The scene to be recovered is flood illuminated with an intensity modulated beam oscillating at a reference modulation frequency fm and a single-pixel camera combined with a lock in amplifier
collects the return signal. Figure 3.10 shows the experimental setup of the lock-in single-pixel cam- era. Here, the sinusoid modulated amplitude beam is created from a continuous wave (CW) beam by an electro-optic modulator (EOM). In more details, a CW linearly polarized Gaussian beam of wavelength λ = 532 nm and power P=150 mW propagates through the optical system shown in Fig. 3.10 (a). The beam outgoing from the laser is collimated by a set of lenses not shown in the figure. The half-waveplate and the polarizing beam splitter (PBS) set the beam power at 130 mW. The beam passes through an electro-optic amplitude modulator (EOM) in order to produce a laser beam whose amplitude is sinusoid modulated in time at a reference frequency. A converging lens L4 of focal f = 100 mm focuses the beam into the EOM. Acting as a variable waveplate, the EOM changes the polarization state of the laser according to an external driving voltage. We then change the temporal modulation of the beam amplitude by placing at the EOM output a linear polarized (LP) whose axis is perpendicular to the input beam polarization. We then apply a sinusoid ampli- tude modulated external voltage by a programmable function generator. Since the EOM requires a voltage of 170 V to induce a 90◦change in the beam polarization, we amplify the 10 V amplitude sinusoid signal. The bi-convex lens L5 of focal length f=100 mm collimates the diverging beam outgoing from the EOM. The sinusoidal beam at the output of the EOM oscillates in time at a modulation frequency of 5 MHz.
Figure 3.10 (b) shows the lock-in single-pixel camera setup. A sinusoid amplitude modulated beam is flood-illuminating a 45x45 cm2 3D scene by the bi-concave lens L1 of focal length f=- 50 mm. The return signal is collected from a single pixel camera by the lens L2 (focal length f=50 mm). A DMD and a Silicon photomultiplier detector (SiPM, C14455-3050GA) compose the single-pixel camera. The SiPM detector (or single channel Multi-Pixel Photon Counters, module C14455-3050GA) is manufactured by Hamamatsu Photonics and it has an effective photosensitive area of 3 mm of diameter and a PDE of 34% at 532 nm. All the 2836 the pixels of the SiPM are connected to the unique analog output of the single channel SiPM. The DMD is manufactured by Texas Instruments and it has 1024x768 micromirrors of 16x16 µm2.
A 50 mm focal length lens (L3) collimates the beam after the DMD and a long working distance microscope objective (magnification factor 50X, Mitutoyo Plan Apo) focuses the transmitted beam on a free-running SiPM detector. In order to isolate the desired signal from the background light of external sources present in the scene, we use a 532 nm band-pass filter with a 40 nm bandwidth
before the detector. A lock-in amplifier extracts the desired signal from the analog output of the SiPM sensor according to the reference signal. The reference signal is provided by a copy of the electric signal generated with the programmable function generator. We acquire the return signal by 64 x 64 pixels raster scan masks on the DMD and collect the reflected light onto the detector. Each raster scan mask collects the return signal scattered back from a 0.7x0.7 cm2 transverse portion of the field of view for an overall imaging area of 45x45 cm2. The masks projection on the DMD and the lock-in amplifier acquisition are synchronized by a Matlab software code.
In order to evaluate the depth resolution of the proposed method, the scene is composed by a 24x24 cm2 square target shown in Fig. 3.11(b). The target consists of a series of 6x6 or 12x12 cm2squares, 6x12 cm2rectangles and a "T" letter. The targets are placed at varying depth within a range of 0-22 mm in order to evaluate the depth resolution of the suggested method. In details, the targets are located at an increasing relative depth of 0, 5, 6, 7, 10, 11, 12, 14, 16, 17, 21, 22 mm respect to the farthest target.
L4 x z y CW Laser, 532 nm EOM HV amplifier function generator 2 PBS waveplate LP sinusoidal amplitude modulated beam (b) (a) L5 x z y 532 nm filter Objective Lock-In amplifier SiPM detector 3D scene L1 L2 imaging lens sinusoidal amplitude modulated beam L3 illumination backscatter reference signal
Figure 3.10: 3D imaging by a lock-in single-pixel camera. a) A CW beam passes through an electro-optic modulator (EOM) to obtain a sinusoid modulated amplitude beam. The EOM acts as a Pockels cell modulator that varies the polarization of the beam linearly with the applied voltage. A copy of the electric signal produced by the function generator is provided in input to the lock-in amplifier as a reference. b) A sinusoid amplitude modulated beam flood-illuminates the 3D scene and a single-pixel camera composed by a SiPM detector and a DMD collects the signal scattered back from the 45x45 cm2 field of view. The lock-in amplifier then filters the detected signal according to the reference signal and provides the in-phase and the 90◦out-of-phase component of the return at each acquisition.
In order to set the lock-in cut-off frequency and efficiently isolate the return signal, we use a filter order n = 5 and a time constant τ = 100 ms for a 5 MHz modulation frequency. These values correspond to a settling time of 1.48 s and a cut-off frequency bandwidth fBW = 0.60 Hz, as
reported in Tab. 3.1. In this case the acquisition time of the lock-in poll duration is 0.1 seconds per mask at a sampling rate of 132. The lock-in amplifier provides in output the in-phase and the 90◦out-of-phase component (Eqs. 3.9) of the return at each acquisition. We then proceed with the 3D retrieval of the scene following the procedure described in Section 3.2.