Review

. 2022 Jun 20;8(6):174.

doi: 10.3390/jimaging8060174.

Nonlinear Reconstruction of Images from Patterns Generated by Deterministic or Random Optical Masks-Concepts and Review of Research

Daniel Smith¹, Shivasubramanian Gopinath², Francis Gracy Arockiaraj³, Andra Naresh Kumar Reddy^{4

5}, Vinoth Balasubramani⁶, Ravi Kumar⁷, Nitin Dubey⁷, Soon Hock Ng¹, Tomas Katkus¹, Shakina Jothi Selva³, Dhanalakshmi Renganathan², Manueldoss Beaula Ruby Kamalam³, Aravind Simon John Francis Rajeswary⁸, Srinivasan Navaneethakrishnan², Stephen Rajkumar Inbanathan³, Sandhra-Mirella Valdma⁸, Periyasamy Angamuthu Praveen^{8

9}, Jayavel Amudhavel^{8

10}, Manoj Kumar⁸, Rashid A Ganeev^{5

11}, Pierre J Magistretti⁶, Christian Depeursinge⁶, Saulius Juodkazis^{1

12}, Joseph Rosen⁷, Vijayakumar Anand^{1

8}

Affiliations

¹ Optical Sciences Center and ARC Training Centre in Surface Engineering for Advanced Materials (SEAM), School of Science, Computing and Engineering Technologies, Optical Sciences Center, Swinburne University of Technology, Hawthorn, Melbourne, VIC 3122, Australia.
² PG & Research Department of Physics, Thiagarajar College, Madurai 625009, India.
³ PG & Research Department of Physics, The American College, Madurai 625009, India.
⁴ Hee Photonic Labs, LV-1002 Riga, Latvia.
⁵ Laboratory of Nonlinear Optics, University of Latvia, Jelgavas 3, LV-1004 Riga, Latvia.
⁶ Division of Biological and Environmental Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia.
⁷ School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 8410501, Israel.
⁸ Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia.
⁹ Organic Optoelectronics Research Laboratory, Department of Physics, Indian Institute of Science Education and Research (IISER), Tirupati 517507, India.
¹⁰ School of Computing Science and Engineering, VIT Bhopal University, Bhopal 466114, India.
¹¹ Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, National Research University, Kori Niyozov Str. 39, Tashkent 100000, Uzbekistan.
¹² Tokyo Tech World Research Hub Initiative (WRHI), School of Materials and Chemical Technology, Tokyo Institute of Technology, 2-12-1, Ookayama, Meguro-ku, Tokyo 152-8550, Japan.

PMID: 35735973
PMCID: PMC9225382
DOI: 10.3390/jimaging8060174

Review

Nonlinear Reconstruction of Images from Patterns Generated by Deterministic or Random Optical Masks-Concepts and Review of Research

Daniel Smith et al. J Imaging. 2022.

. 2022 Jun 20;8(6):174.

doi: 10.3390/jimaging8060174.

Authors

Affiliations

¹ Optical Sciences Center and ARC Training Centre in Surface Engineering for Advanced Materials (SEAM), School of Science, Computing and Engineering Technologies, Optical Sciences Center, Swinburne University of Technology, Hawthorn, Melbourne, VIC 3122, Australia.
² PG & Research Department of Physics, Thiagarajar College, Madurai 625009, India.
³ PG & Research Department of Physics, The American College, Madurai 625009, India.
⁴ Hee Photonic Labs, LV-1002 Riga, Latvia.
⁵ Laboratory of Nonlinear Optics, University of Latvia, Jelgavas 3, LV-1004 Riga, Latvia.
⁶ Division of Biological and Environmental Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia.
⁷ School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 8410501, Israel.
⁸ Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia.
⁹ Organic Optoelectronics Research Laboratory, Department of Physics, Indian Institute of Science Education and Research (IISER), Tirupati 517507, India.
¹⁰ School of Computing Science and Engineering, VIT Bhopal University, Bhopal 466114, India.
¹¹ Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, National Research University, Kori Niyozov Str. 39, Tashkent 100000, Uzbekistan.
¹² Tokyo Tech World Research Hub Initiative (WRHI), School of Materials and Chemical Technology, Tokyo Institute of Technology, 2-12-1, Ookayama, Meguro-ku, Tokyo 152-8550, Japan.

PMID: 35735973
PMCID: PMC9225382
DOI: 10.3390/jimaging8060174

Abstract

Indirect-imaging methods involve at least two steps, namely optical recording and computational reconstruction. The optical-recording process uses an optical modulator that transforms the light from the object into a typical intensity distribution. This distribution is numerically processed to reconstruct the object's image corresponding to different spatial and spectral dimensions. There have been numerous optical-modulation functions and reconstruction methods developed in the past few years for different applications. In most cases, a compatible pair of the optical-modulation function and reconstruction method gives optimal performance. A new reconstruction method, termed nonlinear reconstruction (NLR), was developed in 2017 to reconstruct the object image in the case of optical-scattering modulators. Over the years, it has been revealed that the NLR can reconstruct an object's image modulated by an axicons, bifocal lenses and even exotic spiral diffractive elements, which generate deterministic optical fields. Apparently, NLR seems to be a universal reconstruction method for indirect imaging. In this review, the performance of NLR isinvestigated for many deterministic and stochastic optical fields. Simulation and experimental results for different cases are presented and discussed.

