Terahertz frequency modulated continuous wave imaging advanced data processing for art painting analysis

A terahertz image of a painting is not a single photograph waiting to be revealed. A frequency-modulated continuous-wave scanner records a depth-dependent response at every lateral position, and different processing choices can emphasize surface relief, support structures or local interfaces. This study develops that processing for two easel paintings and shows how Gaussian fitting can extract useful depth information even when the physical scan step is comparatively coarse.

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Turning FMCW range data into conservation images

The experiments used an electronic reflection scanner sweeping from approximately 0.23 to 0.32 THz. The 90 GHz modulation bandwidth provided millimeter-scale range resolution. At each pixel, the beat signal encoded reflections as a function of apparent depth, allowing the researchers to construct several complementary maps rather than relying on a single amplitude value.

Two works with different surfaces and histories were scanned. One was a modern acrylic painting of boats on a lake; the other was an eighteenth-century oil painting showing a pastoral scene. The contemporary work was sampled on a 594 by 499 lateral grid with 1 mm spacing and a depth range from about -70 to +70 mm. The older painting used a 799 by 600 lateral grid, again with 1 mm spacing, and finer 0.2 mm depth sampling over approximately -25 to +25 mm.

The team compared maps of the global maximum reflection, amplitude integrated over selected depth intervals, amplitude at a fixed depth, the position of the maximum and the full width at half maximum of the return. Each parameter responds differently. A maximum-amplitude map emphasizes strong surface changes. Integrating over a depth window can suppress the surface and reveal a wooden stretcher or another rear feature. Peak position tracks the local surface distance, while width can respond to roughness or unresolved neighboring interfaces.

Surface texture, support structures and Gaussian fitting

On the contemporary painting, the maximum-amplitude image reproduced major elements of the composition and highlighted thick dark brushstrokes. Canvas texture was visible in some regions. A rectangular anomaly corresponded to a label attached to the reverse, and integration over a selected negative-depth interval revealed the underlying wooden frame. Comparison of signals recorded over canvas alone and over the framed area confirmed the secondary reflection associated with the support.

An important difficulty was that the painting plane was not perfectly aligned with the scanner’s focal plane. A raw depth map therefore contained both meaningful surface relief and a broad geometric tilt. Moreover, a 1 mm depth step limits the precision with which a sampled maximum can be located. Reducing the step mechanically would increase acquisition time substantially.

The authors addressed this by fitting each range response with a single Gaussian function. The fitted amplitude, centroid and width provide continuous-valued parameters even though the original samples are discrete. At one representative pixel, the centroid was estimated at -2.312 mm with a coefficient of determination of 0.999. Across the image, the fitted centroid mapped a surface variation of several millimeters, indicating that one corner lay closer to the focal plane than the opposite corner. Smaller local changes followed raised paint features and brushwork.

Gaussian fitting is a pragmatic model, not a complete description of every multilayer reflection. It works best when a single dominant return controls the waveform. Closely spaced interfaces, strongly asymmetric peaks or multiple comparable echoes may require a multi-component model or a broadband time-domain measurement. The study uses the fit to refine parameter extraction, not to claim physical separation below the information content of the scanner.

Why advanced processing matters for heritage imaging

For conservation, the significance lies in extracting several structural views from one non-contact scan. Surface-relief maps can document deformation and impasto. Depth-window integration can localize the stretcher, labels or other rear structures. Peak-width and centroid maps can identify regions that deserve comparison with visible, infrared or X-ray observations. These outputs can guide targeted examination while preserving a record of the painting before intervention.

FMCW instruments also offer a practical speed and hardware advantage over many pulsed systems, but their lower bandwidth limits separation of thin layers. Signal processing can improve parameter precision and compensate for orientation; it cannot manufacture axial resolution that the frequency sweep does not contain. Material interpretation remains cautious because contrast may arise from geometry, roughness, thickness, refractive index or absorption rather than from a uniquely identifiable pigment.

The study combines terahertz engineering, data analysis and restoration expertise. That collaboration is visible in the choice of real paintings and in the effort to relate electromagnetic parameters to conservation-relevant structures. The publication supports the use of FMCW imaging as an investigational heritage tool, not as a standalone attribution or condition-assessment method.

More broadly, the work shows that an imaging system should be judged together with its processing sequence. Global maxima, integrated depth bands and fitted peak parameters answer different questions. By selecting those observables deliberately, a moderate-bandwidth electronic scanner can provide a richer account of a painting’s surface and support than a single conventional intensity image would suggest.

This publication also connects with our broader work on art and cultural heritage and FMCW radar expertise.

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