage of noise in solving largescale optimization problems. Devices based on spatial light modulation are scalable to larger sizes and can potentially host systems consisting of millions of spins. In particular, our computing setting can exploit the potential of nanophotonic light-modulation devices. Tunable dielectric metasurfaces, which allow to control both phase and polarization of the optical wavefront with subwavelength spatial resolution [START_REF] Kamalia | A review of dielectric optical metasurfaces for wavefront control[END_REF], can act as high-density phase modulators, enabling the integration of SLM-based Ising machines on a photonic chip. For example, more than 10 6 optical spins over square millimeter could be obtained through the development of novel SLM technologies that integrate nanoantennas into liquid crystal cells [START_REF] Li | Phase-only transmissive spatial light modulator based on tunable dielectric metasurface[END_REF]. Alternative nanophotonic platforms that employ electrooptic microcavity arrays would allow to achieve high fill factors along with phase-only modulation at GHz speeds [START_REF] Peng | Design of high-speed phase-only spatial light modulators with two-dimensional tunable microcavity arrays[END_REF]. At present, the iteration time of our Ising machine can be reduced to a few milliseconds by exploiting the most recent microelectromechanical SLM technologies [START_REF] Blochet | Focusing light through dynamical samples using fast continuous wavefront optimization[END_REF][START_REF] Tzang | Wavefront shaping in complex media with a 350 KHz modulator via a 1D-to-2D transform[END_REF]. Spatial-photonic Ising machines are thus a promising approach for large-scale ultra-fast optical computing.

In conclusion, introducing a noisy-feedback mechanism in an SLM-based scheme, we have demonstrated the existence of an optimal noise level enhancing the machine performance on frustrated Ising models. Noise can hence be exploited as a tunable parameter to improve the exploration of energy landscapes with many minima, an interesting property that has been identified also in neuralnetwork-based nanophotonic Ising samplers [START_REF] Roques-Carmes | Heuristic recurrent algorithms for photonic Ising machines[END_REF][START_REF] Prabhu | A recurrent Ising machine in a photonic integrated circuit[END_REF]. Photonic Ising machines with controllable noise represent a route to realize photonic simulations of phase transition and finite-temperature phenomena. Our results show that noise is a valuable resource for optical computing, opening important possibilities for realizing classical and quantum annealing.

Figure 1 :

 1 Figure 1: Photonic Ising machine by spatial light modulation. (a) The spins σ i ±1 are encoded by a spatial light modulator (SLM) into binary optical phases ϕ 0, π in separated spatial points of the optical wavefront. Intensity modulation is employed to set the spin interaction via the amplitude distribution ξ i . Recurrent feedback from the far-field camera allows evolution of the phase configuration towards the Ising ground state. (b) Intensity detected on the camera (CCD) modes for a random spin state and for the ground state of a ferromagnetic Ising model. Insets are illustrations of the corresponding spin state in energy landscape. Experimental fluctuations allow spontaneous changes in the spin configuration.

Figure 2 :

 2 Figure 2: Ising machine's ground states without noise control. (a-c) Results for ferromagnetic and (d-f) frustrated models with 100 spins (ρ 0). Problem graphs for (a) mean-field (infinite-range) Ising model and (d) Mattis spin glass with positive and negative couplings. For clarity, only links starting from the two black nodes are drawn. Insets show the corresponding target images I T . (b, e) Contour maps showing the evolution of the spin configuration during a single run of the machine (green regions are domain walls). (c, f) Normalized histograms of the ground-state energy obtained for the instances in (a) and (d), respectively. The red lines in (c) and (f) indicate the minimum energy known from exact solution of the models.

Figure 3 :

 3 Figure 3: Optimal noise level in spatial-photonic Ising machines. (a, c, e) Success probability and (b, d, f) mean Hamming distance varying the noise level for various N = 100 Ising models: (a-b) mean-field Ising model, (c-d) dense and (e-f) sparse Mattis spin glasses. The problem graphs are inset. Different colors in (a, c, e) indicate data obtained at the specified accuracy level. Shaded regions indicate statistical error intervals. The existence of an optimal noise level for frustrated models is signaled by a minimum in the Hamming distance and a corresponding maximum in the success probability [dotted line in (d) and (f)].

Figure 4 :

 4 Figure 4: Scaling properties. Optimal noise level (blue circles) as a function of the number of spins for dense Mattis spin glasses (inset graph). Purple dots indicate the measured Hamming fraction (h/N) for various system sizes.

Acknowledgments: We acknowledge funding from Sapienza Ateneo, SAPIExcellence 2019 (SPIM project), Quan-tERA ERA-NET Co-fund (Grant No. 731473, project QUOMPLEX), PRIN PELM 2017 and H2020 PhoQus project (Grant No. 820392). We thank Mr. MD Deen Islam for technical support in the laboratory.


Yohann Pitrey
email: ayohann.pitrey@insa-rennes.fr

Marie Babel
email: marie.babel@insa-rennes.fr

Olivier Déforges
email: olivier.deforges@insa-rennes.fr

Jérôme Viéron
email: bjerome.vieron@thomson.net

ρ-domain based Rate Control Scheme for Spatial, Temporal and Quality Scalable Video Coding

Keywords: video coding and transmission, rate control, MPEG-4 Scalable Video Coding, ρ-domain

Rate control is a capital issue in video coding. It allows a regulation of the bitrate out from the encoder, to cope with some network transmission or quality constraints. Scalable Video Coding emerged several years ago as an answer to the growing need of application-adaptable video streams. Although the interest of scalable video coding has been confirmed by recent studies, it can not be used in practical contexts without proper rate control techniques. In this paper we present a new rate control scheme for scalable video, based on a simple yet attractive bitrate modelling framework called ρ-domain. Our scheme performs accurate rate control on spatial, temporal and quality scalabilities, while maintaining a constant PSNR. Inter layer prediction is also handled effectively.

INTRODUCTION

Video streaming over communication networks has known a tremendous expansion over the last decade. With numeric television, internet broadcasting and video-capable mobile devices, efficient video coding is becoming a central need. To reduce the amount of data to transmit, video coding techniques such as MPEG-4 AVC/H.264 have been developed. Based on spatial and temporal redundancy removal, together with arithmetic coding, they allow to condense the data in a quite effective way. Nevertheless, today's heterogeneous networks and manifold video-reading devices call on more adaptible video streams. MPEG-4 AVC/H.264 was designed to address any fixed setup and fails to provide flexible video streams. The new MPEG-4 Scalable Video Coding (SVC) standard has been proposed as a response to this need for flexibility. It provides three types of scalability. Spatial scalability acts on the frame resolution, and addresses heterogeneous display devices. Temporal scalability increases the number of frames per second, thus improving the motion smoothness. Quality scalability improves the signal-to-noise ratio of the decoded video stream. A MPEG-4 AVC/H.264-compatible base-quality layer is first encoded, and further enhanced by additional layers. The standard also provides a new tool called inter-layer prediction. This feature allows enhancement layers to use information from a given base layer for prediction, and yields to better coding performances.

As it is based on both spatial and temporal statistical redundancy removal, the performances of video coding can vary, depending on the nature of the sequence to be processed. Thus, the bitrate at the output of the encoder can fluctuate, leading to quality and bandwidth wastage. Rate control is designed to regulate the output bitrate so that it fits to a given constraint. It has been widely studied on MPEG-4 AVC/H.264 and previous video coding standards. [START_REF]MPEG-2 test model 5[END_REF][START_REF] Li | Adaptive basic unit layer rate control for JVT[END_REF] More recently, few propositions were made for rate control of scalable video. [START_REF] Xu | Rate control for scalable video model[END_REF][START_REF] Liu | Rate control of h.264/AVC scalable extension[END_REF] In this contribution, we present a new simple yet effective rate control scheme based on the ρ-domain modelling framework. [START_REF] He | ρ-domain bit allocation and rate control for real time video coding[END_REF] This scheme operates on each type of scalability and is able to deal with inter layer prediction, while keeping a very low computational complexity. The quality of the reconstructed video stream is constant, which is of great importance for human quality perception. The paper first introduces the ρ-domain bitrate representation, then describes the implemented rate control scheme. We further illustrate the performance of our scheme by analyzing some practical results. Frame bitrate (bpp) ρ (%)

Figure 1. R(ρ) relationship on a hierarchical B frame in the highest enhancement layer of a three-layer spatial-scalable video stream using inter-layer prediction.

