The MAI consists of a wide-field-of-view optical system, a filter combination wheel, and a CCD area array detector. The number of effective pixels of the CCD array is 256× 256, and the pixel size is 26× 26 μ m. The MAI contains six observational bands, totaling 13 channels^{[16, 17, 18]}. The specific channel settings are shown in Table 1.

Table 1

Table 1

Table 1 Spectral channel characteristics of the MAI Channel Central wavelength/nm Band width/nm Polarization Polarization direction Main mission 1 2 3 565 565 565 20 20 20 yes yes yes -60° 0° 60° Cloud, aerosol, earth radiation budget 4 5 6 670 670 670 20 20 20 yes yes yes -60° 0° 60° Cloud, aerosol, earth radiation budget 7 8 9 865 865 865 40 40 40 yes yes yes -60° 0° 60° Cloud, aerosol, earth radiation budget 10 763 10 no - Cloud top pressure 11 765 40 no - Cloud top pressure 12 910 20 no - Water vapor amount 13 - - - - Dark current

Table 1 Spectral channel characteristics of the MAI

A total of 104 403 frames of observational data were acquired by the MAI from September 2016 to March 2018, with each frame containing observational data from the instrument’ s 13 channels. We used all the observational data available during this period for our analysis in this paper.

Assuming there are sufficient observational samples, i.e., the samples observed by each CCD pixel have the same ergodicity; if the response characteristics of each CCD pixel are consistent, the sample mean value obtained by all CCD pixels should be consistent. Otherwise, the results obtained will be non-uniform.

Based on this principle, this paper presents a full-range multi-section analysis and correction method, based on long-term on-orbit observational data, to monitor and correct the inconsistency in the response characteristics of TG-2/MAI CCD pixels.

In order to analyze and correct the inconsistency in the response characteristics of the MAI pixels, the concept of a reference image is introduced. For each channel, the 104 403 data corresponding to each CCD pixel are sorted in ascending order according to the scale of the DN value, and then the 104 403 data are equally divided into 30 parts according to the DN value from the smallest to the largest.Thus, to average the data, each pixel then gets 30 reference DN values. The reference DN value of all pixels in the same part constitutes a layer of the reference image. Similarly, each channel can get 30 reference images with different ranges of DN values.

In addition, since the absolute radiation calibration of the MAI is processed for 5× 5 pixels in the CCD center, and assuming that the CCD center pixels are the standard, the DN value of the 5× 5 pixels in the center of each layer of the reference image is therefore averaged as the standard DN value of the reference image of the layer.

Because the MAI has no onboard correction system, the reference image, instead of the uniform irradiation, was used to quantitatively analyze the inconsistency in the pixel response during the MAI’ s operation on-orbit. In fact, the inconsistency in the pixel response behavior is the horizontal non-uniformity of imaging under uniform irradiation conditions. Therefore, a quantitative evaluation index for the inconsistency in the CCD pixel response is given, combined with the laboratory’ s non-uniformity measurement index. Generally, there are two quantitative assessment method types that can be employed:a task-based metric method, which is less commonly adopted because of the greater degree of subjectivity; or a measurement method, based on objective formulas, for which the method of expression varies. In this paper, we combine the actual demand, based on the standard variance measurement method, to define the inconsistency in the pixel response (ICPR). More specifically, this is the ratio of the root-mean-square value, which is the difference between each pixel’ s DN value and the average DN value of the reference image, corresponding to when the standard DN value is one-half of the saturation exposure, and the average DN value of the reference image, under uniform irradiation conditions. Mathematically, the expression is as follows:

ICPR=1DNij¯1N∑i=1256∑j=1256(DNij-DNij¯)2

Here, DNij¯represents the average DN value of the reference image, N represent the CCD’ s number of pixels (here, N=65 536), and DN_ij is the DN value of the pixel at (i, j).

Due to various objective factors, an onboard correction system was not set up on the MAI. At the same time, in the pre-laboratory calibration stage, an analysis and correction of the non-uniformity of CCD pixels was conducted, for gains and offsets of representative pixels in a limited direction.Therefore, in order to analyze the inhomogeneity of each channel during on-orbit operation, we first examined the response characteristics of the polarized and non-polarized channels using the full-range multi-section analysis method, based on long-term on-orbit observational data.

