# Photometric Correction of Chang’E-1 Interference Imaging Spectrometer’s (IIM) Limited Observing Geometries Data with Hapke Model

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## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Data Set

#### 3.1. Sample Data

#### 3.2. Preprocessing of the Sample Data

## 4. Results and Discussion

#### 4.1. Photometric Characteristics of the Three Areas

#### 4.2. Hapke Model Parameters Calculation

#### 4.3. Photometric Correction Results of the Reflectance Data

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Three areas we divided: ‘maria’, ‘new highland’ and ‘old highland’ (The different of ‘new highland’ and ‘old highland’ is the maturity of the Lunar soil. The maturity of lunar soil in ‘new highland’ was low while that in ‘old highland’ was high) (base map is global mosaic of the moon by Lunar Reconnaissance Orbit (LRO), resolution is 200/pixel, http://wms.lroc.asu.edu/lroc/view_rdr/WAC_GLOBAL).

**Figure 2.**(

**a**) Density plot of I/F at orbit 2525; (

**b**) The histogram of the I/F of sample data at orbit 2525; (

**c**) density plot of I/F; (

**d**) density plot of I/F after ‘albedo filtering’.

**Figure 3.**Global false color image mosaic with Clementine UV/VIS spectral data (R = 750/415 nm, G = 750/1000 nm, B = 415/750 nm, https://planetarymaps.usgs.gov) and the three areas.

**Figure 4.**Globe fluctuation distribution map of the moon and the three areas. Fluctuation of ‘maria’ is between 0 and 70 m, ‘old highland’ is between 0 and 300 m, ‘new highland’ is between 0 and 500 m.

**Figure 6.**The phase functions of the sample data for the 757 nm band. The red curve represents the Hapke model we fitted.

**Figure 7.**Reflectance data of orbit 2576 with phase range 0~15° before (

**a**) and after (

**b**) photometric correction by Hapke model.

**Figure 8.**Mosaic of two adjacent images (part of orbit 2576 and 2885) before (

**a**) and after photometric correction with empirical (

**b**) and Hapke model (

**c**) (In the red box, 3.73 < i < 4.89, 0.013 < e < 5.86, 2.20 < g < 6.52).

Area | Parameter | |||
---|---|---|---|---|

$\mathit{w}$ | $\mathit{b}$ | ${\mathit{B}}_{\mathit{s}0}$ | ${\mathit{h}}_{\mathit{s}}$ | |

Maria | <0.29 | >0.259 | >1.9 | >0.0558 |

New highland | (0.38, 0.475) | (0.232, 0.255) | (1.5867, 1.72235) | >0.0626 |

Old highland | >0.48 | <0.232 | <1.5867 | >0.0626 |

Orbit | Start Latitude | End Latitude | Start Line | End Line |
---|---|---|---|---|

2525 | 28 | 16 | 7300 | 9000 |

2568 | 44 | 29 | 5300 | 7590 |

2576 | 0 | −11 | 11,860 | 13,580 |

2576 | −17 | −26 | 14,540 | 15,870 |

2600 | 33 | 7 | 6624 | 10,610 |

2611 | 38 | 30 | 6147 | 7374 |

2845 | 30 | 17 | 6700 | 8600 |

2894 | 19 | −11 | 8340 | 12,960 |

2914 | 25 | 19 | 7392 | 8320 |

Symbols | Name | Value |
---|---|---|

$\omega $ | Single scattering albedo | Fitting |

$b$ | Henyey-Greenstein double-lobed single particle phase function parameter | Fitting |

$c$ | Henyey-Greenstein double-lobed single particle phase function parameter | Equation (8) |

Amplitude of Coherent Backscatter Opposition Effect (CBOE) | 0 | |

${h}_{c}$ | Angular width of CBOE | 1.0 |

${B}_{s0}$ | Amplitude of Shadow Hiding Opposition Effect (SHOE) | Fitting |

${h}_{s}$ | Angular width of SHOE | Fitting |

$\overline{{\theta}_{p}}$ | Effective value of the photometric roughness | 0 |

$\varphi $ | Filling factor | 0 |

$\mathit{w}$ | $\mathit{b}$ | ${\mathit{B}}_{\mathit{s}0}$ | ${\mathit{h}}_{\mathit{s}}$ | |
---|---|---|---|---|

original parameter ranges | <0.29 | >0.259 | >1.9 | >0.0558 |

results | 0.275988 | 0.700692 | 1.38499 | 0.0754915 |

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**MDPI and ACS Style**

Xu, X.; Liu, J.; Liu, D.; Liu, B.; Shu, R.
Photometric Correction of Chang’E-1 Interference Imaging Spectrometer’s (IIM) Limited Observing Geometries Data with Hapke Model. *Remote Sens.* **2020**, *12*, 3676.
https://doi.org/10.3390/rs12223676

**AMA Style**

Xu X, Liu J, Liu D, Liu B, Shu R.
Photometric Correction of Chang’E-1 Interference Imaging Spectrometer’s (IIM) Limited Observing Geometries Data with Hapke Model. *Remote Sensing*. 2020; 12(22):3676.
https://doi.org/10.3390/rs12223676

**Chicago/Turabian Style**

Xu, Xuesen, Jianjun Liu, Dawei Liu, Bin Liu, and Rong Shu.
2020. "Photometric Correction of Chang’E-1 Interference Imaging Spectrometer’s (IIM) Limited Observing Geometries Data with Hapke Model" *Remote Sensing* 12, no. 22: 3676.
https://doi.org/10.3390/rs12223676