Large-area single photon compressive imaging based on multiple micro-mirrors combination imaging method

Qiu-Rong Yan; Hui Wang; Cheng-Long Yuan; Bing Li; Yu-Hao Wang

doi:10.1364/OE.26.019080

1. Introduction

Single photon imaging is a kind of high sensitivity imaging detection method for ultra-weak illumination [1]. It has been applied in various fields, such as night vision, biological imaging, remote sensing, spectral imaging in astronomy [2–8], etc. To realize high-sensitivity imaging, several types of spatially resolving detector have been developed, such as the intensified CCD (ICCD), electron multiplying CCD (EM-CCD), APD arrays, etc. The ICCD and EM-CCD working in photon counting mode, require a very high frame rate and very low circuit noise, so deep cooling is a necessity and the manufacturing cost is not modest. Because of difficulties in fabrication and unstable performance, the resolution of APD arrays is still relatively low [9–11]. An alternative method to obtain high resolution image is scanning imaging plane with a point or small-APD arrays detector, but this method reduces the stability of the system and significantly increases imaging time due to low photon collection efficiency [12–14].

Single-pixel imaging based on compressed sensing (CS) theory provides a new solution to problems above [15–17]. In the scheme of single-pixel imaging, the optical image is modulated by a DMD and then focused on a single point detector. The two-dimensional image can be reconstructed from light signals detected by single point detector and random patterns loaded into DMD. This technique can significantly reduce the number of measurements and then shorten the imaging time. Also, because the luminous flux collected by a single photon point detector in each measurement is much larger than that in scanning detection, single pixel imaging achieves much larger measurement signal-to-noise ratio (SNR) [18,19]. In 2012, Wen-Kai Yu et al. proposed a single photon compressive imaging method based on single-pixel imaging technique. Compared with traditional photon counting imaging, higher sensitivity has been verified theoretically and experimentally [12,20,21].

In a single-pixel imaging system, like a CCD in a conventional camera, the DMD is placed on imaging plane of the objective. The larger the area of the DMD used for the image plane, the easier it is to achieve large-aperture, wide-field imaging. The larger the objective image on the DMD, the higher resolution image can be reconstructed. However, the reconstruction of high resolution image based on CS theory needs large amount of calculation and huge memory occupation, the pixel number of single pixel imaging system is restricted in practical applications [20,22,23]. The existing single-pixel imaging systems generally select a small DMD array as imaging area. In Wen-Kai Yu’s setup, 1 × 1 mm object imaging on 64 × 64 regions of the DMD, the resolution of reconstructed image is 64 × 64 pixels. In 2012, Howell et al. proposed a compressive depth mapping scheme using a single-pixel photon-counting detector and obtained 64 × 64 pixels depth image as well [24,25]. To realize high resolution image reconstruction, the whole DMD region is proposed to be divided into several sub-regions, and images on those sub-regions are reconstruction by CS one by one. Finally, all the images of sub-region are stitched together to form a high-resolution image [18,21]. Obviously, this method is at the cost of long imaging time and low photon collection efficiency.

In this paper, we propose a multiple micro-mirrors combination imaging method and demonstrate a fast single photon compressive imaging technique with the image plane up to the entire DMD work area. It has important application prospects in the large-aperture and wide-field single photon imaging systems.

2. Large-area single photon imaging with compressive sensing

The experimental setup is shown in Fig. 1. The light emitted from the LED is collimated into parallel light by a collimator to reduce the influence of light scattering on imaging resolution. The intensity of light can be adjusted by number of attenuators and a diaphragm. The object is illuminated by the light source and then imaged onto the DMD via a convex lens. The DMD (0.7 XGA DDR DMD) consists of a 1024 × 768 micro-mirror array and the size of each mirror is 13.68 × 13.68 μm. Each mirror can be individually controlled to deflect ± 12 degrees by loading binary random matrix into DMD controller, realizing the intensity modulation of image on DMD. In order to effectively collect light reflected from the full screen of DMD, we set a focusing lens along the + 12 degrees direction of DMD,and a photon counting PMT (Hamamatsu Photonics H10682-110 PMT) with an effective photosensitive area of Φ 8 mm in focal plane of the lens. A specially developed control and counting circuit based on FPGA is used to load binary random matrix into DMD controller for each measurement and count single photon pulse output from PMT. As shown in Fig. 2, the compressive sampling parameters are send to the circuit through USB2.0 from personal computer. The synchronization control pulse is generated and input to the measurement matrix loader and the gated photon counter simultaneously. When a rising edge of this synchronization pulse signal is received, a random binary matrix is loaded into DMD and the photon counter starts to count up from zero. When the next pulse signal is coming, the photon counting value and random binary matrix are sent to PC for image reconstruction through CS algorithm.

