Full color single pixel imaging by using multiple input single output technology

Le Wang; Le Wang; Shengmei Zhao; Shengmei Zhao; Shengmei Zhao

doi:10.1364/OE.432864

1. Introduction

Single pixel imaging (SPI) is regarded as a fascinating optical imaging technique [1] due to it offers great advantages in terms of high spatial resolution [2–4] and detection sensitivity [5,6]. SPI can reconstruct the images of objects by the calculation of speckle patterns and bucket detection signals. SPI is a technique closely related to ghost imaging (GI) [7,8]. In addition, SPI is also referred to as single pixel camera [1,9], which has two imaging configurations, one called single-pixel camera configuration (the digital mirror device (DMD) is used to apply a measurement mask to the image of object and then a bucket detector is used to measure the light transmitted through this mask) and the other one called structured illumination configuration (DMD is used to produce the speckle patterns to illuminate the object and then a bucket detector is used to measure the light from the object) [1]. Therefore, SPI has received wide attentions [10–14] and furthermore some researchers focus on constructing a SPI system to realize the full color imaging [15–21].

One way to achieve the full color SPI is that three spectrally filtered single pixel bucket detectors are used to measure three colored (red, green and blue) speckle patterns interacting with the object, respectively. Then a full color image can be achieved by synthesizing three colored component images reconstructed from three bucket detectors [15–17]. However, the weakness of this scheme is that three independent spectrally filtered single pixel bucket detectors are required to be used in the system simultaneously, which increases the cost of SPI system and limits the practical application of SPI system because the bucket detector is usually expensive or even unavailable in some spectral ranges. In addition, a spectrometer can be used instead of three spectrally filtered single pixel bucket detectors to realize full color SPI, however, the disadvantage of high cost and unavailability of full color SPI is still not overcome because the price of spectrometer is much higher than that of bucket detector and the spectrometer is harder to be produced in some spectral ranges.

Alternatively, the time division multiplexing (TDM) technology is employed to the full color SPI scheme [18–21]. Specifically, the full color SPI scheme with TDM (named FCSPI-TDM) divides the whole sampling time into three independent periodic time slots, where in a specific time slot, the specific colored (red, green or blue) speckle pattern is projected onto the object and then is measured by only one bucket detector to obtain the bucket detection signal of the specific time slot. Then a full color image can be achieved by synthesizing three colored component images reconstructed from the bucket detection signals of three time slots. FCSPI-TDM can realize the full color imaging without the requirement of multiple independent bucket detectors, however, the imaging quality is subject to the interference of the intensity fluctuations of the natural and artificial ambient light, such as the sunlight in outdoor and the incandescent lamp in indoor [22,23]. Therefore, it is unsuitable for FCSPI-TDM to realize the full color imaging suffered from the interference of ambient light.

Recently, a novel SPI scheme is proposed by using the multiple-input-single-output (MISO) technology which is widely used in wireless communications [24] to improve the image quality and decrease the sampling time. Inspired by the concepts of MISO technology, we propose a novel full color SPI scheme by using MISO technology, which is referred to as FCSPI-MISO. In the FCSPI-MISO scheme, the red, green and blue source respectively generate a light field whose spatial amplitude is uniform and temporal waveform is a cosine waveform with the specific frequency (multiple input), and then the spatial amplitude of the three light fields are modulated by a DMD to form the spatial speckle pattern to illuminate on an unknown object simultaneously. Then only one single pixel bucket detector with a large wavelength range is exploited to measure the intensity of the light field from the object (single output). In the process of image reconstruction, the detection signal of the bucket detector can be separated into three components effectively by Fourier transform, where the three detection signal components correspond to the detection signal from three color light fields, respectively. Then a red (green or blue) component image of object can be recovered by utilizing the speckle patterns and corresponding detection signal components. Finally, a full color image of object can be produced by synthesizing the reconstructed red, green and blue component images.

