Minimum resolvable temperature difference (MRTD) is a key figure of merit used to characterize the performance of thermal imaging systems. It is a subjective test providing a combined measure of system thermal sensitivity and spatial resolution. The test requires the operator to determine the temperature difference resolvable at various spatial frequencies, typically using four-bar target patterns.
Drift in ambient temperature (top) can introduce errors in differential radiance (bottom).
Consistency of MRTD test results is dependent upon the stability and repeatability of the target projection system. With thermal imagers now tested in a variety of conditions (laboratory, production, depot, field, etc.), recent experiments have shown that as the ambient temperature varies, some test systems may fail to maintain a stable and repeatable differential target image. As spatial and thermal resolution for thermal imagers continue to evolve, these test issues become more significant. stability and repeatability
Typical target projectors can maintain differential temperatures of ±0.001°C, but as ambient temperature varies, the target temperature can drift, resulting in an unstable image that affects the consistency of the test results. Other effects caused by non-ideal and spectrally dependent mirror reflectance also introduce errors. The magnitude of these errors is dependent on the rate of change of the ambient temperature and other system-specific factors such as target and blackbody emissivity, optical baffling, and target-edge characteristics.
Thermal imagers do not directly measure temperature differences (ΔT) but rather sense radiance (L) and differential radiance (ΔL). Since radiance is a nonlinear function of temperature, a given thermometric ΔT does not always produce the same ΔL. This effect is small in laboratory conditions but can be readily detected by many modern thermal imagers.
The differential radiance seen by a unit under test (UUT) looking at an ideal target/blackbody system may be expressed as the difference between blackbody radiance LB and target radiance LT:
ΔL = LB - LT
For real-world blackbody and target surfaces with non-unity emissivity (ε < 1.0), the calculation of ΔL must include the reflected ambient components of the radiance. We can then express the differential radiance as a sum of the Planck terms for each emitted and reflected radiance source:
The non-linearity of the Planck function gives rise to a variation in differential radiance with ambient temperature changeeven when thermometric ΔT is maintained. This variation is known as a radiometric ΔT error (see figure).
In lab environments, this error equates to 5% imager response variation in the mid-wave IR and 2% in the long-wave IR. Under field and depot conditions, the error increases to 25% response variation in the mid-wave IR and 10% in the long-wave IR. Depending upon UUT thermal resolution and other performance specs, these errors may be problematic in characterizing system MRTD. system solutions
Based on ambient temperature and system optical properties, software and firmware can adjust blackbody temperature in real time to preserve differential radiance in the test target in the presence of varying ambient temperature. Target non-uniformity caused by varying ambient temperature can be removed by using a reflected background target projector configuration. Such projectors typically include precision reflective gold target surfaces, and two blackbodiesone for control of target and one for control of background.
The ability to control both target and background temperature minimizes the effect of ambient drift upon target uniformity and allows UUT testing at user-selectable background temperatures. With careful optical baffling and ambient temperature control, such reflective target projection systems provide stable, repeatable MRTD measurement capability over spatial frequency ranges resolvable by modern high-performance thermal imagers. oe
Paul Bryant is technical director/chief engineer at Santa Barbara Infrared Inc., Santa Barbara, CA.