Study on a terahertz biosensor based on graphene-metamaterial

The interaction between the terahertz wave propagating in free space and the sample is weak, which leads to the weak signal of the sample, which cannot meet the detection needs of trace samples. In order to meet the detection of trace samples, a kind of metamaterial absorber (the basic unit of the absorber is composed of gold-high resistance silicon-aluminum three-layer structure) is designed, and the monolayer graphene is transferred on the surface of the metamaterial absorber to construct the graphene-metamaterial absorber heterostructure. The transmission spectrum of the resonant cavity is simulated and measured by terahertz time domain spectroscopy system, and the obvious resonance frequency shift is observed. The results show that the graphene-metamaterial absorber heterostructure can detect josamycin antibiotic solution with concentration of 0.02 mg/L (the mass of josamycin is 0.2 ng). Compared with using the same structure metamaterial absorber to detect josamycin antibiotics, the sensitivity is increased by an order of magnitude. Using graphene-metamaterial heterostructure to detect the relative change of heterostructure reflectivity caused by josamycin antibiotics can reach 40%. The research in this paper provides a new technical means for accurate and rapid detection in terahertz band.

Optical Strain Gauge Prototype Based on a High Sensitivity Balloon-like Interferometer and Additive Manufacturing

An optical strain gauge based on a balloon-like interferometer structure formed by a bent standard single-mode fiber combined with a 3D printer piece has been presented and demonstrated, which can be used to measure displacement. The interferometer has a simple and compact size, easy fabrication, low cost, and is repeatable. The sensor is based on the interference between the core and cladding modes. This is caused by the fiber's curvature because when light propagates through the curved balloon-shaped interferometer region, a portion of it will be released from the core limitation and coupled to the cladding. The balloon has an axial displacement as a result of how the artwork was constructed. The sensor head is sandwiched between two cantilevers such that when there is a displacement, the dimension associated with the micro bend is altered. The sensor response as a function of displacement can be determined using wavelength shift or intensity change interrogation techniques. Therefore, this optical strain gauge is a good option for applications where structure displacement needs to be examined. The sensor presents a sensitivity of 55.014 nm for displacement measurements ranging from 0 to 10 mm and a strain sensitivity of 500.13 pm/μϵ.

High-fidelity intensity diffraction tomography with a non-paraxial multiple-scattering model

We propose a novel intensity diffraction tomography (IDT) reconstruction algorithm based on the split-step non-paraxial (SSNP) model for recovering the 3D refractive index (RI) distribution of multiple-scattering biological samples. High-quality IDT reconstruction requires high-angle illumination to encode both low- and high- spatial frequency information of the 3D biological sample. We show that our SSNP model can more accurately compute multiple scattering from high-angle illumination compared to paraxial approximation-based multiple-scattering models. We apply this SSNP model to both sequential and multiplexed IDT techniques. We develop a unified reconstruction algorithm for both IDT modalities that is highly computationally efficient and is implemented by a modular automatic differentiation framework. We demonstrate the capability of our reconstruction algorithm on both weakly scattering buccal epithelial cells and strongly scattering live C. elegans worms and live C. elegans embryos.

Simultaneous measurement of displacement and temperature using a balloon-like hybrid fiber sensor

A fiber sensor based on a silica capillary in a balloon-like shape for simultaneous measurement of displacement and temperature is proposed and experimentally demonstrated. The sensor is fabricated by splicing a segment of a hollow-core fiber between two single-mode fibers (SMF) and by creating a balloon shape with the capillary at the top-center position. The SMF-capillary-SMF configuration excites an antiresonant (AR) guidance, and the balloon shape enhances the Mach-Zehnder interferometer (MZI). Experimental results show that, for a balloon length of 4.0 cm and a capillary length of 1.2 cm, the AR is insensitive to displacement and its sensitivity to temperature is 14.3 pm/°C, while the MZI has a sensitivity to displacement of 1.68 nm/mm in the range between 0 and 5 mm and a sensitivity to temperature of 28.6 pm/°C, twice the value of the AR. The proposed fiber sensor has only one sensing element in one configuration, which makes it simple to fabricate as well as low cost.

