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Abstract
Ghost imaging is a promising technique for shape reconstruction using two spatially correlated beams: one beam interacts with a target and is collected with a bucket detector, and the other beam is measured with a pixelated detector. However, orthodox ghost imaging always provides unsatisfactory results for unstained samples, phase objects, or highly transparent objects. Here we present a dark-field ghost imaging technique that can work well for these “bad” targets. The only difference from orthodox ghost imaging is that the bucket signals rule out the target’s unscattered beam. As experimental proof, we demonstrate images of fine copper wires, quartz fibers, scratched and damaged glass plates, a pure phase object, and biospecimens.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Dark-field imaging is a standard imaging technique widely employed in biology and structural analysis that provides high contrast images [1]. Unlike bright-field imaging, it accentuates high spatial frequencies and can therefore be used to reveal and emphasize feature details. This technique is ubiquitous, and there are hundreds of works about dark-field imaging every year. Besides the most popular source, x-ray [2], other kinds of sources are constantly adopted with this technique, such as electrons [3], neutrons [4], luminescence [5], and Terahertz [6]. In applications, beyond bioimaging [7], this technique is also used in macroscopic object imaging [8] and atom-by-atom structural analysis [9]. This technique has achieved great success in local imaging and detection. However, there is no apparent report relating to its application in nonlocal imaging-ghost imaging.
Ghost imaging, as a novel imaging technique, has been attracting more and more attention over the last decades [10–32]. In ghost imaging, one spatially resolvable signal, having no interaction with the target, is applied to reconstruct the image by correlating it with another spatially indistinguishable signal that interacts with the target. Pittman et al. reported the first ghost image with quantum-entangled photons in 1995 [10]. Seven years later, a ghost image with a classical source [11] aroused a heated discussion about its fundamental physics [12,13]. Since then, there have been many works examining resolution and visibility [14–16]. To date, ghost imaging has been demonstrated with a variety of sources, such as, sunlight [17], x-rays [18–20], atoms [21], and others [22–25]. In order to obtain a high-quality image, many new techniques, such as computational ghost imaging [26,27], compressive ghost imaging [28], differential ghost imaging [29], and others [30–32] have been recently introduced and developed.
In recovering the targets’ shapes, the schemes mentioned above offer significant advantages, including fine resolution, high contrast, less sampling, low hardware requirements, and turbulence-free. However, only several a few strategies have been proposed for transparent pure-phase objects with entangled photons [33] and classical sources [34–36]. The reason is that orthodox ghost imaging (OGI) can produce the image for the square modulus of the transparency function of the target in mathematical representation, indicating that OGI is effectively unable to image pure phase objects directly. Nearly all these schemes utilize Fresnel diffraction or Fourier transforms between the correlated reference signal and object signal. They seldom provide satisfactory images for highly transparent objects. Moreover, a greater transparent area (reflected for reflection detection) always leads to lower visibility for ghost imaging. Although there are various methods to increase the visibility, noise will be simultaneously enhanced.
In this paper, we show a new approach for ghost imaging to recover the shapes of highly transparent objects. It is based primarily on dark-field bucket detection, and we call it dark-field ghost imaging (DFGI). DFGI can increase visibility significantly and generate the image of phase objects without need of an interferometer. We will present theoretical analysis and experimental results in the next parts, and demonstrate images for binary amplitude objects, complex amplitude objects, pure phase objects, and biospecimens.