2.1.1 Polarized channels

Polarization observations have unique advantages for the inversion of parameters such as cloud phase, the effective radius of cloud droplets, and aerosol optical thickness^{[17, 18, 19, 20, 21]}. In order to ensure the accuracy of the inversion of these various physical parameters, it is necessary to carry out quality control on the MAI Level 0 data. Taking the 865 nm band (channels 7, 8 and 9) as an example, the response characteristics of the pixels of the MAI polarized channels are analyzed.

The area array CCD includes a large number of pixels. To simplify the description, the center pixel of each 51× 51 pixel area is taken as a representative pixel, and the calculation results of 25 representative pixels only are given. Figures 1(a), (c) and (e) show the responses of the three channels in the 865 nm band for each pixel under different incident radiation. The abscissa is the standard DN value of each layer of the reference image, and the ordinate is the actual output DN value corresponding to each pixel. In the figure, the line colors represent CCD edge pixels, centric pixels, and edge pixels, in the order from blue to red. Figures 1(b), (d) and (f) show the relative deviation between the DN value of each pixel and the standard DN value of the reference image of the three channels under different incident radiation conditions.

Figure 1 shows that the MAI CCD pixels exhibit a significant nonlinear response, and the nonlinear response characteristics of each pixel are inconsistent. Also, the response of the CCD edge pixel is significantly lower than that of the center pixel. Subsequently, under different irradiation conditions, due to the distinctresponse for each pixel, the horizontal non-uniformity of the MAI imaging is different

Fig.1

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	Fig.1 Pixel response function and relative deviation distribution in the 865 nm band:(a) channel 7; (c) channel 8; (e) channel 9. Panels (b), (d) and (f) show the relative deviation of the pixel response from the standard response for channels 7, 8 and 9, respectively

under different uniform irradiation conditions. In addition, the response characteristics of three polarization channels with different orientation angles of the same band are similar, but there are also clear differences. By contrast, the distribution of the relative deviation of the channels with a polarizer orientation angle of 0° is more concentrated than that of the other channels.

2.1.2 Non-polarized channels

Taking the 910 nm band (channel 12) as an example, the response characteristics of non-polarized channel pixels are analyzed. Like in Figure 1, Figure 2 shows the response function and the relative deviation distribution of each representative pixel. The results show that, as the standard DN value increases, non-polarized channels also (like polarized channels) have the problem of inconsistent nonlinear pixel response characteristics.

Fig.2

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	Fig.2 The (a) pixel response functions and (b) relative deviation between the pixel response and standard response for the 910 nm band (channel 12)

Compared with the pixel response characteristics of the polarized band, the non-polarizedchannel pixel response characteristics are more similar to the polarizedchannelswhose polarization plate has an orientation angle of 0° . The distribution of the relative deviation curve of most pixels is more concentrated. In adidtion, the maximum relative deviation of the non-polarized channel is significantly lower than that of polarized channels.

In order to quantify the inconsistency in the pixel response characteristics of each channel during MAI operation on-orbit, this paper approximates the 30th layer of the reference image as the MAI imaging result when onehalf of the saturated exposure is under uniform irradiation conditions. Figure 3 demonstrates quantitatively the inconsistency in the pixel response characteristics of each channel of the MAI.

Fig.3

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	Fig.3 Inconsistent response characteristics of pixels in each channel of the MAI

Figures 3 shows that there is significant inconsistency in the CCD pixel response characteristics of each channel. Also, the inconsistency in the pixel response characteristics of channel 4 is the lowest, at about 4%, while channel 12 is the highest, up to about 10%. Therefore, the pixel response characteristics of the polarized channels and non-polarized channels have certain differences. In the polarized channels, the inconsistency in the pixel response characteristics between different polarized bands is quite different. The 565 nm band (channels 4, 5 and 6) is relatively low, at about 4%, while the 865 nm band (channels 7, 8 and 9) is relatively high, reaching about 7%.The inconsistency in the pixel response characteristics between the three polarized channels in the same polarization band have some similarities, although there are certain differences, and the difference in pixel response inconsistency is basically within 1%.For non-polarized channels, the inconsistency in the pixel response characteristics between channels is also very different, with channel 10 being the lowest, at about 4%, and channel 12 the highest, reaching about 10%.

