Sea surface skin temperature (SST_Skin) is the seawater temperature at a depth of about 10 μm. Satellite infrared radiometers can be employed to obtain long-time series of SST_Skin data over a large area. However, as their accuracy can be easily affected by the environment, it is necessary to adopt field data to verify their data accuracy. When obtaining field data, the spatio-temporal mismatch of the sea-sky field of view will introduce uncertainties to the measurement. Thus, we propose an SST_Skin correction method, which utilizes a circulating water-film device designed, a non-cooled infrared thermal imager, and corresponding algorithms to calculate sky radiation. Compared with applying an infrared radiometer to measure sky radiation, this method can indirectly obtain the sky radiation distribution over a larger range. Additionally, the infrared thermal imager simultaneously observes the circulating water-film device and sea surface to realize the synchronous measurement of sky radiation and sea surface radiation. Therefore, this method can reduce the error introduced by the spatio-temporal mismatch of the sea-sky field of view and lower the measurement equipment cost, thus obtaining high-precision SST_Skin.

The infrared thermal imager operates in the 8–14 μm spectral bands. Therefore, when the imager measures the SST_Skin, the total radiation received in the corresponding band is composed of two parts, including radiation emitted by the sea surface and downward radiation from the sky reflected by the sea surface. Thus, after knowing the received radiation, if the sea surface emissivity and the sky radiation can be obtained, the accurate SST_Skin can be inverted. According to the empirical formula, the sea surface emissivity is 0.97994 when the observation angle is 45°. To obtain the sky radiation distribution and reduce the instrument cost, we design the circulating water-film device whose surface can form a smooth water film with uniform temperature. The cold skin effect is the phenomenon where the seawater temperature at the sea-air interface is lower than that of the deeper seawater. In the circulating water-film device, the surface layer of the water film and the water body below the surface layer are fully mixed through the water circulation. Finally, the differences between the skin temperature (depth of about 10 μm) and the water body temperature are eliminated to accurately measure the water-film skin temperature. Based on knowing the true skin temperature of the water film and the measured value of water-film skin temperature by the thermal imager, the sky radiation can be obtained by combining it with the radiation characteristics of the water film. After calculating the sky radiation, the influence of the sky radiation on SST_Skin measurement can be removed by the sea surface emissivity to obtain accurate SST_Skin data. Based on this theory, combined with the circulating water-film device and the thermal imager, we design two SST_Skin correction schemes. Meanwhile, a comparison scheme that employs the sky radiation measured by the infrared radiometer to correct the measured SST_Skin value is formulated to verify the correction effect of the designed two schemes.

In indoor simulation experiments, a background radiation simulation panel is leveraged to simulate the sky with uniform brightness temperature distribution. After correction, the thermal imager's measurement error of water-film surface temperature decreases from 0.203 K to 0.005 K (Fig. 6). In outdoor experiments, when the sky radiation varies in time and space, the designed two schemes are better than the comparison scheme in correcting measurement of water surface temperature, indicating that the two schemes can reduce the error introduced by the spatio-temporal mismatch of the sea-sky field of view (Fig. 10 and Table 1). Before algorithm correction, the average value of water surface temperature measurement error is -0.503 K. After the correction with Scheme 1, the error is -0.081 K. After the correction with Scheme 2, the error is -0.041 K.

We propose an SST_Skin correction method by the circulating water-film device and the infrared thermal imager, which can reduce the error introduced by the spatio-temporal mismatch of the sea-sky field of view. In the circulating water-film device, the water-film skin temperature can be accurately measured by the thermometer through the water circulation. This method employs the thermal imager to measure the skin temperature of the water film and seawater simultaneously and corrects the measured SST_Skin value through the differences between the real and measured values of water-film skin temperature. As a result, the influence of sky radiation on the SST_Skin measurement can be removed and accurate SST_Skin data is obtained. In indoor simulation experiments, after correction, the thermal imager's measurement error of water-film surface temperature decreases from 0.203 K to 0.005 K. In outdoor experiments, after correction, the thermal imager's measurement error of water surface temperature decreases from -0.503 K to -0.041 K. The experimental results show that the proposed method can improve the measurement accuracy of water surface temperature when sky radiation is variable in time and space, and reduce the measuring equipment cost. In the future, this system will conduct on-site SST_Skin measurement comparison experiments with an infrared sea surface temperature autonomous radiometer (ISAR). We hope to study the influence of sky radiation on the temperature measurement accuracy of the rough sea surface to further improve the proposed method, providing a new technical approach for obtaining field SST_Skin data to verify satellite remote sensing data.

