CN112461191B - Sun height calculating method based on underwater refraction and scattering coupling polarization degree - Google Patents

Sun height calculating method based on underwater refraction and scattering coupling polarization degree Download PDF

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CN112461191B
CN112461191B CN202011307244.6A CN202011307244A CN112461191B CN 112461191 B CN112461191 B CN 112461191B CN 202011307244 A CN202011307244 A CN 202011307244A CN 112461191 B CN112461191 B CN 112461191B
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杨健
赵谦
郭雷
胡鹏伟
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Beihang University
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Abstract

The invention relates to a solar altitude calculation method based on underwater refraction and scattering coupling polarization degree. Firstly, designing a compound eye-imitating multidirectional underwater polarization sensor, defining an included angle of observation directions of the sensor, and acquiring underwater polarization degree and underwater polarization azimuth angle information of the three observation directions of the polarization sensor; then, analyzing the light propagation direction change in the scattering and refracting processes based on a Rayleigh scattering theory and a refraction law, and determining the incident angle of the atmospheric light incident to the sensor; then, determining the atmospheric polarization degree of the light rays incident to each observation direction of the sensor by utilizing a Rayleigh scattering theory and a Fresnel theorem; and finally, calculating the maximum polarization degree according to the polarization degree constraint relation in the atmosphere, and determining the solar altitude angle. The invention establishes a solar altitude angle calculation method based on an underwater refraction and scattering coupling polarization degree mode under a horizontal posture, and can be used for navigation and positioning of an underwater carrier.

Description

Sun height calculating method based on underwater refraction and scattering coupling polarization degree
Technical Field
The invention relates to a solar altitude calculation method based on underwater refraction and scattering coupling polarization degree, which realizes calculation of solar altitude by using underwater polarization degree information in consideration of changes of refraction and scattering effects on the underwater light transmission direction and polarization degree, and belongs to the field of underwater polarized light navigation.
Background
The ocean is the largest natural geographic unit on the earth's surface, contains abundant natural resources, and is the "second space" on which humans rely for survival and development. Various underwater vehicles play an important role in the development and utilization of marine resources. However, satellite navigation is difficult to use in underwater environments due to the rapid attenuation of electromagnetic waves in water; the inertial navigation has accumulated errors and cannot be used for underwater tasks during long-term navigation; the phenomenon of ground unlocking is easy to occur in the Doppler velocity meter; geophysical field navigation methods rely on high-precision a priori information. Therefore, the existing underwater navigation technology is difficult to meet the requirement of long-term navigation of the underwater vehicle in unfamiliar complex sea areas, and becomes a bottleneck for limiting the operation function and efficiency of the underwater vehicle, and a passive and radiation-free underwater navigation method which is fully autonomous and has no error accumulated along with time is urgently needed.
Organisms in nature have abundant motion information perception ability, and organisms such as mantis shrimp, rainbow trout, solenopsis invicta, honeybee, monad butterfly can perceive polarized light in the environment to navigate and position, and through the study to biological navigation mechanism, the bionical polarization navigation technology has formed, has the advantage of intelligence, adaptability, autonomy, robustness, can provide the thinking for solving the difficult problem of navigation under water. One of the important functions of the bionic polarization navigation is to realize global positioning, and the premise of realizing the positioning function is to solve high-precision solar altitude angle information.
However, the existing method for calculating the solar altitude by using the polarization navigation method is mainly applicable to the atmospheric field, and does not consider the optical characteristics of the underwater environment. Chinese patent CN201510303533.1 proposes a method for calculating the global maximum polarization degree based on the atmospheric polarization degree information and calculating the solar altitude; chinese patent CN201810592616.0 proposes a method for calculating solar azimuth and altitude by using polarization degree of compound eye-like multi-channel polarization sensor, and improves calculation accuracy by weighting according to sensor position. In the above patents, the solar altitude is calculated based on the atmospheric polarization model of single rayleigh scattering, and underwater complex optical effects such as water surface refraction and water body scattering are not considered, so that the method is not suitable for resolving the solar altitude in an underwater environment.
Disclosure of Invention
The technical scheme of the invention is as follows: aiming at the problem that the polarization navigation method is difficult to apply to the underwater environment, on the basis of researching the distribution characteristics of the underwater polarization degree considering factors such as single Rayleigh scattering of the atmosphere, refraction on the water surface and Rayleigh scattering under the water, the solar altitude angle calculating method based on the coupling polarization degree of the underwater refraction and scattering is provided, is used for navigation positioning of an underwater carrier, and has the advantages of strong environmental adaptability, complete autonomy and no error accumulation.
