I. INTRODUCTION

Section:

ChooseTop of pageABSTRACTI. INTRODUCTION <<II. THEORYIII. SIMULATIONIV. EXPERIMENTV. RESULTSVI. DISCUSSIONVII. CONCLUSIONREFERENCESOptical coherence tomography (OCT) was first proposed in 1991.11. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991). https://doi.org/10.1126/science.1957169 OCT is a non-contact, non-invasive imaging technique for a non-homogeneous medium that produces high-resolution cross-sectional images. Based on the principle of low-coherence interference, OCT combines the lights reflected from the measurement and the reference paths to represent the distribution of optical properties of the target in the depth direction. OCT systems have been used in commercial applications, with significant results in ophthalmology and optometry, where they can obtain detailed images from the inside of the retina. Recently, it has been used to help in the diagnosis of cardiology and dermatological cases.2–42. T. Gambichler, G. Moussa, M. Sand, D. Sand, P. Altmeyer, and K. Hoffmann, “Applications of optical coherence tomography in dermatology,” J. Dermatol. Sci. 40, 85–94 (2005). https://doi.org/10.1016/j.jdermsci.2005.07.0063. H. Sinclair, C. Bourantas, A. Bagnall, G. S. Mintz, and V. Kunadian, “OCT for the identification of vulnerable plaque in acute coronary syndrome,” JACC Cardiovasc. Imaging 8, 198–209 (2015). https://doi.org/10.1016/j.jcmg.2014.12.0054. E. C. Sattler, R. Kästle, and J. Welzel, “Optical coherence tomography in dermatology,” J. Biomed. Opt. 18(6), 061224 (2013). https://doi.org/10.1117/1.JBO.18.6.061224 OCT is also used in most biomedical multilayer scattering media, such as organs and skins.5,65. R. F. Spaide, J. G. Fujimoto, N. K. Waheed, S. R. Sadda, and G. Staurenghi, “Optical coherence tomography angiography,” Prog. Retinal Eye Res. 64, 1–55 (2018). https://doi.org/10.1016/j.preteyeres.2017.11.0036. P. Xue, T. Yuan, Y. Chen, W. Chen, and D. Y. Chen, in Coherence Domain Optical Methods in Biomedical Science and Clinical Applications III, edited by V. V. Tuchin and J. A. Izatt (SPIE, 1999), Vol. 3598, pp. 18–25. This imaging technique is very important in the early detection of skin cancer.77. M. Y. Kirillin, A. V. Priezzhev, and R. Myllylä, “Role of multiple scattering in formation of OCT skin images,” Quantum Electron. 38, 570–575 (2008). https://doi.org/10.1070/qe2008v038n06abeh013842Skin can be treated as a multi-layered scattering media in the near-infrared range. OCT measurements of multilayer scattering media always obtain a target signal with the scattering influence because reflected light is attenuated and scattered in the scattering media when the light is propagated with depth.8–108. T. Tamaki, B. Yuan, B. Raytchev, K. Kaneda, and Y. Mukaigawa, “Multiple-scattering optical tomography with layered material,” in Proceedings of the 2013 International Conference on Signal-Image Technology and Internet-Based Systems, SITIS (IEEE, 2013), pp. 93–99.9. G. J. Tearney, M. E. Brezinski, B. E. Bouma, M. R. Hee, J. F. Southern, and J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 20, 2258 (1995). https://doi.org/10.1364/ol.20.00225810. D. Levitz, L. Thrane, M. H. Frosz, P. E. Andersen, C. B. Andersen, S. Andersson-Engels, J. Valanciunaite, J. Swartling, and P. R. Hansen, “Determination of optical scattering properties of highly-scattering media in optical coherence tomography images,” Opt. Express 12, 249 (2004). https://doi.org/10.1364/opex.12.000249 This kind of attenuation on OCT can be reduced by methods, such as multi-angle incidence measurements and increasing the number of measurements.11,1211. A. Badon, D. Li, G. Lerosey, C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” in Optics InfoBase Conference Papers (AAAS, 2017), Vol. 2, pp. 1–9.12. V. Ntziachristos, “Going deeper than microscopy: The optical imaging Frontier in biology,” Nat. Methods 7, 603–614 (2010). https://doi.org/10.1038/nmeth.1483 Nevertheless, in an unknown scattered media or even if the attenuation from strong scattering has refrained, the media’s influences on the signal intensity of the target cannot be eliminated. The scattering media may change the measurement light direction or delay by time. It is difficult to determine the target’s precise