Single-Photon Computational Imaging System Based on Multi-Pixel Photon Counter

Abstract

Existing single-photon computational imaging systems always combine single-photon avalanche diode (SPAD)/photomultiplier tube (PMT) and time-correlated single-photon counting (TCSPC) together to collect the signals for imaging. However, the high equipment complexity and cost limit the wide applications of single-photon computational imaging systems. To overcome this problem, in this paper we propose to employ multi-pixel photon counter (MPPC) as the signal receiver to simplify the system. Due to the linearity of the output amplitude of MPPC, the number of received photons can be directly quantized; thus, the TCSPC is not necessary in our proposed imaging system. Experimental results show that the proposed system could obtain the 256 × 256 pixels images through 2000 measurements; the photons per pixel could be reduced to about 0.1.

1. Introduction

Single-photon imaging is an emerging optical computational imaging technique [1,2,3,4], which has great potential in cutting-edge research and precision system engineering. Such systems typically employ single-photon sensitivity detector and photon counter to receive light intensity signals and acquire valuable information, propelling the rapid developments in 3D imaging and laser lidar [5,6,7,8,9], biological imaging [10,11,12], underwater imaging [13,14,15,16,17], astronomical detection [18,19,20], and quantum technology [21,22,23,24,25]. Early single-photon imaging systems utilized point-scanning mechanisms and single-photon detectors to collect photon data. However, mechanical scanning leads to time-consuming measurements and high complexity in imaging systems; the image distortion caused by scanning error may also be introduced.

To avoid the problems in point-scanning mechanism, single-pixel imaging (SPI) scheme is introduced for single-photon imaging [26,27,28,29,30,31]. SPI employs spatial light modulators (SLM) or digital micromirror devices (DMD) to generate multiple illumination patterns that interact with the object; then, the single-pixel detector is used to capture the total light intensity transmitted or reflected by the object. Finally, the object image is reconstructed through various algorithms [32]. Compared with point-scanning mechanism, single-pixel imaging requires a much smaller number of measurements for imaging. Since the output of single-photon detectors such as avalanche photodiode (APD) [33,34], single-photon avalanche diode (SPAD), and photomultiplier tube (PMT) has low linearity and limited amplitude, existing single-photon computational imaging systems always employ the time-correlated single-photon counting (TCSPC) technique to quantize the number of received photons for imaging [28,29,30,31]. Such systems are complex and costly. Additionally, superconducting nanowire single-photon detectors (SNSPD) [35,36] and transition edge sensors (TES) [37] have excellent performance in terms of detection efficiency, dark count rate, and response rate, and could identify photon number information. However, low temperature usage and higher costs hinder the widespread applications of single-photon imaging.

In order to reduce the complexity and cost of existing single-photon imaging systems, we propose a system with multi-pixel photon counter (MPPC) as the only detector. MPPC has the advantages of high linearity, low cost, fast response, and insensitivity to magnetic fields [38]. Since the number of received photons can be directly quantized by the readout amplitude of MPPC, the TCSPC equipment is not necessary in our proposed system. Thus, the complexity and cost of single-photon imaging system could be significantly reduced. In the proposed system, Hadamard patterns are employed to encode objects. The object image is reconstructed through inverse Hadamard transformation. Experimental results show the effectiveness of our system. The two sets of results show that images can be reconstructed when photons per pixel is about 0.1.

The remaining sections of this paper are organized as follows. Section 2 presents the principles of the proposed method. Section 3 shows the experimental results. Section 4 presents the discussion on our experimental results. Section 5 concludes the whole paper.

2. Methods

2.1. Principle of the Imaging System

The schematic of single-photon computational imaging system is shown in Figure 1. The system is developed based on the single-pixel imaging scheme. A pulsed laser is used as the light source and the light passes through a beam expander (BE) and an attenuator; the target image is illuminated by the light. A digital micromirror device (DMD) is used to generate a set of Hadamard basis patterns to modulate the light reflected from objects. The modulated light intensity signals are measured by MPPC, the data acquisition (DAQ) device converts the received light intensity signal into digital signal for processing. Since the number of received photons can be directly quantized by the readout amplitude of MPPC, the TCSPC equipment is not necessary in our proposed system.

2.2. Principle of MPPC

The MPPC is a new type of single-photon detector composing of multiple single-photon avalanche photodiodes (SPAD). As shown in Figure 2a, a SPAD unit includes a quenching resistor and an avalanche photodiode (APD) operating in Geiger mode. The Geiger mode allows obtaining a large output by way of discharge even when detecting a single photon. Once the Geiger discharge begins, it continues as long as the electric field in the APD is maintained [38]. To halt the Geiger discharge and detect the next photon, a quenching resistor connected in series with the APD is used to stop avalanche multiplication in the APD. In this technique, when the output current due to Geiger discharge flows through the quenching resistor, a voltage drop occurs and the operating voltage of the APD connected in series drops [39]. In addition, the MPPC has an integrated temperature control circuit, which can keep the MPPC running stably in an environment with fluctuating temperature and reduce the impact of noise such as dark count.