The method obtains polarization information by utilizing a coplanar symmetrical compound eye-imitating three-channel polarization sensor which is horizontally arranged, inverts the polarization degree and the propagation direction of atmospheric light based on physical principles such as Rayleigh scattering theory, refraction law, Fresnel theorem and the like, and calculates the maximum polarization degree d by utilizing the atmospheric polarization degree constraint relationmaxAnd finally obtaining the solar altitude. In practical situations, the distribution mode of the polarization degree is easily influenced by external weather and water conditions, and particularly the polarization degree at a certain point is easily subjected to large fluctuation, so that the error of a calculation result is large; the method solves the solar altitude angle by calculating the global maximum polarization degree of the atmospheric polarization field, can improve the environmental adaptability of the polarization navigation method in the underwater complex environment, and expands the application field of polarization navigation.
The technical scheme adopted by the invention for solving the technical problems is as follows: a solar altitude calculation method based on underwater refraction and scattering coupling polarization degree comprises the following implementation steps:
step (1), designing a compound eye-imitating multidirectional underwater polarization sensor, wherein the underwater polarization sensor has three observation directions which are positioned in the same plane and are respectively T1,T2,T3Wherein, T1For subjective direction measurement of the sensor, T2,T3For the sensor to assist in observing the direction, and T2,T3And T1The included angle of (b) is eta; respectively obtaining underwater polarization degree d measured by three polarization sensors in observation directionkAzimuth of underwater polarization
Figure BDA0002788654120000021
Wherein k is the observation direction number of the polarization sensor, and k is 1,2 and 3;
step (2) utilizing the step (1) to arrangeThe included angle eta of the observation direction of the polarization sensor of the meter is used for determining the incident polarization sensor T based on the Rayleigh scattering theory and the change of the light propagation direction in the underwater scattering and water surface refraction processes in the law of refractionkIncident angle i of atmospheric light in observation directionk；
Step (3) combining the underwater polarization degree d obtained in the step (1)kAzimuth of underwater polarization
Figure BDA0002788654120000023
And the atmospheric light incident angle i acquired in the step (2)kDetermining incidence polarization sensor T based on Rayleigh scattering theory and Fresnel theoremkAtmospheric polarization degree d of light in observation directionik；
Step (4) combining the atmospheric light incident angle i acquired in the step (2)kBased on the atmospheric polarization degree d of the incident light obtained in the step (3)ikAnd calculating the maximum polarization degree of the atmospheric polarization field according to the polarization degree constraint relation in the atmosphere, thereby determining the solar altitude angle.
Further, the step (1) designs a compound eye-imitating multidirectional underwater polarization sensor and obtains underwater polarization degree d of each observation directionkAzimuth of underwater polarization
Figure BDA0002788654120000022
The specific requirements are as follows:
in order to obtain underwater polarization information, a compound eye-imitating multidirectional underwater polarization sensor is designed, and the sensor has three observation directions which are respectively T1,T2,T3And each observation direction can independently measure the polarization degree and the polarization azimuth angle information of the direction. Wherein, T1As main sensor observation direction, T2,T3To assist the sensor in observing the direction. When the multi-directional polarization sensor imitating compound eye is horizontally arranged, T1The observation direction is vertically upward and points to the zenith direction; auxiliary observation direction T2,T3Are respectively located at T1Two sides, T1,T2,T3Three observation directions are positioned in the same vertical directionIn plane, and T2,T3Observation direction about T1Symmetrical in direction, with T1The included angles between the directions are eta. The underwater polarization degree measured in each observation direction of the polarization sensor is dkThe underwater polarization azimuth angle is
Figure BDA0002788654120000031
And k is the observation direction number of the polarization sensor, and k is 1,2 and 3.
Further, the step (2) is used for analyzing the light propagation direction change in the underwater scattering and water surface refraction processes based on Rayleigh scattering theory and refraction law, and determining the incident angle i of the atmospheric light incident into the sensorkThe method is concretely realized as follows:
is incident to T2,T3The incident angle of the atmospheric ray in the observation direction on the water surface is i2,i3Due to T2,T3The viewing directions being symmetrical about the zenith axis, so that the incident angles of the corresponding rays are equal, i.e. i2＝i3＝i。
Figure BDA0002788654120000032
Wherein n isaAnd nwThe refractive indices of air and water, respectively.
