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Abstract
We demonstrate lensless single-fiber ghost imaging, which allows illumination and collection using a single optical fiber without a transmission-type system. Speckle patterns with relative coincidence degrees of 0.14 were formed by image reconstruction using improved differential ghost imaging. Employing fiber with a diameter of 105 µm, we achieved a spatial resolution of 0.05 mm in an observing area of ${9}\;{{\rm mm}^2}$, at a working distance of 10 mm. Compared to a conventional neuroendoscope at a power density of ${94}\;{{\rm mW/cm}^2}$, our imaging could be realized by extremely weak illumination at a laser power density of ${0.10}\;{{\rm mW/cm}^2}$. Using our lensless single-fiber ghost imaging, with 30,000 speckle patterns and implementing a diffuser, we attained an average coincidence degree of 0.45.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
Advanced optical endoscopy has achieved remarkable progress, obtaining revolutionary images by tailoring the nature of the light used, such as using a broadband spectrum, coherence, and even polarization [1–4]. Optical endoscopy helps diagnose diseases inside a body’s deep blood vessels and can assist in surgery [5,6]. Its application has been expanded to medical diagnosis and industrial inspections [7]. To date, lensless fiber imaging has attracted attention for use in minimally invasive diagnosis [8]. There are two minimally invasive fiber imaging solutions using a multimode optical fiber and an optical fiber bundle [9,10]. Ultrathin fiber imaging with a diameter below 100 µm applying light shaping through a multimode optical fiber has been proposed [10–14]. Thin fiber imaging can create images by analyzing light wave propagation in multimode optical fiber and solving the inverse problem. This fiber imaging can record dynamic changes of macroscopic objects in a far field of several 100 mm. In contrast, a holographic lensless optical fiber bundle endoscope with a diameter below 1 mm, consisting of several 10,000 optical fibers, achieved microscopic imaging of unstained biological tissues with a high spatial resolution of 0.89 µm at a distance of several 100 µm from the top of the fiber instrument [15–18]. Such fiber imaging is a candidate for endoscopy for rapid medical diagnosis. In recent years, spatial-frequency tracking adaptive beacon light-field-encoded endoscopy has been proposed to enhance the imaging signal-to-noise ratio and achieve super-resolution endoscopy at 250 nm [19].
However, even innovative research is limited to far-field images or close proximity to the distal end of the optical fiber probe to prevent speckle artifacts [9–19]. The meso-field between several mm and several 10s of mm from the fiber probe is an unexplored region that cannot be captured by conventional single-fiber imaging. In particular, angioscopy in catheter treatments often requires observing objects in the meso-field below several ${{\rm mm}^2}$ at a distance below 10 mm from the end of the optical fiber [20]. Furthermore, conventional angioscopy using optical coherent tomography and a small CMOS camera requires a saline flush due to blood removal [21], which involves a risk of causing rapid changes in intravascular pressure inside thin blood vessels on plaques. Therefore, conventional optical angioscopy cannot be applied to the clinical environment mentioned above because of the high invasiveness required. Optical angioscopy without a saline flush, such as intravascular ultrasound, is strongly required. For this purpose, it is important to develop an advanced optical endoscopy technique that is resistant to image deterioration through opaque scattering conditions, such as blood.
For this, speckle correlation using rigorous phase retrievals has been proposed as an approach toward imaging under a scrambled light field [22]. Concurrently, differential ghost imaging, in which images are generated by enhancing the signal-to-noise ratio from covariance between a speckle pattern and scattering light, has proven its superiority in image reconstruction through scattering media [23,24]. The initial potential of these techniques promised to facilitate the development of a new generation of optical fiber endoscopy, overcoming the fundamental problems of optical endoscopes. Ghost imaging with multicore or multimode fiber illumination, illustrated in Fig. 1(a), produces images by transmission through an object and using an external detector [25–30]. However, studies have been limited to creating images using optical systems other than endoscopes. Furthermore, they were constrained to performing transmission-type image generation due to the difficulty of maintaining illumination stability. Even single-fiber ghost imaging, as illustrated in Fig. 1(b), where a single optical fiber is used for illumination and collection, has not been realized. To the best of our knowledge, there are no reports of single-fiber ghost imaging under scattering media, as shown in Fig. 1(c), having been achieved. Single-fiber imaging with a small aperture makes collecting photons backscattered from an object more difficult. Illumination with high power density will, conversely, cause burn injury to the body. Therefore, it is important for single-fiber imaging to create high-contrast images with weak illumination and low power density. It has been shown that Hadamard transform imaging can retrieve images under low signal-to-noise ratio conditions [31], and may be a key to extremely minimally invasive single-fiber imaging. Based on this background, we focused on solutions for the unexplored regions of ultrathin fiber imaging, the power density of illuminating light, and optical scattering problems.