Overall, the nonlinear response characteristics of MAI pixels present significant inconsistencies, and there is clear channel dependence. The three main reasons for these characteristicsmight be as follows:Firstly, there is inconsistency in the nonlinear response of pixels in the MAI CCD itself.Secondly, there are differences in the performance of the filters used in each channel, and this problem is difficult to avoid because even when the same filter from the same manufacturer is used, the problem still exists. Thirdly, in the polarized channels, in addition to the effect of the filter, the difference in the polarization angle of the polarizer results in distinct response characteristics of the different polarized channels in the same polarized band.

In this paper, the full-range multi-section correction method is used to correct the inconsistency of the CCD pixel response characteristics. The theoretical model is as follows:

For a p× q area array CCD, the illumination intensity corresponding to the CCD response from zero to saturation is divided into m illumination levels, and the corresponding CCD output image V_ref(i, j, k) is measured at the illumination levels φ ₁, φ ₂, …, φ _m, where i=1, 2, …, p, j=1, 2, …, q, k=1, 2, …, m. V_ref(i, j, k) are called the reference image corresponding illuminance φ _k, which expresses the non-uniform response of the CCD under illumination φ _k.

In order to correct the inconsistency of the CCD pixel response characteristics, the response value V_avg(k) of the CCD center pixel under the illumination φ _k is used as the standard response.

For any image to be corrected V_d(i, j), it is first determined, pixel-by-pixel, which region of the reference image V_ref(i, j, k) the DN value of the pixel V_d(i, j) falls within, according to to determine the k.

Finally, the corrected image V_c(i, j) can be obtained according to the following equation

Vc(i, j)=Vavg(k+1)-Vavg(k)Vref(i, j, k+1)-Vref(i, j, k)×(Vd(i, j)-Vref(i, j, k))+Vavg(K)

Based on the actual situation of the MAI, a correction model based on MAI measured data is given.

(1) Construction of reference image

The range of the MAI CCD DN value is 0~4 095. To make it possible to correct the inconsistency in the pixel response characteristics in each illumination range, construct a 30-layer reference image. In the actual correction process on-orbit, the division is directly performed according to the scale of the pixel DN value. In this paper, the observational data of each channel of the MAI from September 2016 to March 2018 are sorted in ascending order, pixel-by-pixel, and divided into 30 equal parts.Each part is averaged for each channel and each pixel to obtain a reference image V_ref(i, j, k), 30 layers of reference images can be obtained for each channel.

(2) CCD standard response

Assuming that the CCD center pixel is a standard response.Accordingly, due to the influence of the optical lens, filters, etc., the center of the CCD imaging tends to deviate from its geometric center. Therefore, the center point obtained by the collimated light tube geometry calibration is used as the center of the CCD. The average value of the center of the reference image 5× 5 pixel DN values V_avg(k) is taken as the standard response of the layer.

(3) Correction algorithm of the inconsistent response characteristics

Assuming that the count value of the pixel (i, j) to be corrected is V_d(i, j), and the corresponding corrected count value is V_c(i, j), the value of k is firstly determined according to V_ref(i, j, k)≤ V_d(i, j)≤ V_ref(i, j, k+1). Then, the corrected count value V_c(i, j) of the pixel of the channel is calculated according to the correction formula given in Section 4.1.

If the DN value of the pixel to be corrected falls outside the 1st or 30th layer of the reference image, extrapolation is performed using the 1st layer and the 2nd layer, and the 29th layer and the 30th layer, respectively.

In order to intuitively express the changes before and after correction of the inconsistency in the response characteristics of the pixels of the MAI CCD, Figure 5(a) gives the imaging of channel 7 on September 23, 2016 as a correction example. Figures 5(b) and (c) are the corrected image and deviation image before and after correction, respectively. According to Figure 5(c), the deviations before and after correction are mainly concentrated on the four corners or edge regions of the image. Figures 5(a), (b) and (c) show that, after the correction, the low-response area is obviously improved, which reaches the same level as the response of surrounding pixels. The dependence on the observational zenith angle of the CCD pixel response is significantly reduced. And the image contrast is significantly improved, the cloud and coastline contours are clearer. The image is smoother, and the graininess is basically eliminated. Also, the scenes of some areas have changed— especially targets with a reflectivity between low and medium reflectivity, such as broken cloud, and so on. Therefore, the nonlinear response of CCD pixels will have a considerable impact on the subsequent quantitative product generation.