Keywords: Fresnel incoherent correlation holography; coded aperture imaging; computational imaging; diffractive optics; holography; nonlinear reconstruction; rotating point spread function; scattering.

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Conflict of interest statement

Christian Depeursinge has financial interests in Lyncee Tec and Nanolive; Pierre J Magistretti has financial interests in Lyncee Tec.

Figures

**Figure 1**
Optical configuration of imaging systems. The optical modulator can be a bifocal lens (FINCH), regular lens (direct imaging), spiral phase plate (vortex beam), an axicon (Bessel beam) or a random pinhole array (scattered beam).

**Figure 2**
Comparison between different phase modulators according to functions and distributions that related to image reconstruction and resolution.

**Figure 3**
(a) Autocorrelation with NLR followed by raising the image to the power of p = 2 and their respective MTF profiles. (b) The influence of p on a grayscale slope.

**Figure 4**
Simulated intensity distribution for a test object and the reconstruction results for p = 1, 2 and 3.

**Figure 5**
(a) Recorded PSF and (b) object intensity response. Reconstruction results using (c) NLR (p = 1), (d) NLR (p = 2) and (e) NLR (p = 3) for LI-COACH with a QRL.

**Figure 6**
(a) Recorded PSF, (b) object’s response pattern. Reconstruction results using (c) NLR (p = 1), (d) NLR (p = 2) and (e) NLR (p = 3) for random array of pinholes.

**Figure 7**
(a) Optical microscope image of the central part of the QRL fabricated using electron-beam lithography. (b) Recorded PSF, (c) object’s response pattern. Reconstruction results using (d) NLR (p = 1), (e) NLR (p = 2) and (f) NLR (p = 3).

**Figure 8**
(a) Image of the QRL fabricated using lens grinding with sandpaper. (b) Recorded PSF, (c) object’s response pattern. Reconstruction results using (d) NLR (p = 1), (e) NLR (p = 2) and (f) NLR (p = 3).

**Figure 9**
(a) Image of the photon-sieve axicon fabricated using femtosecond ablation. (b) Recorded PSF, (c) object’s response pattern. Reconstruction results using (d) NLR (p = 1), (e) NLR (p = 2) and (f) NLR (p = 3).

**Figure 10**
(a) Recorded PSF, and (b) object’s response pattern. Reconstruction results using (c) NLR (p = 1), (d) NLR (p = 2) and (e) NLR (p = 3) for a diffractive lens.

**Figure 11**
(a) Recorded PSF, (b) object’s response pattern. Reconstruction results using (c) NLR (p = 1), (d) NLR (p = 2) and (e) NLR (p = 3) for a spiral Fresnel zone lens with L = 1.

**Figure 12**
(a) Recorded PSF, (b) object’s response pattern. Reconstruction results using (c) NLR (p = 1), (d) NLR (p = 2) and (e) NLR (p = 3) for a spiral Fresnel zone lens with L = 5.

**Figure 13**
(a) Recorded PSF, (b) object’s response pattern. Reconstruction results using (c) NLR (p = 1), (d) NLR (p = 2) and (e) NLR (p = 3) for lens–axicon pair.

**Figure 14**
(a) Recorded PSF, (b) object’s response pattern. Reconstruction results using (c) NLR (p = 1), (d) NLR (p = 2) and (e) NLR (p = 3) for FINCH with random multiplexing configuration.

**Figure 15**
(a) Optical microscope image of the randomly multiplexed bifocal diffractive lenses. (b) Recorded PSF, (c) object’s response pattern. Reconstruction results using (d) NLR (p = 1), (e) NLR (p = 2) and (f) NLR (p = 3) for FINCH with spatial random multiplexing configuration.

**Figure 16**
(a) Phase image of the multifunctional DOE. (b) Recorded PSF, (c) object’s response pattern. Reconstruction results using (d) NLR (p = 1), (e) NLR (p = 2) and (f) NLR (p = 3) for double-helix beam with rotating PSF.

See this image and copyright information in PMC

References

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Nonlinear Reconstruction of Images from Patterns Generated by Deterministic or Random Optical Masks-Concepts and Review of Research

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Nonlinear Reconstruction of Images from Patterns Generated by Deterministic or Random Optical Masks-Concepts and Review of Research

Authors

Affiliations

Abstract

Conflict of interest statement

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