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Passive multispectral imaging polarimeter for remote atmospheric and surface studies: design based on optical coatings SAMUEL F. PELLICORI1,*
AND
ELLIOT BURKE2
1
Pellicori Optical Consulting, P.O. Box 60723, Santa Barbara, California 93160, USA HighTide Instruments, 740 Thomas St., Oak View, California 93022, USA *Corresponding author: [email protected]
2
Received 28 September 2015; revised 8 December 2015; accepted 23 December 2015; posted 23 December 2015 (Doc. ID 250842); published 17 February 2016
The passive imaging polarimeter architecture is based on optical coatings and thereby avoids the complexities of current systems that use rotating polarizers, phase-modulating retarders, and birefringent elements. Coatings on stationary elements separate spectral regions and their polarized components to simultaneously produce images of the Stokes linear polarization intensities in fields of view (FOVs) ≥30°. Wavelength and FOV coverages are limited only by the telescope and relay optics employed. The images are collected in identical spectral passbands that can extend from UV to shortwave IR. An example relevant to remote sensing in the 360–900 nm range is given. An on-board calibration and stability monitor is included. © 2016 Optical Society of America OCIS codes: (010.0280) Remote sensing and sensors; (010.0010) Atmospheric and oceanic optics; (120.5410) Polarimetry; (280.1100) Aerosol detection. http://dx.doi.org/10.1364/AO.55.001291
1. INTRODUCTION Polarimetry over wide spectral ranges and fields of view (FOVs) enables the study and quantification of optical properties in remote scenes. Polarimetric imaging of atmospheric, terrestrial, and aquatic properties from space or airborne platforms contains diagnostic and monitoring information complimentary to that obtained from intensity measurements alone. Scenes of interest for climate and Earth resource monitoring include aerosols, greenhouse gases, vegetation and ground surfaces, hydrosols, ocean color dissolved organic matter (CDOM), and chlorophyll density. Extension of measurements to wavelengths as short as 350 nm is desired for better characterization and monitoring of aerosol and ocean color properties that are associated with climate-changing effects. Extraterrestrial applications include atmospheric, surface, and climate-science research on Earth-like planetary bodies. Medical applications include detection and identification of abnormal scatter patterns in animal tissues. Other applications of polarimetry are directed to distinguishing artificial from natural surfaces. A multidisciplinary workshop provided an overview of instrumentation technology and applications [1]. The popular polarimetric techniques as summarized there are variable liquid crystal retarders and micropolarizer array mosaics covering sensor pixels. A polarization analyzer (polarimeter) is able to quantify the polarization properties of a remote scene by isolating individual 1559-128X/16/061291-11$15/0$15.00 © 2016 Optical Society of America
polarized components for measurement and subsequent analysis. A basic conventional instrument requires a high extinction ratio between orthogonal polarization vectors and a minimum polarization-modifying signature. It is desirable for obtaining maximum polarization accuracy (minimum uncertainty) to characterize and monitor residual stray light and surface contaminating effects peculiar to the polarimeter architecture, thereby enabling accurate retrieval of scene polarization properties. Many polarimeter designs have evolved with these goals in mind but have associated inherent wavelength- and field-coverage limitations. The new polarimeter concept and architecture described here overcomes many of the limitations present in conventional or existing polarimeters designs. The advanced coating deposition technology currently available enables the new design to become a practical alternative approach and hardware implementation. Section 2 reviews the historical development of remote polarimeters and the current state of the technology. In Section 3, the details of the individual thin-film components of the new concept and their functions and operation are described. Section 4 presents a discussion of polarization analysis. Section 5 describes the advantages offered by the new design approach. Section 6 presents a summary. Appendix A provides background for historical use of coatings in the space environment.
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2. CURRENT STATE-OF-THE-TECHNOLOGY Early polarimeter applications were directed toward astronomical applications. The designs were based on Wollaston birefringent prisms with high extinction ratios to provide analysis of orthogonal components. That polarimeter design has a long and common heritage that extends from ground-based to balloon flight stellar and planetary instruments, to planet fly-by missions, and eventually to the Research Scanning Polarimeter (RSP) aircraft instrumentation and its offspring, the Aerosol Polarimetry Sensor (APS) instrument [2–6]. Applications now include atmospheric and terrestrial monitoring as well as identification of artificial surface treatments. Polarimeters are defined by their operational mode as reviewed by Tyo et al. who identified four imaging polarimetry architectures according to the division of time, amplitude, aperture, or focal plane array [7]. Each technique has its relative advantages and disadvantages. We further group and categorize the instrumental approach as applied to remote sensing. One approach uses individual analyzers and multiple telescopes and is constructed of multiple individual polarimeters that are sequentially scanned, with the RSP and the APS as examples [3,8]. These polarimeters are composed of hundreds of optical elements, with high cost and initial and long-term alignment issues in harsh environments. Another approach uses a single telescope and S-plane and P-plane analyzers and varies retardance in the optical path to generate the Stokes vector components at 45° and 135°. Varying the retardance requires mechanical motion or electrically produced photoelastic modulation. Sequential measurement systems that rotate the analyzers to generate the different Stokes vector components sacrifice simultaneity, which is important for viewing changing events or scenes. Both approaches are active procedures and also have limited spectral effectiveness due to nonachromatic properties of polarization optics. Most polarimeter designs also employ mechanical motion to change spectral passbands. A nanowire polarizer array mounted to the sensor plane as a mosaic of individual grids oriented at 45° is an example of the passive approach. Its disadvantages are noncoincident imaging and the potential for crosstalk. The polarization state that is not transmitted is reflected and returns to other components of the preceding optics where it can retroreflect and contaminate or dilute the degree of linear polarization (DoLP). When mounted on the sensor array diffraction by the wires can also reduce both spatial resolution and polarization discrimination. In Section 3, we describe a new concept that overcomes the individual limitations of the current polarimetry architectures without sacrificing spectral, temporal, or angular capabilities. Existing polarimeters that employ the two data collection techniques described above include RSP and APS, Polarization and Directionality of Earth Reflectances (POLDAR), Multiangle Spectro-Polarimetric Imager (MSPI), and HyperAnglular Research Polarimeter (HARP). RSP represents the latest in the lineage of Wollaston polarimeters and has a heritage of aircraft flights [8]. The RSP employs six individual fixed telescopes and birefringent crystal analyzers (Wollaston prisms) in 0°–90° and 45°–35° orthogonal pairs for linear polarization analysis. With its small instantane-
