All-fibre-coupled terahertz single-pixel imaging for biomedical applications

Domain: physics
Published: 2026-01-12
Editorial outcome: minor_revision

Abstract
Real-time, non-invasive imaging techniques are essential for advancing biomedical diagnostics and material analysis, yet existing terahertz (THz) systems often suffer from limited speed, bulky designs, and poor adaptability to in situ environments. Addressing these challenges, we present a fully fibre-coupled THz attenuated total internal reflection single-pixel imaging system, offering a compact, flexible, and robust platform for non-destructive spectroscopy and in vivo imaging. This all-fibre architecture enables seamless integration for in situ biomedical applications, including measurements directly on patients. Central to our design is a THz spatial light modulator based on an unpassivated silicon wafer, facilitating high-speed modulation and enabling video-rate imaging with a spatial resolution down to 360 μm. Despite being in the reflection geometry and using fibre-coupled light, our system achieves an imaging throughput exceeding 30,000 pixels per second for 64-by-64 images-over five-fold higher than the state of the art-representing a substantial improvement in real-time THz imaging capabilities.

Introduction
Terahertz (THz) light has emerged as a non-destructive and non-ionising alternative to X-rays in spectroscopy and imaging due to its low photon energy (few meV), making it particularly well-suited for biological tissue evaluation. Furthermore, THz exhibits high sensitivity to water content in biological tissues, as water strongly attenuates THz signals. This property enables THz spectroscopy to differentiate between cancerous and normal tissues by exploiting the distinct THz attenuation characteristics resulting from different water content1–3. This also provides the capability to monitor transdermal drug delivery processes4–7, assess skin occlusion effects8,9, and evaluate the impact of cosmetics on skin hydration10. Another advantage of THz spectroscopy is its ability to detect spectral features arising from characteristic rotational and vibrational modes, facilitating its applications in other fields such as agriculture and environmental science. For instance, Martinez et al. demonstrated the identification of fungal infections in chestnuts by leveraging the unique spectral signatures of infected tissues11. Mushtaq et al. revealed that THz spectra offer valuable insights into the impact of heavy metal exposure on diatom chain length12.

THz transmission spectroscopy is widely used for investigating thin films13,14, dielectrics (e.g., paper, plastics, and ceramics)15,16, polymers17, and semiconductors18. In contrast, attenuated total reflection (ATR) is particularly advantageous for measuring aqueous samples and other highly absorptive materials. In a typical THz ATR setup, THz light undergoes total internal reflection (TIR) at the prism-sample interface, generating an evanescent field within the sample. Typically, the sample thickness exceeds the penetration depth of the evanescent field, ensuring sufficient attenuation of the evanescent field within the sample. THz ATR has been widely utilised for material characterisation in various applications, including the evaluation of tetracycline hydrochloride solutions19, DNA molecules20, and rat brain injuries21. Recently, Wu et al. developed a triple internal reflection prism to enhance the sensitivity of THz ATR spectroscopy22. Fu et al. introduced a method to apply ATR to samples thinner than the penetration depth. TIR also plays a critical role in manipulating THz polarisation using Fresnel wave retarders23,24 and phase-compensated mirror-TIR devices25, controlling THz carrier-envelope phase26, and improving the modulation depth of THz photomodulators27,28.

THz imaging has seen growing application in biomedical fields. For instance, Osman et al. developed a handheld portable THz scanner to assess and monitor burn injuries in porcine skin in vivo29. Qi et al. employed a THz quantum cascade laser (QCL) confocal imager to differentiate human skin pathologies30, while Wang et al. applied THz imaging to evaluate the effectiveness of silicone gel sheeting in scar treatment31. However, most reported THz imaging systems rely on mechanical raster scanning, which results in slow image acquisition rates. THz computational single-pixel imaging (SPI)28,32–40 offers a promising solution to achieve high frame rates and spatial resolution without adding significant costs to the overall system. In a THz SPI system, the THz beam is encoded using a series of patterned masks generated by a THz spatial light modulator (SLM). The modulated THz light is then reflected off or transmitted through a sample, after which the signals are detected by a single-element detector, and the image is reconstructed using the known mask patterns and the corresponding THz signals. Mechanical41,42 and optically controllable28,43,44 THz SLMs have been proposed. Optically controllable THz SLMs typically use a digital micromirror device (DMD) to encode visible light, which is then projected onto a semiconductor wafer, such as silicon. The modulated semiconductor wafer acts as the THz SLM. The performance of an optically modulated semiconductor SLM is highly dependent on the carrier lifetime45. While a longer carrier lifetime enhances the THz modulation depth, it degrades the spatial resolution and the switching speed. Off-the-shelf silicon wafers without passivation typically exhibit short carrier lifetimes (several microseconds), resulting in limited modulation depth. To overcome this limitation, surface passivation techniques44–47 can be employed to engineer the carrier lifetime, achieving an optimal balance between modulation depth, spatial resolution, and switching rate. For example, Romain et al. developed an electrically tunable THz photomodulator, where the carrier lifetime can be flexibly adjusted via a bias voltage46.

Despite the promising potential of ATR and THz SPI for biomedical applications, the integration of these two technologies has been hitherto applied only to sub-THz continuous wave sources in free space34. Versatile, flexible, all-fibre-coupled broadband THz ATR SPI has yet to be explored. Here we have developed an all-fibre-coupled design, including the spatial patterning of the broadband THz beam by visible light, making it highly adaptable for the development of compact and portable THz ATR SPI modules that can function as handheld devices29,48 or be seamlessly integrated with robotic systems49. This advanced imaging system will enable real-time, in vivo, and in situ imaging of biological tissues, unlocking transformative potential for applications such as non-invasive skin cancer diagnosis and precision-guided surgical interventions.

Results
THz power transmittance
Figure 1a shows the all-fibre-coupled THz ATR SPI system. Figure 1b illustrates the ATR SPI module in detail, and the inset shows the light path inside the prism and silicon wafer. A photograph of the system is shown in Supplementary Fig. 2. The system is built based on a commercial THz time-domain spectrometer. A detailed description of the setup is presented in the section Materials and methods.

The Fresnel coefficients determine the power transmittance. Both polarisation and birefringence affect the Fresnel coefficients. The Fresnel coefficients of s- and p-polarised lights are governed by distinct formulas, and birefringence influences these coefficients through an angle-dependent refractive index. Figure 2a compares the power transmittances of s- and p-polarised THz light. A detailed calculation method is presented in the Supplementary Information. The horizontal axis represents the angle of incidence within the quartz prism. The power transmittance accounts for the dual transmissions at the quartz-silicon interface and a single reflection at the silicon-air interface (see the inset in Fig. 1b). As illustrated in Fig. 2a, the power transmittance of p-polarised light exhibits distinct trends: it decreases to zero as the angle of incidence increases from zero to the Brewster angle at the silicon-air interface, sharply increases from the silicon-air Brewster angle to the silicon-air critical angle, gradually rises to the global maximum at the quartz-silicon Brewster angle, and finally drops to zero as the angle increases from the quartz-silicon Brewster angle to 90°. In contrast, the power transmittance of s-polarised light increases to its maximum as the angle of incidence increases from zero to the silicon-air critical angle, after which it steadily declines to zero between the silicon-air critical angle and 90°.

Both p- and s-polarised light undergo TIR at the silicon-air interface beyond the critical angle. Notably, at the quartz-silicon Brewster angle, p-polarised light undergoes no transmission loss, favouring the attenuated total reflection (ATR) single pixel imaging (SPI) module. The optical axis of the quartz prism is perpendicular to the two parallel surfaces of the quartz prism. The p-polarised THz light is also an extraordinary wave. The prism’s base angle of 57.9° equals the Brewster angle for a p-polarised THz light at the quartz-silicon interface from quartz to silicon. The inset shows the light path inside the prism and the silicon wafer.

