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Distributed Theory in Applications of Autonomous Vehicles
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Production and Calibration of a Lambertian Surface Based on Barium Sulfate (BaSO4) for the Calibration of Multispectral Cameras
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1
Department of Civil Engineering, Campus Apucarana-PR, Universidade Tecnológica Federal do Paraná, Apucarana 86812-460, Brazil
2
Department of Surveying, Campus Pato Branco-PR, Universidade Tecnológica Federal do Paraná, Pato Branco 85503-390, Brazil
3
Department of Cartographic Engineering, College of Science and Technology (FCT), Campus Presidente Prudente-SP, Universidade Estadual Paulista Júlio de Mesquita Filho, Presidente Prudente 19060-900, Brazil
4
College of Science, Technology and Education (FCTE), Campus Ourinhos-SP, Universidade Estadual Paulista Júlio de Mesquita Filho, Ourinhos 19903-302, Brazil
*
Authors to whom correspondence should be addressed.
Received: 26 April 2025 Accepted: 19 June 2025 Published: 26 June 2025
© 2025 The authors. This is an open access article under the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).
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Drones Veh. Auton.
2025,
2(3), 10012;
DOI: 10.70322/dav.2025.10012
ABSTRACT:
Drones, or unmanned
aerial vehicles (UAVs), are increasingly utilized across diverse fields such as
agriculture, environmental analysis, and engineering due to their ability to
capture high-quality multispectral imagery. To ensure the accuracy of these
images, radiometric calibration of onboard multispectral cameras is essential.
This study aimed to develop and calibrate a low-cost Lambertian surface using
barium sulfate (BaSO4) for radiometric calibration of UAV-mounted
multispectral cameras. A stainless steel mold was designed to compact BaSO4,
and the resulting surface was calibrated using an ASD FieldSpec HandHeld UV/NIR
spectroradiometer and a Spectralon plate as the reference standard. Results
showed a strong correlation (Pearson’s r = 0.9988) between the BaSO4 surface and the Spectralon plate, confirming that the BaSO4-based
surface is a cost-effective alternative for producing diffuse Lambertian
surfaces with performance comparable to the standard.
Keywords:
UAV; Multispectral; Surface;
Diffuse
1. Introduction
Since the late 1960s, Brazil has advanced remote sensing capabilities through the National Institute for Space Research (INPE), establishing infrastructure and training professionals to apply these techniques effectively [1]. Remote sensing enables non-contact data collection from the Earth’s surface by capturing reflected or emitted electromagnetic energy, which is transformed into actionable information about the target area. Applications include environmental monitoring, agriculture, and urban planning, among others.
Remote sensors, mounted on platforms such as aircraft, unmanned aerial vehicles (UAVs), or satellites, convert electromagnetic energy into signals that reveal insights about the study site. When electromagnetic energy interacts with surfaces, it may be reflected, absorbed, or transmitted, depending on the surface’s physical and chemical properties, the wavelength of the incident radiation, and the angle of incidence. These interactions produce unique spectral signatures for different materials (e.g., vegetation, soil, water), enabling their identification in multispectral imagery, as shown in Figure 1.
Therefore, accurate interpretation of multispectral images requires precise calibration of the cameras to ensure reliable data. Calibration involves using a Lambertian surface—A surface with ideal diffuse reflectance that exhibits uniform radiance regardless of viewing angle (Figure 2).
According to [4], typically, an integrating sphere coated with highly reflective materials like magnesium oxide, barium sulfate (BaSO4), or polytetrafluoroethylene (PTFE) is used to measure diffuse reflectance. Spectralon, a fluoropolymer with near-perfect diffuse reflectance (99%) and exceptional whiteness, is the standard material for such calibrations [5] but is costly.
As UAVs expand in popularity and application, the need for affordable and effective calibration methods grows. Multispectral camera calibration enhances image quality, reduces processing time, and improves integration with systems like Global Navigation Satellite Systems (GNSS), leading to greater efficiency and lower operational costs [6]. Recent comprehensive studies have also emphasized the critical role of radiometric calibration in ensuring data reliability for UAV-based remote sensing applications. For instance, ref. [7] provide practical guidance for environmental mapping using UAS, highlighting the fundamental importance of calibration surfaces to achieve consistent and trustworthy reflectance data under varying field conditions. However, existing calibration systems are often expensive or inaccessible, limiting their adoption.
Therefore, this study is of particular importance, given that the calibration of cameras on board drones is currently expensive or does not yet have an adequate system with affordable prices to ensure the best image acquisition, which would allow for accurate data on the object and/or phenomenon under study.