Fringe projection profilometry has been widely used due to its high accuracy, high robustness, and non-contact characteristics. In this paper, we aim to improve the speed and accuracy of the fringe projection profilometry method, especially its performance in jittery environments. In-depth research is conducted. Typical optical 3D sensing technologies mainly include photometric stereo vision, binocular multi-eye stereo vision, time of flight method, laser line scanning method, defocus shape recovery method, and structured light projection method. Structured light projection also includes stripe projection and speckle projection methods. The decoding schemes in fringe projection profilometry are divided into the spatial phase unwrapping method and the temporal phase unwrapping method. The former only requires one phase map to recover the absolute phase, but it relies on the phase values of adjacent pixels, which cannot achieve reliable decoding for discontinuous or isolated objects. The latter projects a series of patterns for decoding, and the absolute phase value corresponding to each pixel is independently calculated, independent of the surrounding pixels. Therefore, theoretically, any shape of the object surface can be unfolded. In the binary fringe method, in order to enhance the contrast of the stripe pattern, binary fringes are used instead of projecting sinusoidal fringes. However, traditional methods require more stripes. For example, the classic method of stripe edge detection requires adding reverse stripes to achieve accurate stripe decoding and positioning. The goal of this paper is not only to reduce the number of stripes but also to effectively improve the accuracy of localization.

Edge localization of binary fringes is a key issue. Song et al. proposed a three-dimensional measurement method based on stripe edge detection. The use of binary stripes instead of sinusoidal stripes as projection patterns greatly enhances the contrast of stripe patterns. At the same time, edge points of binary fringes are detected to reduce interference caused by infrared imaging. Ye et al. combined the stripe edge detection method with near-infrared light to perform a three-dimensional reconstruction of dynamic scenes. However, the stripe edge detection method itself has no resistance to potential jump errors that may occur during the decoding process. To eliminate jump errors, Feng et al. proposed a global codeword correction method that restores continuous and complete point cloud information. By combining stripe edge detection with the global codeword correction method, it is possible to achieve 3D measurements with higher accuracy than traditional phase shift methods. When the measured object experiences shaking, there will be a deviation between the forward and reverse binary fringes, causing the edge points of the two to no longer be in the same position. The stripe edge detection method will calculate the edge points, resulting in a deviation. By taking the periodic ambiguity of gray code order as an example, which is four pixels, the stripe edge detection encoding scheme requires the same number of reverse stripes to be combined. In other words, an additional double of the corresponding reverse stripe projection must be added to solve for edge points. Further, jitter often causes positioning deviation, which leads to errors. That is an important source of error. The performance in a jitter environment will be improved by using a new method in this article. The proposed method does not require specialized projection of reverse stripes corresponding to forward binary stripes and can achieve accurate edge point localization using adjacent images.

The method proposed in this article can effectively eliminate the problem of inaccurate edge point positioning caused by jitter. Furthermore, the effectiveness and accuracy of the method are validated through measurement experiments in jitter scenarios. In the new scheme, only one cyclic reverse stripe pattern needs to be added at the beginning and end of the binary stripe sequence. In the method proposed in this article, the reverse stripe corresponding to the forward binary stripe is not necessary. In addition, achieving accurate edge point positioning is based on adjacent images to obtain the final accurate information. The traditional stripe edge detection method can cause offset in the forward and reverse binary fringes in jitter scenarios, resulting in errors. The new method accurately corrects errors and achieves good results. The experimental results demonstrate that the new method achieves precise positioning of binary stripe edge points through adjacent three frame stripe images. The measurement object is used as the standard to measure the quality of the measurement results. The results are shown in Table 1. The proposed new scheme reduces the number of stripes and uses three adjacent cyclic reverse stripes to locate edges, resulting in more accurate edge points.

In terms of edge localization of binary fringes, this method not only reduces the number of fringes but also effectively resists positioning offset caused by jitter. Compared with the traditional stripe edge detection encoding scheme, in the traditional scheme, a reverse stripe with the same number of stripes as the original encoding is required to obtain the encoding result. The method proposed in this article can achieve more accurate results with fewer stripes, which is significantly superior to traditional methods.

Spectroradiometers are used to determine the spectral characteristics and brightness of radiation sources, which are widely used in many different fields. This study is based on the circular variable filter type spectroradiometer, where the wavelength transmitted by the main spectroscopic component, the circular variable filter is linearly related to the angle, and the spectroradiometer is constructed with a unit detector. This type of spectroradiometer has the advantages of a wide spectral range and a wide temperature range for the target, so it has a wider range of applications. However, there are fewer studies on circular variable filter spectroradiometers in China and abroad, and the development of domestic machines for circular variable filter spectroradiometers is gradually being carried out in China. Radiation calibration is the process of converting the original signal measured by the instrument into a physical quantity with practical significance. The main methods of radiation calibration for infrared spectroradiometers are currently the single point method, the two points method, and so on. The single point method is suitable for cases with low resolution and a small amount of spectral measurement data. The two-point method is suitable for situations where the instrument has good linearity, and the number of measurement points is high. Due to the wide operating band of the circular variable filter type infrared spectroradiometer and the wide range of the target temperature, which causes non-linearity problems, the traditional two-point calibration method cannot achieve accurate radiation calibration. In this paper, a divisional linearity-based responsivity radiometric calibration method is proposed to solve this problem.

