Modeling Precision and Accuracy of a LWIR Microgrid Array Imaging

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Modeling precision and accuracy of a LWIR microgrid array imaging polarimeter [5888-31]

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Boger, J K

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5888

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2005

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Modeling Precision and Accuracy of a LWIR Microgrid Array Imaging Polarimeter James K. Bogera , J. Scott Tyoa *, Bradley M. Ratliffb , Matthew P. Fetrowc **, Wiley T. Blackb , and Rakesh Kumara a University

of New Mexico, Department of Electrical and Computer Engineering, Albuquerque, NM, USA 87131 b Applied Technology Associates, 1300 Britt St. S.E., Albuquerque, NM 87123-3353 c Air Force Research Laboratory ABSTRACT Long-wave infrared (LWIR) imaging is a prominent and useful technique for remote sensing applications. Moreover, polarization imaging has been shown to provide additional information about the imaged scene. However, polarization estimation requires that multiple measurements be made of each observed scene point under optically different conditions. This challenging measurement strategy makes the polarization estimates prone to error. The sources of this error differ depending upon the type of measurement scheme used. In this paper, we examine one particular measurement scheme, namely, a simultaneous multiple-measurement imaging polarimeter (SIP) using a microgrid polarizer array. The imager is composed of a microgrid polarizer masking a LWIR HgCdTe focal plane array (operating at 8.3-9.3 µm), and is able to make simultaneous modulated scene measurements. In this paper we present an analytical model that is used to predict the performance of the system in order to help interpret real results. This model is radiometrically accurate and accounts for the temperature of the camera system optics, spatial nonuniformity and drift, optical resolution and other sources of noise. This model is then used in simulation to validate it against laboratory measurements. The precision and accuracy of the SIP instrument is then studied. Keywords: Imaging Polarimeter, Nonuniformity Correction, Infrared Polarization

1. INTRODUCTION Imaging polarimeters are designed to provide polarization information pixel-by-pixel across a scene. While polarimeters are designed to accurately measure the polarization properties, each class of imaging polarimeter has its own corresponding set of artifacts that must be quantified and calibrated. The intent of this paper is to explore the accuracy and precision of a particular imaging polarimeter that we refer to as a microgrid polarizing array. The device in question is designed to work in the long wave infrared (LWIR) and has a wire-grid polarizer array placed on a HgCdTe focal plane array (FPA). A schematic of this is shown in fig. 1. Alternately this effort might be thought of as exploring the errors introduced into measurements of polarized images as a consequence of the instrument. The approach is to model the instrument and explore effects of various input conditions. A justification for this effort and the approach to understanding the problem is evident with a brief explanation of the measurement problem and the dimensionality of input conditions. A polarization state describes the temporal properties of the electric field of light.1 Because the electric field is a random complex vector, four parameters are necessary to describe it in a given measurement plane. These first two parameters are simply the amplitudes of the orthogonal vector components in a plane. A third parameter affecting the nature of the light is the phase between the two orthogonal vector components. The fourth parameter is related to degree of polarization, and provides the portion of the radiation that is polarized and the portion that is unpolarized. * E-mail: [email protected], Telephone: 1 505 277-1412, ** Email: [email protected], Telephone: 1 505 853-3523

Polarization Science and Remote Sensing II, edited by Joseph A. Shaw, J. Scott Tyo, Proc. of SPIE Vol. 5888 (SPIE, Bellingham, WA, 2005) · 0277-786X/05/$15 · doi: 10.1117/12.613658

Proc. of SPIE 58880U-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/17/2015 Terms of Use: http://spiedl.org/terms

Micro-grid Superpixel

Reconstruction Point

Figure 1. Layout of the microgrid FPA. Any 2 × 2 region of the microgrid defines a superpixel, which is the minimum number of pixels required to make a polarization measurement. The black circles indicate the points at which the polarization images are reconstructed.