Imaging of cartwheel sample
We imaged a cartwheel sample using a full set of [1 −1] masks. Images are obtained at each temporal point in a 6-ps-wide window with a step of 0.05 ps, a DMD switch rate of 10 kHz, and a 64-by-64 pixel resolution. Each image is an average of 20 image measurements and normalised to a THz beam reference image (more details on the normalisation process are given in the Supplementary Information). We call the resulting intensity the normalised THz signal (see Supplementary Eq. 16) and the unnormalised one the receiver signal, for example, the signal shown in Fig. 2b. In this work, the DMD masks are constructed using a Paley type-I Hadamard matrix, ensuring all masks exhibit similar spatial frequencies. This uniformity enables an easy selection of a subset of masks for undersampling to improve image frame rate28. Each 2D mask is flattened into a 1D vector, and the collection of these 1D vectors forms the measurement matrix. Simultaneously, each mask corresponds to a single output from the single-pixel detector, and the detector outputs for all masks collectively form the measurement vector. Image reconstruction is achieved by multiplying the pseudoinverse of the measurement matrix by the measurement vector50,51. The pseudoinverse matrix is calculated based on the regularisation method described in ref. 51.

A gold cartwheel was fabricated on a 2 mm-thick z-cut quartz substrate. In the experiment, the cartwheel side attaches to the silicon surface. Edible sunflower oil is employed at the quartz-silicon and silicon-sample interfaces to eliminate air gaps. The THz light incident on the gold cartwheel is reflected back and detected by the receiver. In contrast, because of the Brewster angle, the remaining THz striking the quartz substrate fully transmits into the substrate. THz imaging is performed within a time window centred at the time delay corresponding to the reflection at the silicon-sample interface. Although the THz light transmitted into the substrate experiences total internal reflection and arrives at the receiver, the time delay is outside the time window of interest and thus does not affect the imaging result. As a result, only the THz light incident on the gold cartwheel contributes to the THz imaging.

Figure 3 shows the imaging results of the cartwheel sample. The first row shows the images at the peak (Fig. 3a) and trough (Fig. 3b) in the time domain, and the image at the peak of 0.63 THz (Fig. 3c) in the frequency domain. The inset in Fig. 3a shows the optical image of the cartwheel sample with a red square indicating the THz imaging region. Time-domain images are normalised using a THz beam reference image to eliminate the effects of inhomogeneous THz or blue light distribution. The frequency-domain images are obtained by Fourier transforming the normalised time-domain signal at each pixel. All images show high absolute THz signal values in the metal cartwheel regions, while the quartz regions exhibit very low absolute THz signal values due to the Brewster angle.

A representative pixel on the cartwheel is marked with a circle in the first row. Figure 3d plots the normalised THz signal as a function of time at the marked pixel, with vertical red and blue dashed lines indicating the peak and trough, respectively. These lines correspond to the time delays for the images shown in Fig. 3a, b. Figure 3e plots the spectrum of the THz signal shown in Fig. 3d, with a red dashed line marking the spectral peak. The line corresponds to the frequency for the images shown in Fig. 3c. The solid lines in Fig. 3d, e represent the mean values, and the shaded regions denote the standard deviations across repeated measurements. We also fabricated a knife-edge sample to estimate the resolution, signal-to-noise ratio, and image contrast to characterise the performance of the system. The results (Supplementary Figs. 5, 6) and the method are presented in the Supplementary Information.

Undersampling and imaging speed
A high frame rate is desirable for real-time THz imaging, and reducing the total number of measurements via undersampling is a widespread strategy to increase the frame rate. The frame rate (f_img) can be expressed by the following formula:

f_img = 1 / (t_0 + t_dmd) = 1 / (t_0 + N^2 * k * r / f_dmd) (1)

where t_0 = 50 ms is the waiting time to synchronise the DMD, data acquisition card, and probe delay line to detect the THz pulse28. t_dmd = N^2 * k * r / f_dmd indicates the DMD active time to obtain an image frame. N represents the pixel resolution, for example, N = 64 for a 64-by-64 pixel resolution. k is the number of DMD masks required to construct a measurement mask, where k = 1 for the [1 0] mask and k = 2 for the [1 −1] mask. r is the undersampling ratio, and f_dmd is the DMD switching rate. It is evident from the formula that the maximum frame rate limit is 1/t_0. When t_0 >> t_dmd, f_img approaches 1/t_0. Conversely, when t_dmd >> t_0, f_img becomes proportional to 1/t_dmd, and thus is proportional to DMD switching rate f_dmd. Eq. (1) shows that f_img decreases with N, leading to a difficulty in comparing the performance of an imaging system for different N. In the discussion below, we use instead the number of pixels per second (PPS), f_pxl = N^2 * f_dmd, to get a fair comparison between different imaging systems52.

Figure 4 shows the undersampling result using [1 −1] mask and maximum DMD switching rate f_dmd of 20 kHz. Figure 4a displays the ground truth, obtained by averaging 40 measurements using a complete set of [1, −1] masks, corresponding to r = 1. Figure 4b–f shows images reconstructed with progressively increasing undersampling ratios from 0.1 to 1, each averaged over 30 image measurements. All the images are normalised to the reference image of the THz beam.

The increasing undersampling ratio reduces the frame rate while improving the structural similarity index (SSIM)28,53. Figure 4g illustrates the relationship between SSIM and the undersampling ratio, with the ground truth in Fig. 4a used as the reference image for the calculations. The red circles represent the SSIM values for the images shown in Fig. 4b–f. The SSIM values (0.85, with a full set of masks) are comparable to our previous results28 (0.81). Measurements were repeated, and standard deviations were found to be smaller than the symbols in Fig. 4g, h. We note that the oscillations shown in Fig. 4g arise from the different sets of measurement masks rather than measurement uncertainty. Although the Paley type-I masks exhibit similar spatial frequencies, they do not show the same spatial frequency. This leads to lower SSIM for a higher sampling ratio, i.e., the oscillations.

Figure 4h shows the frame rate as a function of the undersampling ratio for various combinations of mask type, DMD switching rate, and pixel resolution. The red curve shows the frame rate versus the undersampling ratio for the experimental parameters used for the images in the first row (N = 64, k = 2, and f_dmd = 20 kHz). The red circles represent the frame rate of the images shown in Fig. 4b–f. The blue curve shows the frame rate versus the undersampling ratio for the parameters employed by Stantchev et al. (N = 32, k = 1, and f_dmd = 4 kHz)28. They achieved a frame rate of 6.6 FPS (6,758 PPS) for 32-by-32 imaging at a sampling ratio of 0.4, as indicated by the blue diamond symbol. The short lifetime of the intrinsic silicon wafer used in this work allowed us to utilise the DMD’s maximum switching rate of 20 kHz. The black curve shows the frame rate versus the undersampling ratio in this work for N = 32, k = 1, and f_dmd = 20 kHz. Compared with the results reported by Stantchev et al.28, we improved the frame rate to 14.2 FPS (14,540 PPS) at the same sampling ratio of 0.4, as indicated by the black diamond symbol, approaching the maximum frame rate limit 1/t_0 = 20 FPS. The parameter t_0 limits FPS and PPS. This effect on PPS reduces with increasing N. We reach 31,049 PPS (7.58 FPS) with N = 64, approaching the PPS of the ideal case, that is, t_0 = 0. For this case, PPS is 50,000 and independent of N. By utilising a single-pixel imaging approach with a rapid DMD switching rate, the PPS exceeds that achievable in mechanically-swept THz QCL imaging systems, typically f_pxl = 2,700 PPS30 to 4,100 PPS54.