FCSPI-MISO has the advantages that it can be robust against the interference of the intensity fluctuations of ambient light and thus improve the imaging quality comparing with FCSPI-TDM scheme. Moreover, FCSPI-MISO requires only one single pixel bucket detector, which reduces the numbers of bucket detectors that need to be used comparing with the full color SPI scheme with three bucket detectors. Therefore, FCSPI-MISO is of great value for constructing an imaging system in some spectral ranges where the bucket detector is usually expensive or even unavailable. Our scheme provides a promising avenue to realize the full color SPI. Furthermore, based on the ideal of FCSPI-MISO, our scheme has potential to be extended to high quality multispectral SPI by using only one single pixel bucket detector with a large wavelength range.

The organization of the paper is as follows. In Section 2, the proposed FCSPI-MISO scheme is presented. The performance of the proposed scheme is discussed by experiments in Section 3. Finally, Section 4 concludes the paper.

2. FCSPI-MISO scheme

The schematic diagram of FCSPI-MISO is shown in Fig. 1. Note that there are three colored sources in the FCSPI-MISO, which are red, green and blue sources, and are represented by $n=1,2,3$ respectively. Therefore, $n$th source generates a light field whose spatial amplitude is uniform and temporal waveform is a cosine waveform with frequency $f_n$, $a+b/2\cos (2\pi f_n t)$, where $a$ and $b$ are the direct current (DC) offset and the amplitude of the cosine waveform, respectively. Then a superposed light field can be obtained by superposing the light fields from all three colored sources. Then the spatial amplitude of the superposed light field is modulated by a DMD to generate a spatial speckle pattern, $I^{m}(x,y)$, where $m$ represents the $m$th speckle pattern and the Walsh-Hadamard speckle patterns [11] are used in the FCSPI-MISO scheme. Hence, the $m$th spatiotemporal modulated speckle pattern, $S^{m}(x,y,t)$, is

(1)$$S^{m}(x,y,t)=\sum_{n=1}^{3}I^{m}(x,y)\left[a+\frac{b}{2}\cos(2\pi f_n t)\right],$$

where $m=1,2,\ldots ,M$. $M$ is the number of speckle patterns.

Fig. 1. (a) The schematic diagram of FCSPI-MISO. (b) The schematic diagram of FCSPI-MISO reconstruction algorithm.

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When the colored object is illuminated by $S^{m}(x,y,t)$ and then the reflecting or transmitting light is measured by a single pixel bucket detector, the bucket detection signal, $B^{m}(t)$, will be produced,

(2)$$\begin{aligned}B^{m}(t)&= \eta\int_{A} [S^{m}(x,y,t)O(x,y) + N(x,y,t)] dxdy,\\ &= \frac{\eta b}{2}\int_{A} \sum_{n=1}^{3}I^{m}(x,y)\cos(2\pi f_n t)O_{n}(x,y) dxdy + \alpha +n(t), \end{aligned}$$

where $\eta$ represents the responsivity of the single pixel bucket detector, and $A$ represents the region illuminated by $S^{m}(x,y,t)$. $O(x,y)$ represents the colored object, and $O_{n}(x,y)$ with $n=1,2,3$ represents the red, green and blue component of the colored object. $N(x,y,t)$ is the ambient light. $n(t)=\eta \int _{A} N(x,y,t) dxdy$, which represents the interference of the intensity fluctuations of ambient light at $t$-time. Usually, the interfering signal from ambient light can be described by [23]

(3)$$n(t)= \sum_{m=1}^{\infty}n_{m}\cos(2\pi f_0 mt+\phi_m),$$

where $n_{m}$ and $\phi _m$ are the amplitude and phase of the each harmonic component of the basic frequency $f_0$. For example, for the interfering signal from the incandescent lamp, the basic frequency $f_0$ equals to 100Hz and $n_{m}\approx 0$ for $f_0 m\geq 2kHz$ because only the first harmonics (up to 2kHz) of the signal from the incandescent lamp carry a significant amount of energy [23]. $\alpha$ represents the superimposed signal composed of the three bucket detection results from the specific colored component of the object, which is

