Interference elimination based on the inversion method for continuous-wave terahertz reflection imaging

Yifan Wang; Yifan Wang; Yuye Wang; Yuye Wang; Yuye Wang; Degang Xu; Degang Xu; Degang Xu; Limin Wu; Limin Wu; Guoqiang Wang; Guoqiang Wang; Bozhou Jiang; Bozhou Jiang; Taoying Yu; Chao Chang; Chao Chang; Tunan Chen; Jianquan Yao; Jianquan Yao

doi:10.1364/OE.396611

1. Introduction

Since the first report of the terahertz (THz) imaging by B. B. Hu and Nuss in 1995 [1], it has been proved as a promising approach and applied in numerous fields such as security inspection [2], nondestructive detection [3] and cancer diagnosis [4]. There are two branches during the development of THz imaging. One is the terahertz pulsed imaging (TPI) mainly based on THz time domain spectroscopy (THz-TDS) [5,6], and another is the continuous-wave (CW) THz imaging. For TPI, optical parameters of the sample can be obtained from the THz image with the detection of the phase and amplitude. However, it suffers a slow data acquisition time [1], which is a fatal weakness for the practical application. Especially, the broadband THz wave suffers a frequency dependent focal spot which induces a low spatial resolution [7]. The CW-THz imaging was developed at the beginning of this century [8–11]. This system often employs a single frequency laser and an intensity detector, which sacrifices the broadband spectrum information but enhances the spatial resolution and shortens the imaging time. According to these advantages of THz-CW imaging system, it has been well studied for many practical applications, especially in the biomedical field. The common CW sources include backward wave oscillator (BWO), Gunn diode, Schottky diode, optically pumped gas laser, photomixing based photoconductor and terahertz quantum cascade laser (THz-QCL). Terahertz BWO, Gunn diode and Schottky diode always operate at low frequency. Therefore, a relatively low spatial resolution limits its application [12]. The optically pumped gas laser is popular with its high output power. However, it also has the disadvantages of high cost, bulkiness and severe power fluctuation. THz source based on the photomixing have shown its potential in THz imaging recently [13]. Photomixing based photoconductor is a kind of tunable CW-THz source indicating the advantage in broadband spectrum. But its output power and the energy conversion efficiency need to be improved to meet more practical applications [14]. THz-QCL is going to be a widely used source in CW-THz imaging due to its prominent advantages of compactness, high-stability and easy operation [15]. The spatial resolution will be greatly improved as THz-QCL always operated at high frequency. Although the absorbance at high frequency becomes more severe with the frequency increasing, the high output power can overcome this problem. Thus, a THz image with high resolution and dynamic rage could be obtained by THz-QCL. Moreover, the imaging speed based on THz-QCL have been greatly improved by employing the dedicated detectors [16–18].

Currently, most CW-THz imaging systems are based on transmission mode, because the transmission system is easy to be realized and its systematic error is relatively low. However, the sample thickness should be strictly limited considering its absorption of THz wave. Especially for the freshly biological sample, the sample thickness should be less than several micrometers due to the high absorption of water, which induces a complicated sample preparation. However, for reflection model, the sample with smooth surface can be directly placed in the imaging system. When the sample is liquid or biological tissues, an imaging window is necessary because of the severe diffuse scattering of these samples with rough surface or uncertain shape. Usually, tissues are placed on the imaging window so that the THz wave can be reflected at the interface. It is worth noting that the imaging principle of the CW-THz reflection imaging is quite different from the THz pulsed reflection imaging. Considering that the pulse width of the TPI system is as short as several picoseconds and the thickness of the imaging window is between 1 to 2 mm, the time delay induced by the imaging window is much longer than a pulse duration. Therefore, the waves reflected from the front and rear surfaces are separated, and the signal wave from the sample interface can be purely obtained [19]. However, for CW-THz reflection imaging, there exists interference between the two surfaces of the imaging window, which induces a severe noise to the THz image. Polarization imaging method was proposed to eliminate the Fresnel reflection in order to avoid the interference. The reflectance difference between normal and cancerous tissues with interference was lower than 3% whereas the value without interference was enlarged to over 7% [20]. But this method causes an extreme energy loss which would induce a poor dynamic range. Thus, an effective method to filter out the interference noise of THz image is clearly imperative for the CW-THz reflection imaging.

