A space-borne multi-view polarimetric spectral imaging system for aerosol optical parameter measurement

Abstract

The application provides a star-borne multi-view polarization spectrum imaging system for aerosol optical parameter measurement, and belongs to the technical field of optical imaging. The system is carried on a satellite platform, and comprises a telescope objective, a multi-slit assembly, a light-splitting prism, a collimating lens group, a plane grating group, an imaging lens group, a depolarization light-splitting prism group, a polaroid group and a detector group. The system is based on static multi-view synchronous observation design, and realizes high-precision detection of aerosol optical parameters through multi-view, hyperspectrum and full-polarization multi-dimensional information fusion.

Description

Technical Field

[0001] This invention belongs to the field of optical imaging technology, specifically relating to a spaceborne multi-view polarization spectral imaging system for measuring aerosol optical parameters. Background Technology

[0002] The importance of polarization spectral imaging systems in aerosol optical parameter measurement stems from their unique multi-dimensional information acquisition capabilities. The optical properties of aerosols, such as scattering phase functions and complex refractive index, depend not only on wavelength but also on the polarization state of the incident light. Traditional spectral imaging only records intensity information, making it difficult to distinguish the aliasing of scattering signals caused by different polarization responses. Especially in complex atmospheric environments dominated by non-spherical aerosols, a single intensity dimension can easily lead to multiple solutions in parameter inversion. Polarization spectroscopy, by simultaneously acquiring the spectral distribution of Stokes parameters, can analyze the modulation law of the scattering field by microscopic characteristics such as particle shape and orientation. Essentially, it reduces the uncertainty of optical parameter inversion through the joint constraint of polarization and spectral dimensions. This multi-dimensional feature extraction can effectively separate the coupling effect between aerosols and background radiation, playing an irreplaceable role in improving the high accuracy of aerosol layer identification and quantifying key climate parameters such as radiative forcing of absorbent aerosols. It also has significant application value in satellite remote sensing atmospheric correction and regional pollution monitoring. Changchun University of Science and Technology describes an airborne pushbroom hyperspectral polarization integrated imaging system and its assembly method in Chinese patent application CN118794536A. This system, through a combination of an objective lens group, a slit, a collimating lens group, a prism-grating beam splitter module, and a polarization detector, combined with the forward pushbroom motion of the airborne platform, simultaneously acquires the intensity, spectrum, and polarization information of the target. The patent proposes that the combined application of these three types of information can double the image contrast and emphasizes the precision advantages of the prism-grating assembly. However, this system can only generate polarization spectral information from a single viewpoint, and the acquisition of its polarization information mainly depends on the design of the polarization detector, rather than actively generating polarized light. In their paper "Optical and system performance of SPEXone, a multi-angle channeled spectropolarimeter for the NASA PACE mission." Proc. of SPIE Vol. 11852 (2021): 1185234," Jeroen Rietjens et al. of the Netherlands Space Research Institute (SRON) proposed a multi-angle polarization spectral imaging system for high-precision remote sensing measurements of optical parameters of aerosols and clouds. This system acquires target signals in five fields of view through three reflective telescope objectives. Combining a freeform surface mirror, a reflective grating, and a dual-beam polarization modulation assembly, it encodes linear polarization into a spectrum with periodically varying intensity, enabling snapshot-style polarization spectral measurements without moving parts. However, this system has high requirements for stray light suppression, and the stray light correction algorithm relies on empirical models, potentially introducing unmodeled system errors. Furthermore, the optical system is highly complex, and the manufacturing and alignment of the freeform surface are demanding, increasing cost and long-term stability risks. Summary of the Invention

[0003] The purpose of this invention is to propose a spaceborne five-view polarization spectroscopy detection system for measuring aerosol optical parameters. By synergistically utilizing spatial, spectral, and polarization multidimensional information, it comprehensively improves the accuracy of aerosol optical parameter detection in complex scenarios.

[0004] To achieve the above objectives, the technical solution of the present invention is: a spaceborne multi-view polarization spectral imaging system for measuring aerosol optical parameters, the system being mounted on a satellite platform and comprising a telescope objective, a multi-slit assembly, a beam splitter, a collimating lens group, a planar grating group, an imaging mirror group, a depolarization beam splitter group, a polarizer group, and a detector group.