Imaging of porcine tissue
We imaged a porcine tissue to demonstrate the sensitivity of the all-fibre-coupled THz ATR SPI system to biomedical tissues. A full set of [1 −1] masks, a DMD switch rate of 10 kHz, and a 64-by-64 pixel resolution were employed. We covered the tissue with cling film to prevent dehydration during the experiment. Images are obtained at each temporal point in a 6-ps-wide window with a step of 0.05 ps. Each image is an average of 20 measurements. Reference images of the THz beam were obtained with a bare silicon wafer using the same experimental parameters to normalise time-domain images, e.g., Fig. 5a.

Receiver signals of the reference and sample at each pixel are Fourier transformed. We define the ratio between the Fourier transforms as a complex transfer function H_b(ω), which can be written as:

H_b(ω) = S_smp(ω) / S_air(ω) = r_smp(ω) / r_air(ω) (2)

where S_smp(ω) and S_air(ω) are the Fourier transforms of the sample and reference time-dependent receiver signals, ω is the THz angular frequency, r_smp(ω) and r_air(ω) are Fresnel reflection coefficients at the silicon-sample and silicon-air interfaces. The time-domain receiver signal is the convolution of the THz electric field and the response function of the receiver. In the frequency domain, the receiver signal is given by the product of the THz electric field and the response function, i.e., S(ω) = E(ω)F_i(ω), and F_i(ω) is the receiver function. Although F_i(ω) cancels in Eq. (2), it is not expected to cancel completely for our normalised images, such as Fig. 3c, as we sum over the frequency spectrum during normalisation to improve signal-to-noise ratio. However, we note that this frequency summation does not qualitatively affect the resulting images, which suggests the frequency dependence of F_i(ω) is weak in the frequency range of this work. Thus, one can roughly assume the receiver signal is proportional to the THz electric field.

The magnitude |H_b(ω)| illustrates the amplitude ratio of the THz signal. The argument arg(H_b(ω)) stands for the phase difference between S_smp(ω) and S_air(ω), i.e., Δϕ(ω) = arg(H_b(ω)) = arg(S_smp(ω)) - arg(S_air(ω)). Fig. 5a shows the normalised time-domain image of a porcine tissue sample at the peak. Figure 5b, c plot the images of |H_b(ω)| and arg(H_b(ω)), i.e., Δϕ(ω) at 0.73 THz. The inset in Fig. 5a presents the optical image of the sample with a red square indicating the THz imaging region. This region comprises protein and fat separated by a diagonal boundary. In the first-row images, the dashed white diagonal line marks the boundary between protein and fat. The red and blue circles mark the representative points in the protein and fat regions. The second row illustrates the normalised time-domain THz signal (Fig. 5d), |H_b(ω)| (Fig. 5e) and Δϕ(ω) (Fig. 5f) for the representative points marked in the protein and fat regions. The solid lines in Fig. 5d–f represent the mean values, and the shaded regions denote the standard deviations. The black dashed lines in the second row highlight the time and frequency points for the images in the first row. The spectra shown in Fig. 5e, f clearly distinguish between protein and fat across the full frequency range. Similarly, the time-dependent normalised THz signal curve in Fig. 5d differentiates protein and fat, except at the zero-crossing points.

In vivo real-time imaging of scab on wound
We used the all-fibre-coupled THz ATR SPI system to image a scab and normal skin on a volunteer’s arm, demonstrating its capability to assess skin in vivo. The imaging is carried out at the peak of the THz pulse trough with a full set of [1 −1] masks, a DMD switch rate of 20 kHz, and a 64-by-64 pixel resolution, leading to 2.2 FPS (8912 PPS). The images were averaged over 20 measurements and normalised with the same method shown in the Supplementary Information. Figure 6a shows the resulting THz image of the scab together with a photo (inset). The THz image successfully distinguished the scab and the surrounding healthy skin. It also correctly depicts the shape of the scab shown in the optical photo. The scab region exhibits a stronger reflected THz signal (darker colour in Fig. 6a) compared with the surrounding healthy skin because the scab is drier and therefore gives a greater reflection coefficient than the healthy skin. Figure 6b shows the THz image of normal skin, which attenuates the THz signal homogeneously to a level comparable to the healthy surrounding skin shown in Fig. 6a. Figure 6c shows the normalised THz beam for comparison. We also recorded a video (see Supplementary Movie 1) to illustrate the measurement of the scab and demonstrate the ability of the proposed system for real-time in vivo applications.

Methods
Experimental setup
The setup is based on a commercial THz time-domain spectrometer (Menlo Terasmart). As shown in Fig. 1, a fibre-based femtosecond laser delivering femtosecond pulses with a central wavelength of 1550 nm and a repetition frequency of 100 MHz was applied to generate and detect THz light. The THz spectrometer integrates a delay line to vary the time delay between the THz pulse and the probe laser pulse. The power of the laser delivered to the fibre-coupled photoconductive emitter (Fraunhofer TERA15-TX-FC) and receiver (Fraunhofer Tera15-RX-FC) is around 20 mW. The emitter is biased with 100 V DC, emitting THz with a power of 84 μW. The signal from the receiver is amplified with a transimpedance amplifier (Femto LCA-S10) and then read by a data acquisition (DAQ) device (NI USB-6351). THz light from the emitter is collimated by a TPX lens and focused by another TPX lens through a quartz prism and a silicon wafer to the silicon-sample interface. THz light reflected from the silicon-sample interface is collimated by a TPX lens and focused by another TPX lens to the receiver. The detected THz pulse exhibits a pulse duration of 0.94 ps, with a spectrum peaked at 0.63 THz and a full-width-half-maximum of 0.78 THz.

A diode laser (Lasertack LAB-450-5000) generates continuous-wave 450 nm-wavelength blue light. The blue light is encoded with a DMD (Vialux V4395) to imprint programmed patterns onto it. A multi-core image fibre (Fujikura FIGH-100-1500N) transmits the patterned blue light from the input to the output. Subsequently, the blue light is projected onto the silicon surface through the quartz prism by an objective lens. The projected laser patterns modulate the silicon wafer, generating carrier patterns replicating the same profile as the incident light. The image fibre comprises 100,000 picture elements and exhibits a large core diameter of 1.4 mm. We applied a 10× microscope objective lens to match the image size from the active area of the DMD to the area of the fibre bundle and also to match the numerical aperture of the lens to the acceptance angle of the fibres. A more complete description of the optimisation of the fibre projection system is presented in the Supplementary Information. The total optical transmission of the fibre projection system for the blue light is 21%, allowing the delivery of 882 mW blue light to the silicon wafer from a laser output of 4.2 W. The beam size on the silicon wafer is 8 mm × 8 mm, resulting in a pump fluence of 13 mW/mm2.

Carrier lifetime plays a vital role in modulation depth, switching speed and image spatial resolution45. Here by, we used an unpassivated 200-μm-thick, double-side polished, (100) float-zone silicon wafer with a carrier lifetime of 7 μs (the calculation of the carrier lifetime is explained in the Modulation Depth section of the Supplementary Information) and resistivity greater than 10,000 Ω ⋅ cm. This high-resistivity silicon wafer with a low effective lifetime allows us to achieve high resolution (360 μm) single-pixel imaging with a high frame rate supported by the highest DMD switching rate (20 kHz) and a THz modulation depth of 12%. While this may seem like a low modulation depth, it works well in practice because the switch-off time is shorter than if a higher modulation depth were used. To increase the modulation depth we would need to use a wafer with a longer carrier lifetime, which would improve signal to noise, but at the cost of imaging time and poorer resolution. Therefore, using the short effective lifetime of 7 μs allows us to utilise the highest DMD switching rate to achieve high imaging speed. It also gives rise to high imaging resolution, representing a good trade-off between modulation depth, imaging speed, and resolution.