In this paper, an interference elimination method for CW-THz imaging is proposed based on the inverse calculation. Through the study on the imaging window of the CW-THz reflection imaging with the interference mechanism, the inverse processing is given to realize the interference elimination. The high resistivity float-zone silicon (HRFZ-Si) is selected as the imaging window based on the theoretical calculation to improve the dynamic range of the THz image. Liquids of water and ethanol are used to demonstrated the feasibility of the method with a THz quantum cascade laser (QCL) lasing at 4.3THz. The results show a good agreement with the theoretical value. Moreover, the interference elimination method is performed on the THz images of fresh biological tissues. The accurate information of the tissues is obtained, which shows the advantage on the enhancement of image contrast.

2. Method and experimental setup

2.1 Analysis of the imaging window

Figure 1 shows the model of the imaging window for THz reflection imaging. The sample is placed on the rear surface of the imaging window with contact pressure for imaging. THz wave reflected from the sample-window interface carries the information of the sample. According to the Fresnel’ s law, optical parameters of the sample can be obtained. Here, ${\tilde{n} = n}\,\textrm{ + }\,\textrm{i}\mathrm{\kappa }\; $ represents the complex refractive indices of the medium, where n is the refractive index and $\mathrm{\kappa }{\; }$ is the extinction coefficient. θ₁ is the incident angle. θ₂ is the refractive angle. θ₃ is the emergence angle. The reflection coefficient of the rear surface is defined by Fresnel’s equation:

(1)$${\tilde{r}_s} = \frac{{{{A^{\prime}}_{2s}}}}{{{A_{2s}}}} = \frac{{{{\tilde{n}}_2}\cos {\theta _2} - {{\tilde{n}}_3}\cos {\theta _3}}}{{{{\tilde{n}}_2}\cos {\theta _2} + {{\tilde{n}}_3}\cos {\theta _3}}}$$

(2)$${\tilde{r}_p} = \frac{{{{A^{\prime}}_{2p}}}}{{{A_{2p}}}} = \frac{{{{\tilde{n}}_2}\cos {\theta _3} - {{\tilde{n}}_3}\cos {\theta _2}}}{{{{\tilde{n}}_2}\cos {\theta _3} + {{\tilde{n}}_3}\cos {\theta _2}}}$$

where corner marks s and p represent s and p polarizations, A₂ and ${A}{{^{\prime}}_\textrm{2}}$ are the amplitudes of the incident wave and reflection wave on the rear surface respectively, ${{\tilde{n}}_\textrm{2}}$ and ${{\tilde{n}}_\textrm{3}}$ are the complex refractive indices of the imaging window and sample.

Fig. 1. The model of the imaging window

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Due to the reflection on the front surface and the absorption of the window, A₂ is hard to obtain. Thus, a reference signal is necessary for the calculation of the optical parameters of the sample. The reference signal is usually reflected by a background sample whose optical parameters have been already known. Here, s-polarization is taken as the example, a relative reflection coefficient can be defined as

(3)$${\tilde{r}^{\prime}_s} = \frac{{{{A^{\prime}}_2}}}{{{A_{ref}}}} = \frac{{{{A^{\prime}}_2}}}{{{A_2}}} \cdot \frac{{{A_2}}}{{{A_{ref}}}} = \frac{{{{\tilde{n}}_2}\cos {\theta _2} - {{\tilde{n}}_3}\cos {\theta _3}}}{{{{\tilde{n}}_2}\cos {\theta _2} + {{\tilde{n}}_3}\cos {\theta _3}}} \cdot \frac{{{{\tilde{n}}_2}\cos {\theta _2} + {{\tilde{n}}_{ref}}\cos {\theta _{ref}}}}{{{{\tilde{n}}_2}\cos {\theta _2} - {{\tilde{n}}_{ref}}\cos {\theta _{ref}}}}$$

where $\; {{\tilde{n}}_{{ref}}}$ is the complex refractive indices of the background, and θ_ref is the emergence angle of the background, ${{A}_{{ref}}}$ is the amplitude of the signal reflected from the background. By taking the real and imaginary parts of the Eq. (3) and referring to Snell’s law:

