This PDF file contains the front matter associated with SPIE Proceedings Volume 8873, including the Title Page, Copyright information, Table of Contents, Introduction (if any), and Conference Committee listing.

Broad and narrow-band wire grid polarizer (WGP) products suitable for MWIR and LWIR applications requiring high contrast were developed on antireflection (AR) coated silicon using Moxtek nanowire patterning capabilities. Accurate metrology was gathered in both transmission and reflection from the SWIR to LWIR using a combination of FTIR and dispersive spectrometers, as well as laser-based light sources. The WGP structures were analyzed using SEM, FIB, and STEM techniques and optical data was derived from IR VASE, transmission, and reflectance measurements. Modeling of device performance was achieved using rigorous coupled wave analysis. Laser damage thresholds were determined and various damage mechanisms identified.

We present a method for checking the consistency of a Mueller matrix measurement. The method is based upon the rotational properties of a Mueller matrix. An anisotropic sample is placed in the polarimeter in a precision rotation stage. The Mueller matrix is then measured as a function of sample rotation. Each Mueller matrix is then transformed by matrix rotation back into the Mueller matrix at zero angle. The consistency between these resulting matrices is then taken as an indication of measurement uncertainties. The method is demonstrated with two different samples measured on two different polarimeters.

The single-element rotating-polarizer ellipsometer is where a rotating polarizer is inserted into the incident beam and the reflected-signal intensity is detected using a photodetector. The polarizer is either rotated mechanically or electromagnetically. The angle of incidence of the beam is adjusted to detect the angles where the detector signal is dc. The ellipsometric function of the film-substrate system under measurement is of a unity magnitude at those detected angle(s). The number of required measurements (such angles of incidence) is related (directly proportional) to the number of system parameters to be determined: film thickness is one parameter, film optical constant is two parameters, and substrate optical constant is two parameters. The more parameters to be determined, the more the number of measurements required. This creates film-thickness bands, which number and width depend on the system physical properties and the wavelength used for measurement, and where a continuum exists above a certain film-thickness value. Accordingly, full characterization of film-substrate systems is limited to systems with large film thicknesses for the required multiple angles of incidence to exist. In this paper, we use only one detected angle of incidence to fully characterize the film-substrate system. This allows for film-substrate systems with much smaller film thicknesses to be fully characterized. A fast genetic algorithm is used to heuristically obtain all the system parameters: film thickness and optical constants of the film and the substrate, or any subset thereof.

Combined reflection and transmission ellipsometry of film-substrate systems provides a wealth of experimental information that proves helpful with extracting the system parameters. In such a technique, both the reflection and transmission ellipsometric functions are simultaneously measured. The technique itself requires a special design of the sample for fixed and for multiple angles of incidence measurements. The data reduction could be done using numerical methods which are tedious and time consuming resulting in an overall slower technique. A closed-form inversion for the system parameters (film thickness, film optical constant, and substrate optical constant) would render a fast technique that is suitable for real-time applications. The sample used is a three-film-thickness sample and measurements are carried out at two angles of incidence. Real simple closed-form equations are derived through successive transformations and algebraic manipulations to obtain the optical constants of the film and the substrate, in addition to the film thickness. We propose the use of obtained several values of the film thickness to provide a measure of the accuracy of the experimental measurements. In addition, the special case of a bare-substrate system is considered, and the use of the several values of the substrate refractive index to provide a measure of the accuracy of the experimental measurements in such a case is also proposed. A simple software program, with a limited number of code lines, is developed and tested yielding perfect results.

Polarization imaging sensors using the division-of-focal-plane paradigm have recently emerged on the market. These sensors, due to their compact design, are ideal for field work. One of the major drawbacks in these sensors is the spatial variation of the optical response of individual pixels across the imaging array. These spatial variations are due to variations in the nanowires of the pixelated polarization filters. In this paper, we describe and compare two methods for calibrating a division of focal plane sensors. We present theoretical and experimental data for these calibration methods.

The measured Mueller matrices contain until sixteen independent parameters for each measurement configuration (spectral profile of the wave probe of the polarimeter, angle of incidence, observation direction...) and for each spatially resolved element of the sample (imaging polarimetry). Thus, the polarimetric techniques are widely used for the study of a great variety of material samples in optics and remote sensing. Nevertheless, the relevant physical information does not appear explicitly in the measured parameters and thus the best knowledge of the structure of the physical information contained in a Mueller matrix is required in order to develop appropriate procedures for the polarimetric analysis. In this paper, the physically invariant polarimetric quantities are identified and decoupled, and the main approaches for serial and parallel decompositions of measured Mueller matrices into simple components are reviewed.