Fig. 1. Comparison between previous studies and our lensless single-fiber ghost imaging. (a) Transmission-type approach using an external bucket detector. (b) Our single-fiber ghost imaging using illumination and collection through a common optical fiber. (c) Our single-fiber ghost imaging using scattering media.
Here, we demonstrate lensless single-fiber ghost imaging. We clarified the stability and relative coincidence of structured light through an optical fiber. For reconstructed images, we determined the spatial resolution of our imaging. For comparison to a neurosurgery fiber bundle endoscope, we also investigated the effectiveness of our imaging under extremely weak illumination. We finally evaluated our imaging reconstruction under opaque scattering conditions.
2. METHODS
A. Principle of Single-Fiber Ghost Imaging
Achieving lensless single-fiber imaging requires forming structured light after passing through a multimode optical fiber, which then allows the spatial coordinates to be registered. We observe speckle patterns as the structured light, although speckling has been treated as a problem in previous single-fiber imaging research [9–19]. Figure 2 shows the concept of our lensless single-fiber ghost imaging. Light generated from a pseudo-thermal light source is incident onto a rotating diffuser. After the diffuser, the scattered light is collected and focused on the top of a multimode optical fiber by an objective lens. The spatial code can be obtained from the speckle pattern generated after passing through the multimode optical fiber. The light beam with the speckle pattern then passes through a diffuser and the light beam is separated into back and forward scatterings, depicted by ${b_s}$ and ${f_s}$, respectively. The forward-scattering light illuminates the object, and the light scattered by the object illuminates the diffuser again. A multimode optical fiber corrects the scattered light represented by $f_s^\prime$. A single-pixel detector then detects the light signal. The basic principle of our lensless single-fiber ghost imaging is to detect components of the speckle pattern scattered by the diffuser that propagates straight ahead without scattering. This is achieved through spatial sorting using the optical fiber and extremely weak light detection in ghost imaging. In our procedure, preregistered speckle patterns and light signals are correlated by a computer. Two images ${G_K}$ are obtained with and without the object, A and B, and the image of $G$ is retrieved by subtracting A from B. Finally, the contrast of the object image is improved by normalizing the maximum and minimum values of the retrieved image.
Fig. 2. Concept of our lensless single-fiber ghost imaging. Light from a pseudo-thermal light source is incident onto a rotating diffuser. The scattered light is collected by an objective lens and focused onto the top of a multimode optical fiber. The light beam, which is spatially coded by a speckle pattern, illuminates an object through a diffuser. Here, the light beam is separated into backscatterings and forward scatterings, ${b_s}$ and ${f_s}$, respectively. The forward-scattered light illuminates the object. The light scattered by the object illuminates the diffuser again. The multimode optical fiber corrects the scattering light, represented by $f_s^\prime$. A single-pixel detector detects the light signal. A computer correlates preregistered speckle patterns and light signals.