(4)$${n_1}\sin {\theta _1} = {n_2}\sin {\theta _2} = {n_3}\sin {\theta _3}$$

the complex refractive indices of the sample ${{\tilde{n}}_\textrm{3}}$ can be easily obtained.

The reflection wave from the front and rear surface can be spatially separated in the TPI system. However, the reflection waves will superimpose and interfere in the CW imaging system. The interference in the imaging window is analogous to the multi-beam interference in a parallel plate which can be represented as:

(5)$$\tilde{A} = {A_0}[\frac{{{r_1} - {r_2}{r_1}{{r^{\prime}}_1}\exp ({i\delta } )+ {r_2}{t_1}{{t^{\prime}}_1}\exp ({i\delta } )}}{{1 - {r_2}{{r^{\prime}}_1}\exp ({i\delta } )}}]$$

where $\tilde{A}$ is the complex amplitude of the interference wave, A₀ is the real part of $\tilde{A}$, $\mathrm{\delta }{= (4\pi nh)/\; \lambda \cos}{\mathrm{\theta }_{2}}$ is the phase factor, r₁ and r₂ are the reflection coefficients of the front and rear surfaces, t₁ is the transmission coefficient of the front surface, ${r}{{^{\prime}}_{1}}{ ={-} }{{r}_{1}}$ and ${t}{{^{\prime}}_{1}}{ = \; }{{t}_{1}}$ are the reflection and transmission coefficients when the wave is propagating from the negative direction. In conjunction with R = r² and ${tt^{\prime}\; }\,{ = \; }\,{1} - {R}$, the interference intensity finally can be represented as

(6)$$I = \tilde{A} \cdot {\tilde{A}^ \ast } = {I_0}\frac{{{R_1} + {R_2} - 2\sqrt {{R_1}{R_2}} \cos \delta }}{{1 + {R_1}{R_2} - 2\sqrt {{R_1}{R_2}} \cos \delta }}$$

Here, R₁ and R₂ are the reflectivities of the air-window interface and window-sample interface, which relate to the relative complex refractive indices ${{\tilde{n}}_{{21}}}$ and ${{\tilde{n}}_{{32}}}$, respectively. And there are ${{\tilde{n}}_{{21}}}{\; }\,{ = \; }\,{{\tilde{n}}_{2}}{\; /\; }{{\tilde{n}}_{1}}$ and ${{\tilde{n}}_{{32}}}{\; }\,{ = \; }\,{{\tilde{n}}_{3}}{\; /\; }{{\tilde{n}}_{2}}$. For simplicity, the influence of extinction coefficient to the reflectivity can be ignored since it is much smaller than the influence of refractive index for both window and sample. Then, an approximation can be taken as ${{\tilde{n}}_{{21}}} \approx {\; }{{n}_{2}}{\; /\; }{{n}_{1}}{ = }{{n}_{{21\; }}}$ and ${{\tilde{n}}_{{32}}} \approx {\; }{{n}_{3}}{\; /\; }{{n}_{2}}{\; = \; }{{n}_{{32}}}$. Considering the interference intensity is determined by R₁ and R₂, Fig. 2 illustrates the relationship of the reflectivity (R₁ or R₂) and the relative refractive index (n₂₁ or n₃₂) at different incident angles under s-polarization. Due to the fact that the refractive index of the imaging window n₂ is always larger than n₁, R₁ is proportional to the n₂₁. However, the situation is more complex for R₂, where R₂ varies non-monotonically as the relative refractive index changes. It is noticed that R₂ varies more sensitive at the interval ${0\; }\, \le {\; }\,{n32\; }\, \le {\; }\,{1}$, which means a larger difference as the relative refractive index changes. When the relative refractive index was greater than 1, the reflectivity will decrease to a small value which will cause a low dynamic range. Therefore, the relative refractive index n₃₂ should be smaller than 1 in order to obtain a THz image with high contrast. Thus, the optimization of the imaging window is necessary for the choice of relative refractive index.

