Absolute radiometric calibration with lunar surface reflectance as reference for earth-observing VNIR camera

Abstract

The absolute radiometric accuracy of earth-observing camera is crucial for the applications of natural resources, environment, agriculture and other industries. To continue the progress in this filed, a lunar surface reflectance based radiometric calibration approach is given in this paper. We chose IIM, M3, SP lunar models as references and GF-4 VNIR camera as sensor under calibrating. The lunar calibration sites were MS-2 site, Apollo-16 site and CE-3 site. The equivalent reflectance models of lunar were retrieved by Multiplying and integrating with the spectral response function of VNIR camera. Absolute radiometric calibrations with the equivalent reflectance models of lunar were carried out for 520–590nm, 630–690nm and 770–890nm spectral bands. The ground-based validation experiments were conducted with low, medium and high reflectance targets. The calibration accuracy was evaluated by comparing the relative errors of derived radiance after radiometric calibration with the benchmarks of TOA radiance transferred by in-situ measured reflectance. Lunar-based calibration models, lab and on-orbit filed-based models were used to compare the relative errors between proposed method and traditional way. The results showed that using IIM lunar model had better radiometric accuracy than other models, and SP model had the similar performance with traditional on-orbit filed-based model. The results indicated that using lunar to calibrate the earth-observing camera had the capability to improve the radiometric calibration accuracy.

Remote sensing, Earth-observing camera, Lunar surface reflectance, Radiometric calibration, Validation experiment.

1. Introduction

Radiometric calibration is a regular routine for earth-observing cameras after launching. The mostly used method is field-based calibration with specific calibration sites [1]. During calibration period, the demands for the spectral stability of calibration fields, the clarity of atmosphere, the synchronous cooperation of the measuring instruments are strict. Under the influence factors of field-based calibration, especially the uncertainties involved in the calibration process, the final radiometric accuracy has an inherent limitation of 5–7% [2, 3]. Besides, the nadir observing necessity of calibration filed and the costs of finance, humanity and instruments restrict the calibration frequency. The two aspects have negative effects on ground-based radiometric calibration for earth observing camera.

Lunar is an observable solar illumination sources in space for earth orbit satellite. The spectral stability of lunar is about 10⁻⁸ per year [4]. For the purpose of calibrating LEO or GEO optical camera using lunar, an advantage is the surface of lunar has no absorbing or scattering atmosphere molecules comparing with earth observing. Another is that the calibration frequency is about 1–2 times per months in one lunar phase varying period with the improving of satellite maneuvering ability. Among all the extraterrestrial bodies, lunar is studied mostly [5, 6, 7]. After decades of development in lunar explorations, the radiometric models of lunar have marched toward higher geometric and spectral properties. Research manuscripts reported large datasets that are deposited in a publicly available resolution and more detailed spectrum information, such as Apollo series [8], M3 [9], LROC [10], ROLO [11] of America, SELENE of Japan [12], Chang’E (CE) series of China [13, 14]. Several calibration researches of earth-observing mission are implemented experimentally, such as FY series [15], SeaWiFS [16], MODIS [17] and Pleiades [18]. Because of the differences in bandwidth, spectral response, observing parameters and other factors, each lunar radiometric model shows different surface reflectance, but a same increasing tendency as wavelength becoming longer in visible and near infrared spectrum [19, 20].

The surface reflectance of lunar is the key for calibrating the space-borne optical instruments that use lunar as illumination reference [21, 22]. In this study, we used the IIM model, M3 model and SP model to calibrate the GF-4 visible and near infrared (VNIR) camera [23] and verified the effectiveness by ground-based validating experiments.

2. Data overview

GF-4 VNIR camera has observed lunar periodically during March 2018 to April 2020. The whole observation acquired about 657Gb image data., covering lunar phases of -90°, -60°, -30°, -10°, -3.7°, +0.8°, +30°, +62° and +89°. The image sketches of typical phase angles showed in Figure 1(a-d). The continuous lunar observations during 2018–2020 found that the brightness of lunar varied as phase changing, but kept stable in the same phase. The property of 30° phase lunar was used mostly [24, 25, 26, 27], this study also chose 30° phase lunar data as scheme in Figure 1(b). In this imaging situation, the bore-sight of GF-4 VNIR camera is pointing to the center of lunar surface with satellite maneuvering, and the solar incident angle is 30°.