Incident on the polarization sensor T1The atmospheric light in the observation direction is incident perpendicular to the water surface, the incident angle is 0, no refraction occurs, and therefore:
Figure BDA0002788654120000033
wherein ikFor incidence in the direction of observation T of an underwater polarization sensorkAngle of incidence of atmospheric light on the water surface, naAnd nwThe refractive indices of air and water, respectively, and γ is the rayleigh scattering angle.
Further, the step (3) determines the atmospheric polarization of the light incident to the sensor based on Rayleigh scattering theory and Fresnel theoremDegree dikThe method is concretely realized as follows:
to polarization sensor T2,T3For the observation direction, the atmospheric polarized light enters the sensor through the water surface refraction and the underwater Rayleigh scattering, and corresponds to the atmospheric polarization degree d of the lightikDegree of underwater polarization d measured by polarization sensorkThe relationship is as follows:
Figure BDA0002788654120000034
polarization sensor T1The incident light in the observation direction is incident perpendicular to the water surface, so no refraction and scattering occur, and di1＝d1. In summary, there are:
Figure BDA0002788654120000041
wherein d isikFor incidence in the direction of observation T of an underwater polarization sensorkThe degree of polarization of atmospheric light in the atmosphere, dkFor observing direction T of polarization sensorkThe measured underwater polarization degree, gamma is the Rayleigh scattering angle,
Figure BDA0002788654120000042
for observing direction T of polarization sensorkIs the rotation angle of the rotation matrix.
Further, in the step (4), based on the atmospheric polarization degree of the incident light obtained in the step (3), according to a polarization degree constraint relationship in the atmosphere, the maximum polarization degree of the atmospheric polarization field is calculated, and the solar altitude angle is determined, which is specifically realized as follows:
the atmospheric polarization degree d obtained in the step (3)ikAnd the light incidence angle i obtained in the step (2)kAnd obtaining a first order equation and a second order equation based on the constraint relation between the atmospheric polarization degree and the maximum polarization degree:
Figure BDA0002788654120000043
wherein the content of the first and second substances,
di1＝d1
Figure BDA0002788654120000044
Figure BDA0002788654120000045
a＝2cosi
α6＝4a2-a4
α5＝2a4di1+(4a2-2a4)di2+(4a2-2a4)di3
Figure BDA0002788654120000046
Figure BDA0002788654120000047
Figure BDA0002788654120000048
Figure BDA0002788654120000049
Figure BDA00027886541200000410
the maximum polarization degree d of the atmospheric polarization field can be obtained by the 6 th order constraint equationmax. Solar zenith angle theta and polarization sensor T1Degree of polarization d of observation direction1And maximum degree of polarization d of atmospheric polarization fieldmaxThe relationship of (1) is:
Figure BDA0002788654120000051
Figure BDA0002788654120000052
the solar altitude ζ is:
Figure BDA0002788654120000053
compared with the prior art, the invention has the following advantages:
the existing polarization navigation method is mostly applied to the atmospheric environment, and the calculation method of the underwater solar altitude and the underwater polarization degree distribution characteristic are not sufficiently researched. The invention considers the optical effects of water body such as refraction, scattering and the like, and expands the application field of the bionic polarization navigation method; in addition, the method calculates the maximum polarization degree of the atmospheric polarization field to calculate the solar altitude, and improves the underwater environmental adaptability of polarization navigation.
Drawings
FIG. 1 is a flow chart of a method for resolving solar altitude based on coupling polarization degree of underwater refraction and scattering according to the present invention;
FIG. 2 is a schematic view of the observation direction of a compound eye-imitating multi-directional underwater polarization sensor designed by the invention;
fig. 3 is a schematic diagram of the refraction and scattering effect of light.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and all other embodiments obtained by a person skilled in the art based on the embodiments of the present invention belong to the protection scope of the present invention without creative efforts.
