1. Introduction

Attenuated total reflection (ATR) has been applied to spectroscopy and imaging applications in a wide variety of multidisciplinary research topics [1–4]. It is realized by guiding the beam from a denser medium to an absorptive rarer medium at an angle greater than the critical angle. Since the evanescent wave excited at the interface interacts with the sample with an amplitude decaying exponentially with the orthogonal distance from the interface, ATR is very useful to record the superficial layer characteristics of liquids and solids.

Terahertz (THz) waves can be used to extract physical and chemical information from many macro-biomolecules [5], since their rotational and vibrational energy levels are located in this frequency range. The common methods, either transmission or reflection, have some limitations in obtaining THz spectra and images. Transmission of THz waves through polar substances suffers from significant absorption [6], while the traditional reflection method has to avoid diffuse reflection and combine several complex reference calibrations [7]. THz-ATR can avoid such limitations and obtain the reference precisely. It has experienced a rapid development, especially in spectroscopy, including the theoretical calculation of optical constants, as well as experimental determination and differentiation of samples [8–11]. In contrast, only a few studies concentrated on imaging. The reason may be the relatively low responsivity of focal plane array (FPA) imagers in the THz frequency range and their high cost, being inferior to those enabled by similar devices in the infrared range [12–15]. Hence, it is more common and cost-effective to get THz-ATR images via scanning. The existing scanning methodologies can be categorized into two types. One is to scan the sample deposited on the patch in close contact with a prism made of the same kind of material. By moving the patch above the fixed prism, it has been used to get the THz-ATR images of living cells [16]. The other one is the so-called vertically scanning method, where the prism is moved in the vertical plane to have the sample on its top surface scanned. It simplifies the system and has been used to record the THz-ATR images of biological tissues [17].

There are several works focusing on the nature of THz-ATR spectroscopic systems [18,19]. However, few studies have been conducted to develop new imaging methodology or to analyze imaging systems. In this paper, we aim towards this goal by giving an in-depth analysis of the vertically scanning imaging system, trying to account for related phenomena and propose corresponding solutions to the problems encountered during scanning. The work discusses mainly the basis of prism design and polarization selection. The prism angle has a significant impact on the occurrence of total internal reflection, effective ATR imaging area, prism utilization, output height of the reflected beam, and spatial resolution. The polarization of the beam affects the data accuracy provided that secondary reflection and prism deflection are considered. The experimental results agree well with the theoretical calculations. The study on performance optimization is helpful for accuracy improvement in quantitative studies and the promotion of THz-ATR scanning imaging technique in practical applications.

2. Setup and method

The setup of the vertically scanning imaging system is shown by Fig. 1(a), showing similarities to the one in [17]. The utilized beam power of the THz laser (FIRL100, Edinburgh Instruments Ltd) exceeds 40 mW at 2.52 THz. To eliminate the influence of power fluctuations, two Golay cells (GC-1P, Tydex Ltd) are used to simultaneously detect the signal and reference beams, which are divided by a silicon plate acting as a beam splitter. The beam chopped at 50 Hz is incident onto a silicon (n_p = 3.42, α = 0.05 cm⁻¹) Dove prism along the + x axis. The prism is connected with a motorized translation stage (SHOT-302GS, Sigma Koki Ltd) enabling its movement in the y-z plane. The aspherical Tsurupica lenses focus the incident beam onto the prism-sample interface, and subsequently collect the outgoing beam into the detector. The intensity of each pixel is recorded and reconstructed to form the final image through a LabVIEW program. The scanning speed is determined by the stage and approximates to 10 pixels/s in the present system. The step size is set to 200 μm for the imaging experiment.

 

Fig. 1 (a) Experimental setup and (b) principle of the THz-ATR scanning imaging system.

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The imaging principle is illustrated by Fig. 1(b). m, h, and n_p are the side length, height, and refractive index of the prism, respectively. θ, θ₁, θ₂, and θ₃ are the base angle, the incident and refractive angles at the slant surface, and the incident angle at the top surface, respectively. When the prism moves along the y axis, the sampling spot scans the sample along the same axis with the same step. When the prism moves along the z axis with a step d, the spot scans the sample along the x axis with another step r that satisfies the relation in Eq. (1).