Figure 1.

Sketches of four lunar phase angles imaged by GF-4. (a) +0.8° phase; (b) +30° phase; (c) +89° phase; (d) -30° phase.

The surface reflectance models of three lunar sites in 30°phase are given below, namely, MS site (18.7°N, 21.4°E) in Figure 2(a) [28], Apollo-16 site (9.0°S, 15.1°E) in Figure 2(b) and CE-3 landing site (44.1281°N,19.5110°W) in Figure 2(c). The CE-3VNIS data is the in-situ measured results and Apollo-16 sample data is measured in lab, the lefts are all acquired by spectrometers of lunar detecting probes. The spectrums of Apollo-16 sample, CE-3 VNIS, IIM, M3 and SP are all covered the 520–890nm spectrum, and Apollo-16 sample and CE-3 VNIS datasets were only suitable for their own sites. Thus, IIM, M3 and SP datasets were used as calibration references in this work.

Figure 2.

Sketches of different surface reflectance models of lunar in three sites [28]. (a) MS-2 site; (b) Apollo-16 site; (c) CE-3 site.

3. Methods

3.1. Spectral modification

The chosen lunar models are built based on specific detectors and probes. The differences in spectral responses and sampling bandwidths brought different reflectance curves in Figure 2(a-c). To normalize the differences, this paper modified the lunar photometric models using the spectral response functions of each spectrum of GF-4 VNIR camera. The modified equivalent surface reflectance model is computed as:

$${\rho }_i=\frac{\underset{{\lambda }_1}{\overset{{\lambda }_2}{\int }}{S}_i\left(\lambda \right)\cdot {\rho }_{\mathrm{r}}\left(\lambda \right)d\lambda }{\underset{{\lambda }_1}{\overset{{\lambda }_2}{\int }}{S}_i\left(\lambda \right)d\lambda }$$ (1)

Where ${\rho }_{\mathrm{r}}\left(\lambda \right)$ is the reflectance model of lunar with the wavelength of λ, $S_i\left(\lambda \right)$ is the normalized spectral response function of spectrum i of GF-4 VNIR camera, and ${\rho }_i$ is the equivalent surface reflectance of spectrum i of GF-4 VNIR camera, λ₁ and λ₂ are the beginning and ending wavelengths for spectrum i. Based on Eq. (1), the equivalent surface reflectance in three lunar sites of SP, IIM, and M3 were given in Table 1.

Table 1.

The equivalent surface reflectance of SP, IIM and M3.

Models	520–590nm	630–690nm	770–890nm
MS-2 site
SP	0.038048	0.047368	0.055852
IIM	0.033737	0.03934	0.046395
M3	0.034689	0.041252	0.04623
Apollo-16 site
SP	0.074333	0.092111	0.110232
IIM	0.062586	0.073529	0.086398
M3	0.063699	0.076269	0.091415
CE-3 site
SP	0.026833	0.031131	0.035680
IIM	0.034002	0.038744	0.045010
M3	0.044155	0.054222	0.061262

3.2. Radiometric calibration

Radiometric calibration is to convert the gray-scale of image to the received radiance of the optical camera. For the earth-observing sensors, the relation between the digital expression of image and physical expression of radiance are linear [29]. Using the $L_i^{\ast }$ as the standard reference radiance, the absolute radiometric calibration model was given in Eq. (2).

$$L_i^{\ast }=k_i\cdot D_i+b_i$$ (2)

Where $D_i$ is the gray-scale of image, $k_i$ and $b_i$ are the radiometric calibration coefficients.

In this study, The 30° lunar phase image captured by GF-4 (on July 25,2018) was used to keep the same phase angle with the reference site models in Figure 2 (a–c). We employed a basic radiometric model [30] of lunar as follows:

$$Re{f}_i=\frac{\pi \cdot L_i\cdot d^2}{{\mu }_s{E}_i}$$ (3)

Where $Re{f}_i$ is the equivalent surface reflectance of spectrum i of GF-4 VNIR camera, $L_i$ is radiance of spectrum i, d is the sun to moon distance factor (the ratio of actual sun-lunar distance to the standard sun-lunar distance (149,597,870km)) and computed by Eq. (4), $E_i$ is the modified solar irradiance of band i of GF-4 and expressed as:

$$D=\frac{297.8502042+445267.115168\cdot T-0.00163\cdot T^2+T^3/545868-T^4/113065}{149597870}$$ (4)

$$E_i=\frac{\int S_i\left(\lambda \right)\cdot E_0\left(\lambda \right)d\lambda }{\int S_i\left(\lambda \right)d\lambda }$$ (5)

In Eq. (4), Where T is the Julian date. In Eq. (5), where $E_0\left(\lambda \right)$ is the standard solar irradiance.

