Although infrared focal plane array (IRFPA) detectors have been commonly used, nonuniformity correction (NUC) remains an important problem in the infrared imaging realm. Nonuniformity severely degrades image quality and affects radiometric accuracy in infrared imaging applications. Residual nonuniformity (RNU) significantly affects the detection range of infrared surveillance and reconnaissance systems. More effort should be exerted to improve IRFPA uniformity. A novel NUC method that considers the surrounding temperature variation compensation is proposed based on the binary nonlinear nonuniformity theory model. The implementing procedure is described in detail. This approach simultaneously corrects response nonlinearity and compensates for the influence of surrounding temperature shift. Both qualitative evaluation and quantitative test comparison are performed among several correction technologies. The experimental result shows that the residual nonuniformity, which is corrected by the proposed method, is steady at approximately 0.02 percentage points within the target temperature range of 283 K to 373 K. Realtime imaging shows that the proposed method improves image quality better than traditional techniques.
I. INTRODUCTION
Infrared focal plane array (IRFPA) technology has recently undergone significant progress. However, the nonuniform response of IRFPA remains a serious issue as it significantly reduces the quality of acquired images and degrades the temperature resolvability of the imaging system. Thus, nonuniformity correction technology is a necessary preprocess in infrared imagery
[1

3]
. Moreover, external conditions such as surrounding temperature and variation in transistor bias voltage cause the spatial nonuniformity to drift slowly in time, thus requiring repeated compensation for the nonuniformity during sensor operation. Two kinds of nonuniformity correction (NUC) are traditionally used for infrared imaging: the calibrationbased correction and scenebased correction methods. The calibrationbased NUC includes the one, two, and multipoint methods. Although simple and convenient, the calibration effect is ineffective in complicated applications, such as cases with a large dynamic range of target radiation. Meanwhile, such calibration has to be repeated once surroundings change or when surrounding stability problems arise
[2]
. Compared with the calibrationbased correction technique, the scenebased NUC technique does not require a blackbody radiation source for calibration. The estimated parameters of calibration are updated in concurrence with the imaging process. These NUCs adapt the slow characteristic drift of the detector over a period of time. However, these algorithms require the movement of the scene. Given that complex calculation is a significant load, new algorithms need to be developed to improve efficiency and to meet the demand for further highspeed treatment
[4]
. The binary nonlinearity nonuniformity model, which considers both the environmental radiation influence on the signal output of IRFPA and the nonlinearity of a large dynamic range of radiation temperature, is introduced in this study. According to this theoretical model, a novel NUC algorithm based on surrounding temperature compensation was proposed. The correction quality is evaluated both through qualitative and quantitative methods. The correction performance of the proposed technique is compared with that of conventional NUC methods.
II. NOVEL CORRECTION APPROACH
According to Planck’ law, infrared radiation power is expressed as a function of temperature
T
and wavelength
λ
.
Based on this theory, the binary nonlinear nonuniformity model proposes that the response signal of the IRFPA detector is a binary function of target infrared radiation temperature
T_{b}
and surrounding infrared radiation temperature
T_{s}
[4

6]
. For an
N
×
M
array of IRFPA, the theoretical model is expressed as Equation (2).
where
V_{ij}
(
T_{b}
,
T_{s}
) is the response voltage of pixel (i,j) to target temperature
T_{b}
and surrounding temperature
T_{s}
.
b_{ij}
> 0,
d_{ij}
> 0,
e_{ij}
> 0, 1 ≤
i
≤
N
, 1 ≤
j
≤ M, and (
a_{ij}
,
b_{ij}
,
c_{ij}
,
d_{ij}
,
e_{ij}
) are the
N
×
M
array nonuniformity coefficients of each pixel. Expression (2) is the set of a series of “S” type curve surfaces.
Based on the foregoing theoretical model, IRFPA is mainly affected by two factors: target radiation and surrounding radiation temperature. Thus, target radiation and environmental influence must be considered and corrected to improve the correction accuracy and extend the application range of the NUC algorithm.