Fig. 1 Experimental apparatus for large-area single photon compressive imaging. LED: led lamp, DMD: digital micromirror device, PMT: photomultiplier, FPGA: field programmable gate array, PC: personal computer.

Download Full Size | PDF

Fig. 2 Block schematic for the control and counting circuit based on FPGA, including a synchronization control pulse generator, pulse stretching, a gated photon counter, a measurement matrix generator, a measurement matrix loader and two USB interfaces.

Download Full Size | PDF

In order to continuously perform a single photon compressive imaging experiment in which the sampling frequency is f, the number of measurements is M, and the number of repetitions is R, we specifically design a synchronization control pulse generator. The signal timing is shown in Fig. 3. When the rising edge of the start measuring signal is received, sampling frequency signal and gated square wave signal will be generated. Sampling frequency signal with frequency f can be generated by dividing the system clock. The gated square wave signal should contain R square waves, each square wave should have a width of M + 1 sampling pulses. The generation process of the gated square wave signal is as follows: (1) when the rising edge of the sampling frequency pulse comes, register that store number of repetitions minus one; (2) delay $t_{1}$ by counting the system clock ( $T_{n H} < t_{1} < T_{n}$ ), then output high level (logic 1) ; (3) count the rising edge of sampling frequency pulses until the count value is equal to M + 1; (4) delay $t_{2}$ by counting the system clock ( $T_{n H} < t_{2} < T_{n}$ ), then output low (logic 0) ; (5) delay $t_{3}$ , then if value of register that store number of repetitions is not equal to 0, repeat steps (1)- (4), otherwise operation completed. Finally, AND the sampling frequency signal to the gated square wave signal to obtain the synchronization control signal.

Fig. 3 Timing diagram for generating the synchronization control signal. T_n: A period of the sampling frequency signal. T_nH: The high-level duration of one period of the sampled frequency signal. Delay $t_{1}$ , $t_{2}$ must satisfy: $T_{n H} < t_{1} < T_{n}$ and $T_{n H} < t_{2} < T_{n}$ .

Download Full Size | PDF

3. Multiple micro-mirrors combination imaging method

If each micro-mirror is defined as one pixel, the imaging resolution of the whole DMD work area is 1024 × 768 pixel. Assuming a sampling ratio of 0.5, 512 × 768 measurements are needed. In addition, the time spent and the memory used will also be large for imaging reconstruction after compressive sampling. In order to achieve a fast large-area imaging with fewer pixels, we proposed a multiple micro-mirrors combination imaging method shown in Fig. 4(a). The whole DMD work area is divided into P × Q combined pixels and each combined pixel is comprised of (1024/P) × (768/Q) micro-mirrors array. All micro-mirrors in a combined pixel are simultaneously controlled to turn to the same direction to realize modulation of light in each measurement. In order to achieve this function, the random binary matrices loaded in DMD are specially designed. Figure 4(b), 4(c), and 4(d) show the modulation effect of the same image (capital letter C) when the sizes of the combined pixel are 32 × 24, 16 × 12, and 8 × 6 respectively. With this method, lower resolution imaging of the whole DMD work area can be realized without additional hardware and meanwhile the time for measurement and reconstruction is greatly reduced. Taking the reconstruction experiment of 64 × 64 pixels for an example, assuming the sampling ratio is 0.5 and the sampling time is the same each time, there is 99.48% reduction in acquisition time compare to non-micro-mirror combination.

Fig. 4 Schematics of multiple micro-mirrors combination imaging method. (a) The division of the full screen of DMD when the resolution of reconstructed image is P × Q. (b), (c), and (d) is the modulation effect when the sizes of combined pixel are 32 × 24, 16 × 12, and 8 × 6 respectively.

Download Full Size | PDF

4. Signal-to-noise ratio and detection limit

Below we analyze the SNR and detection limit of conventional raster scanning (RS). Based on this, we will further analyze the SNR and detection limit of multiple micro-mirrors combination imaging method.