The lunar images of 520–590nm, 630–690nm and 770–890nm spectral bands acquired by GF-4 VNIR camera showed in Figure 3(a-c). The pixel coordinates of MS-2, Apollo-16 and CE-3 lunar sites located after geometric calibrating of camera, and schemes are given in Figure 4(a-c).

Figure 3.

Lunar mages acquired by GF-4 VNIR camera. (a) 520–590nm; (b) 630–690nm; (c) 770–790nm.

Figure 4.

Schemes of three sites on lunar surface (red mark represented the location of site). (a) MS-2 site; (b) Apollo-16 site; (c) CE-3 site.

The gray-scale values (DN) of three sites with different exposure time of GF-4 VNIR camera were given in Tables 2, 3, 4.

Table 2.

Gray-scale values (DN) of MS-2 site.

Band/nm	Exposure time
520–590	16ms	20ms	30ms
	65	75	97
630–690	12ms	20ms	30ms
	68	103	153
770–890	16ms	20ms	30ms
	67	85	125

Table 3.

Gray-scale values (DN) of CE-3 site.

Band/nm	Exposure time
520–590	16ms	20ms	30ms
	65	69	83
630–690	12ms	20ms	30ms
	61	79	115
770–890	16ms	20ms	30ms
	61	69	96

Table 4.

Gray-scale values (DN) of Apollo-16 site.

Band/nm	Exposure time
520–590	16ms	20ms	30ms
	76	93	129
630–690	12ms	20ms	30ms
	103	175	258
770–890	16ms	20ms	30ms
	112	144	219

In Table 1, the reflectance of three lunar sites is at the low side of the dynamic range for earth-observing camera. The radiometric calibration experiments in lab and on orbit indicated that the radiometric responding linearity of GF-4 VNIR camera was above 0.9998 [31] from DN of 9–1020, thus this study adopted the linear fitting algorithm to fit the relation of radiance and image gray-scale according to Eq. (2). The measured radiances of three lunar sites were computed by Eqs. (3), (4), and (5), and the image gray-scales were picked from lunar images, here are the linear fitting curves of each site in Figure 5(a–i).

Figure 5.

Linear fitting curves of green, red and near infrared band with different exposure times. (a) 12ms exposure time of green band; (b) 20ms exposure time of green band; (c) 12ms exposure time of green band; (d) 16ms exposure time of red band; (e) 20ms exposure time of green band; (f) 30ms exposure time of red band; (g) 16ms exposure time of near infrared band; (h) 20ms exposure time of near infrared band; (i) 30ms exposure time of near infrared band.

4. Results

Ground-based validation experiment is a common tool to verify the errors of radiometric calibration for earth-observing camera [32]. The top-of-atmosphere (TOA) radiance-based validation was used in this work. By comparing the radiance of specified objects after calibration in remote sensing image with TOA radiance transferred by in-situ measured reflectance of the same ground targets, the relative errors of calibration were derived [33].

4.1. Ground-based measuring process

The actual reflectance was obtained by ground-based or airborne spectral measuring instruments. This study conducted three ground-based experiments with three kind ground objects of different reflectance. Clean sea water was chosen as the lowest, wet sand on beach was the medium and dry grassland was the high reflectance sample. The flowchart of validation experiment is given in Figure 6.

Figure 6.

Flowchart for conducting validation experiment.

The ground-based validation sites are flat areas with almost the same spectral properties. In this study, dry grassland site is in Inner Mongolia, and wet sand site is in Beihai city and clean seawater site is in North Bay of China. GF-4 satellite image products are available on the website of China Centre for Resources Satellite Data and Application. Table 5 showed the details of three sites, and image sketches in GF-4 image are shown in Figure 7(a–c).

Table 5.

Details of ground-based validation experiment sites.