[0005] The telescope objective lens is used to receive and converge light from multiple different fields of view, wherein the light from the multiple different fields of view is spectral light containing target and background information from infinity;

[0006] The multi-slit assembly is located at the focal plane of the telescope objective and has multiple parallel slits arranged perpendicular to the optical axis. Each slit corresponds to a field of view and is used to spatially separate light rays from different fields of view. The arrangement direction of the multiple slits is perpendicular to the satellite's orbital direction.

[0007] The beam splitter is disposed in the outgoing light path of the multi-slit assembly and is used to split the light from the multi-slit assembly into two paths: transmitted light and reflected light.

[0008] The collimating lens group includes a first collimating lens and a second collimating lens, which are respectively disposed in the transmission light path and the reflection light path of the beam splitter, and are used to collimate diverging rays from different fields of view into parallel beams with different propagation directions.

[0009] The planar grating group includes a first planar grating and a second planar grating, which are respectively disposed in the outgoing light paths of the first collimating lens and the second collimating lens, and are used to diffract and disperse the incident parallel beam so that light of different wavelengths is emitted at different angles.

[0010] The imaging lens group includes a first imaging lens group and a second imaging lens group, which are respectively disposed in the outgoing light paths of the first planar grating and the second planar grating, and are used to perform telecentric imaging of the diffracted light.

[0011] The depolarization beam splitter group includes a first depolarization beam splitter and a second depolarization beam splitter, which are respectively disposed in the outgoing light paths of the first imaging mirror group and the second imaging mirror group, and are used to split the incident light into two paths: transmitted light and reflected light.

[0012] The polarizer group includes a first polarizer, a second polarizer, a third polarizer, and a fourth polarizer with different polarization directions. They are respectively arranged in the four optical paths after the beam is split by the depolarizing beam splitter and are used to modulate the polarization of the incident light.

[0013] The detector group includes a first detector, a second detector, a third detector and a fourth detector, which are respectively set in the output optical path of the four polarizers to synchronously record spectral images under different polarization directions.

[0014] The system reconstructs spectral images from four detectors simultaneously recorded under different polarization directions by pushing and sweeping motion along the satellite's orbit, generating a four-dimensional data cube containing two-dimensional spatial information, one-dimensional spectral information, and one-dimensional polarization information, which is then used for the inversion calculation of aerosol optical parameters.

[0015] Preferably, the system further includes a field-of-view adjustment mirror group; the field-of-view adjustment mirror group is located in the incident light path of the telescope objective lens, and is used to change the propagation direction of field rays that are larger than the inherent imaging field of view of the telescope objective lens by reflection, so that the light rays enter the telescope objective lens at an angle within the inherent imaging field of view of the telescope objective lens.

[0016] Preferably, the plurality of different fields of view include a 0° field of view, a +20° field of view, a -20° field of view, a +50° field of view, and a -50° field of view;

[0017] The field-of-view adjustment mirror group uses two sets of plane mirrors to remap the light rays from the +50° and -50° fields of view to +10° and -10° respectively before they enter the telescope objective lens.

[0018] Preferably, the beam splitter, the first depolarizing beam splitter, and the second depolarizing beam splitter are all cubic prisms made by bonding two right-angle prisms together, with the bonding surface coated with a semi-transparent and semi-reflective film to achieve a beam splitting ratio of 50% transmittance and 50% reflectance.

[0019] Preferably, the diffraction orders of the first planar grating and the second planar grating are +1 and -1, respectively.

[0020] Preferably, the first planar grating and the second planar grating both have a grating count of 100 lines / mm.

[0021] Preferably, the four polarizers are 0° polarizer, 45° polarizer, 90° polarizer and 135° polarizer.

[0022] Preferably, the spectral detection range of the system is 380 nm to 900 nm.

[0023] Preferably, the first detector, the second detector, the third detector and the fourth detector are all area array CMOS sensors with a pixel size of 5.5μm and an area array pixel size of 2048×2048;

[0024] The system performs 4×4 merging of detector pixels, resulting in an equivalent pixel size of 22μm and an equivalent area array pixel size of 512×512.