Fig.5

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	Fig.5 Comparison of channel 7 imaging results before and after correction on September 23, 2016. Panels (a), (b) and (c) are the channel 7 pre-correction image, corrected images, and deviation image, respectively

In order to verify the correction results, Metop-B/GOME-2 hyperspectral data were used to cross-contrast with the MAI Level 1 products. The specific data-matching method employed is described in^[22]. Figure 6 shows the cross-contrast results after the correction, and Table 2 shows the results before and after correction. Analysis of Figure 6 and Table 2 shows that, after the correction, the average absolute deviations of the reflectance of the MAI 565, 670 and 763 nm bands and the GOME-2 reference reflectance were significantly reduced, from 1.6%, 4.2% and 2.2% to 0.5%, 2.6% and 0.4%, respectively. In addition, the relative deviation also reduced, from 12.3%, 27.0% and 26.0 to 1.9%, 11.9% and 3.8%, respectively.

Table 2

Table 2

Table 2 Comparison of cross-contrast results before and after calibration Pre-correction/% corrected/% C_565 1.6 0.5 C_670 4.2 2.6 C_763 2.2 0.4 R_565 12.3 1.9 R_670 27.0 11.9 R_763 26.0 3.8 Note:C represents the average absolute deviation; R represents the relative deviation.

Table 2 Comparison of cross-contrast results before and after calibration

Fig.6

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	Fig.6 Calibration results after correction (a):565 nm band; (b):670 nm band; (c):763 nm band

In addition, the standard deviation of the cross-contrast before and after the correction was also calculated, but the expected improvement was not achieved. The reasons may be as follows:Firstly, there are relatively few areas for matching samples— particularly, in the region corresponding to the CCD edge, with a large amount of correction. Secondly, the difference in the spatiotemporal matching of the sample has a certain influence on the cross-contrast results.

The purpose of quality-controlling the MAI Level 0 products is the quantitative application of data. In order to analyze the influence of the correction on the quantitative application of data, the results of MAI cloud detection are analyzed, and then verified against the MODIS product.

The MAI observational result on January 1, 2017 was selected, and the multi-band threshold method was used to perform cloud detection before and after correction according to the same conditions. Figure 7 shows the visible image and cloud detection results of the MAI and MODIS at a similar time, where in the boxed areas in Figures 7(e) and (f) are the intersection areas of the MAI and MODIS, respectively. Figure 7 shows that, after the correction, the overall effect of the MAI reflectance image did not change significantly, but the cloud detection results did change significantly. Compared with the MODIS cloud detection product at a similar time, the corrected MAI cloud detection result looks more accurate. For example, for the region near (26° N, 117° E), most regions were identified by the MAI as clear sky before correction; but, after correction, they were identified as having the presence of broken clouds. This is in agreement with the MAI visible image, MODIS visible composite image, and MODIS cloud identification products. Therefore, the MAI imaging quality can be significantly improved by full-range multi-section correction, in particular, the accuracy of the target images whose reflectance between the low and medium values(broken cloud, ground surface, vegetation, etc.) can be improved.

Fig.7

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	Fig.7 MAI cloud detection product verification:(a, b) MAI visible image and cloud detection results before correction; (c, d) MAI visible image and cloud detection results after correction; (e, f) three-channel synthesis image and cloud detection products of MODIS at a similar time

The correction laid the foundation for the target feature recognition and data quantification application for the later period.

However, there are still some differences between the corrected MAI cloud detection results and the MODIS cloud detection products. There are two possible reasons for this:Firstly, the transit time of TG-2 and AQUA differ by 13 minutes. The unstable clouds in the area seem to disappear, move, and so on, which may cause some differences in the targets observed by sensors at the same location. And secondly, the MAI only has visible and near-infrared bands.Without infrared channels, there may be some errors in identifying some targets based on multi-channel cloud detection methods.

Overall, comparison of the cross-contrast and cloud-detection results show that this method can effectively deal with the errors caused by the inconsistency in the response characteristics of the pixels, thereby significantly reducing the error of MAI level 0 data, and at the same time improving the quality of level 1 products.