3. Results and discussions

3.1 Prism design

The total internal reflection (TIR) condition must be always fulfilled. Distilled water (n = 2.05 at 2.52 THz) is used in this paper as the standardized sample for its certain representativeness and universality. In the absence of water, the incident intensity is completely reflected at the prism-air interface with a critical angle of 17°. In the presence of water, the reflected intensity at the prism-sample interface with a critical angle of 37° is reduced relative to the incidence. Therefore, the base angle of the prism should be larger than 21° to reach the prerequisites.

The effective ATR imaging area is a key factor to consider during prism design. As can be seen from Figs. 2(a) and 2(b), there are two kinds of prisms with different base angles leading to different imaging areas. In the former case, the base angle ranges from 21° to 38°, so that only part of the surface can be imaged in the ATR geometry. In the latter case, the base angle is larger than 38°, so that the entire surface can be imaged. The effective ATR imaging area, where ATR really takes place, depends mainly on the side length along the x axis rather than that along the y axis. Therefore, it is assessed by the effective scanning length along the x axis, as indicated by dotted lines with arrows at their ends. Two types of ATR prisms were designed and fabricated to verify the significance of the effective ATR imaging area. Prism 1 (θ = 30°, m = 34.6 mm, h = 10 mm) and Prism 2 (θ = 49°, m = 34.8 mm, h = 20 mm) exemplify these two cases, respectively. The upward movement of the prism causes the scanning spot to move from Point A to Point D. We classify the range of incidence relative to the prism along the z axis into three parts. When a beam from Part (1) enters, it is higher than the top surface to have the sample penetrated. When a beam from Part (2) enters, the scanning spot falls into the effective ATR imaging area, making the collected intensity partially reduced due to ATR absorption. Beams ① and ② indicate the beginning and end of the effective imaging, with Points B and C correspondingly marking the position of their spots on the sampling surface. For Prism 1, BC < AD, showing that the imaging area is smaller than the top surface of the prism. For Prism 2, BC = AD, showing that the imaging area equals to the top surface of the prism. Beam ③ illuminates the center of the surface at Point O. When the beam enters from Part (3), e.g., Beam ④, no intensity can be collected into the detector. The theoretical calculation reveals that the effective ATR scanning length of the two prisms are 19.8 mm and 34.8 mm, respectively. The ineffective length AB in Prism 1 is 7.4 mm. We scanned these two prisms at a step size of 100 μm to perform the verification. The results are displayed with normalized intensities in Figs. 2(c) and 2(d), respectively, each showing the pixel intensities of an arbitrary line parallel to the x axis at their top sides. The experimental results conclude that the effective ATR scanning lengths are 19.3 mm for Prism 1 and 34.4 mm for Prism 2. The ineffective length in Prism 1 is 7.3 mm. These results agree with the theoretical ones. The region between the 310th and 370th pixels in Fig. 2(c) accounts for the air gap between the prism and its mount, where THz waves can be collected but will not enter the prism.

 

Fig. 2 (a) and (c) scanning process and THz-ATR imaging results, respectively, of Prism 1; (b) and (d) scanning process and THz-ATR imaging results, respectively, of Prism 2.

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The ratio of the effective ATR imaging area to the entire upper surface is quantified by Eq. (4),

Figure 3 shows the relationship of η_eff and η_uti with the base angle using the black and red curves, respectively. It is seen that the actual base angle cannot be too small or too big. When it approaches the lower limit, η_eff significantly decreases, making proper sample placement challenging, as only a fraction of the prism can be used for imaging. Besides, the convergence angle of the focused beam impinging on the sampling surface may break the TIR condition. On the contrary, when the base angle is large enough for η_eff to reach its maximum, the utilization of the prism along the z axis is not recommended. Since the ATR reflectivity will be increased with the base angle θ, which increases with the incident angle θ₃ at the sampling surface, the intensity attenuation and image contrast will be reduced. Given that the beam spot along the propagation direction is projected onto the sampling surface under an angle, the actual sampling beam size is bigger than its optimal value. This effect becomes more severe with the increasing base angle, resulting in worse spatial resolution.

 

Fig. 3 Effective ATR imaging area percentage and the utilization curve of the prism.

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The beams reflected from the prism will not always possess the same height. There is a height difference Δh along the z axis which is illustrated by Fig. 4(a). It can be calculated by Eq. (6) and mapped by Fig. 4(b), with m_s signifying the scanning length along the x axis within the effective ATR imaging area.

