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This paper reports the reflective features of a water surface covered with an oil film expressed by the dependence of the reflectance on the angle of light incidence and wavelength and film thickness with respect to downward and upward light fluxes. The sensitivity of the shape of these functions on the oil type appears especially strong in case of the upward light fluxes as opposed to downward fluxes.
©2000 Optical Society of America
1. Introduction
Oil films on sea and inland water surfaces are seen relatively often (e.g. on the Baltic Sea about 500 times per year [1]), but the period of time which they last in the aquatic environment as homogenous films is relatively short and probably does not exceed several weeks due to the bacterial, solar and wind activity and sea surface motion. Currently, there are a number of techniques for oil film detection [2], for observations of the visibility of oil film [3] and for estimating thickness using images in VIS and NIR [4]. However, there is a relative lack of theoretical considerations, predictions and explanations. In order to create a theoretical basis for the detection of oil substances in VIS, it is necessary to determine the optical properties of the oil film on the water surface, including reflectivity R and transmissivity T. The determination of these parameters, separately for downward and upward light flux, both formulated as a function of the angle of incidence υ and wavelength λ, is a key part of modeling the light field in the water column, as well as the upwelling radiance above the water surface. Up to four functions are necessary for above the water surface upward light field modeling, as follows:
- reflectivity for both directions of radiance: downward R ↓(υ,λ) and upward R ↑(υ,λ),
- transmissivity: downward T ↓(υ,λ) and upward T ↑(υ,λ).
Light absorption in the oil film causes the mutual independence of four functions R ↓(υ,λ), R ↑(υ,λ), T ↓(υ,λ) and T ↑(υ,λ). In the case of water with a clean surface, one without oil film, the coefficients can be easily calculated using the traditional Fresnel reflectance formulae.
2. Materials
The preliminary analyses of the real part of the refractive index m for various types of oil, such as crude oil, lubricate oil, petrol, revealed that two types of crude oil, Petrobaltic and Romashkino, are characterized by different values of m (the difference of which is about 0.04). At the same time, light absorption coefficients a vary by two orders of magnitude. The optical parameters of other types of oil which can create a surface film on the water do not exceed the range determined by parameters m and a of the Petrobaltic and Romashkino oil (for Petrobaltic both m and a were the lowest, for Romashkino they were the highest). Therefore, to analyze the influence of oil type on the optical parameters of a water surface covered with oil, these two types of oil were used.
3. Methods and results
Two stages of work are necessary in order to estimate the reflective features of a water surface polluted by an oil film. The first is the measurement of the spectra of factors of the complex refractive index n=m-ik and the second is to calculate the previously mentioned R ↓(υ,λ) and R ↑(υ,λ).
3.1 Determination of the range of changes of the complex refractive index
3.1.1 Measurements of the real part (m) of the refractive index
Measurements of the real part of the refractive index were taken with an Abbe type refractometer which allows for temperature stabilization using an external thermostat. The measurements were taken in a temperatures range from 0°C to 20°C. The refractometer was illuminated with monochromatic light applied in the 400 nm to 700 nm wavelength range. This monochromatic light was supplied by a 100 W halogen lamp and a Specol 10 spectrophotometer. The results of measurements were derived using the least square method with the polynomial of the third order and the curves were extrapolated down to 350 nm and up to 750 nm.
The results of the measurements of m are presented in a graphic form in Fig. 1A. The value of m for the Petrobaltic crude oil at a temperature of 10° changes from 1.473 (λ=750 nm) to 1.492 (λ=350 nm), while in the case of Romashkino crude oil, it varies from 1.488 to 1.518.
Fig. 1. Spectral variation of the real part of the refractive index (A) and the imaginary part of the refractive index (B) of two types of oil: (a) crude Romashkino and (b) crude Petrobaltic
3.1.2 Measurements of the imaginary part (k) of the light refractive index
Measurements of the imaginary part of the light refractive index k were taken after the spectral changes of light absorption index a had been made and calculated to fit the parameter k=0.25 aλπ-1 [4]. The light absorption index a (unit: m-1) was measured with a Specord M40 spectrophotometer for ranges from 350 nm to 750 nm. Particular types of oil were placed in the form of n-hexane solutions in 1 mm long quartz cuvettes. After the spectra of oil solutions had been determined for several concentrations ρ, parameter a was determined for particular wavelengths as the value of function f(ρ) (1) when extrapolated to ρ=100%.
where:
T — light transmittance of an oil solution in n-hexane for particulate index ρ
To — light transmittance of clear n-hexane
d - length of cuvette [m]
ρ - concentration index of oil solution [%].
