A standard target for triangles or how to transfer TOD to MTDP

Triangle Orientation Discrimination (TOD) developed by TNO Human Factors and Minimum Temperature Difference Perceived (MTDP) developed by Fraunhofer IOSB are competitive measurement methods for the assessment of well and under sampled thermal imagers. Key differences between the two methods are the different targets, bars for MTDP and equilateral triangles for TOD, and the measurement methodology. MTDP bases on a threshold measurement whereas TOD uses a psychophysical approach. All advantages and disadvantages of the methods trace back on these differences. The European Computer Model for Optronic System Performance Prediction (ECOMOS) includes range performance assessments according to both methods. This triggered work at Fraunhofer IOSB to do comparative TOD and MTDP measurements. Idea was checking if TOD- and MTDP-curves fall together when transferring the two target descriptive parameters, reciprocal angular subtense (one over triangle size expressed in angular units) and spatial frequency respectively, into each other using a conversion factor or function. Surprisingly, literature does not include such a measurement-based comparison to date. Extending IOSBs existing MTDP set-up with triangle targets and the associated turntable and shutter enabled the comparative measurements. The applied TOD measurement process uses the guidelines found in literature with some necessary adaptions. Both measurements included the same components (blackbody, collimator, monitor etc.) except the targets. Additionally the trained MTDP-observer also did the TOD measurements. Only the methods itself thus should cause differences in the results. Four thermal imagers with different magnitude of under sampling (MTF at Nyquist frequencies about 8 %, 14 %, 32 %,and 73 %) are the basis for the comparison. Their measurements allowed deriving a standard target for triangles according to the process known from target acquisition assessment. These calculations result in 1.5±0.2 line pairs on target. Multiplying reciprocal angular subtense with this factor gives corresponding MTDP and TOD curves when TODis based 62.5 % instead of the standard 75 % probability. 62.5 % corrected for chance are 50 % probability and thus in correspondence with the threshold assumption of the MTDP. Deviations occur, when reciprocal angular subtense is near the cut-off because of unaccounted sampling effects. The proposed way to overcome this is normalizing spatial frequency and reciprocal angular subtense with camera line spread function full width at half maximum. A sigmoidal transition function is able to describe the resulting connection. This function could be valid for all thermal imagers, as indicated by the assessment of two additional ones. However, as the assessment bases only on six thermal imagers and one observer further comparative measurements by a larger number of observers or, alternatively, modeling is necessary.