 

Fig. 4 (a) Schematic diagram of the height difference of the output beams. (b) Dependence of the height difference on the base angle and scanning length.

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Since the optical path from the fixed lens to the sampling surface changes during scanning, the beam focal point will be deviated, as shown in Fig. 5. The focusing lens is fixed at Point A. When the beam illuminates the prism at Point B, its focal point will be situated at the center of the surface indicated by Point C. When the beam illuminates the prism at Point D, there is a deviation between the focal point E and the sampling point F. Such deviation makes the image resolution deteriorated from its center towards its boundaries along the x axis. To observe the spatial resolution and assess the optimal scanning area of our system, we can calculate the deviation length of the beam focus to compare with the Rayleigh range of the incident beam. The Rayleigh range corresponds to a Gaussian beam, and is defined as the distance from the beam waist to where the spot increases by a factor of $\sqrt{2}$. The beam inside this range exhibits its minimum spread with an acceptable increase in its spot diameter. If the focal deviation is within the Rayleigh range, the deterioration extent of the spatial resolution is acceptable.

 

Fig. 5 Schematic diagram of the focal deviation.

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According to the product specifications, the THz laser operates in its fundamental mode. It is assumed that the incident beam is Gaussian. When the beam focal point is at Point C, the propagation can be characterized by Eq. (7) with the complex beam parameters of each element and the ABCD matrix of the prism-air interface [21].

Figure 6 shows the dependence of the deviation length on the base angle and scanning length. The deviation increases with m_s to a more severe extent for smaller base angles, but decreases with θ to a more severe extent for greater scanning lengths. The Rayleigh ranges of the beams were measured by using the same scanning imaging system without a prism inserted in the optical path prior to THz-ATR imaging. The results for the focal lengths of 30 mm, 50 mm, and 100 mm are 1.4 mm, 2.3 mm, and 8.4 mm, respectively, through the typical knife-edge method. Then, the defocusing effect can be assessed by imaging solid blood agars of different lengths via prisms with different base angles under different focal lengths. We sliced three agars with lengths of 3.5 mm, 5.5 mm, and 12.0 mm, and put them at the surface center along the x axis in Fig. 7(a). Figures 7(b)–7(d) show the imaging results via Prism 1 with a base angle of 30° and focal lengths of 30 mm, 50 mm, and 100 mm, respectively. Figures 7(e)–7(g) show the imaging results via Prism 2 with a base angle of 49° and focal lengths of 30 mm, 50 mm, and 100 mm, respectively. It is seen that the defocus effect is more severe for the base angle of 30° than 49°. The blurring effect observed in Fig. 7(g) may be attributed to the large sampling beam size resulting from it being projected onto the sampling surface under an angle. The optimal spatial resolutions along the y axis at around the centers in Figs. 7(b)-7(g) were measured by the knife-edge method to evaluate the performance of each system. They were recorded as 439 μm, 626 μm, 870 μm, 369 μm, 334 μm and 1215 μm, respectively. These values might be related to the sample position, as well as the beam projections on the slant and top surfaces of the prism. The spatial resolutions on the left and right sides of the center should exhibit a bilateral symmetry. However, it is rather challenging to place the objects at the exact surface center. Therefore, by qualitatively comparing the spatial resolutions along the y axis, the defocus effect is more severe with the base angle of 30° than 49°, for the same shift from the center along the x axis.

 

Fig. 6 Dependence of the focal deviation on the base angle and scanning length.

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Fig. 7 THz-ATR imaging of solid blood agars with different lengths.

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3.2 Polarization selection

The final ATR image consists of the ratios of the pixel intensities in the image obtained with the sample (sample image) to the image without the sample (reference image). However, the accuracy of the sample image and reference image will be affected by the secondary reflection and prism deflection to varying degrees. In order to assess the data accuracy of the final ATR image under different polarizations, the attenuation rate is used thereafter to discuss the above effects via Eq. (10), where I_target and I_background are the averaged values of the selected target and background regions in the final ATR image, respectively.

