3D Fourier ghost imaging via semi-calibrated photometric stereo.

We achieved three-dimensional (3D) computational ghost imaging with multiple photoresistors serving as single-pixel detectors using the semi-calibrated lighting approach. We performed imaging in the spatial frequency domain by having each photoresistor obtain the Fourier spectrum of the scene at a low spectral coverage ratio of 5%. To retrieve a depth map of a scene, we inverted, apodized, and applied semi-calibrated photometric stereo (SCPS) to the spectra. At least 93.5% accuracy was achieved for the 3D results of the apodized set of images applied with SCPS in comparison with the ground truth. Furthermore, intensity error map statistics obtained at least 97.0% accuracy for the estimated surface normals using our method. Our system does not need special calibration objects or any additional optical components to perform accurate 3D imaging, making it easily adaptable. Our method can be applied in current imaging systems where multiple detectors operating at any wavelength are used for two-dimensional (2D) imaging, such as imaging cosmological objects. Employing the idea of changing light patterns to illuminate a target scene and having stored information about these patterns, the data retrieved by one detector will give the 2D information while the multiple-detector system can be used to get a 3D profile.

[1]  Daniel J. Lum,et al.  Photon counting compressive depth mapping , 2013, Optics express.

[2]  C. McCutchen.  Two Families of Apodization Problems , 1969 .

[3]  Giuliano Scarcelli,et al.  Remote spectral measurement using entangled photons , 2003, quant-ph/0407164.

[4]  Robert W Boyd,et al.  Quantum and classical coincidence imaging. , 2004, Physical review letters.

[5]  Rama Chellappa,et al.  A Method for Enforcing Integrability in Shape from Shading Algorithms , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Qian Chen,et al.  Adaptive compressed 3D ghost imaging based on the variation of surface normals. , 2019, Optics express.

[7]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[8]  Jeffrey H. Shapiro,et al.  Computational ghost imaging , 2008, 2009 Conference on Lasers and Electro-Optics and 2009 Conference on Quantum electronics and Laser Science Conference.

[9]  E. Tajahuerce,et al.  Single-pixel digital ghost holography , 2012, 1305.7069.

[10]  Daniele Pelliccia,et al.  Ghost tomography , 2018, Optica.

[11]  Ling-An Wu,et al.  Table-top X-ray Ghost Imaging with Ultra-Low Radiation , 2017 .

[12]  A. Gatti,et al.  High-resolution ghost image and ghost diffraction experiments with thermal light. , 2005, Physical review letters.

[13]  Bi-frequency 3D ghost imaging with Haar wavelet transform. , 2019, Optics express.

[14]  Enrong Li,et al.  Structured image reconstruction for three-dimensional ghost imaging lidar. , 2015, Optics express.

[15]  Qionghai Dai,et al.  Efficient single pixel imaging in Fourier space , 2015, 1504.03823.

[16]  Alessia Pasquazi,et al.  Time-Resolved Nonlinear Ghost Imaging , 2018, ACS Photonics.

[17]  Jun Xiong,et al.  Lensless ghost imaging of a phase object with pseudo-thermal light , 2014 .

[18]  O. Katz,et al.  Ghost imaging with a single detector , 2008, 0812.2633.

[19]  Federica Villa,et al.  Non-Line-of-Sight Three-Dimensional Imaging with a Single-Pixel Camera , 2019, Physical Review Applied.

[20]  Wolfgang Elsäßer,et al.  Ghost Spectroscopy with Classical Thermal Light Emitted by a Superluminescent Diode , 2018 .

[21]  Graham M. Gibson,et al.  Simultaneous real-time visible and infrared video with single-pixel detectors , 2015, Scientific Reports.

[22]  Wenlin Gong,et al.  Three-dimensional ghost imaging lidar via sparsity constraint , 2016, Scientific Reports.

[23]  E.J. Candes.  Compressive Sampling , 2022 .

[24]  Graham M. Gibson,et al.  3D single-pixel video , 2016 .

[25]  Lei Zhang,et al.  Improving the noise immunity of 3D computational ghost imaging. , 2019, Optics express.

[26]  Zibang Zhang,et al.  Three-dimensional single-pixel imaging with far fewer measurements than effective image pixels. , 2016, Optics letters.

[27]  Ming-Jie Sun,et al.  Single-Pixel Imaging and Its Application in Three-Dimensional Reconstruction: A Brief Review , 2019, Sensors.

[28]  C. David,et al.  Ghost imaging at an XUV free-electron laser , 2018, Physical Review A.

[29]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[30]  Ronen Basri,et al.  From Shading to Local Shape , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[31]  Mark R. Freeman,et al.  3D Computational Imaging with Single-Pixel Detectors , 2013 .

[32]  J. Howell,et al.  Photon-counting compressive sensing laser radar for 3D imaging. , 2011, Applied optics.

[33]  H. Latifi,et al.  Three-dimensional imaging through scattering media using a single pixel detector. , 2019, Applied optics.

[34]  Minghua Chen,et al.  Time-encoded single-pixel 3D imaging , 2019, APL Photonics.

[35]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[36]  Wenlin Gong,et al.  Ghost Imaging Lidar via Sparsity Constraints in Real Atmosphere , 2013 .

[37]  Ting Sun,et al.  Single-pixel imaging via compressive sampling , 2008, IEEE Signal Process. Mag..

[38]  Jingang Zhong,et al.  Single-pixel imaging by means of Fourier spectrum acquisition , 2015, Nature Communications.

[39]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[40]  Un,et al.  Real-time imaging of methane gas leaks using a single-pixel camera , 2017 .

[41]  Eric Lantz,et al.  Temporal ghost imaging with pseudo-thermal speckle light , 2017 .

[42]  M. Soriano,et al.  Low-cost Fourier ghost imaging using a light-dependent resistor , 2019 .

[43]  Depth acquisition in single-pixel imaging with multiplexed illumination. , 2021, Optics express.

[44]  E. Hendry,et al.  Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector , 2015, Science Advances.

[45]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[46]  Robert J. Woodham,et al.  Photometric method for determining surface orientation from multiple images , 1980 .

[47]  D. Slepian.  Analytic Solution of Two Apodization Problems , 1965 .

[48]  Graham M. Gibson,et al.  Single-pixel three-dimensional imaging with time-based depth resolution , 2016, Nature Communications.

[49]  A. Gatti,et al.  Ghost imaging with thermal light: comparing entanglement and classical correlation. , 2003, Physical review letters.

[50]  Olivier D. Faugeras,et al.  Shape From Shading , 2006, Handbook of Mathematical Models in Computer Vision.

[51]  Shih,et al.  Optical imaging by means of two-photon quantum entanglement. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[52]  Zibang Zhang,et al.  Simultaneous spatial, spectral, and 3D compressive imaging via efficient Fourier single-pixel measurements , 2018 .

[53]  R. Boyd,et al.  "Two-Photon" coincidence imaging with a classical source. , 2002, Physical review letters.

[54]  G. Thomas,et al.  Sidelobe apodization in Fourier imaging , 2001, Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.No.01CH37256).

[55]  M. Fukushima,et al.  Levenberg–Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints , 2004 .

[56]  In So Kweon,et al.  Semi-Calibrated Photometric Stereo , 2020, IEEE Transactions on Pattern Analysis and Machine Intelligence.