distribution and thus unable to obtain an appropriate image of the target in scattered media.13,1413. L. Borcea, J. Garnier, G. Papanicolaou, and C. Tsogka, “Coherent interferometric imaging, time gating and beamforming,” Inverse Problems 27, 065008 (2011). https://doi.org/10.1088/0266-5611/27/6/06500814. Y. Choi, T. R. Hillman, W. Choi, N. Lue, R. R. Dasari, P. T. So, W. Choi, and Z. Yaqoob, “Measurement of the time-resolved reflection matrix for enhancing light energy delivery into a scattering medium,” Phys. Rev. Lett. 111, 243901 (2013). https://doi.org/10.1103/PhysRevLett.111.243901Recently, many light manipulation techniques have been used to recover imaging through scattered media.15–2615. K. Lee and Y. Park, “Exploiting the speckle-correlation scattering matrix for a compact reference-free holographic image sensor,” Nat. Commun. 7, 13359 (2016). https://doi.org/10.1038/ncomms1335916. S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010); arXiv:1005.0532. https://doi.org/10.1038/ncomms107817. J. Bertolotti, E. G. Van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012). https://doi.org/10.1038/nature1157818. O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014); arXiv:1403.3316. https://doi.org/10.1038/nphoton.2014.18919. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008). https://doi.org/10.1038/nphoton.2007.29720. Y. Luo, S. Yan, H. Li, P. Lai, and Y. Zheng, “Focusing light through scattering media by reinforced hybrid algorithms,” APL Photonics 5, 016109 (2020). https://doi.org/10.1063/1.513118121. C. M. Woo, Q. Zhao, T. Zhong, H. Li, Z. Yu, and P. Lai, “Optimal efficiency of focusing diffused light through scattering media with iterative wavefront shaping,” APL Photonics 7, 046109 (2022). https://doi.org/10.1063/5.008594322. S. Zhu, E. Guo, J. Gu, L. Bai, and J. Han, “Imaging through unknown scattering media based on physics-informed learning,” Photonics Res. 9, B210 (2021). https://doi.org/10.1364/prj.41655123. S. Yoon, M. Kim, M. Jang, Y. Choi, W. Choi, S. Kang, and W. Choi, “Deep optical imaging within complex scattering media,” Nat. Rev. Phys. 2, 141–158 (2020). https://doi.org/10.1038/s42254-019-0143-224. G. Ongie, A. Jalal, C. A. Metzler, R. G. Baraniuk, A. G. Dimakis, and R. Willett, “Deep learning techniques for inverse problems in imaging,” IEEE J. Sel. Areas Inf. Theory 1, 39–56 (2020);arXiv:2005.06001. https://doi.org/10.1109/jsait.2020.299156325. S. Ludwig, P. Ruchka, G. Pedrini, X. Peng, and W. Osten, “Scatter-plate microscopy with spatially coherent illumination and temporal scatter modulation,” Opt. Express 29, 4530 (2021). https://doi.org/10.1364/oe.41204726. T. Inoue, Y. Junpei, S. Itoh, T. Okuda, A. Funahashi, T. Takimoto, T. Kakue, K. Nishio, O. Matoba, and Y. Awatsuji, “Spatiotemporal observation of light propagation in a three-dimensional scattering medium,” Sci. Rep. 11, 21890 (2021). https://doi.org/10.1038/s41598-021-01124-6 The ghost imaging (GI) technique is getting attention because it can be used to solve the problem of distinguishing between signal and noise.27–2927. D. B. Lindell and G. Wetzstein, “Three-dimensional imaging through scattering media based on confocal diffuse tomography,” Nat. Commun. 11, 4517 (2020). https://doi.org/10.1038/s41467-020-18346-328. J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008); arXiv:0807.2614. https://doi.org/10.1103/physreva.78.06180229. V. Katkovnik and J. Astola, “Compressive sensing computational ghost imaging,” J. Opt. Soc. Am. A 29, 1556 (2012). https://doi.org/10.1364/josaa.29.001556 With the development of ghost imaging using a single detector,3030. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009); arXiv:0812.2633. https://doi.org/10.1103/physreva.79.053840 GI has been used in many fields,31,3231. P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10, 167–170 (2016). https://doi.org/10.1038/nphoton.2015.27432. F. Devaux, P.-A. Moreau, S. Denis, and E. Lantz, “Computational temporal ghost imaging,” Optica 3, 698 (2016); arXiv:1603.04647. https://doi.org/10.1364/optica.3.000698 for example, light detection and ranging,3333. C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012); arXiv:1203.3835. https://doi.org/10.1063/1.4757874 3D imaging,3434. W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103, 221106 (2013). https://doi.org/10.1063/1.4836995 astronomical observation of turbulent atmospheres,3535. C.