Fig. 2. The relationship between the R₁ (R₂) and n₂₁(n₃₂) under the s-polarized wave at the incident angle of 0°, 15°, 30°.

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Usually, the quartz plate with the low refractive index dispersion, low Fresnel reflection and low THz absorption is adopted as the imaging window. However, when the refractive index of sample is close to the quartz at high frequency, n₃₂ will be close to 1 [21]. Thus, R₂ will be decreased to a small value as shown in Fig. 2, leading to a low dynamic range of CW-THz image. An alternative is to find a high refractive index material. High resistivity float-zone silicon (HRFZ-Si) is a stable, nontoxic and easy processing material. It is an ideal imaging window with a non-dispersion refractive index of 3.42 at THz band. The high reflectivity of the HRFZ-Si is helpful to obtain THz image with high dynamic range.

In addition, the incident angle is also an important factor contributing to the reflectivity. Figure 2 shows that the reflectivity at larger incident angle is higher than the reflectivity at smaller incident angle under the same relative refractive index. The oblique incidence may increase the dynamic range of the system. However, it is known that the reflectivities of s and p polarized waves at the oblique incidence are quite different, and the parabolic mirror often used in the THz imaging system can make a mixing polarization of the beam [22], which will cause an unpredictable reflectivity. Especially, if the incident angle met the Brewster condition, the interference would become extremely complex. Thus, the normal incident was chosen in the following experiment to avoid this problem.

2.2 Method of interference elimination

Most CW-THz imaging system needs a chopper due to the low responsivity of the THz detector. The CW-wave is chopped to a sinusoidal signal thus the interference will always exist. Here, the temporal distribution of the output intensity from the CW source can be represented by a function f(t). If the multi-path interference was nearly instantaneous compared to the response time of the detector, the measured average power (or intensity) could not be influenced by the temporal distribution of the intensity. Equation (6) can be directly used to get the reflectivity at the window-sample interface. However, If the response time of the detector reached the same order of magnitude as the multi-path interference time, the temporal distribution should be taken into consideration. It is assumed that the time delay of a round induced by the imaging window is Δt, then there is:

(7)$$f(t )\approx f({t + \Delta t} )$$

Based on Eq. (7), the temporal distribution of THz intensity would not influence on dual-beam interference, but would induce a complex interference under the multi-beam. Considering that the intensity of the first and second reflection waves of HRFZ-Si are much higher than the third reflection wave so that the third reflection wave can be ignored. Therefore, for the process of interference elimination, the multi-beam model can be replaced by dual-beam model as follows:

(8)$${A^2} = a_1^2 + a_2^2 + 2{a_1}{a_2}\cos \delta$$

where A is the interference amplitude, a₁ and a₂ are the amplitudes reflected from the front and rear surfaces, δ is the phase factor mentioned above. Taking the temporal distribution of the output intensity into account, Eq. (8) changes into

(9)$$\int\limits_\tau {{A^2}(t )} dt = \int\limits_\tau {a_1^2(t )+ a_2^2(t )+ 2{a_1}(t ){a_2}(t )\cos \delta dt}$$

where τ is the sinusoidal cycle. According to the Fresnel’s law,

(10)$${a_1}(t) = {r_1}\sqrt {f(t)}$$

(11)$${a_2}(t) = {t_1}{t^{\prime}_1}{r_2}\sqrt {f(t)}$$

Equation (9) can be reconstructed as follows:

(12)$$\int\limits_\tau {{A^2}(t )} dt = \int\limits_\tau {{R_1}f(t )+ {R_2}{{({1 - {R_1}} )}^2}f(t )+ 2({1 - {R_1}} )\sqrt {{R_1}{R_2}} f(t )\cos \delta dt}$$