Assuming that the surrounding temperature
T_{s}
remains constant, only the target radiation temperature variable
T_{b}
affects nonuniformity. Thus, the theoretical model is simplified as Expression (3).
where coefficient (
a_{ij}
,
b_{ij}
) represents the dynamic range of IRFPA detector response to target radiation temperature. The nonuniformity coefficients (
a_{ij}
,
b_{ij}
) of each pixel (
i
,
j
) are determined by measuring the IRFPA response dynamic ranges to uniformity blackbody. Taking the logarithm of both sides of Expression (3) yields the following expression:
Equation (4) is simplified to a linearity function:
By measuring the voltage
V_{ij}
(
T_{b}
) to extended blackbody temperature
T_{b}
, the nonuniformity coefficients (
c_{ij}
,
d_{ij}
) were determined using Equations (5) and (6). The relationships between each pixel response signal and the extended blackbody temperature
V_{ij}
(
T_{b}
)
T_{b}
are confirmed. The “
S
” type nonlinear, nonuniform response curve is illustrated in
Fig. 1
(a).
Figure 1
(a) shows that the response curves
S
_{(i,j)}
of each pixel (
i
,
j
) correspond to different parameter values (
a_{ij}
,
b_{ij}
,
c_{ij}
,
d_{ij}
). The expectation curve
S_{e}
must first be confirmed during the course of correction.
Fig. 1
(b) shows the expectation curve after nonuniformity correction. The expectation response function is expressed as Equation (7):
Response curves of IRFPA detectors to blackbody temperature and their expectation response curve.
The nonlinearity coefficient (
a_{e}
,
b_{e}
,
c_{e}
,
d_{e}
) must be determined to correct the response curve of each pixel to expectation curve
S_{e}
. In this work, the expectation of the nonuniformity coefficient of each pixel is assumed as the nonlinearity coefficient (
a_{e}
,
b_{e}
,
c_{e}
,
d_{e}
) of the expectation curve
S_{e}
. We thus derive the following expression:
where
x
represents
a
,
b
,
c
, and
d
.
The mapping relationship between original pixel response curves
S_{ij}
and correction expectation curve
S_{e}
is then established and expressed as Equation (9):
where
is the correction coefficient matrix vector.
By solving equations (8), (9), and (10), the nonuniformity correction coefficient matrix (
A_{ij}
,
B_{ij}
,
C_{ij}
,
D_{ij}
) is obtained.
where
x
represents
a
,
b
,
c
,
d
and X represents
A
,
B
,
C
,
D
.
The foregoing nonuniformity coefficient matrixes (
a_{ij}
,
b_{ij}
,
c_{ij}
,
d_{ij}
) of IRFPA pixels are determined by measuring the individual detector pixel response of a different extended blackbody temperature under stable surrounding temperature conditions. The correction coefficient matrixes (
A_{ij}
,
B_{ij}
,
C_{ij}
,
D_{ij}
) calculated from Expression (11) are used to correct the nonuniformity attributed to target radiation.
Assuming that target radiation temperature remains constant, the effect of ambient radiation is considered in this section. According to the binary nonlinear model, the effect of environment radiation on the nonuniform response is expressed as Equation (12).
where nonuniformity coefficient matrix
e_{ij}
is obtained by testing the IRFPA individual pixel voltage corresponding to ambient radiation temperature variation. Compensating for the effect of environment temperature shift on IRFPA sensor nonuniformity, an expectation response relationship between the detector response signal and surrounding temperature must first be determined. Based on the binary nonlinear model, the expectation curve
L_{e}
can be expressed as Equation (13).
where
e_{e}
is the expectation gain coefficient, which is equal to the expectation of all pixel nonuniformity coefficients
e_{ij}
.