-L. Luo, P. Lei, Z.-L. Li, J.-Q. Qi, X.-X. Jia, F. Dong, and Z.-M. Liu, “Long-distance ghost imaging with an almost non-diffracting lorentz source in atmospheric turbulence,” Laser Phys. Lett. 15, 085201 (2018). https://doi.org/10.1088/1612-202x/aac54a and microscopy.3636. L. Olivieri, J. S. T. Gongora, L. Peters, V. Cecconi, A. Cutrona, J. Tunesi, R. Tucker, A. Pasquazi, and M. Peccianti, “Hyperspectral terahertz microscopy via nonlinear ghost imaging,” Optica 7, 186 (2020); arXiv:1910.11259. https://doi.org/10.1364/optica.381035 GI has also included applications in OCT. Ghost optical coherence tomography (GOCT) uses the pulse-to-pulse variations of the spectral field of the supercontinuum source as a pattern and calculates the signal.3737. C. G. Amiot, P. Ryczkowski, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost optical coherence tomography,” Opt. Express 27, 24114–24122 (2019). https://doi.org/10.1364/oe.27.024114 This method takes advantage of GI’s ability to reconstruct the image even if the signal-to-noise ratio is low. Compared with conventional OCT, GOCT can reduce the number of measurements. However, this method does not reveal any information about obtaining a target optical profile without the scattering influence.Inspired by those works in imaging through strong scatterers,38–4238. F. Li, M. Zhao, Z. Tian, F. Willomitzer, and O. Cossairt, “Compressive ghost imaging through scattering media with deep learning,” Opt. Express 28, 17395 (2020). https://doi.org/10.1364/oe.39463939. W. Gong and S. Han, “Correlated imaging in scattering media,” Opt. Lett. 36, 394 (2011). https://doi.org/10.1364/ol.36.00039440. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309 (2007). https://doi.org/10.1364/ol.32.00230941. H. Wu, P. Ryczkowski, A. Friberg, J. M. Dudley, and G. Genty, “Temporal ghost imaging with wavelength conversion,” in Optics InfoBase Conference Papers (IEEE, 2019), pp. 1–5.42. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010); arXiv:0910.5436. https://doi.org/10.1103/PhysRevLett.104.100601 we propose a new method to obtain the target image distribution in a multi-layered scattered media by combining Ghost Imaging and OCT (GI-OCT). Using this method, a target image distribution without scattering influence can be obtained. Unlike conventional OCT, the GI-OCT method does not apply OCT probe light focused on a certain point but illuminates the light within a definite area like the full field-OCT (FF-OCT). GI-OCT can take the same 2D image with a single detector. FF-OCT directly takes cross-sectional 2D images vertically against the optical axis using a camera, enabling target distribution imaging without orthogonal movements of the probe. FF-OCT can not obtain a target distribution without the scattering influence.4343. L. Vabre, A. Dubois, and C. Boccara, “Thermal-light full-field optical coherence tomography,” Opt. Lett. 27, 530–532 (2002). https://doi.org/10.1364/OL.27.000530 FF-OCT uses a megapixel camera to achieve cellular-level imaging. Each pixel in the FF-OCT image is a point measurement of the target, which is the same as conventional OCT. FF-OCT image is affected by the scatter and includes delay in the scattering media.In GI-OCT, we use a digital mirror device (DMD) chip44,4544. D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” in MOEMS Display and Imaging Systems, edited by H. Urey (International Society for Optics and Photonics, SPIE, 2003), Vol. 4985, pp. 14–25. https://doi.org/10.1117/12.48076145. B. Hellman and Y. Takashima, “Angular and spatial light modulation by single digital micromirror device for multi-image output and nearly-doubled étendue,” Opt. Express 27, 21477 (2019). https://doi.org/10.1364/oe.27.021477 to generate different illumination light patterns, and the reflected lights from the target in scattering media are detected with a single photodiode. GI method calculates the correlation between the detected light intensity and illuminated optical patterns to reconstruct the sample distribution. The scatterer distribution from the sample distribution is used to correct the target distribution.