The most common description of polarized light is the intensity a Stokes vector.1 Equation 1 is the typical Stokes vector definition ⎡ ⎤ ⎡ IH + IV s0 ⎢ s1 ⎥ ⎢ IH − Iv ⎥ ⎢ S=⎢ ⎣ s2 ⎦ = ⎣ I45 − I135 s3 IR − IL

parametrization of the state in the form of ⎤ ⎥ ⎥, ⎦

(1)

where IH and IV are the intensities of horizontally and vertically polarized light, I45 and I135 are the intensities of linearly polarized light at ±45◦ , and IR and IL are the intensities of right and left circularly polarized light. Often we will need to use the normalized Stokes vector, which we will notate as S=

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(2)

In the pursuit of measuring the four Stokes parameters, (three in the case of linear polarization only) we are confronted with a conundrum: the Stokes parameters cannot be directly measured. This coupled with the fact that we need multiple measurements to describe multiple polarization parameters means that some clever way must be found to make the measurement. One technique commonly used is to make multiple measurements sequentially in time. In between each measurement the polarization character of the optical system is modified such that maximum sampling of the Poincaré sphere is achieved.2, 3 In our modeling work here we refer to this class of instruments as the time-sequential multiple-measurement imaging polarimeter (TIP). A TIP is of course most susceptible to changes which may occur during the measurement such as scene movement. A second approach is to make multiple measurements in the spatial domain. A simultaneous multiple-measurement imaging polarimeter (SIP), as we have called it, specifically addresses the fundamental sensitivity of the TIP. In a SIP each polarimetric image is measured at the same instant in time. This approach is particularly advantageous to imaging polarimeters in which there is interest in expanding to video applications. Such measurements can be made with division of amplitude systems4 or division of aperture systems.5 In this paper, our instrument accomplishes the polarization measurement using a third strategy that makes the multi-measurements in the spatial domain just as an RGB mosaic color camera does. Successful instruments have been made which have a mosaic pattern of wire microgrid polarizers masking the pixels in the FPA. We limit our discussion of the SIP class of polarimeters to microgrid FPAs that are restricted to measurements of linear polarization only. Just as the TIP has an obvious limitation so does the microgrid array. The microgrid array limitation is that error-free measurements can only be made on spatially uniform scenes. Since the microgrid instrument is presented as an imaging polarimeter, this limitation is alarming. The microgrid polarimeter seems to have put two critical functions of the instrument, imaging and polarization measurement, directly at odds. Images depend on spatial variations and accurate polarimetry depends on


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Figure 2. Block diagram of the microgrid instrument simulation model.

spatially uniform signals. Naturally we must be able to accept some error in the polarization measurement, and we must be willing to accept some loss in image resolution. To evaluate the trade space, we have created an instrument model where truth images can be compared to simulated measurements of these images.

2. MODEL DESCRIPTION We have developed and implemented an instrument model in C++ to simulate the LWIR microgrid imaging polarimeter in our laboratory. The sensor was built by DRS Technologies under contract to AFRL. The FPA is a 640 × 480 HgCdTe detector with a microgrid polarizing array superimposed. It operates in the waveband of 8.3 to 9.3 µm with a 25 µm pixel pitch. The microgrid instrument simulator can be described in four stages. The first stage explains the truth scene image creation process. The second stage deals with propagating these simulated images through the optical system model and the third stage describes the empirical model we employ for FPA detection. Finally, the last stage describes data processing. Here the same procedures for processing real instrument data are used for processing the simulated instrument data as well. This includes all nonuniformity correction (NUC), Stokes estimation and other image processing tasks. A block diagram illustrating the key stages of our microgrid instrument model is shown in fig. 2.

2.1. Truth image creation In the first stage of the simulation we generate a set of high resolution images that describe the full polarization state of the simulated (truth) scene to be imaged. This set of images is useful in that complex scenes not measurable in laboratory or field can be generated to test the instrument model in extreme situations. To characterize the full polarization state of the simulated scene, the set of test images include a temperature, T , emissivity, , and three normalized Stokes images S. Using these test images, the full set of Stokes images at the front of the optical system can be generated for a given waveband. This is performed by first using the temperature and emissivity images via the blackbody equation to compute the spectral radiance image, s0 (λ). Then, the s1 (λ), s2 (λ), and s3 (λ) images are computed by simply multiplying each normalized Stokes image with the generated s0 (λ) image on a pixel-by-pixel basis. Hence, for a given spectral range, the flux from the simulated scene is represented discretely in four dimensions, i.e., two spatial, one Stokes and one spectral. For notational simplicity, we omit spatial indices in the following equations and note that all computations are performed for each pixel in the simulated truth images. The spectral flux for each pixel is given by s0 (λ) = L(λ, , T )Ad ΩL cos4 θ,


(3)

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Figure 3. Optical layout of the microgrid array LWIR polarimeter instrument.

where L is the spectral radiance as radiated into a hemisphere, Ad is the area of the detector and ΩL represents the solid angle of the lens or collection optics. The product Ad ΩL gives the optical throughput of the system and converts the spectral radiance into spectral flux. θ is the off-axis field angle. We next multiply each normalized Stokes vector by the corresponding spectral flux to generate the spectrally-dependent Stokes vector, i.e., S(λ) = L(λ, , T )Ad ΩL cos4 θS.