Research Article ous FOV (IFOV) of 0.82°, it is not an area imager but requires a large object-space rotating mirror mechanism to timesequence an across-axis swath of the field to the individual telescopes. This approach is necessitated by the limited size of birefringent material available and the small acceptance angle of the Wollaston prism. Strings of dichroic and individual passband filters occupy each analyzed beam. The use of common optical elements in the orthogonal-analyzing paths makes the design vulnerable to potential polarization cross-contamination from surface scatter and contamination. Telescope bore sighting error between the individual FOVs is potentially a serious source of polarization error. POLDER requires a large filter wheel to sequence individual spectral and polarizing filters, six for photometry and three (443, 667, and 865 nm) for polarimetry. Three flat polarizers are mounted to the three supposedly identical bandpass filters. A measurement of polarization is obtained by sequencing the filter wheel and requires 0.6 s. To obtain simultaneous measurements on a single FOV requires prism wedges to steer the beam and compensate for satellite motion [9]. The Observing System Including PolaRization in the Solar Infrared Spectrum is an extension of POLDER and adds a second instrument to cover four bands at the shortwave IR wavelengths [10]. MSPI uses dual photoelastic modulators (PEMs) to introduce retardance for analyzing the polarization vectors. Polarimetry is performed at wavelengths 470, 660, and 1595 nm. Polarization accuracy and operational stability of PEM-based polarimeters are influenced by the nonuniform birefringence present across the optical beam, by thermal effects on retardance, and by acceptance angle and limited beam diameter. Risk modes include loss of synchronization of the modulation frequency and driver failure [11,12]. Reported polarization uncertainty is 0.5%. PEMs do not have a heritage in space flight application and require monitoring of their retardance to maintain stability. The HARP polarimeter is a compact passive instrument that provides simultaneous Stokes linear vector image products over a 120° FOV. The HARP polarimeter is the only known operational system that uses thin-film coatings for partial polarization analysis. Polarization separation into three image ports is achieved through beam-dividing coatings at the interfaces of a Philips-type prism. Four spectral passbands are located in the range ∼400–900 nm. Extension to shorter wavelengths is limited by absorption in the glasses of the wide-angle lens and the prism [13]. The spectral passbands commonly included in atmospheric, landmass, water-body measurements and climate-product monitoring, along with their FWHM (BW), are: 388/ 410 nm (20 nm), 443 (20), 490 (20), 555 (20), 670 (20), 763 (10), 765 (40), 865 (40), 910 (20), 1370 (40), 1650 (40), 2150 (40) [14]. Aerosol and hydrosol researchers are requesting extension to 350 nm. The passive multispectral imaging polarimeter (PMSIP) described here provides the required measurements with lower risk and coverage to shorter UV wavelengths than available with existing instruments. The new polarimeter design can be adapted to operate in passbands anywhere in the ∼350 to ∼2200 nm range. For example, the
Research Article use of InGaAs sensor arrays would enable coverage to ∼1700 nm. 3. DESCRIPTION AND KEY FEATURES OF THE PASSIVE MULTISPECTRAL IMAGING POLARIMETER DESIGN A. Optical System
The PMSIP design provides the ability to analyze polarization without moving parts and extend polarimetry to wavelengths shorter than visible/near-UV wavelengths. Thin-film coatings divide the incident beam from the telescope into two or more spectral branches with the advantage versatile adaptability to different spectral bandpass regions. The spectrally separated beam paths are then further separated into polarization analyzing channels. PMSIP can be considered as an evolution of the HARP design [13], which uses coatings internal to a Philipstype beam-splitting prism. Because natural surfaces and suspended particles scatter only linear polarization and very little if any elliptical polarization, the intensities are measured from which only linear Stokes vectors are derived. The advantage provided by thin-film coated elements in contrast to active and birefringent components is that they can be made to unlimited sizes, with uniform properties thereby permitting larger field angles to be covered in trade for larger optics sizes. The key components of the PMSIP concept are the thin-film nonpolarizing spectral beam dividers (NPSBDs) and the partially polarizing beam dividers (PPBDs). All-dielectric coatings are used as the reflecting and beam-dividing coatings because they have higher reflection than metals and no absorption losses. Dielectric coatings introduce low retardance, and as a result the introduction of elliptical polarization is minimized or avoided. Efficient antireflection (AR) coatings that are optimized for specific spectral passbands and incident angles minimize any
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polarization separation created at surfaces. The Macleod Thin Film program has been used for design and analysis (www. thinfilmcenter.com). Figure 1 illustrates the arrangement of the components that make up the PMSIP polarimeter. Energy from the telescope exits the field-defining aperture, is collimated by the relay lens, and then divided into two spectral branches by the NPSBD. Each spectral branch is filtered by a multibandpass filter (MBPF). The MBPF defines and isolates identical mission-specific passbands in each of the two spectral regions and provides high out-of-band rejection. The common beam of each branch is next divided by PPBDs into paths that contain the S-, 45°, and P-intensity components. (The “S-plane” is perpendicular to the plane of reflection, which is the common plane for all of the PPBDs.) Nanowire polarizers eliminate residual cross polarization from the PPBDs by increasing the extinction ratios to ∼1000:1. Finally, imaging lenses focus the field stop onto the individual S-, 45°, and P-sensor pixels that are covered by strip arrays of bandpass filters. The strip filters assign specific rows of pixels to the previously defined passbands. The strip filter passbands are wider than those defined by the MBPF. A similar spectral-band isolation system is used in HARP. One strip of pixels is separately assigned to the calibration and stability monitor LED source described below. Figure 2 presents a ray trace through the individual components of the PMSIP optical system. The common telescope objective lens images the field on a field-defining aperture. The relay lens system produces parallel rays for each sector of the FOV, thereby eliminating filed-dependent sensitivity. The following lens relays the pupil 1:1 and collimates the beam. Larger relative beam size is traded for large FOV coverage according to the optical invariant principle. In the example described here, the optical components are ∼37 mm in diameter
Fig. 1. Key components of the PMSIP. The wavelength section covering 350–500 nm is shown folded upward in the plane of the paper; an identical section covering 500–900 nm is partially shown going to the right.
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Fig. 2. Field and pupil ray trace through the optics of the passive polarimeter (PMSIP) designed to cover spectral bands between 350 and 900 nm. Scene radiance enters the telescope from the left direction. NPSBDs and PPBDs produce spectral-region and polarization-component separation, respectively. Calibration LED sources transmitted by the NPSBD follow the polarization optical paths and can be switched on to provide intensity and polarization monitoring. The optical layout is planar.
and the marginal ray angle is 8.4° for a 30° FOV. The long focal lengths of the relay optics collimators increase the collimated space path length and reduce the field angle at the beam dividers and partial polarizers. The relay optics consist of two infinite-conjugate lenses that are, in the example, design identical and transmit the wavelength range from 350 to 900 nm. The objective lens and collimator consist of five air-spaced elements in the preliminary design. Each lens group is corrected separately. Good image quality is obtained with this design: the spot size is less than two pixel widths (∼15 μm) over the entire field. The initial design is greatly over constrained; for example, the image at the field stop does not require high image quality, and the objective lens can be optimized as part of the entire optical system. Further, only the objective lens and first group of the relay optics need to be corrected for the entire wavelength range of the instrument. The second lens group of the relay need only be correct for the optics in the 350–500 nm and 500–900 nm branches. Correcting over the entire wavelength range requires glasses appropriate for apochromatic operation. Some degree of residual chromatic aberration remains at the shortest wavelengths of ∼350 nm. By optimizing the second group of relay optics for each wavelength band, the chromatic correction need only be achromatic. Optical glasses with high transmission to the Hg 365 nm line are used. Elements made from calcium fluoride and glasses with similar properties are employed. Imaging lenses of a common design reimage the
field onto the 2D sensor arrays (for example, the KAI04070 from Truesense Imaging, Inc.). While the design described here covers a nominal 30° FOV, the aft-optics design can function with an objective lens of longer or shorter focal length. For example, substitution of a long focal length objective, such as a reflecting telescope, can be used to obtain polarization measurements at the subarcsecond angular scale. The ensquared energy is ∼90% within 1.5 pixels for the system, which has been optimized for a 30° FOV and 380 nm wavelength, as shown in Fig. 3. Out-of-band (spectral) energy and residual reflections from surfaces are potential sources of polarimetric error in imagers
Fig. 3. Ensquared energy versus radius for the PMSIP system working in the 380 nm wavelength range and optimized for 30° FOV.