[0025] Preferably, the aerosol optical parameters include aerosol optical thickness, single scattering albedo, complex refractive index, and scattering phase function.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] The core of this invention consists of a field-of-view adjustment mirror group, a telescope objective lens, a multi-slit assembly, a polarization-depolarizing beam splitter, a collimating lens, a plane grating, an imaging mirror group, a polarization-depolarizing beam splitter, polarizers with different polarization directions, and detectors. Utilizing satellite motion, it simultaneously captures four-dimensional information (polarization, spectrum, and two-dimensional space) from five different viewpoints using four detectors. Based on an image reconstruction algorithm, it stitches together slit images of the same wavelength into a complete data cube, ultimately outputting the target's two-dimensional space, spectrum, and full polarization characteristics. This system achieves large field-of-view coverage without mechanical scanning, and features high stability, low calibration complexity, and efficient data acquisition capabilities, effectively improving the accuracy of aerosol optical parameter detection.

[0028] The system combines spectral imaging technology with polarization technology, which not only leverages the fine resolution advantage of spectral features in material identification, but also utilizes polarization characteristics to enhance the contrast between the target and the background, effectively overcoming the technical bottlenecks of large background interference and single feature extraction in traditional single-dimensional detection. Attached Figure Description

[0029] Figure 1 This is a simplified architecture diagram of the system of the present invention;

[0030] Figure 2 This is a detailed architecture diagram of the system of the present invention;

[0031] Figure 3 This is a matrix dot diagram of the system of the present invention under different wavelengths and fields of view;

[0032] Figure 4 The field curvature and distortion curves of the system of this invention;

[0033] Figure 5 This is the modulation transfer function curve of the system of the present invention at the center wavelength of 650nm.

[0034] In the picture:

[0035] 1: Telescope objective lens; 2: Multi-slit assembly; 3: Beam splitter; 4-1: First collimating lens; 4-2: Second collimating lens; 5-1: First planar grating; 5-2: Second planar grating; 6-1: First imaging lens group; 6-2: Second imaging lens group; 7-1: First depolarizing beam splitter; 7-2: Second depolarizing beam splitter; 8-1: First polarizer; 8-2: Second polarizer; 8-3: Third polarizer; 8-4: Fourth polarizer; 9-1: First detector; 9-2: Second detector; 9-3: Third detector; 9-4: Fourth detector; 10-1: First planar mirror group; 10-2: Second planar mirror group. Detailed Implementation

[0036] The following is in conjunction with the appendix Figure 1-5 The technical solution of the present invention will be described in detail below.

[0037] This invention proposes a spaceborne multi-view polarization spectral imaging system for measuring aerosol optical parameters. The system includes: a telescope objective (1), a multi-slit assembly (2), a beam splitter (3), a collimating lens group, a plane grating group, an imaging mirror group, a depolarization beam splitter group, a polarizer group, a detector group, and a field-of-view adjustment mirror group; wherein, the collimating lens group includes a first collimating lens (4-1) and a second collimating lens (4-2), the plane grating group includes a first plane grating (5-1) and a second plane grating (5-2), the imaging mirror group includes a first imaging mirror group (6-1) and a second imaging mirror group (6-2), and the depolarization beam splitter group includes a first imaging mirror group (6-1) and a second imaging mirror group (6-2). The polarization beam splitter assembly includes a first depolarization beam splitter (7-1) and a second depolarization beam splitter (7-2). The polarizer assembly includes a first polarizer (8-1), a second polarizer (8-2), a third polarizer (8-3), and a fourth polarizer (8-4) with different polarization directions. The detector assembly includes a first detector (9-1), a second detector (9-2), a third detector (9-3), and a fourth detector (9-4). The aerosol optical parameters include aerosol optical thickness, single scattering albedo, complex refractive index, scattering phase function, etc. The spectral detection range of the system is 380 nm to 900 nm.

[0038] The system of the present invention is mounted on a satellite platform for push-broom detection; the five fields of view of the system are 0°, ±20° and ±50°; the system introduces the ±50° field of view into the ±10° path of the system through secondary reflection of the first plane mirror group (10-1) and the second plane mirror group (10-2) along the track direction.