B. Differential Ghost Imaging with Normalization
Differential ghost imaging has been proposed to enhance the signal-to-noise ratio of reconstructed images in [23,24]. In Fig. 2, the speckle patterns registered with $n$ images are captured by a CMOS camera as ${I_n}({x, y})$, and detected as a bucket signal ${B_n}$ by an avalanche photodiode (APD). Conventional differential ghost imaging $G({x, y})$ is expressed as
where $\langle \cdots \rangle$, ${\Delta}{I_n}({x, y})$, and ${\Delta}{B_n}$ are an ensemble average, the intensity fluctuations of speckle patterns, and that of the bucket signal, respectively. Their fluctuations can be rewritten asThe bucket signal can be rewritten as
The ensemble average of the scattering property of the object is represented as a ratio of the bucket signals ${B_{1n}}$ and ${B_{2n}}$. ${B_{2n}}$ is also expressed as
Using maximum and minimum intensities on the reconstructed image of $G({x, y})$, we retrieved an image of the object as
C. Reconstructed Image under Scattering Conditions
The essence of our strategy is to reconstruct an image of an object under scattering conditions. As shown in Fig. 2, the object is placed behind a diffuser sheet. We designed an imaging method using scattering light after passing through the diffusers. In the case of no diffuser, the scattering condition $S({x, y})$ is expressed as
In contrast, we obtained the scattering condition without an object as
Inserting an object as a sample, the scattering light consists of backscattered light ${b_s}({x, y})$, forward scattered light ${f_s}({x, y})$, object scattered light ${O_s}({x, y})$, and forward scattered light $f_s^\prime ({x, y})$ after scattering from the object. The scattered light is given as
3. RESULTS
A. Experimental Setup
We show the experimental setup for single-fiber ghost imaging in Fig. 3 and also in Fig. S1 in Supplement 1. A laser diode (LD, LTC56B, Thorlabs) and a thermal controller (TC, TED200C temperature controller, Thorlabs) were employed to generate a stable light beam. A rotating diffuser (RD, DG100X100-120, Thorlabs) performed as a speckle generator. An isolator was used, composed of a Glan–Thompson prism polarizer (P, GTH10M-B, Thorlabs) and a Fresnel rhomb (FR, R600QM, Thorlabs), to block the returned light. The light with a speckle pattern generated by the rotating diffuser was collected by an objective lens (OL, M-Plan Apo 20X, Mitutoyo). It was incident into an optical fiber for illumination. We employed two branch multimode optical fibers (MMF, BFY105, Thorlabs) to prevent returned light from the end face of the optical fiber and an optical circulator. A rotation stage (PS60BB-360 R, Coms) was used to control the speckle patterns. We captured the speckle patterns using a two-dimensional sensor (2DS, STC-MBS43U3V, Omron Sentech). The backscattered light was passed through another optical fiber and the scattering intensity was measured by an avalanche photodiode (APD, APD440A2, Thorlabs). The voltage signal from the photodiode was recorded by an input module (NI-9239, National Instruments). The rotation stage, CMOS, avalanche photodiode, and input module were controlled by LabVIEW (National Instruments). The captured image was processed by a custom Python code.
Fig. 3. Speckle pattern property in lensless single-fiber ghost imaging. (a) Experimental setup. (b) Speckle patterns generated through a multimode optical fiber at a distance of (b1) $z = {10}\;{\rm mm}$ and (b2) 20 mm from the optical fiber. (c) Time-sequential coincidence degree of speckle pattern. (d) Histogram of degree of coincidence calculated for ${30} \times {30}\;{\rm pixels}$ and $N = {6{,}000}$. The scale bars in (b1) and (b2) are 1 mm.
The speckle pattern control is schematically shown in Fig. 3(a). (See Fig. S1 in Supplement 1 for the experimental setup.) We employed a laser diode (LD) controlled by a thermal controller (TC), with a central wavelength of 840 nm and a spectral bandwidth of 1 nm. The diffuser was mounted on a rotation stage with a resolution of 0.01°. We applied an output laser power of 0.287 mW through the optical fiber. This experimental setup could produce different speckle patterns at every angle of the rotating diffuser.
