# On-Orbit Relative Radiometric Calibration of the Bayer Pattern Push-Broom Sensor for Zhuhai-1 Video Satellites

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## Abstract

**:**

## 1. Introduction

#### 1.1. OVS Satellites Overview

^{2}of data can be captured in each strip image. Contrary to the conventional linear push-broom mode, the Bayer pattern push-broom mode uses the Bayer pattern detector group, which utilizes two rows of imaging detectors as the smallest imaging unit. This achieves the same multi-level TDI function as the linear array push-broom satellite by increasing or decreasing the number of Bayer pattern rows. Figure 4 shows a comparison of a conventional linear array push-broom and a Bayer pattern push-broom. The imaging data in the push-broom direction is the imaging data collected by a single detector in a single band, while the Bayer pattern push-broom obtains data from multiple bands.

#### 1.2. Relative Radiometric Calibration

## 2. Methods

#### 2.1. Bayer Pattern Conversion

#### 2.2. Bayer Pattern Position Determination

- 1.
- Calculate the linecounter value $LineCounte{r}_{i}$ of the ith row of Bayer pattern data.
- 2.
- Determine the first position of a complete Bayer pattern. If $LineCounte{r}_{i}$ is odd, the following equation holds:$$\left(\left(LineCounte{r}_{i}+1\right)\%2\right)=0,$$
- 3.
- Determine whether the ith row Bayer pattern data is continuous with the adjacent imaging data and Bayer pattern according to the following rules:$$\left|LineCounte{r}_{i}-LineCounte{r}_{i+1}\right|=1.$$$$\left|LineCounte{r}_{i-1}-LineCounte{r}_{i}\right|=1.$$If the ith iteration meets the above formula, the ith row is the starting row of the complete Bayer pattern data. Otherwise, the ith data will be discarded and the calculation $i=i+1$ must be performed before returning to step (1).
- 4.
- Repeat steps 1–3 to determine the locations of all complete Bayer pattern data.

#### 2.3. Relative Calibration Parameter Solving

- 5.
- Calculate the DN number of the imaging data acquired by the ith detector, as in the following equations:$$PixelNum{s}_{i}\left(k\right)=PixelNum{s}_{i}\left(k\right)+1,$$$$TotalPixelNum{s}_{i}=TotalPixelNum{s}_{i}+1,$$
- 6.
- Establish the cumulative probability distribution function, ${P}_{i}\left(k\right)$, of each sensor detector according to Equation (7).
- 7.
- $${P}_{i}\left(k\right)={\displaystyle \sum}_{j=0}^{k}\frac{PixelNum{s}_{i}\left(k\right)}{TotalPixelNum{s}_{i}}.$$
- 8.
- Set the cumulative probability distribution function of the imaging gray data of all the sensor detectors as the reference cumulative probability distribution function for each band, ${P}_{G}\left(k\right)$,${P}_{B}\left(k\right)$, and ${P}_{R}\left(k\right)$:$${P}_{G}\left(k\right)={\displaystyle \sum}_{k=0}^{{2}^{n}-1}{\displaystyle \sum}_{j}^{{N}_{total}}\frac{PixelNum{s}_{j}\left(k\right)}{TotalPixelNum{s}_{j}},\phantom{\rule{0ex}{0ex}}\left(j=1,4,5,8,9,12,13\dots \right),$$$${P}_{B}\left(k\right)={\displaystyle \sum}_{k=0}^{{2}^{n}-1}{\displaystyle \sum}_{j}^{{N}_{total}}\frac{PixelNum{s}_{j}\left(k\right)}{TotalPixelNum{s}_{j}},\phantom{\rule{0ex}{0ex}}\left(j=2,6,10,14\dots \right),$$$${P}_{R}\left(k\right)={\displaystyle \sum}_{k=0}^{{2}^{n}-1}{\displaystyle \sum}_{j}^{{N}_{total}}\frac{PixelNum{s}_{j}\left(k\right)}{TotalPixelNum{s}_{j}},\phantom{\rule{0ex}{0ex}}\left(j=3,7,11,15\dots \right),$$
- 9.
- Obtain the imaging response model of each sensor detector by mapping the cumulative probability distribution function of each sensor detector to the reference cumulative probability distribution function based on Equations (11) and (12):$${P}_{R}\left(k-x\right)\le {P}_{i}\left(k\right)\le {P}_{R}\left(k+y\right),\text{}\mathrm{and}$$$$k=\{\begin{array}{c}k-x,\left|{P}_{R}\left(k-x\right)-{P}_{i}\left(k\right)\right|-\left|{P}_{i}\left(k\right)-{P}_{R}\left(k+y\right)\right|\le 0\\ k+y,\left|{P}_{R}\left(k-x\right)-{P}_{i}\left(k\right)\right|-\left|{P}_{i}\left(k\right)-{P}_{R}\left(k+y\right)\right|0\end{array},$$

