We demonstrate an adaptive reconstruction technique to significantly improve the depth of focus and contrast of three-dimensional reflection-mode terahertz imaging. A laterally scanned virtual transceiver element records reflections from the object of interest. A synthetic aperture focusing technique maintains fine spatial resolution over a large image depth. Measuring the spatial coherence of the received signals across the transceiver aperture provides a non-iterative self-adaptive approach to significantly improve image contrast. Test images show a spatial resolution of 0.4 mm maintained over a 16 mm depth of field, and up to a 30 dB improvement in signal-to-noise ratio.
© 2009 OSA
There is considerable interest in using electromagnetic terahertz (THz) pulses for imaging [1–3], especially in security and nondestructive testing [4–6]. Practical applications benefit from high resolution three-dimensional (3-D) imaging. Conventional THz time-domain imaging systems mechanically scan a focused THz beam over the object of interest. Finest spatial resolution requires low f-number (f/#) optics, but this comes at the expense of extremely short depth-of-focus. This in turn requires scanning over all three dimensions of the object, leading to excessively long acquisition times. As an alternative, the depth-of-focus can be extended by using larger f/# optics. However, this reduction in acquisition time comes at the expense of degraded lateral resolution.
We are exploring a virtual transceiver approach with an adaptive reconstruction algorithm to overcome these limitations. The virtual transceiver is laterally scanned over a single two-dimensional (2-D) region above the object of interest. Signal samples from multiple transceiver positions are combined to produce a synthetic aperture focused at a particular image point . The focusing quality can be significantly improved by using an amplitude weighting factor based on the spatial coherence of the recorded signals . This significantly improves image quality by suppressing undesired sidelobes in a non-iterative self-adaptive manner. To our knowledge, this is the first demonstration of a non-iterative adaptive reconstruction technique for high resolution 3-D THz imaging.
2.1 Synthetic aperture focusing technique (SAFT)
Figure 1(a) shows the basic imaging geometry, where low f/# optics sharply focus THz waves above the object of interest. The THz focus is treated as both a virtual source and receiver of broadband THz waves. This virtual transceiver is laterally scanned over the object of interest to produce a synthetic array focused at a particular image point, as shown in Fig. 1(b). The signal samples um(t) from multiple transceiver positions are combined according to :
In Eq. (1), Δtm is the round trip propagation time between a transceiver element and the desired image point. M is the number of elements required to maintain the desired focal ratio for the transceiver aperture. Relatively few transceiver elements are required to reconstruct image points near the array. Image points at larger depths require a larger value of M. When an image point coincides with an actual object, the samples um(Δtm) add constructively. Conversely, destructive interference among the samples occurs when an image point is located away from an object.
2.2 Coherence weighting
SAFT processing produces excellent depth-of-focus in THz imaging. Image quality can be further improved in an adaptive manner by exploiting the coherent nature of the THz signals. When an image point coincides with an actual object, the delayed signal samples um(Δtm) from each transceiver element are all in-phase to produce constructive interference. This corresponds to high spatial coherence across the transceiver array elements, as shown in Fig. 2(a) . When the synthetic focus is steered away from an object, the delayed signal samples are out-of-phase to produce destructive interference. This corresponds to low spatial coherence across the transceiver array, as shown in Fig. 2(b). Low spatial coherence also occurs in image regions containing primarily noise, where the signal phases are randomly aligned (Fig. 2(c)). Therefore, the spatial coherence of the delayed signal samples can serve as a weighting factor to suppress sidelobes and noise. The coherence factor (CF) at a reconstructed image point is defined by [8–10]:
In Eq. (2), the CF measures the spatial coherence of the delayed signals across the array aperture. The CF is close to unity for image points resulting from high signal coherence. Likewise, image points resulting from low coherence produce a CF close to zero. The final image is obtained by multiplying each image pixel uSAFT with its corresponding CF. This amplitude weighting is self-adaptive in nature since the CF is based entirely on the received data. This combination of SAFT and coherence weighting has been used to improve image quality in ultrasound and photoacoustic imaging [11–13]. We demonstrate that such adaptive processing can produce high resolution 3-D THz images with large depth-of-focus.
2.3 Terahertz imaging system
Imaging experiments are performed with a standard THz time-domain system employing a femtosecond Ti:Sapphire oscillator emitting sub-30 fs pulses. THz pulses are generated by a photoconductive antenna biased with a 20 Vpp square wave at a frequency of 63 kHz. A 6 mm thick high-resistivity silicon beamsplitter directs incident THz pulses to an f/1 parabola. The parabola focus serves as both a virtual source and detector of THz pulses. The beamsplitter directs received THz pulses to a 1 mm thick ZnTe electro-optic sensor employing lock-in detection. For ease of experiment, the object is mechanically scanned to produce the synthetic aperture.
3.1 Point spread function
The point spread function of the THz imaging system was estimated from cross-sectional images of a 0.8 mm diameter steel wire placed at various depths below the virtual THz transceiver. For each wire depth, the wire is horizontally scanned in 0.10 mm increments over a 10 mm distance. Signals are averaged 64 times before storage. In Fig. 3 , the images at different depths are combined to facilitate image display. The wire is parallel to the y-axis in each image (i.e. perpendicular to the image plane). Figure 3(a) shows the result of conventional THz reconstruction, where each image column is obtained from a single scan line. The wire target is in sharp focus at the top of the image, but clearly becomes increasingly out of focus at larger depths. This is the drawback of conventional THz imaging with low f/# optics.