In advance, we conducted a registration of speckle patterns with ${I_n}(x,y)$ using a two-dimensional sensor (2DS) at a distance of $z$ from the top of the optical fiber, where $n$, $x$, and $y$ are the index number and coordinates, respectively. The CMOS camera enables us to capture speckle patterns at 25 frame/s. By rotating the rotating diffuser at rotation angle steps of 0.06° over 4 min, we captured different speckle patterns with numbers of $n = {6{,}000}$. To obtain more speckle patterns, an $x$ axis stage was used to incrementally shift the scanning area on the diffuser. In this way, we generated several clusters of speckle patterns with $n = {6{,}000}$. The speckle patterns recorded are shown in Visualization 1. After performing this registration, we replaced the sensor with a sample. The sample was illuminated with the speckle patterns in the registration, and the scattered light was passed through the second of the two optical fibers. The scattering intensity of ${B_n}$ was detected by an avalanche photodiode (APD). In our experiments, we employed a CMOS camera with ${720} \times {540}\;{\rm pixels}$. The images captured by the CMOS camera were resized to ${540} \times {540}\;{\rm pixels}$. After resizing, the image resolution was reduced to ${100} \times {100}\;{\rm pixels}$ by pixel skipping, which is known as decimation. Figure S2 in Supplement 1 shows a comparison of the images before and after the decimation. The decimated image reflected an original image with ${540} \times {540}\;{\rm pixels}$.
B. Sample Preparation and Laser Drawing System
First, we declare that we did not conduct any experiments using human or animal blood. For this reason, our experiments do not require ethical review for human or animal experimentation.
To perform our single-fiber ghost imaging, the objects, which were made of infrared reflected tape (Hansha, Custom), were manually fabricated. Thus, dark areas on the reconstructed images indicate air. The object was fabricated by a laser drawing system controlled by two-axis motorized stages, as shown in Fig. S2 in Supplement 1. The dark areas on the reconstructed image indicate burnt spots. See Fig. S2 in Supplement 1 for our fabricated samples. We also show our laser drawing system in Fig. S2(d) in Supplement 1.
C. Test of Spatial Resolution
To estimate the spatial resolution of this imaging, we measured the speckle sizes at $z = {10}\;{\rm mm}$ and 20 mm, which is shown in Fig. 3(b). The speckle sizes had diameters of $0.07\pm {0.01}\;{\rm mm}$ and ${0.13} \pm {0.01}\;{\rm mm}$, respectively. These results represent the spatial resolutions of this imaging. In our experiments, we also evaluated the stability and difference by the number of speckle patterns. Figure 3(c) shows the time stability of a speckle pattern over 30 min. The speckle pattern was compared to the image at time $t = {0}\;{\rm s}$. The speckle pattern was stable over 4 min with a coincidence degree of 0.98. The coincidence degree between images was calculated by $C = {S_{{AB}}}/({S_A} \cdot {S_B})$, where ${S_{{AB}}}$, ${S_A}$, and ${S_B}$ denote the sample covariance between images A and B and the standard deviations of A and B, respectively. Note that we defined the coincidence degree to avoid confusion with the optical correlation in the ghost imaging. It is necessary for our imaging to be able to distinguish the speckle patterns in each recorded image. We computed the coincidence degrees using 6,000 images, which recorded different speckle patterns at $z = {10}$ and 20 mm, as shown in Fig. 3(d). The averages of the coincidence degrees at $z = {10}$ and $z = {20}\;{\rm mm}$ were 0.14 and 0.04, respectively. These results prove that our structured light generator suppresses the memory effect of the speckle patterns. To evaluate the spatial resolution of our endoscopic fiber imaging we fabricated two 0.5 mm squares as samples and measured the relative position of the centers on the two squares as a function of displacement as measured by a micrometer. See Figs. S2 and S3 in Supplement 1. Note that the material of the samples included infrared reflective tape, which uses a conventional infrared marker. Figure 4(a) shows a schematic diagram of the sample, with the displacement $x$ given to the right square of the two squares. Figure 4(b) shows two images of ${100} \times {100}\;{\rm pixels}$ at micrometer positions of $x = {0.00}$ and 0.05 mm. We measured the position of the center on the right square over a range of displacements up to 1.00 mm, shown in Fig. 4(c). See Fig. S4 for the reconstructed images with displacements at every 0.05 mm in Supplement 1. For these measurements, we reconstructed the endoscopic fiber imaging with a spatial resolution of 0.05 mm. This resolution accorded with a speckle size of 0.07 mm. Note that the spatial resolution was limited by the laser diode’s wavelength, the optical fiber’s NA, and the pixel size on the CMOS. See Fig. S5 in Supplement 1 for the relationship between the speckle size and the wavelength and fiber diameter.
