Non-destructive Testing With FMCW-Terahertz for Industrial Applications

The basic principle is based on measuring the transit time of emitted terahertz signals. These are reflected by the test object or material interfaces inside and then recorded by the measuring system. The distance can be determined from the signal propagation time – and in the case of transparent materials, a precise 3D reconstruction is possible.

As terahertz radiation is an electromagnetic wave that travels at the speed of light, the signal propagation times are very short and difficult to measure directly. The FMCW method solves this problem by translating the propagation time information into a frequency shift. This frequency change can be recorded much more precisely. The schematic structure is outlined in the following figure.

DAQ = Data Acquisition, FG = Function Generator, VCO = Voltage-Controlled Oscillator, xFM = Frequency Multiplier, PA = Power Amplifier,
HA = Horn Antenna, DUT = Device Under Test, s_T(t) = Transmitted Signal, s_R(t) = Received Signal, s_M(t) = Mixed Signal

The schematic structure shows the core of the method: a ramp generator produces a linear frequency ramp with a defined duration (Tₛ) and bandwidth (B). Part of this signal is transmitted as a measurement signal via a transmitter, while the other part serves as a stable reference signal within the measuring device.

The delay of the received signal compared to the reference signal is denoted by τ_d. It is directly proportional to the distance between the measuring system and the reflecting structure in the test object. After reception, the reflected signal is superimposed with the reference signal in the mixer. This produces a low-frequency mixed signal that provides depth-resolved information about the internal structure.

The mixing signal can be recorded using fast data acquisition (DAQ) and then digitally processed and evaluated.

In FMCW radar, the signal transit time is not determined directly, but via a frequency measurement. With modern signal processing and a Fourier transformation, the original propagation time can be reconstructed and used as distance information for the volumetric measurement of test objects.

We rely on three different technological solutions for the practical application of FMCW technology.

1. Waveguide-Based FMCW Systems

This approach uses waveguide-based, fully electronic components. They take over:

• signal generation (e.g. with voltage-controlled oscillators)
• frequency multiplication and amplification (e.g. using diode-based multipliers, mixers or amplifiers)
• as well as emission and detection (e.g. via directional couplers and horn antennas).

The advantage: high transmission power can be achieved. The disadvantage: Waveguides are limited to certain frequency bands – this restricts the bandwidth. Typically, frequencies up to around 500 GHz are covered.

2. Fully Integrated Chip Technology

Thanks to modern semiconductor technologies (such as indium phosphide, silicon-germanium or gallium arsenide), highly integrated »on-chip« solutions for high-frequency circuits can now be developed. In these systems, signal generation, multiplication and amplification take place without waveguides. This opens up great potential for miniaturization and cost-effective series production. However, the achievable bandwidths and signal power are currently still lower than with waveguide systems. Current fully integrated FMCW radar chips for the terahertz range operate up to around 300 GHz.

3. Photonic FMCW Radar: Amplification and Detection

A photonic approach is used to circumvent the bandwidth limitations of classic waveguides. Lasers are used here that can be tuned over a wide frequency range and transmitted via silicon lens.

The diagram of a fiber-coupled photonic FMCW radar with an optical setup for a collinear beam path is shown in the following figure. Two CW (continuous wave) diode lasers generate a beat signal in the terahertz range by superposition – the frequency of which corresponds to the difference frequency of the lasers. For FMCW operation, a fast tunable laser is used together with a fixed frequency laser. This allows the center frequency of the laser beat signal to be freely adjusted in a range of around 4.5 THz. Frequency ramps above 2 THz enable a depth resolution of less than 100 µm.

DAQ = Data Acquisition, SL = Sweeping Laser,  FFL = Fixed-Frequency Laser, OA = Optical Amplifier, PCA = Photoconductive Antenna, Rx = Receiver,
Tx = Transmitter, DC = Direct Current Voltage Bias, TIA = Transimpedance Amplifier, DUT= Device Under Test , s_T(t) = Transmitted Signal,
s_R(t) = Received Signal, s_M(t) = Mixed Signal

Photonic FMCW Radar: Amplification and Detection

The superimposed optical signal is fed into an optical amplifier to operate both a terahertz emitter (Tx) and a terahertz detector (Rx). The terahertz signals are coupled out and in via silicon.

The received echo signal is then mixed with the laser levitation signal. The output signal of the mixer receiver is forwarded to a fast data acquisition unit (DAQ).

A key factor for every FMCW radar sensor is the distance or depth resolution. It describes the ability to clearly distinguish between two reflectors at different distances.

In an FMCW radar, this depends on the frequency bandwidth B and can be calculated using the following equation (3 dB criterion):

where

• 𝛿r is the distance resolution
• c₀ is the speed of light in a vacuum

For example, the following distance resolutions result for typical FMCW systems used by us:

Bandwidth and Signal Shape

As the bandwidth of technical FMCW systems is always limited, the time domain response of a reflective surface does not appear as a narrow delta function. Instead, it has an extended sinc shape as a first approximation.

The following figure clearly shows how strongly the bandwidth influences the resolution of the measurement signal.

Distance Resolution Versus Distance Measurement Accuracy

With FMCW radar systems, it is important to distinguish between range resolution and range measurement accuracy:

• Distance resolution (δᵣ) describes the ability of the system to distinguish between two reflective boundary surfaces lying one behind the other. If the distance between two defects is below the distance resolution, they can no longer be clearly separated from each other.
• Distance accuracy, on the other hand, refers to the precision with which the distance of a single reflection can be determined. This accuracy is usually significantly higher than the nominal resolution, as modern signal processing methods such as zero-padding or the evaluation of the phase information of the complex FMCW signal are used.

Further information on the topic of resolution in terahertz imaging can be found here.

Various signal processing methods are available for the evaluation of FMCW signals. The following methods are primarily used for material testing:

• Peak Detection: With peak detection, the individual reflection peaks of the material interfaces in the FMCW signal are directly identified and evaluated. If the distance between two defects is below the distance resolution, they can no longer be clearly separated from each other.
• Model-Based Evaluation: The expected FMCW signal is simulated on the basis of preliminary information about the test object and compared with the actual measurement signal. An optimization algorithm adjusts parameters such as distances or layer thicknesses until the best possible match is achieved. This method is particularly helpful for the detection of thin layers and often makes it possible to fall below the physical distance resolution of the FMCW radar.

The approaches described each offer specific strengths:

• Waveguide and chip-based FMCW systems are preferred for testing thicker samples of several millimetres. Due to the slightly higher bandwidth, waveguide-based systems also tend to be able to resolve thinner layers. Another advantage: waveguide-based measuring systems achieve very short measuring times of 100 µs and less. Chip-based sensors, on the other hand, score with low manufacturing costs due to mass production (for quantities of approx. 100,000 units or more).
• Photonic FMCW systems offer maximum flexibility: the center frequency and bandwidth can be adjusted via software settings without the need to physically replace the sensor. The achievable bandwidths are significantly greater than with individual waveguide or chip-based systems. This means that even very thin layers from a few 10 µm can be reliably detected. Photonic systems are also easy to scale: Several sensors can be connected to a common control unit and operated in parallel, which significantly reduces the costs per measurement channel.