Tags	Detail information
Site type	High reflectance	Medium reflectance	Low reflectance site
Measuring time	Sep.10,2018	Mar.19, 2019	Mar.19, 2019
Site location	48.460N, 124.320E	21.450N,109.110E	21.000N,109.150E
Site climate	North temperate continental monsoon climate	Subtropical monsoon climate	Subtropical monsoon climate
Measuring area (km2)	1	1	100
Sampling interval(m)	50	50	500
Total sampling times	441	441	441

Figure 7.

Schemes of experimental sites in GF-4 images. (a) dry grass land; (b) wet sand; (c) clean sea-water.

The ASD HH2 spectrometer measured the spectral characteristics of ground objects. The GPS locator recorded the longitude, latitude and altitude information of each test point were recorded by GPS. The portable weather station measured wind speed and direction in the clean seawater site. The Microtops II photometer measured optical parameters of atmosphere, the aerosol optical thickness at 550nm wavelength (AOD@550nm) is computed by Langley method [34] based on the output channels of Microtops II, the water vapor content and O₃ content after averaging processing were got from output files. The Microtops II photometer record atmospheric data 80–100 times during each synchronous imaging period of GF-4 satellite in 30 min, the averaging value with outliers removed and deviation were given in Table 6.

Table 6.

Measurements of atmospheric and meteorological parameters.

Details	Site information
Tag	Inner Mongolia	Beihai	North Bay
AOD (@550nm)	0.1455	1.3249	1.6397
	Δ = –0.04∼+0.07	Δ = –0.06∼+0.08	Δ = –0.05∼+0.09
Water vapor content (g/cm2)	1.4140	3.1435	3.2516
	Δ = –0.11∼+0.13	Δ = –0.12∼+0.12	Δ = –0.09∼+0.10
O3 content (g/cm2)	0.375	0.322	0.319
	Δ = –0.02∼+0.03	Δ = –0.01∼+0.02	Δ = –0.01∼+0.02
Solar zenith angle (°)	50.61	22.45	22.31
Wind speed (m/s)	-----	-----	1.6–2.2 m/s
Wind direction	-----	-----	South-west

The ASD HH2 collected data of ground objects and diffuse reflector also. Based on transforming model given in the manual of ASD HH2, the reflectance of ground objects ${\rho }_{\mathrm{s}}^{\text{land}}\left(\lambda \right)$ was computed as Eq. (6).

$${\rho }_{\mathrm{s}}^{\text{land}}\left(\lambda \right)=\frac{v_{\mathrm{s}}\left(\lambda \right)}{v\left(\lambda \right)}\cdot \rho \left(\lambda \right)$$ (6)

Where $v_s\left(\lambda \right)$ and $v\left(\lambda \right)$ are the measuring radiance for ground objects and diffuse reflector by instrument, $\rho \left(\lambda \right)$ is the reference reflectance of diffuse reflector. And for clean sea water, the leave water reflectance was computed as Eq. (7) [35].

$${\rho }_{\mathrm{s}}^{\text{water}}\left(\lambda \right)=\rho \left(\lambda \right)\cdot \frac{v_{\mathrm{s}}^{\text{water}}\left(\lambda \right)-v_{\mathrm{s}}^{\text{sky}}\left(\lambda \right)\cdot 0.028}{v\left(\lambda \right)}$$ (7)

Where $v_{\mathrm{s}}^{\text{water}}\left(\lambda \right)$ is the instrument measuring radiance above water and $v_{\mathrm{s}}^{\text{sky}}\left(\lambda \right)$ is the measuring radiance of sky.

The TOA reflectance of specified targets was computed by radiation transfer model [36]. The radiation transfer model simulated the absorbing and scattering effects of atmosphere in the upward radiance transferring path and output the radiance over atmosphere. 6S radiation transfer model was used in this work, the inputting atmospheric and solar zenith parameters were given in Table 3. The TOA reflectance ${\rho }_{\lambda }^{\text{TOA}}$ transferred after 6S simulation was computed by Eq. (8) [37].

$${\rho }_{\lambda }^{\text{TOA}}=\left[{\rho }_{\lambda }^{\text{path}}+\frac{{\tau }_s\cdot {\rho }_{\lambda }^s\cdot {\tau }_v}{\left(1-{\rho }_{\lambda }^s\cdot S_{\lambda }\right)}\right]\cdot T_{\lambda }$$ (8)