2. Method
In OGI, a laser beam is usually injected into a diffuser to generate a dynamic speckle source (often called pseudothermal light), which is split into two identical parts. One is transmitted to a target and is completely collected by a single-pixel detector (called a bucket detector). A camera records the other one, and correlation measurement between them generates an image of the target. The setup for DFGI is similar to the setup for OGI, the only difference being that there is a block before the bucket detector to stop the transmitted light. The experimental apparatus for DFGI is shown in Fig. 1. A He-Ne laser (wavelength λ = 632.8 nm) impinges on a plate of slowly rotating ground glass (GG) with a rotation frequency of $2 \times {10^{ - 3}}$ Hz to generate the random speckle source. After passing through an iris diaphragm (ID), which allows the paraxial rays to pass, the light is split by a beam splitter (BS). The reflected beam from the BS is recorded by a charge-coupled device camera (CCD, Mintron MTV-1881EX). The transmitted beam first passes through the target, then the transmitted part from the target will be blocked by a beam dump (B), and the scattered component from the target will be recorded by a bucket detector (BD, which is composed of a large-caliber optical lens and a CCD). The distance from the GG to CCD is 30 cm. The setup is readily converted into the scheme for OGI by removal of the beam dump.
Fig. 1. Experimental setup. A beam of pseudothermal light generated from the modulation of a laser beam by a GG passes through an ID to form a paraxial source and splits into two identical beams by a BS. One beam interacts with a target and is recorded by a BD without the center part. The other beam is recorded by a CCD directly. The CCD and T are symmetrically placed about the BS. GG: ground glass; BS: beam splitter; T: target; B: beam dump; BD: bucket detector.
From the view of thermal-light correlation, in which the source is regarded as a phase-conjugate mirror [37,38], one can understand the geometrics of the experimental setup at a glance. The original dark-field imaging scheme is shown in Fig. 2(a) [39]. The hollow focused light illuminates a highly transparent target, and most light is directly transmitted, which is blocked by the edges of the aperture. The rest of the light, scattered light, enters a lens and produces an image on the screen. Interestingly, our imaging setup can be understood in an analogous way, as shown in Fig. 2(b). In the phase-conjugate mirror model, the BD works as a light source, the light from the BD travels backward to the target, and the scattered light arrives at the GG. Because the GG works as a phase-conjugate mirror, the reflected light from the GG will form an image at the target’s position. To demonstrate it clearly, we “fold” the reflected beam to the other side of the GG. Thus the setup of our DFGI becomes comprehensible, and a theory is briefly given below.
Fig. 2. Dark-field imaging setup (a) and geometrical optical view of DFGI (b). BD, GG, and CCD are the same as in Fig. 1.
After the discussing visualized view, we will present a theoretical analysis with thermal correlation. We assume the fields on the GG plane and CCD plane are ${E_0}({x_0})$ and $E(x)$, where ${x_0}$ and $x$ are the respective transverse coordinates. Because the target and CCD are placed symmetrically, the field on the target plane can be described by $E(x)$. The relation between ${E_0}({x_0})$ and $E(x)$ can be written as
The normalized second-order correlation between the two detectors can be described as
However, DFGI can go beyond these limitations. For a highly transparent object, most areas of the object will allow the beam pass through without distortion. This part is omitted because of the beam dump and the scattered part goes on to enter the BD. In the formula, the intensity from BD in the DFGI scheme will be replaced by
For our scheme, the quadric term in the exponential function can be ignored, and it has no significant influence on the output. Then, the second integration in Eq. (4) evolves into the Fourier transform of the object field, i.e.
If there is no beam dump, which means $P(x^{\prime}) = 1$, all frequency terms in Eq. (5) will be collected and the ${I_B}$ equals the value for OGI. However, in DFGI, the beam dump blocks the center portion, that is $P(x^{\prime}) = 1 - circ(x^{\prime}/r)$, where $circ({\cdot} )$ is a circle function and $r$ is the radius of the beam dump. So, $P(x^{\prime})$ works as a high-pass filter in DFGI. That means the target to be imaged in DFGI is not the original one. It is the high-frequency part of the target, and we designate it as $T^{\prime}(x)$, which indicates the alteration of $T(x)$. So, the position of the beam dump can influence the attributes of this modification. To achieve dark-field imaging, it must block the transmitted light completely. Since the high-pass filter often gives image sharpening, such as the Laplacian of the object field [41], i.e. $T^{\prime}(x) \approx {\nabla ^2}T(x)$, DFGI can work for pure phase objects. For a transparent phase object $T(x) = {e^{i\varphi (x)}}$, where $\varphi (x)$ is the phase distribution. We immediately find that $|{T(x)} |= const$, while $|{T^{\prime}(x)} |\approx |{{\nabla^2}\varphi (x)} |\ne const$. This is the key theory for the success of DFGI. Because $T^{\prime}(x)$ incorporates much less transmitted area, visibility is enhanced significantly. We note that there has been a recent work about computational ghost imaging of occluded objects with a simple and convenient scheme [42]. However, our scheme can provide high contrast and clear images. In the next section, we will demonstrate the images with DFGI for different kinds of objects.