Equation (12) shows the analytical formula of the interference at the imaging window. The aim of the interference elimination is to inverse the actual sample reflectivity R₂. Considering that the left part of the Eq. (12) can be directly obtained by the detector, and R₁ and cosδ can be calculated when the refractive index and thickness of the imaging window are determined, R₂ can be easily inversed with these parameters. After the R₂ of each pixel has been inversed, a real image without the interference can be obtained. It should be mentioned that the if interference elimination is processed under the dual-beam interference model, there will exist some error compared to the multi-beam interference. Theoretical calculation shows that the error is sensitive to the phase factor. Take the air as the example, the intensity of the dual-beam interference at the constructive phase is 15% (normalized to the total intensity) higher than that of the multi-beam in the Si window. And this difference will decrease nonlinearly with the phase changing from constructive to destructive. Overall, If the temporal distribution of the intensity of the source can be ignored, then Eq. (6) can be directly used to inverse the image. Otherwise, dual-beam model may help to simplify the complex multi-beam interference.

The analysis above is based on the ideal interference, only considering the difference of the amplitudes of the interference beams. Actually, the interference is also influenced by other two main factors: spectral width and beam size. Because the linewidth of CW-THz laser is narrow, the influence of the spectral width can be ignored. For raster scanning, the beam must be focused to the sample in order to obtain a high-resolution image. Thus, the spots on the front and rear surfaces are not at the same size, which will cause a partial overlap of the beams reflected from the front and rear surfaces. The partial interference adds errors to the left part of Eq. (6) or Eq. (12), disturbing the result of interference elimination. Therefore, a modified interference model should be taken into consideration. Here, the detected intensity by the detector consists of two parts: one is from the overlap part of beams contributing to the interference and another is from the non-overlap part of beams that can be considered as the background. It is assumed that the detected intensity can be represented by I, and then there is I = I_a+I_b, where I_a is the overlap part and I_b is the background part. In order to obtain the real THz image of sample, only the overlap part I_a can be substituted into Eq. (6) or Eq. (12) to inverse the actual reflectivity of the sample R₂, whereas the background part I_b must be removed from the raw THz image before the process of interference elimination. Especially, it should be mentioned that reflective intensities from both front and rear surfaces of the window contribute to the background I_b. Thus, I_b is not a constant but changing with the reflectivity of the sample. The different samples may cause different errors in I_b. If the refractive indices of samples were 1.7 and 2.0, the error in reflectivity of rear surface of the Si window would be below 5%. Considering that both the reflectivity of the sample and the ratio of the contribution from front and rear surfaces are unknow, an approximation must be taken here. Since the beam is focused on the rear surface of the imaging window, the beam on the front surface is bigger than that on the rear surface. Therefore, it is assumed that the beam from front surface dominates the background. Thus, I_b could be determined using the air background ignoring the influence of the sample by the comparison between the theoretical and experimental interference intensities.

Figure 3 shows the flowchart of the interference elimination approach, including three steps as follows.

• Step 1: Window characterization: the refractive index and thickness of the window must be measured first to acquire the reflectivity R₁ at the air-window interface and the phase factor cosδ.
• Step 2: Background filtering: comparing the theoretical and experimental interference intensity at the same phase under the air to determine the background part I_b. Then, subtracting I_b from the raw THz image.
• Step 3: Inversion of R₂: Substituting R₁, cosδ and preprocessed image into Eq. (6) or Eq. (12) to calculate R₂ of each pixel. Then, the interference eliminated THz image is obtained.

Fig. 3. The flow chart of the process of interference elimination in three steps.

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It should be mentioned that cosδ is a key factor in the interference elimination. Errors in the measurements of window thickness and refractive index may induce an unpredictable impact on the final result. For example, a 1μm measurement error will induce a 1.5% intensity error at constructive phase but a 17% intensity error at destructive phase at 4.3THz under the Si window. The intensity error varies nonlinear with the phase factor and it will be enlarged with the phase changing from constructive to destructive, which indicates that the better choice of the window is near the constructive phase. Also, the phase factor cosδ could be modified by the experimental result.