Without losing generality, we consider a binary object imaged on the entire DMD work area via optical system and a DMD of reflectivity 1. If each micro-mirror is used as one pixel, the imaging resolution N is 1024 × 768. We assume that the image is K-sparse, the average photon count rate reflected by the micro-mirror corresponding to the pixel with a grayscale value of 1 is I_ph cps. If the scan time is t for a pixel, the measured photon count in RS is:

N_{p h} = I_{p h} t

In actual measurement, it is not possible to detect N_ph separately. The pulse count output by the detector is the sum of the signal photon number N_ph, the background photon count N_b, and the dark count N_d. N_ph is calculated by subtracting (N_b + N_d) from (N_ph + N_b + N_d). As the illumination on the object is at the single photon level, the measurement noise in our imaging system is dominated by Poisson shot noise. From this, each noise component can be regarded as an independent factor, so the total noise component can be analyzed as follows [26]:

n_{R S}^{2} = {(\sqrt{N_{p h} + N_{b} + N_{d}})}^{2} + {(\sqrt{N_{b} + N_{d}})}^{2}

We assume that background photon count rate is I_b and the dark count rate is I_d. The SNR of single photon imaging system with RS then will be:

S N R_{R S} = \frac{N_{p h}}{n_{R S}} = \frac{I_{p h} t}{\sqrt{I_{p h} t + 2 (I_{b} t + I_{d} t)}} = \frac{I_{p h} \sqrt{t}}{\sqrt{I_{p h} + 2 (I_{b} + I_{d})}}

This means that the SNR can be improved as the measurement time is made longer. The total measurement time for scanning a whole picture can be expressed as:

T = N t

The noise equivalent power (NEP) indicates the lower limit of light detection, the NEP is the light level required to obtain a SNR of 1. In photon counting mode, if we define the detection limit as the light level where the SNR equals to 1 and the measurement time is one second, the photon counting rate at the detection limit can be approximated below.

I_{p h} = \frac{1 + \sqrt{1 + 8 (I_{b} + I_{d})}}{2} \approx \sqrt{2 (I_{b} + I_{d})}

For single photon imaging system with compressive sensing described above, under the condition that m micro-mirrors are grouped together as one pixel, the imaging resolution N_m is equal to N/m, the image sparse K_m is equal to K/m. Assuming that the random matrix has a sparse ratio of μ, and that each measurement time is t, the total number of measurements is M. The measured photon count at a time can be expressed as:

N_{s} = m I_{p h} i t,

where i is the total number of pixels corresponding element 1 in the random matrix and gray value is 1. The probability distribution of i can be approximated below.

P (i) = C_{K_{m}}^{i} μ^{i} {(1 - μ)}^{K_{m} - i} \approx \frac{{(μ K_{m})}^{i} e^{(- μ K_{m})}}{i!}

The average number of measured photons for M measurements can be approximated as:

N_{s} = \sum_{i = 1}^{M} \frac{{(μ K_{m})}^{i} e^{(- μ K_{m})}}{i!} \cdot m I_{p h} t i \approx m I_{p h} t μ K_{m} .

Correspondingly, the average noise of M measurements is:

\begin{matrix} n_{C S}^{2} = \sum_{i = 1}^{M} \frac{{(μ K_{m})}^{i} e^{(- μ K)}}{i!} \cdot {(\sqrt{m I_{p h} t i + 2 (I_{b} t + I_{d} t)})}^{2} \\ = m I_{p h} t μ K_{m} + 2 (I_{b} t + I_{d} t) . \end{matrix}

The average SNR for M measurements of single photon imaging with CS then will be:

S N R_{C S} = \frac{N_{s}}{n_{C S}} = \frac{m I_{p h} μ K_{m} \sqrt{t}}{\sqrt{m I_{p h} μ K_{m} + 2 (I_{b} + I_{d})}} .

The total measurement time for CS is

T = M t

If we define the detection limit as the light level where the SNR equals to 1 and the measurement time is one second, the photon counting rate at the detection limit can be approximated below.

I_{p h} = \frac{\sqrt{2 (I_{b} + I_{d})}}{m μ K_{m}} = \frac{\sqrt{2 (I_{b} + I_{d})}}{μ K}

Comparing Eq. (5) and Eq. (12), it can be seen that the detection sensitivity of CS is μK times that of RS. Equation (12) also means that the detection sensitivity can be improved as the sparse ratio of random matrix μ is made larger. In addition, Eq. (12) shows that the detection sensitivity does not decrease when the m micro-mirrors are grouped together at the same measurement time.