The results of measurements of the dependence of the imaginary part of the refractive index k on wavelength are presented in graphic form in Fig. 1B. The imaginary part k of the refractive index in the Petrobaltic oil at a temperature of 10o varies from 23·10-6 (λ=700 nm) to 56·10-4 (λ=350 nm), while in the case of Romashkino oil the parameter varies from 3·10-3 to 15·10-3, respectively.
3.2 Determination of optical properties of a water surface covered by an oil film
In general, calculating the light reflectance for a water surface polluted by an oil film means summing the series of wave-fronts which were repeatedly reflected off the interfaces, like air-oil and oil-water (for downward incidence) and water-oil and oil-air (for upward incidence). The reflectance of the light polarized perpendicularly and horizontally to the incidence plane is determined separately. The net reflectance is determined as an arithmetic average of two components of the polarized light. The overall theoretical assumptions and principles of such techniques were described in the 1950s [5,6]. Only in the last decade have numerous computer analyses of the optical features of oil films (homogenous and inhomogeneous) become possible [7]. It was revealed that the shapes of both spectral and angular plots of reflectance functions for a particular medium depend mainly on the real part of the light refractive index. It is well known that the influence of the imaginary part on the reflectance is significant only for media which absorb light strongly, for example metallic mirrors. It should be noted that not all types of oil absorb light strongly. In cases when thin oil films are considered, light absorption in the layer should influence the intensity of waves which come from subsequent reflections at media interfaces. The resulting reflected electromagnetic wave is dominated by the waves coming from the air-oil interface or coming from the oil-water interface.
Oil films are in permanent motion in natural environments. This is the reason their thicknesses fluctuate. Due to thickness instability, the close oscillations obtained from the calculations are invalid and only the averaged values of reflectance represent the actual situation.
The software prepared for the work employed the Maxwell solution for a multi-layer system. The program interface allows various configurations of optical spectral parameters of the substances which the film and surrounding media are made of to be used.
Fig. 2A presents the results of the calculation of reflectance for the downward incidence of light on a water surface covered with an oil film of changeable thickness for two types of crude oil whose optical properties drastically differ (Romashkino and Petrobaltic). The averaged (without close oscillations) plots of reflectance from a water surface covered with an oil film are similar in shape (red line for Romashkino, blue for Petrobaltic). The values of the reflectance for various types of oil are always slightly lower than 0.04. However, the comparison of these plots with those from Fig. 2B, which were obtained for upward radiation, reveals significant differences for various types of oil. The shapes of plots for upward light flux are very different for different types of oil. The film made of an oil which is transparent to some extent and has a low value of absorption coefficient a is characterized by a slow decrease in reflectance as the film thickness increases. A water surface covered with an oil film characterized by a relatively high absorption coefficient a shows a constant value of reflectance, 0.004, even for an oil film of several micrometers. This reflectance value is five times lower than that for a clean water surface. Such a low reflectance value, in the case of relatively transparent oil, is not obtained until the film reaches a thickness of several dozen microns. The plots in Fig. 2B reveal that a water surface which is covered with film made of relatively transparent oil (15 micrometers thick) presents similar reflective properties as a clean surface. An analogous effect is obtained for a 1 micrometer thick film of strongly light absorbent oil.
Fig. 2. Dependence of reflectance for perpendicular downward (A) and upward (B) light illuminating a water surface covered with an oil film. Two types of oil: (a) crude Petrobaltic at a temperature of 10°C, wavelength 600 nm (n=1.473, k=0.00006) and (b) crude Romashkino under the same conditions (n=1.488, k=0.00303). Colored lines show the averaged values of reflectance.
Fig. 3. Dependence of reflectance for perpendicular downward (A) and upward (B) light illuminating a water surface covered with an oil film 20 µm thick on wavelengths. Two types of oil: (a) crude Petrobaltic at a temperature of 10°C and (b) crude Romashkino at the same temperature. Colored lines show the averaged values of reflectance. Line ‘c’ represents the reflective features of a clean water surface.