ρ-DOMAIN BASED RATE MODEL

One of the main issues of rate control is to find an accurate relationship between the bitrate at the ouput of the encoder and the quantization parameter (QP). This way, it is possible to predict the number of bits needed to encode a frame with a given QP, before encoding it. Quantizing a frame introduces a loss from the original data, also known as distorsion. Various rate control approaches try to formulate the relationship between the output bitrate and the distorsion, which are closely related. This relationship can be approximated using a Laplacian or a Gaussian distribution. [START_REF] Jin Lin | Bit-rate control using piecewise approximated rate-distortion characteristics[END_REF][START_REF] Ribas-Corbera | Rate control in DCT video coding for low-delay communications[END_REF] Then, a relationship between the distorsion and the QP is established so that the link between the bitrate and the QP can be found. First introduced in 5, ρ-domain is a slightly different approach. Let ρ be the percentage of zero coefficients in a frame after quantization. The output bitrate linearily decreases when ρ increases (see figure 1). [START_REF] He | Linear rate control for JVT video coding[END_REF] As a relationship can be easily found between ρ and the QP, ρ can be used as an intermediate to get a relationship between the bitrate and the QP. Given the transform coefficients of a frame after the DCT, it is straightforward to determine how many will be coded as zeros after quantization. Let c m ij be the coefficient at position (i, j) in the macroblock m. This coefficient is coded as a zero if its value is below a dead zone threshold. Due to the adaptive quantization used in H.264, this threshold depends on the position of the coefficient in the transformed macroblock and the value of the QP. [START_REF] Shin | Rate control using linear rate-ρ model for h.264[END_REF] The relationship between ρ and the QP can be written as:

ρ(q) = 1 M m,i,j z(c m ij , i, j, q), (1)
where M is the total number of coefficients in the frame, and z(c m ij , i, j, q) ∈ {0, 1} is a function that indicates if a coefficient is under the dead zone threshold (details on the dead zone threshold can be found in 9). Under small QP variations (i.e.: below 6), the relationship between ρ and the bitrate can be approximated quite accurately by a linear model. This assumption has been validated for MPEG-2 video streams 5 and for MPEG-4 AVC/H.264. [START_REF] Shin | Rate control using linear rate-ρ model for h.264[END_REF] In our previous work, [START_REF] Pitrey | ρ-domain for low-complexity rate control on MPEG-4 Scalable Video Coding[END_REF] we also validated it for MPEG-4 SVC streams, as presented on figure 1. In 9, the relationship between ρ and the bitrate is established as follows:

ρ(R) = R 0 -R × (1 -ρ 0 ) R 0 , (2)
where R 0 and ρ 0 are initial values which are determined by pre-encoding the frame. Using ( 1) and ( 2), we can establish a relationship between the bitrate and the QP which allows us to predict the output bitrate before encoding a frame.

RATE CONTROL SCHEME FOR MPEG-4 SVC

A rate control scheme classically contains two modules. First, a budget allocation policy is used to dispatch the available bitrate according to the constraint to fit with. Then, respecting the target budget is handled by a QP selection module. Controlling the bitrate at the output of the encoder can be quite difficult, due to activity variations along the sequence to be processed. When it comes to scalable video, we have to deal with several video layers, interacting with each other using inter-layer prediction. The relationships beween the bitrates from the different layers can be quite complex and make rate control harder to achieve. In this paper we focus on the design of a rate control scheme that is able to control each layer separately. This section describes the rate control scheme we developed for MPEG-4 SVC, based on the model described in section 2.

Budget allocation

Our goal is to respect a given bitrate-per-second constraint, while aiming for a constant quality in the reconstructed video stream. Quality fluctuation leads to bad user experience and is to avoid. We specify a bitrate constraint for each layer, and layers are handled separately. Our budget allocation policy operates both at group-of-pictures (GOP) and at frame levels.

GOP-level budget allocation

First, we allocate a target budget to each GOP, by simply converting the bitrate-per-second constraint C l for layer l to a bitrate-per-GOP constraint G l :

G l = S l × C l F l + δ, (3)
where S l is the size of a GOP in layer l, F l is the number of frames per second in layer l and δ is a small feedback term to compensate allocation errors over previous GOPs.

Relative frame complexity

Once a target budget is assigned to a GOP, we need to dispatch it among its frames. Each type of frame (i. e.: I, P and B) uses different coding tools, and has different coding efficiency. I frames use only intra-frame prediction and are the most reliable. However, their coding efficiency is not as good as P frames which allow inter-frame prediction. B frames allow bidirectional prediction and have even better coding efficiency. To aim for constant quality throughout the GOP, we need to allocate more budget to key-frames (i.e. : I, P) than to B frames. We define a complexity measure K T l , to represent the relative coding efficiency of a given frame type T in a given layer l. To understand the construction of this measure, we need to look at the quantization scheme of H.264, which is the same as in MPEG-4 SVC. [START_REF]264 and Mpeg-4 Video Compression: Video Coding for Next-Generation Multimedia[END_REF] After finding a prediction, each residual macroblock is transformed using a DCT. The transformed coefficients are then quantized by a scalar quantizer. A quantized coefficient Z ij can be expressed as :

Z ij = round(W ij × M F 2 qbits ), (4)
where W ij is the corresponding transformed coefficient, M F is a factor given in 11 and qbits = 15 + f loor(q/6).

(

) 5
As we look for a relative complexity measure, the constant terms in equations ( 4) and ( 5) can be discarded, as well as the rounding operations. Then, equation ( 4) can be reformulated as:

2 q/6 × Z ij = W ij . (6)
The transformed coefficients W ij are a good indicator of the coding complexity of a macroblock. If a good prediction was found, the amount of residual information is small and the transform coefficients contain quite small values. However, if the prediction is bad, the transform coefficients contain large values. Therefore, we use 2 q/6 × Z ij as a macroblock complexity measure. At frame-level, the complexity measure is defined as the sum of macroblocks complexities:

K T l = 2 q/6 × i,j Z ij . (7)
Once quantized, the coefficients are sent to the entropy coder, which is the last step in the encoding process.

The number of bits needed to code a frame and the values of the quantized coefficients are thus closely related. As a result, in equation ( 7) it is possible to replace the quantized coefficients Z ij with the number of bits needed to code it, say b. Thus, the final frame complexity measure can be expressed as follows:

K T l = 2 q/6 × b. (8)
This complexity measure was designed so that I frames have a higher complexity than P frames, and that P frames have a higher complexity than B frames. For each type of frame in each layer, we handle a separate complexity K I l , K P l and K B l . To take advantage of the hierarchical B frames GOP structure used in MPEG-4 SVC, B frames complexities also depend on their temporal level t, so K B l is actually K B l,t (but is noted as K B l for simplicity).

Frame-level budget allocation

The GOP budget is dispatched according to the frames complexities. The target budget for a frame is processed as follows:

R target = K T l K T OT AL l × G l + , (9)
where T ∈ {I, P, B} is the type of the frame, K T OT AL l is the sum of complexities of all frames in the current GOP and is a small feedback term. As it is not possible to know the complexities of all frames in the GOP in advance, we use weighted mean values as estimations for frames that have not been encoded yet. These mean values are updated as follows after encoding each frame:

K T l = A × KT l + B × KT l A + B , ( 10
)
where KT l is the previous mean complexity value, KT l is the complexity of the current frame and A and B are two weighting constants (for our tests we used A = 5 and B = 3).