This paper proposed a new method to obtain a target’s corrected optical property distribution at a certain depth of the scattering media with the following objectives: (1) to explain the concept and theory of GI-OCT, (2) to establish the principle experiment of GI-OCT, and (3) to verify our method for correcting the target distribution in the scattering media.

II. THEORY

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. THEORY <<III. SIMULATIONIV. EXPERIMENTV. RESULTSVI. DISCUSSIONVII. CONCLUSIONREFERENCES

A. Concept of GI-OCT

In the OCT measurements, we simplify the target in the scattering media (scattering sample) in two parts. The former part is the scatter layer before the light hits the target. The latter part is the target layer. When the conventional OCT measures the target layer in the scattering sample, a three-dimensional image can be constructed by the reference path’s change (A-scan) and the probe’s orthogonal movement (B-scan), as shown in Fig. 1(a). However, the measured intensity distribution from the target layer is modulated because the image always has some uneliminated effects from the former scattering layers. For example, when OCT measures the optical properties (transmittance and absorbance) of the target layer, the former scattering layers’ distribution may change the direction of the light or delay the received signal of the target layer due to the scatter’s influence. As a result, the modulated optical properties of the target layer are detected.Figure 1(b) shows the GI-OCT concept that the GI-OCT light passes through an expander and a spatial light modulation (SLM), and generated light patterns illuminate the target layer within the scattering sample. The light intensity from the target and the scatter layers is collected using a single detector. An A-scan signal in GI-OCT is a series of light intensities in the depth direction with each illuminated light pattern. These series of light intensity can be separated as the summed intensity of each layer distribution with the OCT axial resolution. After repetitive measurements using different light patterns, the correlation between those patterns and the summed intensity of each separated layer are calculated with the GI method to get each layer distribution. Each separate layer is reconstructed under the multi-layered sample structure.

In GI-OCT, compared to conventional OCT setup using a point measurement, we use 2D measurement with a single detector. The measurement of lights going into other directions or the signal delayed by the scattering media can be concurrently summed and detected by this single detector. They are treated as scatter distribution and shown in the results. Then we can computationally reconstruct the target layer distribution by the GI method and the former scattering layer distribution with the same procedure. The target layer’s optical properties can be corrected using the former scatter layer distribution.