Route to flexible metamaterial terahertz biosensor based on multi-resonance dips

A flexible terahertz (THz) metamaterial biosensor is theoretically and experimentally investigated. The metamaterial unit cell of the periodic structure array was simply composed of three non-overlapping cut wires with different length parameters on a flexible thin-film (parylene-C) to improve sensitivity. The biosensor sample was fabricated using a lithography process and characterized by a THz time-domain spectroscopy (TDS) system. The metamaterial exhibited multi-resonance dips in transmission spectrum at 0.6-2.0 THz, which can self-correct errors in biosensing. Numerical results show that the Q-factor, figure of merit (FOM) and sensitivity can change in dynamic ranges with the geometric parameters (space and width) of three-cut-wire metamaterial. When space distance was 40 µm and other parameters were default, the sensitivity, FOM and Q-factor reached 710 GHz/RIU (Refractive Index Unit), 9, and 20, respectively. Therefore, through proper design and preparation, the metamaterial can be applied to biochemical detection.

Advances in Waveguide Bragg Grating Structures, Platforms, and Applications: An Up-to-Date Appraisal

A Bragg grating (BG) is a one-dimensional optical device that may reflect a specific wavelength of light while transmitting all others. It is created by the periodic fluctuation of the refractive index in the waveguide (WG). The reflectivity of a BG is specified by the index modulation profile. A Bragg grating is a flexible optical filter that has found broad use in several scientific and industrial domains due to its straightforward construction and distinctive filtering capacity. WG BGs are also widely utilized in sensing applications due to their easy integration and high sensitivity. Sensors that utilize optical signals for sensing have several benefits over conventional sensors that use electric signals to achieve detection, including being lighter, having a strong ability to resist electromagnetic interference, consuming less power, operating over a wider frequency range, performing consistently, operating at a high speed, and experiencing less loss and crosstalk. WG BGs are simple to include in chips and are compatible with complementary metal-oxide-semiconductor (CMOS) manufacturing processes. In this review, WG BG structures based on three major optical platforms including semiconductors, polymers, and plasmonics are discussed for filtering and sensing applications. Based on the desired application and available fabrication facilities, the optical platform is selected, which mainly regulates the device performance and footprint.

Full-Stokes Retrieving and Configuration Optimization in a Time-Integration Imaging Polarimeter

A time-integration imaging polarimeter with continuous rotating retarder is presented, and its full-Stokes retrieving and configuration optimization are also demonstrated. The mathematical expression between the full-Stokes vector and the time-integration light intensities is derived. As a result, the state of polarization of incident light can be retrieved by only one matrix calculation. However, the modulation matrix deviates from the initial well-conditioned status due to time integration. Thus, we re-optimize the nominal angles for the special retardance of 132° and 90° with an exposure angle of 30°, which results in a reduction of 31.8% and 16.8% of condition numbers comparing to the original configuration, respectively. We also give global optimization results under different exposure angles and retardance of retarder; as a result, the 137.7° of retardance achieves a minimal condition number of 2.0, which indicates a well-conditioned polarimeter configuration. Besides, the frame-by-frame algorithm ensures the dynamic performance of the presented polarimeter. For a general brushless DC motor with a rotating speed of over 2000 rounds per minute, the speed of polarization imaging will achieve up to 270 frames per second. High precision and excellent dynamic performance, together with features of compactness, simplicity, and low cost, may give this traditional imaging polarimeter new life and attractive prospects.

Terahertz Metamaterial Sensor for Sensitive Detection of Citrate Salt Solutions

Citrate salts (CSs), as one type of organic salts, have been widely used in the food and pharmaceutical industries. Accurate and quantitative detection of CSs in food and medicine is very important for health and safety. In this study, an asymmetric double-opening ring metamaterial sensor is designed, fabricated, and used to detect citrate salts combined with THz spectroscopy. Factors that influence the sensitivity of the metamaterial sensor including the opening positions and the arrangement of the metal opening ring unit, the refraction index and the thickness of the analyte deposited on the metamaterial sensor were analyzed and discussed from electromagnetic simulations and THz spectroscopy measurements. Based on the high sensitivity of the metamaterial sensor to the refractive index of the analyte, six different citrate salt solutions with low concentrations were well identified. Therefore, THz spectroscopy combined with a metamaterials sensor can provide a new, rapid, and accurate detection of citrate salts.