2.3 Experimental setup

Figure 4 shows the setup of the imaging system based on the THz-QCL lasing at 4.3THz with an output power of 1.7W. The Golay cell (GC-1P, Tydex Ltd.) is used as detectors operating at room temperature. A chopper is set in front of the laser to fit the response rate of the Golay cell. The THz wave is collimated by the gold coated 90° off-axis parabolic (OAP1 and OAP2) mirrors with a focus length and a diameter of 50.8 mm. Collimated wave is focused to the sample with an incident angle of 0 degree. Since the reflectivity of the p and s polarized waves are quite different at the oblique incidence, the normal incidence is chosen to avoid the disturbance of the wave polarization [22]. A sample holder is mounted on a computer-controlled x-y linear motored stage (LTA-HS Newport Ltd.) for raster scanning. The HRFZ-Si with different thicknesses is used as image window. The soft tissues or liquid samples are placed on the HRFZ-Si window and was adjusted to closely contact with the sample holder. The biological tissues can keep hydrated during the measurement with the scanning speed of 10pixels/s and room temperature of 20℃. A beam splitter is to reflect the beam from the sample to the detector. The signal collected by the Golay cell is restored in a lock-in amplifier (SR830, Stanford Research Systems Ltd.). The intensity of each pixel in the lock-in amplifier is reconstructed to form an image through a LABVIEW program.

Fig. 4. The experimental setup for the reflection geometry imaging system.

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3. Results and discussions

3.1 Liquid samples

In order to study on the interference phenomenon of the HRFZ-Si window experimentally, the air background, water and ethanol are chosen as the tested sample. Considering the uniformity of samples, the reflectivity of a point is firstly studied here. The refractive index of the air, ethanol and water at 4.3THz are about 1, 1.45 and 2, respectively [23,24]. The extinction coefficient of the water is about 0.3, whereas it is almost equal to zero for ethanol and air due to the weak absorption. The reflectivity of the air (i.e. the reflectivity from Si-air interface), ethanol and water (i.e. the reflectivity from Si-sample interface) are calculated to be 0.30, 0.16 and 0.08 under the THz normal incidence, respectively. Figure 5 illustrates the theoretical interference intensity of the three samples changing with the phase factor cosδ. It should be mentioned that due to the half-wave loss at the front surface of the imaging window, the constructive interference intensity appears when cosδ equals to -1, whereas the destructive interference intensity appears when cosδ equals to 1. It can be found that the interference intensities of different samples show a larger difference when cosδ is smaller than 0.7. The difference disappears when cosδ is greater than 0.7. Moreover, the interference intensity near the destructive phase is relatively low which will induce a low dynamic range.

Fig. 5. The relationship of the interference intensity and phase factor.

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To make sure the influence of the phase factor, HRFZ-Si plates with different thicknesses of 474μm, 486μm, 971μm, 1058μm and 775μm are chosen as the imaging window. The corresponded values of the phase factor cosδ are -0.994, -0.347, -0.242, 0.463 and 0.941, respectively. The total injected THz power to the Si window was used for the normalization. Figure 6 illustrates the experimental measurement of the interference intensity of the three samples at different phases. With the phase changing from constructive to destructive, the interference intensities for three samples decrease gradually, which correspond well with the theoretical calculation. Different samples show a decreasing difference on the interference intensity as the phase factor cosδ changing from -1 to 1. It is worth noting that the experimental interference intensity is a little different from the theoretical value. Table 1 shows the comparison of the theoretical and experimental interference intensities of the air background at different phases. It is seen that the experimental value is smaller than the theoretical value for the first four data whereas the experimental value is larger than the theoretical value for the last data near the destructive phase. This phenomenon corresponds well with the analysis in section 2.2. The theoretical calculation is based on the ideal interference. But the partial overlap of the reflected beams from two surfaces of imaging window causes the difference between the experiment and the theoretical calculation. In other words, a part of the input intensity to the imaging window makes no contribution to the interference due to the partial overlap of the reflected beams, which won’t change with the phase factor and can be regarded as the background intensity. When cosδ is near the destructive phase, the theoretical interference intensity for air is close to zero, whereas the experimental value is greater than the theoretical value due to the background intensity. However, the data of 775μm still deviates from the calculated intensity too much after removing the background. As is mentioned above, measurement errors may account for it. Therefore, we slightly modified the phase factor of 775μm window.