When observing a spatially complex mix of aerosols and clouds in a single relatively large field-of-view, nature entangles their signals non-linearly through polarized radiation transport processes that unfold in the 3D position and direction spaces. In contrast, any practical forward model in a retrieval algorithm will use only 1D vector radiative transfer (vRT) in a linear mixing technique. We assess the difference between the observed and predicted signals using synthetic data from a high-fidelity 3D vRT model with clouds generated using a Large Eddy Simulation model and an aerosol climatology. We find that this difference is signal—not noise—for the Aerosol Polarimetry Sensor (APS), an instrument developed by NASA. Moreover, the worst case scenario is also the most interesting case, namely, when the aerosol burden is large, hence hase the most impact on the cloud microphysics and dynamics. Based on our findings, we formulate a mitigation strategy for these unresolved cloud adjacency effects assuming that some spatial information is available about the structure of the clouds at higher resolution from “context” cameras, as was planned for NASA’s ill-fated Glory mission that was to carry the APS but failed to reach orbit. Application to POLDER (POLarization and Directionality of Earth Reflectances) data from the period when PARASOL (Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar) was in the A-train is briefly discussed.

The Airborne Multiangle SpectroPolarimetric Imager (AirMSPI) is an ultraviolet/visible/near-infrared pushbroom camera mounted on a single-axis gimbal to acquire multiangle imagery over a ±67° along-track range. The instrument flies aboard NASA’s high-altitude ER-2 aircraft, and acquires Earth imagery with ~10 m spatial resolution across an 11- km wide swath. Radiance data are obtained in eight spectral bands (355, 380, 445, 470, 555, 660, 865, 935 nm). Dual photoelastic modulators (PEMs), achromatic quarter-wave plates, and wire-grid polarizers also enable imagery of the linear polarization Stokes components Q and U at 470, 660, and 865 nm. During January-February 2013, AirMSPI data were acquired over California as part of NASA’s Polarimeter Definition Experiment (PODEX), a field campaign designed to refine requirements for the future Aerosol-Cloud-Ecosystem (ACE) satellite mission. Observations of aerosols, low- and mid-level cloud fields, cirrus, aircraft contrails, and clear skies were obtained over the San Joaquin Valley and the Pacific Ocean during PODEX. Example radiance and polarization images are presented to illustrate some of the instrument’s capabilities.

In addition to spectral information acquired by traditional multi/hyperspectral systems, passive electro optical and infrared (EO/IR) polarimetric systems also measure the polarization response of different materials in the scene. Such an imaging modality offers a complete optical description of a surface that can be utilized in identifying objects with complex morphological and camouflaged structures. The polarization property of the radiation from a remotely sensed surface, however, depends on the observation geometry of the system. Therefore, acquiring a polarimetric image in a single viewing direction is not sufficient to improve the material discriminability in the absence of a priori knowledge about the object geometry. Hence, this paper presents a novel multi-view polarimetric system for improving the target-background discriminability. The proposed system takes the approach of imaging the scene in three different viewing directions to infer the physical characteristics of the observed surface by utilizing the angular variation in the polarization response. The sensitivity analysis of the proposed polarimetric system that relates target-background discriminability to various scene related parameters indicates the imaging conditions under which the material discriminability is maximized. Furthermore, scenarios where polarization information can be very useful in improving the target contrast are identified by comparing the detection performance of the proposed system to that of a multispectral system.

Because of the increasing variety of applications for polarization imaging and sensing, there is a growing need for information about polarization phenomenology in the natural environment, including the spectral distribution of polarization in the atmosphere. A computer model that has been validated in comparisons with measurements from our all-sky polarization imager has been used here to simulate the spectrum of clear-sky polarization at a many locations around the world, with a wide variety of underlying surface-reflectance and aerosol conditions. This study of the skylight polarization spectral variability shows that there is no simple spectrum that can be assumed or predicted without knowledge of the atmospheric aerosol properties and underlying surface reflectance.