QP processing

Once the budget allocation is performed, the optimal value of QP is computed for each frame. We proceed in two steps. First using (2), we process the target value of ρ, say ρ target , corresponding to the target bitrate R target .

Then we search for the QP that generates the closest bitrate to ρ target using (1). This search is performed by computing equation ( 1) for each value of QP between 0 and 51. To evaluate R 0 and ρ 0 from equation ( 2), we pre-encode the frame with an initial QP.

EXPERIMENTAL RESULTS

We will now analyze the performance of our rate control scheme on MPEG-4 SVC. For each type of scalability, three layers were encoded. Table 1 sums up each tested set. Dyadic scalability was used in the spatial scenario (increase of the frame dimensions by two from one layer to another). For quality scalability, coarse-grain scalability (CGS) was used, and each layer used the lower layer as a reference ID. The GOPs structure was 'PBBB', except for temporal scalability, for which the base layer only contains P frames and the middle layer has a 'PB' structure. Inter layer prediction was activated, allowing a layer to search for motion and texture information in the lower layer. The constraint bitrates for each layer were inspired by the SVC Verification Test Plan, 12 but were not designed to reach equal quality on each layer. To evaluate the effectiveness of the rate control, we measure both the allocation error and the signal-to-noise ratio (PSNR) in the reconstructed stream. For this, we report the absolute allocation error on each frame :

∆ = |R target -R real | R target , (11)
where R real is the actual number of bits generated after encoding the frame. Table 2 shows that our rate control scheme reaches the constraint bitrate very accurately. The allocation error is below 3% for most encoded layers, and below 5% in worst cases. Inter layer prediction is handled correctly and the method even achieves good performances on SOCCER, which is quite difficult to encode because of the high motion and texture activity observed along the sequence. The PSNR remains quite constant, showing only small variations. Visually, the quality looks constant with no unpleasant effect. On every tested configuration, we observed that the difference in terms of PSNR measured between P frames and B frames inside a GOP is below 1 dB. In our budget allocation scheme, each frame is allocated a number of bits that depends on its relative complexity in front of the other frames in the GOP. The ability of our scheme to reach a constant quality lies on the complexity measure we defined in section 3.1.2, thus proving to be quite accurate. This is confirmed by the graphics in figure 2, which present the allocated and achieved bitrates at frame level for each type of scalability. The saw-toothed shape shows the behaviour of our budget allocation scheme. More bits are granted to P frames than to B frames. Moreover, the highest temporal level B frames are allocated less bits than the lowest ones (the bitrates are displayed in encoding order, so the lowest temporal level B frames appear first). Figure 2 also shows the accurate bitrate matching achieved by our scheme. The final number of bits is very close to the target bitrate for most frames. For a few frames, we can see a mismatch, which is due to abrupt activity changes requiring large QP variations. They cause important changes in the prediction modes, and make it difficult to predict the output bitrate at frame level. [START_REF] Pitrey | ρ-domain for low-complexity rate control on MPEG-4 Scalable Video Coding[END_REF] Figure 3 presents the achieved bitrates per second and frame PSNR for each scalability. Once again, the bitrate matches the constraint very closely. The allocation errors we noticed at frame level are taken into account and well compensated by modifying the budget of the following GOPs. The global PSNR variations are due to activity changes in the input sequence. The curve remains quite smooth and shows that locally, frames have a comparable PSNR, regardless to their type.

CONCLUSION

In this paper we presented a new rate control scheme for MPEG-4 SVC, based on the ρ-domain framework. This very simple yet efficient rate control scheme manages to respect the specified layer constraints with very small allocation error, and keeps a constant PSNR over the reconstructed sequence. A budget dispatching method is first performed at GOP level, then at frame level. The relative frame types complexities are used to maintain a constant quality throughout the entire GOP. The ρ-rate model is then used to choose a QP value for the whole frame. Tests on spatial, temporal and quality scalabilities show that our scheme is capable of regulating the output bitrate with very little error. Inter layer prediction is handled correctly, which is very promising for scalable video streams. Moreover, the very low computational complexity of our scheme make it almost insignificant in front of the rest of the encoding process. Our scheme can still be enhanced by including some buffer control. Furthermore, choosing a different QP for each macroblock could improve the whole bitrate regulation, at the expense of a dramatic computational complexity increasement. In our future work, we will focus on cross-layer rate control, fully exploiting the inter layer prediction tool. Pre-encoding pass removal and human quality perception shall also be areas of interest.

Table 1 .

 1 Test scenarii for each type of scalability.

			frame size	frames per	rate (kbps)	GOP size
				second
		base layer	QCIF	30	160	4
	SPATIAL	enh. layer 1	CIF	30	480	4
		enh. layer 2	4CIF	30	1400	4
		base layer	CIF	30	300	4
	QUALITY	enh. layer 1	CIF	30	600	4
		enh. layer 2	CIF	30	900	4
		base layer	CIF	15	240	1
	TEMPORAL	enh. layer 1	CIF	30	480	2
		enh. layer 2	CIF	60	960	4

Table 2 .

 2 Table 2 reports the mean value and standard deviation of ∆ and PSNR for each type of scalability. Allocation error and PSNR for each type of scalability.

				HARBOUR			SOCCER
			µ∆	σ∆	µP SN R	σP SN R	µ∆	σ∆	µP SN R	σP SN R
		base layer	0.62%	13.31	36.83	0.80	1.21%	6.76	39.40	1.98
	SPATIAL	enh. layer 1	1.32%	20.66	30.76	0.47	3.18%	8.14	36.05	2.22
		enh. layer 2	4.16%	17.30	26.07	0.32	4.71%	10.31	32.67	2.30
		base layer	5.58%	15.51	29.44	0.45	2.76%	11.75	33.41	1.87
	QUALITY	enh. layer 1	2.18%	15.99	32.35	0.42	4.45%	12.84	36.93	2.12
		enh. layer 2	0.73%	11.24	35.08	0.40	2.54%	10.95	39.79	2.32
		base layer	0.30%	3.78	29.24	0.31	1.83%	18.96	33.94	1.70
	TEMPORAL	enh. layer 1	0.19%	8.49	27.45	1.41	1.36%	8.16	32.99	1.69
		enh. layer 2	2.67%	9.39	26.98	2.66	1.14%	11.19	31.66	2.27


Nattawut Chaomuang
email: nattawut.ch@kmitl.ac.th

Parinya Singphithak

Onrawee Laguerre

Rachit Suwapanich

Temperature control in a horticultural produce supply chain in Thailand and its influence on product quality

Keywords: Nattawut Chaomuang Conceptualization, Methodology, Investigation, Validation, Formal analysis, Investigation, Writing -Original Draft Preparation, Visualization, Project administration, Funding acquisition Parinya Singphithak Investigation, Software, Visualization, Validation, Supervision Field investigation, postharvest handing, temperature, cold chain, baby corn, physiological quality

The present study was conducted in order to investigate the temperature conditions in the horticultural produce cold chain in Thailand, and fresh-cut baby corn was chosen for a case study. The field investigation together with in-person interviews were performed at 4 growers' premises and one packing house. The information collected provided details on current postharvest conditions at individual stages from the growers' premises to an export distribution center. Temperature measurements were carried out to explore the time-temperature profiles throughout these stages. The results showed that the total duration of these stages was almost 32 h, and the temperature variations were between 6 and 33°C. Precooling was delayed for at least 9 h, since baby corn cobs were primarily processed by dehusking and bulk packing. The baby corn was maintained at a temperature below 6.0°C in a cold room for almost half of the total duration. The effect of the postharvest temperature conditions on the product quality evaluation was assessed by measuring various physiological quality attributes during storage.