As shown in Figure 2b, the output current caused by the Geiger discharge is a pulse waveform with a short rise time ~10 ns, while the output current when the Geiger discharge is halted by the quenching resistor is a pulse waveform with a relatively slow fall time ~100 ns [39]. Each pixel in the MPPC outputs a pulse at the same amplitude when it detects a photon. For one photon, the output voltage is ~30 mV. The final output signal is a superposition of multiple pixel output signals. The greater the number of photons illuminated to the MPPC, the greater the amplitude. The current maximum voltage of MPPC is 2 V, so the dynamic range of the measured photon number is from 0 to about 67.

2.3. Hadamard SPI Method

Due to Hadamard single-pixel imaging having better noise-robustness than Fourier single-pixel imaging [40,41,42], we employ Hadamard basis patterns to obtain measurement values. A series of Hadamard patterns is projected onto the target object; the different voltage signals are detected using a single-pixel detector and recorded by a data acquisition device. This process can be expressed as follows:

$$D(u,v)=E+k{\displaystyle \sum _{x=1}^M{\displaystyle \sum _{y=1}^{M}O(x,y)\cdot P(x,y;u,v)}},$$

(1)

where $k$ is a scale factor whose value is determined by the size and position of the detector's detection surface; $O(x,y)$ is the target object;$E$ represents the detector's response to the background light. $P\left(x,y;u,v\right)$ represents $M\times M$ Hadamard basis patterns, which can be obtained by applying an inverse Hadamard transform (IHT) to a delta function $\delta \left(u,v\right)$,

$$P(x,y;u,v)=H^{-1}\{\delta (u,v)\}$$

(2)

where $\left(x,y\right)$ is the coordinate in the spatial domain and $\left(u,v\right)$ is the coordinate in the Hadmard domain. $H^{-1}\left\{\right\}$ denotes an inverse Hadamard transform (IHT), and,

$$\delta (u,v)=\left\{\begin{array}{l}1,u=u_0,v=v_0\\ 0,\mathrm{otherwise}\end{array}\right..$$

(3)

in the initial basis patterns $P(x,y;u,v)$, the element values are "+1" and "−1", but the DMD cannot modulate the negative light intensity values. Thus, differential measurement methods are used for measurements. Dividing $P(x,y;u,v)$ into two patterns: positive pattern $P_{+}(x,y;u,v)$ and negative pattern $P_{-}(x,y;u,v)$, satisfies the following relationship:

$$P(x,y;u,v)=P_{+}(x,y;u,v)-P_{-}(x,y;u,v),$$

(4)

where,

$$\begin{array}{l}{P}_{+}(x,y;u,v)=[1+H^{-1}\{\delta (u,v)\}]/2\\ P_{-}(x,y;u,v)=[1-H^{-1}\{\delta (u,v)\}]/2.\end{array}$$

(5)

After performing the differential measurement, the following equation is obtained:

$$\begin{array}{l}{D}_H(u,v)=D_{+}(u,v)-D_{-}(u,v)\\ =k{\displaystyle \sum _{x=1}^M{\displaystyle \sum _{y=1}^{M}O(x,y)\cdot P_{+}(x,y;u,v)}}-k{\displaystyle \sum _{x=1}^M{\displaystyle \sum _{y=1}^{M}O(x,y)\cdot P_{-}(x,y;u,v)}},\end{array}$$

(6)

where $D_{+}(u,v)$ is called the positive coefficient and $D_{-}(u,v)$ is called the negative coefficient. According to Equation (6), each spectral coefficient of the reconstructed image is obtained and the ambient noise is eliminated.

Finally, the IHT is conducted to reconstruct the object image; the reconstruction equation can be expressed as follows:

$$I_O=H^{-1}\left\{D_H\right\}.$$

(7)

where $I_O$ denotes the reconstructed image; $D_H$ is the spectrum composed of spectral coefficients.

3. Results

The picture of imaging system is shown in Figure 3. The wavelength of the pulsed laser (Cnilaser, MDL-PS-450-60 mW, Changchun, China) is 450 nm and the repetition frequency is set as 5 MHz. The magnification of BE is 10. A USAF resolution chart is used as the imaging target. The DMD (ViALUX, V-9501, Chemnitz, Germany) contains 1920 × 1080 individual mirrors with the size of 10.8 µm × 10.8 µm. The DMD carries out a set of 256 × 256 pixels Hadamard basis patterns to modulate the object. Here, we combined 4 × 4 micromirrors as one cell. Then, an MPPC (Hamamatsu, C13852-3050GA, Shizuoka, Japan) is used to collect the photon signals. Finally, the oscilloscope (RIGOL, MSO7054, Suzhou, China) is used to record signals. For each pattern, the peak value of the pulse is recorded as the measured value.