The main objective was to develop a low-cost Lambertian surface using BaSO4 for calibrating UAV-mounted multispectral cameras and validate its performance against a Spectralon plate, the industry standard for calibrating such cameras.
2. Materials and Methods
First, a stainless steel part was developed, a material resistant to oxidation, for compacting BaSO4, a low-cost chemical material, white in color and not harmful to health, which can be handled without the use of personal protective equipment (PPE). The design of the part, front and top view, is shown in Figure 3.
In Figure 4, you can see the machined stainless steel part, according to the design and dimensions shown in Figure 3.
The part was then filled with BaSO4 (Figure 5) up to the upper edge, later adjusted in the hydraulic-mechanical press (Figure 6a)—Belonging to the Concrete Laboratory of the Federal Technological University of Paraná—Pato Branco Campus. After adjusting the stainless steel part in the press (Figure 6b), a pressure of 100 tons-force (tf) was applied (Figure 6c) for compaction, equivalent to 124,861.676 N/mm2. The tests carried out proved that this was the pressure considered ideal since the compacted material did not present cracks or superficial fissures, which is important for the homogenization of the BaSO4 in the stainless steel part.
The surface of the compacted BaSO4 presented irregularities due to the removal of the upper part of the part (Figure 7). Sandpaper with grits 2000 and 3000 was used to remove these imperfections in order to obtain a homogeneous finish free from compression marks (Figure 8) in the hydraulic press, which could interfere with the final texture of the Lambertian surface.
The next step was the calibration of the compressed BaSO4, using the ASD FieldSpec HandHeld UV/NIR spectroradiometer and the Labsphere Spectralon plate (25 × 25) cm (Figure 9), both belonging to the Sensor Integration Laboratory of the Department of Certography of the Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP)—Presidente Prudente Campus, state of São Paulo, Brazil.
The calibration was performed in a dark room whose entire interior was painted matte black so that there would be no reflection of the light source in the environment nor interference from external light, with only one light source falling on the Spectralon plate (Figure 10), which was maintained throughout the process with the same intensity and angle, in order to provide results under the same conditions for the objects used in the experiment. In addition, care was taken not to remain close to the equipment since reflective surfaces could interfere with the spectroradiometer reading process. This equipment provides results in the electromagnetic spectrum range (Figure 11) between wavelengths 325 to 1075 nm, that is, from ultraviolet to near infrared.
The spectroradiometer, with a 1º IFOV (Instantaneous Field of View) lens on the Spectralon plate and BaSO4, was configured using the Malvern Panalytical RS3 software to perform 10 reading sessions, capturing the reflectance for each wavelength. First, the readings were performed on the Spectralon plate (Figure 9), which was adopted as the standard for the other observations, and then on the BaSO4 compressed in the stainless steel piece (Figure 12).
After the observations were performed, the data obtained were transferred to the computer using the ASD Viewspec Pro software, version 6.2. The raw data were corrected using equations to calculate the elements needed to obtain the corrected reading values for the Spectralon plate and BaSO4. For this step, the data were tabulated in a spreadsheet, and the averages between the 10 reading sessions for each wavelength were calculated. Next, the reflectance correction factors were calculated for each average between the Spectralon plate and BaSO4 (Equation (1)), adapted from [10]:
where:
Fc—correction factor;
MS—average between Spectralon readings for each wavelength;
Mp—average between barium sulfate readings for each wavelength.
Therefore, to obtain the corrected readings of the observed electromagnetic spectrum (325 to 1075 nm) for BaSO4, Equation (2) [10] is adopted:
where:
C—corrected reading for the wavelengths obtained for BaSO4.
To calculate the reflectance (R), Equation (3) is used.
where:
FCMP—correction factor of the averages between the BaSO4 readings.
Figure 3. Stainless steel part design—Millimeter units.
Figure 4. Machined stainless steel part.
Figure 5. Stainless steel part filled with BaSO<sub>4</sub>.
Figure 6. (<b>a</b>) Adjustment of the part in the hydraulic press. (<b>b</b>). Stainless steel part adjusted in the hydraulic press. (<b>c</b>) Pressure of 100 tf for compacting BaSO<sub>4</sub>.
Figure 7. Irregularities on the surface of compacted BaSO<sub>4</sub>.
Figure 8. Irregularities on the BaSO<sub>4</sub> surface removed with 2000 and 3000 grit water sandpaper.