We describe here Mueller matrix microscopy, an imaging technique for investigating the anisotropic properties of the refractive index in biological samples. Tissue properties probed by polarization are the anisotropic real and imaginary parts of the refractive index that modify the polarization. Physical Sciences Inc. has developed a robust polarization microscope that is capable of performing complete Mueller matrix imaging in both transmission and reflection configuration. The system’s capabilities are illustrated on biological samples.

The neuroimaging technique 3D-polarized light imaging (3D-PLI) has opened up new avenues to study the complex nerve fiber architecture of the human brain at sub-millimeter spatial resolution. This polarimetry technique is applicable to histological sections of postmortem brains utilizing the birefringence of nerve fibers caused by the regular arrangement of lipids and proteins in the myelin sheaths surrounding axons. 3D-PLI provides a three-dimensional description of the anatomical wiring scheme defined by the in-section direction angle and the out-of-section inclination angle. To date, 3D-PLI is the only available method that allows bridging the microscopic and the macroscopic description of the fiber architecture of the human brain. Here we introduce a new approach to retrieve the inclination angle of the fibers independently of the properties of the used polarimeters. This is relevant because the image resolution and the signal transmission inuence the measured birefringent signal (retardation) significantly. The image resolution was determined using the USAF- 1951 testchart applying the Rayleigh criterion. The signal transmission was measured by elliptical polarizers applying the Michelson contrast and histological slices of the optic tract of a postmortem brain. Based on these results, a modified retardation-inclination transfer function was proposed to extract the fiber inclination. The comparison of the actual and the inclination angles calculated with the theoretically proposed and the modified transfer function revealed a significant improvement in the extraction of the fiber inclinations.

MoDDIFS (Multi-option Differential Detection and Imaging Fourier Spectrometer) is a DRDC Valcartier technology built around a differential Fourier Transform Infrared (FTIR) spectrometer optimized for optical subtraction in the long wave infrared (LWIR). MoDDIFS is a dual use hyperspectral prototype offering two fore-optics configurations: "long range", specialized for the detection of small quantities of gaseous substances, and "polarization", built to investigate liquids and powders spills. We report and present a preliminary analysis of a series of measurement tests made with the polarization configuration. The tests were performed under indoor and outdoor environments. Different liquid and solid substances were deposited on different types of surfaces. Many liquid targets and some solid materials produce a noticeable linearly-polarized signal, with a more or less characteristic spectral modulation. For the liquids, the behavior of the observed radiance spectrum seems more predictable when the liquid is thick, or when it is deposited at any thickness on non-absorbing and weakly-reflective substrates. The behavior of the radiance spectrum observed becomes more complex when a thin layer of the liquid is deposited on a smooth and strongly-reflective substrate, or on an absorbing substrate. The parameter chosen to analyze the relative amount of polarization is the degree of linear polarization. When its value is noticeable, the polarized hyperspectral radiance measurements bring additional information on both targets and the backgrounds, as compared to standard unpolarized hyperspectral measurements. The tests performed can then help assess the materials for which the detection and the identification will be improved with polarized measurements.

We report and analyze recent results obtained with the MoDDIFS sensor (Multi-option Differential Detection and Imaging Fourier Spectrometer) for the passive polarization sensing of liquid contaminants in the long wave infrared (LWIR). Field measurements of polarized spectral radiance done on ethylene glycol and SF96 probed at distances of 6.5 and 450 meters, respectively, have been used to develop and test a GLRT-type detection algorithm adapted for liquid contaminants. The GLRT detection results serve to establish the potential and advantage of probing the vertical and horizontal linear hyperspectral polarization components for improving liquid contaminants detection.

Channeled spectropolarimetry can measure the complete polarization state of light as a function of wavelength. Typically, a channeled spectropolarimeter uses high order retarders made of uniaxial crystal to amplitude modulate the measured spectrum with the spectrally-dependent Stokes polarization information. A primary limitation of conventional channeled spectropolarimeters is related to the thermal variability of the retarders. Thermal variation often forces frequent system recalibration, particularly for field deployed systems. However, implementing thermally stable retarders results in an athermal channeled spectropolarimeter that relieves the need for frequent recalibration. Past work has addressed this issue by developing athermalized retarders using two or more uniaxial crystals. Recently, a retarder made of biaxial KTP and cut at a thermally insensitive angle was used to produce an athermal channeled spectropolarimeter. This paper presents the results of the biaxial crystal system and compares the two thermal stabilization techniques in the context of producing an imaging thermally stable channeled spectropolarimeter. A preliminary design for a snapshot imaging channeled spectropolarimeter is also presented.