Research Article because they can cross-contaminate the polarized beams and dilute their extinction ratios. Measures incorporated in the PMSIP design to reduce the intensities of ghost images and crosstalk rays include employing all curved and flat surface wide-angle AR coatings specific to the passbands and spacing and tilting the nanowire polarizers to prevent reflections from incidence on the sensor. For example, the AR coatings on the lens surfaces have R averages as low as ∼0.2% within the specific 20 to 40 nm passbands over the range of incidence angles. Reflection between neighboring surfaces and the sensor window and pixels is a common cause for polarization dilution and cross-contamination in imagers. The AR coatings on the imaging lens elements near the sensor arrays are designed to minimize retroreflection for their respective polarization orientation, thereby minimizing this source of error. B. Spectral Beam Division by Nonpolarizing Spectral Beam Dividers
The NPSBD coatings divide the incident beam into two spectral branches to enable simultaneous IFOV multispectral passband measurements. The NPSBD substrate is a high-index, low-dispersion glass 0.5 to 1 mm thick. The incident surface of the NPSBD element is coated with an AR coating whose reflection is minimized in the specific passbands. The airincident 30° external angle is refracted, for glass of index 1.84 at 400 nm, to an internal incident angle on the coating to 16°. Refracted angles from the edge of the FOV add to the 30° tilted angle. At small internal incidence angles, polarization splitting is reduced to a small level. Dispersion in the glass causes small angular separations of the wavelengths, but this is of no consequence because passband isolation is later relegated to specific lines of pixels by strip filters on the sensor arrays. We illustrate the performance of our thin-film design for a NPSBD that is applicable for wavelengths between ∼350 nm and ∼1200 nm. The thin-film spectral beam-divider separates the wavelength regions into two branches in this example: reflecting from 350 to 470 nm and transmitting from 500 to 900 nm. The coating is on the second surface, thereby operating at a reduced (internal) angle of incidence. The measured performance of this proof-of-concept example is shown in Fig. 4
Fig. 4. Measured P- and S-transmittances at 30° incidence for the proof-of-concept NPSBD. Wavelengths shorter than 410 nm are reflected; wavelengths 530 to >950 nm are transmitted. The diattenuation (polarizance) for passbands of interest is 950 nm. The reflected or transmitted polarizance property (also known as diattenuation [15]) of a polarizing optical element is calculated from the intensities, (Imax − Imin)/(Imax + Imin). Because Rs ∼ Rp and Ts ∼ Tp, the introduced polarization spectral polarizance for the example NPSBD shown is ≤0.2% for the spectral bands at 375, 410, 480, 560, 670, 865, and 910 nm. Centering the passbands for different specific spectral bands can be achieved by a simple design alteration. This coating consists of multilayers of silicon dioxide and tantalum pentoxide; the latter has some absorption below ∼400 nm. For wavelength operation shorter than ∼350 nm, hafnium dioxide would be substituted for tantalum pentoxide, and a reflective telescope would be used trading for a smaller FOV. For wavelengths longer than 2300 nm, a NPSBD that separates longer wavelengths would be added. An advantage to the spectral separation technique provided by the PMSIP design is that the optimum sensor for a specific wavelength region can be used. For example, separate silicon image sensor arrays, one optimized for UV and another optimized for longer wavelengths, are made possible with the design. This ability provides SNR improvement over existing designs that attempt to cover a wide spectral range with a single spectral response. Another advantage to separate sensor utilization is the further attention of out-of-band energy that may be residual after filtering by the MBPF, described below. C. Multispectral In-Band Definition and Out-of-Band Rejection
A novel bandpass-isolating component is introduced that produces identical center wavelengths and passbands for each spectral region. The MBPF in each wavelength branch eliminates passband differences and wavelength uncertainties in the polarization analysis channels that may be caused by instrument artifacts, thus insuring that each passband is identical. The performance of the MBPF concept has been demonstrated using the unique design and deposition controlling software created by Southwell [16]. The MBPF defines the passbands and rejects energy outside the desired passbands to at least 1%, and on average to 0.1%, relative to the in-band transmittance. Because it is placed at the system pupil image, all rays from the field travel a common path at the same incidence angles insuring that each polarization analysis path has identical passbands. Thus, potential errors that may exist in other polarimeter designs that can originate from switching filters or from using physically different filters or different optical paths are avoided. Polarization sensitivity caused by incidence angle effects on focal plane filters has been discovered and characterized [17]. This effect varies with pixel location at the focal plane and is eliminated in the present design by the introduction of the MBPF at a pupil image. Another advantage made possible with the MBPF is the ability to design to the relative signal levels by scaling the individual passband transmittances to accommodate the range of radiances from specific scene objects. For example, in remote
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Fig. 5. Predicted transmittance of a MBPF design example as integrated over a 15° cone for passbands centered at 440, 550, 670, and 865 nm that are the bands in the visible-near infrared section of the polarimeter of interest for atmospheric studies. Out-of-band blocking is to optical density (OD) 3 avg. The design can be modified to transmit a different set of bands.
sensing from orbit, radiance levels vary greatly between bright snow and cloud coverage in visible wavelengths versus the low radiance in water absorption bands. This design feature permits the dynamic range of the sensor to be limited and results in maintaining linearity and the total data range. Figure 5 shows the predicted transmittance of a MBPF design for four specific passbands within the 400–900 nm region as integrated over a 15° incident cone. In-band transmittance is high and the average between-band and band-to-band rejection is 103 to 104 . Other passbands within the 350 to 450 nm wavelength range can be chosen at the MBPF design stage. An example demonstrating the ability to manufacture a multiline filter, Fig. 6, shows the transmittance/reflectance of a manufactured rugate filter that exhibits identical performance to its theoretical design. While a multiband reflection filter coating is shown, the same software-controlled deposition process is used to design and produce the MBPF for isolation of multispectral transmission bands in the PMSIP polarimeter architecture. To isolate the passbands to specific pixel rows on the sensor arrays, an array of strip filters is mounted to the sensor arrays. The bandwidths of these focal-plane strip filters are made wider to include the specific bandpasses transmitted by the MBPF without conflicting overlap. The majority of the out-of-band rejection is provided by the MBPF, thereby lessening that re-
Fig. 6. Agreement between the Southwell design and the deposited multiband reflection filter (MBPF) represents the ability of the coating technology to produce the multiple reflection bandpasses shown as notches in this transmission curve. (Table Mountain Optics, Westlake Village, California. Manufactured by Optical Coating Solutions, Camarillo, California.)
