Reflections

Reflections from ambient sources are reasonably constant over short periods of time and can be eliminated. A thermal image is collected before the incremental heating of the specimen which is then subtracted from the post heating data. A reflection and initial condition reduced image I(x,y) is in the form

where DF(x,y) is the photon flux resulting from the added heat or heat lost since the capture of the initial image and e(x,y) is the emissivity map. This reduction of reflections even allows work on surfaces prepared with high-gloss paints (illustrated in the data shown below).

Emissivity effects

If all structures had perfectly uniform coatings, the simple unidirectional gradient method would be sufficient to locate cracks. However, gradients caused by emissivity variances can often be misconstrued as cracks. The total gradient in the x-direction I_x(x,y) of the corrected images I(x,y) is by the product rule

At this point in the development of the technique an emissivity gradient has the same effect as a structural defect. The fundamental principle behind Coating Tolerant Thermography is that only the thermal spatial derivative of a true structural anomaly will change sign with opposing heat flow. As shown below, when the heat is flowing from the left, the gradient is positive (as defined) because the heat builds up behind the crack on the left. When heat is flowing from the right, the gradient changes sign becoming negative because now heat builds up behind the crack on the right side. Only a true structural flaw has this characteristic.

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Thermal Image of a Crack

Gradient - Heat Flow from the Left

Gradient - Heat Flow from the Right

Heat Conducting from Left	Heat Conducting from Right

Click either image above to view
a short animation (30K).

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