(4)$$\alpha=\sum_{n=1}^{3} \eta a\int_{A} I^{m}(x,y)O_{n}(x,y) dxdy.$$

Then a full color image of object can be reconstructed by the FCSPI-MISO reconstruction algorithm, which is shown in Fig. 1(b). In the first step of the FCSPI-MISO reconstruction algorithm, we can efficiently separate three components of bucket detection signals, $B^{m}_{n}$, corresponding to $I^{m}(x,y)$ and $n$th source, from $B^{m}(t)$ by Fourier transform with a specific frequency $f=f_n$. Specifically, Fourier transform is firstly performed on $B^{m}(t)$,

(5)$$\begin{aligned}F\{ B^{m}(t)\} &= \int^{\infty}_{-\infty} B^{m}(t) \exp^{{-}j2\pi f t} dt\\ &= \frac{\eta b}{4} \sum_{n=1}^{3}\int_{A}I^{m}(x,y)O_{n}(x,y) dxdy [\delta(f-f_n)+\delta(f+f_n)]+ \alpha\delta(f)\\ &+ \sum_{m=1}^{\infty}\frac{n_{m}}{2}[\delta(f-f_0 m)\exp^{j\phi_m}+\delta(f+f_0 m)\exp^{{-}j\phi_m}], \end{aligned}$$

where $F\{ \cdot \}$ represents Fourier transform and $\delta (\cdot )$ is the delta function. Then $B^{m}_{n}$ can be obtained, which equals to the amplitude of the Fourier transform component with specific frequency $f_n$,

(6)$$\begin{aligned} B^{m}_{n}&=\left|F\{ B^{m}(t)\}_{f=f_n} \right|\\ &\propto \int_{A} I^{m}(x,y)O_{n}(x,y) dxdy, \end{aligned}$$

where $\left |\cdot \right |$ represents the modulus of complex number. From Eq. (6), we can find that when the frequency of the intensity fluctuation of the ambient light is different with the modulated frequency $f_n$, the interference of the ambient light can be effectively eliminated or suppressed for FCSPI-MISO. Note that the frequency of the intensity fluctuation of the ambient light is usually in some special frequencies, for example, the interfering signal from the incandescent lamp is an almost perfect sine wave with a frequency of 100Hz and only the first harmonics (up to 2kHz) carry a significant amount of energy [23]. Therefore, we can choose the modulated frequency $f_n$ that are not the frequencies of the intensity fluctuation of the ambient light to effectively eliminate or suppress the the interference of the ambient light for FCSPI-MISO. Similarly, the superimposed signal $\alpha$ can also be eliminated, which will not interfere with three (red, blue and green) detection signal components.

Therefore, we can obtain three detection signal components, $B^{m}_{n}|_{n=1,2,3}$, corresponding to three colored component of the object interacting with the speckle pattern $I^{m}(x,y)$. After the bucket detector performs $M$ measurements for $M$ speckle patterns, we can recover the specific colored component image of the object by using all speckle patterns $I^{m}(x,y)|^{m=1,2,\ldots ,M}$ and corresponding detection signal components, $B^{m}_{n}|^{m=1,2,\ldots ,M}$. Here the fast Walsh-Hadamard transform (FWHT) algorithm [11] is used to reconstruct the specific colored component images of the object,

(7)$$\hat{O}_{n}(x,y)= {FWHT}\{B^{m}_{n}|^{m=1,2,\ldots,M}\},$$

where ${FWHT}\{\bullet \}$ represents the FWHT operation with a butterfly computation structure. Finally, the object’s full color image $\hat {O}(x,y)$ is reconstructed by synthesizing the reconstructed red, green and blue component images $\hat {O}_{n}(x,y)$ with $n=1,2,3$.

It is shown that FCSPI-MISO can reconstruct a full color image of the object with only one single pixel bucket detector, which reduces the numbers of bucket detectors comparing with the full color SPI scheme with three bucket detectors. Moreover, FCSPI-MISO can also be robust against the interference of the intensity fluctuations of ambient light because the specific component of bucket detection signal is obtained by Fourier transform of $B^{m}(t)$ with a specific frequency, which can effectively filter the interfering signal without the specific frequency.

