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Abstract
The extinction coefficient of oil films on the sea surface was inversion using a physical model based on two-beam interference and the equal-thickness difference method. The coefficient is simplified to a quadratic equation in one variable related to oil-film thickness and incident angle and wavelength of light. Through a laboratory-simulated oil spill experiment, the reflectivities of oil films of different thicknesses were obtained. The extinction coefficients of the oil film under visible light were inversion. The model considered the light beam on the oil-film surface and effects of scattering properties and photon attenuation of the oil film on spectral reflectance.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
Corrections
Zhenduo Zhang, Wei Li, Zhanjun Ma, Shuang Dong, Ming Xie, and Ying Li, "Oil-film extinction coefficient inversion based on thickness difference: erratum," Opt. Express 32, 6700-6700 (2024)https://opg.optica.org/oe/abstract.cfm?uri=oe-32-4-6700
1. Introduction
With the development of shipping and freight transportation, the shipping industry occupies an increasing proportion of transportation, resulting in an increase in the number of ships sailing at sea. However, in recent years, there have been many large and medium-scale oil spill accidents around the world which have caused serious damage to marine ecology and marine economy [1]. At present, most marine monitoring centers at home and abroad use optical remote sensing technology to detect and identify oil spill areas and types of oil spills on the sea surface. The research on oil spill monitoring using traditional optical remote sensing methods has achieved some practical results, mainly using the spectral data of oil films to identify different types of oil spills on the sea surface form oil films. However, the oil film formed by the oil spill on the sea surface is often a mixture of various types of oil. The method we propose has the potential to identify multiple oil mixtures. Therefore, we conducted a preliminary study on this issue. In the future, our research hopes to unmix and identify different components of mixed oil by extinction coefficient according to the absorption characteristics of different oils. The key to solving related oil spill events is to be able to effectively identify and detect oil spill areas. The study of the extinction coefficient of the oil film formed by different oil species is to prepare for the optical remote sensing to identify different types of oil spills on the sea surface [2,3].
At present, research on optical constants in the infrared range, such as extinction coefficient, mainly focuses on dielectrics, semiconductors, and other solids and oils; however, oils use in the shipping industry have not been considered in such works. [4–7]. Methods to determine the extinction coefficient of oil include using a standard spectrophotometer to measure the ultraviolet extinction coefficient of oil [8], using an ellipsometer to inversion and using a laser to measure the extinction coefficient of the oil [9,10]. Research on the extinction coefficient of oil using a laser mainly targeted crude oil, and the experimental values can cause a deviation in the extinction coefficient because of the measurement of additional unwanted fluorescence. In traditional ellipsometry [11,12], the optical properties of a thin film are obtained through an extremely complicated solution spectrum calculation, which involves very complex trigonometric function calculations, and the nonlinearity and non-positive definiteness of solving equations increase the difficulty of numerical calculation. Therefore, the calculation of dielectric film parameters from ellipsometry parameters has become an important issue in the application of spectroscopic ellipsometry. Lu et al. [13] studied the extinction coefficient of oil and regarded the uniformly distributed oil film as a parallel plate. The radiative transmission process of the oil film to the incident light was analyzed to establish a quantitative inversion model of oil-film thickness by remote sensing based on the two-beam interference at the oil film. The relationship between the oil-film reflectivity and wavelength for different oil-film thicknesses was experimentally obtained, and the relation ${A_2} = 2a/cos\theta $ was obtained for wavelengths of 400–750 nm; here A2is a parameter; A2gradually decreases as wavelength increases; here a is the extinction coefficient. Li et al. [6] proposed an optical cell based on two glass plates and a liquid sample layer. The optical constants of liquid hydrocarbon fuels were experimentally determined [14,15]. Ogusu et al. [16] use of the Brewster angle for measuring the refractive index and the absorption coefficient of an absorbing parallel plate.