[1 0] & [1 −1] masks
SPI can be carried out with the mask [1 0] or [1 -1]. The mask [1 0] uses the measured difference in reflection between photoexcitation and no photoexcitation to reconstruct the image. In comparison, the mask [1 −1] uses the measured difference in reflection between a photoexcitation mask [1 0] and its inverse [0 1]. Experimentally, the mask [1 −1] is performed by projecting a [0 1] mask immediately following a [1 0] mask. The signals were then subtracted to give a signal equivalent to using a [1 −1] mask. The subtraction procedure is adopted because a [1 −1] mask cannot be directly projected as the DMD micromirrors have only two states, i.e., on (1) and off (0).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "his work reports a single-pixel imaging system that combines fiber-coupled visible light modulation with a terahertz (THz) attenuated total reflection (ATR) geometry. By using a digital micromirror device (DMD) to modulate light patterns transmitted to a silicon wafer surface via imaging fiber bundles, the system achieves spatial modulation of terahertz waves. The authors demonstrated its imaging capabilities on porcine tissue samples and human skin wound areas, claiming advantages such as 'all-fiber-coupled', 'real-time imaging', and 'high resolution'.\nThe results are solid, experiments are properly executed, and it delivers good spatial resolution and frame rates. Supplementary materials also include theoretical analyses and modeling derivations. However, considering terminology accuracy, technological novelty, and biomedical applicability, I do not think this manuscript meets Nature Communications' high standards for originality and broad impact in the field. My detailed concerns are as follows.\n1. Overclaims.\n(i) The term 'all-fibre-coupled' in the title and text is inaccurate and misleading. This is because,\n(1) Only 450 nm visible light patterns are transmitted via imaging fibers.\n(2) THz wave generation, propagation, modulation, and detection rely entirely on free-space optics (TPX lenses, ATR prism, free-space-coupled THz-TDS system).\n(3) The 'fiber-based' component is limited to visible light modulation; the primary THz signal path remains free-space. No fiber-compatible THz source/detector is proposed.\nThis contradicts the common understanding of 'all-fibre-coupled' in THz/optical imaging and may mislead readers into assuming system portability or encapsulation feasibility.\n(ii) Additionally, the terms 'in vivo', 'in situ', and 'real-time imaging' are overstated. The system can only detect skin or air-exposed tissues due to its fundamental limitation: modulation requires direct contact between the silicon wafer and the target. This restricts its applicability for genuine biomedical scenarios where internal body operation is essential. In terms of 'real-time imaging', the 2–7 fps frame rate is relatively slow.\n2. Engineering Integration Over Core Innovation. Key components are taken from existing technologies:\n(1) DMD + silicon wafer for optical THz modulation is a common design.\n(2) Hadamard encoding and [1 −1] masking are conventional single-pixel imaging methods.\n(3) ATR structures are not new to THz applications.\n(4) Image reconstruction uses basic normalized linear superposition, lacking advanced compressive sensing or deep learning approaches.\nThe performance improvements (2–7 fps frame rate, ~100 µm resolution) stem from component optimization, not fundamental methodological or physical breakthroughs.\n3. Limited Imaging Validation and Clinical Relevance\nDespite the authors demonstrated the method by imaging porcine tissues and human skin wounds:\n(1) Sample diversity is insufficient to represent broad biomedical scenarios.\n(2) Results are qualitative; no quantitative comparison exists against clinical standards (e.g., OCT, infrared thermography, ultrasound).\n(3) No histopathological registration confirms imaged structures' physiological significance.\n(4) Statistical evaluations (SNR, CNR, recognition rates) or cross-sample comparisons are absent.\n4. Low Modulation Efficiency Limits Performance\nSupplementary material reveals a modulation efficiency of ~12%, with only 21% of initial blue light energy reaching the silicon wafer due to losses in fibers/lenses. This low signal contrast necessitates strong normalization and background suppression, potentially compromising imaging depth and stability under low-SNR conditions.\nIn conclusion, this work demonstrated solid engineering capabilities in system implementation and offers a reference for THz imaging integration. However, its contributions remain confined to optimizing existing components rather than delivering field-leading innovation. Coupled with misleading terminology, overclaims, narrow application validation, and overstated clinical significance, the manuscript falls short of Nature Communications' standards.", "reviewer_2": "Dear Authors,\nI was asked to review your manuscript NCOMMS-25-44759 \"All-fibre-coupled terahertz single-pixel imaging for biomedical applications\".\nIn the manuscript you describe the results obtained with a fibre-coupled terahertz single-pixel imaging system.\nA terahertz source is spatially modulated using an optically controlled silicon SLM.\nThe telecom laser for the terahertz source and detector is fibre coupled and the THz frequency is imaged using TPX lenses, the blue light, used for modulation is fibre coupled using an imaging fibre.\nYour work improves on previous experiments in two ways:\n1. The shorter lifetimes of carriers in your silicon SLM allows for faster modulation and ultimately higher frame rates.\n2. The demonstration of an all fibre coupled experimental setup paves the way for integration of the method onto handheld devices.\nI am convinced that your evaluation of your data is valid and your collected data is robust and I can't find any technical flaws with your manuscript.\nHowever, I want to recommend to comment on measurement uncertainties in your manuscript.\nAs far as I understand, most of your measurements are averaged results, it should be straight forward to include confidence intervals/standard deviations in your plots in figures 3-5.\nYour work improves on previous results by an increased frame rate and integrating your setup in an all fibre-coupled manner, which means the inclusion of an imaging fibre.\nThe telecom fibre for the THz source and detector were already fibre coupled in previous work.\nThe core methodology of your experiment, however, stays identical.\nI still want to argue that advancing technology in this way is still significant, especially in applied sciences, where the step from the lab into the field often can be challenging.\nYour presentation is very clear and easily understandable.\nI only have a few suggestion for improvements on your manuscript.\n1. As already mentioned a more detailed analysis of errors.\n2. You are not comparing the structural similarity (SSIM) with your previous work. I would argue that SSIM and FPS/PPS play an\nimportant role when benchmarking your experiments against each other.\n3. Fig 5c seems to be taken at lower resolution. Why is that?\n4. Formatting of formulas in the supplement is often unconventional ($\\times$ is often used).\nOtherwise, I have no concerns for your manuscript being published in Nature Communications.", "reviewer_3": "The authors present an interesting article on the intriguing combination of multiple techniques for a useful THz imaging system. The authors also present rudimentary measurements on biological samples, which round the paper off nicely. The methodology seems sound and the information provided is sufficient.\nHowever, the structure of the text does not correspond to that of the journal. The 'Results' section contains a great deal of detail about the setup and methods, which should be found in the 'Methods' section.\nThe discussion of the effect of THz polarisation on resolution anisotropy is not fully convincing and is not supported by references, simulations or other evidence. Without this, it is merely an assumption and, as such, should not be discussed in such detail.\nThe core achievement is the ability to image at high resolution and high measurement rates. While the resolution target presented provides a rough idea of the imaging capabilities, some aspects are unclear.\n- Resolution: The measurements with the resolution target (Siemens star) indicate varying resolution throughout the image.\nGiven the provided data, this could be due to the orientation of an edge (similar to astigmatism) or the position within the field of view.\n- Contrast: The achievable contrast in this image is not provided. It is stated that the background is zero, which would result in infinite contrast; this is certainly not the case.\n- Homogenity: The images of the resolution target show a highly non-homogeneous image in terms of contrast, signal strength and resolution. While this is not surprising, it needs to be quantified. Is it possible to partially compensate for this inhomogeneity by calibrating each pixel?\n- Noise: The image noise has not been quantified. This can occur between neighbouring pixels that are expected to have the same signal strength, as well as between subsequently recorded images.