According to an embodiment of the invention, as shown in fig. 1, the solar altitude calculation method based on the underwater refraction and scattering coupling polarization degree mode of the invention includes the following steps:
step (1), designing a compound eye-imitating multidirectional underwater polarization sensor, as shown in figure 2, wherein the underwater polarization sensor has three observation directions which are positioned in the same plane and are respectively T1,T2,T3And x, y and z are polarization sensor body coordinate systems. Wherein, T1For subjective direction measurement of the sensor, T2,T3For the sensor to assist in observing the direction, and T2,T3And T1The included angle of (b) is eta; respectively obtaining underwater polarization degree d measured by three polarization sensors in observation directionkAzimuth of underwater polarization
Figure BDA0002788654120000054
Wherein k is the observation direction number of the polarization sensor, and k is 1,2 and 3;
step (2) determining the incident polarization sensor T by utilizing the observation direction included angle eta of the polarization sensor designed in the step (1) and based on the Rayleigh scattering theory and the light propagation direction change in the underwater scattering and water surface refraction processes in the law of refractionkIncident angle i of atmospheric light in observation directionk。
Is incident to T2,T3The incident angle of the atmospheric ray in the observation direction on the water surface is i2,i3Due to T2,T3The viewing directions being symmetrical about the zenith axis, so that the incident angles of the corresponding rays are equal, i.e. i2＝i3I, the corresponding refraction angle is r, and the following relationship is obtained according to the law of refraction:
Figure BDA0002788654120000061
wherein n isaAnd nwIs the refractive index of air and water;
after atmospheric light enters water through refraction, the refraction light is scattered in the water, and the scattering is carried out based on a Rayleigh scattering modelAngle of refraction, angle of scattering and polarization sensor T when the angle is gamma2,T3The relationship of zenith angles in the observation direction is as follows:
r＝η-γ
incident on the polarization sensor T2,T3The incident angle of the atmospheric light on the water surface in the observation direction is as follows:
Figure BDA0002788654120000062
incident on the polarization sensor T1The atmospheric light of observation direction is perpendicular to the surface of water and is incident, and the incident angle is 0, does not take place refraction, promptly:
Figure BDA0002788654120000063
wherein ikFor incidence in the direction of observation T of an underwater polarization sensorkAngle of incidence of atmospheric light on the water surface, naAnd nwIs the refractive index of air and water;
step (3) combining the underwater polarization degree d obtained in the step (1)kAzimuth of underwater polarization
Figure BDA0002788654120000064
And the atmospheric light incident angle i acquired in the step (2)kDetermining incidence polarization sensor T based on Rayleigh scattering theory and Fresnel theoremkAtmospheric polarization degree d of light in observation directionik. The propagation path of the polarized light entering the sensor from the atmosphere via the refraction of the water surface and the scattering of the water body is shown in FIG. 3, wherein i2,i3Respectively incident on the polarization sensor T2,T3Atmospheric angle of incidence, r, of two rays in the observation direction2,r3The angle of refraction gamma of two beams on the water surface2,γ3Scattering angle of two beams of light rays subjected to Rayleigh scattering under water, eta is T2,T3Observation direction and T1The angle between the viewing directions.
To polarizationT of sensor2,T3For observation direction, atmospheric polarized light enters the sensor through surface refraction and underwater Rayleigh scattering, wherein incident light can be decomposed into a component E parallel to a plane||Component E perpendicular to the plane⊥According to the Fresnel theorem, the light intensity of each component varies before and after refraction as follows:
Figure BDA0002788654120000071
Figure BDA0002788654120000072
the degree of polarization d of the refracted ray is definedrComprises the following steps:
Figure BDA0002788654120000073
obtaining the change relation of the polarization degrees before and after the water surface refraction:
Figure BDA0002788654120000074
Figure BDA0002788654120000075
wherein d isiDegree of polarization of incident light, drIs the degree of polarization of the refracted light.
The polarization state change of the refracted light when rayleigh scattering occurs underwater can be described by a mueller matrix:
SO＝MSDMSSr
wherein S isOAnd SrThe Stokes vectors of the incident light and the water surface refraction light of the sensor respectively have the expression
Figure BDA0002788654120000076
MSMueller matrix being underwater Rayleigh scattering, MSDFor the rotation matrix, the expressions are:
Figure BDA0002788654120000077
Figure BDA0002788654120000078
where σ is the rotation angle of the rotation matrix:
Figure BDA0002788654120000079
then T2,T3Underwater polarization degree d measured by sensorkAzimuth of underwater polarization
Figure BDA00027886541200000710
With the degree of atmospheric polarization d of the light incident on the sensorikThe relationship of (1) is:
Figure BDA0002788654120000081
polarization sensor T1The incident light in the observation direction is incident perpendicular to the water surface, so no refraction and scattering occur, and di1＝d1. In summary, there are:
Figure BDA0002788654120000082
wherein d isikFor incidence in the direction of observation T of an underwater polarization sensorkThe degree of polarization of atmospheric light in the atmosphere, dkFor observing direction T of polarization sensorkThe measured underwater polarization degree, gamma is the Rayleigh scattering angle,
Figure BDA0002788654120000083
for observing direction T of polarization sensorkIs the rotation angle of the rotation matrix.