[0039] The telescope objective (1) converges light from different fields of view to each slit of the multi-slit assembly (2); the light from different fields of view is spectral light from infinity containing target and background information; the light converged to each slit of the multi-slit assembly (2) is telecentric light, the number of slits of the multi-slit assembly (2) corresponds to the number of fields of view of 5, and the light converged to each slit of the multi-slit assembly (2) is along the direction perpendicular to the optical axis, from top to bottom, the 5 slits correspond to the system field of view of +20°, +50°, 0°, -50° and -20° respectively.

[0040] The beam splitter (3) is made of two right-angled prisms glued together; the glued surface is coated with a semi-transparent and semi-reflective film; the beam splitter (3) transmits and reflects the outgoing light from the multi-slit assembly (2) into two beams of light with equal intensity.

[0041] The first collimating lens (4-1) and the second collimating lens (4-2) collimate the light rays from different fields of view of the beam splitter (3) to the first planar grating (5-1) and the second planar grating (5-2);

[0042] The first planar grating (5-1) and the second planar grating (5-2) diffract and disperse the incident light according to the grating equation; the diffraction order of the first planar grating (5-1) is +1, and the diffraction order of the second planar grating (5-2) is -1; the number of lines of the first planar grating (5-1) and the second planar grating (5-2) is 100 lines / mm.

[0043] The first imaging lens group (6-1) and the second imaging lens group (6-2) respectively perform telecentric imaging of the light rays diffracted from the first planar grating (5-1) and the second planar grating (5-2).

[0044] The first depolarizing beam splitter (7-1) and the second depolarizing beam splitter (7-2) are both made of two right-angle prisms bonded together; the bonded surface is coated with a semi-transparent and semi-reflective film; the first depolarizing beam splitter (7-1) transmits and reflects the light from the telecentric imaging of the first imaging lens group (6-1) into two beams of light with equal intensity, and the second depolarizing beam splitter (7-2) transmits and reflects the light from the telecentric imaging of the second imaging lens group (6-2) into two beams of light with equal intensity.

[0045] The first polarizer (8-1), the second polarizer (8-2), the third polarizer (8-3), and the fourth polarizer (8-4) with different polarization directions are a 0° polarizer, a 45° polarizer, a 90° polarizer, and a 135° polarizer, respectively. The first polarizer (8-1), the second polarizer (8-2), the third polarizer (8-3), and the fourth polarizer (8-4) are respectively set in the four optical paths after the beam splitter is diffracted by the depolarizing beam splitter, selectively allowing light vibrations in a specific direction to pass through while blocking light vibrations in other directions, thereby generating polarized light.

[0046] The first detector (9-1), the second detector (9-2), the third detector (9-3), and the fourth detector (9-4) respectively detect slit images of different wavelengths under 0° polarization, slit images of different wavelengths under 45° polarization, slit images of different wavelengths under 90° polarization, and slit images of different wavelengths under 135° polarization.

[0047] All four detectors are CMOS sensors with an area array of 2048×2048 pixels and a pixel size of 5.5μm. To increase the signal-to-noise ratio, the system performs 4×4 pixel merging on the detector pixels. After merging, the detector is equivalent to a 22μm detector with an area array of 512×512 pixels.

[0048] The specific implementation process of the five-field polarization spectral imaging system of the present invention is as follows: along the track direction, the ±50° field of view is introduced into the ±10° path of the system through the first plane mirror group (10-1) and the second plane mirror group (10-2) via secondary reflection. At this time, the ±50° field of view light rays are mapped to the ±10° field of view light rays for the telescope objective (1). The telescope objective (1) telecentrically images the five field of view light rays of +20°, +10°, 0°, -10° and -20° onto the multi-slit assembly (2). The five slits of the multi-slit assembly (2) perpendicular to the optical axis direction from top to bottom correspond to the five fields of view of +20°, +50°, 0°, -50° and -20° of the system, respectively. The beam splitter (3) transmits 50% and reflects 50% of the slit image. After being collimated by the collimating lens group to form a parallel beam, it enters the system. The light is diffracted and dispersed by a planar grating group; the diffracted light then passes through an imaging mirror group for telecentric converging imaging; before imaging, the transmitted and reflected light, after being dispersed by the grating, passes through a depolarizing beam splitter group, where 50% transmission and 50% reflection are performed again, forming four beams of equal intensity. These beams then pass through the first polarizer (8-1), the second polarizer (8-2), the third polarizer (8-3), and the fourth polarizer (8-4), respectively, and are imaged onto the detector group. Slit images of different wavelengths under 0° polarization, 45° polarization, 90° polarization, and 135° polarization are formed on the first detector (9-1), the second detector (9-2), the third detector (9-3), and the fourth detector (9-4), respectively. After satellite platform pushbroom and image reconstruction, four-dimensional data in polarization, spectrum, and two-dimensional space are obtained.