A novel design for a earth observation combined spectrometer and polarimeter is presented. The goal of the instrument is to measure both intensity (radiance) and the state of polarization. Some backgrounds for this instrument are presented but the main part of this article will be on the optical design and the ideas behind it.

Metal-based nano-wire grid polarizer (NWGP) is widely used in division of focal plane (DoFP) imaging sensors to capture polarization information of the imaged environment. In this paper, we present a procedure for fabricating aluminum pixelated NWGP structures using electron beam lithography (EBL) and reactive ion etching (RIE). We evaluate optical performance of the NWGP structures in terms of different orientations (0°, 45°, 90°, 135°), line widths (50nm to 500nm), and spectral response (460nm to 625nm).

Without moving parts, the snapshot imaging polarimeter utilizing Savart plates is capable of stable and fast measurements of spatiallly distributed Stokes parameters. To increase feasibility of the optical design, we propose modi cations that enable a wider eld-of view. By changing the Savar plates' con guration and improving the calibration procedure, the unwanted effects associated with the increase in the eld of view can be reduced. We carried out the veri cation experiments of the wide eld of view snapshot imaging polarimeter.

Nighttime active SWIR imaging has resolution, size, weight, and power consumption advantages over passive MWIR and LWIR imagers for applications involving target identification. We propose that the target discrimination capability of active SWIR systems can be extended further by exerting polarization control over the illumination source and imager, i.e. through active polarization imaging. In this work, we construct a partial Mueller matrix imager and use laboratory derived signatures to uniquely identify target materials in outdoor scenes. This paper includes a description of the camera and laser systems as well as discussion of the reduction and analysis techniques used for material identification.

Axially symmetric polarized beams have attracted great interest recently in the field of optics. There have been several viable proposals concerning axially symmetric polarizers, also referred to as radial polarizers. In contrast, proposals for axially symmetric wave plates have strong dependence on wavelength. Moreover, the structure of the axially symmetric wave plates inherently introduces spatial dispersion. As a solution to these problems, we propose an achromatic axially symmetric wave plate based on internal Fresnel reflection that does not introduce spatial dispersion. It is possible to generate the achromatic axially symmetric polarized beam. In this paper, we show the principle of the achromatic axially symmetric wave plate and the evaluation results of the optical element using a Mueller matrix polarimeter.

Spatial heterodyne interferometry (SHI) is a spectral measurement technique based on Fourier Transform Spectroscopy (FTS). One main benefit of an FTS lies in its higher spectral resolving power over direct measurement (dispersive) systems; however, accessing this higher resolving power can result in longer measurement times without heterodyning techniques. In this paper, the calibration and modeling of a polarization SHI is detailed, based on the Jones matrix formalism. With this, we explore non-ideal aspects of the polarization grating, such as zero-order light leakage. This light leakage causes crosstalk that can introduce errors in the spectral calibration. To minimize error, a calibration procedure is introduced based on a linear operator theory. Finally, the Jones matrix model and calibration procedure are validated through a series of experiments.

Several implementations of spectroscopic polarimeters using spatial carriers are presented. The first implementation incorporates two Savart plates and a spectrometer including a two-dimensional CCD to generate a spectrum with spatial carriers. The frequency filtering along the spatial coordinate at each wavelength allows us to conduct the snapshot measurement of the wavelength-resolved Stokes parameters. The spectral resolution of the SOP measurement can be enhanced up to that of the spectrometer. In the second implementation, two achromatic birefringent prism pairs are used to decrease the limitation in the design of the spectroscopic polarimeter. Finally, the present method is combined with a channeled spectroscopic polarization state generator so that the spectroscopic Mueller matrix of a sample can be determined by the snapshot measurement of the two-dimensional spectrum.