In this work, the proposed method can be explained in two steps. The first step is to reconstruct the image of one layer (the sample layer) transmittance intensity distribution with the GI-OCT method. The second step is the target image correction with the scatter layer intensity distribution.

B. Sample distribution reconstruction

The schematic diagram of the GI-OCT method to detect the sample layer distribution is shown in Fig. 2. Different patterns of lights from the DMD chip illuminate the sample layer to obtain the OCT light intensity, defined as the following equation:where αn is the light pattern with m × m speckles illuminated from the DMD chip; β(sample) is the transmittance distribution of the sample layer; and In is the received light intensity summed from all speckles’ intensities, which is the OCT interference light intensity. In Fig. 2, we set m = 2 and use n as the measurement index. β′(sample) is the reconstructed image of the sample layer’s transmittance distribution using the computational ghost imaging (CGI) method by calculating the correlation between αn and In asβ′(sample)CGI=1N∑n=1N(αn−⟨αn⟩)In,(2)where ⟨αn⟩=1N∑n=1Nαn is the average of light patterns. The CGI result needs a large sampling ratio to reconstruct a high-quality image.4646. M. Don, “An introduction to computational ghost imaging with example code,” Technical Report No. ARL-TR-8876, 2019; available at https://www.researchgate.net/publication/339569732_An_Introduction_to_Computational_Ghost_Imaging_with_Example_Code. The sampling ratio in percent is defined as 100N/M. N is the number of different illuminated patterns, and M = m × m is the number of pixels in each light pattern.To reduce the number of measurements and to improve the reconstructed image quality, we tested differential ghost imaging (DGI), pseudo-inverse ghost imaging (PGI), and differential pseudo-inverse ghost imaging (DPGI) for the adequate application to OCT imaging. The DGI is calculated using the following equation:β′(sample)DGI=1N∑n=1N(αn−〈αn〉)In−〈I〉〈I′〉In′=1N∑n=1N(αn−〈αn〉)In⋆,(3)where In′ is the total light intensity of each light pattern without sample, and In⋆ is called the light transmission relative variance. Depending on the light transmission relative variance, DGI can have signal-to-noise ratios several orders of magnitude higher than CGI.4747. F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010). https://doi.org/10.1103/PhysRevLett.104.253603Moreover, we used PGI to reduce the number of measurements by computing the pseudo-inverse matrix composed of each pattern vector.46–4846. M. Don, “An introduction to computational ghost imaging with example code,” Technical Report No. ARL-TR-8876, 2019; available at https://www.researchgate.net/publication/339569732_An_Introduction_to_Computational_Ghost_Imaging_with_Example_Code.47. F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010). https://doi.org/10.1103/PhysRevLett.104.25360348. C. Zhang, S. Guo, J. Cao, J. Guan, and F. Gao, “Object reconstitution using pseudo-inverse for ghost imaging,” Opt. Express 22, 30063–30073 (2014). https://doi.org/10.1364/oe.22.030063 GI can be explained as a series of matrix operations. When the sample transmittance βn(sample) is set at a matrix of m × m, the DMD chip generates the illuminated pattern αn of m × m speckles. One pattern can be represented as a 1 × m2 row vector. For N measurements, we get a matrix of N × m2 called Φ,Φ=α1(1,1)α1(1,2)⋯α1(m,m)⋮⋮⋱⋮αn(1,1)αn(1,2)⋯αn(m,m)⋮⋮⋱⋮αN(1,1)αN(1,2)⋯αN(m,m).(4)The PGI requires the pseudo-inverse of Φ, recorded as Φ+, which can be acquired by singular value decomposition (SVD), and the PGI is calculated asβ′(sample)PGI=1NΦ+(I1,I2,…,In)T.(5)The DPGI is also calculated asβ′(sample)DPGI=1NΦ+(I1⋆,I2⋆,…,In⋆)T.(6)