The radiometric calibration of circular variable filter spectroradiometers is based on the divisional linearity method, which is used to solve the non-linearity problem of this type of spectroradiometer due to the large temperature range of the measurement target and the wide operating band. The main technical principle is to divide the temperature interval of the target to be measured into several subintervals, collect the measured spectrums corresponding to several different temperature blackbodies in the target temperature interval, and calculate the responsivity function at each temperature. During the infrared spectroscopy measurements, the target spectrum is compared with the spectrums of different temperature points recorded in the interval to determine the upper and lower limits of the temperature subinterval to which the target to be measured belongs. Based on the responsivity function calculated for the subinterval, a linear interpolation is performed to find the responsivity function of the target to be measured for radiometric calibration. In addition, external ambient temperature variations, atmospheric disturbances, and the instrument's thermal radiation are taken into account in the calibration process.

In this paper, we propose a divisional linearity-based responsivity radiometric calibration method, which can effectively solve the non-linearity problem caused by the wide wavelength range and wide temperature range of the target measurement by zoning the target temperature into sub-regions. We compare the difference between the measured calibration data and the theoretical Planck curve at different temperatures. Figure 12 shows the relative deviation of the radiometric calibrations of two detectors at different blackbody temperatures. Figure 12 shows that the relative deviations of the radiometric calibrations are better than 1% for most of the band intervals for both detectors. The large relative deviations in some bands are due to two reasons: 1) the low responses of the InSb detector in the 2.4-3 μm region and the MCT detector in the 13.5-14.3 μm region are due to the low signal-to-noise ratio of the collected signals in this region, which affects the calibration accuracy; 2) the InSb detector in the 4.2-4.5 μm region is due to the interference of CO₂ atmospheric absorption in this band. The interference of CO₂ atmospheric absorption exists. The experimental results show that this method can effectively meet the radiometric calibration requirements, and the calibration results are in good agreement with the theoretical values, with an equivalent temperature deviation of less than 2%.

The large temperature range and the wide operating band of the circular variable filter spectroradiometer make for a significant non-linear response in the radiometric calibration process. Different temperature targets also have different degrees of responsiveness, so the traditional two-point method does not work well for radiometric calibrations. In addition, external ambient temperature variations, atmospheric disturbances, and the instrument's thermal radiation are taken into account in the calibration process. In this paper, a divisional linearity-based radiometric calibration method is proposed, which can effectively solve the non-linearity problem caused by the wide wavelength range and temperature range of the target measurement by zoning the target temperature into sub-regions. The experimental results show that the method can effectively meet the radiometric calibration requirements, and the calibration results are in good agreement with the theoretical values, with an equivalent temperature deviation of less than 2%. The zoned linear radiometric calibration method in this paper is also applicable to other spectroradiometers of the spectral type to solve the non-linearity problem caused by the measurement of targets with a wide wavelength and temperature range.

Silicon-based modulators feature small size, low power consumption, and easy integration. However, compared with lithium niobate modulators, they suffer poor linearity, which limits their performance in analog communication systems such as radio over fiber access networks. Various improvement methods have been proposed to improve the linearity of silicon-based modulators, including optimizing the p-n junction design, modifying the doping concentration of the p-n junction, and adopting novel waveguide structures, electrode structures, and driving methods. However, these methods generally require altering the physical characteristics or structures of the devices or adding additional driving circuits. The modulator linearity is typically fixed once the device fabrication or packaging is completed, which makes it difficult to change afterward. Currently, there is a lack of compensation schemes for Si modulator linearity after device fabrication or packaging. Therefore, we want to propose a way from the system perspective to conduct the performance compensation caused by the poor linearity of Si modulators.