quirement for the strip filter assembly. Strips of field are sequentially measured as the polarimeter is scanned in a direction perpendicular to the strip filter long dimension. Previous instruments [moderate resolution imaging spectroradiometer (MODIS), visible infrared imaging radiometer suite (VIIRS), and others] employ similar strip filters integrated to focal plane arrays to define the passbands but suffer from spectral and polarization interactions due to the spatially varying incidence angle [17]. D. Polarization Separation
After leaving the spectral beam divider and MBPF, the spectrally filtered beam is divided into three intensity components by the thin-film PPBDs. Refer to Figs. 1 and 2. The incident beam is partially reflected and partially transmitted by the first partial partially polarization beam divider, PPBD 1. The two PPBDs work in conjunction to produce balanced polarized energy throughputs of ∼33% in the three analyzer channels. PPBD 1 transmits ∼33% of the P-plane polarization intensity to its image sensor and reflects residual S- and P-energy to PPBD 2. At PPBD 2, S-plane light is reflected to its image sensor and combined reflected and transmitted S- and Pcomponents from PPBD 1 and PPBD 2 are sensed as the 45° intensity components, which are used to compute the orientation of the polarization. PPBD coatings are deposited on the entrance surface of the glass, and the exit face has an efficient AR coating optimized for the passbands of interest. Following each PPBD is a plate-type nanowire linear polarization analyzer with its axis oriented to pass the desired polarization and remove the undesired orthogonal polarized residuals. The reflected S-plane intensity from the PPBD is analyzed by a nanowire analyzer whose transmission axis is oriented to pass only S-plane intensity. Similarly, an analyzer with P-plane orientation filters the transmitted Pplane channel. The combined transmitted beam from PPBD 2 is analyzed by a polarization analyzer oriented to pass the 45° components. These combined analyzers produce extinction ratios of >1000:1 [18]. With this arrangement of beam dividers and analyzers, the scene is simultaneously mapped with high polarization isolation in each of the three Stokes linear intensity components. Figure 7 shows the computed performances of PPBD 1 designed in this example for wavelengths from 350 to 475 nm. The excess P-plane polarization is transmitted by PPBD 1 to the P-plane sensor, and residual S (0°) and P (90°) intensities are
Fig. 7. Computed reflectance (R) and transmittance (T) performances for the partially polarizing beam-divider, PPBD 1.
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visible, near-IR,IR and IR wavelength section configurations of the PMSIP.
4. POLARIMETRIC ANALYSIS AND UNCERTAINTY The PMSIP polarimeter collects three intensity images: I0°, I90°, and I45°. The analyzer angles are referenced to the reflection plane of the beam-divider optics. The three measured intensities comprise the Stokes vectors for linearly polarized light [19], where A’s are amplitudes along the S- and P-plane axes, I’s are intensities, and δ is the phase difference,
Fig. 8. Computed T and R for the PPBD 2.
reflected to PPBD 2, as shown in Fig. 1. PPBD 2 reflects the excess S-plane intensity to its sensor and transmits the 45° combined residual intensity components. The acceptance angle includes a cone half-angle of 12.6° (corresponding to a 45° FOV), which is significantly larger than is possible with a Wollaston birefringent polarizing prism. Larger beam areas are readily accommodated with thin-film elements in trade for large incidence angles according to the optical invariant rule. This property produces the advantage that a constant degree of polarization separation will be maintained over large objectspace field angles. The PPBD designs in Figs. 7 and 8 consist of 38 and 26 layers, respectively, where all layers are of nonquarter wave optical thickness with no unmanageably thin layers. Nanowire polarizers that follow the PPBDs increase the total extinction ratio for each analyzed component to ∼1000:1. The low sensitivity of the polarization separation in PPBDs to the incidence angle for wide FOVs is further reduced by these nanowire analyzers, since they pass only their polarization orientation. Their wide acceptance angles allow them to be tilted in the beams to avoid retroreflection of the orthogonal (nontransmitted) polarization orientation, which might introduce ghost images and dilute polarization isolation in the other channels. Since they are situated in a collimated beam and removed from an image plane, their influence on image quality is small. The diffraction and direct obscuration of pixels that occurs with grid polarizer matrices in the division of focal plane polarimeter designs is thereby avoided. A section containing longer wavelengths can be folded out with an additional NPSBD, as illustrated in Fig. 1. The design and the analysis process would be repeated for the subsequent
S0 As2 Ay2 I0 I90 S1 As2 − Ay2 I0 − I90 S2 2AsAy cos δ I45 − I135 S3 2AsAy sin δ Ileft circ: − Iright circ:: The first three components are necessary and sufficient to solve for DoLP, the fourth applies to circular polarization which is negligible in natural surfaces. It can be shown that the 135° component orthogonal to 45° is redundant. The three measurements made with PMSIP give for S2, S2 2I45 − I0 I90 and DoLP SQRTS12 S22 ∕S0: A potential contributor to polarimetric uncertainty can be contributed near the crossover from reflection to transmission where short- and long-wavelength regions are not strictly polarized. The thin-film design approach provides the versatility that the curves can be flattened in the in-band R and T passbands, and the values can be maximized to minimize polarization separation. This can be accomplished by positioning the transition wavelength between reflection and transmission to accommodate the particular set of mission-dictated passbands. In the following example for NPSBD design containing 31 layers, Rs and Rp were maximized for wavelengths between ∼380 and 420 nm. We analyzed the behavior to different total angle content by combining a cone of rays corresponding to the FOV combined with the 30° tilt angle of the NPSBD element. Curves in Fig. 9 show that the computed reflectance and transmittance curves for FOVs of 30°, 45°, and 60° exhibit low sensitivity of the design to field angle. Transmittance (%)
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Fig. 9. (a) Modeled polarized reflectances and (b) transmittances of a NPSBD at unpolarized incidence angles resulting from FOVs of 60°, 45°, and 30°. S-planes or 0° (red) are wider in reflectance than the P-planes (90°). The performance has not been optimized in all of the transmitted bands in this example.
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Fig. 10. Calculated DoLP versus FOV within 380 and 420 nm for the NPSBD design used in Fig. 8.