Effects of water salinity on the multi-angular polarimetric properties of light reflected from smooth water surfaces

Salinity is an important environmental factor regulating the aquatic system structure of lakes and other water bodies. Changes in salinity, which can be caused by human activities, can adversely impact the life of water organisms. The refractive index, which can be directly related to water salinity, also controls the polarimetric properties of light reflected from the water surface. In this study, polarimetric measurements of smooth water surfaces with different salinity content were performed at different viewing zenith angles in the wavelength range of 450-1000 nm in the specular reflection directions. The results show that the light reflected from the water surface (defined as reflectance factor) in one measurement direction can be replaced by the reflectance factor derived from polarimetric measurements, and if the polarizer absorptance is considered, the average relative difference is less than 3%. The degree of linear polarization (DOLP) was used to retrieve the refractive indices of water with different salinities based on the Fresnel reflection coefficient. The inverted refractive indices not only have high accuracy (uncertainty from 0.9% to 1.8%) but also have a very strong relationship with the water salinity content. Our study shows the possibility of estimating the variation in water salinity using multi-angular polarimetric measurements.

Real-time and high-sensitivity refractive index sensing with an arched optofluidic waveguide

Refractive index (RI) sensing plays an important role in analytical chemistry, medical diagnosis, and environmental monitoring. The optofluidic technique is considered to be an ideal tool for RI sensor configuration for its high integration, high sensitivity, and low cost. However, it remains challenging to achieve RI measurement in real time with high sensitivity and low detection limit (DL) simultaneously. In this work, we design and fabricate a RI sensor with an arched optofluidic waveguide by monitoring the power loss of the light passing through the waveguide, which is sandwiched by the air-cladding and the liquid-cladding under test, we achieve RI detection of the sample in real time and with high sensitivity. Furthermore, both numerical simulation and experimental investigation show that our RI sensor can be designed with different geometric parameters to cover multiple RI ranges with high sensitivities for different applications. Experimental results illustrate that our sensor is capable to achieve a superior sensitivity better than -19.2 mW/RIU and a detection limit of 5.21×10^-8 RIU in a wide linear dynamic range from 1.333 to 1.392, providing a promising solution for real-time and high-sensitivity RI sensing.

Dual-wavelength surface plasmon resonance holographic microscopy for simultaneous measurements of cell-substrate distance and cytoplasm refractive index

Studying the basic characteristics of living cells is of great significance in biological research. Bio-physical parameters, including cell-substrate distance and cytoplasm refractive index (RI), can be used to reveal cellular properties. In this Letter, we propose a dual-wavelength surface plasmon resonance holographic microscopy (SPRHM) to simultaneously measure the cell-substrate distance and cytoplasm RI of live cells in a wide-field and non-intrusive manner. Phase-contrast surface plasmon resonance (SPR) images of individual cells at wavelengths of 632.8 nm and 690 nm are obtained using an optical system. The two-dimensional distributions of cell-substrate distance and cytoplasm RI are then demodulated from the phase-contrast SPR images of the cells. MDA-MB-231 cells and IDG-SW3 cells are experimentally measured to verify the feasibility of this approach. Our method provides a useful tool in biological fields for dual-parameter detection and characterization of live cells.

A Review of Sensitivity Enhancement in Interferometer-Based Fiber Sensors

Optical fiber sensors based on an interferometer structure play a significant role in monitoring physical, chemical, and biological parameters in natural environments. However, sensors with high-sensitivity measurement still present their own challenges. This paper deduces and summarizes the methods of sensitivity enhancement in interferometer based fiber optical sensors, including the derivation of the sensing principles, key characteristics, and recently-reported applications.The modal coupling interferometer is taken as an example to derive the five terms related to the sensitivity: (1) the wavelength-dependent difference of phase between two modes/arms ∂ϕd/∂λ, (2) the sensor length Lw,A, (3) refractive index difference between two modes/arms Δneff,A, (4) sensing parameter dependent length change α, and (5) sensing parameter dependent refractive index change γ. The research papers in the literature that modulate these terms to enhance the sensing sensitivity are reviewed in the paper.