#### 2.4. Quality Assessment

## 3. Results

#### 3.1. Calibration Results

#### 3.2. Visual Assessments

#### 3.3. Accuracy Assessments

## 4. Discussion

## 5. Conclusions

- (1)
- reconstructing the order of each detector of the Bayer pattern sensor and converting it into a virtual linear array sensor to separate the RGB three-band components from the Bayer pattern; and
- (2)
- designing a positioning method linked by “linecounters” to detect the specific position of each detector of each Bayer pattern.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**CMOS arrangement of the focal plane of the OVS satellite (

**a**), “GBRG” Bayer pattern (

**b**), and “GRBG” Bayer pattern (

**c**).

**Figure 4.**Schematic of multi-level TDI in (

**a**) a linear array push-broom sensor and (

**b**) a Bayer pattern push-broom sensor.

**Figure 5.**Uniform ocean zone images captured from an OVS Bayer sensor: (

**a**) raw Bayer data, (

**b**) color reconstructed image without relative radiometric calibration, and (

**c**) color reconstructed image after relative radiometric calibration.

**Figure 7.**Schematic of Bayer pattern changes caused by a row data loss (

**a**) from a GBRG Bayer pattern to (

**b**) a RGGB Bayer pattern in lines 3–4.

**Figure 10.**Bayer pattern data (

**a**); conversion to push-broom data, including the red band data (

**b**); green band data (

**c**); and blue band data (

**d**).

**Figure 11.**Relative radiometric calibration parameters of OVS mapping between the raw digital numbers (DNs) and the calibrated DNs (

**a**), and radiometric response curves of various detectors under low, medium, and high DNs (

**b**).

**Figure 12.**The relative corrected reconstructed Bayer data, including red band data (

**a**), green band data (

**b**), and blue band data (

**c**).

**Figure 13.**Relative corrected images for various feature types of ocean (

**a**–

**c**), clouds (

**d**–

**f**), and urban areas (

**g**–

**i**): raw Bayer pattern images (

**a**,

**d**,

**g**); uncalibrated Bayer interpolation images (

**b**,

**e**,

**h**); and calibrated Bayer interpolation images (

**c**,

**f**,

**i**).

**Figure 14.**Comparison of a specific Bayer image enlarged four times: (

**a**) raw Bayer data, (

**b**) uncalibrated Bayer interpolation data, and (

**c**) calibrated Bayer interpolation data.

**Figure 15.**Distribution of column means of level zero image (

**a**) and RGB band streaking metrics (

**b**–

**d**) before and after relative correction.

**Figure 17.**Anomalous changes in the radiometric response of CMOS edge detectors of the OVS at specific times during calibration of the 2019 data: (

**a**) 26 October; (

**b**) 28 October; (

**c**) 29 October; (

**d**) 30 October; (

**e**) 1 November; and (

**f**) 2 November.

Parameter | Value |
---|---|

Ground swath | 22.5 km @ 500 km |

Imaging mode | Staring video mode: frame rate: 10–25 fps Push-broom mode |

Resolution | 0.9 m |

Quantization bits | Video mode: 8 bits Push-broom mode: 10 bits |

Color | Bayer pattern |

Modulation Transfer Function | ≥0.12 @ Nyquist frequency |

Signal To Noise Ratio | ≥35 dB (Sun elevation angle ≥ 50°) |

CMOS | Zone | Band | Average DNs | Streaking Metrics (%) | RMS (%) |
---|---|---|---|---|---|

