heat source. The general form of the sinusoidal curve fit that was applied to each point is
as follows:
T(t) = A+B*cos(2rft + 7- () 6-12)
T = Temperature
t = Time
f = Frequency of heat source modulation (1/pulse duration)
D = Phase shift (measured in radians)
A = Average offset
B = Amplitude of sine wave
Note that when the phase shift is zero, the temperature response is a scaled function
of the modulated heat input. For the case of a 500 second pulse duration, the peak output
of the heat source occurs at 250 sec. The resulting phase shift for Point 1 (above the
defect area) was -0.86 rad. This quantity indicates that the peak value of the sinusoidal
curve-fit occurs 68 seconds later at t = 318 sec. The phase shift for each of the defect free
pixels was -0.73 rad which corresponds to a lag in the peak response of 58 sec. The
important thing to recognize is that the computed phase shift is independent of amplitude.
In the example provided, the defect-free region described by Point 3 has greater
amplitude than the defect area throughout the entire pulse duration. The phase shift,
however, is less for the defect-free area since the flow of heat from the surface into the
concrete is not interrupted (slowed down) by the defect. By applying this procedure to
each pixel in a series of thermal images, it is possible to generate a single phase image
that is independent of amplitude.