5. Experimental results and discussion

5.1 Effect of the imaging quality with size of combined pixel

The size of combined pixel is related to the resolution of reconstructed images. Within a certain acquisition time, how to choose the size of combined pixel could obtain the higher quality images is our concern. The m micro-mirrors are grouped together as one pixel. At the same sampling ratio α = M/N_m and the same total sampling time T, the measurement time of each sample can be expressed as:

t = \frac{T}{M} = \frac{T}{N_{m} α} = \frac{T m}{N α} .

Substituting into Eq. (10) results in:

S N R_{C S} = \frac{N_{s}}{n_{C S}} = \frac{I_{p h} μ K \sqrt{\frac{T m}{N α}}}{\sqrt{I_{p h} μ K + 2 (I_{b} + I_{d})}} .

From Eq. (14), we can see that although the imaging resolution will decrease when more micro-mirrors are combined as one pixel, the average SNR at each measurement will be greater. It means micro-mirrors combination imaging method is more suitable for faster imaging in a weaker light-level environment.

In order to verify the above conclusion, we set up imaging experiments of customized mask with the same acquisition time and different sizes of combined pixel. The sizes of combined pixel are 32 × 24, 16 × 12, and 8 × 6 corresponding to imaging resolutions of 32 × 32, 64 × 64, and 128 × 128 respectively. All acquisition time is 2048 s and all sampling ratios are 0.5. The TVAL3 (Total variation Augmented Lagrangian Alternating Direction Algorithm) is used to reconstruct images from the obtained data. The algorithm effectively combines an alternating direction technique with a nonmonotone line search to minimize the augmented Lagrangian function at each iteration, and it is verified more efficient and robust than other TV algorithm packages [27–29]. Figure 5 shows the experimental results under these conditions. From Fig. 5, we can see that the imaging quality shown in (a) is poor, this is because the imaging resolution is too low when the size of combined pixel is made too large, and thus the details of the imaged object cannot be displayed. However, the imaging quality shown in (c) is poor too, this is because when the sampling ratio is uniform, high resolution imaging requires more measurements. Each measurement takes less time when the total measurement time is equal. From Eq. (14), we can see that the average SNR of each measurement is lower, which ultimately results in the quality of image reconstructed in high resolution being not as good as that of image reconstructed in low resolution. Thus, too large or too small size of combined pixel will reduce the quality of reconstructed images.

Fig. 5 Imaging results with the same acquisition time but different sizes of combined pixel. (a) Image resolution of 32 × 32 with each combined pixel of 32 × 24 (b) Image resolution of 64 × 64 with each combined pixel of 16 × 12 (c) Image resolution of 128 × 128 with each combined pixel of 8 × 6. All acquisition time is 2048 s and all sampling ratios are 0.5.

Download Full Size | PDF

5.2 Effect of the imaging quality with measurements number

According to the CS theory, the more measurements, the higher signal recovery accuracy. This is easily verified in the imaging system. However, whether there is a similar conclusion about reconstruction experiments within a certain total acquisition time. The relationship between the measurements number M and each measurement time t can be expressed as

t = \frac{T}{M} .

Substituting into Eq. (10) results in:

S N R_{C S} = \frac{N_{s}}{n_{C S}} = \frac{I_{p h} μ K \sqrt{\frac{T}{M}}}{\sqrt{I_{p h} μ K + 2 (I_{b} + I_{d})}} .

from Eq. (16), we can see that when the number of combined micro-mirrors and the sampling time T are fixed, the more measurements, the shorter each measurement time will be, and then the smaller the average SNR of each measurement will be.