(4)

These Stokes vectors are thought of as radiant fluxes that have units of watts per µm. It is important to note that the generation of the Stokes images is an artificial procedure that is not intended to follow any natural phenomena, rather our intent is to create polarized scenes that will stress the instrument model. The test images are created at a resolution much higher than the dimensions of the FPA because the are used to simulate the true analog scene. For all test images presented in this paper, each spatial dimension of the test images are a factor of 4 larger than the detector size. Downsampling to the FPA resolution is eventually performed in the detection stage of the simulation, and is accomplished by integrating in both the spatial and spectral dimensions. The details of the detection stage are discussed thoroughly below. At this point in the simulation we have obtained the desired input Stokes truth images.

2.2. Optical system model In the second stage of the instrument simulation, the simulated Stokes truth images are propagated through the front-end optics. The optics are modeled using the same formalism as employed by most optical ray tracing programs. As in these programs, we track the flux through the optical system from scene to detector in a surface-by-surface fashion. The surfaces that make up our optical model are illustrated in fig. 3. In addition to the optical components, we also account for the problems introduced by finite apertures and optical aberrations. We do this by first convolving the optical point spread function (PSF) with each generated Stokes image. Notice that this is not the complete point response function, which also includes the finite pixel sampling along with the PSF. It is important to note that our model does not propagate rays through the finite aperture; rather it is restricted to the optic axis of the system. With regards to the spatial characteristics of the system, only the optical throughput is obtained. We then capture off-axis cosine roll-off by applying it to the optical throughput, as shown in Eq. (3). Each optical surface in our modeled instrument is represented by a unique spectrallydependent 4 × 4 Mueller matrix, Mk (λ), where k indicates the kth optical surface. Each element’s Mueller matrix is used to propagate the generated Stokes vector to the next surface in the system. Additionally, since our instrument is a LWIR sensor, it is also necessary to include the spectral radiance emitted from each surface. Each surface’s radiance contribution, Sk (λ), is thus accounted for by adding it to the Stokes vector leaving the respective optic. Hence, the Stokes vector leaving the kth optical component at each point is given by Sk (λ) = Mk (λ)Sk−1 (λ) + Sk (λ),


(5)

where k = 0 indicates the initial Stokes vector at the front of the optical system. The process defined by Eq. (5) is repeated until all optical surfaces have been exhausted (six in our case). Completing this procedure across all test image pixels will thus successfully propagated the input Stokes images through the optical system to the FPA.

2.3. Detection The detection stage of the microgrid simulator models the HgCdTe FPA sensor of the instrument. In the optical system model, the high-resolution Stokes input images were propagated through the optical system to yield the system-affected high-resolution Stokes images in spectral radiance. Because of the spectral dependence of the Stokes images, this procedure is repeated for several wavelengths across the spectral band of the instrument. For our instrument, the spectral response is from 8.3 to 9.3 µm. In a typical simulation, we usually sample the waveband with a resolution of 5 samples. Once we obtain the high-resolution Stokes images from each sampled wavelength, we next convert the s0 (λ) images into units of photons. This is accomplished by integrating the Stokes images across the spectral dimension. The number of impinging photons for each pixel in the highresolution image space is computed as N −1 τ P˜ = s0 (λn )λn dλn , hc n=1

(6)

where P˜ is the number of photons at the given pixel in the high-resolution image, N is the number of wavelength samples, λn is the nth sampled wavelength, dλn = λn+1 − λn , τ is the integration time of the FPA and hc = 1.9865 × 10−19 . After this spectral integration is performed for all pixels we obtain the high-resolution photon image. Next we perform a spatial integration of this image to move from the high-resolution space to the detector resolution. This is accomplished by computing the spatial average of all high resolution image points that fall upon each 25 µm detector, i.e., the photon count for each detector pixel is P =

