where MTF(ξ) is the system modulation transfer function, σ(ξ) is the noise filtered in kelvin by the display and visual system in Kelvin-root seconds, Stmp is the scene temperature difference that corresponds to half the display brightness (from zero brightness), and α is a calibration factor with units of root hertz. In the current military imager models, all systems are considered to be separable in the horizontal and vertical directions. Equation (1) provides the CTF calculation in its basic form. This general equation includes optical, detector, electronic, and display characteristics.
The system CTF provides the performance with respect to two primary conditions under which sensors operate. The first condition is a noise-limited realm where
is larger than 1. Under these conditions, the observer can see the noise in the image as can be demonstrated in uncooled microbolometers, first generation FLIR, and second generation FLIR systems. The second condition is where
is smaller than 1 and the noise is not visible to the observer. Under this condition, the information in the image is limited by the eye contrast threshold function and the image blur, as these are the only components of Eq. (1)
that are important. Systems that operate in this realm are staring InSb sensors, MCT staring sensors and other photon detector systems that have medium to low f-numbers with an associated medium to wide field-of-view (FOV). Plenty of signal and/or integration time (resulting in many photo-electrons) is a requirement for this condition.
The procedure for calculating/predicting field range performance is shown in Fig. 1
. A target is characterized by the characteristic dimension (square root of target area) in meters, source contrast, and task discrimination difficulty (N50
). The contrast is propagated through the atmosphere and an apparent contrast is determined at the sensor. The intersection of sensor CTF and the apparent target contrast is called the “limiting frequency,” or the highest frequency resolved through the sensor at that particular contrast. In the ACQUIRE method, this limiting frequency, in cycles per milliradian, is converted to “cycles on target” by multiplying the limiting frequency by the target angular subtense (characteristic dimension divided by range). The cycles on target are compared to the N50, or discrimination criterion--sometimes called the Johnson criterion, to determine the probability. The N50
is different for detection, recognition, and identification. N50
gets larger as the task gets more difficult (identification requires more resolution on the target). The ratio of cycles on target to N50
is input to the target transfer probability function (TTPF) and is used to determine a probability value for a specific range. This process is performed iteratively for various ranges and the probability is plotted as a function of range.
Fig. 1. ACQUIRE and TTP Process.
The TTP [2
2. R. Vollmerhausen, E. Jacobs, and R. Driggers, “New metric for predicting target acquisition performance,” Opt Eng. 43, 2806–2818 (2004). [CrossRef]
] approach replaces the ACQUIRE approach for most applications. It varies from the ACQUIRE approach in that a systems resolution and sensitivity is accounted for by integrating the systems CTF, as shown in Eq. (2)
where the ratio of the target contrast to the system CTF is considered the excess contrast that the human can see on the target. The limits on the integral start and end where the target contrast intersects the system CTF. This integration is performed twice, once on the horizontal CTF of the system and then again on the vertical CTF of the system; Eq. (1)
is assumed to be separable. The geometric mean is then taken of the results. The result is compared to the discrimination criterion, V50
, to determine the probability. A different TTPF is used for the ratio of V to V50
than is used in the ACQUIRE process.
The TTPF is the function that converts the ratio of N to N50 or the ratio of V to V50 into a probability. The TTPF takes the form of
where the coefficient, β, for the TTP is 1.51+0.24(V/V50). The coefficient for ACQUIRE traditionally is 2.7+0.7(N/N50), but a single coefficient value of 3.8 gives very close results. The traditional ACQUIRE coefficient has been used in many sensor specifications and combat simulations, however, a great deal of real field data has been shown to match a more gradual probability curve with coefficient equal to 1.75+0.35(N/N50) or a single coefficient of 2.7.
The TTP process provides a much more accurate prediction of field performance than the ACQUIRE process as has been demonstrated in numerous recognition and identification experiments. [3
3. J. Ratches, R. Vollmerhausen, and R. Driggers, “Target Acquisition Performance Modeling of Infrared Imaging Systems: Past, Present, and Future,” IEEE Sens. J. 1, 31–40 (2001). [CrossRef]
] Search and detection is more complicated (under clutter-limited conditions) and will be discussed in the following section.
When performing the search and detection process, the difficulty in detecting the target is highly dependent on target contrast and the competing clutter level. ACQUIRE-LC [4
4. B. O’ Kane, G. Page, D. Wilson, and D. Bohan, “Cycle criteria for detection of camouflaged targets,” Proceedings of the NATO Panel on Sensors and Sensor Denial by Camouflage, Concealment and Deception. (NATO, 2004).
5. B. O’Kane, G. Page, M. Cook, D. Bennett, D. Wilson, and D. Bohan, “Modeling the Detection of Moving Thermal Targets,” Proceedings of the Parallel Military Sensing Symposium (SENSIAC, 2004).
] was developed to predict detection probability against camouflaged targets, but has been recently modified to work against conventional targets.
Fig. 2. ACQUIRE-LC (left) and Detect05 (right) (ΔTRSS in Kelvin).
required for the detection of a target in various backgrounds (and clutter levels) is shown, left side of Fig. 2
, as a function of target contrast (RSS) differential temperature in Kelvin and for different background environments.
The N50 is the number of cycles on target required for a 50 percent probability of detection. This N50 is used in the ACQUIRE process described in the previous section to convert sensor CTF and the target detection task into a probability of detection as a function of range.