SAFT processing of this same data produces the result in Fig. 3(b). SAFT refocuses signals to maintain fine spatial resolution at larger depths. For any given depth, the proper number of elements was chosen to maintain a f/2 synthetic aperture. The signal values involved in SAFT processing are also used to compute the CF at each image point. The resulting CF map is multiplied with the SAFT image to produce the final image in Fig. 3(c). Clearly, a much cleaner image is produced when SAFT and coherence weighting are used together. SAFT typically produces a point spread function with strong sidelobes , which appear as the “wing-like” features surrounding each wire target in Fig. 3(b). Coherence weighting suppresses these sidelobes to significantly improve image quality. At larger depths, a faint artifact is located to the right of each wire target (near x = 7 mm). These are due to stray reflections from the sample holder and are not a result of SAFT + CF processing. The illuminating THz beam diameter increases with target depth, leading to stronger stray reflections. Digitally removing the spurious signals from the recorded THz data produces an artifact-free image (not shown in Fig. 3), supporting the above hypothesis. The slightly asymmetric appearance of the wire target images in Fig. 3(b) and (c) is due to a small misalignment in the THz focusing optics. Analyzing the wire target signals of Fig. 3(a) reveals the THz beam propagates at an 11 degree angle with respect to the z-axis. We have performed imaging simulations accounting for such an angular deviation, and have successfully reproduced the slightly asymmetric appearance of the wire targets.
3.2 Signal-to-noise ratio
Improved signal-to-noise ratio (SNR) is evident in the SAFT image of Fig. 3(b). The SNR improvement is a natural result of the synthetic aperture process, where signal summation essentially acts as a form of signal averaging. Coherence weighting further improves SNR in an adaptive manner. As shown in Eq. (2), the numerator of the CF is essentially a coherent sum while the denominator is an incoherent sum. Image regions containing primarily noise will therefore produce a low CF value. In one sense, the noise suppresses itself in the final image. By contrast, image regions corresponding to actual objects are preserved by coherence weighting. This adaptive noise suppression leads to enhanced SNR in the image of Fig. 3(c).
Quantitative comparisons of lateral resolution and SNR are shown in Fig. 4(a) and (b) , respectively. At a particular target depth, resolution is defined as the −6 dB width of the wire image. SNR is defined as the ratio of the average signal intensity in the brightest portion of the wire image to the average noise intensity at the same depth. In conventional processing, resolution degrades by an order of magnitude over the 16 mm range of target depths. This is accompanied by extremely poor SNR at large depths. The refocusing effect of SAFT processing significantly improves both lateral resolution and SNR. At the largest target depth, the SAFT image exhibits a five-fold improvement in resolution and a 14 dB improvement in SNR compared to conventional processing. Additional improvement is obtained with coherence weighting, resulting in a nearly depth-independent spatial resolution of 0.4 mm. At the largest target depth, the SNR is 30 dB higher than conventional THz imaging (i.e. no processing).
3.3 High resolution three-dimensional THz imaging
High resolution 3-D imaging is achieved with SAFT + CF processing. A 21 gauge needle was placed 9 mm in front of a metal razor blade. This 3-D object was laterally scanned over a 50 x 50 pixel grid in 0.2 mm increments. The THz transceiver depth coincides with the front side of the needle. Figure 5(a) shows separate en face images of the needle and razor blade without processing. The dynamic range is adjusted in order to visualize the noisy and blurred image of the razor blade. Figure 5(b) shows the result of SAFT + CF processing. The razor blade is clearly reconstructed with significantly improved resolution and SNR. A stack of SAFT + CF images within a 10 x 10 x 10 mm volume are displayed in the 3-D rendered image in Fig. 5(c). It is worth emphasizing that 3-D image reconstruction only requires the virtual transceiver to be scanned over a single 2-D grid of positions. The ability to resolve the tapered tip of the hollow needle (less than 0.8 mm thick) demonstrates the fine depth resolution of THz time-domain imaging. Therefore, more complicated 3-D objects can be reconstructed accurately with the excellent lateral and depth resolution of our adaptive THz imaging approach.
4. Discussion and Conclusions
SNR improvement with SAFT and SAFT + CF processing is achieved even at the nearest wire target, where 3 transceiver elements are used in image reconstruction. SAFT alone is expected to produce a SNR gain of 10log10(3) = 4.8 dB, in close agreement with experiment. The SAFT image shows a nearly monotonic decrease in SNR with image depth, as shown in Fig. 4(b). SAFT processing sums together M signals to produce an M-fold improvement in SNR . The value of M is proportional to the transceiver-to-object distance R, assuming a 1-D synthetic aperture with constant f/#. However, this improvement is offset by the approximately 1/R4 power decay of the diverging THz field during transmit and receive. The more complicated depth dependence of the SNR in the SAFT + CF image is currently under investigation. Additional SNR improvement is expected from a two-dimensional (2-D) array, where the number of elements scales with R2. This suggests that SAFT + CF processing has the most significant impact for en face and 3-D imaging, both of which require 2-D scanning.
We have demonstrated an adaptive THz imaging technique for high resolution 3-D imaging. Our approach uses a virtual-transceiver with a synthetic aperture focusing technique and coherence weighting to produce images with fine spatial resolution over a large depth range. Furthermore, signal-to-noise ratio is improved by over 30 dB at large depth ranges. This self-adaptive imaging technique improves image quality without any advanced knowledge of the object. 3-D imaging requires scanning over a single 2-D aperture, resulting in a significant reduction in data acquisition time. The non-iterative nature of coherence weighting does not add significant computational burden to image reconstruction. We are currently extending this adaptive reconstruction approach to improve image quality in sparsely sampled transceiver arrays and 3-D imaging of objects within inhomogeneous media.
This research was supported by the University of Delaware Research Foundation.
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