1. Introduction

Longwave infrared (LWIR) imagers or radiometers deployed outdoors for remote sensing measurements often require a weatherproof enclosure with an optical window or hatch to protect the instrument from precipitation or sea spray. Mechanical hatches or shutters, which require no window compensation, have been used on infrared sky imagers [Infrared Cloud Imager (ICI); Shaw et al. 2005; Thurairajah and Shaw 2005] and infrared spectroradiometers (Han et al. 1997; Minnett et al. 2001; Knuteson et al. 2004). Windows used in radiometrically calibrated systems require compensation for their optical effects. For example, the Calibrated Infrared In situ Measurement System (CIRIMS) is a shipborne infrared radiometer whose data are corrected for the effects of an intervening window using a multiparameter curve fit (Jessup et al. 2002; Jessup and Branch 2008). Another example is a multiwavelength microwave and infrared sky radiometer whose infrared channel views the sky through an infrared window. The optical effects of the window are compensated for with a combination of laboratory measurements and real-time removal of a reflection term determined with a small temperature-controlled plate located at the specular angle of the tilted window (R. Ware 2009, personal communication). The approach we describe here is better suited to applications where the LWIR sensor has a wide field of view (larger than approximately 10°).

The window correction routine presented here was developed to compensate for the optical effects of a germanium window on a compact version of the ICI system called the ICI2, which has been developed at Montana State University (MSU) in collaboration with the Jet Propulsion Laboratory (JPL). The ICI2 is a radiometrically calibrated thermal infrared imager designed to measure cloud distribution and transmittance in potential Earth–space optical communication paths (Nugent et al. 2009; Nugent 2008), which builds on the legacy of the original ICI system developed for climate studies (Shaw et al. 2005; Thurairajah and Shaw 2005). In the ICI2 system, a LWIR camera and electronics are mounted inside a weatherproof enclosure (Fig. 1). Owing to size and complexity constraints, the ICI2 uses a germanium infrared window with an external hard-carbon coating to protect the instrument from precipitation, as shown in Fig. 1.

The camera used in the ICI2 is based on the FLIR Photon 320, which consists of a sensor with 324 × 256 pixels with noise equivalent temperature difference (NETD) of 33 mK. The version of the ICI2 discussed here has a 62° full-angle field of view (FOV) along the diagonal achieved with the 14.25-mm lens from FLIR (bandwidth ∼8.6–13.2 μm). Replacing the FLIR lens with a custom-made 8.6-mm wide-angle lens allows for a version of the ICI2 with a 110° diagonal FOV (bandwidth ∼8.8–13.5 μm). Details of this system and the radiometric calibration method are discussed elsewhere (Nugent et al. 2009; Nugent 2008).

The radiometrically calibrated ICI data, in conjunction with dedicated software, allow for cloud detection and classification through a two-step process. First, the atmospheric emission is removed from the radiometric sky data. The atmospheric emission is derived from models based on Moderate Resolution Atmospheric Transmission (MODTRAN) (Anderson et al. 1999) simulations of clear-sky emission for varying conditions, and are tuned to the spectral bandwidth of a given detector–lens combination (Nugent 2008; Shaw et al. 2005; Thurairajah and Shaw 2005). When available, radiosonde profiles of atmospheric temperature and humidity are used as inputs in these models. Once the atmospheric emission is removed, clouds are detected and classified by optical and physical properties based on the isolated cloud-emitted radiance (Nugent et al. 2009; Nugent 2008).

Two hindrances to the radiometric calibration had to be overcome to accomplish cloud detection with the compact ICI2 systems. First, these systems are based on a camera without a thermoelectric cooler (TEC) and the system response drifts with camera focal-plane-array (FPA) temperature. Software routines were developed at MSU to stabilize the camera response for changes in FPA temperature using a real-time reading of the FPA temperature and laboratory-measured calibration parameters. These routines allow for a radiometric calibration to be maintained without physical temperature stabilization (Nugent 2008).

The second hindrance to calibration was the radiometric impact of the germanium window. The FPA-temperature stabilization and radiometric calibration measurements are made without the germanium window to allow the camera characteristics to be separated from the window characteristics. The addition of the germanium window limits the accuracy of these data, because the signal measured behind the window is not an accurate measure of the scene radiance. Therefore, when the system operates behind the window, the algorithms described in this paper are used to correct for the window effects in the observed data.

2. Correcting for infrared window effects

Initial tests showed that the signal from the window was not spatially uniform because of reflection of emission from the camera and warm sources located behind the camera. A shroud (or baffle) was used to block the spatially nonuniform reflections, but this shroud is still a source of emission. The measured radiance L_m is not a direct measure of scene radiance, but can be represented as a sum of scene radiance L_s multiplied by the band-averaged window transmittance τ_w, radiance emitted inside the enclosure L_e multiplied by the band-averaged window reflectance ρ_w, and radiance emitted by the window L_w, as expressed by Eq. (1) and as indicated graphically in Fig. 2. The band-averaged reflectance ρ_w is a combination of the reflectance off the bottom antireflection-coated and top hard-carbon-coated surfaces of the window, with the top surface reflection reduced by the square of the window transmittance. However, because there was not sufficient information to isolate these two values, we derive a value of ρ_w that is effectively a combination of these terms:

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With characterization of the window, the radiance observed by a camera inside the enclosure can be corrected to yield the scene radiance that would be measured without the window. In this work, we describe a matrix-inversion technique that identifies the transmittance, reflectance, and emissivity of an infrared window averaged across the spectral response of the camera. This technique provides a method of compensating for window effects in our radiometrically calibrated infrared sky images. First, the matrix-inversion relationship is derived and explained. Next, the technique is applied to an ICI2 cloud imaging system, and the results are compared from two sets of collocated imagers in which one imager views the sky through a germanium window and the other views the sky directly.

a. Derivation of the window correction equation

To determine the scene radiance from a measurement taken through the window, Eq. (1) can be solved for L_s:

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The emissions from the internal enclosure L_e and the window L_w depend on the emissivity of each respective surface. If we assume that the emission from within the enclosure arises from blackbody objects at the camera temperature with emissivity equal to 1 but the band-averaged window emissivity ɛ_w is unknown, then the scene radiance can be expressed as

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where L_wbb is blackbody radiance at the window temperature. If the windowless scene radiance, emission from within the enclosure, and the temperature of the window were all known, then the band-averaged properties of the window τ_w, ρ_w, and ɛ_w could be determined.

With these values determined, the radiative effects of the window could be removed, enabling the camera inside the enclosure to measure the scene radiance, as measured by a camera outside the enclosure. The equation for the effective scene radiance proposed in Eq. (3) is similar to the correction used on the CIRIMS system (Jessup et al. 2002; Jessup and Branch 2008). However, for the correction derived here, there are two differences. First, our correction method is based entirely on a radiometric model of the window that allows values of τ_w, ρ_w, and ɛ_w to be determined in the correction procedure. Second, the cameras used in the ICI2 systems have a relatively wide FOV, and therefore our correction takes into account angular variation of the correction across the camera’s FOV. We note also that this technique is based on field measurements and can therefore be applied through periodic side-by-side operation of two sky imagers to account for slow changes of window parameters over time.

3. Deriving a window correction from sky images

The window correction was developed and tested by using two identical LWIR cameras (both with 62° FOV): one operating in the enclosed system with a germanium window (the JPL-ICI2) and the other operating without a window (the MSU-ICI2). The MSU-ICI2 provided a “ground truth” measurement of the actual scene radiance L_s. Side-by-side operation of these two systems during March 2008 provided a set of data of simultaneous measurements of L_s (from MSU-ICI2) and L_m (from JPL-ICI2), the scene and measured radiances, respectively. In a previous experiment in October 2007, the JPL-ICI2 was run alongside a prototype of a 110° FOV system (110-ICI2). The 110-ICI2 system was run without a germanium window and thus allowed for a fully independent set of data, against which the window correction algorithms could be tested. The experiments used in this derivation and the following validation experiments were conducted from a rooftop deployment on the MSU campus in Bozeman, Montana.

a. Matrix-inversion technique

During this experiment, the internal emission from within the enclosure was assumed to be from the camera, and the internal temperature of the camera T_int was used to calculate L_e. It was also assumed that the temperature of the window largely followed the external air temperature near the enclosure T_air. This temperature was used to calculate the blackbody emission of an object at the window temperature L_wbb. The air temperature was available from the Montana State University weather station collocated with the two cloud imagers during the experiment. These values were used to create a matrix,

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These data were loaded into software routines that calculated the Moore–Penrose pseudoinverse matrix as indicated by the following:

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Multiplying the inverted matrix by the set of MSU-ICI2-measured external radiance L_s allows the calculation of the variables in Eq. (3). The window band-averaged transmittance τ_w is found as 1 over the first element of the resulting vector. Multiplying the other two elements of this vector by τ_w yields estimated values of ρ_w and ɛ_w, the window band-averaged reflectance and emissivity, respectively. For accurate characterization of these parameters, the datasets needed to contain the range of T_int and T_air, over which the imager was expected to operate. These temperatures ranged from 10° to 32°C for T_int and from 6° to 21°C for T_air, with a range of T_int–T_air from 2° to 12°C.

b. Angle-dependent IR window correction

The physical properties of the window τ_w, ρ_w, and ɛ_w vary with angle throughout the camera’s field of view. This could be ignored in a narrow field-of-view system or a nonimaging system; however, because the ICI2 systems are relatively wide-angle imagers with incidence angles on the window up to 31°, the angular dependence cannot be ignored. For the LWIR cameras used in the ICI2 systems the per-pixel pointing angle had previously been measured (Nugent 2008). This allowed for the coefficients τ_w, ρ_w, and ɛ_w to be measured uniquely for each pixel and represented as functions of angles τ_w(θ), ρ_w(θ), and ɛ_w(θ), where θ is the pointing angle of each pixel measured from the optical axis.

The values of τ_w(θ), ρ_w(θ), and ɛ_w(θ) do not follow a simple physical model based on Fresnel reflection equations. This is in part because of the action of the carbon coating on the external window surface, antireflection coating on the inside surface, and dust and other contaminants that can settle on the window over time. Although, with sufficient information, it may be possible to develop a physical model to predict the angle-dependent parameters of the window, it is more practical to directly measure these parameters in the laboratory or to infer them from field measurements using an imager with a window alongside a system without a window. We adopted the latter approach and chose to express the angle dependence of the matrix-inversion results with a fifth-order polynomial fit to each parameter as a function of angle. To reduce measurement variations caused by pixel-to-pixel noise, the data were averaged into angle bins of width Δθ = 0.1°. Figure 3 shows the angle-binned data and the corresponding fifth-order polynomial fits to τ_w(θ), ρ_w(θ), and ɛ_w (θ).

During the experiments, both systems were pointed nominally at the zenith; however, a misalignment of approximately 1° from vertical and 2° in azimuth existed. To accommodate this problem, the data were processed to align the images, which required that the data near the edge of each camera’s FOV be left out of the final result. Thus, Fig. 3 shows plots of τ_w(θ), ρ_w(θ), and ɛ_w(θ) only out to an angle of 26.6°. The transmittance for the window was observed to vary from 0.859 on axis to 0.850 at 26.6°. This on-axis value is close to the Fourier transform infrared (FTIR) spectrometer measurement of 0.90 that was made when the window was new. At the time of the measurements described in this work, the window had been deployed outside for a period of months, and some degradation was expected.

To validate our results, one should consider that, for a material in thermal equilibrium, the sum of the transmittance, reflectance, and emissivity for each angle θ must be

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Experimentally, we found that the mean value of τ_w, ρ_w, and ɛ_w measurements over the observed angles was instead 1.012, with a standard deviation of 4.1 × 10⁻⁴. The mean value calculated from the sum of the polynomials used to fit these data was again 1.012, and the standard deviation was 3.6 × 10⁻⁴. This sum is then close to the expected quantity of 1 at all angles, with a mean bias of ∼1.2% high. This summation adds support to the reliability of this method for retrieving the window optical properties. Possible sources of the error in this summation are the uncertainty in the enclosure temperature, the window temperature, the emissivity of the enclosure interior, and the camera calibration. Whereas a 10°C error in the window temperature could account for the entire 1.2% error (a 20% error in ɛ_w), the source is most likely a combination of these uncertainties.

Using the empirical models for τ_w(θ), ρ_w(θ), or ɛ_w(θ) with the measured pointing angle for each pixel, a unique τ_w, ρ_w, and ɛ_w can be calculated for each pixel of the imager. Using these calculated values with the radiance measured inside the enclosure L_m, the external scene radiance L_s can be calculated from the following equation, thereby providing a method to remove the effect of the IR window on the measured radiance values:

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4. Validation of the window correction with independent sky imagers

The window correction algorithm was validated by applying it to infrared sky images and comparing the results to measurements from a similar system operating without a window. This was done using data from two separate outdoor deployments. The first set to be analyzed was obtained in April 2008, five weeks after the measurements from which the correction was derived. During this experiment, the JPL-ICI2 (62° FOV) weatherproof system with an infrared window was operated next to the MSU-ICI2 (62° FOV) system without a window. The second dataset was obtained in October 2007, more than five months before the measurements from which the IR window correction algorithm was derived. During this earlier experiment, the JPL-IC2 (62° FOV) weatherproof system was operated next to the 110-ICI2, with 110° FOV, which operated without a window. This second set of data was used to provide a comparison independent of the instrument used to derive the window correction.

For each of these datasets, the data measured by the JPL-ICI2 with the IR window were corrected using Eq. (7), the fifth-order polynomial model of window properties, and the measured pointing angle of each pixel. It is also important to note that these validation experiments compare window-corrected data with no-window data from two totally different imagers, the MSU-ICI2 and the 110-ICI2.

The sky measurements used in these comparisons were processed to provide both cloud presence and cloud type. This cloud classification scheme is based on the dependence of cloud emission on cloud emissivity and temperature and on the strong dependence of cloud emissivity on cloud thickness for thin clouds (Nugent et al. 2009; Sassen and Mace 2002). The cloud classification scheme used to process these data is shown in Table 1. The table also lists cloud optical depth, which is commonly used to classify thin clouds, particularly cirrus. The optical depth represents the total extinction of the cloud and is also related directly to the total optical loss for a signal (e.g., sunlight or a laser) transmitted through the cloud. The visible-wavelength cloud optical depth is derived from the measured thermal emission for cirrus clouds (Nugent et al. 2009). Clouds with an optical depth above 3 act as blackbodies, and the cloud emission no longer depends on cloud thickness but rather on cloud temperature (Sassen and Mace 2002).

c. Results of the validation

Both the temporal and the spatial cloud data demonstrate that the window correction greatly reduces the differences between simultaneous cloud data measured with different imaging systems. When the time series plots of spatially averaged radiance from the two 62° FOV systems were compared (see Fig. 4), the window correction reduced the rms differences from 4.9 to 0.77 W m⁻² sr⁻¹. For comparison, the calibration accuracy of ICI2 systems has been determined to be near ±0.45 W m⁻² sr⁻¹ without the window (Nugent 2008). Therefore, the expected variation between the two imagers resulting from calibration uncertainty was ±0.63 W m⁻² sr⁻¹ (Nugent 2008). In the spatial data, the only persistent differences between the 62° JPL system and the other systems occurred near the cloud borders, which are highly sensitive to any angular misalignment between the two cameras. Differences observed in both temporal and spatial data were small enough to be generally lower than the cloud identification threshold radiance values.

An additional benefit of this comparison is that the rms deviation between the two imager signals can be used to estimate the calibration uncertainty of the windowed imager after correction for the window effect. We follow Bevington’s treatment of propagation of errors (Bevington 1969), which says that the variances add for independent data, as indicated in the following:

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where σ_x represents the standard deviation of the difference between the window-corrected signal from the JPL-ICI2 and the windowless MSU-ICI2, σ_a represents the calibration uncertainty of the windowless MSU-ICI2, and σ_b represents the calibration uncertainty of the windowed JPL-ICI2 after window correction. We can then obtain an estimate of the calibration uncertainty of the window-corrected JPL-ICI2 by solving Eq. (8) for σ_b:

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Applying this equation to the measured data leads to an uncertainty of ±0.64 W m⁻² sr⁻¹ for the window-corrected JPL-ICI2. This uncertainty is higher than the value of ±0.45 W m⁻² sr⁻¹ that was calculated for a windowless ICI2, and it therefore limits the JPL-ICI2 to a minimum threshold of level-2 clouds (see Table 1) for accurate cloud detection and classification. Thus, when this system is run with its germanium IR window, it can accurately classify clouds with a 550-nm optical depth greater than 0.25 (see Table 1), which includes all but the thinnest clouds.

This level of sensitivity is sufficient for an infrared cloud imaging system in many applications. For example, in an Earth–space optical communication system, this level corresponds to a cloud-dependent loss of approximately 1 dB, which is likely to be acceptable for Earth–space communication links with near-Earth platforms. It has also been suggested that a sensitivity threshold of 0.25 for cloud optical depth provides the best fit with traditional cloud climatology (performed by human observers), in particular when used as a detection threshold for lidar-based systems in the Arctic (Eloranta et al. 2008). Thus, the ICI2, when operating in the enclosure and behind the germanium window, can provide the required accuracy and sensitivity needed for cloud cover studies with consistent day and night detection. Operation without a window can produce better sensitivity, but it is at the expense of somewhat increased mechanical complexity through the use of a remotely operated protective hatch.

5. Conclusions

We have described a technique based on field measurements to determine the transmittance, reflectance, and emissivity of an infrared window, including angular dependence over a moderately wide-angle image. This technique produces a correction for thermal infrared imagery taken through a germanium window and requires data from two collocated thermal infrared cameras, internal camera temperature, and external air temperature. This technique has been applied successfully to measure the LWIR band-averaged transmittance τ_w, reflectance ρ_w, and emissivity ɛ_w of a germanium IR window in a thermal infrared camera enclosure over a 62° FOV.

With this correction applied, the signal measured by the camera behind the IR window can be corrected to represent the true scene radiance to within ±0.64 W m⁻² sr⁻¹. Through the application of this correction, the weatherproof JPL-ICI2 can operate independently with a detection sensitivity capable of detecting all but the thinnest cirrus clouds. The compact JPL-ICI2 system, which utilizes the IR window, can provide high-temporal-resolution cloud measurements with no difference in day/night sensitivity during periods of adverse weather.

With adequate data, including the enclosure internal temperature (currently estimated as the camera temperature) and external temperature, this correction can be applied in real time. This allows the JPL-ICI2 system to run without support from the MSU-ICI2, which is run in a weather-hardened enclosure, and to achieve continuous observation and classification of cloud cover with only a small reduction of sensitivity (clouds with optical depth greater than 0.25). Future improvements in the camera and calibration procedures and the additional measurement of enclosure and window temperatures should continue to improve the minimum level of cloud sensitivity.

These experiments were performed over a range of internal enclosure temperatures (from 10° to 32°C) and external weather conditions (from 6° to 21°C) with a range of internal-to-external temperature differences (from 2° to 12°C). Currently, the JPL-ICI2 cloud imaging system is deployed at the Jet Propulsion Laboratory Table Mountain Facility, California, and data from this deployment will allow the assessment of this algorithm under a wide variety of weather conditions. Data from this deployment will also help determine if the window correction is sufficiently stable to allow a calibrated LWIR camera to operate inside a weather-hardened enclosure over an extended period of time.