\nI suggest applying the razor blade method as a simple experiment to quantify the above values. Place a razor blade, or another sharp, well-defined edge, at the sample plane, then take images at different blade positions. Rotate the blade by 90 degrees and repeat. The images can then be compared with the well-known and simple ground truth and the values above can be extracted. I am willing to help if the authors would like to discuss this in more depth.\nOther comments:\nLine 103. What does 'short' refer to? Please provide an order of magnitude.\nLine 128 and following: This focuses on the setup and details rather than the results.\nLine 163 and following: This paragraph seems to explain fundamental optics; I suggest shortening it drastically.\nLine 179: Why 'also'?\nLine 206 and following: Why are both polarizations discussed in detail when the experiment uses just one of them?\nLine 297: The e-field is certainly not zero.\nLine 299: See above.\nFig. 3c). The plots have the unit 'electric field', but this is imprecise because it is not clear where this electric field is located. I believe the authors plotted the receiver signal, which is not fully linear in the electric field due to the receivers' frequency-dependent roll-off. Furthermore, the setup will have some frequency dependence due to the optics involved and their adjustment. Therefore, for d) and e), I suggest using the term 'receiver signal', and for a to c, I recommend normalising to a full metal mirror as the sample and using the term 'image contrast' or similar. The same applies to other pictures later in the manuscript.\nLine 490 and following: Please revise the naming of the components used. If you are unsure, please consult the manufacturer for the correct terminology."}, "author_response": "We thank the reviewers for their feedback on our paper. We address all the points below\non a point-by-point basis. Our responses are in blue font. We have done the experiments\nsuggested and agree that adding these into the paper make it stronger.\nReviewer #1 (Remarks to the Author):\nThis work reports a single-pixel imaging system that combines fiber-coupled visible light\nmodulation with a terahertz (THz) attenuated total reflection (ATR) geometry. By using a\ndigital micromirror device (DMD) to modulate light patterns transmitted to a silicon wafer\nsurface via imaging fiber bundles, the system achieves spatial modulation of terahertz\nwaves. The authors demonstrated its imaging capabilities on porcine tissue samples and\nhuman skin wound areas, claiming advantages such as 'all-fiber-coupled', 'real-time\nimaging', and 'high resolution'.\nThe results are solid, experiments are properly executed, and it delivers good spatial\nresolution and frame rates. Supplementary materials also include theoretical analyses\nand modelling derivations. However, considering terminology accuracy, technological\nnovelty, and biomedical applicability, I do not think this manuscript meets Nature\nCommunications' high standards for originality and broad impact in the field. My detailed\nconcerns are as follows.\n1.1. Overclaims.\n(i) The term 'all-fibre-coupled' in the title and text is inaccurate and misleading. This is\nbecause,\n(1) Only 450 nm visible light patterns are transmitted via imaging fibers.\n(2) THz wave generation, propagation, modulation, and detection rely entirely on free-\nspace optics (TPX lenses, ATR prism, free-space-coupled THz-TDS system).\n(3) The 'fiber-based' component is limited to visible light modulation; the primary THz\nsignal path remains free-space. No fiber-compatible THz source/detector is proposed.\nThis contradicts the common understanding of 'all-fibre-coupled' in THz/optical imaging\nand may mislead readers into assuming system portability or encapsulation feasibility.\nAnswer: We thank the reviewer for their comments but would like to point out where they\nhave misunderstood our THz set up and why we disagree with their opinion that we are\noverclaiming. We point out that there is fibre coupling in ALL the THz emission/detection\npathways as well as in the optical illumination pathway. By “all-fibre-coupled” we mean\nthat the THz emitter and detector in the imaging head (Fig. 1b) are fibre-coupled to the\nfiber laser as well as the light modulation path, so points (1-3) of comment 1.1 are\nincorrect. This makes the imaging head portable and ultimately it will be compatible with\na robot arm. The reviewer is right in that the optics inside the imaging head are free-space\noptics, but this is the part where the THz light meets the skin so it has to be. The point is\nthat the laser light from the fiber laser (to the THz emitter and detector) and from the UV\nlaser (after passing through the DMD and objective lenses) is fiber-coupled. These fibre-\ncoupled THz antennas are well accepted as fibre-coupled optics in the THz community\nto distinguish them from the free-space sources such as ZnTe, LiNbO3 and two-colour\nplasma. Indeed, the fibre-coupled antennas are widely employed to design portable THz\nimaging systems, such as the device presented in Ref. 29 (Adv. Photonics Res. 3, 2100095\n(2022)).\nReviewer 2 supported the above justification and appreciated the “all-fibre-coupled”\nidea, commenting on this aspect positively: “Your work improves on previous results\nby an increased frame rate and integrating your setup in an all fibre-coupled manner,\nwhich means the inclusion of an imaging fibre.”\n(ii) Additionally, the terms 'in vivo', 'in situ', and 'real-time imaging' are overstated. The\nsystem can only detect skin or air-exposed tissues due to its fundamental limitation:\nmodulation requires direct contact between the silicon wafer and the target. This\nrestricts its applicability for genuine biomedical scenarios where internal body operation\nis essential. In terms of 'real-time imaging', the 2–7 fps frame rate is relatively slow.\nAnswer: The term “in vivo” simply means that the subject being measured is living\nwithout having to be excised or sliced to be thin enough for a transmission measurement,\nwhich is the exact reason for the reflection configuration. As demonstrated in Fig. 6, we\nsucceeded in applying our imaging system to measure living human skin. The term “in\nsitu” is closely related to the “all-fibre-coupled” idea. The imaging head is all-fibre-\ncoupled so that it is portable and can be directed to the region of interest. The system\nintrinsically exhibits the “in situ” attribute as it is “all-fibre-coupled” and we are working\non integrating this imaging system with a robot arm to fully exploit its “in situ” capability\n(similar to the point measurement THz probe in the Picobot, Ref 49 (Sci. Rep. 15, 4568\n(2025)). Regarding the term “real-time imaging”, we’d like to point out a frame rate of 7 fps\nhas already been accepted as real-time in the THz imaging community as shown in Ref.\n28 (Nat. Commun. 11, 2535 (2020)). We demonstrated that our system outperforms the\nprevious system (with the same masks and undersampling ratio) as shown in Fig. 4h in\nthe main text. Compared with the results reported in Ref.28, we improved the frame rate\nto 14.2 fps.\nFinally, the terms “in vivo” “in situ” and “real-time imaging” hereby are not assumed to be\napplicable to internal body operation. Due to the attenuation properties of the THz light,\nit is widely agreed that it more suitable for skin/surface detection.\n1.2. Engineering Integration Over Core Innovation. Key components are taken from\nexisting technologies:\n(1) DMD + silicon wafer for optical THz modulation is a common design.\n(2) Hadamard encoding and [1 −1] masking are conventional single-pixel imaging\nmethods.\n(3) ATR structures are not new to THz applications.\n(4) Image reconstruction uses basic normalized linear superposition, lacking advanced\ncompressive sensing or deep learning approaches.\nThe performance improvements (2–7 fps frame rate, ~100 μm resolution) stem from\ncomponent optimization, not fundamental methodological or physical breakthroughs.\nAnswer: As explained above, the key point (and breakthrough) shown in the manuscript\nis that this system is all-fibre-coupled. Selecting and optimising the correct combination\nof existing technologies to realise the all-fibre-coupled design for the SPI application\nitself is a significant achievement. We’d like to point that the realisation of the wanted\ndesign is very challenging rather than straight-forward. It requires deep knowledge of core\nphysics as well as dexterity with optics.\nFor example, even the selection of THz polarization needs intensive theoretical derivation\nof the formulas as shown in the SI and careful theoretical calculations and experimental\nverification as shown in Fig. 2 in main text.\nAgain, regarding the image reconstruction, it does not use basic normalized linear\nsuperposition approach. Instead, it is reconstructed by multiplying a reconstruction\nmatrix which is obtained by Fourier regularization of the measurement matrix with the L2-\nnorm constraint of the usual compressed sensing minimization problem as shown in Ref.\n52 (Opt. Express 26, 20009 (2018)) and 28 (Nat. Commun. 