Sensors and Instruments for Brix Measurement: A Review

Quality assessment of fruits, vegetables, or beverages involves classifying the products according to the quality traits such as, appearance, texture, flavor, sugar content. The measurement of sugar content, or Brix, as it is commonly known, is an essential part of the quality analysis of the agricultural products and alcoholic beverages. The Brix monitoring of fruit and vegetables by destructive methods includes sensory assessment involving sensory panels, instruments such as refractometer, hydrometer, and liquid chromatography. However, these techniques are manual, time-consuming, and most importantly, the fruits or vegetables are damaged during testing. On the other hand, the traditional sample-based methods involve manual sample collection of the liquid from the tank in fruit/vegetable juice making and in wineries or breweries. Labour ineffectiveness can be a significant drawback of such methods. This review presents recent developments in different destructive and nondestructive Brix measurement techniques focused on fruits, vegetables, and beverages. It is concluded that while there exist a variety of methods and instruments for Brix measurement, traits such as promptness and low cost of analysis, minimal sample preparation, and environmental friendliness are still among the prime requirements of the industry.

Tomographic measurement of dielectric tensors at optical frequency

The dielectric tensor is a physical descriptor of fundamental light-matter interactions, characterizing anisotropic materials with principal refractive indices and optic axes. Despite its importance in scientific and industrial applications ranging from material science to soft matter physics, the direct measurement of the three-dimensional dielectric tensor has been limited by the vectorial and inhomogeneous nature of light scattering from anisotropic materials. Here, we present a dielectric tensor tomographic approach to directly measure dielectric tensors of anisotropic structures including the spatial variations of principal refractive indices and directors. The anisotropic structure is illuminated with a polarized plane wave with various angles and polarization states. Then, the scattered fields are holographically measured and converted into vectorial diffracted field components. Finally, by inversely solving a vectorial wave equation, the three-dimensional dielectric tensor is reconstructed. Using this approach, we demonstrate quantitative tomographic measurements of various nematic liquid-crystal structures and their fast three-dimensional non-equilibrium dynamics.

Dynamic spectroscopic imaging ellipsometry

A dynamic spectroscopic imaging ellipsometer (DSIE) employing a monolithic polarizing interferometer is described. The proposed DSIE system can provide spatio-spectral ellipsometric phase map data Δ(λ, x) dynamically at a speed of 30 Hz. We demonstrate the ultrafast mapping capability of the spectroscopic ellipsometer by measuring a patterned 8-inch full wafer with a spatial resolution of less than 50 × 50 µm² in an hour.

Computational multi-wavelength phase synthesis using convolutional neural networks [Invited]

Multi-wavelength digital holographic microscopy (MWDHM) provides indirect measurements of the refractive index for non-dispersive samples. Successive-shot MWDHM is not appropriate for dynamic samples and single-shot MWDHM significantly increases the complexity of the optical setup due to the need for multiple lasers or a wavelength tunable source. Here we consider deep learning convolutional neural networks for computational phase synthesis to obtain high-speed simultaneous phase estimates on different wavelengths and thus single-shot estimates of the integral refractive index without increased experimental complexity. This novel, to the best of our knowledge, computational concept is validated using cell phantoms consisting of internal refractive index variations representing cytoplasm and membrane-bound organelles, respectively, and a simulation of a realistic holographic recording process. Specifically, in this work we employed data-driven computational techniques to perform accurate dual-wavelength hologram synthesis (hologram-to-hologram prediction), dual-wavelength phase synthesis (unwrapped phase-to-phase prediction), direct phase-to-index prediction using a single wavelength, hologram-to-phase prediction, and 2D phase unwrapping with sharp discontinuities (wrapped-to-unwrapped phase prediction).

Effects of osmolality and solutes on the morphology of red blood cells according to three-dimensional refractive index tomography

Phosphate-buffered saline (PBS) and Alsever's solution (AS) are frequently used as media in blood-related studies, while 0.9% normal saline (NS) is frequently used in transfusion medicine. Despite the frequent use, the effects of these solutions on the shape and volume of red blood cells (RBCs) have not been reported. We collected blood samples from five healthy adults and used three-dimensional refractive index tomography to investigate the changes in the morphology of RBCs caused by changes in osmolality and solutes at the single-cell level. After diluting 2 μL of RBCs 200-fold with each solution (PBS, AS, and 0.9% NS), 40 randomly selected RBCs were microscopically observed. RBC shape was measured considering sphericity, which is a dimensionless quantity ranging from 0 (flat) to 1 (spherical). RBCs in plasma or AS showed a biconcave shape with a small sphericity, whereas those in 0.9% NS or PBS showed a spherical shape with a large sphericity. Moreover, we confirmed that sodium chloride alone could not elicit the biconcave shape of RBCs, which could be maintained only in the presence of an osmotic pressure-maintaining substance, such as glucose or mannitol. Although 0.9% NS solution is one of the most commonly used fluids in hematology and transfusion medicine, RBCs in 0.9% NS or PBS are not biconcave. Therefore, as the debate on the use of NS continues, future clinical studies or applications should consider the effect of glucose or mannitol on the shape of RBCs.