Figure 10. Light source on the Spectralon plate.
Figure 12. Spectroradiometer making observations on BaSO<sub>4</sub>.
```latex \mathrm{Fc}=\frac{\mathrm{M_S}}{\mathrm{M_P}} ```
```latex \mathrm{C=M_P\cdot F_C}```
```latex \mathrm{R}=\frac{\mathrm{F}_{\mathrm{CMP}}}{\mathrm{M}_{\mathrm{S}}}```
3. Results and Discussions
Since the tabulated wavelengths are listed every 1 nm, it is impossible to reproduce the data in full since they total 752 lines of the spreadsheet. Therefore, a partial reproduction of these data is made every 50 nm. Table 1 presents the means and respective standard deviations for the dimensionless reflectance factors of the Spectralon plate and BaSO4, as a function of the wavelengths, in the range of 350 to 1050 nm.
From the data in Table 1, the graph shown in Figure 13 was obtained.
Although the corrections for the reflectance factors have not yet been applied, Figure 13 shows a direct relationship between the Spectralon and BaSO4 graphs, with a value of 0.9988 for Pearson’s correlation, i.e., a strong linear relationship, according to [11]. It is also possible to infer from the data, reproduced in part in Table 1 and observed in Figure 13, that the maximum difference between these is 0.00071 and the minimum is −0.000004, which, due to its magnitude, ends up corroborating the correlation above.
By applying Equation (3), it is possible to calculate the R-value of BaSO4, even without correction, in order to compare it with the R of the Spectralon plate, whose value is 1 (Figure 14).
Since the Spectralon plate is the standard for obtaining R, there is a correlation of 0.9620 between the reflectances of these two elements, that is, a strong linear relationship, according to [11], which was expected, given that Figure 13 already demonstrated this trend.
Therefore, in order to have a perfect relationship between these elements, the corrections for the reflectance factors of BaSO4 were calculated, given by Equations (1) and (2), presented in Table 2.
Equation (1) provides the values for the CFs, while Equation (2) allows the calculation of the corrected reflectance factors for BaSO4. After that, these factors were compared with those of the Spectralon plate (Table 3) in order to verify the possibility of BaSO4 being adopted as a Lambertian surface.
The differences observed in Table 3 indicate that BaSO4 can be used as a Lambertian surface, as it presents results identical to the Spectralon plate, as shown in Figure 15.
The overlap of the graphs of Spectralon and corrected BaSO4 demonstrate the perfect agreement between their reflectance factors, corroborating what was stated in the previous paragraph.
In turn, Figure 16 shows the graphs of the reflectances of Spectralon and BaSO4, which, as previously stated, were expected to overlap with R equal to 1 since there is a strong linear correlation between them.
Table 1. Reflectance factors for wavelengths.
| Wavelength (nm) | Averages of Reflectance Factors | Standard Deviations * | ||
|---|---|---|---|---|
| Spectralon | BaSO4 | σS | σB | |
| 350 | 0.000010483 | 0.000005812 | ±0.001148534 | ±0.000862482 |
| 400 | 0.000066462 | 0.000036626 | ||
| 450 | 0.000185969 | 0.000107591 | ||
| 500 | 0.000396167 | 0.000242135 | ||
| 550 | 0.000693409 | 0.000440373 | ||
| 600 | 0.001047372 | 0.000692338 | ||
| 650 | 0.001402429 | 0.000953264 | ||
| 700 | 0.001761664 | 0.001229098 | ||
| 800 | 0.002357676 | 0.001707109 | ||
| 850 | 0.002543110 | 0.001867201 | ||
| 900 | 0.002807288 | 0.002088002 | ||
| 950 | 0.003055473 | 0.002301816 | ||
| 1000 | 0.003174858 | 0.002403606 | ||
| 1050 | 0.003232645 | 0.002510302 | ||
* Standard deviations: σS—Spectralon; σB—BaSO4.
Figure 13. Averages of the reflectance factors of Spectralon and BaSO<sub>4</sub> as a function of wavelengths.
Figure 14. Reflectance of Spectralon and BaSO<sub>4</sub> plate—Without correction—as a function of wavelengths.