Figure 8(a) and Figure 8(b) illustrate the optical paths during the scanning with a sample, showing clearly the secondary reflections in the effective ATR imaging area. The solid Beam ① and dashed Beam ② indicate the outgoing beams in a single reflection and a secondary reflection, respectively. They are parallel, since θ₄, θ₆, and θ₈ equal to θ₂, and θ₇ equals to θ₃. The sampling spot to be investigated is marked by Point A, which is located in the background region and sample region in Figs. 8(a) and 8(b), respectively. Points B and C represent the subsequent illuminating positions on the top surface due to the secondary reflections. The positions of Points B and C may not all be covered by the sample. If one point is covered, we label it “s.” If it is not covered, we label it “b.” Therefore, eight different situations can be grouped for Points “ABC” as “bss,” “bsb,” “bbs,” “bbb,” “sss,” “ssb,” “sbs,” and “sbb.” Fig. 8(a) exemplifies the former four situations, while Fig. 8(b) exemplifies the latter four. To simplify the discussion, the homogeneous distilled water was used as the sample in simulating the sample image and the reference image without the sample. Figures 8(c) and 8(d) show the theoretical attenuation rate of Point A in these two cases, respectively. The solid and dashed curves correspond to p- and s-polarizations, respectively. There may exist a deviation over the different situations under the same polarization in each figure. It is attributed to the mixture of the absorption from Point B and Point C with that from Point A. This effect increases the uncertainty of the attenuation rate that is subjected to the size, location and homogeneity of a sample. Furthermore, the attenuation rates in Fig. 8(c) under s-polarization, and under p-polarization for base angles above 31°, are greater than 0. They are clearly deviated from the ideal situation, where the attenuation rate for the background should be 0. Therefore, this phenomenon will degrade image quality with nonuniform background, and cause inaccurate attenuation rate due to the errors of I_target and I_background. When the base angle is below 31°, the difference of the attenuation rates over the four possible situations is negligible for p-polarization, whether Point A is located in the background region or sample region. Hence, p-polarization brings less error. It should be mentioned in the actual operation that the background region is recommended to be selected at a position shifted from the sample along the y axis by the value of the sample size along the x axis for error reduction.

 

Fig. 8 Schematic diagram of the secondary reflection effect with the investigated sampling spot in the (a) background region and (b) sample region, respectively. Attenuation rate of the investigated sampling spot in the (c) background region and (d) sample region, respectively, under different polarizations and various secondary reflection situations.

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The experimental verification was carried out by imaging a drop of water. Figures 9(a) and 9(b) were obtained by ATR imaging using the prism with a base angle of 30° under p- and s-polarizations, respectively. Figures 9(c) and 9(d) were obtained by ATR imaging using the prism with a base angle of 49° under p- and s-polarizations, respectively. The color bars show the normalized ATR reflectivity. The background intensity is obviously more uniform under p-polarization, but is nonuniform for the shaded area on the left side of the sample under s-polarization. The simulated and the measured attenuation rates of the shaded area and the sample are displayed in Table 1. The simulated results include all the possible situations, while the measured results show an average value. This is because the attenuation rate is affected by the matter covering Points A, B, and C, targeting the exact area in either the background region or the sample region that suits a specific situation is challenging. The satisfactory agreement between the simulated and measured results proves the above analysis of the secondary reflection effect to be correct.

 

Fig. 9 THz-ATR imaging results of a drop of water that prove the secondary reflection effect. (a) and (b) correspond to the base angle of 30° under p- and s-polarizations, respectively. (c) and (d) correspond to the base angle of 49° under p- and s-polarizations, respectively.

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Table 1. Simulated and measured attenuation rate of the shaded area and the sample

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Prism deflection within the incident plane also influences the data accuracy. Figure 10 shows the schematic diagrams of the counter-clockwise and clockwise deflections of a prism. The beam suffers from a two times higher angle deflection outside of the prism compared with that of the prism. This angle, together with the distance between the prism and lens, determines the shift of the beam spot on the lens along the z axis. The acceptable upper limit of this shift is up to the effective aperture of the lens.

 

Fig. 10 Prism undergoing a counter-clockwise (left) or a clockwise (right) deflection.