C. Target Image Correction

In the GI-OCT measurement, we aim to correct the modulated target layer distribution in the scattering sample, and the schematic diagram is shown in Fig. 3.In the OCT signal of Fig. 3, the red hatched part is the scatter layer signal. The blue hatched part is the original target layer signal, but the brown hatched part is modulated by the scatter layer. After the DMD illuminates the light pattern on the sample, the scatter layer intensity is obtained using Eq. (1), and the modulated target layer intensity as In(s, t) is represented in the following equation:In(s,t)=αn(β(scatter)×β(target)),(7)where β(scatter) × β(target) is the transmittance distribution of the scattering sample with the scatter and target layers and (β(scatter) × β(target))′ is the reconstructed result using CGI calculation shown in the following equation:(β(scatter)×β(target))′=1N∑n=1N(αn−⟨αn⟩)In(s,t).(8)Combining Eqs. (6) and (8), the target layer signal relative variance modulated by the scatter layer is In(s,t)⋆, and the scatter layer signal relative variance is In(s)⋆. We can correct the target layer distribution β′(target) using the DPGI calculation with the scatter layer signal In(s)⋆ as follows:β′(target)=1NΦ+I1(s,t)⋆I1(s)⋆,I2(s,t)⋆I2(s)⋆,…,In(s,t)⋆In(s)⋆T.(9)

III. SIMULATION

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. THEORYIII. SIMULATION <<IV. EXPERIMENTV. RESULTSVI. DISCUSSIONVII. CONCLUSIONREFERENCESIn order to decide the appropriate measurement parameters for our OCT application, we implemented CGI, DGI, PGI, and DPGI calculations in a range of sampling ratios 90% ∼ 1500% as shown in Figs. 4 and 5. The original and reconstructed images are normalized to make image values in the gradation 0 ∼ 255 before calculating the peak signal to noise ratio (PSNR), which is an approximation to human perception of reconstruction quality. This is calculated using the following equation:PSNR=10⋅log10MAX2MSE,(10)where MSE is the mean squared error of the original image β and reconstructed image β′. MAX is the maximum possible pixel value in the image. In an 8 bit image, acceptance values for the PSNR in the original and reconstructed images should be over 30 dB to achieve the higher reconstruction quality.4949. S. T. Welstead, Fractal and Wavelet Image Compression Techniques (SPIE Press, 1999), Vol. 40.In this work, m is set to 10 in the simulation using our equations. During the OCT measurement, noise often degrades OCT image quality due to the slight movement of the sample, limited light bandwidth, phase aberrations of propagating beam, the aperture of the detector, and multiple scattering within the coherence length. This noise is set 10% of the signal intensity in the OCT measurement (signal to noise ratio ≈10%). Therefore, we simulate both noiseless and noisy cases. In Fig. 4, the simulation results are in noiseless case, and we can see that when the sampling ratios increased to over 100%, DPGI had the highest PSNR value, PGI is the second-highest value, and DGI and CGI are the worst. DGI and CGI need a quite high sampling ratio of >25000% to make the PSNR over 30 dB. When the matrix is singular, we can obtain a unique matrix that satisfies generalized inverse by using SVD. Both DPGI and PGI use pseudo-inverse to produce results efficiently. For this reason, they get very high PSNR values in low sampling ratios.In Fig. 5, the light intensity value of In(noise) = In + V(noise) is used to calculate the PSNR in each equation. V(noise) is the random value on each pattern in the gradation −25 ∼ 25, which is 10% image value in the 8 bits image. The DPGI result is the best at 10% noise intensity over 200% sampling ratios. We can see that when the sampling ratios increased to over 800%, DPGI still has the highest PSNR value and beyond the acceptance value of 30 dB. PSNR’s values of PGI, DGI, and CGI are all below the acceptance value. At the same time, noise significantly influences DPGI and PGI results, causing the PSNR values to drop quickly compared to the noiseless case but still better than CGI and DGI. It can be concluded that DPGI has the best reconstruction efficiency for our OCT application.