In order to verify the above conclusion, we set up a set of imaging experiments of a mask printed with NCU (the abbreviation of Nanchang University) with the same acquisition time but different number of measurements. The reconstructed images are shown in Fig. 6(a). All acquisition time is 600s and the image resolution is 64 × 64 with each combined pixel of 16 × 12. To quantify the quality of reconstructed images, the Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), and Mean Structure Similitary Index (MSSIM) of reconstructed image versus the number of measurements are given in Fig. 6(b). From Fig. 6, we can see that at the very beginning, the quality of reconstructed images has been significantly improved with increase of measurements. But when the number of measurements continues to increase, the quality of reconstructed images shows a downward trend. This is because that with increase of measurements, the average time of each measurement is reduced. When the average time of each measurement is relatively long, the number of measurements is the main factor limiting system performance. Therefore, image reconstruction performance is enhanced with the increase of measurements to some extent. However, with continuously decrease of average time of each measurement, we can see the average SNR of each measurement will be smaller from Eq. (16). This causes the quality of the reconstructed image to be severely affected by Poisson shot noise. The average time of each measurement becomes the key factor limiting system performance. We can see when measurements number M increases to a certain degree, the image reconstruction quality begins to deteriorate. Thus, to obtain the higher quality image within a certain acquisition time, increase the measurements number but ensure that average time of each measurement is sufficient to suppress Poisson shot noise.

Fig. 6 Experimental results with the same acquisition time but different number of measurements. All acquisition time is 600s and the image resolution is 64 × 64 with each combined pixel of 16 × 12. (a) Imaging results with the same acquisition time but different number of measurements. M is the number of measurements, t is the average time of each measurement. (b) MSE, PSNR and MSSIM of reconstructed images versus the number of measurements.

Download Full Size | PDF

6. Conclusion

In this paper, a large-area single photon compressive imaging system is built. In order to achieve a fast large-area imaging, we proposed a multiple micro-mirrors combination imaging method. The theoretical derivation of SNR and detection limit of the imaging system shows that the detection sensitivity of compressive sensing imaging is μK times that of raster scanning imaging and does not decrease when m micro-mirrors are grouped together as one pixels, and that the detection sensitivity can be improved as the sparse ratio of random matrix μ is made larger. Theoretical analysis and experimental results show that micro-mirrors combination imaging method is more suitable for faster imaging in a weaker light level environment. In order to achieve high imaging quality, the size of the combined pixels and the average time of each measurement should be moderate, so that the impact of Poisson shot noise is minimized. Therefore, the multiple micro-mirrors combination imaging method has important application prospects in the large-aperture and wide-field single-photon imaging.

Funding

National Natural Science Foundation of China (No. 61565012); China Postdoctoral Science Foundation (No. 2015T80691); the Science and Technology Plan Project of Jiangxi Province (No. 20151BBE50092); the Funding Scheme to Outstanding Young Talents of Jiangxi Province (No. 20171BCB23007).

References

1. R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004). [CrossRef] [PubMed]

2. V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109(26), E1679–E1687 (2012). [CrossRef] [PubMed]

3. X. Shi, H. Li, Y. Bai, and X. Fu, “Negative influence of detector noise on ghost imaging based on the photon counting technique at low light levels,” Appl. Opt. 56(26), 7320–7326 (2017). [CrossRef] [PubMed]

4. K. Zang, X. Jiang, Y. Huo, X. Ding, M. Morea, X. Chen, C. Y. Lu, J. Ma, M. Zhou, Z. Xia, Z. Yu, T. I. Kamins, Q. Zhang, and J. S. Harris, “Silicon single-photon avalanche diodes with nano-structured light trapping,” Nat. Commun. 8(1), 628–633 (2017). [CrossRef] [PubMed]

5. K. Taguchi and J. S. Iwanczyk, “Vision 20/20: Single photon counting x-ray detectors in medical imaging,” Med. Phys. 40(10), 100901 (2013). [CrossRef] [PubMed]

6. Y. Yang, J. Shi, F. Cao, J. Peng, and G. Zeng, “Computational imaging based on time-correlated single-photon-counting technique at low light level,” Appl. Opt. 54(31), 9277–9283 (2015). [CrossRef] [PubMed]

7. R. M. Willett, M. F. Duarte, M. A. Davenport, and R. G. Baraniuk, “Sparsity and structure in hyperspectral imaging,” IEEE Signal Process. Mag. 31(1), 116–126 (2014). [CrossRef]

8. P. A. Morris, R. S. Aspden, J. E. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015). [CrossRef] [PubMed]

9. B. F. Aull, D. R. Schuette, D. J. Young, D. M. Craig, B. J. Felton, and K. Warner, “A Study of Crosstalk in a 256×256 Photon Counting Imager Based on Silicon Geiger-Mode Avalanche Photodiodes,” IEEE Sens. J. 15(4), 2123–2132 (2015). [CrossRef]