Fig. 4. Resolution of lensless single-fiber ghost imaging. (a) Schematic diagram of sample setup. (b) Reconstructed images at displacements of (b1) $x = {0}$ and (b2) $x = {0.05}\;{\rm mm}$. (c) Difference in displacement measured from the centers of the two squares. The scale bars in (b1) and (b2) are 1 mm.
D. Comparison to Conventional Bundle Fiber Imaging with a Lens
To demonstrate single-fiber imaging of a sample with a complex shape, we fabricated a cross with a dimension of 2 mm as a sample, as shown in Fig. 5(a); also see Fig. S2 in Supplement 1. The sample was placed at $z = {10}\;{\rm mm}$ from the top of the optical fiber. To compare to a conventional endoscopic image, we captured an image using a neuroendoscope (NEU-4, Machida Endoscope Co., Ltd.; overall length 580 mm, diameter 4.2 mm), which is a bundle of 5,000 400 nm diameter optical fibers with a lens at the top of the fiber bundle, with a neuroendoscope image of the cross-shaped sample shown in Fig. 5(b). We then conducted single-fiber ghost imaging of the cross using recorded speckle patterns. Figures 5(c)–5(e) show the results using speckle patterns of $n = {1{,}000}$, 10,000, and 30,000, respectively; also see Fig. S6 in Supplement 1 for a comparison with images reconstructed between GI and differential GI. Figure 5(e) exhibits a sharp edge on the cross compared to Fig. 5(b). Figure 5(f) shows the coincidence degree between the reconstructed images by our method and the conventional endoscopic image in Fig. 5(b). Two coincidence degrees are depicted for the cross sample and a square sample, by red triangles and blue squares, respectively, with the reconstructed image and conventional endoscopic image of the square shown in Figs. 5(f1) and 5(f2), respectively. The maximum coincidence degree of the cross and the square are 0.70 and 0.78, respectively. According to [32], these values imply strong correlations. The coincidence degrees were calculated with the conventional endoscopic fiber images shown in Figs. 5(b) and 5(f2), respectively. Note that the images shown in Figs. 5(b) and 5(f2) were used as standard images for the calculation of coincidence degree, despite not being clear images. The laser powers used for the conventional endoscopic imaging and our method were 105 mW and 0.287 mW, respectively. The results show that our fiber ghost imaging enables the reconstruction of images at an extremely low laser power.
Fig. 5. Experimental results of lensless single-fiber ghost imaging without scattering media. (a) Picture of a sample. (b) Image by a conventional neuroendoscope. Reconstructed images with speckle patterns of: (c) $n = {1{,}000}$, (d) 10,000, and (e) 30,000. (f) Coincidence degree for cross and square samples against the number of recorded speckle patterns. Images of the square sample using (f1) our fiber imaging and (f2) conventional endoscopic imaging.
E. Single-Fiber Ghost Imaging with Extremely Weak Illumination
To investigate our lensless single-fiber ghost imaging using extremely weak illumination, we fabricated a sample in the shape of a letter “s,” as shown in Fig. 6(a); also see Fig. S2 in Supplemental 1. Using the conventional endoscopic fiber imaging mentioned above, we captured the sample at power densities of ${94}\;{{\rm mW/cm}^2}$ and ${1800}\;{{\rm mW/cm}^2}$, as shown in Figs. 6(b1) and 6(b2), respectively. The intensity in Fig. 6(b1) is very weak. Moreover, the image quality in Fig. 6(b2) is poor. We conducted single-fiber ghost imaging of the “s” sample. Figures 6(c)–6(e) show images obtained at power densities of 0.1, 1.0, and ${2.5}\;{{\rm mW/cm}^2}$, respectively. In Fig. 6(f1), we show the coincidence degree compared to the reconstructed image in Fig. 6(b2). The red circles were normalized by a common maximum and minimum power density from 0.10 to ${0.50}\;{{\rm mW/cm}^2}$. The blue circles were calculated with individual maxima and minima. Note that the difference between common and individual metrics lies in the normalization. The normalization based on the individual maximum and minimum values defined for each obtained image resulted in sharper images compared to the normalization using common maximum and minimum values throughout this experiment.