It was found that the marketability of the baby corn subjected to such postharvest temperature conditions remained possible with a salable period of up to two weeks. The result made it possible to identify the stages during which temperature control was inadequate, and recommendations were proposed to the stakeholder partner in order to modify the postharvest conditions in order to extend the product shelf life.

Introduction

The supply chain incorporating low-temperature control is referred to as the "cold chain" in which refrigeration is the prime technology used to provide a cold environment [START_REF] Olatunji | Advances in cooling technologies to preserve horticultural produce[END_REF]. Temperature is by far the most important environmental factor affecting the quality and safety of fruit and vegetables [START_REF] Watada | Fresh-cut produce[END_REF]. Insufficient use of refrigeration can result in food loss and waste. As reported by the International Institute of Refrigeration (IIR), around 360 million tons of foods are lost annually across the globe due to a lack of refrigeration [START_REF] Iir | The role of refrigeration in worldwide nutrition[END_REF]. For fresh fruit and vegetables, poor temperature management may cause produce losses ranging from 25 to 50% [START_REF] Kelly | A novel approach to determine the impact level of each step along the supply chain on strawberry quality[END_REF]. Although the total percentages of losses in developed countries may not significantly differ from those in developing countries, the difference becomes significant when one looks into individual stages. In developed countries, losses of fruit and vegetables mostly occur at the supermarket and consumer stages, whereas in developing countries, the losses are mainly at the postharvest and distribution stages [START_REF] Goedhals-Gerber | Identifying temperature breaks in the export cold chain of navel oranges: A Western Cape case[END_REF][START_REF] Kitinoja | Measuring postharvest losses of fresh fruits and vegetables in developing countries[END_REF][START_REF] Porat | Postharvest losses of fruit and vegetables during retail and in consumers' homes: Quantifications, causes, and means of prevention[END_REF]. In Thailand, [START_REF] Rattanawong | Reduce loss during transportation: a case study of fresh vegetables in Thailand[END_REF] observed 20 to 50% losses of fresh vegetables during long-distance transport from the production area in the northern region to the packing house in the central region. At least 27% of such losses were due to an unsuitable temperature environment.

Temperature control at all stages in the cold chain makes it possible to delay the deterioration of produce quality but poses a great challenge [START_REF] Mercier | Time-temperature management along the food cold chain: A review of recent developments[END_REF].

Although refrigeration is broadly applied in developed countries, numerous published studies show that there are temperature breaks at all stages in the cold chains, particularly at the transport and retail stages [START_REF] Ndraha | Time-temperature abuse in the food cold chain: Review of issues, challenges, and recommendations[END_REF]. These temperature break, even for a few hours, may have a significant impact on product organoleptic quality evolution [START_REF] Loisel | Cold chain break detection and analysis: Can machine learning help[END_REF]. Field studies similar to those conducted in developed countries are performed to a lesser extent in developing countries [START_REF] Mercier | Time-temperature management along the food cold chain: A review of recent developments[END_REF]. The development of cold chains has been observed recently in certain developing countries such as Brazil, China, and India [START_REF] Salin | Global cold storage capacity report[END_REF][START_REF] Salin | Global cold storage capacity report[END_REF]. A similar trend was also observed in Thailand where the cold storage capacity has increased from 0.94 million metric tons in 2015 to 1.57 million metric tons in 2021 [START_REF] Dit | Warehouse, silo, and cold storage[END_REF][START_REF] Ongkittikul | The Cold Chain in Thailand[END_REF]. This progress requires to address the current status of time-temperature conditions in the cold chain so that the stages where temperature abuse arises are identified, and consequently suitable remedial strategy can be implemented in an effective manner [START_REF] Ndraha | Time-temperature abuse in the food cold chain: Review of issues, challenges, and recommendations[END_REF]. According to the authors' knowledge, cold chain field studies together with J o u r n a l P r e -p r o o f investigation of the impact of the cold chain on food quality are rare, particularly in Thailand where the ambient temperature is high. The most relevant field study was conducted in Belgium by [START_REF] Rediers | Evaluation of the cold chain of fresh-cut endive from farmer to plate[END_REF]. In this study, the temperature profile of freshcut endive in a real cold chain and its impact on product microbiological safety was evaluated.

The objective and the originality of the present study was firstly to acquire knowledge of the temperature conditions in the existing horticultural produce cold chain in Thailand, and secondly to study its impact on product quality. A cold chain for fresh-cut baby corn (Zea mays L.) was chosen for a case study because this product is one of the major crops in Thailand and is thus important to the Thai economy. Being the largest exporter, Thailand accounts for 80% of exports of baby corn in the world [START_REF] Singh | The Export Value Chain of Baby Corn in India: Governance, Inclusion and Upgrading[END_REF]. This product is highly perishable and a shelf life is only six days under ambient storage conditions (25°C) and 21 days under cold storage conditions (4°C) [START_REF] Sakhornyen | Postharvest handling systems on quality of baby corn[END_REF].

In this study, postharvest handling was investigated at several growers' premises and at a packing house. Temperature measurements were then undertaken by using temperature dataloggers to monitor baby corn from the growers' premises to an export distribution center.

Finally, the effects of such postharvest handling and its temperature conditions on the product quality during storage was evaluated in a laboratory. The knowledge acquired in this study provides an insight into the current status of the cold chain operated by smallholders and could be used as a basis for future research on the development of an efficient cold chain in Thailand.

Materials and methods

Field investigation

Postharvest conditions in a fresh-cut baby corn cold chain were investigated from growers' premises to an export distribution center. A field investigation was conducted in December 2020 to observe product handling at a packing house and four growers' premises located in Tha Maka district (Kanchanaburi province, eastern region of Thailand). This packing house was chosen based on several reasons including the willingness of the operators to perform the field investigation and to share the data, the presence of a refrigeration facility, and the marketing mode for both the export and domestic supply chains. Interviews were conducted with the operators and the growers in order to obtain detailed information. The exporters and the domestic wholesalers who procured the baby corn from the packing house were also interviewed. The interview questionnaire used in the study was certified by the research ethics committee of King Mongkut's Institute of Technology Ladkrabang (EC-KMITL 63-017) to ensure respondent confidentiality. Based on the information acquired, temperature J o u r n a l P r e -p r o o f measurements and a quality assessment were set up with the methodologies described in the following sub-sections.

Temperature measurement

Temperature dataloggers (Elitech ® RC-5, Jiangsu Jingchuang Electronics, Jiangsu, China; ±0.5°C accuracy in the range of -20°C /+40°C) were used in the study. Generally, the measured value represents the air temperature adjacent to the product because it is difficult to place this sensor on the surface and at the core of the product due to the sensor size. In order to help interpretation of temperatures measured by the datalogger, an experiment was firstly undertaken in a laboratory refrigerator (PC-1355, Power Cool Systems, Samut Prakan, Thailand, with a temperature setting of 8°C). A comparison of temperatures measured by datalogger (denoted as "DL") and by three calibrated T-type thermocouples (200 μm diameter, ±0.2°C accuracy in the range of -5°C/+30°C) was carried out. These thermocouples were installed to measure the core (denoted as "CT") and surface (denoted as "ST") temperatures of baby corn and the air temperature at 10 mm from the product surface (denoted as "AT"). The thermocouples were connected to a switching unit (34907A, Agilent Technologies, Santa Clara, California, USA) for data acquisition of every 10 s. The datalogger and the instrumented baby corn were placed together on a foam tray. Two sets of dataloggers and thermocouples (i.e., six thermocouples in total) were used simultaneously to ensure result consistency.

Field temperature measurement was carried out in the baby corn cold chain from the growers' premises to the export distribution center (referred to as "upstream stages" in this paper). The temperature was recorded every 10 s. Because of practical difficulties, the product temperature at different stages in the supply chain could not be measured continuously.

