# Design and Construction of an LED-Based Excitation Source for Lock-In Thermography
## 3 Experimental Specifications
### Signal Response Characteristic  
The infrared LED lamp is compared to two other modulated sources: an electrically modulated 150 W halogen reflector lamp of the type 64635 HLX and the same halogen lamp modulated by a Thorlabs MC2000-EC mechanical chopper. The signal of the LED excitation source and the chopper setup are measured with a BPW34 photodiode. The diode is driven with 9 V in reverse bias and connected to the input of the lock-in amplifier. Amplitude and phase are measured with an SR860 lock-in amplifier, whose reference output also provides a sinusoidal modulation signal. For the halogen lamp, the analogue reference signal is converted to a 22 kHz pulse width modulated signal by a modulation unit. As the halogen lamp is basically a black-body radiator, its emission spectrum changes within each period due to changes in temperature. In combination with the limited sensitivity of the BPW34 photodiode in the mid-infrared spectrum, this would lead to systematic errors. Therefore, the lamp emission is not monitored directly. Instead, a piece of black-painted aluminium foil is used as an absorber, whose temperature is monitored with a thermography system (Infract ImageIR 8380S). The temperature signal of the aluminium foil is phase-shifted with respect to the optical power signal. The frequency response of the aluminium foil is measured via excitation with an optical power source, whose frequency response is known. For this, the foil is excited with the LED excitation source, which has a negligible phase  
Figure 7: **(top)** Radiant intensity distribution of the excitation source in the C0–C180 (blue) and C90–C270 plane (black) without (**a**) and with focusing optic (**b**). **(bottom)** Irradiance on an area of 1.0 m \(\times\) 0.8 m at a distance of 0.5 m without (**a**) and with focusing optic (**b**). delay up to modulation frequencies of 10 Hz. The measured frequency response of the aluminium foil is then subtracted from the measurement data of the halogen lamp. The frequency responses of the three different excitation sources are shown in Figure 8. The halogen lamp has a cutoff frequency of approximately 1 Hz and a modelled attenuation of 90.0% (\(-20\) dB) at a frequency of 10 Hz. To approximate the measured frequency response, a model consisting of two parallel first order lag elements is constructed. This model is explained from the physical structure of the halogen bulb. A part of the radiation emitted by the filament is absorbed by other lamp parts, which in turn emit their own radiation as they heat up. The frequency response of the halogen lamp is thus modelled by  
\[G_{\mathrm{halogen}}(\omega)=\frac{1}{1+j\omega\cdot 0.17\,\mathrm{s}}+\frac{0.5 }{1+j\omega\cdot 22\,\mathrm{s}}\,. \tag{4}\]  
Within the measured frequency range from 0.05 Hz to 10 Hz, the phase is modelled with an accuracy of 3.2\({}^{\circ}\). The halogen lamp, previously modulated electrically, is also used in combination with a mechanical chopper. The chopper allows for modulation frequencies between 4 Hz and 200 Hz, but it shows a non-constant phase for frequencies up to 32 Hz. This limits its use at low frequencies. Further investigation with a digital oscilloscope shows that these artifacts are not a result of phase noise, as the measured standard deviation for 200 signal periods is lower than 3\({}^{\circ}\) in all cases. The newly developed LED excitation source shows a linear amplitude response up to a frequency of 40 kHz, where it drops by 1 dB. The phase response is negligible up to a frequency of 1 kHz, where it amounts to 1\({}^{\circ}\). The frequency response is modelled by using three serial first order lag elements, i.e.,  
\[G_{\mathrm{LED}}(\omega)=\frac{1}{1+j\omega\cdot 1.8\,\mathrm{\SIUnitSymbolMicro s }}\cdot\left(\frac{0.5}{1+j\omega\cdot 0.14\,\mathrm{\SIUnitSymbolMicro s}} \right)^{2}. \tag{5}\]  
Figure 8: Bode plots of the halogen lamp, the halogen-chopper combination, and the LED excitation source. The lines represent the modelled frequency responses.