Fig. 4. Dependence of reflectance for perpendicular downward (A) and upward (B) light illuminating a water surface covered with an oil film 20 µm thick on the angle of incidence. Two types of oil: (a) crude Petrobaltic at temperature of 10°C, wavelength 600 nm (n=1.473, k=0.00006) and (b) crude Romashkino under the same conditions (n=1.488, k=0.00303). Line ‘c’ represents the reflective feature of a clean water surface.
The changes of reflectance with changes of wavelength (Fig. 3) and angle of incidence (Fig. 4) were also analysed. With regards to the role of light flux direction (downward or upward) and oil type, these analyses led to conclusions which were similar to those described above for changes in oil film thickness. Namely, oil type influences the shape of the reflectance function and is the most significant in the case of upward light flux. The spectral plots of the reflectance for upward light flux and oil which absorbs light show that the averaged reflectance is constant (line ‘b’ at Fig. 3B), while, if the film is made of relatively transparent oil in the spectral range to 500nm, a constant increase in reflectance is observed up to the point when it becomes constant (line ‘a’ at Fig. 3B) and remains on the level for the downward light flux observed at Fig. 3A, i.e. 0.04.
In the case of angular reflectance, the function of the upward light flux for the type of oil is significant at the critical angle for the water—air interface (48.6°), which is shown in Fig. 4B. The type of oil does not influence the value of the critical angle, but it does strongly influence the plot shapes. When light attenuating oil is used the angular plots of reflectance oscillate around the average value, which is obtained for thick oil film (when the thickness exceeds several dozen micrometers).
4. Discussion
The examples presented indicate the significant role of oil type, especially for upward light fluxes. This influence is so significant because the amount of light absorbed while passing through the oil determines which of the fluxes dominates the light reflected, that from the reflection on the oil-air or that from the reflection on the water-oil interfaces. In the first case, light reaches the interface at which a rapid decrease of the real part of the light refractive index occurs (from about 1.5 to 1.0) which results in total light reflection when the angle of incidence greater than 48.6°. The light wave reflected from the water-oil interface then interferes with the wave reflected from the oil-air interface, resulting in oscillations of the reflectance. When the oil absorbs light relatively well or the film is thick, light which is even totally reflected from the oil-air interface is not very intense. Therefore, while the interference with the light reflected from the water-oil interface influences only the magnitude of oscillations of the reflectance function, its averaged shape does not differ from the shape obtained for the reflection of a thick oil layer. In general, light reflected from the oil-air interface dominates for oil films of relatively strong transparency (in reflected flux) at small incidence angles, thin film thickness and short wavelengths exceeding 500nm. However, with thick oil films of not very transparent oils light reflected from the interface of the small refractive index gradient (water-oil) dominates at large incidence angles and short wavelengths. This domination is caused by the attenuation of light passing through the film to the oil-air interface, as well as by the attenuation of light reflected on that interface while passing back through the film.
5. Conclusions
The value of the reflectance of an oil-covered water surface oscillates around 0.04 and practically depends only on the gradient of the real part of the refraction index in the oil-water interface. However, with upward light the range of reflectance values should be expected. Then the mean values of reflectance (excluding close oscillations) can vary from 0.004 to 0.04, with respect to values of the imaginary part of the light refraction index of the oil. In this case the real part of the refraction index of the water or oil plays a moderated role.
It could be expected that the optical features of water covered with a thin oil film which are described in this paper strongly influence the light fluxes measured from planes or orbital remote sensing platforms. Therefore, optical features of a polluted water surface should be included in radiative transfer models in which the Fresnel formulas for the air-water interface must be replaced by reflectances and transmittances, as the four following analytical expressions: R↓(υ,λ), R↑(υ,λ), T↓(υ,λ), and T↑(υ,λ)) adequate for a thin oil film covering on a water surface. The first trials in applying these expressions to determine the optical features of the sea surface under various environmental conditions were carried out by the author [8,9].
Currently, the author is conducting research on the quantitative determination of reflectance and transmittance expressions as a function of wavelength and angle of light incidence for various thicknesses of oil film and various kinds of oil to complete the data base of optical features of a water surface covered by thin oil films.
6. Acknowledgements
This paper was supported by a grant from the Gdynia Maritime Academy.
References and links
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