According to the information of postharvest conditions (details in Section 3.1), the temperature measurements were therefore separated into four periods and then linked together to represent the entire temperature profile of the cold chain for exported baby corn.

In Period I (Stages 1, 2, 3, and 4, Fig. 1a), two dataloggers were inserted, one at the top and one at the bottom of four baskets (Fig. 2a) from three different growers' premises. In Period II (Stage 5, Fig. 1a), ten baby corn cobs were sampled, and the core temperature was measured prior to and after hydrocooling by using a digital handheld thermometer equipped with two Ktype temperature probes (54-IIB, Fluke Corporation, Everett, Washington, USA; ±0.3°C accuracy in the range of -10°C /+50°C). The cooling water temperature was also measured at 20 positions in the bath (10 positions at 100 mm and another 10 positions at 400 mm from the surface of the water) using the same sensor. The measurements were undertaken on two batches J o u r n a l P r e -p r o o f to ensure result repetition. In Period III (Stages 6 and 7, Fig. 1a), five dataloggers were placed on the packaging tables to measure the ambient temperature in a packaging room. Before the packed products were transferred to the cold room, these dataloggers were randomly placed on the top of the five foam boxes (Fig. 2c) to monitor the air temperature during storage. The air relative humidity in the cold room were also measured every five minutes using a hygrometer (174H, Testo, Titisee-Neustadt, Germany; ±3%RH accuracy in the range of 2 to 98%RH). This sensor was installed underneath the return air inlet of the refrigeration unit. Due to the lack of permission for intervention with the export products, the dataloggers were withdrawn from the boxes before the boxes were loaded onto the refrigerated truck of the export distributor.

Accordingly, in Period IV (Stage 8, Fig. 1a), two dataloggers were installed at the mid-height of the front and the rear of the truck to record the air temperature during the time interval between loading at the packing house and unloading at the distribution center. The driver was asked to return the dataloggers to the laboratory.

Quality assessment

Sample procurement and preparation

To evaluate the effects of postharvest temperature conditions on the product quality, a quality assessment was conducted on two groups of baby corn cobs: Group 1 (product for export) and Group 2 (product for domestic markets). The differences between these groups were the presence of precooling (hydrocooling) prior to cold storage and the time of packaging as shown in Fig. 1. Photos of the retail packaging of Groups 1 and 2 are displayed in Figs. 2b and2d, respectively. The products in both groups were sampled at the packing house in the same day as the temperature measurement was undertaken and were transported to our laboratory the next morning using a refrigerated truck to prevent product degradation at this stage to the greatest possible extent. The sample of Group 1 was the packed baby corn in a foam box which was randomly chosen from Stage 6 while the sample of Group 2 was fresh baby corn filled in the four instrumented baskets which were taken after Stage 4 and stored in the cold room without precooling. In the foam box, three dataloggers were also installed at the top, in the middle and at the bottom to monitor the internal temperature variation at this stage.

At the laboratory, all packs of baby corn were removed from the foam box and individually weighed using digital scales (PB1502-L, Mettler Toledo, Columbus, Ohio, USA; 0.01 g readability and ±0.02 g accuracy). This measured value was considered as the initial weight for the weight loss evaluation. Then, the packs were evenly loaded into two refrigerators (MIR-253, Sanyo, Osaka, Japan) with temperature settings of 2.1 ± 0.1°C and 4.3 ± 0.1°C J o u r n a l P r e -p r o o f respectively, prior to the quality assessment. Meanwhile, the fresh baby corn in the baskets was processed in a similar manner as in the packing house: cleaned, trimmed, and packed in a Styrofoam tray (190 mm × 105 mm) sealed with polyvinyl chloride (PVC) plastic wrap (Fig. 2d). Each pack was weighed and stored in the two refrigerators.

Quality measurement

Various physicochemical quality attributes of baby corn including weight loss, visual appearance, color, firmness, and total soluble solid (TSS) content were evaluated under temperature-controlled storage. Measurements were undertaken on the day of arrival at the laboratory (Day 0 -Control) and every two days over the 14-day storage period using the following procedures. Two packs were randomly sampled from each refrigerator (i.e. four packs for each group). The quality attributes of the baby corn in the sampled packs were then measured on each evaluation day. All data were reported as the mean value of n samples ± standard deviation (SD).

(i) Weight loss. Each pack was weighed (n = 2) and its weight loss was determined and expressed as the percentage loss from its initial weight: %Loss = (W initial -W final ) W initial ⁄ .

(ii) Visual appearance. Ten baby corn cobs were sampled from each pack and assessed for visual quality by three trained panels (n = 60). The visual quality was scored on a scale of 5 to 0 according to the quality index describing the extent of browning developed on the baby corn: 5 refers to no browning, 4 to browning exhibited on 1-10% of the total ear area, 3 to 11-20%, 2 to 21-30%, 1 to 31-40%, and 0 to more than 40% (adapted from [START_REF] Leelaphiwat | Design of modified atmosphere packaging systems for baby corn[END_REF]). . It should be noted that 𝐿 * value signifies the degree of lightness of which the value ranges from 0 (black) to 100 (white). Hue angle and chroma value signify the extent of browning where the angle of 0° to 90° exhibits the color span between redness and yellowness, while the chroma value indicates its saturation.

(iv) Firmness. The same baby corn cobs used for the color assessment were then determined for their firmness (n = 10) by using a texture analyzer (TA-XT plus, Stable Micro Systems, Surrey, UK) equipped with a knife blade (HDP/BS) to measure cutting force. The measurement was performed at 3 cm from the ear tip with the cutting velocity of 120 mm•min - J o u r n a l P r e -p r o o f

1 . The maximum cutting force, expressed in Newton (N), was determined from the time-force profile by using the interfaced software (Exponent version 4.0.9.0, Stable Micro Systems, Surrey, UK).

(v) TSS content. All baby corn cobs in individual packs were blended and the juice was extracted. The TSS content of the juice, expressed in %Brix, was measured five times (n = 10) using a digital refractometer (PAL-1, Atago, Tokyo, Japan; ±0.2% accuracy in the range of 0-53%Brix).

Results and discussion

Description of postharvest condition

The on-site investigation and the in-person interviews took place at the growers' premises and the packing house. Product handling including equipment or facilities used at individual stages along the upstream stages (Fig. 1) are presented in detail as follow.

The growers begin to harvest baby corn in the morning (5:00 a.m. to 8:00 a.m.). During harvesting, the baby corn cobs are put in sacks and are later transferred using a cart, a scooter with a side trailer, or an open-bed truck to the growers' premises for primary screening and minimal processing. About 3.5 kg of non-defective baby corn cobs are wrapped in a plastic liner and placed in a plastic basket equipped with a lid (Fig. 2a). The basket is made of polypropylene, measures 330 mm in width × 200 mm in length × 110 mm in height and the perforation area is about 30%.

The investigated packing house is a community enterprise where most baby corn is procured from the growers engaged by contract and from other packing houses in nearby districts. Open-bed trucks are commonly used to collect the baby corn without cloth or tarpaulin covers during transport (except in the rainy season). At the packing house, the baby corn is unloaded and stored in an open hall under ambient conditions. Some baby corn is sold to domestic wholesalers in bulk (Fig. 1b) while the baby corn for export undergoes further processing in the evening (usually starting at 6:00 to 6:30 p.m.). The product is first precooled in a cold-water tub with the water temperature set at 10°C. No standard precooling procedures such as product quantity for each batch, cooling time, and final product temperature are applied because the operator considers that the procedure has an insignificant effect on the product quality.

After precooling, the product is sorted and sized according to the exporter's requirements.