In this study, a physical model based on two-beam interference in multilayer media was proposed to calculate the extinction coefficient of oil films under visible light. The the reflectance spectrum [17,18] of oil films of different thicknesses was obtained through a laboratory-simulated oil spill experiment, and the extinction coefficients were inversion by the equal-thickness difference method, which is more convenient to calculate than spectroscopic ellipsometry. This model also considers the effects of the scattering characteristics of the light beam on the oil-film surface and the influence of the photon attenuation in the oil film on the spectral reflectance, Thus, it closely reproduces the actual situation. The extinction coefficient calculation method proposed in this paper provides a new method for the identification of offshore oil films.
2. Theoretical basis
The complex refractive index of crude oils is an essential parameter for the study of radiative properties, which has important and wide applications in remote sensing analysis and identification of oil pollution [19]. The extinction coefficient studied in this paper is actually the imaginary part of the complex refractive index.
An offshore oil film forms a three-layer medium of air–oil film–seawater (Fig. 1). According to the basic principle of the electromagnetic wave passing through a three-layer medium, the electromagnetic wave brightness of the oil film should change periodically with the increase in the film thickness. By using the multi-frequency electromagnetic wave measurement method, we can detect oil films on the sea surface and also measure the thickness of the sea surface [20]. The refractive indices of the three media are obviously different, and the incident light will be refracted and reflected in the oil-film layer. Therefore, the oil-film layer on the water surface can be regarded as a uniform parallel plate with air as the top layer (refractive index: n1), oil film as the middle layer (refractive index: n2and thickness: d), and seawater as the bottom layer (refractive index: n3). Light passes from the air layer to the oil film layer. The atomic luminescence duration of the incident light is very short, and the correlation between the light at different times is low, that is, the coherence length is extremely short. Then, the parallel plate interference of the incident light can be simplified as two-beam interference [21,22].
Suppose the electric field strength of the incident light is $\overrightarrow {{E_0}} .$ When the incident light enters the oil-film layer from the air layer, the transmittance of the upper surface of the oil film is t12 and reflectivity is r12. Then, f the reflectivity of the interface between the lower surface of the oil slick and the sea water is r23.
The transmitted light in the oil-film layer is reflected by the lower surface of the oil film and then transmitted from the upper surface of the oil-film layer into the air with transmittance t21. The electric vector intensity of the first reflection of the incident light on the upper surface of the oil film is E1=r12E0. The photoelectric vector intensity of the first transmission into the oil film is t12E0, and the electric vector intensity of the transmitted light in the oil-film layer after reflection at the lower surface of the oil film is t12r23E0. The light transmitted through the oil-film layer is reflected by the lower surface of the oil film and then transmitted to the air layer through the upper surface of the oil film. Its electric vector strength is E2. Considering that the propagation paths of E1 and E2 differ by length Δ, there is a phase delay kΔ between the two beams. The extinction coefficient of the light beam during propagation in the oil-film layer is α, and the light beam reflected at the lower surface of the oil film and reflected back to the air travels through the oil film with a path length of S. Then, the transmitted photoelectric vector intensity is E2=t12r23t21eikΔ-as The parallel plate interference involves reflected light E1 and the light passing through the oil film and back into the air layer E2. The electric vectors of the two are superimposed to produce two-beam interference. On the focal plane of the detector, the superposition of E1 and E2 produces interference. The electric power entering the remote sensor system is E = E1+E2.
Then, the oil-film reflectivity R can be calculated as follows [13]:
In the equation, θ is the angle between the transmitted light and the vertical line of the oil film; d is the measured oil-film thickness; λ is the wavelength of the incident light.
3. Methodology
3.1 Establishment of extinction coefficient solving model
The extinction coefficient can be inversion based on the two-beam interference model of the multilayer medium, but this calculation directly involves the refractive indices and transmittances of different interfaces. Light undergoes multiple reflections and refractions at the interfaces, and hence, the measurement error increases drastically as the difference in the refractive indices between the adjacent media at these interfaces increases [23]. Therefore, we propose the equal-thickness difference method for calculation. We selected three thicknesses of oil film (d1, d2, andd3) corresponding to three reflectivities (R1, R2, andR3, respectively). We assumed that d1<d2<d3 and d2−d1=d3−d2=D. The difference between the diesel oil films of different thicknesses corresponding to Eq. (1) was compared in pairs. The refractive index and transmittance can be eliminated because they remain the same for the same oil film. The calculation of the extinction coefficient can be simplified as It is only related to the incident light angle and wavelength, which greatly simplifies the calculation process [24].Using Eq. (1), we get the following:
The phase delays corresponding to the three oil films are kΔ1, kΔ2 and kΔ3, and they can be simplified as follows:We studied the derived model and found that the accuracy of the inversion extinction coefficient is related to the experimental data used. Therefore, when using experimental data to obtain the results, the inversion results will be more accurate using the data in which the reflectance decreases with an increase in the thickness of the oil film.
