# Terahertz Single-Pixel Imaging Improved by Using Silicon Wafer with SiO\({}_{2}\) Passivation
## 2 Experimental Setup  
Figure 1 illustrates the light-controlled THz modulation and single-pixel imaging system based on a home-built THz time-domain spectroscopy (THz-TDS) system [19]. A pair of biased low-temperature-grown GaAs (LT-GaAs) photoconductive antennas, which are illuminated by femtosecond laser pulses (\(\lambda=800\) nm, \(<\)100 fs, 80 MHz; Coherent Vitesse 800-5), are used to generate and detect THz radiations. Collimated THz wave with a diameter of 3.82 mm is directed onto a high-resistance silicon wafer (2000 \(\Omega\)-cm, 500 \(\upmu\)m thick), both surfaces of which are passivated with SiO\({}_{2}\). The passivation is realized following a high-temperature thermal oxidation process that is routine in the field of solar cells [20]. The transmitted THz wave is then collected by a single-pixel THz detector. The beam profile (size 4 mm \(\times\) 4 mm) of an 808 nm linearly polarized (the polarization is parallel to the optical platform) continuous-wave (CW) laser is first patterned by a digital micromirror device (DMD). The DMD, detached from DLP3000 (Texas Instruments), has 608 \(\times\) 684 micro-mirrors, each of which has a pitch of 7.6 \(\upmu\)m and behaves as a binary reflector with the maximum frame rate reaching 4000 Hz. The laser beam is then projected onto the passivated silicon. Unless otherwise specified, all the experiments in this work were performed with a high laser power of 330 mW. When the laser spot reflected by the DMD is changed from black to white, the THz transmittance through the passivated silicon decreases from a high level to a low level, i.e., from \"1\" to \"0\". For terahertz single-pixel imaging based on compressed sensing (CS) approach [7; 11; 21], the target, such as a cartwheel patterned in a gold film, is deposited on top of the front SiO\({}_{2}\) layer. Figure 1: Schematic of the experimental setup for the THz single-pixel imaging. The CW laser is reflected on the modulator by DMD, and target objects are cartwheels patterned in gold film, which is deposited on the modulator substrate. For a THz image of \(N\times N\) pixels to be measured, a series of masks are projected onto the target. The cumulative signal is collected using a single-pixel detector. A series of such measurements with the total number of \(M\) lead to [7; 21]  
\[Y^{\text{CS}}=P^{\text{CS}}X\,, \tag{1}\]  
where \(Y^{\text{CS}}\) is an \(M\times 1\) vector of measurements, \(X\) is the image with \(N\times N\) pixels ordered in a \(N^{2}\times 1\) vector, and \(P^{\text{CS}}\) denotes the series (with the number of M) of \(N\times N\) projection masks \(p^{\text{CS}}_{N\times N}\) ordered in an \(M\times N^{2}\) matrix. For each measurement, the projection mask \(p^{\text{CS}}_{N\times N}\) can be generated with Hadamard coding, which consists of \"1\" and \"\(-\)1\" elements with each row orthogonal to all other rows [22]. In experiments, the Hadamard projection mask \(P^{\text{CS}}\) composed of \"1\" and \"\(-\)1\" elements is replaced by the substation of two masks \(P^{\text{CS,I}}\) and \(P^{\text{CS,II}}\), both of which consist of \"1\" and \"0\" elements [12], i.e.,  
\[P^{\text{CS}}=P^{\text{CS,I}}-P^{\text{CS,II}}\,, \tag{2}\]  
Therefore, \(Y^{\text{CS}}\) in Equation (1) should be replaced by \(Y^{\text{CS}}=Y^{\text{CS,I}}-Y^{\text{CS,II}}\), where \(Y^{\text{CS,I/II}}=p^{\text{CS,I/II}}X\). Using the CS approach, the number of measurements for assembling the image can be much smaller than the number of image pixels that is \(M\ll N^{2}\). The sampling ratio is defined as  
\[S_{\text{R}}\equiv M/N^{2}\,, \tag{3}\]  
Even with highly undersampled measurement sets, the image can still be accurately reconstructed.