We present a Stokes polarimeter based on two ferroelectric liquid crystal monopixel panels. This architecture presents advantages associated to dynamic polarimeters and also, allows very fast polarization measurements. A ferroelectric liquid crystal panel can be modeled as a waveplate with a constant retardance and, with two possible orientations for its fast axis when a bipolar electrical sign is addressed. We have calibrated the optical features of our ferroelectric liquid crystal panels: retardance and rotation of the optical axis. In addition, we have carried out an optimization of the orientation of these panels in the setup in order to obtain a minimum condition number of our polarimeter and so, minimize the propagation of noise. Afterwards, we have conducted a tolerance analysis of the elements involved in the setup, focusing for a 2% of accuracy in the Stokes vectors measurements. Then, an experimental calibration is carried out and several measurements are taken in order to analyze its performance.

Polarized light in the oceans carries intrinsic information that can be utilized to estimate the optical and microphysical properties of the oceanic hydrosols. It is especially sensitive to the scattering coefficient, which cannot be retrieved from the unpolarized light used in current ocean color remote sensing algorithms. Through the unpolarized remote sensing reflectance (R_rs), these classical algorithms can only estimate backscattering coefficients b_b, but the total scattering coefficient b could be solely retrieved based on the characteristics of polarized light. The correlation is quantified in this paper. Based on extensive simulations using the vector radiative transfer program RayXP, the attenuation-to-absorption ratio (c/a), from which b is readily computed, is shown to be closely related to the degree of linear polarization (DoLP). The relationship is investigated for the upwelling polarized light for several wavelengths in the visible part of the spectrum, for a complete set of viewing geometries, and for varying concentrations of phytoplankton, non-algal particles, and color dissolved organic matter (CDOM) in the aquatic environment. It is shown that there is an excellent correlation between the DoLP and c/a for a wide range of viewing geometries. That correlation is investigated theoretically using fitting techniques, which show that it depends not only on the general composition of water but also on the particle size distribution (PSD) of the (mainly non-algal) particles. A large dataset of Stokes components for various water compositions, measured in the field with a hyperspectral and multi-angular polarimeter, then provides the opportunity to validate the parameterized relationship between DOLP and c/a. This study opens the possibility for the retrieval of additional inherent optical properties (IOPs) from air- or space-borne DoLP measurements of the ocean.

We describe the design and phenomenology imaging results of a fully polarimetric W-band millimeter wave (MMW) radiometer developed by Pacific Northwest National Laboratory for wide-area search. Operating from 92–94 GHz, the W-band radiometer employs a Dicke switching heterodyne design isolating the horizontal and vertical mm-wave components with 40 dB of polarization isolation. Design results are presented for both infinite conjugate off-axis parabolic and finite conjugate off-axis elliptical fore-optics using optical ray tracing and diffraction calculations. The received linear polarizations are down-converted to a microwave frequency band and recombined in a phase-shifting network to produce all six orthogonal polarization states of light simultaneously, which are used to calculate the Stokes parameters for display and analysis. The resulting system performance produces a heterodyne receiver noise equivalent delta temperature (NEDT) of less than 150m Kelvin. The radiometer provides novel imaging capability by producing all four of the Stokes parameters of light, which are used to create imagery based on the polarization states associated with unique scattering geometries and their interaction with the down welling MMW energy. The polarization states can be exploited in such a way that man-made objects can be located and highlighted in a cluttered scene using methods such as image comparison, color encoding of Stokes parameters, multivariate image analysis, and image fusion with visible and infrared imagery. We also present initial results using a differential imaging approach used to highlight polarization features and reduce common-mode noise. Persistent monitoring of a scene using the polarimetric passive mm-wave technique shows great promise for anomaly detection caused by human activity.

Passive millimeter-wave (mmW) sensors are especially suited to persistent surveillance applications due to their ability to operate during day/night conditions and through transient atmospheric obscurants such as clouds, rain and fog. The contrast of targets will change throughout a diurnal heating cycle and this change will be polarization dependent. Simulations are presented from a ray tracing program developed for the mmW regime that has been modified to account for polarization information. Results are shown demonstrating periods during the day when the contrast of certain targets drop to zero for a linear polarization state while the orthogonal state still maintains a high contrast.

A new method for characterization of unknown targets using passive multispectral polarimetric imagery is pre sented. Previous work makes use of a pBRDF derived equation for the degree of linear polarization and with the aid of multiple incidence angles estimates refractive index and re ection angle. This work uses known incidence and re ection angles along with dispersion equations and polarimetric data at multiple wavelengths to recover the index of refraction. Experimental results are presented showing the new method's ability to characterize a range of materials.