3. Results
3.1 Pure amplitude binary object imaging
First, we choose a simple amplitude object made of two cross copper wires (diameter $35\mu \textrm{m}$), as shown in Fig. 3(a). The inset in Fig. 3(a) shows the details of the wires. Figure 3(b) shows the normalized second-order correlation between the center pixel and the whole plane on the CCD, reflecting the resolution of this system. Figure 3(c) is the image with DFGI after 30,000 sampling frames. For contrast, the OGI image is presented in Fig. 3(d). In Fig. 3(c), we can distinguish a prominent cross image with much lower noise. The resolution of this image is as expected as in Fig. 3(b). However, the image is hardly discernable in Fig. 3(d) because of the intense noise and small diameter (smaller than the resolution of the system) of the wires. In comparison with the OGI image in Fig. 3(d), the DFGI image has better contrast, since the scatted light of the sample is collected and the background is depressed.
Fig. 3. Correlation imaging of copper wires. (a) The object of cross wires and its details in the inset. (b) Normalized second-order correlation between the center pixel and the whole plane. (c) The image by DFGI. (d) The image by OGI.
3.2 Strongly refracted object imaging
For the second test, we replaced the copper wires with quartz fibers (diameter $200\mu \textrm{m}$), as shown in Fig. 4(a). The inset in Fig. 4(a) shows the details of the fibers. Figure 4(b) shows the image with DFGI, and the image is also evident and with good contrast. It is the image of the fibers’ profile, not just the image of the edges because the fibers partially transmit and strongly refract. Figure 4(c) shows the image with OGI, and it is not difficult to discern the outline image drowned in the noise. We can see that the image in Fig. 4(c) has reversed contrast. It is the real image and reasonable because the fibers attenuate the light.
Fig. 4. Correlation imaging of quartz fibers. (a) The quartz fibers and details in the inset. (b) The image by DFGI. (c) The image by OGI.
3.3 Damage imaging
Here, we will explore the images of two strongly scattered objects. The first is scratches on a glass plate, shown in Fig. 5(a). The line width is about $15\mu \textrm{m}$ as depicted in the inset. Figure 5(b) shows a good contrast image obtained with DFGI. For comparison, Fig. 5(c) shows the equivalent image with OGI. We can observe no trace of the scratches, and this is because the object lets nearly the all light pass through unimpeded.
Fig. 5. Correlation imaging of scratches. (a) The photo of a scratched glass plate and its details in the inset. (b) The image by DFGI. (c) The image by OGI.
The second scattered object is a damaged glass plate shown in Fig. 6(a). To clarify its structure, we provide a sketch in Fig. 6(b). The upper green region is the air, and the blue area is glass. The black line denotes the edge, and the three red lines are fractures in the glass. The correlation image with DFGI is presented in Fig. 6(c), where the edge and damaged sections are clearly visible. Here, it is notable that the left and right fractures are more conspicuous than they are in the photograph in Fig. 6(a). Like the last object, we cannot find any features in the correlation image by OGI in Fig. 6(d).
Fig. 6. Correlation imaging of the damaged glass plate. (a) The photo of a damaged glass plate and its details in the inset. (b) Sketch of the object. (c) The image by DFGI. (d) The image by OGI.