3.2 Experiment instruments
The radiance of different types of oil films were experimentally obtained to verify the accuracy of the algorithm used in this study. The collection of experimental data were carried out in a dark room to eliminate the interference of external background light on the optical measurement of oil slicks on the sea surface as much as possible. In this experiment, an arched support (zenith arc support) (Fig. 2(a)) with a radius of 2.3 m was set up to measure the intensity of incident light and reflected light, and a square water basin was used to add seawater to simulate the sea surface. The sample oil container was completely wrapped with black tape to reduce the interference factor of the reflected light beams at the bottom of the pool and around it. Using a pipette, we added a certain amount of the sample oil and let it stand to form an oil film of uniform thickness.
Fig. 2. Schematic diagram of the experimental device structure. (a) Overall experimental device structure; (b) high-sensitivity and high-resolution variable-focus push-broom hyperspectral sensor used in the experiment; (c) light source and collimated lens; (d) spectral storage computer.
In the experiment, the hyperspectral sensor was used to measure the oil film reflectance spectrum [25] using a push-broom type hyperspectral sensor with high sensitivity and high resolution (shown in Fig. 2), which was independently designed and assembled by the Institute of Environmental Information. This high-performance industrial and scientific camera is designed and manufactured to the highest quality standards and offers USB 3.1 Gen 1, USB 2.0 and Gigabit Ethernet interfaces. At the same time, the leading ExView HAD II technology is used to provide rich textures for hyperspectral cameras with high sensitivity and high-quality imaging. Force is a good choice for near-infrared (NIR) imaging. The latest USB 3.0 technology is used for the fastest image transfer at the best resolution of the hyperspectral sensor, and image capture can be synchronized using hardware or software triggers. The FPGA function supports an additional 128MB of onboard memory for frame buffering, ensuring reliable image transfer to overcome demanding machine vision systems. On the other hand, this instrument buffering technology delivers all frames at full speed and maximum resolution, overcoming latency issues to increase buffering rates.
A push-broom high-sensitivity and high-resolution variable focus hyperspectral sensor is used to measure the reflected light spectrum. The spectral range of this hyperspectral instrument is 392.00∼1162.67 nm, of which there are 1936 optical channels in total, the average spectral resolution is 0.35 nm, and the length of each sampling grating is 1456 pixels. The zenith angles of 6 groups of incident light and reflected light (15°, 30°, 45°, 60° and 75°) were measured for oil film samples with different configurations. Each zenith angle measurement was applied for 8 to 10 seconds with subsequent data processing. The exposure time was kept at 10 ms, that is, the measured frequency was 100 groups/second. A total of 800-1000 sets of hyperspectral data samples were obtained by measuring the spectrum at the same position of a set of angles, and a total of 1.5488×106∼1.936×106 sets of hyperspectral data samples were measured at different positions of a set of angles. we use a dark blue matte sea surface to simulate a clean and rough sea surface (Fig. 2) to minimize the influence of reflected light from the ground. The experimental setup is shown in Fig. 2.
In the laboratory, a semi-circular arc bracket that can flexibly and quickly adjust the light source and hyperspectral camera is built to adjust the angle of incident light. The bracket can ensure that the collimating mirror and the spectrometer are symmetrical about the normal and that the outgoing beam enters the spectrometer slit after being reflected by the liquid surface. The radius of the bow bracket to simulate the actual scene of satellite scanning sea surface is 2.3 ± 0.1 m. The oil sample container used in the experiment is a pure silicon glass jar with a size of 45×45×20 cm, which is insoluble in organic solvents. In order to simulate the depth of sea water more realistically, the inner wall of the glass jar is sprayed with black paint and the outer wall is sprayed with black paint. The container is wrapped with black cloth and covered with dark blue sponge to simulate a large area of the real sea surface and to eliminate the interference of other stray light from the external environment as much as possible.