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(7)

k=i−F/2 =j−F/2

where i and j are the indices of the high resolution image point that correspond to the center of the given detector pixel, F is the high-resolution image upsample factor, and P˜ (k, ) is the photon count of the kth pixel in the high-resolution image. We now have obtained the desired photon count image in detector space. This image is next used by our detector model to obtain the final simulation output in units of detector counts. Due to the complexity of a physics-based detector model, we instead chose to employ an empirical model that is based on response data collected from a real HgCdTe FPA sensor. This does not allow us to explore the physics of detection and its impacts on the microgrid polarimeter, but it does allow us to explore the limits of our detector to various input scenes. The empirical data consists of response curves that were obtained by imaging an unpolarized blackbody source from 0C to 120C in five degree increments. Figure 4 plots somes of these experimentally obtained response curves sampled uniformly across the array. Notice that we have converted the temperature axis to photons so that the obtained photon image can be directly converted to detector counts through a simple look-up procedure. The resulting counts image is thus in the same form as data collected from the real instrument. One major advantage of the empirical detector model is that it is able to accurately capture the true nonlinearities in each detector response. Fixed pattern noise (FPN), or spatial nonuniformity, is a major problem that is particularly problematic for LWIR sensors, and is perhaps one of the most limiting factors of the microgrid instrument. A clear limitation of this detector model is that it places a restriction on the range of truth scenes that may be inputted. At this point the instrument simulation is complete.

2.4. Simulating instrument calibration The severe FPN that is present in LWIR imagers requires that frequent nonuniformity correction (NUC) be performed. Nonuniformity is even more problematic for LWIR polarimetric imagers due to the adjacent pixel


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subtractions that are performed in estimating the Stokes parameters. As a consequence, NUC data must be regularly collected and the NUC parameters continually updated. If a NUC is not applied often enough radiometric and polarimetric accuracy of acquired imagery are compromised. Clearly, FPN strongly impacts the measurement ability of the microgrid instrument and was accounted for in the simulation through the empircal detector model of section 2.3. NUC is typically performed by acquiring one or more scene measurements of an unpolarized uniform temperature blackbody source. In order to properly simulate operation of the real LWIR instrument, we use the instrument model to generate such uniform-temperature scenes. For all NUC in this paper, both real and simulated, we use a standard two-point calibration. In all cases, the two blackbody scenes used for NUC are acquired or simulated at 15C and 50C. The reason for these chosen temperatures is that they tend to bound the range of scene temperatures being measured is our data. In general it is difficult to choose NUC temperatures that are optimal across a wide range of input scenes. Now that the instrument simulation has been used to generate both scene and blackbody imagery, we next discuss how these data are used to generate estimates of the scene polarization.

2.5. Data processing The instrument model has carefully attempted to generate data that mimics images obtained from the real microgrid sensor. As such, the following discussion is equivalent for processing both simulated and real sensor data. The first step in data processing is to perform a NUC on the acquired images. As stated above, we use a two-point calibration. The goal of the two-point calibration is to find a linear transformation for each pixel such that all detector responses are uniform. Hence, under this constraint, it is assumed that each detector has a response according to yk (i, j) = a(i, j)xk (i, j) + b(i, j),

(8)

where yk (i, j) is the ijth detector response at time k in counts, a(i, j) and b(i, j) are the detector gain and bias, respectively, and xk (i, j) is the true temperature of the ijth scene point at time k. Because we have acquired two flat-field blackbody images at temperatures x1 and x2 , each detector’s gain and bias can be estimated simply by a ˆ(i, j) =

yx2 (i, j) − yx1 (i, j) x2 − x1

ˆb(i, j) = yx (i, j) − a ˆ(i, j)x1 , 1

(9) (10)

where a ˆ(i, j) and ˆb(i, j) are the estimated gain and bias and yx2 (i, j) and yx1 (i, j) are the measured detector counts at temperatures x2 and x1 , respectively. Once the gain and bias maps have been obtained, each pixel in the image can be nonuniformity corrected to yield an estimate of the scene temperature, i.e., x ˆk (i, j) =

yk (i, j) − ˆb(i, j) . a ˆ(i, j)


(11)