3.4 Pure phase objects imaging
Pure phase objects are difficult to image without interferometers. Even for first-order correlation imaging, interferometers are necessary [43]. Because of this inherent disability, OGI cannot provide an image of a pure phase object. In this section, we will demonstrate the advantage of DFGI for imaging phase objects. We choose an object present in Fig. 7(a). The edge of a glass substrate is visible in Fig. 7(a), and the phase sample is located in the red box. Because the phase object is completely transparent, we provide a sketch of the area within the red box, in Fig. 7(b). The genuine phase object is composed of two Chinese characters with a phase $\pi$ over the substrate. The result of the DFGI is shown in Fig. 7(c), and we can observe the characters clearly. However, the image just shows the edges of the characters; this is because DFGI just presents the regions with modification. The areas inside and outside of the characters’ edges are homogeneous and thus, are undetected by DFGI. As expected, OGI does provide no information about the phase object, as shown in Fig. 7(d).
Fig. 7. Correlation imaging of the pure phase object. (a) The photo of the phase object. (b) Sketch of the features in red box area in (a). (c) The image by DFGI. (d) The image by OGI.
3.5 Biospecimens imaging
The last object we chose was a mosquito shown in Fig. 8(a), (a) number of features were examined. First, we put the mosquito wing on a glass plate and illuminate the area within the dotted circle, as shown in Fig. 8(b). The line width of veins is just about $10\;\mu \textrm{m}$, and most veins are close to this, so we introduced a demagnified imaging lens pair with a demagnification of $0.6$. The wing image with DFGI is presented in Fig. 8(c), and we can easily observe the veins and wing edge. For comparison, the corresponding OGI is presented in Fig. 8(d), and it hardly reveals any information. The second feature we examined was a leg, as shown in Fig. 8(e). The width of the first segment is about $150\;\mu \textrm{m}$ as shown in the inset of Fig. 8(e). We can produce a high-quality image of this leg with DFGI in Fig. 8(f). Similar to the image of the phase object, the image displays the edges of the leg. This is also because the area inside the leg is homogeneous. Figure 8(g) is the image obtained with OGI, we can with some effect see the outline of the leg, but the contrast is extremely low. In addition, the area of the left end of the leg in Fig. 8(f) is much brighter than other areas, this is because there is a tiny drop of glue that is more efficient at scattering the light. Furthermore, horizontal striped backgrounds were observed in all the images, this is especially noticeable in Fig. 8(g). The presence of such artifacts suggest that the speckles patterns generated by the rotating ground glass are not completely independent from one another. This defect generates nearly the same magnitude influence on all results. However, it is more significant for low contrast images like Fig. 8(g), and relatively inconspicuous for high contrast image like Fig. 8(f).
Fig. 8. Correlation imaging of the biospecimens. (a) The photo of the biospecimen: a mosquito. (b) The photo of a wing to be imaged. (c) The image of the wing by DFGI. (d) The image of the wing by OGI. (e) The photo of a leg to be imaged. (f) The image of the leg by DFGI. (d) The image of the leg by OGI.
4. Conclusions
We have demonstrated ghost imaging for highly transparent objects by omitting the transmitted light from the bucket detection. The DFGI scheme collects the scattered light from the target and provides clear images with good contrast. It has the advantage that it can also generate images for pure phase objects, which is impossible for OGI. Compared to other techniques, DFGI is especially suitable for highly transparent, scattering or refractive objects. In addition to its suitability for human-made objects, it would be suitable for biological tissue, especially for live and unstained biological samples. Also, it inherits the merit of robustness with respect to turbulence [44], and generates high-contrast features above noise levels.
To data, several ingenious schemes have been proposed and demonstrated for ghost imaging, such as, blind ghost imaging, computational ghost imaging, and compressive ghost imaging. They present many of advantages in ordinary ghost imaging. Our scheme is not mutually exclusive with respect to them. Combined with the method of DFGI, these schemes should also work and would extend their applicability to objects which allow strong transmission and biological samples.
Funding
National Natural Science Foundation of China (11504271).
Disclosures
The authors declare no conflicts of interest related to this paper.
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