Fig. 6. Single-fiber ghost imaging with weak illumination. (a) Picture of a sample. (b) Images of a conventional neuroendoscope at power densities of (b1) 94 and (b2) ${1800}\;{{\rm mW/cm}^2}$. (c)–(e) Images reconstructed with speckle patterns of $n = {6{,}000}$ at power densities of (c) 0.1, (d) 1.0, and (e) ${2.5}\;{{\rm mW/cm}^2}$. (f) Comparison of power density properties of coincidence degree and CNR by normalization criteria: (f1) coincidence degree and (f2) CNR. The red circle data were normalized by a common maximum and minimum in the power density from 0.10 to ${0.50}\;{{\rm mW/cm}^2}$ while the blue circle data were calculated from the maxima and minima in individual images.
At a power density of ${0.10}\;{{\rm mW/cm}^2}$, the maximum coincidence degree was 0.79, implying a strong correlation. See Fig. S7 in Supplement 1 for a comparison of images reconstructed between DGI with common and individual normalization. The contrast noise ratios (CNR) obtained by ${\rm CNR} = ({\bar A - \bar M})/\sqrt {{\sigma _A^2} + {\sigma _M^2}}$ are also shown in Fig. 6(f2). Here, $\bar A$ and $\bar M$ denote the average intensities on an aperture and a mask of the cross and ${\sigma _A}$ and ${\sigma _M}$ are the standard deviations of these intensities, respectively. The maximum CNR was 1.50 at a laser power density of ${0.10}\;{{\rm mW/cm}^2}$. Our endoscopic fiber image was able to produce an image for an extremely weak illumination with a magnitude of 1/940 of that of the conventional neuroendoscope. Note that the decrease in the coincident degree and CNR with a higher power density in an individual normalization resulted from the blurred image of the neurosurgical endoscope in Fig. 6(b2), which was used for comparison. Normalization for our imaging method effectively improved the coincidence degree and CNR of our imaging with extremely weak illumination.
Fig. 7. Demonstration of single-fiber ghost imaging under scattering conditions. (a) Experimental setup. To compare our imaging to conventional fiber imaging, we conducted an experiment using a conventional endoscope. (b) Images captured by a conventional neuroendoscope using a square sample with no scattering. (c) Neuroendoscopic image after passing through a diffuser: (c1) Image after computation of (c2)–(c3). (c2) Image captured through the diffuser after inserting the square sample. (c3) Image captured through the diffuser before inserting the sample. (d) Image reconstruction process under a scattering field. (d1)–(d5) Images reconstructed with speckle patterns of $n = {1{,}000}$, 5,000, 10,000, 20,000, and 30,000, respectively. The scale bars in (b)–(d) are 1 mm. (e) Coincidence degree, compared to images shown in (b), against the number of speckle patterns. (f) Microscopic image of the sample.
F. Single-Fiber Imaging Through Opaque Scattering Media
One of the strong points of ghost imaging is the resistance to imaging deterioration due to scattering. To obtain an image reconstructed through a scattering media, we built the optical layout shown in Fig. 7(a). We used a sample consisting of a 0.5 mm square and a CMOS at $z = {20}\;{\rm mm}$, and inserted a diffuser sheet (#No. 4, Renian) at $z = {10}\;{\rm mm}$. Note that the distance to the sample is different from the previous experiment setup shown in Fig. 3 because of the insertion of the diffuser. We also observed the square using a conventional endoscope for comparison. Figure 7(b) shows the neurosurgical endoscopic image under a halogen lamp. Note that the image quality is not good because of the low spatial resolution of this endoscope. Figure 7(c1) shows an image of the sample reconstructed after passing through the diffuser. This image was calculated by $I = {I_A} - {I_B}$ from two images, where ${I_A}$ and ${I_B}$ denote the images through the diffuser with and without the sample, as shown in Figs. 7(c2) and 7(c3), respectively. Note that the retrieved image shown in Fig. 7(c1) lost sight of the sample because of the influence of the scattering media.