The ACQUIRE-LC curve is really a signal-to-clutter detection model, where the performance of a human/sensor pair can be characterized as a function of “complexity,” which might be a soft term for clutter. The Detect05 curve is on the right in Fig. 2
and the equation is a single equation.
where C is the complexity. C is 1, 1.5, 2.0, and 2.7 for low, medium-low, medium, and high complexities, respectively. Figure 3
shows some examples of complexity background levels.
Fig. 3. Clutter complexity levels.
It is the intention of the military imager modeling community to transition from ACQUIRE-LC to Detect05 for both low contrast and conventional targets and for both sensor design and combat simulations. The models presented so far allow for the ACQUIRE process implementation of both ACQUIRE-LC and Detect05, but implementation in the TTP process requires the relationship between V50 and N50. For either curve, the relationship between V50 and N50 is:
This equation allows the implementation of either ACQUIRE-LC or Detect05 in the TTP process.
3. Data collection
The testing area consisted of the pier, on which the sensors and data collection equipment were placed, and an inlet off of the Potomac River. The water area facing the pier had an extent of approximately 800m to the opposing shoreline. There was a channel through the center of this inlet. A channel marker was used to delineate the far right side of the test space (and is visible just inside the right side of the sensor FOV). Ranges were marked in the water with buoys on the left side of the water space. These buoys also served as the left edge marker of the test space. Figure 4
is a picture of the test range from the aspect of the sensor.
Fig. 4. Imagery Collection Site Layout
The swimmer signature data was collected at close range (25m) from a number of aspect angles. It was also both swimming (breast stroke) and treading water. The infrared imagery data was calibrated through the use of two black bodies set at 22 and 42 degree Celsius respectively.
The swimmer was ferried to a drop site by boat left in the water. The boat moved out of the field of view and the wake of the boat was allowed to subside until not visible in the FLIR imagery. Digital video clips were then captured using the camera’s digital output and a framegrabber. The safety boat would then return to the swimmer and the range/bearing data from sensor to swimmer were noted. Additionally, a single frame, with the swimmer location was captured as a location ground truth image. The swimmer location could vary dynamically due to wind and current at an observed rate of up to 1 degree/minute during portions of the data collection.
7. Modeling results
The military thermal imaging system performance model, NVTherm, was used to model the sensor detection performance against the swimmer at both night and day. The night data fit is shown in Fig. 7
. The model was fit to the data points by placing the sensor parameters (see the sensor section) into NVTherm along with the target parameters (from the signature section) and adjusting the V50
(number of integrated cycles on target for a 50% probability of detection) to fit the data. The 50% probability of detection point for the observers occurred at 832m. These results are compared in the figure. The data point at 450 meters was not used since this data point corresponded to the first range data collected and there was significant wave signatures (i.e., clutter) that competed with the target. By the time the other four data points were taken, the inlet had become calm with very little wave clutter competing with the target signature. The V50
corresponding to the fit was 0.85 cycles on target, an extremely low value compared to other detection scenarios. This was a bounding fit, where a bland background is extremely low in clutter, so there is nothing competing with the target. That is, the target signature in the search process is “contrast-limited” where the contrast threshold of the eye is taxed.
Fig. 7. Night Data and NVTherm Model Fit.
The daytime results are shown in Fig. 8
. In this case, the sensor model does not work as well and the target transfer probability function (TTPF) is very smooth compared to the rapid drop of performance with range of the data. Note, that in this case, the background associated with the solar reflections provided for an extremely high clutter level that made it very difficult to find the target. This realm could be considered “clutter-limited.” The V50
associated with the NVTherm model fit was 4.0 integrated cycles on target. This value drives the 50% probability of detection point with range. Note that the data and the model both have the same 50% probability of detection range of 193 meters. The high clutter value could account for the dramatic drop in performance with range and future versions of NVTherm may allow for the coefficients of the TTPF to adjust for the performance rate of decline.
Fig. 8. Day Data and NVTherm Model Fit.
The swimmer detection task’s discrimination criteria, V50, from the analysis of the results is a V50 that ranges from 0.85 under extremely low clutter conditions (no waves or solar reflection) to 4.0 under clutter conditions (choppy waves with solar reflections). While this is a wide range of calibration values, it bounds the range performance and the conditions associated with the detection of swimmer targets.
For low clutter scenes, the target signature and the sensor noise (or contrast limit) combine to determine detection ranges. For moderate clutter scenes, the signal to clutter drives the range performance. For the night cases, the wave clutter began very small but continued to become smaller and almost negligible by the end of the night data collection. The sun and the waves during the day made for a moderate clutter environment where the target was extremely difficult to detect. Even though the conditions made for a moderate clutter case, it was obvious that the clutter could approach even higher levels. It is also worth mentioning that daytime clutter is much higher in the midwave infrared (3–5 micrometers) than in the longwave infrared (8 to 12 micrometers). This is a result of solar reflections dominating clutter in the MWIR. This is not the case in the LWIR band.
A day and night MWIR swimmer detection experiment was conducted to determine the target characteristics, task difficulty criteria, and clutter complexity value. It was demonstrated that unresolved and resolved swimmer detection is very easy in the MWIR when there is negligible clutter and is well predicted by the existing model. The swimmer in the presence of solar clutter was a much more difficult detection target. The probabilities of detection results were much steeper than the model predicts. Performance in this environment is dependent on the signal to clutter ratio. In this effort we characterized the daytime solar clutter with the DETECT05 complexity value. It is likely that detection occurred when the shape/target extent is discriminable (actually more like recognition than detection). This explains the steepness of the probability results. For the daytime case here, the resolved cycles on target at 193m (50% Probability of detection) is 3.0. This is the same as the Johnson’s criteria recognition discrimination level.