A mapping relationship between actual nonuniformity and the uniformity expectation responsive curve
L_{e}
is established to compensate for the effect of environment temperature on IRFPA nonuniformity.
where
is the compensation coefficient matrix vector. The compensation coefficient matrix
E_{ij}
of the surrounding temperature variations is calculated from Equations (12), (13), (14), and (15).
where coefficient matrix
E_{ij}
is used to compensate for the effect of surrounding temperature variation on IRFPA nonuniformity.
In summary, nonuniformity correction based on surrounding temperature compensation comprises seven procedures. The foregoing six procedures are focused on calibration and coefficient calculation. Despite the numerous calculation loads, these procedures do not require prolonged correction time because they are processed offline before the correction. After calibration and calculation, the nonuniformity correction coefficients (
A_{ij}
,
B_{ij}
,
C_{ij}
,
D_{ij}
,
E_{ij}
) are stored in a system flash memory. The last correction procedure was performed by accessing the correction coefficients and then correcting the raw data on infrared imagery through Equation (9) and/or (15). The realtime correction performance is determined by the correction coefficient accessing time and by the calculation time of Equation (9) and/or (15). Coefficients (
A_{ij}
,
B_{ij}
,
C_{ij}
,
D_{ij}
) are applied to correct the nonlinear nonuniformity response of IRFPA to target radiation temperature. Coefficient
E_{ij}
is used to compensate for the nonuniformity, which is inflected by the surrounding radiation temperature variation.
III. EXPERIMENT RESULTS AND ANALYSIS
The performance of the proposed approach was studied using real infrared imagery. Image quality correction and correction accuracy were evaluated and compared with those of the traditional correction method. The data were collected from two different cameras. The first camera was a 320×240 longwave infrared uncooled microbolometer detector (UL 01 01 1, ULIS). The device was sensitive to radiation within an 8 μm to 14 μm spectral region. The second camera was a mediumwave infrared Cadmium Mercury Telluride cooled detector with 640×512 format (E3701 Hawk, SELEX) which was sensitive to radiation within the 3.7 μm to 4.95 μm spectral range. The data on these two cameras were digitized to 14bit.
Imaging qualitative evaluation was first performed. Infrared imagery was corrected through twopoint correction (TPC) and the proposed surrounding temperature compensation nonuniformity correction (STCNUC). The captured image framed by the first camera is shown in
Fig. 2
(a), (b), and (c).
Fig. 2
(a) shows the initial image without nonuniformity correction.
Fig. 2
(b) shows the TPC image with outdoor correction under an environmental temperature of 308 K. The two calibration points were 288 and 338 K. Correction
Comparison of TPC and STCNUC in an outdoor scene using longwave uncooled detector.
Conventional and novel NUC correction comparison using mediumwave cooled detector.
coefficients were obtained at 296 K under lab environmental conditions. The severe nonuniformity of raw data was evidently eliminated by TPC, as shown in
Fig. 2
(b). However, stripe nonuniformity remained in the image because the correction coefficients used were obtained from an ambient temperature different from the environment. The quality of the corrected image was degraded by these remaining stripes.
Fig. 2
(c) shows an outdoor imaging result of STCNUC. The image quality in
Fig. 2
(c) is clearer and better than that of
Fig. 2
(b) because of stripe elimination.
Qualitative evaluation and comparison were applied to a different scene and sensor (640×512). The results of the second camera are shown in
Fig. 3
(a) and (b).
Fig. 3
(b) indicates that the novel correction is better than the conventional NUC correction shown in
Fig. 3
(a). In conclusion, the conventional NUC is unsuitable for a varied environmental situation. This drawback limits its application field to a stable environment temperature condition. However, the STCNUC is adapted for surrounding temperature variation.
Quantitative evaluation of STCNUC was also performed. The NUC quality was characterized in terms of residual nonuniformity (RNU) magnitude. The RNU of the first camera was measured by the infrared imagery test system called METS11300. The original infrared image nonuniformity, onepoint nonuniformity correction (OPNUC) infrared image RNU, multipoint nonuniformity correction (MPNUC) infrared image RNU, and STCNUC infrared image RNU were measured and compared. The calibration point of OPNUC was 303 K. The calibration points of MPNUC were 293, 323, and 353 K. The test target for this experiment was uniformity extended blackbody. The experimental environment temperature was 296 K. The extended blackbody temperature ranged from 283 K to 373 K, with each 10 K as a test point. For the direct comparison of the three approaches, their test data are illustrated in a trend chart shown in
Fig. 4
. The yaxis of this figure is a logarithm coordinate.