IV. EXPERIMENT

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. THEORYIII. SIMULATIONIV. EXPERIMENT <<V. RESULTSVI. DISCUSSIONVII. CONCLUSIONREFERENCESThe experimental setup of GI-OCT is shown in Fig. 6. In the GI-OCT, the axial resolution is defined as δz=0.44λ02/Δλ, where λ0 = 856 nm is the central wavelength of the Superluminescent diodes (SLD) light source with Gaussian distribution, and if FWHM is Δλ = 32.1 nm spectral bandwidth, then δz ≈ 10.1 μm. The reference mirror of GI-OCT consists of a steady rotating motor and a fixed mirror to complete the axial scanning (A-scan).50–5350. T. Shiina, Y. Moritani, M. Ito, and Y. Okamura, “Long-optical-path scanning mechanism for optical coherence tomography,” Appl. Opt., 42, 3795 (2003). https://doi.org/10.1364/ao.42.00379551. M. Tanaka and T. Shiina, “Micro crack analysis of optical fiber by specialized td-oct,” Opt. Laser Technol. 116, 22–25 (2019). https://doi.org/10.1016/j.optlastec.2019.02.05752. K. Saeki, D. Huyan, M. Sawada, Y. Sun, A. Nakamura, M. Kimura, S. Kubota, K. Uno, K. Ohnuma, and T. Shiina, “Measurement algorithm for real front and back curved surfaces of contact lenses,” Appl. Opt. 59, 9051–9059 (2020). https://doi.org/10.1364/ao.39919053. K. Saeki, D. Huyan, M. Sawada, A. Nakamura, S. Kubota, K. Uno, K. Ohnuma, and T. Shiina, “Three-dimensional measurement for spherical and nonspherical shapes of contact lenses,” Appl. Opt. 60, 3689–3698 (2021). https://doi.org/10.1364/ao.419721 The measurement path has the optical probe, which is composed of a collimator, a convex lens with f1 = −12 mm, and a concave lens with f2 = 95 mm, to make the beam diameter expand to more than 3.76 mm. At the same time, the DMD chip (DLP2000 DMD) is set in the measurement area. The sample is put between the DMD chip and the OCT probe. The DMD chip orientation in our experiment is shown in Fig. 7. The micromirrors are arranged in a matrix of 640 × 360 with a total size of 4.84 × 2.72 mm2 on the DMD chip. Each mirror size is 7.56 × 7.56 μm2, and the deflection angle is ±12° on the diagonal axis, divided into “on” and “off” states. The DMD chip is rotated counterclockwise by 45° in the vertical plane against the optical axis to make the diagonal axis vertical and tilted the mirror surface 12° against the optical axis to reflect the light to the optical axis when its state is “on” [Fig. 7(a)]. This DMD orientation makes a line of interference signals from the right-side to the left-side micromirrors in the time domain. The number of micromirrors at each distance forms a triangular distribution with an FWHM of 110 μm, as shown in Fig. 7(b). Therefore, the GI algorithm adapts their integral intensities as In. The DMD chip is controlled to display 10 × 10 speckles patterns in the 2 × 2 mm2 DMD chip area. Each speckle has 26 × 26 micromirrors.

To verify our GI-OCT concept, we prepare the target in the scattering media sample, which has two layers: the former part is the scatter layer, and the latter part is the target layer. Both of them were painted with water-based pigments on a side glass, and the scatter layer was half-covered with paint, while the target layer has the character “F.” The water-based pigments regard as uniform solidification on the side glasses.

We put the scattering sample on the GI-OCT measurement area, and the expended light passes through the SLM to illuminate this sample. The reflected pattern light from this sample goes back to the OCT probe. In our experiment, we put the DMD c