3. Experimental results

The experimental system of FCSPI-MISO is shown in Fig. 2. There are three colored LED sources in the FCSPI-MISO, whose optical spectrum measured by a spectrometer (Thorlabs CCS100) is shown in Fig. 3. The light generated from three LEDs is modulated by three cosine wave signals (the frequencies of the three cosine wave signals are 90kHz, 110kHz and 190kHz for green, red and blue LED sources, respectively, but all cosine wave signals have the amplitude $4Vpp$ with a DC offset $3V$) from the Arbitrary Waveform Generators (Keysight 33612A). Then a superposed light field can be obtained by superposing the light fields from all three colored sources, and the light from the superposed light field is modulated by DMD (ViALUX V-7001) to generate a spatial speckle pattern $I^{m}(x,y)$. The total internal reflection (TIR) prism is used to ensure the speckle patterns reflected from the DMD to the optical axis of the incident light, and the speckle patterns are then projected onto an object by a projecting lens. Here the colored image, “flowers” or “fruits”, printed on a transparent plastic thin sheet is used as the object. Then a photodetector (Thorlabs PDA100A2, wavelength range 320-1100 nm) is used to measure the intensity of the speckle pattern from the object to generate the bucket detection signals $B^{m}(t)$ which are recorded by ADC (National Instruments PCIe-6374 with the sampling rate $3MS/s$). Then we can reconstruct a full color image of object by the FCSPI-MISO reconstruction algorithm with the bucket detection signals $B^{m}(t)$ and the speckle patterns $I^{m}(x,y)$. In addition, in order to verify that FCSPI-MISO has the ability to resist the interference caused by the intensity fluctuations of ambient light, a white LED modulated by a waveform signal $n(t)$ from an Arbitrary Waveform Generator is used as an interfering signal, which is shown in the red dashed square of Fig. 2.

Fig. 2. The experimental system of FCSPI-MISO. LED: Light emitting diode. DMD: Digital mirror device. PD: Photodetector. ADC: Analog-to-digital converter. L: Lens. M: Mirror. BS: Beam splitter. The device in the red dashed square is used to simulate the interference caused by the intensity fluctuations of ambient light.

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Fig. 3. The optical spectrum of three colored LED sources used in the FCSPI-MISO experiment.

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The mean square error (MSE) is used to quantitatively evaluate the imaging quality of FCSPI-MISO, which is defined as [11]

(8)$$MSE=\frac{1}{N} \sum_{x,y} (\hat{O}(x,y)-O(x,y))^2 ,$$

where $O(x,y)$ and $\hat {O}(x,y)$ denote the intensity values of the original image and the reconstructed image, respectively. $N$ is the number of pixels of the reconstructed image.

We first verify the feasibility of the FCSPI-MISO scheme by numerical simulation and experiment, which are shown in Fig. 4 and Fig. 5. We use the speckle patterns whose pixel size is $128\times 128$ and the number of speckle patterns is $M=16384$ to perform the numerical simulation and experiment, and the results are shown in Fig. 4. Fig. 5 is the results with $M=4096$ $64\times 64$-pixels speckle patterns. The picture time is setup as $200\mu s$. The bucket detection signal $B^{5}(t)$ for the fifth speckle pattern is acquired by the photodetector and shown in Fig. 6, where Fig. 6(a) is the bucket detection signal $B^{5}(t)$ for the fifth $128\times 128$-pixels speckle pattern with the “flowers” object, and the amplitude of Fourier transform of $B^{5}(t)$ is shown in Fig. 6(b). Then the red, green and blue components of bucket detection signals can be obtained from Fig. 6(b), which are $B^{5}_{1}=59.29$, $B^{5}_{2}=42.01$, $B^{5}_{3}=35.17$. The bucket detection signal $B^{5}(t)$ for the fifth $64\times 64$-pixels speckle pattern with the “flowers” object is shown in Fig. 6(c), whose the amplitude of Fourier transform is shown in Fig. 6(d). We can obtain $B^{5}_{1}=61.18$, $B^{5}_{2}=39.56$, $B^{5}_{3}=33.99$ from Fig. 6(d). Both numerical simulation results and experimental results of Fig. 4 and Fig. 5 show that the reconstructed red, green and blue component images of the FCSPI-MISO scheme have a high imaging quality and smaller MSEs. The imaging quality of the full color image synthesized from the reconstructed red, green and blue component images is also very high. However, the quality of the images by experiment is lower than that of the numerical simulation and the MSEs of experimental results are larger than that of numerical simulation results, which are caused by the imperfect experimental devices such as nonuniform intensity of LED sources and intrinsic noise from the photodetector.