Fig. 6. The experiment result of the interference intensity for air background, ethanol and water.

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Table 1. Comparison of the experimental and theoretical interference intensity at different phase under the air background

View Table

Based on the analysis above, to finally determine the reflectivity of the samples, the background part must be removed before the interference elimination. After removing the background, the data must be normalized before the inversion processing. The reflectivity of the air was chosen as the standard value to calculate the normalized ratio. Considering the Golay cell used in the experiment is a kind of low response detector, the temporal distribution of the intensity can be ignored so that the inversed method should be based on Eq. (6). The results of the interference elimination on point data for ethanol and water are illustrated in Fig. 7. The reflectivity of the air is also presented as a comparison. The black dotted lines represent the theoretical reflectivity of the air, ethanol and water, which are 0.3, 0.16 and 0.08, respectively. Except the window thickness of 775μm, the reflectivities of the ethanol and water measured using HRFZ-Si windows with different thicknesses are close to the theoretical values. The average inversed reflectivities of the ethanol and water are 0.165 and 0.086 with the standard deviation of 0.013 and 0.004 respectively, which correspond well with the theoretical values. The fluctuation of the reflectivity of the ethanol and water under different windows are mainly caused by the THz power fluctuation and measurement errors. It is noticed that the error of the calculated reflectivities becomes large near the destructive phase. As is mentioned above, the measurement errors will be enlarged with the phase changing from constructive to destructive. That is the reason why the data of 775μm window deviates so much. Thus, it indicates that the imaging window with proper thickness should be selected near the constructive phase and to avoid the destructive phase.

Fig. 7. Calculated reflectivity of air, water and ethanol at different interference phases.

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3.2 Biological tissues

The method of interference elimination has been proved effectively to restore the reflective intensity of the point data. Thus, it has a great potential for applications of THz imaging. Usually, THz biomedical imaging needs an imaging window to overcome the severe absorption and scattering of the fresh tissues. Therefore, the interference phenomenon induced from the imaging window always exists in CW-THz biological imaging. It heavily degrades the image quality and has a negative impact in assisting biomedical diagnosis. In this part, THz reflection imaging of fresh tissues based on interference elimination method is demonstrated. Here, fresh swine tissues and excised brain tissues of mice are selected as the imaging samples. The animal experiments were performed in accordance with the China animal welfare legislation and were approved by the Third Military Medical University Committee on Ethics for the Care and Use of Laboratory Animals.

Figure 8 illustrates optical images, raw THz images and processed THz images of the biological tissues mentioned above. The THz images are under the same colorbar. The size of the THz images are 75pixels×55 pixels with the scanning step of 100μm. Figures 8(a) and (b) show the visual and raw THz image of fresh swine tissue. The profile of the tissues in the raw THz image is relatively clear and corresponds well with the visual image. However, it should be noticed that the difference between muscle and fat in the raw THz image is quite obscure. Figure 8(c) shows the THz image of swine tissue after the process of interference elimination. The boundary of the profile becomes more sharpen compared with the background, and the muscle and fat can be easily identified in the processed THz image. Figure 8(d) is the processed THz image of Fig. 8(b) with image adjust algorithm. The boundary in Fig. 8(d) is still unclear comparing with Fig. 8(b). Figures 8(e) and (i) shows the visual image of the brain tissues of mice with and without glioma. The glioma is marked by the red cycle on the visual image. Figure 8(f) and (j) show the raw THz images of the normal and cancerous mice brains. Since the brain tissue is soft and there always exists a contact pressure to cling the tissues to the imaging window, the profile of the brain in the THz image is a little different from the visual image. Also, it is seen that the glioma area shows an obscure difference with the normal area in Fig. 8(j). Figures 8(g) and (k) is the processed image of the normal and cancerous tissues through the interference elimination, respectively. H&E-stained images for the samples in Figs. 8(e) and (i) are taken to illustrate the actual position of the glioma, as indicated in Figs. 8(h) and (l). It can be found that the image of normal brain in Fig. 8(g) shows an enhanced contrast to the air background with a great evenness. For the glioma sample, the low reflectivity area of the brain in Fig. 8(k) indicates the glioma area comparing to the H&E-stained image. The position of glioma shifts a little, which can be explained by the contact pressure from the sample holder.