Where ${\rho }_{\lambda }^{\text{path}}$ is the intrinsic reflectance of atmosphere, $S_{\lambda }$ and $T_{\lambda }$ are the semi-sphere albedo and transmittance of atmosphere, ${\tau }_s$ and ${\tau }_v$ are cosine of the solar incident and sensor viewing angle. The TOA radiance $L_{\lambda }^{\text{TOA}}$ is derived by Eq. (9).

$$L_{\lambda }^{\text{TOA}}=\frac{{\rho }_{\lambda }^{\text{TOA}}{E}_{\lambda }{\tau }_s}{\pi \cdot {\left(r/r_{\mathrm{o}}\right)}^2}$$ (9)

Where $E_{\lambda }$ is the solar spectral irradiance, r and r_o are the actual sun-earth distance and standard sun-earth distance. Multiplying and integrating the TOA radiance in Eq. (9) with the spectral response function of the GF-4 VNIR camera, the equivalent measured TOA radiance $L_i^{\text{TOA}}$ of each spectral band is given by Eq. (10).

$$L_i^{\text{TOA}}=\frac{\underset{{\lambda }_1}{\overset{{\lambda }_2}{\int }}{S}_i\left(\lambda \right)\cdot L_{\lambda }^{\text{TOA}}\left(\lambda \right)d\lambda }{\underset{{\lambda }_1}{\overset{{\lambda }_2}{\int }}{S}_i\left(\lambda \right)d\lambda }$$ (10)

Where i is the band id of GF-4 VNIR camera.

4.2. Relative error analyzing

This study compared the radiance of each validation experiment site in GF-4 image derived after radiometric calibration with the equivalent TOA radiance transferred by in-situ measured reflectance with ASD HH2. Image based radiance included radiometric calibration with SP, IIM and M3 lunar models, lab and on-orbit field-based calibration [38] results. The radiance datasets were given in Tables 7, 8, 9.

Table 7.

Radiance of Inner Mongolia site.

Band/nm	Radiance (W/m2/μm/sr)
	SP	IIM	M3	Lab	On-orbit	ASD HH2
520–590	70.3241	68.8085	61.9993	60.9171	70.2835	66.0130
630–690	73.3357	71.9134	73.1793	62.7426	73.0203	69.0950
770–890	110.0218	98.7906	97.8694	94.9582	98.2900	104.5990

Table 8.

Radiance of Beihai site.

Band/nm	Radiance (W/m2/μm/sr)
	SP	IIM	M3	Lab	On-orbit	ASD HH2
520–590	95.8036	94.5350	85.1678	82.3507	92.7870	90.2310
630–690	77.9549	70.4852	70.0197	65.4956	67.7248	73.7720
770–890	52.5168	46.9058	45.9650	43.6465	52.8075	49.7600

Table 9.

Radiance of North Bay site.

Band/nm	Radiance (W/m2/μm/sr)
	SP	IIM	M3	Lab	On-orbit	ASD HH2
520–590	67.7992	68.7002	67.9786	63.3392	67.7938	72.6490
630–690	45.5309	45.9092	45.5317	42.9468	45.1728	48.4960
770–890	21.4518	21.4086	24.3934	19.7110	21.1900	22.7950

Using the equivalent TOA radiance as the benchmark to verify the errors of lunar calibration results, the relative error between the retrieved radiance and the equivalent TOA radiance is obtained from Eq. (11).

$${\Delta }_i=\frac{\left|L_i^{\text{TOA}}-L_i^{\ast }\right|}{L_i^{\text{TOA}}}\times 100\%$$ (11)

The relative errors were shown in Tables 10, 11, 12.

Table 10.

Relative errors of Inner Mongolia site.

Band/nm	Relative errors
	SP	IIM	M3	Lab	On-orbit
520–590	6.53%	4.23%	-6.08%	-7.72%	6.47%
630–690	6.14%	4.08%	5.91%	-9.19%	5.68%
770–890	5.18%	-5.55%	-6.43%	-9.22%	-6.03%

Table 11.

Relative errors of Beihai site.