In our paper, a novel enhanced maximum-ratio combined receiver (EMRC-Rx) is proposed and demonstrated through proof-of-concept experiments, and it is conducted to mitigate the system performance degradation caused by the low linearity of Si modulators when the modulators are deployed in passive optical network (PON)-based access networks. The EMRC-Rx leverages the advantages of both direct detection receiver (DD-Rx) and lite coherent detection receiver (Lite CO-Rx) by utilizing the maximum signal-to-noise ratio contribution from both the receiver types to significantly improve receiver sensitivity and mitigate the system performance degradation. The proposed EMRC algorithm considers the contribution of multiple Lite CO-Rx components to the output signal-to-noise ratio, thereby increasing the proportion of signal-to-noise ratio in the lite coherent receiver and further enhancing the receiver sensitivity. As a result, the EMRC-Rx in the Si modulator system could achieve similar performance compared with the MRC-Rx in the lithium niobate modulator system. The EMRC-Rx consists of three components including DD-Rx, Lite CO-Rx #1, and Lite CO-Rx #2 (Fig. 3). The results of the three components are aggregated and calculated by the EMRC algorithm from Equation 1 to obtain the final output of the EMRC-Rx. The corresponding digital signal processing flow for DD-Rx, Lite CO-Rx #1, and Lite CO-Rx #2 is illustrated in Fig. 3.

The experimental results show that when the bit error rate (BER) exceeds the KP4-FEC threshold at 1.0 × 10^-4, the receiver sensitivity of EMRC-Rx is improved by 5.5 dB and 8.8 dB compared with standalone DD-Rx and Lite CO-Rx respectively, with corresponding improvements in error vector magnitude (EVM) of 32.5% and 41.1% (Figs. 8 and 9). Finally, the system performance is significantly improved. Through further comparative experiments with lithium niobate modulators, the EMRC-Rx based on Si modulators can improve the receiver sensitivity by 3.5 dB and 7.9 dB respectively compared with the Lite CO-Rx and DD-Rx employing lithium niobate modulators (Fig. 11). A comparable system performance with the MRC-Rx in the lithium niobate modulator is realized. The results indicate that the EMRC-Rx can compensate for the performance degradation caused by the low linearity of Si modulators. For the entire experimental system, the optimal range for the frequency spacing between the downlink and uplink optical carrier is 10 GHz to 18 GHz. Beyond this range, the system performance starts to degrade (Fig. 9). Considering that DD-Rx, Lite CO-Rx #1, and Lite CO-Rx #2 all occupy a certain bandwidth, the total bandwidth utilization within the photodetector (PD) bandwidth is calculated as 70.45%. At different fiber transmission distances (0-40 km), the EMRC-Rx performance is significantly superior to other receivers (Fig. 10).

The bandwidths of the Si modulator and PD employed in our paper are 33 GHz and 22 GHz respectively. By employing higher-order signal modulation schemes and larger bandwidth PDs, further improvements in transmission rates can be achieved and frequency overlap is avoided. On the other hand, the signal beating in the PD indicates that signal-signal beating interference (SSBI) occurs when the two sidebands of the downlink signal beat each other, which can distort across the entire baseband range. However, when the spacing between the carrier and sidebands is sufficiently large, the influence of SSBI is significantly reduced. In the proposed system, Lite CO-Rx #1 and Lite CO-Rx #2 have a significant guard band, allowing them to remain unaffected by SSBI (Fig. 12). As for the DD-Rx component, the left half of the signal may be influenced by SSBI. However, due to the high carrier-to-sideband power suppression ratio (CSPR) in the system, it is sufficient to minimize the influence of SSBI. Therefore, the effect of SSBI in the system in our study can be generally considered negligible.

In terms of system cost, compared with other reported representative lite coherent systems, the proposed EMRC-Rx does not introduce additional hardware but mainly differs in the digital signal processing part where the EMRC algorithm is employed. The additional digital signal processing can optimize receiver sensitivity and mitigate the performance degradation caused by the low linearity of Si modulators. The higher receiver sensitivity not only reduces the correction costs of system error but also allows for higher split ratios in the optical distribution network (ODN), further decreasing the deployment costs of PON. From a system perspective, leveraging the advantages of silicon-based devices in CMOS compatibility and large-scale production can further reduce equipment costs when Si modulators are extensively deployed in PONs. Additionally, for distributed units (DUs) and remote radio units (RRUs), integrating more chip-level devices such as lasers, detectors, passive components, and amplifiers can reduce costs and power consumption, which is beneficial for both operators and end-users.

We propose an EMRC-Rx that leverages the advantages of both direct detection and coherent detection to significantly improve receiver sensitivity and mitigate the system performance degradation caused by the low linearity of Si modulators. By employing EMRC-Rx, the system can ensure consistent transmission performance both under low-received power and high-received power scenarios. During the experimental validation, EMRC-Rx demonstrates superior performance compared with other receivers, making it a promising solution to the challenges associated with Si modulator linearity in optical communication systems. The proposed EMRC-Rx is an algorithm-based linearization compensation scheme specifically designed for Si modulators. It serves as a system-level performance optimization solution for devices after fabrication or packaging to fill a current gap in the industry. Our study provides a valuable guidance for the construction of high-reliable and low-cost photonic integrated access networks based on silicon modulators in the 5G era.