1 | 1 | R | 174.464505 | 0.252942 | 0.553052 |

G | 303.027251 | 0.128574 | 0.389035 | ||

B | 299.120944 | 0.101004 | 0.286782 | ||

2 | R | 145.834542 | 0.602074 | 0.689595 | |

G | 278.809108 | 0.434780 | 0.380873 | ||

B | 280.663032 | 0.358834 | 0.377148 | ||

3 | R | 187.183937 | 0.834730 | 0.602284 | |

G | 330.415927 | 0.708178 | 0.472996 | ||

B | 322.815496 | 0.643862 | 0.382063 | ||

4 | R | 633.844315 | 0.505590 | 1.452498 | |

G | 885.569805 | 0.469941 | 1.384834 | ||

B | 689.440504 | 0.438069 | 0.987072 | ||

2 | 1 | R | 213.339061 | 0.391711 | 0.654857 |

G | 331.792004 | 0.289577 | 0.598556 | ||

B | 313.929878 | 0.224774 | 0.529018 | ||

2 | R | 183.932816 | 0.818849 | 1.050736 | |

G | 306.118564 | 0.706289 | 0.998101 | ||

B | 298.570655 | 0.656120 | 0.635410 | ||

3 | R | 210.372869 | 0.212614 | 0.598503 | |

G | 334.387692 | 0.315220 | 0.538775 | ||

B | 318.118987 | 0.379993 | 0.545816 | ||

4 | R | 677.060288 | 0.188683 | 0.637184 | |

G | 918.258576 | 0.158117 | 1.107705 | ||

B | 706.071616 | 0.130670 | 0.643381 | ||

3 | 1 | R | 167.416066 | 0.234464 | 0.402989 |

G | 301.497830 | 0.108619 | 0.220347 | ||

B | 301.903464 | 0.093085 | 0.289550 | ||

2 | R | 126.881600 | 0.549097 | 0.769455 | |

G | 254.414065 | 0.357859 | 0.607761 | ||

B | 272.225351 | 0.286836 | 0.363299 | ||

3 | R | 623.796314 | 0.814639 | 1.237399 | |

G | 882.974602 | 0.780348 | 1.039002 | ||

B | 694.270148 | 0.748270 | 0.548426 | ||

4 | 1 | R | 210.705489 | 0.437302 | 0.733809 |

G | 327.850046 | 0.337556 | 0.424513 | ||

B | 301.488013 | 0.273422 | 0.451469 | ||

2 | R | 169.106208 | 0.420492 | 0.866250 | |

G | 282.933319 | 0.297154 | 0.726361 | ||

B | 273.462593 | 0.230403 | 0.564223 | ||

3 | R | 194.781064 | 0.151181 | 0.828773 | |

G | 314.900084 | 0.073915 | 0.573989 | ||

B | 296.537163 | 0.091034 | 0.663551 | ||

4 | R | 678.343272 | 0.188817 | 0.616931 | |

G | 919.031208 | 0.159909 | 0.740941 | ||

B | 681.249269 | 0.131942 | 0.742365 | ||

5 | 1 | R | 234.104145 | 0.098038 | 0.885455 |

G | 386.938663 | 0.043580 | 0.674836 | ||

B | 381.137859 | 0.080850 | 0.595346 | ||

2 | R | 179.405221 | 0.160321 | 0.135142 | |

G | 319.111673 | 0.037737 | 0.185095 | ||

B | 333.812995 | 0.036985 | 0.176527 | ||

3 | R | 212.526180 | 0.542912 | 0.638558 | |

G | 364.433856 | 0.434148 | 0.476657 | ||

B | 372.303330 | 0.381670 | 0.367203 |

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## Share and Cite

**MDPI and ACS Style**

Li, L.; Li, Z.; Wang, Z.; Jiang, Y.; Shen, X.; Wu, J.
On-Orbit Relative Radiometric Calibration of the Bayer Pattern Push-Broom Sensor for Zhuhai-1 Video Satellites. *Remote Sens.* **2023**, *15*, 377.
https://doi.org/10.3390/rs15020377

**AMA Style**

Li L, Li Z, Wang Z, Jiang Y, Shen X, Wu J.
On-Orbit Relative Radiometric Calibration of the Bayer Pattern Push-Broom Sensor for Zhuhai-1 Video Satellites. *Remote Sensing*. 2023; 15(2):377.
https://doi.org/10.3390/rs15020377

**Chicago/Turabian Style**

Li, Litao, Zhen Li, Zhixin Wang, Yonghua Jiang, Xin Shen, and Jiaqi Wu.
2023. "On-Orbit Relative Radiometric Calibration of the Bayer Pattern Push-Broom Sensor for Zhuhai-1 Video Satellites" *Remote Sensing* 15, no. 2: 377.
https://doi.org/10.3390/rs15020377