Fig. 4. The numerical simulation and experimental results by using FCSPI-MISO with speckle patterns whose pixel size is $128\times 128$ and the number of speckle patterns is $M=16384$.

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Fig. 5. The numerical simulation and experimental results by using FCSPI-MISO with speckle patterns whose pixel size is $64\times 64$ and the number of speckle patterns is $M=4096$.

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Fig. 6. The bucket detection signal $B^{5}(t)$ for the fifth speckle pattern acquired by the photodetector in the experiment. (a) is bucket detection signal for the fifth $128\times 128$-pixels speckle pattern with the “flowers” object, whose the amplitude of Fourier transform is shown in (b). (c) is bucket detection signal for the fifth $64\times 64$-pixels speckle pattern with the “flowers” object, whose the amplitude of Fourier transform is shown in (d).

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Furthermore, we verify the performance of the FCSPI-MISO scheme with different picture time and modulation frequency. The picture time defines the time that a DMD can maintain the display of a speckle pattern, and it is also the time that the bucket detector can sample the intensity of transmitted or reflected light from the object illuminated by a speckle pattern. The experimental results by using FCSPI-MISO with different picture time are shown in Fig. 7 and Fig. 8. Fig. 9 and Fig. 10 show the experimental results by using FCSPI-MISO with different modulation frequency. The speckle patterns with the pixel size $128\times 128$ and the number of speckle patterns $M=16384$ are used to perform the experiment. The results of Fig. 7 and Fig. 8 show that when the picture time is longer than $200\mu s$, the imaging quality will be better and the value of MSE is smaller. Furthermore, with the increase of the picture time, the imaging quality will be almost unchanged. However, when the picture time is $100\mu s$, the imaging quality will be worse and the value of MSE will be increased. Hence, we can choose an appropriate picture time to obtain a better imaging quality. On the other hand, we use four sets of modulation frequencies to perform the experiment to obtain the results in Fig. 9. It is found that the imaging quality of FCSPI-MISO will be almost unchanged with different modulation frequency. Note that, the results in the last row of Fig. 9 and Fig. 10 show that even if the frequency difference between the modulation frequencies is 5kHz, the imaging quality is still not deteriorated.

Fig. 7. The experimental results by using FCSPI-MISO with different picture time. The modulated frequency is setup as $f_1=$110kHz, $f_2=$90kHz, and $f_3=$190kHz.

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Fig. 8. The MSE results of reconstructed images as a function of picture time for FCSPI-MISO. (a) are the results for the “flowers” object and (b) are the results for the “fruits” object.

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Fig. 9. The experimental results by using FCSPI-MISO with different modulated frequency. The picture time is setup as $200\mu s$.

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Fig. 10. The MSE results of reconstructed images as a function of frequency difference for FCSPI-MISO. (a) are the results for the “flowers” object and (b) are the results for the “fruits” object.

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In addition, in order to verify that FCSPI-MISO has the ability to be robust against the interference of the intensity fluctuations of ambient light and thus improve the imaging quality comparing with FCSPI-TDM scheme, we use a white LED modulated by a modulated waveform $n(t)$ to be an interfering signal and the experimental results are shown in Fig. 11, Fig. 12 and Fig. 13. The experimental results by using both FCSPI-MISO and FCSPI-TDM under the interference of Gaussian random noise with bandwidth 1kHz are shown in Fig. 11. Fig. 12 shows the experimental results by using both FCSPI-MISO and FCSPI-TDM under the interference of pseudo random binary sequence (PRBS) signals with 100bps bit rate and sequence type PN7. The spectrum characteristics of Gaussian random noise and PRBS signal are very close to that of white noise. The speckle patterns with the pixel size $128\times 128$ and the number of speckle patterns $M=16384$ are used to perform the experiment. The picture time for FCSPI-MISO is $200\mu s$. Simultaneously, we use the red, green and blue LED sources in turn for SPI to obtain the corresponding red, green and blue component images to realize the FCSPI-TDM scheme. For the sake of fair comparison, the picture time for FCSPI-TDM is setup as one-third of that of FCSPI-MISO. Here signal-to-noise ratio (SNR) is used to evaluate the ratio of the signal power to the noise power,