First, we compare the reconstruction results of USAF resolution chart at different average photons per measurement (PPM). The number of measurements is set to 4000 and the average photons per measurement is 0.97, 3.9, 11.3, 27.9, and 44.7, respectively. The reconstruction results are shown in Figure 4a. The images are 256 × 256 pixels. As can be seen, the image quality is better at 2.73 PPP (photons per pixel) because more photons are received by the MPPC due to higher light intensity. When PPM is reduced to 11.3 and 27.9, the image could still be reconstructed well, corresponding to 0.69 and 1.71 PPP. However, compared to the last image, the image surrounding information like the number “3” and “4” is invisible, although the image contrast seems high. When PPM is reduced to 0.97 and 3.9, corresponding to 0.06 and 0.24 PPP, the image quality is low, but the stripes can still be distinguished. In addition, we take images with the same photon count and measurement time using a CMOS camera; the results are shown in Figure 4b. The camera can capture USAF resolution chart at 44.7 PPM but cannot capture images at other PPM. This demonstrates the low-light imaging capability of our system.

Next, we compare the reconstruction results at different measurements, which are 1000, 2000, 3000, and 4000, respectively. For the letter “M”, the average photons per measurement is 8.1, corresponding to 0.12, 0.24, 0.37, and 0.49 PPP. For the USAF resolution chart, the average photons per measurement is 3.9, corresponding to 0.06, 0.12, 0.18, and 0.24 PPP. We use image contrast to provide a quantitative metric [27]. The image contrast is defined as: $C=(I_{\max }-I_{\min })/(I_{\max }+I_{\min }).$ The reconstruction results are shown in Figure 5a. For the letter “M”, at 1000 measurements, the image is slightly mosaicked, although the image contrast is well. From 2000 to 4000 measurements, the image quality and contrast are gradually getting better. For the USAF resolution chart, when the number of measurements is below 1000, the resolution chart cannot be recognized, and the image contrast is low. As the number of measurements increases, the image quality also becomes higher. At 3000 and 4000 measurements, the details of reconstructed images could be clearly distinguished. In addition, cross-sectional analysis of the local area of the recovered images (shown as the red line in Figure 5a) is shown in Figure 5b. The results show that image details can be distinguished when the number of measurements is 2000, corresponding to 0.12 PPP.

Finally, we compared several different single-photon imaging methods, and the results are shown in

Table 1. The comparison of different single-photon imaging methods.

Method	Resolution	PPP	Detector
GI [27]	35,000 pixels	0.2	SPAD + ICCD
FFPGI [29]	128 × 96 pixels	0.1	SPAD + TCSPC
HSPS [30]	64 × 64 pixels	19.5	SPAD + TCSPC
Ours	256 × 256 pixels	~0.1	MPPC

. From Table 1, our system has the better performance in terms of resolution and PPP. In addition, the other three methods all use the combination of SPAD and ICCD (intensified CCD, used as a bucket detector) or TCSPC, which generally has a higher cost. In contrast, our system uses a MPPC that costs less than $2000, promoting development for practical applications.

4. Discussion

The experimental results confirm the effectiveness of the proposed system. For conventional single-photon detectors like the commonly used SPAD, the price is generally more than $20,000. In addition, TCSPC equipment is required, and the price is generally more than $30,000 [26,27,28,29,30,31]. For SNSPD [35,36] and TES [37], the price is usually over $100,000. The proposed system uses an MPPC instead of these devices to collect light intensity, thus, this system has a lower cost (~$2000) and has better performance in terms of resolution and PPP. Although the system includes a DMD, the cost is not high because the cost of a single DMD chip is as low as a few hundred dollars.

However, the linear dynamic range of MPPC is relatively narrow, so it is easily saturated under high light intensity conditions. This may cause signal distortion, limiting their application in some strong light detection scenarios. Moreover, since MPPC is an array of multiple pixel cells, crosstalk may occur between adjacent pixels, which will reduce the accuracy of the detector.

In future research, it becomes critical to improve the resolution of the images, e.g., 512 × 512 pixels, 1024 × 1024 pixels (megapixel), and larger if possible. This is achievable because existing DMDs can reach megapixels. Moreover, image reconstruction algorithms should be improved further for large-scale and low-light images. These improvements will facilitate the application of the method in various environments, e.g., long-range imaging and biomedical imaging.

5. Conclusions

In this paper, we present a single-photon computational imaging system based on MPPC. The number of received photons can be directly quantized by the readout amplitude of MPPC, thus, the TCSPC equipment is not necessary in our proposed system. Experimental results show that our system restores the image of 256 × 256 pixels through only 2000 measurements, achieving imaging with ~0.1 photons per pixel. This system paves the way to achieve low-cost single-photon imaging.