The products are then packed on a Styrofoam tray (120 mm × 120 mm) sealed with PVC plastic J o u r n a l P r e -p r o o f wrap (100-110 g per pack, Fig. 2b) and placed in an expanded polystyrene foam box (120 packs or about 12 kg per box, Fig. 2c). The filled boxes are then transferred to a cold room (with a temperature setting of 2°C). During this stage, all boxes are open in order to promote the cooling of the product by the surrounding air. The boxes are closed just before loading onto the exporter's refrigerated truck the following afternoon (~1:30 p.m.). It is to be noted that the investigated packaging room was equipped with an air conditioning system with a temperature setting of 20°C which provides a reasonable working environment, and product quality deterioration can be slowed down at this stage.

The export distributor uses a refrigerated truck (with a temperature setting of 2°C, and no strip curtains on the trailer doors) to collect the baby corn from the packing house. Based on the interviews, the distributor also collects the baby corn from other packing houses on the way back to the export distribution center located in Damnoen Saduak District, Ratchaburi Province (about 70 km and about 3 h from the studied packing house). At the distribution center, some gel packs (no information was available concerning the type and quantity of gel packs used) are placed in all foam boxes prior to transport that night by a refrigerated truck to the airport (Suvarnabhumi International Airport, Bang Phli District, Samut Prakan Province) located at around 120 km from the distribution center. No further information was available thereafter in our study.

The data obtained in this study were based on only one packing house because it proved to be difficult to find industrial partners. Despite this, the information was in good agreement with the results reported by several studies [START_REF] Anonymous | Baby corn production, processing and marketing in Thailand[END_REF][START_REF] Koslanund | Postharvest management of fruit and vegetables in the Asia-Pacific region: Thailand country report[END_REF][START_REF] Rattanachai | Inbound logistics management of fresh baby corn for export[END_REF][START_REF] Sakhornyen | Postharvest handling systems on quality of baby corn[END_REF] in terms of stages in the cold chain and product handling at a given stage. The methodology developed in this study for time-temperature conditions in the cold chain and its effect on baby corn quality could be applied to other horticultural produce to better represent the current situation in Thailand.

Interpretation of temperatures measured by the datalogger

As shown in Fig. 3, the temperature recorded by the datalogger was in between that of the surrounding air temperature and the product surface temperature measured by the thermocouples. The temperature measured by the datalogger at any given instant was about 0.5-1.6°C higher than the surface temperature and about 1.2-2.3°C higher than the core temperature.

Due to the thermal inertia of the datalogger and the baby corn, the difference between the amplitude of the temperature variation of the datalogger and that of the product surface was small (∆T = (T max -T min ) 2 ⁄ ≤ 0.5°C), compared with that of the surrounding air (∆T ≈ J o u r n a l P r e -p r o o f

1.3°C). Thus, the temperature measured by a datalogger in the field was considered to represent an intermediate value between the temperatures of the product surface and the surrounding air.

Time-temperature evolution

Fig. 4 shows the overall temperature conditions in the fresh-cut baby corn cold chain from the growers' premises to the export distribution center (Stages 1 to 8). It was found that these upstream supply stages accounted for approximately 31.3 h during which the temperature varied between 6 and 33°C. The periods during which temperature abuse occurred were the stages prior to precooling, corresponding to the precooling delay of around 9.2 h. For nearly half of the duration of the upstream stages (~ 16.2 h), the baby corn was stored in a cold room in which the time-averaged temperature was approximately 5.7 ± 1.4°C. This temperature is considered high for the storage of baby corn because the recommended storage temperature is at or below 4°C [START_REF] Sakhornyen | Postharvest handling systems on quality of baby corn[END_REF]. A rapid temperature increase during loading onto a refrigerated truck prior to transport to the export distribution center, then substantial temperature fluctuations were also observed. This can be explained by the fact that the truck trailer was not precooled prior to loading. The following information presents the details of temperature conditions at all individual stages. from the initial value was observed during this stage, possibly because of the heat of product respiration which cannot be easily evacuated under calm air conditions. A decrease in temperature was observed during the transport to the packing house (Stage 3) and this could be attributed to the cooling effect of water evaporation induced by airflow during transport. Again, the temperature constantly increased during ambient storage at the packing house (Stage 4). A temperature of more than 30°C was observed in all baskets at the end of this stage. The increase in temperature in these baskets corresponded to the ambient climate conditions across these supply stages where the air temperature was 1-2°C higher than that of the product (data not shown).

Fig. 5b shows the temperature heterogeneity within the baskets during Period I. For four instrumented baskets, the temperature differences between the top and the bottom were less J o u r n a l P r e -p r o o f than 1.0°C in two baskets and more than 3°C in the other two baskets. This difference can be explained by the basket position in the stack: there was a higher temperature difference in baskets located at the top of the stack due to direct exposure to solar radiation during storage at the growers' premises and transport without thermal protection. This may also lead to quality and shelf-life heterogeneity of the product in the same basket.

Table 1 presents the precooling conditions (Stage 5). Two batches of 180-200 kg of baby corn were precooled. It took 16 minutes to cool the first batch and about 13 minutes to cool the second. The average temperature of the cooling water measured between the two batches was around 19.0°C ± 4.5°C. The average core temperature of baby corn decreased from 30.5°C ± 0.7°C to 24.1°C ± 1.0°C, corresponding to an average temperature drop of 6.4°C ± 1.0°C. The final product temperature of 24°C was still high, but further cooling was applied in the cold room during the following period. because it was exposed to the cold air in the room to a greater extent. A temperature variation of more than 5°C was observed within the same box (Box 6) during the first few hours of storage in the cold room (Fig. 6b). This variation decreased progressively with time until the end of the cold storage period when the temperatures at the bottom and in the middle positions

were almost identical at 5°C, whereas the temperature at the top of the box was 2-3°C lower.

The results highlighted the issue of temperature heterogeneity reportedly found in a cold room [START_REF] Bishnoi | Experimental investigation of air flow field and cooling heterogeneity in a refrigerated room[END_REF][START_REF] Duret | Experimental characterization of airflow, heat and mass transfer in a cold room filled with food products[END_REF] and within a package [START_REF] Gruyters | Modelling cooling of packaged fruit using 3D shape models[END_REF][START_REF] J O U R N A L P R E -P R O O F O'sullivan | Forcedair cooling of polylined horticultural produce: Optimal cooling conditions and package design[END_REF][START_REF] Wu | Unveiling how ventilated packaging design and cold chain scenarios affect the cooling kinetics and fruit quality for each single citrus fruit in an entire pallet[END_REF].

The packaged baby corn cobs in Boxes 1-5 were picked up by the export distributor and transported to the export distribution center. Fig. 7 shows the temperature conditions inside the J o u r n a l P r e -p r o o f truck trailer during transport (Stage 8). It was noted that the truck driver ran the refrigeration unit just before the pickup time and it took about 45 min. to cool down the temperature from its initial value (29.6°C) to 10°C. This observation underscores the importance of driver training on temperature abuse, which can be avoided by product loading only after the air temperature has stabilized inside the truck. According to the provided logistic information, the driver collected the baby corn cobs from the other four packing houses after having collected the baby corn cobs at the investigated packing house. This explained four sharp temperature rises (the spikes in Fig. 7) due to external air infiltration during door openings. The doors of the truck were not equipped with any protective devices such as air curtains or plastic strips, and this explained the pronounced temperature rises during this period. This effect was studied by de [START_REF] De Micheaux | Experimental and numerical investigation of the infiltration heat load during the opening of a refrigerated truck body[END_REF]. No temperature measurements were performed after the product delivery to the export distribution center.

Unlike Boxes 1-5, Box 6 was delivered to the laboratory by our refrigerated truck for quality assessment (Fig. 6b). During the product transfer from the cold room to the truck, temperatures rose 0.6-1.5-°C briefly inside the box and rose 6.6°C outside the box. The refrigeration unit of the refrigerated truck was operated for at least 20 min. prior to loading the products. During the journey that lasted about 3 h, the air temperature outside the box did not significantly fluctuate (average value 2.3 ± 0.3°C) and the temperature inside the box was quite homogeneous (average value of 5.6 ± 0.3°C).