[0049] This invention discloses a five-field-of-view polarization spectral imaging system for aerosol optical parameter detection. Through a static multi-field synchronous observation design, combined with multi-angle, hyperspectral, and full-polarization multi-dimensional information fusion technology, it significantly improves the detection accuracy and system stability of aerosol optical parameters. Its core advantage lies in eliminating traditional dynamic mechanical components, achieving large field-of-view coverage through secondary reflection of the optical path, and employing static optomechanical structures such as depolarization beam-splitting prisms, multi-slit components, planar gratings, and polarizers with different polarization angles. This effectively solves the problems of high system complexity, difficult calibration, and limited field of view caused by reliance on mechanical scanning or filter wheels in existing technologies. The system utilizes four detectors to simultaneously acquire polarization-spectral-two-dimensional spatial information, and combines image reconstruction to generate a four-dimensional data cube, possessing both high signal-to-noise ratio and efficient data acquisition capabilities. This system has significant application value in satellite remote sensing atmospheric correction, regional pollution monitoring, and climate research. Its high stability and low calibration complexity are particularly suitable for dynamic scenarios and large-scale deployment needs, providing reliable technical support for improving the high accuracy of aerosol layer identification and quantifying the radiative forcing of absorbent aerosols in climate model research.

[0050] To use the system described in this invention, the following steps are required:

[0051] Step 1: Using a high-precision theodolite, assemble all optical components according to the attached... Figure 1 The components are assembled, leveled, and aligned in sequence to ensure that the optical axes of the telescope objective (1), multi-slit assembly (2), beam splitter (3), collimating lens group, plane grating group, imaging mirror group, depolarizing beam splitter group, polarizer group, and detector group are strictly coaxially centered to form a stable optical path structure.

[0052] Step 2, System Calibration and Parameter Verification: Use a standard light source to calibrate parameters such as spectral response, polarization direction, and detector sensitivity for each field of view to ensure that the spectral resolution and polarization accuracy meet the design requirements.

[0053] Step 3: Place the system on a stable satellite platform and, based on the satellite platform's angular velocity relative to the ground, ensure frame rate matching during the uniform sweeping process to avoid image stitching errors.

[0054] Step 4, Data Acquisition and Processing: Start the satellite platform and the system moves at a constant speed along the orbit, synchronously triggering four detectors to collect spectral-spatial information under different polarization directions; through image reconstruction, the original data slit image is stitched together according to wavelength, field of view and polarization direction into a four-dimensional data cube of polarization-spectrum-two-dimensional space.

[0055] Step 5: Verify and calibrate the system using standard aerosol samples or scenarios with known optical parameters to ensure the reliability and data consistency of the system's long-term operation. Combine the atmospheric radiative transfer model to retrieve parameters such as aerosol optical thickness, single scattering albedo, complex refractive index, and scattering phase function. Perform stray light correction and system error compensation to output the final detection results.