Passbands centered within the 380 to 435 nm range are reflected; regions at wavelengths longer than 525 nm are transmitted. Our designs for the thin-film beam-dividing components do not introduce significant spectral- or angledependent phase differences (retardance). Large retardance, if present, can dilute the polarization discrimination among the channels and thereby reduce the polarization measurement accuracy. The small spectral dependence of retardance for these thin-film coatings makes them superior to birefringent materials that exhibit large dispersion-related retardance changes, especially at short wavelengths. The retardances between the S- and P-components introduced by the NPSBD for the reflected UV wavelengths are ≤3°; the transmitted retardances are 180° 5° over the visible–near-IR passbands. These small retardances and the fact that reflectance averages I90 98% and I0–0.8%, the calculated values for S2 and S3 are
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Passive multispectral imaging polarimeter for remote atmospheric and surface studies: design based on optical coatings SAMUEL F. PELLICORI1,*
AND
ELLIOT BURKE2
1
Pellicori Optical Consulting, P.O. Box 60723, Santa Barbara, California 93160, USA HighTide Instruments, 740 Thomas St., Oak View, California 93022, USA *Corresponding author: [email protected]
2
Received 28 September 2015; revised 8 December 2015; accepted 23 December 2015; posted 23 December 2015 (Doc. ID 250842); published 17 February 2016
The passive imaging polarimeter architecture is based on optical coatings and thereby avoids the complexities of current systems that use rotating polarizers, phase-modulating retarders, and birefringent elements. Coatings on stationary elements separate spectral regions and their polarized components to simultaneously produce images of the Stokes linear polarization intensities in fields of view (FOVs) ≥30°. Wavelength and FOV coverages are limited only by the telescope and relay optics employed. The images are collected in identical spectral passbands that can extend from UV to shortwave IR. An example relevant to remote sensing in the 360–900 nm range is given. An on-board calibration and stability monitor is included. © 2016 Optical Society of America OCIS codes: (010.0280) Remote sensing and sensors; (010.0010) Atmospheric and oceanic optics; (120.5410) Polarimetry; (280.1100) Aerosol detection. http://dx.doi.org/10.1364/AO.55.001291
1. INTRODUCTION Polarimetry over wide spectral ranges and fields of view (FOVs) enables the study and quantification of optical properties in remote scenes. Polarimetric imaging of atmospheric, terrestrial, and aquatic properties from space or airborne platforms contains diagnostic and monitoring information complimentary to that obtained from intensity measurements alone. Scenes of interest for climate and Earth resource monitoring include aerosols, greenhouse gases, vegetation and ground surfaces, hydrosols, ocean color dissolved organic matter (CDOM), and chlorophyll density. Extension of measurements to wavelengths as short as 350 nm is desired for better characterization and monitoring of aerosol and ocean color properties that are associated with climate-changing effects. Extraterrestrial applications include atmospheric, surface, and climate-science research on Earth-like planetary bodies. Medical applications include detection and identification of abnormal scatter patterns in animal tissues. Other applications of polarimetry are directed to distinguishing artificial from natural surfaces. A multidisciplinary workshop provided an overview of instrumentation technology and applications [1]. The popular polarimetric techniques as summarized there are variable liquid crystal retarders and micropolarizer array mosaics covering sensor pixels. A polarization analyzer (polarimeter) is able to quantify the polarization properties of a remote scene by isolating individual 1559-128X/16/061291-11$15/0$15.00 © 2016 Optical Society of America
polarized components for measurement and subsequent analysis. A basic conventional instrument requires a high extinction ratio between orthogonal polarization vectors and a minimum polarization-modifying signature. It is desirable for obtaining maximum polarization accuracy (minimum uncertainty) to characterize and monitor residual stray light and surface contaminating effects peculiar to the polarimeter architecture, thereby enabling accurate retrieval of scene polarization properties. Many polarimeter designs have evolved with these goals in mind but have associated inherent wavelength- and field-coverage limitations. The new polarimeter concept and architecture described here overcomes many of the limitations present in conventional or existing polarimeters designs. The advanced coating deposition technology currently available enables the new design to become a practical alternative approach and hardware implementation. Section 2 reviews the historical development of remote polarimeters and the current state of the technology. In Section 3, the details of the individual thin-film components of the new concept and their functions and operation are described. Section 4 presents a discussion of polarization analysis. Section 5 describes the advantages offered by the new design approach. Section 6 presents a summary. Appendix A provides background for historical use of coatings in the space environment.
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2. CURRENT STATE-OF-THE-TECHNOLOGY Early polarimeter applications were directed toward astronomical applications. The designs were based on Wollaston birefringent prisms with high extinction ratios to provide analysis of orthogonal components. That polarimeter design has a long and common heritage that extends from ground-based to balloon flight stellar and planetary instruments, to planet fly-by missions, and eventually to the Research Scanning Polarimeter (RSP) aircraft instrumentation and its offspring, the Aerosol Polarimetry Sensor (APS) instrument [2–6]. Applications now include atmospheric and terrestrial monitoring as well as identification of artificial surface treatments. Polarimeters are defined by their operational mode as reviewed by Tyo et al. who identified four imaging polarimetry architectures according to the division of time, amplitude, aperture, or focal plane array [7]. Each technique has its relative advantages and disadvantages. We further group and categorize the instrumental approach as applied to remote sensing. One approach uses individual analyzers and multiple telescopes and is constructed of multiple individual polarimeters that are sequentially scanned, with the RSP and the APS as examples [3,8]. These polarimeters are composed of hundreds of optical elements, with high cost and initial and long-term alignment issues in harsh environments. Another approach uses a single telescope and S-plane and P-plane analyzers and varies retardance in the optical path to generate the Stokes vector components at 45° and 135°. Varying the retardance requires mechanical motion or electrically produced photoelastic modulation. Sequential measurement systems that rotate the analyzers to generate the different Stokes vector components sacrifice simultaneity, which is important for viewing changing events or scenes. Both approaches are active procedures and also have limited spectral effectiveness due to nonachromatic properties of polarization optics. Most polarimeter designs also employ mechanical motion to change spectral passbands. A nanowire polarizer array mounted to the sensor plane as a mosaic of individual grids oriented at 45° is an example of the passive approach. Its disadvantages are noncoincident imaging and the potential for crosstalk. The polarization state that is not transmitted is reflected and returns to other components of the preceding optics where it can retroreflect and contaminate or dilute the degree of linear polarization (DoLP). When mounted on the sensor array diffraction by the wires can also reduce both spatial resolution and polarization discrimination. In Section 3, we describe a new concept that overcomes the individual limitations of the current polarimetry architectures without sacrificing spectral, temporal, or angular capabilities. Existing polarimeters that employ the two data collection techniques described above include RSP and APS, Polarization and Directionality of Earth Reflectances (POLDAR), Multiangle Spectro-Polarimetric Imager (MSPI), and HyperAnglular Research Polarimeter (HARP). RSP represents the latest in the lineage of Wollaston polarimeters and has a heritage of aircraft flights [8]. The RSP employs six individual fixed telescopes and birefringent crystal analyzers (Wollaston prisms) in 0°–90° and 45°–35° orthogonal pairs for linear polarization analysis. With its small instantane-