To realize single-fiber ghost imaging with no image deterioration due to scattering, we captured two images, first without the square sample through the diffuser, as shown in Fig. S2 in Supplement 1, and then with the square sample. We generated the image $G$ of the sample through the scattering medium as $G = {G_A} - {G_B}$, where ${G_A}$ and ${G_B}$ indicate the reconstructed images with and without the sample (see Section 2.3). Figures 7(d1)–7(d5) show images calculated by our imaging using registered speckle patterns with $n = {1{,}000}$, 5,000, 10,000, 20,000, and 30,000, respectively. The images reconstructed for the $n = {1{,}000}$ and 5,000 speckle patterns show nothing identifiable. For $n = {10{,}000}$ [Fig. 7(d3)], the sample is starting to become visible, and the appearance of the sample could be observed for $n = {30{,}000}$ in Fig. 7(d5). We calculated the coincidence degree compared to the conventional image shown in Fig. 7(b). Figure 7(e) shows the coincidence degree against the number of recorded speckle patterns. The maximum coincidence degree reached 0.45 for 30,000 speckle patterns, implying a moderate correlation based on [32]. Although the coincidence degree was not strong, the shape of the image reconstructed in Fig. 7(d5) was similar to the microscopic image without the diffuser in Fig. 7(f). Note that the center of the sample showed low scattering under the optical microscope. Using more speckle patterns, we expected to obtain an image with a high coincidence degree. To evaluate images under optical scattering conditions, we performed further experiments using other diffuser sheets with different scattering levels. See Figs. S8, S9, and S10 in Supplement 1 for reconstructed images under various scattering conditions.
4. DISCUSSION
We demonstrated lensless single-fiber ghost imaging, which allows both illumination and correction using a single optical fiber without a transmission-type system. Using different speckle patterns, we found that the spatial resolution of our fiber imaging was 0.05 mm at $z = {10}\;{\rm mm}$, but this spatial resolution depends on the speckle size of the illuminating light. Generating light with a small speckle pattern requires a laser source with a short wavelength and/or a multimode optical fiber with a large diameter. Employing a laser with a wavelength of 520 nm gave a speckle size of 55 µm diameter. By analyzing multiple speckle patterns, the spatial resolution of single-fiber ghost imaging could be greatly improved. For our experiment shown in Fig. 3(b1), the spatial resolution of the fiber imaging was 5/7 times the speckle size. For a 200 µm diameter optical fiber employed at a wavelength of 520 nm, we estimated the spatial resolution of our fiber imaging to be 25 µm by calculating the speckle size in Fig. S5(e) in Supplement 1, which is sufficient for single-fiber imaging.
In extremely minimally invasive medicine, our imaging method has significant advantages in the clinically meaningful meso-field, allowing image reconstruction under scattering conditions and single-fiber imaging with ultrathin diameter fibers and weak illumination. Such advantages are suitable for observations inside small blood vessels in brains and hearts. Imaging in the meso-field is also important for plaque removal and catheter ablation. In extremely minimally invasive diagnoses, it is necessary to use ultrathin fiber imaging and image objects under optical scattering conditions without a saline flush. We also achieved single-fiber imaging with extremely weak illumination with a power density of 1/940 compared to a conventional endoscope used in neurosurgery endoscopy. However, considering the total irradiation energy, our method provided significantly greater energy. In human bodies, the power density per single shot is crucial from the perspective of the damage threshold. We believe our approach is much safer and superior compared to conventional methods. Considering the thermal diffusion in the bloodstream, our method poses no risk of harm to living tissues.