Clearly, calibration of the true nonlinear detector response with the linear two-point approximation will yield some level of error, and is addressed in more detail below. Once all pixels have been two-point calibrated, we next proceed to reconstruct the polarization images. Recall the layout of the microgrid that was shown in fig. 1. Each full polarization measurement requires a minimum of four pixels from the array, known as a super-pixel. A super-pixel consists of any 2 × 2 pixel window of the FPAmeasured counts image. Notice that such a super-pixel always contains four pixels with intensity measurements at polarizer orientations of 0◦ , 45◦ , 90◦ and 135◦ . In theory we would like each super-pixel measurement to have the same instantaneous field of view. In the microgrid instrument this is not the case. Because of this we assume that the polarization estimate is computed at the center of each super-pixel, rather than the center of each FPA pixel. These “reconstruction” points thus lie on the grid between the actual pixels, as illustrated by the black circles on the grid within fig. 1. To simplify the notation, all calculations below are performed for a single super-pixel. The four two-point calibrated members of each super-pixel are denoted as zˆ0 , zˆ45 , zˆ90 and zˆ135 , where each subscript indicates the corresponding microgrid polarizer orientation. The three linear polarization estimates, sˆ0 , sˆ1 and sˆ2 , are then computed as 1 (ˆ z0 + zˆ90 + zˆ45 + zˆ135 ) 2 sˆ1 = zˆ90 − zˆ0 sˆ2 = zˆ135 − zˆ45 . sˆ0 =

Notice that all sˆ0 computations can be obtained by convolving the entire image with the 2 × 2 kernal

0.5 0.5 K= . 0.5 0.5

(12) (13) (14)

(15)

The normalized linear Stokes parameters are then sˆ1 sˆ0 sˆ2 sˆ¯2 = . sˆ0

sˆ¯1 =

Degree of linear polarization (DOLP) and phase are then computed as DOLP = sˆ¯21 + sˆ¯22

sˆ2 Phase = arctan . sˆ1

(16) (17)

(18) (19)

The above polarization estimation scheme is perhaps one of the simplest for processing microgrid data. Such a scheme provides excellent estimates for s0 , but introduces false edge artifacts in all other polarization images. We have found that these edge artifacts can be reduced by using more sophisticated schemes that first interpolate adjacent like-polarization pixels to the super-pixel reconstruction points. The polarization estimates are then computed from these interpolated values. Such schemes will not be discussed further within this paper and will be the subject of future research. However, this does illustrate the point that different processing schemes can have a significant impact upon the quality of the polarization estimates.

3. IMAGING A SPHERE One of the more difficult tasks associated with developing a polarization imager is identifying a scene with a polarization signature that is both predictable (so that the “truth” is known) and challenging to the camera system. In the past, researchers have used images of polarizers, partially polarized reflections or transmissions, or emission from flat plates.6 In this paper, we use a spherical gray body as a test target, and have found that this


X

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Figure 5. Imaging geometry for the spherical test target.

object provides a controlled polarization signature with DOLP and phase angles that vary predictably in space. Another advantage to the emissive sphere is that it is reasonably easy to create and use with real instruments. It is well known that light emitted from a metal or dielectric will have a polarization signature that is determined by the Fresnel reflection coefficients for the s- and p-states at the surface.7 In addition, when the object has emissivity less than 1, we must also consider the polarized reflection of the (assumed unpolarized) background radiation. Assume that the coordinate origin of the image is at the center of the sphere, and that the sphere has radius R. The coordinates in the scene are the x and y coordinates, and z is along the axis of the imager. The geometry is depicted in fig. 5. The local surface normal at cylindrical position (ρ, φ) in the image is ˆr = sin θ cos φˆ x + sin θ sin φˆ y + cos θˆ z,

(20)

ˆ, we can compute the emission/reflection angle where sin θ = ρ/R. Since the direction of observation is along z as p 2 ˆ · ˆr = cos θ = 1 − cos Ω = z . (21) r Equation (21) and the complex index of refraction n ˜ = n − jk can be used in the Fresnel reflection coefficients to compute the s and p electric field reflection coefficients Rs and Rp . Once the reflection coefficients are known, we can use a modified form of Kirchoff’s laws to provide the polarized emissivities as7 s = 1 − Rs2 , p = 1 − Rp2 .

(22)

Eq (22) assumes that all incident radiation is either absorbed or reflected by the surface, and that the polarized absorptivity is equal to the polarized emmissivity. In addition to the emitted radiation that occurs at the temperature of the sphere, there is also a partially polarized reflection of light that is incident on the sphere at the temperature of the background. Whereas the emitted light is partially p-polarized, the reflected light is partially s-polarized, reducing the overall polarization signature.8 The total radiance then coming from the sphere to the camera due to both emission and reflection is Ls Lp

= s L(Tsp ) + Rs2 L(Tb ) = (1 − Rs2 )L(Tsp ) + Rs2 L(Tb ) = p L(Tsp ) + Rp2 L(Tb ) = (1 − Rp2 )L(Tsp ) + Rp2 L(Tb ),

(23) (24)

where L(T ) is the blackbody radiance at temperature T , and Tsp and Tb are the temperatures of the sphere and backgroundg. Note that when Tsp = Tb , Ls = Lp . This implies that an object in thermal equilibrium with its background does not have a polarization signature.


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Once we have Eq. (23), we can use the model described above to compute the expected polarization images obtained with the microgrid instrument. Figure 6 shows measured and simulated DOLP images of a hollow 45-cm-diameter brass hemisphere painted with a glossy Krylon black paint. The complex index of refraction for glossy Krylon black has been estimated from BRDF measurements to be 1.4 − j0.5. The sphere was heated to a temperature of 50 C, and the background was at a temperature of 30C. The sensor used in this case was in an instrument known as the Long Wave Infrared Polarimeter (LIP).9 The LIP is a rotating retarder system that has been characterized and provides imagery with low noise. We are using the images in fig. 6 to represent the “truth.” Figure 7 shows a comparison between actual Stokes parameter imagery and the model output for our microgrid polarizer instrument. As can be seen from fig. 7, the model is currently underpredicting the residual noise present in the actual imagery. We are currently investigating potential reasons for this.

4. SENSITIVITIES OF THE MICROGRID INSTRUMENT One key advantage of our instrument model is that it gives us the ability to explore many types of systematic errors that effect the performance of the microgrid instrument. These errors can be explored individually or in tandem by propagating them through the instrument model. Rather than trying to simulate the real instrument with all of its potential systematic problems, we instead choose to run the simulation under the assumption of a perfect instrument, perturbing only the variable of interest. For example, we consider the optical properties of the sensor to be ideal so that focus can be placed on the problems of the HgCdTe detector. Two sources of error that we examine here are (1) residual FPN after NUC and (2) optical retardance in the imaging optics. These


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Figure 8. The top row displays the estimated phase images for the sphere at the indicated temperature. The bottom row shows the DOLP-estimated images in the top-half of each image and the truth DOLP scene in the bottom half (separated by the overlayed lines). In each case the background was set to 25 C and n ˜ = 1.4 + j0.5. All DOLP images are scaled to the range of [0,6.1]% to optimize viewing for the 50 C case. As indicated, the two-point calibration NUC procedure was performed at 15 C and 50 C.

errors can be tested for by judiciously choosing simulated truth scenes that will stress the system appropriately. In all studies below we chose the simulated sphere test target as our truth scene, described in section 3.

4.1. Correcting array nonuniformity As discussed in section 2, detector-to-detector FPN is a serious problem that affects all infrared sensors, and was clearly evident in the response curves of fig. 4. The linear two-point calibration NUC procedure we employ was described in section 2.5. Residual FPN that is present after calibration due to our linear approximation to each true nonlinear response is particularly stressing for polarimetry applications as a results of the subtractions performed to estimate the Stokes parameters, as seen in Eqs. (13) and (14).10 To investigate the effects of residual FPN on microgrid instrument performance, we generated emissive sphere truth images at various temperatures. The background of the truth scene is held at 25 C and n ˜ = 1.4 − j0.5. The instrument model was then run for each of these created scenes to generate the detected counts images. Flat-field image sequences were also simulated at 15 C and 50 C to use with a two-point calibration. The polarization images were then estimated from each of these simulated scenes. Figure 8 displays the phase and DOLP images produced from these studies. As seen in the figure, residual FPN can be severely limiting. In both the phase and DOLP images, the polarization estimates for the sphere at both the upper and lower NUC temperatures demonstrate low noise. Once the sphere deviates from these calibration temperatures the quality of the polarization estimates degrade significantly. In particular, notice the 30 C case. Here the sphere and background temperatures are very close to one another. We have found that the ability to measure low DOLP signatures is greatly influenced by the accuracy of the calibration. These issues are discussed in greater detail elsewhere.6, 10

4.2. Optical retardance in imaging optics Another possible source of error is system retardance. The most common source of such retardance is in the optical windows of systems that are often made of crystalline materials that can be birefringent in the LWIR. It is straightforward to introduce retardance into the optical path of the instrument by simply perturbing the linear polarizer orientations. The effect of doing so will convert a portion of the linear inputs to elliptically polarized light, which is a polarization state that the microgrid instrument can not distinguish from unpolarized light. Consequently, DOLP decreases for light whose polarization axis is not aligned with the retardance axis. Figure 9 shows three DOLP images of the test sphere. In these images, retardances of 45◦ and 60◦ are introduced into the front window with the fast axis at 0◦ . With no retardance, the sphere is reproduced with minimum error.


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Figure 9. Affect of introducing system retardance: (a) 0◦ of retardance, (b) 45◦ of retardance and (c) 60◦ of retardance.

As the system retardance is increased, there is no effect on the measured s1 , but the measured s2 decreases, causing the circular contours in fig. 9 to become more square.

5. CONCLUSION In this paper we have presented a model framework that we can use to explore this class of SIP polarimeters. The microgrid instrumnets are not new, but this device is one of the first imaging microgrid polarimeters made to operate in the LWIR. The LWIR regime is a difficult region in which to image, because there are many sources of noise and error. Performing imaging polarimetry in the LWIR is significantly harder. Because of difficulties with collecting and interpreting LWIR polarization data, it is useful to have a model that can predict the performance of an imager under a variety of circumstances that can be carefully controlled. The model allows us to turn various sources of error on and off, providing a better understanding of the effects of each type of error on the final Stokes imagery. In addition, we can create idealized polarization signatures, such as ramps of DOLP or polarization angle, that are difficult to create in real life. Our model is in the early stages of development, but the results presented here indicate that it can be used to simulate the performance of this camera in a variety of polarization imaging scenarios.

ACKNOWLEDGMENTS The authors would like to thank Mike Ratliff at Ratliff Metal Spinning Company, Inc., Dayton, OH, for providing the metallic sphere used in the experiments within this paper.

REFERENCES 1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, North-Holland, New York, 1977. 2. D. S. Sabatke, M. R. Descour, E. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25, pp. 802–804, 2000. 3. J. S. Tyo, “Design of optimal polarimers: maximization of SNR and minimization of systematic errors,” Appl. Opt. 41, pp. 619–630, 2002. 4. R. M. A. Azzam, I. M. Elminyawi, and A. M. El-Saba, “General analysis and optimization of the fourdetector photopolarimeter,” J. Opt. Soc. Am. A 5, pp. 681–689, 1988. 5. D. B. Chenault, A. Lompado, E. R. Cabot, and M. P. Fetrow, “Handheld polarimeter for phenomenology studies,” in Proc. SPIE vol 5432: Polarization: Measurement, Analysis, and Remote Sensing VI, D. H. Goldstein and D. B. Chenault, eds., pp. 145 – 154, SPIE, (Bellingham, WA), 2004. 6. B. M. Ratliff, M. P. Fetrow, J. S. Tyo, and J. K. Boger, “The effect of fixed pattern noise on imaging stokes vector microgrid polarimeters,” in Proceedings of CALCON 2005, Space Dynamics Laboratory, Utah State University, (Logan, Utah), 2005. In Press. 7. O. Sandus, “A review of emission polarization,” Appl. Opt. 4, pp. 1634–1642, 1965.


8. J. A. Shaw, “Degree of linear polarization in spectral radiances from water-viewing infrared polarimeters,” Appl. Opt. 38, pp. 3157–3165, 1999. 9. S. H. Sposato, M. P. Fetrow, K. P. Bishop, and T. R. Caudill, “Two long-wave infrared spectral polarimeters for use in remote sensing applications,” Opt. Eng. 41, pp. 1055 – 1064, May 2002. 10. B. M. Ratliff, R. Kumar, J. S. Tyo, and M. M. Hayat, “Combatting infrared focal plane array nonuniformity noise in imaging polarimeters,” in Proc. SPIE vol. 5888: Polarization Science and Remote Sensing II, J. A. Shaw and J. S. Tyo, eds., SPIE, (Bellingham, WA), 2005. In Press.


Modeling Precision and Accuracy of a LWIR Microgrid Array Imaging

Modeling Precision and Accuracy of a LWIR Microgrid Array Imaging

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