Research Article ous FOV (IFOV) of 0.82°, it is not an area imager but requires a large object-space rotating mirror mechanism to timesequence an across-axis swath of the field to the individual telescopes. This approach is necessitated by the limited size of birefringent material available and the small acceptance angle of the Wollaston prism. Strings of dichroic and individual passband filters occupy each analyzed beam. The use of common optical elements in the orthogonal-analyzing paths makes the design vulnerable to potential polarization cross-contamination from surface scatter and contamination. Telescope bore sighting error between the individual FOVs is potentially a serious source of polarization error. POLDER requires a large filter wheel to sequence individual spectral and polarizing filters, six for photometry and three (443, 667, and 865 nm) for polarimetry. Three flat polarizers are mounted to the three supposedly identical bandpass filters. A measurement of polarization is obtained by sequencing the filter wheel and requires 0.6 s. To obtain simultaneous measurements on a single FOV requires prism wedges to steer the beam and compensate for satellite motion [9]. The Observing System Including PolaRization in the Solar Infrared Spectrum is an extension of POLDER and adds a second instrument to cover four bands at the shortwave IR wavelengths [10]. MSPI uses dual photoelastic modulators (PEMs) to introduce retardance for analyzing the polarization vectors. Polarimetry is performed at wavelengths 470, 660, and 1595 nm. Polarization accuracy and operational stability of PEM-based polarimeters are influenced by the nonuniform birefringence present across the optical beam, by thermal effects on retardance, and by acceptance angle and limited beam diameter. Risk modes include loss of synchronization of the modulation frequency and driver failure [11,12]. Reported polarization uncertainty is 0.5%. PEMs do not have a heritage in space flight application and require monitoring of their retardance to maintain stability. The HARP polarimeter is a compact passive instrument that provides simultaneous Stokes linear vector image products over a 120° FOV. The HARP polarimeter is the only known operational system that uses thin-film coatings for partial polarization analysis. Polarization separation into three image ports is achieved through beam-dividing coatings at the interfaces of a Philips-type prism. Four spectral passbands are located in the range ∼400–900 nm. Extension to shorter wavelengths is limited by absorption in the glasses of the wide-angle lens and the prism [13]. The spectral passbands commonly included in atmospheric, landmass, water-body measurements and climate-product monitoring, along with their FWHM (BW), are: 388/ 410 nm (20 nm), 443 (20), 490 (20), 555 (20), 670 (20), 763 (10), 765 (40), 865 (40), 910 (20), 1370 (40), 1650 (40), 2150 (40) [14]. Aerosol and hydrosol researchers are requesting extension to 350 nm. The passive multispectral imaging polarimeter (PMSIP) described here provides the required measurements with lower risk and coverage to shorter UV wavelengths than available with existing instruments. The new polarimeter design can be adapted to operate in passbands anywhere in the ∼350 to ∼2200 nm range. For example, the
Research Article use of InGaAs sensor arrays would enable coverage to ∼1700 nm. 3. DESCRIPTION AND KEY FEATURES OF THE PASSIVE MULTISPECTRAL IMAGING POLARIMETER DESIGN A. Optical System
The PMSIP design provides the ability to analyze polarization without moving parts and extend polarimetry to wavelengths shorter than visible/near-UV wavelengths. Thin-film coatings divide the incident beam from the telescope into two or more spectral branches with the advantage versatile adaptability to different spectral bandpass regions. The spectrally separated beam paths are then further separated into polarization analyzing channels. PMSIP can be considered as an evolution of the HARP design [13], which uses coatings internal to a Philipstype beam-splitting prism. Because natural surfaces and suspended particles scatter only linear polarization and very little if any elliptical polarization, the intensities are measured from which only linear Stokes vectors are derived. The advantage provided by thin-film coated elements in contrast to active and birefringent components is that they can be made to unlimited sizes, with uniform properties thereby permitting larger field angles to be covered in trade for larger optics sizes. The key components of the PMSIP concept are the thin-film nonpolarizing spectral beam dividers (NPSBDs) and the partially polarizing beam dividers (PPBDs). All-dielectric coatings are used as the reflecting and beam-dividing coatings because they have higher reflection than metals and no absorption losses. Dielectric coatings introduce low retardance, and as a result the introduction of elliptical polarization is minimized or avoided. Efficient antireflection (AR) coatings that are optimized for specific spectral passbands and incident angles minimize any
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polarization separation created at surfaces. The Macleod Thin Film program has been used for design and analysis (www. thinfilmcenter.com). Figure 1 illustrates the arrangement of the components that make up the PMSIP polarimeter. Energy from the telescope exits the field-defining aperture, is collimated by the relay lens, and then divided into two spectral branches by the NPSBD. Each spectral branch is filtered by a multibandpass filter (MBPF). The MBPF defines and isolates identical mission-specific passbands in each of the two spectral regions and provides high out-of-band rejection. The common beam of each branch is next divided by PPBDs into paths that contain the S-, 45°, and P-intensity components. (The “S-plane” is perpendicular to the plane of reflection, which is the common plane for all of the PPBDs.) Nanowire polarizers eliminate residual cross polarization from the PPBDs by increasing the extinction ratios to ∼1000:1. Finally, imaging lenses focus the field stop onto the individual S-, 45°, and P-sensor pixels that are covered by strip arrays of bandpass filters. The strip filters assign specific rows of pixels to the previously defined passbands. The strip filter passbands are wider than those defined by the MBPF. A similar spectral-band isolation system is used in HARP. One strip of pixels is separately assigned to the calibration and stability monitor LED source described below. Figure 2 presents a ray trace through the individual components of the PMSIP optical system. The common telescope objective lens images the field on a field-defining aperture. The relay lens system produces parallel rays for each sector of the FOV, thereby eliminating filed-dependent sensitivity. The following lens relays the pupil 1:1 and collimates the beam. Larger relative beam size is traded for large FOV coverage according to the optical invariant principle. In the example described here, the optical components are ∼37 mm in diameter
Fig. 1. Key components of the PMSIP. The wavelength section covering 350–500 nm is shown folded upward in the plane of the paper; an identical section covering 500–900 nm is partially shown going to the right.
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Fig. 2. Field and pupil ray trace through the optics of the passive polarimeter (PMSIP) designed to cover spectral bands between 350 and 900 nm. Scene radiance enters the telescope from the left direction. NPSBDs and PPBDs produce spectral-region and polarization-component separation, respectively. Calibration LED sources transmitted by the NPSBD follow the polarization optical paths and can be switched on to provide intensity and polarization monitoring. The optical layout is planar.
and the marginal ray angle is 8.4° for a 30° FOV. The long focal lengths of the relay optics collimators increase the collimated space path length and reduce the field angle at the beam dividers and partial polarizers. The relay optics consist of two infinite-conjugate lenses that are, in the example, design identical and transmit the wavelength range from 350 to 900 nm. The objective lens and collimator consist of five air-spaced elements in the preliminary design. Each lens group is corrected separately. Good image quality is obtained with this design: the spot size is less than two pixel widths (∼15 μm) over the entire field. The initial design is greatly over constrained; for example, the image at the field stop does not require high image quality, and the objective lens can be optimized as part of the entire optical system. Further, only the objective lens and first group of the relay optics need to be corrected for the entire wavelength range of the instrument. The second lens group of the relay need only be correct for the optics in the 350–500 nm and 500–900 nm branches. Correcting over the entire wavelength range requires glasses appropriate for apochromatic operation. Some degree of residual chromatic aberration remains at the shortest wavelengths of ∼350 nm. By optimizing the second group of relay optics for each wavelength band, the chromatic correction need only be achromatic. Optical glasses with high transmission to the Hg 365 nm line are used. Elements made from calcium fluoride and glasses with similar properties are employed. Imaging lenses of a common design reimage the
field onto the 2D sensor arrays (for example, the KAI04070 from Truesense Imaging, Inc.). While the design described here covers a nominal 30° FOV, the aft-optics design can function with an objective lens of longer or shorter focal length. For example, substitution of a long focal length objective, such as a reflecting telescope, can be used to obtain polarization measurements at the subarcsecond angular scale. The ensquared energy is ∼90% within 1.5 pixels for the system, which has been optimized for a 30° FOV and 380 nm wavelength, as shown in Fig. 3. Out-of-band (spectral) energy and residual reflections from surfaces are potential sources of polarimetric error in imagers
Fig. 3. Ensquared energy versus radius for the PMSIP system working in the 380 nm wavelength range and optimized for 30° FOV.