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Besides the position, the pixel intensities in both the sample and reference images are also going to be influenced by prism deflection. We simulated the change of the attenuation rate of distilled water for p-polarization and s-polarization on the prism encountering a deflection angle. Every possible secondary reflection case has been considered. The results are mapped in Fig. 11, giving the dependence of the attenuation-rate change on the base angle from 21° to 70° and the deflection angle from 0° to 1°. The first two rows correspond to the prism with a counter-clockwise deflection under p- and s-polarizations, respectively. The next two rows correspond to the prism with a clockwise deflection under p- and s-polarizations, respectively. The four columns correspond to the four situations related to secondary reflection, namely “sss,” “ssb,” “sbs,” and “sbb,” respectively. The scale of the color bar is in the unit of percentage (%), and unified for each situation in the same row. Positive values mean that the attenuation rate is increased compared with that for the standard circumstances without prism deflection. Negative values mean that the attenuation rate is reduced. Change becomes more severe with the increasing deflection angle. By comparing the averaged attenuation-rate changes of the four situations under different polarizations, we get that s-polarization makes for a slightly higher stability than p-polarization. By comparing the results of the four situations in the same row, it is seen that s-polarization exhibits more prominent differences of the attenuation-rate changes across the four situations. In other words, the attenuation-rate change under p-polarization is less susceptible to secondary reflection. The maps exhibit smooth changes of the attenuation rates with the increasing base angle, except for the ones (α_m) around 31° and 32°, where mutations appear. This phenomenon is attributed mainly to the incident angle θ₅ at Point B in Fig. 8. When the base angle is smaller than α_m, θ₅ is smaller than the critical angle for the prism-air interface. Both the sample scan and the reference scan at Point B suffer from ordinary reflection. When the base angle exceeds α_m, θ₅ is larger than the critical angle for the prism-air interface, and will increase with the base angle. When the base angle is equal to α_m and the deflection angle increases from 0° to 1°, θ₅ will intersect the critical angle for the prism-air interface, but will decrease under counter-clockwise deflection and increase under clockwise deflection. In other words, the two kinds of reflections exist at the same time for α_m. The explanation also accounts for the similar mutation effect appearing in the curves of the attenuation rate in Fig. 8.

 

Fig. 11 Simulated change of the attenuation rate of distilled water on the prism encountering a deflection angle ranging from 0° to 1° in the counter-clockwise and clockwise directions.

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To verify the theoretical analysis, we imaged a drop of distilled water, and then compared the attenuation-rate changes under the deflected prism and the aligned prism. A deflection angle of 1° in both the counter-clockwise and clockwise directions was exerted on the prism. Table 2 and Table 3 list the changes in attenuation rate for the base angles of 30° and 49°, respectively. As has been stated, it is challenging to target an exact area described by a specific situation. Hence, along with the simulated results for the four different situations, their average value is also listed in parenthesis for comparison with the experimental values. For the base angle of 30° and p-polarization, the measured and simulated results are reduced by 0.57% and 0.55%, respectively, in the counter-clockwise direction and increased by 0.57% and 0.56%, respectively, in the clockwise direction. For the base angle of 30° and s-polarization, the measured and simulated results are reduced by 0.43% and 0.47%, respectively, in the counter-clockwise direction and increased by 0.49% and 0.51%, respectively, in the clockwise direction. For the base angle of 49° and p-polarization, the measured and simulated results are reduced by 0.94% and 0.96%, respectively, in the counter-clockwise direction and increased by 0.97% and 0.98%, respectively, in the clockwise direction. For the base angle of 49° and s-polarization, the measured and simulated results are reduced by 0.51% and 0.47%, respectively, in the counter-clockwise direction and increased by 0.61% and 0.50%, respectively, in the clockwise direction. The experimental results match well with the above theoretical analysis. Although p-polarization attains a slightly lower stability than s-polarization, it is more likely to avoid the influences brought by secondary reflection. Based on the overall consideration of the secondary reflection and prism deflection, p-polarization is preferred in the vertically scanning THz-ATR imaging system.

Table 2. Changes in the attenuation rate of the sample (deflection angle: 1°, base angle: 30°)

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Table 3. Changes in the attenuation rate of the sample (deflection angle: 1°, base angle: 49°)

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4. Conclusion

Detailed analysis of the optimization for vertically scanning THz-ATR imaging has been presented. The theoretical and experimental results show good agreement. The optimum prism design was studied, considering the total internal reflection condition, effective ATR imaging area, utilization of the prism, output heights of the reflected beams, and spatial resolution. In addition, polarization was studied with the goal of error reduction considering the secondary reflection and prism deflection. Complex beam parameters were introduced to calculate the focal deviation, which were compared with the Rayleigh range to propose the acceptable sample size along the x axis. P-polarized THz waves, especially for base angles below 31°, are recommended to achieve minimum error. This work will contribute to the wider practical application of THz-ATR scanning imaging technique in different fields with improved performance.