The 7ILX150A xenon light source selected as the light source has a power of 150W as shown in Fig. 2(c), which can meet the required light intensity. Because the light source is large in size and belongs to precision equipment, it cannot be directly fixed on the bow bracket, and the light emitted is horn-shaped. outspread. Therefore, in order to transmit the incident light in a collimated manner, the GCX-L type collimating lens is selected as shown in Fig. 2(c). The lens has a spot diameter of 11 mm, a focal length of 40 mm, and a divergence angle of 0.8°.
3.3 Experiment design
In order to achieve the real simulation effect of marine oil spill and eliminate the interference of stray light from the external environment, the spectrum acquisition environment is carried out in a dark room water tank. First, an appropriate amount of seawater is filled in the glass tank, in order to ensure that the dripping oil film can follow the same thickness value. Increase, assuming that the side length of the glass tank is D, then the cross-sectional area, according to the thickness of the oil film that needs to be increased each time, the volume that needs to be dripped can be known, and the volume of oil required can be set by a pipette The scale value is accurately inhaled, and then dripped onto the surface of the seawater, and an oil film of a certain thickness can be formed after uniform diffusion.
Because we use a graduated dropper to drop the oil sample onto the water, the thickness of the oil sample is calculated from the ratio of the volume of oil to the surface area of the water in the square basin. We heat the oil sample to be used in the test to reduce its viscosity before the test. The amount of oil is measured by reducing the volume in the dropper using the scale on the dropper. Because the water surface area in the square glass tank is known. The thickness of the oil film can be known by knowing the volume of the oil sample dropped into it. Drop the oil sample on the water surface to form a stable oil film before measuring. In addition, the pipette used in the test has already extracted diesel oil in advance before the start of the test. And the test is repeated three times to reduce the influence of the oil sample on the inner wall of the pipette on the volume of the oil used in the test. Thereby reducing the oil film thickness error. During the oil film formation process, the oil sample is blown on the water surface with a fan, so that the oil sample is distributed as evenly as possible on the water surface. Leave the oil film to sit overnight after blowing to ensure the thickness is as uniform as possible. After standing overnight, we believe that the slight unevenness of the oil film thickness has little effect on the experimental results and is within the acceptable range. The slight effect of slight unevenness in oil film thickness will be investigated in a future study.
The experimental operation steps are as follows:
- (1) First, turn on the light source and preheat for 10-15 minutes. At this time, a circular light spot will appear on the surface of the glass tank. The reflectance spectrum at different incident angles can be measured by adjusting the spectrometer and lens on the bow bracket.
- (2) We measure the reflected light intensity data of a group of seawater at different angles as a control before the experiment starts. Then operate the pipette to accurately absorb the oil according to the pre-calculated oil film thickness value to obtain the thickness according to the above formula. Oil films are 100, 300 and 500 microns. Data collection was performed after the oil film spread evenly. The acquisition interval was 5-8 seconds. This process is repeated 8-10 times.
- (3) After a set of experiments, the oil film in the glass jar was collected for harmless treatment. And clean the glass jar. After the glass cylinder is dry, change a set of oil samples and repeat the above operation.
- (4) Finally, the reflectance spectra of a set of aluminum standard reflectors with known reflectance at different angles were measured to calculate the reflectance of the oil film.
4. Ellipsometer annealing algorithm
4.1 Ellipsometry principle ellipsometry
The main test tool of an ellipsometer is the ellipsometer measurement. It has the advantages of zero contact, high sensitivity, and no damage. It is widely used in the fields of physics, chemistry, materials science and microelectronics. It is an extremely important optical measurement method [12]. The ellipsometer [26] is shown in Fig. 3.