[0056] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A spaceborne multi-view polarization spectral imaging system for measuring aerosol optical parameters, characterized in that, The system is mounted on a satellite platform and includes a telescope objective, a multi-slit assembly, a beam splitter, a collimating lens group, a planar grating group, an imaging mirror group, a polarization-reducing beam splitter group, a polarizer group, and a detector group. The telescope objective lens is used to receive and converge light from multiple different fields of view, wherein the light from the multiple different fields of view is spectral light containing target and background information from infinity; The multi-slit assembly is located at the focal plane of the telescope objective and has multiple parallel slits arranged perpendicular to the optical axis. Each slit corresponds to a field of view and is used to spatially separate light rays from different fields of view. The arrangement direction of the multiple slits is perpendicular to the satellite's orbital direction. The beam splitter is disposed in the outgoing light path of the multi-slit assembly and is used to split the light from the multi-slit assembly into two paths: transmitted light and reflected light. The collimating lens group includes a first collimating lens and a second collimating lens, which are respectively disposed in the transmission light path and the reflection light path of the beam splitter, and are used to collimate diverging rays from different fields of view into parallel beams with different propagation directions. The planar grating group includes a first planar grating and a second planar grating, which are respectively disposed in the outgoing light paths of the first collimating lens and the second collimating lens, and are used to diffract and disperse the incident parallel beam so that light of different wavelengths is emitted at different angles. The imaging lens group includes a first imaging lens group and a second imaging lens group, which are respectively disposed in the outgoing light paths of the first planar grating and the second planar grating, and are used to perform telecentric imaging of the diffracted light. The depolarization beam splitter group includes a first depolarization beam splitter and a second depolarization beam splitter, which are respectively disposed in the outgoing light paths of the first imaging mirror group and the second imaging mirror group, and are used to split the incident light into two paths: transmitted light and reflected light. The polarizer group includes a first polarizer, a second polarizer, a third polarizer, and a fourth polarizer with different polarization directions. They are respectively arranged in the four optical paths after the beam is split by the depolarizing beam splitter and are used to modulate the polarization of the incident light. The detector group includes a first detector, a second detector, a third detector and a fourth detector, which are respectively set in the output optical path of the four polarizers to synchronously record spectral images under different polarization directions. The system reconstructs spectral images from four detectors simultaneously recorded under different polarization directions by pushing and sweeping motion along the satellite's orbit, generating a four-dimensional data cube containing two-dimensional spatial information, one-dimensional spectral information, and one-dimensional polarization information, which is then used for the inversion calculation of aerosol optical parameters.

2. The spaceborne multi-view polarization spectral imaging system for measuring aerosol optical parameters according to claim 1, characterized in that, The system also includes a field-of-view adjustment mirror group; the field-of-view adjustment mirror group is located in the incident light path of the telescope objective lens, and is used to change the propagation direction of light rays that are larger than the inherent imaging field of view of the telescope objective lens by reflection, so that the light rays enter the telescope objective lens at an angle within the inherent imaging field of view of the telescope objective lens.

3. A spaceborne multi-view polarization spectral imaging system for measuring aerosol optical parameters according to claim 2, characterized in that, The multiple different fields of view include a 0° field of view, a +20° field of view, a -20° field of view, a +50° field of view, and a -50° field of view; The field-of-view adjustment mirror group uses two sets of plane mirrors to remap the light rays from the +50° and -50° fields of view to +10° and -10° respectively before they enter the telescope objective lens.

4. A spaceborne multi-view polarization spectral imaging system for measuring aerosol optical parameters according to claim 1, characterized in that, The beam splitter, the first depolarizing beam splitter, and the second depolarizing beam splitter are all cubic prisms made of two right-angle prisms bonded together. The bonded surface is coated with a semi-transparent and semi-reflective film to achieve a beam splitting ratio of 50% transmittance and 50% reflectance.

5. A spaceborne multi-view polarization spectral imaging system for measuring aerosol optical parameters according to claim 1, characterized in that, The diffraction orders of the first and second planar gratings are +1 and -1, respectively.

6. A spaceborne multi-view polarization spectral imaging system for measuring aerosol optical parameters according to claim 1, characterized in that, The first and second planar gratings both have a grating count of 100 lines / mm.

7. A spaceborne multi-view polarization spectral imaging system for measuring aerosol optical parameters according to claim 1, characterized in that, The four polarizers are a 0° polarizer, a 45° polarizer, a 90° polarizer, and a 135° polarizer.

8. A spaceborne multi-view polarization spectral imaging system for measuring aerosol optical parameters according to claim 1, characterized in that, The spectral detection range of the system is 380nm to 900nm.

9. A spaceborne multi-view polarization spectral imaging system for measuring aerosol optical parameters according to claim 1, characterized in that, The first detector, the second detector, the third detector and the fourth detector are all area array CMOS sensors with a pixel size of 5.5μm and an area array pixel size of 2048×2048; The system performs 4×4 merging of detector pixels, resulting in an equivalent pixel size of 22μm and an equivalent area array pixel size of 512×512.

10. A spaceborne multi-view polarization spectral imaging system for measuring aerosol optical parameters according to claim 1, characterized in that, The aerosol optical parameters include aerosol optical thickness, single scattering albedo, complex refractive index, and scattering phase function.

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