The test results show that multipoint correction accuracy is higher than onepoint correction. The average RNU of OPNUC was ten times higher than that of MPNUC. However, the correction accuracy of STCNUC was better than both OPNUC and MPNUC. The RNU of STPNUC was only half of MPNUC. Although the RNU of OPNUC kept low within a narrow range neighboring the calibration point, it is widely used for normal application since this correction method is simple and convenient. This method stores one coefficient matrix in imagery memory. MPNUC possesses high correction accuracy. Furthermore, this method is suitable for a wide range of dynamic target temperature. However, threepoint correction, which is the simplest method, needs to store five correction coefficient matrixes. This method requires more hardware resources, and needs complicated calculation during the correction. Moreover, MPNUC, same as OPNUC, is unsuitable for application in a varying surrounding temperature. The correction coefficients need to be frequently updated along with ambient temperature variation. STCNUC is suitable for a wide range of dynamic target temperature and varying environment temperature situations. Moreover, the correction accuracy of STCNUC is higher than that of the traditional algorithms even though the calculation procedure of the correction coefficients is complex. The lowest RNU corrected by STCNUC in this experimental test is 0.017 percentage points. The RNU corrected by the proposed method is steady approximately 0.02 percentage points within the target temperature range of 283 K to 373 K. This RNU level is better than the 0.04 percentage point level of the same type of detector reported in the most recent literature
[7
,
8]
.
Figure 4
shows that the RNU trend chart of OPNUC presents a “V” shape curve, while the infrared imagery tested with different temperature extended blackbody. The lowest RNU value presents at the 303 K calibration point. The difference of the target temperature from the calibration point corresponds to higher RNU value, which shows that the correction accuracy lowers down when the target temperature moves farther from the calibration point. MPNUC shows the same situation. The lowest RNU values present at the three calibration points of 293 K, 323 K, and 353 K. RNU goes up when the target temperature moves farther from the calibration point. Considering gain correction, the RNU fluctuation of MPNUC is smoother than that of OPNUC. The RNU trend chart of MPNUC shows a “W” shaped curve. These experimental results of OPNUC and MPNUC are consistent with the theory analysis results reported by Abraham F., Isaac G., E.Gurevich, and A.Fein
[8]
. Moreover, STCNUC possesses the lowest RNU among these three approaches. The RNU trend chart of STCNUC is constantly stable and smooth in the test temperature range. The correction accuracy does not change along with the target temperature fluctuation. Considering surrounding temperature compensation, STCNUC does not need to update the correction coefficient in an unstable environment. Hence, the proposed STCNUC is an effective approach that meets the relatively wide target temperature range and surrounding variation application situation. The correction accuracy is stable even when the target and environment temperature change.
IV. CONCLUSIONS
A novel NUC approach was proposed in this study. The method is not only suitable for the nonlinear condition of IRFPA response, but also compensates for the shift of nonuniformity with surrounding temperature variation. This approach solved the problem of degradation of corrected image quality along with the surrounding variation. Experimental results and evaluation show that the RNU, which was corrected by the proposed method, is steady at approximately 0.02 percentage points within the target temperature range of 283 K to 373 K. The experimental results are consistent with theoretical analysis. This proposed technique improves correction accuracy and infrared imaging quality better than the traditional techniques. Consequently, this technique is applied and employed in a wider application field and environment. However, the temperature range test is limited by the extended blackbody used in this study.
Remainder nonuniformity curve comparison among several NUC approaches.
Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No.61171164), National Defense Preresearch Foundation of China (Grant No. 62201050103). We thank the anonymous reviewers for their constructive comments.
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