Quality evolution during storage

The assessment was performed to evaluate the influence of the postharvest temperature conditions on baby corn quality, which could translate into product marketability. The physiochemical quality attributes of two groups of baby corn cobs (Group 1 for export and Group 2 for domestic markets) were measured during storage under two temperature conditions

(2.1 ± 0.1°C and 4.3 ± 0.1°C) over a period of 14 days. The results are presented in Figs. 8a to 8f.

Weight loss was observed in both groups of baby corn cobs and its percentage increased over the storage period (Fig. 8a). This could be attributed to moisture loss through transpiration [START_REF] Attia | Effect of anti-browning agents and wrapping films on browning inhibition and maintaining quality of baby corn during storage[END_REF]. No significant difference in weight loss was found between the baby corn cobs of the same group stored at 2.1°C and 4.3°C. At the end of the storage period, the weight losses seen in Groups 1 and 2 were 4.4-4.8% and 4.6-5.1%, respectively. These percentages could be considered low because no signs of wilting were detected over the course of the evaluation period. The results agreed well with Sakhornyen J o u r n a l P r e -p r o o f

(2009) who reported that the wilting of baby corn cobs is obvious when the weight loss is more than 10%. Moreover, such low weight loss would also have a negligible effect on the economic value of baby corn cobs as the product is usually purchased on a whole pack and rather than on a weight basis. By performing linear regression, the rate of weight loss was identified based on the slopes (𝑊 = 𝑚 • 𝑡 where 𝑊 is weight loss percentage [%], 𝑡 is time [day], and 𝑚 is slope [% per day]) (adapted from [START_REF] Tirawat | Combination of fogging and refrigeration for white asparagus preservation on vegetable stalls[END_REF]). As reported in Table 2, the rates of weight loss of baby corn cobs in both groups were approximately 0.3-0.4% per day under 2-4°C storage conditions.

Fig. 8b presents the change in the TSS content of baby corn cobs during storage. An increase in TSS content was observed over the storage period in both groups. The increment might be associated with the continual decrease in moisture, thus leading to a higher sugar concentration [START_REF] Mukama | Analysing the dynamics of quality loss during precooling and ambient storage of pomegranate fruit[END_REF][START_REF] Sakhornyen | Postharvest handling systems on quality of baby corn[END_REF]. The result suggested that the loss of moisture through transpiration seemed to be more pronounced than the loss of dry matter (e.g. sugars) through the respiration process. The low storage temperature could be the main reason for this change since it causes a deceleration in respiration rates and an increase in the water vapor pressure deficit between the product surface and the air, thereby enhancing transpiration. At both storage temperatures, the TSS content of the baby corn cobs in Group 1 increased from 7.5-7.6 %Brix to 10.4-10.5 %Brix while it increased from 8.5-8.7 %Brix to 10.3-10.6 %Brix for the baby corn in Group 2. It was demonstrated that the initial TSS values of the baby corn cobs in Group 1 were slightly lower than those in Group 2. This might be due to the initial level of moisture content in the baby corn cobs on the day of arrival at the laboratory. The baby corn cobs in Group 2 were exposed to the cold environments without a protective layer (e.g. plastic wrap) for a relatively long period compared with the baby corn cobs in Group 1, which were already packaged during the same stages (Stage 7, Fig. 6b). Since low temperature exerts a great influence on the moisture loss of unwrapped fresh products [START_REF] Serrano | Maintenance of broccoli quality and functional properties during cold storage as affected by modified atmosphere packaging[END_REF], higher moisture loss in the baby corn cobs in Group 2 would be expected when it arrived at the laboratory. It should be noted that air humidity also exerts an influence on product weight loss, but its influence is much less significant compared to that of temperature because of the high relative humidity in the cold room (average of 92.2 ± 6.0%RH).

The firmness of the baby corn cobs in terms of cutting force is shown in Fig. 8c. It was observed that firmness did not change appreciably with storage time for the product in Group 1. The average cutting force values of the baby corn cobs stored at 2.1°C and 4.3°C lay within the range of 15.9 N to 18.8 N and 15.1 N to 18.7 N, respectively. However, the firmness of the J o u r n a l P r e -p r o o f baby corn cobs in Group 2, regardless of the storage temperature, continuously decreased and remained relatively constant after 6 days of storage (roughly from 16 N to 11 N). Again, the moisture content of baby corn cobs might be the reason for the discrepancy in results since moisture loss plays a key role in the textural quality change of fresh horticultural products [START_REF] Deak | Extending the shelf life of fresh sweet corn by shrink-wrapping, refrigeration, and irradiation[END_REF][START_REF] Zhu | Sweet cherry softening accompanied with moisture migration and loss during low-temperature storage[END_REF].

Figs. 8d and 8e present the color development of the baby corn cobs in terms of 𝐿 * and hue angle, respectively. The results showed that the 𝐿 * values of the baby corn cobs in both groups, regardless of the storage temperature, remained almost constant over the storage period.

Their averages were in the range of 73.0 to 76.0 (Fig. 8d). Despite its trivial change, the hue angle exhibited the slow development of browning on the baby corn cobs in all cases. The average hue angle decreased (i.e. redness became more pronounced) from approximately 88.0° to 86.0° (Fig. 8e). The chroma value appeared to be unchanged and its averages varied between 29.0 and 32.0 (data not shown). Less discoloration can be attributed to the effect of the packaging with film wrapping. Such packaging helps to slow down moisture loss which is recognized as one of the main causative factors affecting undesirable visual quality involving product discoloration [START_REF] Supapvanich | Efficient comparison of calcium chloride and calcium gluconate immersions on quality maintenance and bioactive compounds of ready-to-cook baby corns[END_REF].

The visual score signifying the extent of browning development on the baby corn cobs was evaluated. The browning reaction usually starts at the tip of baby corn cobs then spreads to the other areas [START_REF] Leelaphiwat | Design of modified atmosphere packaging systems for baby corn[END_REF]. The color evaluation was performed at the mid-length of the baby corn cobs (~40 mm); thus, less discoloration was detected in comparison with that at the tip. Browning tended to increase consistently with the prolongation of storage time, i.e. a decrease in the visual score (Fig. 8f). For Group 1, the product stored at both storage temperatures had a visual score decreasing from 5.0 to around 3.6-3.7. For Group 2, the final score was slightly lower (~3.1-3.3). The obtained results underlined the development of undesirable visual quality, i.e. browning, exhibited on the baby corn cobs across 10-20% of its total surface area after a 14-day storage period.

Relationship between postharvest temperature condition and product quality

Overall, the quality evolution of the baby corn cobs in both groups was similar to some extent. The product seemed to be marketable following a 14-day storage period. The weight loss did not exceed the limit that could cause a wilted appearance. The TSS content remained relatively high throughout the storage period, while alteration in the textural quality was minor with some variability. Browning was barely perceived at the mid-length surface of products as the change in hue of color from yellow to red was extremely subtle. However, it was more J o u r n a l P r e -p r o o f obvious at the tips according to a consistent decline in visual score. Notwithstanding this decline, the score remained above the tolerable limit (score > 3.0). These results could be translated into a salable lifespan of baby corn cobs of almost two weeks.

The results from such analyses should be considered carefully, since quality evolution was based on the field temperature conditions only in the upstream stages (Stages 1 to 6 and three-fourths of the duration of Stage 7). After these stages, the temperature conditions were artificially controlled during transport (< 8.0°C, 3 h) and storage (2.1°C and 4.3°C, 14 days) in our laboratory. These time-temperature conditions during the product transfer to our laboratory seem to be better than the real ones. Under real conditions, the product was subjected to a high temperature with large fluctuations during transport to the export distribution center (Stage 8, Fig . 7). This stage should have a great impact on product quality but it was not possible to take samples at the end of this stage for quality evaluation due to the lack of exporter participation.