10. C. Scarcella, A. Tosi, F. Villa, S. Tisa, and F. Zappa, “Low-noise low-jitter 32-pixels CMOS single-photon avalanche diodes array for single-photon counting from 300 nm to 900 nm,” Rev. Sci. Instrum. 84(12), 123112 (2013). [CrossRef] [PubMed]

11. M. Vitali, D. Bronzi, A. J. Krmpot, S. N. Nikolić, F. J. Schmitt, C. Junghans, S. Tisa, T. Friedrich, V. Vukojević, L. Terenius, F. Zappa, and R. Rigler, “A single-photon avalanche camera for fluorescence lifetime imaging microscopy and correlation spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 20(6), 344–353 (2014). [CrossRef]

12. W. K. Yu, “Application of Compressed Sensing in Super-sensitivity Time-resolved Spectral Imaging,” Beijing: University of Chinese Academy of Sciences, 2015.

13. Y. Zhi, R. Lu, B. Wang, Q. Zhang, and X. Yao, “Rapid super-resolution line-scanning microscopy through virtually structured detection,” Opt. Lett. 40(8), 1683–1686 (2015). [CrossRef] [PubMed]

14. Y. Liu, J. Shi, and G. Zeng, “Single-photon-counting polarization ghost imaging,” Appl. Opt. 55(36), 10347–10351 (2016). [CrossRef] [PubMed]

15. J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 14–20 (2008). [CrossRef]

16. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008). [CrossRef]

17. R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24(4), 118–121 (2007). [CrossRef]

18. W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, G. J. Zhai, and Q. Zhao, “Single-photon compressive imaging with some performance benefits over raster scanning,” Phys. Lett. A 378(45), 3406–3411 (2014). [CrossRef]

19. Q. Tong, Y. L. Jiang, H. Y. Wang, and L. M. Guo, “Image reconstruction of dynamic infrared single-pixel imaging system,” Opt. Commun. 410, 35–39 (2018). [CrossRef]

20. W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, S. Q. Gao, G. J. Zhai, Q. Zhao, and M. L. Ge, “Single photon counting imaging system via compressive sensing,” Preprint arXiv:1202.5866, (2012).

21. Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6(1), 6225 (2015). [CrossRef] [PubMed]

22. M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7, 12010 (2016). [CrossRef] [PubMed]

23. G. A. Howland, P. B. Dixon, and J. C. Howell, “Photon-counting compressive sensing laser radar for 3D imaging,” Appl. Opt. 50(31), 5917–5920 (2011). [CrossRef] [PubMed]

24. G. A. Howland, D. J. Lum, M. R. Ware, and J. C. Howell, “Photon counting compressive depth mapping,” Opt. Express 21(20), 23822–23837 (2013). [CrossRef] [PubMed]

25. A. Colaço, A. Kirmani, G. A. Howland, J. C. Howell, and V. K. Goyal, “Compressive depth map acquisition using a single photon-counting detector: Parametric signal processing meets sparsity,” In CVPR, 2012 IEEE Conference on. IEEE, 96–102 (2012). [CrossRef]

26. Q. R. Yan, “Research on time-correlated single photon counting techniques based on MCP position sensitive anode detector,” PhD Thesis, Xi’an: Xi’an Institute of Optics and Precision Mechanics of CAS, (2012).

27. C. B. Li, “An Efficient Algorithm for Total Variation Regularization with Applications to the Single Pixel Camera and Compressive Sensing,” M.S. thesis, Dept. Comput. Appl. Math., Rice Univ., Houston, TX, (2009).

28. C. Li, W. Yin, and Y. Zhang, “User’s guide for TVAL3: TV minimization by augmented lagrangian and alternating direction algorithms,” CAAM report 20, 46–47 (2009).

29. C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented Lagrangian method with applications to total variation minimization,” Comput. Optim. Appl. 56(3), 507–530 (2013). [CrossRef]

Large-area single photon compressive imaging based on multiple micro-mirrors combination imaging method

Abstract

1. Introduction

2. Large-area single photon imaging with compressive sensing

3. Multiple micro-mirrors combination imaging method

4. Signal-to-noise ratio and detection limit

5. Experimental results and discussion

5.1 Effect of the imaging quality with size of combined pixel

5.2 Effect of the imaging quality with measurements number

6. Conclusion

Funding

References

Cited By

Figures (6)

Equations (16)

Optics Express