Step (4) combining the atmospheric light incident angle i acquired in the step (2)kBased on the atmospheric polarization degree d of the incident light obtained in the step (3)ikAccording to the polarization degree constraint relation in the atmosphere, the maximum polarization degree of the atmospheric polarization field is calculated, and therefore the specific method for determining the solar altitude angle is as follows:
the atmospheric polarization degree d obtained in the step (3)ikAnd the light incidence angle i obtained in the step (2)kAnd (3) carrying out constraint relation between the atmospheric polarization degree and the maximum polarization degree to obtain:
Figure BDA0002788654120000084
wherein the content of the first and second substances,
di1＝d1
Figure BDA0002788654120000091
Figure BDA0002788654120000092
a＝2cosi
α6＝4a2-a4
α5＝2a4di1+(4a2-2a4)di2+(4a2-2a4)di3
Figure BDA0002788654120000093
Figure BDA0002788654120000094
Figure BDA0002788654120000095
Figure BDA0002788654120000096
Figure BDA0002788654120000097
the maximum atmospheric polarization degree d can be obtained by the 6 th order constraint equationmax. Sun zenith angle theta and main sensor polarization degree d1And a maximum degree of polarization dmaxThe relationship of (1) is:
Figure BDA0002788654120000098
Figure BDA0002788654120000099
the solar altitude angle ζ is:
Figure BDA00027886541200000910
although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, but various changes may be apparent to those skilled in the art, and it is intended that all inventive concepts utilizing the inventive concepts set forth herein be protected without departing from the spirit and scope of the present invention as defined and limited by the appended claims.

Claims (3)

1. A solar altitude calculation method based on underwater refraction and scattering coupling polarization degree is characterized by comprising the following steps:
step (1), designing a compound eye-imitating multidirectional underwater polarized light sensor, wherein the underwater polarized light sensor has three observation directions which are all positioned in the same plane and are respectively T1,T2,T3Each observation direction can independently measure the polarization degree and the polarization azimuth angle information of the direction, wherein T1For the main direction of observation, T, of the underwater polarized light sensor2,T3For assisting the direction of observation of the underwater polarized light sensor, and the direction of observation T2,T3And T1The included angles between the two are eta; respectively obtaining underwater polarization degree d measured in three observation directions of underwater polarized light sensorkAzimuth of underwater polarization
Figure FDA0003494737570000011
Wherein k is the observation direction number of the underwater polarized light sensor, and k is 1,2 and 3;
step (2) analyzing the change of the light propagation direction in the underwater scattering and water surface refraction processes by utilizing the observation direction included angle eta of the underwater polarized light sensor designed in the step (1) based on Rayleigh scattering theory and refraction law, and determining the observation direction T of the underwater polarized light sensorkIncident angle i of inner atmospheric ray on water surfacek；
Step (3) combining the underwater polarization degree d obtained in the step (1)kAzimuth of underwater polarization
Figure FDA0003494737570000012
And (3) obtaining the incident angle i of the atmospheric light on the water surface in the step (2)kDetermining the direction of observation T of the polarized light sensor incident under waterkDegree of polarization d of atmospheric lightik；
Step (4) combining the incident angle i of the atmospheric light on the water surface acquired in the step (2)kBased on the atmospheric light polarization degree d obtained in the step (3)ikCalculating the maximum polarization degree of the atmospheric polarization field according to the polarization degree constraint relation in the atmosphere, thereby determining the solar altitude angle;
and (3) determining the observation direction T of the polarized light sensor incident to the underwater based on Rayleigh scattering theory and Fresnel theoremkDegree of polarization d of atmospheric lightikThe method is concretely realized as follows:
to the observation direction T of the underwater polarized light sensor2,T3In other words, the atmospheric polarized light enters the underwater polarized light sensor through the refraction of the water surface and the underwater rayleigh scattering, and the corresponding atmospheric light polarization degree dikDegree of polarization d of light refracted from water surfacerkAnd the observation direction T of the underwater polarized light sensorkMeasured degree of underwater polarization dkThe relationship is as follows:
Figure FDA0003494737570000013
Figure FDA0003494737570000014
observing direction T of underwater polarized light sensor1The light ray is incident perpendicular to the water surface and does not refract or scatter, so di1＝dr1＝d1In summary, there are:
Figure FDA0003494737570000021
Figure FDA0003494737570000022
wherein d isikFor incident on the underwater polarized light sensorkDegree of polarization of atmospheric light, drkIs the degree of polarization of the light after refraction through the water surface, dkFor observing direction T of underwater polarized light sensorkMeasured degree of underwater polarization, ikFor incident on the underwater polarized light sensorkAtmosphere (b) ofAngle of incidence of light on water surface, rkFor incident on the underwater polarized light sensorkThe refraction angle of the atmospheric ray on the water surface, gamma is the Rayleigh scattering angle,
Figure FDA0003494737570000023
for observing direction T of underwater polarized light sensorkσ is the rotation angle of the rotation matrix;
in the step (4), the solar altitude is determined, and the method is specifically realized as follows:
the atmospheric light polarization degree d obtained in the step (3)ikAnd the incident angle i of the atmospheric light on the water surface obtained in the step (2)kAnd obtaining a first order equation and a second order equation based on the constraint relation between the atmospheric polarization degree and the maximum polarization degree:
Figure FDA0003494737570000024
wherein the content of the first and second substances,
Figure FDA0003494737570000031
Figure FDA0003494737570000032
a＝2cosi
α6＝4a2-a4
α5＝2a4di1+(4a2-2a4)di2+(4a2-2a4)di3
Figure FDA0003494737570000033
Figure FDA0003494737570000034
Figure FDA0003494737570000035
Figure FDA0003494737570000036
Figure FDA0003494737570000037
wherein i is the observation direction T of the underwater polarized light sensor2,T3The angle of incidence of the atmospheric ray on the water surface, i.e. i ═ i2＝i3A is an intermediate variable, α0～α6Is the coefficient of a unitary sixth order equation;
obtaining the maximum polarization degree d of the atmospheric polarization field by the unary six-order equationmaxSolar zenith angle theta and underwater polarized light sensor observation direction T1Measured degree of underwater polarization d1And maximum degree of polarization d of atmospheric polarization fieldmaxThe relationship of (1) is:
Figure FDA0003494737570000038
Figure FDA0003494737570000039
the solar altitude ζ is:
Figure FDA00034947375700000310
2.the method for resolving the solar altitude based on the coupling polarization degree of underwater refraction and scattering according to claim 1, wherein the method comprises the following steps: in the step (1), when the compound eye-imitating multidirectional underwater polarized light sensor is horizontally arranged, the observation direction T is observed1Vertically upwards and points to the zenith direction; auxiliary observation direction T2,T3Are respectively located at T1Two sides, T1,T2,T3The three observation directions are positioned in the same vertical plane, and the observation direction T2,T3About T1Symmetrical in direction, with T1The included angles between the directions are eta.
3. The method for resolving the solar altitude based on the coupling polarization degree of underwater refraction and scattering according to claim 1, wherein the method comprises the following steps: in the step (2), the change of the light propagation direction in the underwater scattering and water surface refraction processes is analyzed based on Rayleigh scattering theory and refraction law, and the observation direction T of the incident underwater polarized light sensor is determinedkIncident angle i of inner atmospheric ray on water surfacekThe method is concretely realized as follows:
incident into the observation direction T2,T3The incident angle of the atmospheric ray on the water surface is i2,i3Due to the observation direction T2,T3Symmetrical about the zenith axis, so the incident angles at the water surface corresponding to atmospheric rays are equal, i.e. i2＝i3＝i，
Figure FDA0003494737570000041
Wherein n isaAnd nwRefractive indexes of air and water respectively, i is an observation direction T of the polarized light sensor incident underwater2,T3The incident angle of the atmospheric light on the water surface, eta is the observation direction T in the underwater polarized light sensor2,T3And T1Gamma is the Rayleigh scattering angle;
observing direction T of underwater polarized light sensor1The atmospheric light entering perpendicularly to the water surfaceIncident angle is 0, no refraction occurs, so:
Figure FDA0003494737570000042
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