According to [START_REF] Rattanachai | Inbound logistics management of fresh baby corn for export[END_REF], the baby corn cobs were exposed to high temperature during storage at the airport cargo terminal, during air transport, and during domestic land transport in destination countries. High temperature during retailing in refrigerated display cabinets can be also expected [START_REF] Chaomuang | Experimental and numerical investigation of the performance of retail refrigerated display cabinets[END_REF]. Moreover, microbial contamination can result in an even shorter shelf life [START_REF] Tikhamram | Traceback of Thai baby corn implicated in Danish and Australian Shigellosis outbreaks: findings and implications for control, August 2007[END_REF]. Therefore, the results from this study could only suggest that the presented postharvest conditions at the upstream supply stages are satisfactory.

Furthermore, the results revealed some room for improvement that would allow the prolongation of salable and safe conditions for baby corn cobs. The recommendations include 1) minimization of the time interval between primary processing and precooling (~9 h currently); 2) use of thermal protection (e.g. cloth or tarpaulin covers) during ambient storage and non-refrigerated transport to minimize solar radiation effect; 3) a consistent and effective precooling procedure (e.g. cooling temperature, cooling duration, and product quantity in each batch, and use of a temperature monitoring system); 4) pre-cooling of the trailer to the desired temperature before the loading process; and 5) installation of air infiltration protection (e.g. air curtain, plastic air strip) on the truck doors.

Conclusions

The fresh baby corn cold chain in Thailand was investigated in the present study. The field investigation together with in-person interviews were performed at the growers' premises and the packing house. The acquired information revealed the details of postharvest conditions at each supply stage from the growers' premises up to the export distribution center.

J o u r n a l P r e -p r o o f

Temperature measurements were carried out for four periods covering the upstream stages of the baby corn cold chain. The results showed that the total duration of these upstream stages was almost 32 h. The baby corn cobs were subjected to temperature variations of 6 to 33°C along these supply stages. The cold storage stage accounted for almost half of the total duration, during which the product was kept at an average temperature below 6.0°C with moderate fluctuations due to the working cycles of the compressor and regulated defrost cycles.

The time interval prior to precooling was about 9 h, where the products exposed to the temperature above 20°C. Intermittent temperature rises of 5-10°C were also observed in the truck trailer due to the door openings during product loading/unloading. According to the recommended storage temperature for the baby corn (4°C), the monitored temperature condition in these upstream stages appeared to be too high and required improvements.

The effect of temperature conditions on the product quality was evaluated. Various physiological quality attributes potentially influencing the marketability of baby corn cobs were measured during storage. Given that the storage temperature was well below 4.0°C and no temperature abuse occurred after the baby corn cobs were dispatched from the packing house, the product subjected to the current temperature control could be commercialized for a salable period of up to two weeks. Under the same conditions, the same salable period was obtained in the case of the product for domestic markets where precooling was absent prior to cold storage and the packaging was done at 18 h behind the case for export. The results lead to a suggestion that the temperature conditions during the upstream stages had significant influence on the product quality at the sale point. Some corrective measures should be therefore implemented so that the postharvest temperature conditions could be improved, thus increasing the salable period. This field study approach could be applied to other products in order to enrich knowledge of the cold chain in Thailand and other developing countries particularly in Southeast Asia where the ambient temperature is high. Mean and standard deviation (SD) of 20 measured positions (ten positions at 100 mm and another ten positions at 400 mm from the surface of the water)

(ii)
Mean and SD of ten samples of baby corn J o u r n a l P r e -p r o o f Highlights  The export and domestic fresh baby corn cold chains were investigated.  Time-temperature profiles at different stages were examined.  A substantial time interval between harvest and precooling was reported.  Quality assessment was performed in order to evaluate product marketability.  Given the storage conditions, the baby corn cobs remained salable for up to two weeks.

J o u r n a l P r e -p r o o f

(

  iii) Color. The kernel color was measured at the mid-length on two sides of five baby corn cobs sampled from each pack ( n = 20 ) by a spectrophotometer (Color Quest XE, HunterLab, Reston, Virginia, USA). The color values in the color coordinate (L*, a*, b*) were recorded and used to calculate hue angle and chroma value with the following formulae:

Fig. 5a

 5a Fig. 5a depicts the temperature conditions measured from Stages 1 to 4. The temperature displayed in this figure was the average value between the temperature at the top and at the bottom of individual baskets. At the beginning of Stage 1, the temperature in each basket decreased slightly when the dataloggers were inserted in the basket and increased after the basket was fully packed. The duration of ambient storage (Stage 2) at each grower's premises was different and dependent on their work organization. An increase in temperature of 4-5°C

Fig. 6

 6 Fig. 6 shows the temperature evolution during Period III: Stage 6 processing in the packing room and Stage 7 storage in the cold room. The duration of Stage 6 varied depending on the box number. The line confining this stage in Fig.6presents its maximum duration (2 h, from the beginning up until the time at which the last instrumented box was moved to the cold room). The average initial temperature of all instrumented boxes (Boxes 1 to 6) was 21.3 ± 0.4°C. A substantial decrease in temperature was observed in all boxes once the boxes were transferred to the cold room. In the cold room (Stage 7), the small temperature fluctuations are related to the "on/off" compressor working cycles. The large fluctuations every 180 min. for a duration of 20 min. are related to the defrost operation during which the compressor was turned off. The onset temperature (4.5 to 8.7°C) and the amplitude of fluctuations (0.5 to 1.7°C) varied depending on the box position in the stack (Fig.6a). The box at the top of the stack (Box 1) had a lower onset temperature and higher fluctuations than the box at the bottom (Box 5)

  J o u r n a l P r e -p r o o f

Fig. 1

 1 Fig. 1 Flow diagram showing a fresh-cut baby corn supply chain (a) for export and (b) for domestic markets J o u r n a l P r e -p r o o f

Fig. 2

 2 Fig. 2 Forms of baby corn packaging at different supply stages: (a) bulk packaging after processing at growers' premises, (b) retail packaging for export, and (c) bulk packaging after processing at a packing house, and (d) retail packaging for domestic markets. J o u r n a l P r e -p r o o f

Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 8

 34568 Fig. 3 Comparison between the temperature profiles recorded by dataloggers (Elitech ® RC-5) and calibrated T-types thermocouples in a refrigerator (temperature setting: 8°C). DL is the temperature recorded by the dataloggers; AT, CT, and ST are the temperatures recorded by the thermocouples for the air, product core, and product surface, respectively. Numerals are the number of the dataloggers or thermocouples used. J o u r n a l P r e -p r o o f

Table 1 .

 1 The observed precooling conditions at the packing house

	Batch	Water temperature (i)	Core temperature of baby corn (ii) Before After Temperature precooling precooling drop	Precooling time
		(Mean ± SD, °C)		(Mean ± SD, °C)		(min)
	1	19.8 ± 4.7	30.6 ± 0.7	24.5 ± 0.8	6.1± 0.8	16
	2	18.2 ± 4.1	30.4 ± 0.7	23.6 ± 1.0	6.8 ± 1.0	13
	Average	19.0 ± 4.5	30.5 ± 0.7	24.1 ± 1.0	6.4 ± 1.0	14.5
	(i)

Table 2 .

 2 The slope value of weight loss variation with time

	Group	Storage temperature (°C)	Slope value* (% per day)	R-squared
	1	2.1 ± 0.1	0.34	0.9846
		4.3 ± 0.1	0.32	0.9686
	2	2.1 ± 0.1	0.33	0.9940
		4.3 ± 0.1	0.37	0.9877
	*Based on linear regression

Acknowledgments

This research project was funded by KMITL Research Fund under Research Seed Grant for New Lecturer (No. KREF186310). The authors would like to thank Ban Huai Rang Pong Munkong community enterprise for its collaboration.

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