11, 2535 (2020)). This\napproach first calculates the inversion matrix and stores it in memory. The multiplication\nof the stored inversion matrix allows a very fast image reconstruction with image quality\ncomparable to standard minimization problems. And this approach outperforms the\nusual TV-minimization algorithms, which are too slow for real-time display.\nWe appreciate the deep learning approaches mentioned by the reviewer. Indeed, this\nadvanced approach is planned in our future work. This work explicitly focuses on the\nmost urgent task to accomplish the proof-of-principle design of the hardware.\n1.3. Limited Imaging Validation and Clinical Relevance\nDespite the authors demonstrated the method by imaging porcine tissues and human\nskin wounds:\n(1) Sample diversity is insufficient to represent broad biomedical scenarios.\n(2) Results are qualitative; no quantitative comparison exists against clinical standards\n(e.g., OCT, infrared thermography, ultrasound).\n(3) No histopathological registration confirms imaged structures' physiological\nsignificance.\n(4) Statistical evaluations (SNR, CNR, recognition rates) or cross-sample comparisons\nare absent.\nAnswer: We agree that we have not presented a comprehensive study of the biomedical\nsamples – this would be a separate paper. The work presented focuses on the proof-of-\nprinciple work of the all-fibre-coupled design. Thus, porcine tissue and human skin were\nmeasured to verify that the probe developed works as expected rather to demonstrate\nclinical relevance. We agree with the reviewer that the sample diversity, quantitative\ncomparison, histopathological registration and statistical evaluations are very important.\nBut these elements themselves are better be a separate paper.\nThe above justification is supported by Reviewer 3, “The authors also present\nrudimentary measurements on biological samples, which round the paper off\nnicely”.\n1.4. Low Modulation Efficiency Limits Performance\nSupplementary material reveals a modulation efficiency of ~12%, with only 21% of initial\nblue light energy reaching the silicon wafer due to losses in fibers/lenses. This low signal\ncontrast necessitates strong normalization and background suppression, potentially\ncompromising imaging depth and stability under low-SNR conditions.\nAnswer: Losses in optical fibres and lenses are inevitable. By looking at the physics and\noptics carefully we have managed to design a system which works well and balances all\nthe physical processes involved, demonstrating that our approach actually works\nphysically. Arguably, 12% is a nearly optimal trade-off between signal-to-noise ratio and\nimaging resolution/speed. If we had a modulation nearer to saturation (e.g. 90%), the\nswitch off time for that signal is much longer than the charge lifetime (i.e. just because\nwe are nearer to saturation, the drop to 50% signal takes much longer than the next 40%\ndrop to 10%). This would lead to worse imaging resolution and speed. Hence, if we\nwanted to have better signal-to-noise ratio, this is possible by increasing lifetime and/or\noptical intensity, but it is always an inherent trade off with resolution and speed. To further\nillustrate our system’s capabilities, we have added in more experimental results to\nshowcase the resolution and contrast as suggested by Reviewer 3.\nIn conclusion, this work demonstrated solid engineering capabilities in system\nimplementation and offers a reference for THz imaging integration. However, its\ncontributions remain confined to optimizing existing components rather than delivering\nfield-leading innovation. Coupled with misleading terminology, overclaims, narrow\napplication validation, and overstated clinical significance, the manuscript falls short of\nNature Communications' standards.\nAnswer: We sincerely thank Reviewer 1 for the detailed suggestions and comments on\nour manuscript. Having clarified the misunderstanding regarding our imaging design and\nexplained the reasoning behind the used terminology, we hope that Reviewer 1 now\nappreciates the significance of our work.\nReviewer #2 (Remarks to the Author):\nDear Authors,\nI was asked to review your manuscript NCOMMS-25-44759 \"All-fibre-coupled terahertz\nsingle-pixel imaging for biomedical applications\".\nIn the manuscript you describe the results obtained with a fibre-coupled terahertz single-\npixel imaging system.\nA terahertz source is spatially modulated using an optically controlled silicon SLM.\nThe telecom laser for the terahertz source and detector is fibre coupled and the THz\nfrequency is imaged using TPX lenses, the blue light, used for modulation is fibre coupled\nusing an imaging fibre.\nYour work improves on previous experiments in two ways:\n1. The shorter lifetimes of carriers in your silicon SLM allows for faster modulation and\nultimately higher frame rates.\n2. The demonstration of an all fibre coupled experimental setup paves the way for\nintegration of the method onto handheld devices.\nI am convinced that your evaluation of your data is valid and your collected data is robust\nand I can't find any technical flaws with your manuscript\nHowever, I want to recommend to comment on measurement uncertainties in your\nmanuscript.\nAs far as I understand, most of your measurements are averaged results, it should be\nstraight forward to include confidence intervals/standard deviations in your plots in\nfigures 3-5.\nYour work improves on previous results by an increased frame rate and integrating your\nsetup in an all fibre-coupled manner, which means the inclusion of an imaging fibre.\nThe telecom fibre for the THz source and detector were already fibre coupled in previous\nwork.\nThe core methodology of your experiment, however, stays identical.\nI still want to argue that advancing technology in this way is still significant, especially in\napplied sciences, where the step from the lab into the field often can be challenging.\nYour presentation is very clear and easily understandable.\nAnswer: Thank you for your positive comments. We also appreciate your\nacknowledgment of the significant achievement of the successful demonstration of this\nall-fiber configuration.\nI only have a few suggestion for improvements on your manuscript.\n2.1. As already mentioned a more detailed analysis of errors.\nAnswer: We thank the reviewer for suggesting the error analysis. We analysed the errors\nand added them to Fig. 3 d-e and Fig.5 d-f. The errors in Fig.4 g and h are smaller than the\nsymbol size and are therefore not shown. We’d like to point out the oscillations shown in\nFig. 4g arise from the different subsets of measurement masks (they do not stem from\nmeasurement uncertainty). We use Paley type-I Hadamard matrix to ensure all masks\nexhibit similar spatial frequencies and thus to enable an easy selection of a subset masks\nfor undersampling. However, this does not guarantee all the masks have the same spatial\nfrequencies, which results in the possibility that higher sampling ratio leads to lower\nstructure similarity index.\nIn section “Imaging of cartwheel sample” we modified the manuscript to include the error\nanalysis, which reads: “The solid lines in Figs. 3d-3e represent the mean values, and the\nshaded regions denote the standard deviations across repeated measurements.” In\nsection “Undersampling and imaging speed”, we added the error analysis, which reads:\n“Measurements were repeated and standard deviations were found to be smaller than\nthe symbols in Figs. 4g-4h. We note that the oscillations shown in Fig. 4g arise from the\ndifferent sets of measurement masks rather than measurement uncertainty. Although\nthe Paley type-I masks exhibit similar spatial frequencies, they do not show the same\nspatial frequency. This leads to lower SSIM for higher sampling ratio, i.e., the oscillations.”\nIn section “Imaging of porcine tissue” we added the error analysis, which reads: “The\nsolid lines in Figs.5d-5f represent the mean values, and the shaded regions denote the\nstandard deviations.” The indications of the errors are also presented in the captions of\nFigs. 3-5.\n2.2. You are not comparing the structural similarity (SSIM) with your previous work. I\nwould argue that SSIM and FPS/PPS play an important role when benchmarking your\nexperiments against each other.\nAnswer: Thank you for pointing this out. Compared with our previous work, we achieved\na comparable SSIM, indicating the robustness of the undersampling . We got a value of\nSSIM of 0.85 at sampling ratio of 1 (full set of masks) in the current paper and 0.81 in the\nprevious work – we have added the following information in.\n“The SSIM values (0.85, with a full set of masks) are comparable to our previous results\n(0.81)[28]. Measurements were repeated and standard deviations were found to be\nsmaller than the symbols in Figs. 4g-4h. We note that the oscillations shown in Fig. 4g\narise from the different sets of measurement masks rather than measurement\nuncertainty. Although the Paley type-I masks exhibit similar spatial frequencies, they do\nnot show the same spatial frequency. This leads to lower SSIM for higher sampling ratio,\ni.e., the oscillations.”\n2.3. Fig 5c seems to be taken at lower resolution. Why is that?