Research Article because they can cross-contaminate the polarized beams and dilute their extinction ratios. Measures incorporated in the PMSIP design to reduce the intensities of ghost images and crosstalk rays include employing all curved and flat surface wide-angle AR coatings specific to the passbands and spacing and tilting the nanowire polarizers to prevent reflections from incidence on the sensor. For example, the AR coatings on the lens surfaces have R averages as low as ∼0.2% within the specific 20 to 40 nm passbands over the range of incidence angles. Reflection between neighboring surfaces and the sensor window and pixels is a common cause for polarization dilution and cross-contamination in imagers. The AR coatings on the imaging lens elements near the sensor arrays are designed to minimize retroreflection for their respective polarization orientation, thereby minimizing this source of error. B. Spectral Beam Division by Nonpolarizing Spectral Beam Dividers
The NPSBD coatings divide the incident beam into two spectral branches to enable simultaneous IFOV multispectral passband measurements. The NPSBD substrate is a high-index, low-dispersion glass 0.5 to 1 mm thick. The incident surface of the NPSBD element is coated with an AR coating whose reflection is minimized in the specific passbands. The airincident 30° external angle is refracted, for glass of index 1.84 at 400 nm, to an internal incident angle on the coating to 16°. Refracted angles from the edge of the FOV add to the 30° tilted angle. At small internal incidence angles, polarization splitting is reduced to a small level. Dispersion in the glass causes small angular separations of the wavelengths, but this is of no consequence because passband isolation is later relegated to specific lines of pixels by strip filters on the sensor arrays. We illustrate the performance of our thin-film design for a NPSBD that is applicable for wavelengths between ∼350 nm and ∼1200 nm. The thin-film spectral beam-divider separates the wavelength regions into two branches in this example: reflecting from 350 to 470 nm and transmitting from 500 to 900 nm. The coating is on the second surface, thereby operating at a reduced (internal) angle of incidence. The measured performance of this proof-of-concept example is shown in Fig. 4
Fig. 4. Measured P- and S-transmittances at 30° incidence for the proof-of-concept NPSBD. Wavelengths shorter than 410 nm are reflected; wavelengths 530 to >950 nm are transmitted. The diattenuation (polarizance) for passbands of interest is 950 nm. The reflected or transmitted polarizance property (also known as diattenuation [15]) of a polarizing optical element is calculated from the intensities, (Imax − Imin)/(Imax + Imin). Because Rs ∼ Rp and Ts ∼ Tp, the introduced polarization spectral polarizance for the example NPSBD shown is ≤0.2% for the spectral bands at 375, 410, 480, 560, 670, 865, and 910 nm. Centering the passbands for different specific spectral bands can be achieved by a simple design alteration. This coating consists of multilayers of silicon dioxide and tantalum pentoxide; the latter has some absorption below ∼400 nm. For wavelength operation shorter than ∼350 nm, hafnium dioxide would be substituted for tantalum pentoxide, and a reflective telescope would be used trading for a smaller FOV. For wavelengths longer than 2300 nm, a NPSBD that separates longer wavelengths would be added. An advantage to the spectral separation technique provided by the PMSIP design is that the optimum sensor for a specific wavelength region can be used. For example, separate silicon image sensor arrays, one optimized for UV and another optimized for longer wavelengths, are made possible with the design. This ability provides SNR improvement over existing designs that attempt to cover a wide spectral range with a single spectral response. Another advantage to separate sensor utilization is the further attention of out-of-band energy that may be residual after filtering by the MBPF, described below. C. Multispectral In-Band Definition and Out-of-Band Rejection
A novel bandpass-isolating component is introduced that produces identical center wavelengths and passbands for each spectral region. The MBPF in each wavelength branch eliminates passband differences and wavelength uncertainties in the polarization analysis channels that may be caused by instrument artifacts, thus insuring that each passband is identical. The performance of the MBPF concept has been demonstrated using the unique design and deposition controlling software created by Southwell [16]. The MBPF defines the passbands and rejects energy outside the desired passbands to at least 1%, and on average to 0.1%, relative to the in-band transmittance. Because it is placed at the system pupil image, all rays from the field travel a common path at the same incidence angles insuring that each polarization analysis path has identical passbands. Thus, potential errors that may exist in other polarimeter designs that can originate from switching filters or from using physically different filters or different optical paths are avoided. Polarization sensitivity caused by incidence angle effects on focal plane filters has been discovered and characterized [17]. This effect varies with pixel location at the focal plane and is eliminated in the present design by the introduction of the MBPF at a pupil image. Another advantage made possible with the MBPF is the ability to design to the relative signal levels by scaling the individual passband transmittances to accommodate the range of radiances from specific scene objects. For example, in remote
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sensing from orbit, radiance levels vary greatly between bright snow and cloud coverage in visible wavelengths versus the low radiance in water absorption bands. This design feature permits the dynamic range of the sensor to be limited and results in maintaining linearity and the total data range. Figure 5 shows the predicted transmittance of a MBPF design for four specific passbands within the 400–900 nm region as integrated over a 15° incident cone. In-band transmittance is high and the average between-band and band-to-band rejection is 103 to 104 . Other passbands within the 350 to 450 nm wavelength range can be chosen at the MBPF design stage. An example demonstrating the ability to manufacture a multiline filter, Fig. 6, shows the transmittance/reflectance of a manufactured rugate filter that exhibits identical performance to its theoretical design. While a multiband reflection filter coating is shown, the same software-controlled deposition process is used to design and produce the MBPF for isolation of multispectral transmission bands in the PMSIP polarimeter architecture. To isolate the passbands to specific pixel rows on the sensor arrays, an array of strip filters is mounted to the sensor arrays. The bandwidths of these focal-plane strip filters are made wider to include the specific bandpasses transmitted by the MBPF without conflicting overlap. The majority of the out-of-band rejection is provided by the MBPF, thereby lessening that re-
Fig. 6. Agreement between the Southwell design and the deposited multiband reflection filter (MBPF) represents the ability of the coating technology to produce the multiple reflection bandpasses shown as notches in this transmission curve. (Table Mountain Optics, Westlake Village, California. Manufactured by Optical Coating Solutions, Camarillo, California.)