Optical properties of biochemical compositions of microalgae within the spectral range from 300 to 1700 nm

The optical properties of biochemical compositions of microalgae are vital for the improvement of biosensor design, photobioreactor design, biofuel, and biophotonics techniques. A combination method using both the double optical pathlength transmission method (DOPTM) and the ellipsometry method (EM) is called DOPTM-EM, and it is used to acquire the optical constants of protein, lipid, and carbohydrate of Haematococcus pluvialis, Nannochloropsis sp., and Spirulina in both a solid state and a solution state within the visible and near-infrared spectral range. For different types of microalgae, the refractive indices of protein and carbohydrate in the solid state are similar to each other, but show an observed difference from lipid in the solid state. The refractive indices of protein and carbohydrate in the solution state presents a visible distinction in the researched spectral range. The absorption indices of protein, lipid, and carbohydrate in the solid state for these three types of microalgae are close to each other in the spectral range of 300-500 nm. However, an observed difference is shown in the spectral range of 500-1700 nm. For ease of application, the refractive index of biochemical composition of microalgae was fitted based on the Sellmeier equation. We believe this work can provide a reference to obtain the optical properties of biomaterial with high accuracy.

Probing bio-tissue films by optical internal reflectivity: modeling and measurements

In this paper, we develop a detailed theoretical model for the optical reflectivity of a bio-tissue film confined between two flat interfaces based on the anomalous-diffraction approximation. We consider bio-tissue films consisting of a few layers of spheroidal cells surrounded by extracellular medium. We explore numerically the predictions of our model and compare them with simple effective medium theories, sometimes used as a first attempt to understand the optical properties of biological media. Then, we fit the model to experimental reflectivity-versus-angle-of-incidence curves of confined whole-blood films measured in an internal reflection configuration. Measurements were performed by confining a drop of fresh blood between a prism and a coverslip. Our experimental results show that it is possible to measure the coherent reflectance with small enough error to infer microstructural parameters with a good precision. The errors in measuring the coherent reflectance depend on the reflectivity magnitude. For instance, for a reflectivity of about 0.3 the error is below 2%, and the refractive indices of cells and surrounding medium can be obtained with a precision better than 1%. These results also indicate that the present model can readily be used to figure out the physical changes experienced at the microscale in bio-tissue films during a physicochemical process.

Determination of protein concentration in downstream biomanufacturing processes by in-line index of refraction

Protein concentration determination is a necessary in-process control for the downstream operations within biomanufacturing. As production transitions from batch mode to an integrated continuous bioprocess paradigm, there is a growing need to move protein concentration quantitation from off-line to in-line analysis. One solution to fulfill this process analytical technology need is an in-line index of refraction (IoR) sensor to measure protein concentration in real time. Here the performance of an IoR sensor is evaluated through a series of experiments to assess linear response, buffer matrix effects, dynamic range, sensor-to-sensor variability, and the limits of detection and quantitation. The performance of the sensor was also tested in two bioprocessing scenarios, ultrafiltration and capture chromatography. The implementation of this in-line IoR sensor for real-time protein concentration analysis and monitoring has the potential to improve continuous bioprocess manufacturing.

Imaging-based spectrometer-less optofluidic biosensors based on dielectric metasurfaces for detecting extracellular vesicles

Biosensors are indispensable tools for public, global, and personalized healthcare as they provide tests that can be used from early disease detection and treatment monitoring to preventing pandemics. We introduce single-wavelength imaging biosensors capable of reconstructing spectral shift information induced by biomarkers dynamically using an advanced data processing technique based on an optimal linear estimator. Our method achieves superior sensitivity without wavelength scanning or spectroscopy instruments. We engineered diatomic dielectric metasurfaces supporting bound states in the continuum that allows high-quality resonances with accessible near-fields by in-plane symmetry breaking. The large-area metasurface chips are configured as microarrays and integrated with microfluidics on an imaging platform for real-time detection of breast cancer extracellular vesicles encompassing exosomes. The optofluidic system has high sensing performance with nearly 70 1/RIU figure-of-merit enabling detection of on average 0.41 nanoparticle/µm2 and real-time measurements of extracellular vesicles binding from down to 204 femtomolar solutions. Our biosensors provide the robustness of spectrometric approaches while substituting complex instrumentation with a single-wavelength light source and a complementary-metal-oxide-semiconductor camera, paving the way toward miniaturized devices for point-of-care diagnostics.

