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Abstract
The high solar background during the day adversely affects the long distance daytime operations of ghost imaging. It is extremely hard to distinguish the signal light from the background noise light after they are both converted to voltage or current signals by the bucket detector, so spectral filtering before the detector is quite important. In this work, a Faraday anomalous dispersion optical filter (FADOF) is used in eliminating the background light influence in ghost imaging. Results of lab experiment show that the background light noise tolerance of the ghost imaging with FADOF is at least 18 times bigger than that with a 10 nm optical filter. The method has simple structure, great performance and great algorithms compatibility.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Ghost imaging (GI) is an indirect imaging method [1,2]. Different from the direct imaging, GI needs a series of varying light speckle patterns to illuminate the object, and then uses a bucket detector to collect the intensities of the transmitted or reflected light. Using some algorithms [3–6] to deal with the light speckle patterns and the measured light intensities, the reconstructed image of the object can be obtained. The speckle patterns could come from pseudo-thermal light [1], thermal light [7], preset speckle pattern generated by spatial light modulator (SLM) [8,9] or digital micro-mirror device (DMD), and sunlight [10]. The pseudo-thermal light is generated by using a laser through a rotating ground glass (R.G.G). GI has great potential for imaging lidar [11–13], image encryption [14] and low-light imaging [15]. At the same time, in some wavelength bands where area array detectors are expensive, such as X-ray [16,17] and terahertz bands [18–20], GI is receiving more and more attention [21–23].
The main drawback of GI is that a large number of measurements are required to obtain a high-quality reconstructing image. Many researchers have been devoted to solving this problem. Up till now, the number of necessary measurements can be greatly reduced and the image quality improved by several methods, such as compressed sensing [24] and deep learning [25–27]. However, when the background light noise in the practical application of ghost imaging has been taken into consideration, the GI quality sharply declines again [28]. The background light, such as the sunlight, will be added into the measured intensities of the bucket detector, so the bucket values are always inaccurate [29,30].
Fortunately, more and more researchers have paid attention to this problem. A lot of methods have been proposed to handle noise or outliers, including digital filtering [31,32], mode modulation [33], cross-correlation in time domain [34] and modified compressed sensing algorithm [35,36]. The imaging quality of GI in many scenarios of background light has greatly improved. But in the situation where the background light noise is hundreds or thousands of times bigger than the signal, it’s not enough to use only algorithmic methods.
In this work, we use Faraday anomalous dispersion optical filter (FADOF) [37] to minimize the effects of background light. FADOFs are ultra-narrow bandwidth filters and implemented using atomic transitions of atoms [38]. They have been widely investigated in optical filtering because of their high accuracy, ultra-narrow bandwidth [39–41] and high noise rejection [42–44]. The FADOF has shown great importance in optical communication [45], solar observation [46], laser frequency stabilization [47,48] and so on.
2. Methods
2.1 Faraday anomalous dispersion optical filter (FADOF)
FADOF consists of two polarizers, an atomic vapor cell in magnetic field, as shown in the FADOF module in Fig. 1. The polarization directions of two polarizers are perpendicular to each other, one placed in front of the atomic vapor cell and the other behind, and their extinction ratios are about $10^{-5}$. The magnetic field direction is the same as the direction of light propagation. Under the influence of a proper magnetic field, the incident light at the atomic resonance wavelength rotates in the atomic gas in the vapor cell, due to the Faraday effect, and passes through the exit polarizer. On the other hand, the Faraday effect does not occur in the incident light of other wavelengths, so they are filtered out.
The red line in Fig. 2 shows the measured transmission spectrum of FADOF, and the blue line is the measured atomic absorption spectrum. Their measurement experiment setup is shown in Fig. 1. The laser is divided into two parts by beam splitter BS1, one enters vapor cell, and other enters the FADOF. By scanning the laser frequency, we use PD1 to measure the transmittance spectrum of the FADOF, and PD2 the atomic absorption spectrum of the vapor cell. The green dashed in Fig. 2 is the fitted transmission spectrum, which is the result of the FADOF’s theoretical transmission spectrum calculated by ElecSus [49,50] multiplied by a coefficient for peak alignment. The FADOF works in the line center mode, so it has one main transmittance peak which is at the same wavelength as the resonance wavelength of the atom, as shown in Fig. 2. Therefore, FADOF’s work bandwidth is very narrow, generally at the GHz level (around 0.01 nm). This also means that FADOF has strict requirements on the stability of the frequency of the signal light.
Fig. 1. Experiment setup of FADOF, which includes the internal structure of FADOF, and the optical path for measuring the transmission of FADOF. BS1 is a beam splitter. PD1 and PD2 are photodiodes. The gold arrows indicate that the polarization directions of the two polarizers are perpendicular to each other. The blue arrow indicates the magnetic field direction. PD1 is used to measure the transmittance spectrum of the FADOF, and PD2 the atomic absorption spectrum of the vapor cell.