The polarization state of any light wave can be represented by two characteristic parameters, amplitude ratio and phase difference. They are a function of the characteristic parameters of the film being tested. Therefore, in order to calculate the optical constants of thin films, the polarization state of elliptically polarized light must be measured first, which is the basic principle of ellipsometry to measure the optical constants of thin films. As shown in Fig. 4.
4.2 Annealing algorithm to process ellipsometry data
A prerequisite for obtaining equilibrium at each temperature is that the number of iterations of the evaluation function is set as expected. In the simulated annealing process, the premise of obtaining the minimum value of the evaluation function is that the temperature change can satisfy the convergence of the evaluation function until it does not change. The values of the model parameters are output and corresponding to the convergence results, the solutions of the film parameters are obtained. The algorithm flow is shown in Fig. 5.
The extinction oil film coefficient calculated by ellipsometer annealing is shown in Fig. 6.
Fig. 6. Extinction coefficient distribution of diesel oil obtained calculated by ellipsometry after fitting.
5. Results and discussions
5.1 Measurement of reflectivity
Through the theory of the two-beam interference model proposed in the second part section 2 above, this section will measure the reflectance data of diesel oil films with three thicknesses (100 microns, 300 microns and 500 microns) based on experiments. The extinction coefficient of diesel oil film can be calculated with formula 8 using the thickness difference. The distribution of the measured extinction coefficients of the final oil film is as follows:
The extinction coefficient distribution diagram shown in Fig. 7 is the diesel extinction coefficient calculated by this model. The wavelengths and their corresponding extinction coefficient distributions are relatively continuous. It can be seen from the figure that the distribution of some numerical points in the wavelength range of 400–500 nm is discontinuous. This is because during the experiment, due to the influence of various factors, we deleted the numerical points with large fluctuations in the final calculated extinction coefficient value. To more intuitively see the trend of our calculated extinction coefficients with wavelength and to reduce errors, we performed a 6th degree polynomial fit to the obtained data. Overall, the distribution trend of extinction coefficient with wavelength is roughly consistent with the distribution trend of extinction coefficient obtained by ellipsometer annealing and the measured value of extinction coefficient is also very close to the value obtained by ellipsometer annealing.
Fig. 7. The distribution of extinction coefficient measured by the oil film formed by diesel oil under the condition of light incident angle of 60°.
5.2 Comparisons between the model calculation and the measured data
To test the fitting accuracy of the experimental data after fitting the obtained extinction coefficient, we obtained the root-mean-squared error S1 between the fitted curve and data points and the fitted root-mean-squared error S2 between the curve and the true values. We denote the value of the extinction coefficient corresponding to the wavelength i on the fitting curve as yi and that of the experimental data point calculated by this model as yt_i; y is the reference value of the extinction coefficient inversion by ellipsometry.
The root-mean-square-error between the fitted curve and the original value are listed in Table 1.
Table 1. Root-mean-square-error between fitted curve and original value
It can be seen from tab.1 that the data fitting accuracy calculated by this model is relatively high. The error between the fitted curve obtained by ellipsometry annealing and the fitted curve of the extinction coefficient is also small. It shows that the value of extinction coefficient calculated by us is relatively accurate. The extinction coefficients corresponding to different wavelengths are not completely consistent with the real values which may be due to the influence of external noise during the experiment and the uneven distribution of the oil film.
6. Conclusion
From the experiments and error analysis, it is proven that the calculation of the extinction coefficient of the oil film on the sea surface by the equal-thickness difference method based on the two-beam interference model is feasible. This method only needs measured values of the thickness of the oil film (d) and incident angle of light (θ) to determine the extinction coefficient of the oil film for different wavelengths of the incident light. In contrast, the ellipsometry method to obtain the extinction coefficient involves many complicated calculations. The proposed method greatly reduces the amount of calculation and provides relatively accurate calculation results. In this paper, we only study the extinction coefficient of diesel oil and we will study the extinction coefficient of more oil species in the future.
Funding
National Key Research and Development Program of China (2020YFE0201500); Liaoning Revitalization Talents Program (XLYC2001002); Fundamental Research Funds for the Central Universities (3132022149).
Acknowledgments
The authors gratefully acknowledge refractive index test data from Changchun Institute of Optics and Fine Mechanics
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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