Fig. 8. Visual image of (a) swine tissue, (d) mice brain tissue without glioma and (g) mice brain tissue with glioma; original THz image of (b) swine tissue, (e) mice brain tissue without glioma and (h) mice brain; processed THz image of (c) swine tissue, (f) mice brain tissue without glioma and (i) mice brain; H&E-stained images of (h) mice brain without glioma and (l) with glioma; (d) processed THz image by image adjust of swine tissue.

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To evaluate the contrast enhancement of the interference eliminated image, the image contrast is defined as follows:

(13)$$C = \frac{{{I_M} - {I_m}}}{{{I_M} + {I_m}}}$$

where I_M is the maximum value of the image and I_m is the minimum value of the image. The contrasts of raw THz images of Figs. 8(b), (f) and (j) are 0.268, 0.179 and 0.214, respectively. The contrast of Fig. 8(d) is 0.5391. The contrasts of processed THz images of Figs. 8(c), (g) and (k) are 0.858, 0.765 and 0.794, respectively. It is clearly that the image adjust algorithm can enhance image contrast, but not as obvious as the interference elimination does. Comparing with the raw THz images, the contrasts of the processed images are enhanced obviously through the interference elimination method. Furthermore, considering about the power fluctuation and the jitter of the scanning stage, this method may need a further optimization. The incident angle and polarization are also important factors to the CW-THz reflection imaging. Different cases such as oblique incidence or mixed polarization should be take into consideration in the further study.

4. Conclusion

In this paper, we propose an interference elimination approach for the CW-THz reflection imaging through the study on the imaging window. Based on the theoretical calculation, the HRFZ-Si plate with high refractive index is chosen as the imaging window to improve the dynamic range of THz image. Considering about the thickness of the window and the partial overlap of the reflected beam, the interference of image can be eliminated by using the knowledge of the interference mechanism. The method is applied to liquid samples of water and ethanol based on THz-QCL lasing at 4.3 THz. The sample reflectivity can be well restored and corresponded well with the theoretical analysis. Moreover, the interference elimination method is performed on THz images of fresh biological tissues. The accurate information of the tissues is obtained, which shows the advantage on the enhancement of image contrast. This work will contribute to the wider practical application of THz reflection imaging technique in the biomedical field with improved performance.

Funding

National Key Research and Development Program of China (2015CB755403); National Natural Science Foundation of China (61771332, 61775160, 62011540006, U1837202).

Acknowledgments

This work was supported in part by the National Defense Technology Innovation Special Zone.

Disclosures

The authors declare there are no conflicts of interest related to this article.

References

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Phase factor	-0.994	-0.347	-0.242	0.463	0.941
Experimental value	0.510	0.454	0.439	0.367	0.285
Theoretical value	0.710	0.626	0.603	0.397	0.065

Interference elimination based on the inversion method for continuous-wave terahertz reflection imaging

Abstract

1. Introduction

2. Method and experimental setup

2.1 Analysis of the imaging window

2.2 Method of interference elimination

2.3 Experimental setup

3. Results and discussions

3.1 Liquid samples

3.2 Biological tissues

4. Conclusion

Funding

Acknowledgments

Disclosures

References

Cited By

Figures (8)

Tables (1)

Equations (13)

Optics Express