In image reconstruction through a diffuser, the reconstructed image was improved according to the number of speckle patterns, as shown in Fig. 7. However, it is worth noting that it took 20 min to generate 30,000 speckle patterns. This is limited by the stepping motor control used in the rotating diffuser. Using a rotation stage controlled by a DC servo motor with a high-precision encoder and a high-repetition pulse laser, our fiber imaging could reconstruct an image of an object with speeds ranging from 0.1 to 10 frames/s. Moreover, we expect that a stable silicon photonics phased array [26,27] and a high-speed spatial light modulator [33] could be used for high-speed fiber imaging. Measuring a cross-shaped sample, shown in Fig. 7, gave a coincidence degree of 0.70 using 30,000 recorded speckle patterns. To further improve the imaging quality and reduce the number of speckle patterns, deep learning is a potentially effective approach [34–36]. Although we employed a single-fiber composed of twin fibers for illumination and detection in this experiment, we can also realize single-core fiber imaging by introducing an optical circulator with anti-reflective coatings. Moreover, the quality of the image reconstructed under the optical scattering condition would be further improved if detection at a time gate could be introduced by stabilized pulsed lasers.
Here, we address the limitations of our experiment. We applied differential ghost imaging in our experiment and validated the image reconstruction when passing through a diffuser in optical scattering fields. However, the light scattering field in the human body is very complex, and our simplified experimental setup does not fully capture this complexity. Nonetheless, various methods for imaging optical scattering fields have been proposed in previous research, and we expect that incorporating these approaches can improve the imaging results. It is worth noting that there have been no previous demonstrations of imaging optical scattering fields for single-fiber imaging. From this perspective, we expect that our technique will play a crucial role in developing future catheter diagnostic technologies.
Our fiber imaging with weak power density under scattering media is sufficient to prevent heat damage by the laser beam. For this reason, our strategy opens a new route toward extremely minimally invasive medicine. Our approach also offers various possible applications, such as biopsy imaging using hyperspectral imaging [37], three-dimensional imaging [7,14], and even polarization imaging [38]. However, the single-fiber imaging presented here is limited to working as a rigid scope because the speckle patterns are changed by bending the optical fiber. However, various methods to control speckle patterns have been proposed in recent years. In particular, we note that multimode interference can effectively generate various speckle patterns [39,40]. Previous studies have clarified that several mm lengths of multimode optical fiber can exhibit unique electric field propagation. Spectral sweep lasers enable the generation of various speckle patterns. We anticipate that our lensless single-fiber ghost imaging can be applied to medical design and will be useful for various applications in neurology and cardiology.
5. SUMMARY AND OUTLOOK
In summary, we have demonstrated lensless single-fiber ghost imaging, which allows illumination and collection using a single optical fiber without a transmission-type system. We illuminated speckle patterns with relative coincidence degrees of 0.14, using a precise controlled rotating diffuser, and used improved differential ghost imaging for image reconstruction. Our single-fiber ghost imaging with a diameter of 105 µm achieved a spatial resolution of 0.05 mm in an observing area of ${9}\;{{\rm mm}^2}$ at a working distance of 10 mm. Our method provided imaging with extremely weak illumination, using a laser power density 1/940 times that of conventional neuroendoscopes. Our results, using 30,000 speckle patterns and performed through a diffuser, allowed us to achieve an average coincidence degree of 0.45 in image reconstruction compared to images without a diffuser obtained by conventional neuroendoscopes with a lens.
Our strategy enables dimensional measurements in very small holes and pipes. The proposed method requires long-duration imaging, but it can also be enhanced for high-speed imaging, polarization measurement, 3D imaging, and other functionalities. In medical applications, our method has the potential to enable intravascular observations without the need for blood removal.
Funding
Osawa Scientific Studies Grants Foundation; Sumitomo Foundation (2200578); Amada Foundation (AF-2019204-B2, AF-2022217-B3); Uehara Memorial Foundation (2019, 2022); Japan Society for the Promotion of Science (JP20H02157, JP20H05885, JP21H03842, JP22H01499, JP23H01416).
Acknowledgment
We wish to thank Yuta Takahashi (Saitama Medical University) for technical support and advice. The authors thank FORTE Science Communications for English language editing.
Disclosures
The authors declare 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.
Supplemental document
See Supplement 1 for supporting content.
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