(9)$$SNR(dB)=10\log_{10}\frac{P_s}{P_n},$$

where $P_s$ and $P_n$ are the signal power and the noise power respectively. $P_s$ ($P_n$) is the average of the detection results from the photodetector only at the present of speckle patterns (interfering signal). Furthermore, Fig. 13 compares the MSE performance as a function of SNR between FCSPI-MISO and FCSPI-TDM, where Fig. 13(a) and Fig. 13(b) are the results for the interference of Gaussian random noise and PRBS signals, respectively. The results show that the imaging quality of FCSPI-MISO does not decrease at the presence of the interference of both Gaussian random noise and PRBS signals. When the SNR is reduced, the performance of FCSPI-MISO is still almost unchanged. However, the imaging quality of FCSPI-TDM is obviously affected by the interference of Gaussian random noise and PRBS signals. With the decrease of SNR, the imaging quality of FCSPI-TDM will deteriorate gradually and the reconstructed images will be too blurry to see clearly. In addition, the imaging quality of FCSPI-TDM is more affected by PRBS signals than Gaussian random noise because the intensity fluctuations of PRBS signals are larger than that of Gaussian random noise.

Fig. 11. The experimental results by using FCSPI-MISO and FCSPI-TDM under the interference of Gaussian random noise.

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Fig. 12. The experimental results by using FCSPI-MISO and FCSPI-TDM under the interference of pseudo random binary sequence (PRBS) signals.

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Fig. 13. The comparison of reconstructed images’ MSE as a function of SNR between FCSPI-MISO and FCSPI-TDM. (a) are the results for the interference of Gaussian random noise and (b) are the results for the interference of PRBS signals. All of the results are for the “flowers” object.

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4. Conclusion and discussion

We have proposed a novel full color SPI by using MISO technology (FCSPI-MISO) in this paper, where the MISO technology is used to simultaneously produce three (red, green and blue) detection signal components correspond to the red, green and blue components of the object with only one single pixel bucket detector. Then, a full color image of object can be produced by synthesizing the reconstructed red, green and blue component images of object, where three (red, green and blue) component image can be recovered by utilizing the speckle patterns and corresponding detection signal components. Comparing with the existing full color SPI schemes, our scheme has the advantages that it can be robust against the interference of the intensity fluctuations of ambient light and thus improve the imaging quality. Moreover, FCSPI-MISO requires only one single pixel bucket detector, which reduces the numbers of bucket detectors that need to be used comparing with the full color SPI scheme with three bucket detectors. Therefore, FCSPI-MISO is of great value for constructing an imaging system in some spectral ranges where the bucket detector is usually expensive or even unavailable. Our scheme provides a promising avenue to realize the full color SPI. Our scheme has potential to be extended to high quality multispectral SPI by using only one single pixel bucket detector with a large wavelength range.

Funding

National Natural Science Foundation of China (62001249, 61871234); Natural Science Foundation of Jiangsu Province (BK20180755); Open Research Fund Program of the State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University (KF201909); Open Research Fund of Key Lab of Broadband Wireless Communication and Sensor Network Technology, NUPT (JZNY201910); Nanjing University of Posts and Telecommunications Scientific Foundation (NUPTSF) (NY218098, NY220004).

Disclosures

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

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Full color single pixel imaging by using multiple input single output technology

Abstract

1. Introduction

2. FCSPI-MISO scheme

3. Experimental results

4. Conclusion and discussion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (13)

Equations (9)

Optics Express