Fig. 2. The measured transmission spectrum and the measured absorption spectrum of the FADOF. The red line is measured transmission spectrum of FADOF, the green dashed is the fitted transmission spectrum, the blue line is the measured atomic absorption spectrum. FADOF measured the peak transmittance is 0.32, and it is based on potassium atoms. The magnetic field is about 750 Gs, the vapor cell temperature is about 82.6$^{\circ }$C. The equivalent noise bandwidth is 1.3 GHz.
Here, the FADOF we use is based on potassium atoms, whose resonance wavelength is 766.7 nm, equivalent noise bandwidth is 1.3 GHz (0.0025 nm), and peak transmittance is 0.32. The atoms vapor cell temperature is kept in 82.6$^{\circ }$C when FADOF start working, and the magnetic field is about 750 Gs.
2.2 Ghost imaging using FADOF
The process of GI can be described as follows. The object $O(x,y)$ is illuminated by a random speckle pattern sequence $I(x,y)$, and $I_m(x,y)$ represents the $m^{th}$ speckle pattern in the sequence ( $m = 1,2, \cdot \cdot \cdot, M$, $M$ is the number of sampling times in the ghost imaging experiment). The total light intensity measured by a bucket detector in the $m^{th}$ measurement is denoted as $B_m$, which is the total light intensity that speckle pattern transmitted through or reflected by the object, and can be expressed as
The reconstructing image $O_{GI}(x,y)$ of the object can be obtained by the correlation operation between the light pattern sequence $I(x,y)$ and the bucket values $B$ measured by the bucket detector: where $<\cdot >$ denotes the statistical mean of a sequence.The recorded speckle pattern $I_m(x,y)$ has not come into contact with the object, so only $B_m$ contains information about the object. Therefore, to improve the reconstructing image quality and decrease the number of measurements of ghost imaging, the accuracy of $B_m$ should be taken into account.
In practical applications, background light can not be ignored, and the value measured by the bucket detector always contains the background light intensity $N_{bn}$, in other words, is the sum of the signal intensity and the background light intensity. To distinguish it from $B_m$, we denote it by $B'_m$, where $B'_m=B_m+N_{bn}$. It can be known from Equation (2) that if the background light intensity remains constant, it does not affect $O_{GI}$ because it is subtracted. On the other hand, when background light varies irregularly is comparable with or even much higher than the fluctuation of the pure bucket signal, it may cause the failure of reconstructing. Such failure is derived from the lack of object information, which is difficult to solve from the algorithm aspect.
Figure 3(a) shows the simulation results of the effect of the background light noise on two ghost imaging methods, traditional ghost imaging (GI) and compressed ghost imaging (CGI). Because the mean value of noise does not affect GI, we use the standard deviation of noise to denote the noise level. The noise standard deviation is 0.5 times, 1 time, $\cdot \cdot \cdot$ , and 5000 times as the signal standard deviation, respectively. The reconstructing image becomes blurry as the noise standard deviation increases. When the standard deviation of the noise exceeds that of the signal by ten times, ghost imaging fails to reconstruct images, which means that GI obtains almost no information about the object. Such scenes are common in nature. Under normal outdoor conditions, GI is easily affected by background light, such as the sunshine, as the intensity of the received signal light is always much lower than that of the background light, especially in long distance imaging and in daytime. GI requires new methods to exclude interference from the background light.
Fig. 3. (a) simulates the influence of background light noise on GI, (b) adds the FADOF comparing with (a). And show their PSNR in (c). CGI is compressed ghost imaging. In all the above simulations, the number of measurements is 10,000 times, the pixel of reconstructing image is $280 \times 280$. The 0.5 std, 1 std, $\cdot \cdot \cdot$ , 5000 std represent respectively noise standard deviation is 0.5 times, 1 time, $\cdot \cdot \cdot$ , 5000 times as the signal standard deviation. PSNR is the peak signal to noise ratio of reconstructing image.
When using FADOF, the intensity value $B'_m$ measured by the bucket detector can be expressed as
where $\alpha$ is the signal transmission of FADOF, and $\gamma$ is the noise extinction ratio of FADOF. If $B_m \cdot \alpha$ is much larger than $N_{bn} \cdot \gamma$, the bucket detector would obtain a signal with a high signal-to-noise ratio, and the interference of background light noise would be eliminated. Figure 3(b) is a simulation of GI with FADOF and it shows the reconstructing images after using a FADOF. And $\alpha =0.32$, while $\gamma =10^{-5}$, according to actual performance of the FADOF. Compared with Fig. 3(a), ghost imaging with FADOF keeps the reconstructing image quality stable, even if it faces much stronger noises, as shown in Fig. 3(c).3. Experimental results
We test the suppressing effect of FADOF on background light noise in experiments, and compare it with a 10 nm filter. The model of the filter used for comparison is THORLABS FB770-10, and its center wavelength is $\mathrm {770 \pm 2nm}$. The measured transmission of the filter is shown in Fig. 4. FADOF is made by our own research team.