\nAnswer: We thank the reviewer for the careful observation. The blurring shown in Fig. 5c\narises from a spatial Fourier filter we applied to the image. We revised the figure by\nremoving the filter. The revised figure is shown in revised manuscript.\n2.4. Formatting of formulas in the supplement is often unconventional ($\\times$ is often\nused).\nAnswer: Thank you for spotting this, we have checked this and corrected it.\nOtherwise, I have no concerns for your manuscript being published in Nature\nCommunications.\nAnswer: Thank you very much for your positive feedback and constructive comments.\nReviewer #3 (Remarks to the Author):\nThe authors present an interesting article on the intriguing combination of multiple\ntechniques for a useful THz imaging system. The authors also present rudimentary\nmeasurements on biological samples, which round the paper off nicely. The\nmethodology seems sound and the information provided is sufficient.\n3.1 However, the structure of the text does not correspond to that of the journal. The\n'Results' section contains a great deal of detail about the setup and methods, which\nshould be found in the 'Methods' section.\nAnswer: We thank the review for the careful observation. We deleted this section and\nmerged it mainly into the section “Materials and methods”.\n3.2 The discussion of the effect of THz polarisation on resolution anisotropy is not fully\nconvincing and is not supported by references, simulations or other evidence. Without\nthis, it is merely an assumption and, as such, should not be discussed in such detail.\nAnswer: We thank the reviewer for the suggestion. We re-calculated the resolution using\na knife-edge sample. We found that the resolution of the horizontally and vertically\naligned edge is different. The resolutions are 360 and 660 µm respectively for he\nhorizontally and vertically aligned edges. However, this difference may not only arise from\npolarization effect. It can also arise from the reflection configuration. Since the THz light\nobliquely enters and exits the silicon wafer, the enter and exit positions exhibit a\nhorizontal side shift (see the inset of Fig.1 b), which may worsen the horizontal resolution.\nIn the revised main text, we have justified the details of our system’s capabilities with the\nknife edge results. The new section reads: “We also fabricated a knife-edge sample to\nestimate the resolution, signal-to-noise ratio and image contrast to characterise the\nperformance of the system. The results (Supplementary Fig. 5 & 6) and the method are\npresented in the Supplementary Information.\nIn the revised SI, we have updated the discussion of the polarisation effect on the\nresolution, which reads: “The different resolutions for the horizontally and vertically\naligned edges may arise from the effect of THz polarisation and the reflection\nconfiguration. Due to the reflection configuration, the THz light obliquely enters and exits\nthe silicon wafer. The enter and exit positions exhibit a horizontal side shift (see Fig. 1),\nwhich is likely to worsen the horizontal resolution.”\n3.3 The core achievement is the ability to image at high resolution and high measurement\nrates. While the resolution target presented provides a rough idea of the imaging\ncapabilities, some aspects are unclear.\n- Resolution: The measurements with the resolution target (Siemens star) indicate\nvarying resolution throughout the image. Given the provided data, this could be due to\nthe orientation of an edge (similar to astigmatism) or the position within the field of view.\n- Contrast: The achievable contrast in this image is not provided. It is stated that the\nbackground is zero, which would result in infinite contrast; this is certainly not the case.\n- Homogenity: The images of the resolution target show a highly non-homogeneous\nimage in terms of contrast, signal strength and resolution. While this is not surprising, it\nneeds to be quantified. Is it possible to partially compensate for this inhomogeneity by\ncalibrating each pixel?\n- Noise: The image noise has not been quantified. This can occur between neighbouring\npixels that are expected to have the same signal strength, as well as between\nsubsequently recorded images.\nI suggest applying the razor blade method as a simple experiment to quantify the above\nvalues. Place a razor blade, or another sharp, well-defined edge, at the sample plane,\nthen take images at different blade positions. Rotate the blade by 90 degrees and repeat.\nThe images can then be compared with the well-known and simple ground truth and the\nvalues above can be extracted. I am willing to help if the authors would like to discuss this\nin more depth.\nAnswer: Thank you very much for this suggestion. We have fabricated a knife-edge\nsample to estimate the resolution, contrast and signal-to-noise ratio (SNR). We\ndeposited a layer of gold to cover half of a silicon wafer. We first obtained THz images with\na bare silicon as a reference image. Then we imaged the knife-edge sample. The image of\nthe knife-edge sample is normalised with the reference image to mitigate the adverse\ninhomogeneity effects arising from the THz beam and the blue light. The resolution is\nestimated with the profile of a line perpendicular to the edge. The distance related to the\n10–90% step hight in the profile is assumed to be the resolution. This method is much\nmore precise than barely viewing the image colour variation at the edge. The estimated\nresolution for a horizontally aligned edge is 360 um and 660 µm for a vertically aligned\nedge.\nRegarding the homogeneity, the reviewer also agrees that it is common for a image to\nexhibit non-homogeneity. To mitigate the non-homogeneity, the images presented in the\nmanuscript are compensated by normalising the images with a reference image obtained\nwith a bare silicon (functions as a metal mirror due to total internal reflection). The\ndetailed normalisation method is presented in the SI section “Image normalisation”. And\nSupplementary Fig. 4 compares the results with and without normalisation, clearly\nshowing the obvious homogeneity improvement after the normalisation.\nThe SNR is also estimated with an image of the knife-edge sample. We selected the\nbrightest and darkest regions in the image. The ratio of average value of the brightest\nregion to the standard deviation of the darkest region is assumed to be the SNR. The\nestimated SNR is 41.\nThe brightest and darkest regions are also applied to estimate the contrast. We assume\nthat the contrast is the ratio of the difference average values between these two regions\nto the sum of the average values. The estimated contrast value is 0.7.\nWe added a new section “Resolution, signal-to-noise ratio and image contrast” in the\nsupplementary material for the results discussed above. The following two figures\n(Supplementary Fig. 5 & 6) summarises the results of knife-edge sample, which are\ncopied from the mentioned added SI section.\nSupplementary Fig. 5 Image resolution estimation. Images of a horizontally aligned\nknife-edge sample at different positions (a & b). Images of a vertically aligned knife-edge\nsample at different positions (c & d). The second row (e-h) shows the profiles of the white\nlines in the first row The red circles are the experimental data, and the solid lines denote\nthe fitting result in e-f. Fitting parameters x and σ are also presented in each panel.\ndarkest regions are applied to estimate the Signal-to-noise ratio and image contrast.\n3.4 Other comments:\nLine 103. What does 'short' refer to? Please provide an order of magnitude.\nAnswer: The short lifetime refers to the off-the-shelf silicon wafers’ carrier life, which is\nof the scale of several microseconds. We added a notation to indicate this scale, which\nnow reads: “Off-the-shelf silicon wafers without passivation typically exhibit short carrier\nlifetimes (several microseconds)”.\nLine 128 and following: This focuses on the setup and details rather than the results.\nAnswer: We revised this section and merged it mainly into the section, “Materials and\nmethods”.\nLine 163 and following: This paragraph seems to explain fundamental optics; I suggest\nshortening it drastically.\nAnswer: We thank the reviewer for the suggestion. We revised this section and made it\nmore concise. In the previous version, we discussed both the polarisation and power\ntransmission. In the revision, we deleted the discussion of the polarisation as we agree\nwith the reviewer that this part is fundamental and should be clear for most of the\nreaders. We also shortened the remaining discussion of the power transmission. We'd\nlike to point out that the discussion of the power transmission is necessary as it is\nimportant for the polarisation selection and prism design. In addition, the calculation of\npower transmission is quite complicated as shown by the lengthy derivation presented in\nthe SI.\nLine 179: Why 'also'?\nAnswer: The THz light can be decomposed into ordinary and extraordinary waves in\nterms of the crystal birefringence. It can be also decomposed into s- and p-polarized\ncomponents in terms of total internal reflection. As both the birefringence and total\ninternal reflection can lead to ellipticity change, we discussed them together by using\n“also”.