Table 2. Corrections for the reflectance factors of BaSO4.
| Wavelength (nm) | BaSO4 | Correction Factors (FC) | BaSO4 |
|---|---|---|---|
| (No Correction) | (Corrected) | ||
| 350 | 0.000005812 | 1.803586628 | 0.000010483 |
| 400 | 0.000036626 | 1.814606393 | 0.000066462 |
| 450 | 0.000107591 | 1.728482347 | 0.000185969 |
| 500 | 0.000242135 | 1.636141962 | 0.000396167 |
| 550 | 0.000440373 | 1.57459658 | 0.000693409 |
| 600 | 0.000692338 | 1.512804132 | 0.001047372 |
| 650 | 0.000953264 | 1.471186638 | 0.001402429 |
| 700 | 0.001229098 | 1.433298616 | 0.001761664 |
| 800 | 0.001707109 | 1.40446804 | 0.002122530 |
| 850 | 0.001867201 | 1.381092323 | 0.002357676 |
| 900 | 0.002088002 | 1.361990888 | 0.002543110 |
| 950 | 0.002301816 | 1.344485405 | 0.002807288 |
| 1000 | 0.002403606 | 1.327418407 | 0.003055473 |
| 1050 | 0.002510302 | 0.002510302 | 0.003174858 |
Table 3. Comparison between reflectance factors of Spectralon and BaSO4.
| Wavelength (nm) | Spectralon | BaSO4 (Corrected) |
Differences |
|---|---|---|---|
| 350 | 0.000010483 | 0.000010483 | 0.000000000 |
| 400 | 0.000066462 | 0.000066462 | 0.000000000 |
| 450 | 0.000185969 | 0.000185969 | 0.000000000 |
| 500 | 0.000396167 | 0.000396167 | 0.000000000 |
| 550 | 0.000693409 | 0.000693409 | 0.000000000 |
| 600 | 0.001047372 | 0.001047372 | 0.000000000 |
| 650 | 0.001402429 | 0.001402429 | 0.000000000 |
| 700 | 0.001761664 | 0.001761664 | 0.000000000 |
| 800 | 0.002122530 | 0.002122530 | 0.000000000 |
| 850 | 0.002357676 | 0.002357676 | 0.000000000 |
| 900 | 0.002543110 | 0.002543110 | 0.000000000 |
| 950 | 0.002807288 | 0.002807288 | 0.000000000 |
| 1000 | 0.003055473 | 0.003055473 | 0.000000000 |
| 1050 | 0.003174858 | 0.003174858 | 0.000000000 |
Figure 15. Reflectance factors of Spectralon and corrected BaSO<sub>4</sub>.
Figure 16. Reflectance of the Spectralon and BaSO<sub>4</sub> plate—corrected—as a function of wavelengths.
4. Conclusions
The development and calibration of a low-cost Lambertian surface using barium sulfate (BaSO4) demonstrated performance comparable to the industry-standard Spectralon plate, with a Pearson’s correlation of 0.9988. This BaSO4-based surface offers an economically viable alternative for radiometric calibration of multispectral cameras mounted on unmanned aerial vehicles (UAVs), enabling high-quality image acquisition at reduced costs.
To further validate the BaSO4 surface, additional testing with diverse multispectral sensors under varied field conditions is recommended. Such studies will confirm its reliability across real-world applications and environmental settings, potentially broadening its adoption in remote sensing workflows.
Furthermore, the approach developed in this study can be adapted for the calibration of different types of optical sensors, including hyperspectral cameras and portable field spectrometers, provided that the spectral and geometric specifications of each device are considered. Likewise, its application under varying operational conditions—such as changes in natural lighting, ambient temperature, or relative humidity—should be evaluated in future investigations to validate the stability and robustness of the BaSO4 surface in realistic data acquisition scenarios.
Acknowledgements
To my colleague Gabriela Zanchetta, a PhD student in the Postgraduate Course in Cartographic Sciences at UNESP —Presidente Prudente, for her support and guidance in using the ASD FieldSpec HandHeld UV/NIR spectroradiometer and Spectralon plate. To Fábio Larini, owner of the company WD Tron, for his support in the project. To the Brazilian Center for UAVs for Aerolifting—NUBRAVA, for his support of the project.
Author Contributions
Conceptualization and Writing, D.C.G.; Methodology and Supervision, A.R.E.; Software, F.S.Y.W.; Review, H.d.S.F., E.L.P.
Ethics Statement
Not applicable.
Informed Consent Statement
Not applicable.
Data Availability Statement
The data supporting the findings of this study are available from upon reasonable request.
Funding
This research received no external funding.
Competing Interest Statement
AI Usage Statement
During the preparation of this work, the authors used ChatGPT-4 to improve readability and language. After using this tool/service, the authors reviewed and edited the content as necessary and assume full responsibility for the content of the publication.
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