As shown in Fig. 5, our experimental setup mainly contains two modules, the first is the ghost imaging system with FADOF, and the second is the noise test module.
In the ghost imaging module, the laser passes through the rotating ground glass, and then it is divided into two beams by the beam splitter BS1. One beam is directly collected by the camera, and the other beam illuminates the object. The beam of light transmitted through the object is the signal that the bucket detector will collect. This is the common ghost imaging architecture. The difference is, we place a FADOF in front of the bucket detector to blocks the background light and let the signal pass through. Accordingly, the frequency of the laser is locked to the D2 line of potassium (766.7 nm), ensuring it stays within the FADOF’s operating bandwidth. The frequency locking is achieved by electric tuning that controls laser to scan over in a small regime around the absorption line of potassium atoms.
Fig. 5. Experiment Setup. BS1 and BS2 are beam splitters. R.G.G is a rotating ground glass. The background light source is an LED cold light. The transmission controller is a voltage-controlled photoelectric attenuator. The focal length of the Len is 175 mm. The FADOF and 10 nm filter can swap positions so as to compare. The center wavelength of the filter is $\mathrm {770 \pm 2nm}$, and its transmission is shown in Fig. 4.
The second module is used to test the effect of background light on GI and the resistance of FADOF to background light interference. In this module, we use a LED cold light to simulate background light noise. To generate randomly varying background light noise, we placed a voltage-controlled photoelectric attenuator (transmission controller) after the LED light, which changes its transmittance under the control of an external voltage. When we give the transmission controller a random voltage signal, the intensity of the light transmitted through it varies randomly. In our experiments, we first generated a random digital sequence conforming to Gaussian distribution, then convert it into analog voltage signal by a FPGA, and at last input it into the voltage-controlled photoelectric attenuator. In this way, the randomly changing background light is obtained, then it combines with the GI signal light that passes through the object, by the beam combiner BS2.
The specific experimental results are shown in Fig. 6. We perform three sets of comparative experiments, ghost imaging without any filter (GI), ghost imaging using a 10 nm filter (GI with filter), and ghost imaging using FADOF (GI with FADOF). When there is no filter element in front of the bucket detector, the power of the signal reaching the bucket detector is about $0.5\mathrm{\mu } W$ to $0.6\mathrm{\mu } W$. The maximum power of LED cold light is about $1050\mathrm{\mu } W$. The number of measurements for each ghost imaging experiment is 10,000 times. The experimental sampling speed and noise change speed are the same, both are 0.01 seconds once. Under the same noise level, the random number sequence generating noise is the same. The average value of the background light noise remains around $540\mathrm{\mu } W$, while the standard deviation changes from 10.7 to 186.1, as shown in Table 1. As the noise standard deviation increases, GI and GI with filter are gradually affected, resulting in their reconstructing images blurred or even failing to reconstruct. Only GI with FADOF keeps working normally and image quality stable when the amplitude of the change of the background light is hundreds or thousands of times of the signal, and the FADOF shows much greater performance comparing with the 10 nm filter due to its narrower bandwidth. The PSNR and SSIM curve tendency in Fig. 7 better explain the performance of FADOF. The PSNR and SSIM of reconstructing images hardly ever change when GI employs FADOF, as shown in Fig. 7(a) and Fig. 7(c), and this does not change with different algorithms. From Fig. 7(b) and Fig. 7(d), it’s clear that the image quality of CGI remains stable under high noise levels too, for the FADOF eliminates the influence of background light. This also applies to more reconstructing algorithms since they all benefit from remarkable noise reduction.
Fig. 6. Experiment result of GI with FADOF. Three groups of comparative GI experiments were done here, respectively without any filter device (No Filter), with a 10 nm filter (10 nm Filter) and with FADOF (FADOF). The first column of each groups is reconstructed by GI, and the second column is reconstructed by CGI. The number of measurements is 10,000 times, the pixel of image is $280 \times 280$. Noise1 to Noise4 represent different levels of noise, and their details are shown in Table 1.
Table 1. The mean and standard deviation of background light noise. All values are in units of $\mathrm{\mu } W$.
4. Conclusion
In conclusion, we use a physical method—an atomic filter FADOF that gives the bucket detector the ability to distinguish the signal from the background light noise, which keeps GI working normally under strong background noise light. Simulation results show that the ghost imaging with FADOF maintains normally working when the background light noise is thousands of times bigger than the signal. Results of lab experiment show that the background light noise tolerance of the ghost imaging with FADOF is at least 18 times bigger than that with a 10 nm optical filer. The method has simple structure, great performance improvement, and is compatible with almost all reconstruction algorithms.
Funding
National Natural Science Foundation of China (61771067, 61801042, 62071059).
Disclosures
The authors declare that there are no conflicts of interest.
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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