Inspecting hidden structures within materials is critical across various applications, including security screening, industrial manufacturing, medicine, and defense. Terahertz (THz) technology offers unique opportunities due to its ability to penetrate optically opaque materials and capture molecular fingerprint information through rich spectral signatures. Terahertz time-domain spectroscopy (THz-TDS) systems, while extensively used, are single-pixel and require raster scanning, resulting in low speed and throughput. Nonlinear optical processes, while offering non-scanning visualization, have low signal-to-noise ratios (SNR) and require bulky, expensive lasers. Terahertz computational ghost imaging, using spatial light modulators, can achieve high SNR but is limited in speed and complexity by the constraints of THz spatial light modulators. Existing terahertz focal-plane arrays have limited spatial resolution and don't provide time-resolved and frequency-resolved image data. The processing of large-pixel-count image data for 3D volume inspection is bottlenecked by digital storage, transmission, and processing requirements. This paper introduces a diffractive sensor that rapidly detects hidden defects or objects without image formation or digital processing, using a single-pixel spectroscopic terahertz detector and deep-learning-optimized diffractive layers. The system all-optically processes terahertz waves and classifies unexpected sources of secondary waves generated by diffraction from hidden defects or structures, acting as an all-optical sensor for these sources. The diffractive layers, optimized using deep learning, are physically fabricated and form an optical neural network. The measured spectrum reveals hidden defects all-optically, without raster scanning or image processing. The proof-of-concept successfully detected hidden defects in silicon samples by introducing a differential variation in peak spectral intensity near two predetermined terahertz wavelengths, using a single-pixel THz-TDS system with plasmonic nanoantenna-based source and detector.

Existing terahertz imaging techniques face limitations in speed, resolution, and data processing. THz-TDS systems require raster scanning, limiting throughput. Nonlinear optical methods suffer from low SNR. Computational ghost imaging, while offering high SNR, is hampered by the limitations of terahertz spatial light modulators. Terahertz focal-plane arrays have limited resolution and lack time/frequency-resolved data. The large datasets generated by conventional terahertz imaging systems create bottlenecks in storage, transmission, and processing, hindering high-throughput applications. This research addresses these limitations by proposing a novel all-optical approach that eliminates the need for image formation and digital processing.

The single-pixel diffractive terahertz sensor design consists of a series of diffractive layers (Fig. 1). A set of layers acts as a passive diffractive encoder, generating structured illumination impinging onto the 3D sample. Another set acts as a decoder performing space-to-spectrum transformation (Fig. 1a). The forward model is treated as a coherent optical system processing terahertz waves at predetermined wavelengths (λ₁ and λ₂). The spectral intensity values s(λ₁) and s(λ₂) are used to compute a normalized detection score (Sdet), with Sdet ≥ Sth indicating a defect. The diffractive layers are jointly optimized using deep learning, incorporating tens of thousands of subwavelength phase features. The design was validated using a single-pixel THz-TDS system with a plasmonic nanoantenna-based source and detector. The diffractive layers were fabricated using 3D printing (Fig. 2b). A data-driven approach was used to train the diffractive sensor model, simulating 20,000 silicon test samples with varying sizes and shapes of rectangular defects, along with 20,000 defect-free samples for balanced training. The focal cross-entropy loss was used, which reduces penalization from easily classified samples, improving sensitivity for smaller defects. A term was also incorporated to constrain energy distribution and maximize diffraction efficiency at λ₁ and λ₂, enhancing SNR at the desired wavelengths. The testing set consisted of 2000 samples with various defects not included in the training set. The impact of defect geometry and position on detection performance were numerically evaluated, analyzing detection sensitivity as a function of defect size (Dx, Dy, Dz) and position across the detection FOV (Fig. 3). Experimental validation involved ten silicon test samples with various defects, comparing experimental and numerical results (Fig. 5). A linear correction factor was applied to account for the experimental THz source’s spectral profile. The impact of averaging multiple spectral measurements on the false positive rate (FPR) was also analyzed (Fig. 6). The forward model is detailed in the Methods section, including equations for modeling diffractive layers, free-space propagation, and the interaction of light with defects in the sample volume. The training loss function combines a focal loss for defect detection, a term for diffraction efficiency, and a term for constraining spectral energy distribution.

Numerical analysis showed 89.62% detection accuracy for defective samples using an unbiased threshold (Sth = 0.5), with 100% specificity. Analysis of the influence of defect geometry revealed that detection sensitivity decreased as defect size reduced. For example, with larger defects (Dx = Dy = 3 mm, Dz = 0.3 mm), sensitivity reached 100%, but dropped to 57% for smaller defects (Dx = Dy = 0.75 mm). Analysis of defect position showed that detection sensitivity was high in a central circular region of the detection FOV (diameter 1.6 cm), dropping towards the edges. Experimental validation using a THz-TDS setup with 3D printed diffractive layers successfully detected various hidden defects with different sizes and orientations in silicon wafers. The results showed good agreement with the numerical predictions, despite fabrication errors and experimental noise. Averaging five spectral measurements per sample reduced the false positive rate significantly (Fig. 6). Analysis of the terahertz wave field within the detection FOV revealed that the structured illumination at λ₂ significantly contributed to the distribution of the detection scores, with higher values at the center and lower values at the periphery. The method showed the ability to detect defects close to the diffraction limit of light. The proposed approach eliminates image acquisition, processing, storage, and transmission steps, significantly increasing throughput.

The single-pixel diffractive terahertz sensor successfully addresses the limitations of conventional terahertz imaging systems, providing a high-throughput, all-optical approach for rapid defect detection. The elimination of image formation and digital processing drastically reduces computational costs and significantly increases the speed of defect detection. This is particularly advantageous in applications with a low probability of defects, such as industrial quality control and security screening, where traditional methods waste resources processing defect-free samples. The experimental results validate the model's ability to detect defects of varying size and position. The design's robustness to experimental noise is demonstrated by using averaging to reduce the FPR. The method's capability to detect defects near the diffraction limit showcases its potential for high-resolution inspection. This all-optical approach offers a transformative advance in defect detection and materials diagnosis.

This paper presents a novel single-pixel diffractive terahertz sensor for rapid and accurate detection of hidden structures and defects, eliminating the need for image formation and digital processing. The successful experimental validation demonstrates its potential for high-throughput applications in industrial quality control, material inspection, and security screening. Future research could explore extending the detection FOV, increasing the number of diffractive layers to improve accuracy, using shorter wavelengths for smaller defect detection, incorporating more wavelengths for comprehensive defect characterization, adapting the design for reflection mode to handle highly absorbing samples, and developing methods to mitigate mechanical misalignments.

The maximum sample thickness that can be probed in transmission mode is limited by terahertz absorption or scattering. For highly absorbing samples, a reflection-mode configuration could be explored. Uncontrolled mechanical misalignments among diffractive layers could affect performance; however, this could be addressed using misalignment-resilient design strategies. The ability to sense isolated subwavelength features is limited by the detection sensitivity, and the system cannot resolve two closely positioned subwavelength defects.