Band/nm	Relative errors
	SP	IIM	M3	Lab	On-orbit
520–590	6.18%	4.77%	-5.61%	-8.73%	2.83%
630–690	5.67%	-4.46%	-5.09%	-11.22%	-8.20%
770–890	5.54%	-5.74%	-7.63%	-12.29%	6.12%

Table 12.

Relative errors of North Bay site.

Band/nm	Relative errors
	SP	IIM	M3	Lab	On-orbit
520–590	-6.68%	-5.44%	-6.43%	-12.81%	-6.68%
630–690	-6.11%	-5.33%	-6.11%	-11.44%	-6.85%
770–890	-5.89%	-6.08%	7.01%	-13.53%	-7.04%

Relative errors of different radiometric calibration model showed that: (1) For the validation site of Inner Mongolia, the average relative errors of three bands were 5.95%, 4.62%, 6.14%, 8.71% and 6.06% for SP, IIM, M3, lab and on orbit calibration models, the lowest relative error was 4.08% with IIM for 630–690 band. (2) For the site of Beihai city, the average relative errors of three bands were 5.80%, 4.99%, 6.11%, 10.75% and 5.72% for SP, IIM, M3, lab and on orbit calibration models, the lowest relative error was 2.83% with on orbit model for 520–590 band. (3) For the site of North Bay, the average relative errors of three bands were 6.23%, 5.62%, 6.52%, 12.60% and 6.86% for SP, IIM, M3, lab and on orbit calibration models, the lowest relative error was 5.33% with IIM for 630–690 band. The IIM model had the lowest errors among three lunar models, lab and on-orbit models.

For the calibration relative errors by SP model, 520–590nm band had the maximal value and 770–890nm band had the minimal value. For results by IIM model, 770–890nm band had the maximal value and 630–690nm band had the minimal value. For results by M3 models, 630–690nm band had the maximal value and 770–890nm band had the minimal value. Taking consideration of the linear correlation coefficients R² in Figure 5 and the relatives errors in Tables 7, 8, 9, the higher R² brought lower calibration relative errors.

5. Conclusions

In this study, we used lunar reflectance models of SP, IIM and M3 as references to calibrate the earth-observing VNIR camera of GF-4 satellite. The lunar observation conducted about two years from Mar. 2018 to Apr. 2020. The radiometric calibration references were SP, IIM and M3 lunar reflectance models in 30°lunar phase. Radiometric calibration process was performed using 30° lunar phase angle to keep consistent with the referencing lunar models. Spectral modification and calibration coefficients fitting indicated showed the linearity of radiometric calibration model was between 84.53%–99.99%. The ground validation process has been carried out. Dry grass with high reflectance, wet sand with medium reflectance and clean seawater with low reflectance were chosen as validating samples. The relative errors between measured TOA radiance and derived radiance of GF-4 image after radiometric calibration using SP, IIM, M3 lunar models, lab and on orbit field-based models had been computed. The validation results showed that: (1) Calibration models with IIM lunar had the lowest relative errors than SP, M3, lab and on-orbit models, and SP model had the similar performance with on-orbit field-based model. (2)The ranges of relative errors were 5.18%–6.68% for SP model, 4.08%–6.08% for IIM model and 5.09%–7.63% for M3 model. (3) The higher the linear correlation coefficient R² of lunar-based radiometric calibration model brought lower relative errors in validation experiments. We are continuing on the radiometric calibration process using lunar as reference for earth-observing cameras, further study will focus on the effects of lunar phase varying for radiometric calibration. The study of VNIR camera supplies a reference method to the on-orbit radiometric performance of cameras with more detailed and wider spectrum.

Declarations

Author contribution statement

Wei Tan: Conceived and designed the experiment; Performed the experiments; Analyzed and interpreted the data; Wrote the paper.

Xiaoyan Wang: Performed the experiments; Contributed reagents, materials, analysis tools or data.

Hongyan He: Conceived and designed the experiments; Contributed reagents, materials, analysis tools or data.

Wenwen Qi: Performed the experiments; Analyzed and interpreted the data.

Funding statement

Mr. Wei Tan was supported by National Natural Science Foundation of China [42050202], National Key Technologies Research and Development Program of China [2018YFB0504801].

Data availability statement

Data will be made available on request.

Declaration of interest’s statement

The authors declare no conflict of interest.

Additional information

No additional information is available for this paper.

Appendix A. Supplementary data

The following is the supplementary data related to this article: