Calibration of uncooled LWIR microbolometer ...

Calibration of uncooled LWIR microbolometer imagers to enable long-term field deployment Paul W. Nugent and Joseph A. Shaw Electrical and Computer Engineering Department, Montana State University, P.O. Box 173780, Bozeman, MT, USA 59717-3780 ABSTRACT Radiometric calibration methods are described that enable long-term deployment of uncooled microbolometer infrared imagers without on-board calibration sources. These methods involve tracking the focal-plane-array and/or camera-body temperatures and compensating for the changing camera response. The compensation is derived from laboratory measurements with the camera viewing a blackbody source while the camera temperature is varied in a thermal chamber. Results demonstrate absolute temperature uncertainty of ≤0.35 °C in a 24-hour period, with more than half of the uncertainty inherent in the blackbody source to which the data are compared. Although this work was driven by environmental remote sensing applications, the methods are relevant to a wide range of infrared imaging applications. Keywords: radiometry, calibration, infrared imaging, thermal imaging, remote sensing 1.

INTRODUCTION

Obtaining quantitative data from thermal infrared imagers requires a radiometric calibration to convert the output digital numbers to quantities such as radiance or brightness temperature. This is commonly done by measuring the digital output of the camera while it views two or more blackbody sources to create a relationship between the digital output and the desired quantitative measurement. This relationship is often assumed to be valid over a range of operating conditions. However, when working with microbolometers without a thermo-electric cooler (TEC) to stabilize the focal plane array (FPA) temperature, there is large temperature variation and corresponding camera response variation. Therefore, the relationship derived at one FPA temperature cannot be assumed to be valid at another FPA temperature. Consequently, long-term field deployment of such cameras without large and costly blackbody calibration sources requires some method of correction for this variation. 1.1 Motivation Our need for high radiometric accuracy from microbolometers was motivated by our work developing infrared cloud imagers for detecting and classifying clouds1–3 and with field deployable imagers for agricultural and environmental applications.4–6 These systems are all based on radiometrically calibrated microbolometer cameras, support electronics, and enclosures to protect the camera from wind and rain. Because of their outdoor deployment, the camera FPA temperature changes constantly. If left uncorrected, these changes would make maintaining radiometric calibration impossible. 1.2 Calibration methods One method to maintain a highly accurate calibration during long deployments is to view one or more external blackbody sources during deployment, close in time to each scene image.1,7 One blackbody image enables a one-point offset calibration, whereas two or more blackbody images allow for correcting both offset and gain. This technique is very common for long-term deployment of imagers and other instruments in challenging environments, such as the Arctic.1 An alternative approach is to incorporate the FPA temperature into the calibration algorithm. There exist a large number of proposed techniques in scientific and patent literature that use the FPA or camera temperature to calibrate microbolometer cameras.8–15 This paper summarizes two such techniques for keeping a microbolometer camera response stable over long time periods without requiring an external blackbody source. For each technique described in this paper, a mathematical model is presented, followed by examples of experimental validation with quantified achievable accuracy. *[email protected]; phone 1 406 994-7261; fax 1 406 994-5958; www.coe.montana.edu/ee/jshaw

Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXV, edited by Gerald C. Holst, Keith A. Krapels, Proc. of SPIE Vol. 9071, 90710V · © 2014 SPIE · CCC code: 0277-786X/14/$18 · doi: 10.1117/12.2053082

Proc. of SPIE Vol. 9071 90710V-1

The first method described here is based on tracking the FPA temperature and using it, in some cases with its first and second time derivatives, to stabilize the digital output of the camera. The second method uses a modified image of the internal shutter as an equivalent external blackbody reference. Both methods computationally stabilize the camera’s digital output, and to these values a standard multi-point radiometric calibration is then applied. These methods have an advantage over previous methods that they do not require characterizing the camera over all expected temperatures.14 The derivation of these methods and methods for deriving the required coefficients are presented elsewhere for the case of the direct FPAtemperature stabilization,16 and in subsequent journal papers in the case of the shutter-based compensation. 2.

THE CALIBRATION PROCESSES

The purpose of a radiometric calibration is to relate the camera’s digital output to scene radiance or scene temperature. We selected to calibrate the camera in terms of radiance, as this is proportional to optical power, and thus the response of the camera is linear (if scene brightness temperature is needed, it can be calculated from radiance using a radiance-to-temperature look up table). For a radiance calibration, the relation between the camera response, rs, and scene radiance, Ls, can be described by equation 1, where G is the camera gain and D is the camera offset, also known as dark signal. .

(1)

For calibration, this equation is rearranged to express a function to convert the output digital values to a measure of scene radiance: .

(2)

In equation 2 gc and oc are the calibration gain and offset, and are equivalent to the following, .

(3)

Typically gc and oc are determined in a laboratory setting through the use of a range of blackbody reference images and knowledge of the camera’s spectral responsivity. If the FPA-temperature of the camera changes over time, then gc and oc must be a function of the FPA temperature. This model is somewhat simplistic, but it has proven adequate for our calibration work with broadband microbolometer LWIR imagers. 2.1 Direct FPA-temperature compensation Previously, we showed how to derive a function to correct for the FPA-temperature or lens-temperatureinduced errors in the digital output from a camera,15 yielding equation 4. In this equation, rs is the scene response of the camera in digital values, rc is the digital response corrected for changes in camera temperature, b(ΔT) is the offset correction function, m(ΔT) is the gain correction function, and ΔT is the difference between the actual FPA-temperature and a reference FPA temperature (typically 25 °C). Converting the corrected signal, rc, to radiance requires applying the calibration gain and offset, as shown in equation 5, where Ls is the scene radiance, gc is the calibration gain, and oc is the digital number offset.

[

(

)

(

)

(

)

(

)

]

(4) (5)

The terms ( ) and ( ) are functions of the difference of the camera’s current FPA temperature to the referenced FPA-temperature (25 °C in this work). Experiments have found that a scalar is sufficient to describe ( ), whereas ( ) is a more elaborate function described by a higher-order polynomial function of , and in some cases it has been found to depend on the first and second derivatives of . 2.2 Shutter-based FPA-temperature compensation Most microbolometer cameras have an internal shutter (or flag), located between the detector array and the lens, which normally is used to perform a Non-Uniformity Correction (NUC) during operation. The shutter-based FPA-temperature compensation uses a post-NUC image of this shutter and the temperature of the shutter to perform a secondary correction for the FPA-temperature dependence in the camera. This


correction is based on the assumption that a shutter image can be mathematically modified to account for the camera’s lens and create a pseudo external blackbody image. The use of the internal shutter as an equivalent external blackbody requires careful characterization of the shutter and lens. The radiometry of this situation is illustrated for a pixel viewing the blackbody in Figure 1(a) and the shutter in Figure 1(b).

(b)

(a)

Figure 1. Geometric optical layout of the camera viewing an external blackbody through the lens (a) and of the sensor viewing the internal shutter before the lens (b).

If the shutter and blackbody are both at the same temperature, then the only difference between the shutter and blackbody is the radiometric effect of the lens. This effect can be determined from a set of images of the blackbody and the shutter, both over a desired range of temperatures. Then a function can be derived to convert the internal shutter image to an equivalent external blackbody image. This function, as shown in equation 10, is a function of both the internal shutter image (response) rf and the shutter temperature, Tf. {

}

(6)

For the purpose of this paper it is assumed that this function is valid and that it can be derived using images of the internal shutter and external blackbody. A detailed analysis of this process, its derivation, and the detailed form of the function will be reported in subsequent publications. 2.3 Shutter-based offset correction in the presence of FPA-temperature-dependent response Taking the difference between images of the scene and a blackbody reference will cancel the offset in the image data, including any FPA-temperature-dependent offset. This result is shown in equation 7, where rs is the response to the scene, rbb is the response to the blackbody reference, go is a temperature-independent gain, Gt is the temperature-dependent gain as a function of FPA temperature Tfpa, Ls is the scene radiance, and Lbb is the blackbody radiance. [

(

)

)](

(7)

Previously,15 we showed that the temperature dependence in the gain can be described as simply a scalar multiplied by Tfpa; therefore, equation 11 can be reduced to (

).

)(

(8)

In this equation, gt is a constant that can be derived as part of the system calibration process. This equation can be rearranged to give the scene radiance Ls in terms of the blackbody radiance Lbb, measured values (r, rbb, and Tfpa), and camera response terms (go and gt) that can be derived from a laboratory calibration. (

(9)

)

In section 2.2, it was shown that a shutter image can be converted into an equivalent external blackbody response via the function { }, and the radiance of the shutter based-blackbody Lbbs can be calculated using the shutter temperature. Using these parameters, the scene radiance can then be described as { (

} )

.


(10)

In most microbolometer cameras, there is not a direct temperature sensor on the shutter of the camera. Therefore, during the deployment, we make the assumption that the FPA-temperature sensor is sufficiently close to the shutter temperature to not introduce large errors into the calibration. 3.

RESULTS USING A FLIR PHOTON CAMERA

These calibration methods were applied to a Photon 320 with an Ophir 14.25 mm, f/1.2, athermalized lens. The camera was placed in an environmental chamber while viewing a blackbody calibration source that varied between 10 °C and 50 °C while the chamber temperature was varied between 10 °C and 30 °C. During this experiment, data were collected in the following manner. First, a standard non-uniformity correction (NUC) was performed using the shutter in the manufacturer’s intended fashion. Next, an image of the scene was recorded, along with the FPA temperature. The camera’s shutter was then closed and an image of the shutter was collected. Figure 2 shows the blackbody temperature (blue dashed line) and the camera FPA-temperature (red solid line) during this experiment. It was assumed that the FPA-temperature was an accurate representation of the shutter temperature.

Temperature C

50

Blackbody Temperature Camera Temperature

40 30 20 10 0

200

400

600

800

1000

1200

1400

Minutes from Start Figure 2. Blackbody and Camera FPA temperatures during the calibration experiment.

The camera output data from this experiment were calibrated using three different methods: 1) without correction for FPA-temperature dependence; 2) using the FPA-temperature to correct for errors from a calibration derived at 25 °C (Section 2.1); and 3) using the shutter as a blackbody (Section 2.2). 3.1 Calibration without FPA-temperature correction The calibrated response from the camera without any FPA-temperature compensation is shown in Figure 33, and a histogram of the error between the camera output and the blackbody temperature is shown in Figure 4. There is significant error caused by the changing FPA-temperature.


Figure 3. Camera output calibrated without a correction for FPA-temperature-dependent errors.

Number of Occurrences

500 400 300 200 100 0 -10

-8

-6

-4

-2

0

2

Temperature Error C

4

6

8

10

Figure 4. A histogram of the camera output from Figure 4. The temperature errors are centered near zero, but are widely and approximately uniformly dispersed.

3.2 Calibration using only a FPA-temperature correction The FPA-temperature-based calibration was applied to the same data using the FPA-temperature to compensate for deviations from a calibration derived at 25 °C. This calibration process kept the output of the camera accurate as its temperature changed in response to ambient temperature changes. The results are shown as a time-series plot in Figure 5, and as a histogram of the error between the calibrated temperature and blackbody temperature in Figure 6. The temperatures reported by the camera closely follow the blackbody temperature. Further, the histogram shows that these calibrated data have an essentially zero mean error (0.005 °C), and a Gaussian-like distribution. The temporal standard deviation of these data was 0.116 °C and the spatial standard deviation was 0.190 °C.


55 50

Temperature C

45

Mean Measured Temperature Min & Max Measured Temperature Blackbody Temperature

40 35 30 25 20 15 10 0

200

400

600

800

1000

1200

1400

Time (Minutes) Figure 5. Camera output calibrated using only the FPA-temperature to correct for deviations from the camera’s response characterized at an FPA-temperature of 25 °C.

Number of Occurrence

10,000 8000 6000 4000 2000 0 -10

-8

-6

-4

-2

0

2


4

6

8

10

Figure 6. A histogram of the camera output calibrated using the FPA-temperature to track sensor deviations. The temporal standard deviation was 0.116 °C and the spatial standard deviation was 0.190 °C.

3.3 Shutter-based FPA-temperature correction Next, the shutter-based FPA-temperature compensation was applied to these data. Application of this calibration process greatly reduced the FPA-temperature-dependent errors relative to the original measurements. The resulting time-series plot is shown in 7, and a histogram of the error between the calibrated temperature and blackbody temperature is shown in Figure 8. The temperatures reported by the camera closely follow the blackbody set temperature, and the histogram of these calibrated data is centered near zero at 0.25 C, with a Gaussian-like distribution. The temporal standard deviation of these data is slightly higher than the FPA-temperature-based correction, at 0.236 °C, but the spatial standard deviation was lower, at 0.044 °C.


Figure 7. Camera output calibrated using the shutter as an equivalent blackbody and with a correction for Gt, the FPA-temperature-dependent gain.

Number of Occurrences

6000 5000 4000 3000 2000 1000 0 -10

-8

-6

-4

-2

0

2


4

6

8

10

Figure 8. A histogram of the camera output calibrated using the shutter to correct for temperature-induced errors. The temporal standard deviation was 0.236 °C and the spatial standard deviation was 0.044 °C.

3.4 Summary of the Photon camera calibration test results Table 1 shows the variability and errors within the data using each of the calibration methods, and the resulting calibration uncertainty (standard deviation). The individual errors have been combined via a standard propagation of errors in quadrature to yield the final system accuracy. This assumed that the spatial and temporal errors had zero covariance, and the validity of this assumption warrants further study. Note that the final achieved uncertainty includes the additional ±0.25 °C uncertainty inherent in the blackbody calibration source. Table 1. Errors and uncertainty (standard deviation, “Std”) of the camera output with no correction, with FPA-temperature correction, and with the shutter-based correction. Achieved accuracy includes the additional ±0.25 uncertainty in actual output of the blackbody calibration source. Calibration

Mean Error

Std (time)

Std (space)

Combined Accuracy

Achieved Accuracy

Uncalibrated

-0.623 °C

3.982 °C

0.041 °C

±3.980 °C

±3.980 °C

FPA-temp

0.005 °C

0.116 °C

0.190 °C

±0.22 °C

±0.33 °C

Shutter-based

0.251 °C

0.236 °C

0.044 °C

±0.25 °C

±0.35 °C


4.

RESULTS USING A FLIR TAU2 CAMERA

The previous tests were performed over a relatively limited ambient temperature range (10 °C to 30 °C) with a relatively old camera (but one with which we had years of experience). This section reports the results of applying the same calibration methods to a newer camera, the FLIR Tau2 with Ophir 50-mm, f/1.7 lens, over a three-times wider ambient temperature range (-20 °C to 40 °C). The Tau2 was placed inside an environmental chamber, viewing a blackbody that filled its FOV. The chamber temperature was cycled from -20 °C to +40 °C, then back to -20 °C, at three rates: 0.67 °C/min, 1.33 °C/min, and 2.67 °C/min. This was repeated with the blackbody set to 10 °C, 50 °C, and 90 °C. A time-series plot of the blackbody temperature and the camera FPA temperature throughout this experiment is shown in Figure 9, and the resulting output is shown in Figure 10 with no correction (yellow-green) and with FPA-temperature correction (red), along with the blackbody source temperature (blue). The results of a statistical analysis of these data are shown in Table 2.

100 Blackbody Temperature Camera FPA-Temperature

Temperature  C

80 60 40 20 0 -20

0

2

4

6

8 Hours

10

12

14

Figure 9. Blackbody temperature (blue dashed line) and the camera’s internal FPA temperature (green solid line) during the Tau2 calibration experiment.

Figure 10. Tau2 camera output with no FPA-temperature compensation (yellow-green) and with the FPAtemperature compensation (red). The staircase blue line is the blackbody source temperature.


Table 2. Variability and errors if the calibrated data from a FLIR Tau2 using the FPA-temperature only correction. Calibration

Mean Error

Std (time)

Std (spatial)

Combined Accuracy

Achieved Accuracy

Uncalibrated

-6.05 °C

7.11 °C

0.38 °C

±7.12 °C

±7.12 °C

FPA-Temp

0.086 °C

0.95 °C

0.276 °C

±1.05 °C

±1.08 °C

Table 2 shows that the FPA-temperature correction also improved the spatial standard deviation for this camera, meaning the blackbody images were more uniform after the application of the calibration. This suggests that the after-market lens created a need for an improvement over the factory flat-field correction. Overall, the FPA-temperature correction produced a significant performance improvement in this camera, even with the larger temperature range and more rapid temperature changes. The improvement was degraded by a factor of three relative to the previous example with a smaller temperature range and slower temperature changes, but it was still much better than the uncompensated output. Finally, we note that the shutter-based correction was found to be unreliable with the Tau2 camera in previous tests. This could be related to the assumption that the shutter and FPA are at similar temperatures: during periods of rapid temperature change, it is likely that the shutter and FPA would experience wider separations in temperature than during the tests with more slowly changing temperatures. 5.

CONCLUSIONS

This paper has presented two methods that allow reduction of the FPA-temperature-dependence in microbolometer infrared cameras through a direct FPA-temperature correction and the use of the camera shutter as an equivalent external blackbody source. These techniques significantly improve the camera calibration and reduce the errors correlated with the camera/lens temperature. The direct FPA-temperature correction has the best overall performance; however, the shutter-based correction has lower spatial variation across each individual frame. Both methods cause an increase in the variability of the data across an image, although the increase with the shutter-based method may be insignificant. This increase could be caused by spatial variations in the detector temperature, or in the case of the shutter-based method, by spatial and temporal deviations of the shutter temperature from the measured FPA-temperature. The nonzero mean in the error for the shutter and gain calibration could be a sign of an offset between the shutter temperature and the temperature of the detector and lens. When applied to a Photon 320 with an Ophir 14.25 mm, f/1.2 lens, both methods performed well and produced net uncertainty values of ±0.33 °C and ±0.35 °C for FPA temperatures ranging from 20 °C to 32 °C. When applied to a Tau2 camera with an Ophir 50-mm, f/1.7 lens, the FPA-temperature correction method produced a net uncertainty of ±1.08 °C for FPA temperatures ranging from -18 to 38 °C. This procedure is being used in environmental remote sensing systems deployed in widely varying conditions. Results from those deployments will allow quantification of this calibration technique in multi-year camera deployments, which will be reported in future publications. Acknowledgment This material is based on research sponsored by the Air Force Research Laboratory, under agreement number FA9550-10-1-0115. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Research Laboratory or the U.S. Government.


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