Modifying and detecting the polarization of light is increasingly important in many contexts such as Faraday isolators and electro-optical modulators. In order to control the polarization of light, it is necessary to know the polarization characteristics of the materials used in the applications. To be able to (magneto-)optically characterize novel materials, we designed a setup using a single photoelastic modulator (PEM) to simultaneously detect natural and magnetic circular dichroism and circular birefringence over a large spectral range. We then theoretically analyzed and experimentally characterized the effect of non-idealities in the PEM on the setup and the resulting data. Our results demonstrate an influence of PEM non-idealities on the measured signals, resulting in non-negligible mixing of circular birefringence and circular dichroism signals. Our measurements of the wavelength dependence of these non-idealities reveal larger non-idealities towards shorter wavelengths. These results illustrate the necessity to take PEM non-idealities into account when working with PEMs, especially at shorter wavelengths or when dealing with signals spanning different orders of magnitude. PEM non-idealities, while frequently neglected in experimental setup design and theoretical derivations, are expected to be more complicated and possibly exert a larger influence on obtained results for experimental setups with multiple PEMs.

An optical characterization of amber samples from México, the Baltic Sea and fake samples is presented, with the aim of discriminate between genuine and fake samples. We sought to identify the physical variables that could serve as the basis for the development of a device whose operation was able to discriminate between samples of genuine and fake amber. The optical refractive index was determined by Spectroscopic Ellipsometry, Abbe refractometry, and by the Brewster angle. The Raman spectra and the fluorescence optical responses were also determined. The results obtained indicate that the refractive index is not a robust variable that can differentiate between genuine amber and a fake sample. On the other hand, the Raman spectra and the fluorescence responses provide information that allows discriminating between both types of samples. For this reason, we used the results obtained by fluorescence as a basis for the design and construction of a prototype simple, reliable, portable, and affordable for authentication of the Mexican amber.

Motivated by astrobiological remote sensing needs, Sparks et al. (2012)¹ present an approach to spectropolarimetry which offers the prospect of high sensitivity over a very wide wavelength range (UV, optical, IR). Using static, robust components the polarization information is encoded onto one dimension of a two-dimensional data array, while the other dimension records the spectrum. A spatially varying retardance along the spectrograph slit, followed by a polarization analyzer, encodes the Stokes parameters as coefficients of orthogonal trigonometric functions perpendicular to the spectrum. No moving parts are required and all polarimetric information is available on a single data frame, hence the technique is immune to time dependencies, free of fragile modulating components, has the potential for high sensitivity while offering a wide wavelength range with full Stokes spectropolarimetry. Within the Solar System, spectropolarimetry offers diagnostics for dust (cometary, zodiacal, rings), surfaces (rocky, regolith, icy), aerosols (clouds, dust storms) and high energy plasma emission processes. Beyond the Solar System, space-based telescopic spectropolarimetry has important contributions to make in the detection of extrasolar planets and their characterization. There are astrobiological applications for full Stokes polarimetry stemming from the interaction of light with chiral living organisms, which offers the potential for a remote sensing detection capability for microbial life.

We present a novel measurement method of optic axes orientation distribution which uses a relatively simple measurement setup. The principal difference of our method from other well-known methods lies in direct approach for measuring the orientation of optical axis of polycrystalline networks biological crystals. Our test polarimetry setup consists of HeNe laser, quarter wave plate, two linear polarizers and a CCD camera. We also propose a methodology for processing of measured optic axes orientation distribution which consists of evaluation of statistical, correlational and spectral moments. Such processing of obtained data can be used to classify particular tissue sample as “healthy” or “pathological”. For our experiment we use thin layers of histological section of normal and muscular dystrophy tissue sections. It is shown that the difference between mentioned moments` values of normal and pathological samples can be quite noticeable with relative difference up to 6.26.

The Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP), an instrument on the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO), was operated as an atmospheric lidar system to study the impact of clouds and aerosols on the Earth’s radiation budget and climate. This paper discusses the receiver transient response of the CALIOP instrument, which is useful for getting a reliable attenuated backscatter profile from CALIOP data products. The noise tail effect (slow decaying rate) of PMT and broadening effect of the
low-pass filter are both considered in modeling of the receiver transient response. An analytical expression of the CALIOP transient response function was obtained by the least square fitting of lidar measurements from land surfaces.