\nIn the revision, this part is deleted as we agree with the reviewer that this part is\nfundamental and should be clear for most of the readers (see the above reply).\nLine 206 and following: Why are both polarizations discussed in detail when the\nexperiment uses just one of them?\nAnswer: As shown in Fig. 2a, a s-polarised THz experiences a transmission loss at the\nquartz-silicon interface while the p-polarised component undergoes no loss. As a result,\na p-polarised component is more suitable for imaging and therefore p-polarisation is\nselected. We revised the manuscript to clarify this point, which reads: “Notably, at the\nquartz-silicon Brewster angle, p-polarised light undergoes no transmission loss,\nfavouring the imaging application. As a result, p-polarised THz is selected in this work,\nand the prism’s base angle is designed to match the quartz-silicon Brewster angle.”\nLine 297: The e-field is certainly not zero.\nAnswer: Thank you for pointing out this mistake! We have revised the sentence to be: “All\nimages show high absolute THz signal values in the metal cartwheel regions, while the\nquartz regions exhibit very low absolute THz signal values due to the Brewster angle.”\nLine 299: See above.\nAnswer: We updated the discussion with the resolution experimental results and added\nthe discussion of the possible resolution effect by the horizontal side shift (see the reply\nabove)\nFig. 3c). The plots have the unit 'electric field', but this is imprecise because it is not clear\nwhere this electric field is located. I believe the authors plotted the receiver signal, which\nis not fully linear in the electric field due to the receivers' frequency-dependent roll-off.\nFurthermore, the setup will have some frequency dependence due to the optics involved\nand their adjustment. Therefore, for d) and e), I suggest using the term 'receiver signal',\nand for a to c, I recommend normalising to a full metal mirror as the sample and using\nthe term 'image contrast' or similar. The same applies to other pictures later in the\nmanuscript.\nAnswer: Regarding the axis label “electric field”, we agree with the reviewer that receiver\nsignal is not fully linear in the electric field due to the receiver’s frequency-dependent\nroll-off and the setup has some frequency dependence due to the optics involved and\ntheir adjustment. We use “receiver signal” to describe the signal as received (Fig. 2b,\nSupplementary Fig. 3a, Supplementary Fig. 4a and 4b) and “normalised THz signal” for\nthe images and signals normalised with Supplementary Eq. 16. We modified the main\ntext to indicate how the axis are labelled, which reads: “We call the resulting intensity the\nnormalised THz signal (see Supplementary Eq. 16) and the unnormalised one the\nreceiver signal, for example, the signal shown in Fig. 2b”.\nRegarding the normalisation, all the images shown in the manuscript are normalised with\na reference image obtained with a bare silicon wafer. The normalisation method is\ndescribed in SI section “Image normalisation”. And Supplementary Fig. 4 compares the\nresults with and without normalisation, clearly showing the obvious homogeneity\nimprovement after the normalisation. We’d like to point out that a bare silicon functions\nas the metal mirror mentioned by the reviewer. As the system is based on total internal\nreflection, a bare silicon wafer well reflects the THz light. Thus, a real metal mirror is not\nneeded to obtain the reference image.\nLine 490 and following: Please revise the naming of the components used. If you are\nunsure, please consult the manufacturer for the correct terminology.\nAnswer: Thanks for the comment. We have revised the component names."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors addressed most of my concerns. However, it is recommended to provide some quantitative data to support the claim that ‘12% is a nearly optimal trade-off between signal-to-noise ratio and imaging resolution/speed’.", "reviewer_2": "Dear Authors,\nthank you for addressing my concerns with your first manuscript.\nI feel that any issues I raised have been resolved and have no concern for your manuscript to be published in Nature Communications.", "reviewer_3": "Thank you to the authors for the revised manuscript and for addressing all of my comments so comprehensively.\nThank you also for the additional knife-edge measurements. I believe these are highly valuable for evaluating such an imaging system. The methodology is sound, and based on the provided data, the obtained values for resolution, SNR and contrast seem plausible. While the interpretation of the anisotropy of the imaging resolution (astigmatism) does not provide a definitive answer, it does offer possible explanations. It would have been great to see a calculation or simulation of this effect, since resolution is one of the key factors of any imaging system. However, this could be the subject of a follow-up paper or letter in a more technical journal.\nI have no objections to the publication of this manuscript."}, "author_response": "Response to reviewers\nReviewer #1 (Remarks to the Author):\nThe authors addressed most of my concerns. However, it is recommended to provide\nsome quantitative data to support the claim that ‘12% is a nearly optimal trade-off\nbetween signal-to-noise ratio and imaging resolution/speed’.\nAnswer: Thank you for the suggestion to include some quantitative data to support\nour comment in the previous response to reviewer document about the modulation\ndepth. The modulation depth is inherently linked to the lifetime of the carriers: a longer\nlifetime will increase modulation depth and improve signal to noise, but at the cost of\nimaging time, while a shorter lifetime improves imaging speed but at the cost of signal\nto noise. The fastest switching rate of the DMD is 20 kHz with period time of 50 μs.\nWith the same laser fluence applied in this work, we achieved modulation depth up to\n60% using silicon wafer with lifetime of 300 μs at the cost of lowering the DMD\nswitching rate, thus, the imaging frame rate. Besides, longer lifetime also increases\ncarrier diffusion length, worsening the resolution (Sci. Adv. 2016; 2 : e1600190). The 12%\nmodulation depth (corresponding to a 7us carrier lifetime) allows us to utilise the\nfastest DMD switching rate and high imaging resolution. On the other hand, a shorter\nlifetime would not result in a faster imaging speed (limited by the DMD switching rate),\nbut would only be detrimental to signal to noise - this is why it is near optimal. A full\ninvestigation of this complex behaviour would require a modulator with a controllable\nlifetime - something we are currently working on but not able to do at this moment.\nTo convey these points in the paper we have added the following into the paper:\n\"While this may seem like a low modulation depth, it works well in practice because\nthe switch off time is shorter than if a higher modulation depth were used. To increase\nthe modulation depth we would need to use a wafer with a longer carrier lifetime, this\nwould improve signal to noise, but at the cost of imaging time and poorer resolution.\nTherefore using the short lifetime of 7 us allows us to utilize the highest DMD switching\nrate to achieve high imaging speed. It also gives rise to high imaging resolution,\nrepresenting a good trade-off between modulation depth, imaging speed, and\nresolution.\"\nReviewer #2 (Remarks to the Author):\nDear Authors,\nthank you for addressing my concerns with your first manuscript.\nI feel that any issues I raised have been resolved and have no concern for your\nmanuscript to be published in Nature Communications.\nAnswer: We thank the reviewer for recommending the publication of this paper.\nReviewer #3 (Remarks to the Author):\nThank you to the authors for the revised manuscript and for addressing all of my\ncomments so comprehensively.\nThank you also for the additional knife-edge measurements. I believe these are highly\nvaluable for evaluating such an imaging system. The methodology is sound, and based\non the provided data, the obtained values for resolution, SNR and contrast seem\nplausible. While the interpretation of the anisotropy of the imaging resolution\n(astigmatism) does not provide a definitive answer, it does offer possible explanations.\nIt would have been great to see a calculation or simulation of this effect, since\nresolution is one of the key factors of any imaging system. However, this could be the\nsubject of a follow-up paper or letter in a more technical journal.\nI have no objections to the publication of this manuscript.\nAnswer: We thank the the reviewer for appreciating the last response. Regarding the\nanisotropy of the imaging resolution, we currently suppose it is the from the convolved\neffects of THz polarisation and the reflection configuration. We agree with the reviewer\nthat resolution is a key factor of an imaging system. However, it takes time to\ndisentangle the convolved effects. We are working on this, the results will be presented\nin a follow-up paper."}]

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