Application of digital holographic tomography in antitumor effect of cantharides complex on 4T1 breast cancer cells

The study focuses on a methodology providing noninvasive monitoring and evaluation of the antitumor effect of traditional Chinese medicine, cantharides complex (canth), on 4T1 breast tumor cells. Digital holographic tomography (DHT) and developed data post-processing algorithms were used for quantitative estimation of changes in optical and morphological parameters of cells. We calculated and compared data on the refractive index, thickness, and projected area of 4T1 breast tumor cells in control untreated specimens and those treated with doxorubicin hydrochloride (DOX), canth, and their combinations. Post-treatment changes in cellular morphology recorded by DHT demonstrated that the two drugs led to noticeably different morphological changes in cells that can be presumably associated with different pathways of their death, apoptosis, or necrosis. The effect of combined treatment with these two drugs strongly depended on their relative concentrations and could lead to changes characteristic either for DOX or for canth; however, being more profound than those obtained when using each drug solely. The results obtained by DHT are in a good correspondence with commonly used cell viability analysis and immunofluorescent analysis of changes in cellular cytoskeleton.

Terahertz refractive index-based morphological dilation for breast carcinoma delineation

This paper reports investigations led on the combination of the refractive index and morphological dilation to enhance performances towards breast tumour margin delineation during conserving surgeries. The refractive index map of invasive ductal and lobular carcinomas were constructed from an inverse electromagnetic problem. Morphological dilation combined with refractive index thresholding was conducted to classify the tissue regions as malignant or benign. A histology routine was conducted to evaluate the performances of various dilation geometries associated with different thresholds. It was found that the combination of a wide structuring element and high refractive index was improving the correctness of tissue classification in comparison to other configurations or without dilation. The method reports a sensitivity of around 80% and a specificity of 82% for the best case. These results indicate that combining the fundamental optical properties of tissues denoted by their refractive index with morphological dilation may open routes to define supporting procedures during breast-conserving surgeries.

Optimizing illumination in three-dimensional deconvolution microscopy for accurate refractive index tomography

In light transmission microscopy, axial scanning does not directly provide tomographic reconstruction of specimen. Phase deconvolution microscopy can convert a raw intensity image stack into a refractive index tomogram, the intrinsic sample contrast which can be exploited for quantitative morphological analysis. However, this technique is limited by reconstruction artifacts due to unoptimized optical conditions, which leads to a sparse and non-uniform optical transfer function. Here, we propose an optimization method based on simulated annealing to systematically obtain optimal illumination schemes that enable artifact-free deconvolution. The proposed method showed precise tomographic reconstruction of unlabeled biological samples.

Establishing NDRE dynamic models of winter wheat under multi-nitrogen rates based on a field spectral sensor

Field spectral sensors provide real-time, reliable, quantitative monitoring of crop growth. Fitting the continuous growth in the entire growing period from the measurements of limited frequency is helpful to the comparative analysis of interannual growth and fertilizer management in the field. To exploit this capacity, our work presents a model that uses the normalized difference red edge (NDRE) index derived from the field spectral sensor for real-time monitoring of the canopy growth of winter wheat in the whole growing period. We developed this model from experiments in three counties in Hebei province, China, where we obtained the near-infrared and red edge reflectance, grain yield, and canopy parameters for eight growth stages and for various nitrogen (N) rates. Given the correlation between effective accumulated temperature and crop growth, we used the growing degree-days as an adjustment parameter to develop models for dynamic monitoring of the NDRE of the winter wheat canopy during the entire growing period. The results show that high determination coefficients (R²=0.89 to 0.96) are obtained from all models based on relative NDRE and effective accumulative temperature (independent of N fertilization rates). The model based on the rational function is the best of all models tested, with the accuracy for normal and high N fertilization rates being slightly greater than that for low N fertilization rates. Therefore, a relative-NDRE model with the accumulative growing degree-days since sowing could allow monitoring canopy NDRE of winter wheat at any time, which could be helpful for overcoming the shortage of incomparable growth derived from the differences of sensing date, sowing date, and fertilizer, etc.