quirement for the strip filter assembly. Strips of field are sequentially measured as the polarimeter is scanned in a direction perpendicular to the strip filter long dimension. Previous instruments [moderate resolution imaging spectroradiometer (MODIS), visible infrared imaging radiometer suite (VIIRS), and others] employ similar strip filters integrated to focal plane arrays to define the passbands but suffer from spectral and polarization interactions due to the spatially varying incidence angle [17]. D. Polarization Separation
After leaving the spectral beam divider and MBPF, the spectrally filtered beam is divided into three intensity components by the thin-film PPBDs. Refer to Figs. 1 and 2. The incident beam is partially reflected and partially transmitted by the first partial partially polarization beam divider, PPBD 1. The two PPBDs work in conjunction to produce balanced polarized energy throughputs of ∼33% in the three analyzer channels. PPBD 1 transmits ∼33% of the P-plane polarization intensity to its image sensor and reflects residual S- and P-energy to PPBD 2. At PPBD 2, S-plane light is reflected to its image sensor and combined reflected and transmitted S- and Pcomponents from PPBD 1 and PPBD 2 are sensed as the 45° intensity components, which are used to compute the orientation of the polarization. PPBD coatings are deposited on the entrance surface of the glass, and the exit face has an efficient AR coating optimized for the passbands of interest. Following each PPBD is a plate-type nanowire linear polarization analyzer with its axis oriented to pass the desired polarization and remove the undesired orthogonal polarized residuals. The reflected S-plane intensity from the PPBD is analyzed by a nanowire analyzer whose transmission axis is oriented to pass only S-plane intensity. Similarly, an analyzer with P-plane orientation filters the transmitted Pplane channel. The combined transmitted beam from PPBD 2 is analyzed by a polarization analyzer oriented to pass the 45° components. These combined analyzers produce extinction ratios of >1000:1 [18]. With this arrangement of beam dividers and analyzers, the scene is simultaneously mapped with high polarization isolation in each of the three Stokes linear intensity components. Figure 7 shows the computed performances of PPBD 1 designed in this example for wavelengths from 350 to 475 nm. The excess P-plane polarization is transmitted by PPBD 1 to the P-plane sensor, and residual S (0°) and P (90°) intensities are
Fig. 7. Computed reflectance (R) and transmittance (T) performances for the partially polarizing beam-divider, PPBD 1.
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visible, near-IR,IR and IR wavelength section configurations of the PMSIP.
4. POLARIMETRIC ANALYSIS AND UNCERTAINTY The PMSIP polarimeter collects three intensity images: I0°, I90°, and I45°. The analyzer angles are referenced to the reflection plane of the beam-divider optics. The three measured intensities comprise the Stokes vectors for linearly polarized light [19], where A’s are amplitudes along the S- and P-plane axes, I’s are intensities, and δ is the phase difference,
Fig. 8. Computed T and R for the PPBD 2.
reflected to PPBD 2, as shown in Fig. 1. PPBD 2 reflects the excess S-plane intensity to its sensor and transmits the 45° combined residual intensity components. The acceptance angle includes a cone half-angle of 12.6° (corresponding to a 45° FOV), which is significantly larger than is possible with a Wollaston birefringent polarizing prism. Larger beam areas are readily accommodated with thin-film elements in trade for large incidence angles according to the optical invariant rule. This property produces the advantage that a constant degree of polarization separation will be maintained over large objectspace field angles. The PPBD designs in Figs. 7 and 8 consist of 38 and 26 layers, respectively, where all layers are of nonquarter wave optical thickness with no unmanageably thin layers. Nanowire polarizers that follow the PPBDs increase the total extinction ratio for each analyzed component to ∼1000:1. The low sensitivity of the polarization separation in PPBDs to the incidence angle for wide FOVs is further reduced by these nanowire analyzers, since they pass only their polarization orientation. Their wide acceptance angles allow them to be tilted in the beams to avoid retroreflection of the orthogonal (nontransmitted) polarization orientation, which might introduce ghost images and dilute polarization isolation in the other channels. Since they are situated in a collimated beam and removed from an image plane, their influence on image quality is small. The diffraction and direct obscuration of pixels that occurs with grid polarizer matrices in the division of focal plane polarimeter designs is thereby avoided. A section containing longer wavelengths can be folded out with an additional NPSBD, as illustrated in Fig. 1. The design and the analysis process would be repeated for the subsequent
S0 As2 Ay2 I0 I90 S1 As2 − Ay2 I0 − I90 S2 2AsAy cos δ I45 − I135 S3 2AsAy sin δ Ileft circ: − Iright circ:: The first three components are necessary and sufficient to solve for DoLP, the fourth applies to circular polarization which is negligible in natural surfaces. It can be shown that the 135° component orthogonal to 45° is redundant. The three measurements made with PMSIP give for S2, S2 2I45 − I0 I90 and DoLP SQRTS12 S22 ∕S0: A potential contributor to polarimetric uncertainty can be contributed near the crossover from reflection to transmission where short- and long-wavelength regions are not strictly polarized. The thin-film design approach provides the versatility that the curves can be flattened in the in-band R and T passbands, and the values can be maximized to minimize polarization separation. This can be accomplished by positioning the transition wavelength between reflection and transmission to accommodate the particular set of mission-dictated passbands. In the following example for NPSBD design containing 31 layers, Rs and Rp were maximized for wavelengths between ∼380 and 420 nm. We analyzed the behavior to different total angle content by combining a cone of rays corresponding to the FOV combined with the 30° tilt angle of the NPSBD element. Curves in Fig. 9 show that the computed reflectance and transmittance curves for FOVs of 30°, 45°, and 60° exhibit low sensitivity of the design to field angle. Transmittance (%)
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Fig. 9. (a) Modeled polarized reflectances and (b) transmittances of a NPSBD at unpolarized incidence angles resulting from FOVs of 60°, 45°, and 30°. S-planes or 0° (red) are wider in reflectance than the P-planes (90°). The performance has not been optimized in all of the transmitted bands in this example.
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Fig. 10. Calculated DoLP versus FOV within 380 and 420 nm for the NPSBD design used in Fig. 8.
Passbands centered within the 380 to 435 nm range are reflected; regions at wavelengths longer than 525 nm are transmitted. Our designs for the thin-film beam-dividing components do not introduce significant spectral- or angledependent phase differences (retardance). Large retardance, if present, can dilute the polarization discrimination among the channels and thereby reduce the polarization measurement accuracy. The small spectral dependence of retardance for these thin-film coatings makes them superior to birefringent materials that exhibit large dispersion-related retardance changes, especially at short wavelengths. The retardances between the S- and P-components introduced by the NPSBD for the reflected UV wavelengths are ≤3°; the transmitted retardances are 180° 5° over the visible–near-IR passbands. These small retardances and the fact that reflectance averages I90 98% and I0–0.8%, the calculated values for S2 and S3 are
