# Roadmap on Recent Progress in FINCH Technology

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## Abstract

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## 1. Introduction (Joseph Rosen and Vijayakumar Anand)

## 2. Single-Shot Phase-Shifting Fresnel Incoherent Correlation Holography with Dual-Phase Gratings (Teruyoshi Nobukawa)

#### 2.1. Status

#### 2.2. Future Challenges

#### 2.3. Conclusions

## 3. Parallel Phase-Shifting Single-Shot in-Line Fresnel Incoherent Correlation Holography Using a Dual-Focus Checkerboard Lens (Takanori Nomura)

#### 3.1. Status

#### 3.2. Conclusions

## 4. Single-Shot Fresnel Incoherent Digital Holography Based on Geometric Phase Lens (Dong Liang and Jun Liu)

#### 4.1. Status

#### 4.2. Conclusions

## 5. Fresnel Incoherent Correlation Holography with Non-Linear Reconstruction (Vijayakumar Anand and Saulius Juodkazis)

#### 5.1. Status

#### 5.2. Future Challenges

#### 5.3. Conclusions

## 6. FINCH Based on Metasurfaces (Hongqiang Zhou and Lingling Huang)

#### 6.1. Status

**k**space manipulation simultaneously. Hence, various ultra-broadband or multiwavelength behaviors based on metasurfaces have been proposed and demonstrated through smart design and optimization. Metasurfaces have broad applications in metalens, holography, optical encryption, display, beam shaping, active modulation, etc. [71,72,73,74].

#### 6.2. Current and Future Challenges

#### 6.3. Advances of Metalens to Meet Challenges of FINCH

_{2}achromatic metalens can record and reconstruct incoherent fluorescence holography with higher imaging performance in the visible light or UV range.

#### 6.4. Concluding Remarks

## 7. Vortex FINCH in Spiral and Localization Microscopy (Petr Bouchal and Zdeněk Bouchal)

#### 7.1. Status

#### 7.1.1. Demonstration of Spiral FINCH Imaging

#### 7.1.2. Demonstration of Localization FINCH Imaging

#### 7.2. Conclusions

## 8. Three-Dimensional Reconstruction for Living Cell by Using a Femtosecond Laser-Based Phase-Shifting Fresnel Incoherent Digital Hologram (Bang Le Thanh, Munkh-Uchral Erdenebat, and Nam Kim)

#### 8.1. Status

_{s}):

_{1}< z

_{2}< z

_{3}. z

_{1}and z

_{3}are the same as the distance of the recorded hologram.

#### 8.2. Conclusions

## 9. Single-Molecule Localization with FINCH (Peter Kner and Abhijit Marar)

#### 9.1. Status

#### 9.2. Future Work

#### 9.3. Conclusions

## 10. Incoherent Holography Lattice Light-Sheet (IHLLS) (Mariana Potcoava, Christopher Mann, Simon Alford and Jonathan Art)

#### 10.1. Status

#### 10.2. Current and Future Challenges

#### 10.3. Advances in Science and Technology to Meet Challenges

#### 10.4. Conclusions

## 11. Multiwavelength-Multiplexed Incoherent Digital Holography Based on Computational Coherent Superposition (Tatsuki Tahara, Ayumi Ishii, Takako Koujin, Atsushi Matsuda, Yuichi Kozawa, and Ryutaro Oi)

#### 11.1. Status

#### CCS-FINCH

#### 11.2. Other Remarks and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Recording and reconstruction of a hologram in a general self-interference digital holography system.

**Figure 3.**Proof-of-principle experimental results. (

**a**) Captured raw image. (

**b**,

**c**) Reconstructed images through a phase-shifting method and numerical propagation based on an angular spectrum method.

**Figure 6.**Obtained four phase-shifted holograms and reconstructed images at different axial positions.

**Figure 7.**Schematic diagram of the single-shot FINCH system using a GP lens (adapted from [35]).

**Figure 8.**(

**a**) Image of the single-shot raw hologram of a single-plane object and (

**b**–

**e**) four phase-shifted holograms 0, π/4, π/2 and 3π/4, respectively. (

**f**) Reconstruction result of a USAF1951 resolution target. (

**g**) Image of the single-shot raw hologram of a two-planes object consisting of a USAF1951 object and NBS object separated by a distance of 65 mm, (

**h**–

**k**) four phase-shifted holograms 0, π/4, π/2 and 3π/4, respectively. Reconstruction result by numerical propagation to the plane of (

**l**) USAF and (

**m**) NBS. (Adapted from [35].)

**Figure 9.**(

**a**) Fresnel hologram obtained for a point and (

**b**) Fresnel hologram obtained for two points.

**Figure 10.**Optical microscope image of the (

**a**) central part and (

**b**) the outermost part of the fabricated diffractive lens. Images of the (

**c**) PSH and (

**d**) object hologram. (

**e**) Direct imaging at one of the focal planes of the diffractive lens and (

**f**) plot of averaged intensity values of the horizontal and vertical gratings shown in the green dotted box. (

**g**) Reconstruction results and (

**h**) plot of averaged intensity values of the horizontal and vertical gratings shown in the green dotted box. (Adapted from [14].)

**Figure 11.**FINCH optical setup: (

**a**) a Michelson interferometer-type imaging system; (

**b**) a common-path interferometertype based on SLM imaging system. Reprinted with permission from [12]. Copyright (2021) Optical Society of America.

**Figure 12.**COACH optical setup using a synthetic aperture for super-resolution imaging. Reprinted with permission from [66]. Copyright (2021) Optical Society of America.

**Figure 13.**Multifunctional metalens applications. (

**a**) Experimental results of achromatic metalenses. Reprinted with permission from Macmillan Publishers Ltd.: Nature Nanotechnology [72]. Copyright (2018). (

**b**) Schematic illustration of the proposed twofold polarization-selective trifoci metalens (TFML), which establishes three foci at distinct focal planes depending on the linear polarization of incident and transmitted light. Reprinted with permission from Wiley Publisher: Advanced Optical Materials [78]. Copyright (2019). (

**c**) Schematic of a metalens that simultaneously focuses and disperses the incident light. Reprinted with permission from Science [79]. Copyright (2018). (

**d**) Schematic of the device in which a metalens and a DEA with five addressable electrodes are combined to allow for electrical control over the strain field of the metasurfac. Reprinted with permission from Science Advances [81]. Copyright (2018).

**Figure 14.**Schematic of coaxial holography and compress sensing reconstruction based on bifocal metalens [37]. Copyright (2020) Optical Society of America.

**Figure 15.**Illustration of vortex FINCH and spatial light shaping in (

**a**) standard, (

**b**) spiral, and (

**c**) localization FINCH imaging. MO—microscope objective; MD—modulation device; TL—tube lens.

**Figure 16.**Destructive interference of vortex impulse responses (

**a**), and demonstration of intensity images created for (

**b**) and (

**e**) two-point object, (

**c**,

**f**) three-point object, and (

**d**,

**g**) 7 × 5 array of point objects.

**Figure 17.**Imaging of the Palacký University sign, USAF test, and flea created using FINCH and spiral FINCH under incoherent illumination.

**Figure 18.**Localization of 100 nm gold beads by the vortex FINCH microscope: DH PSF and standard deviations for x, y, z coordinates evaluated at seven different depths in the axial range of 13.6 μm.

**Figure 19.**(

**a**) Excitation and emission spectra of the living cell, FINCH with two diffractive lenses: (

**b**) one is positive, and the other is negative, and (

**c**) both are positive (adapted from [39]).

**Figure 20.**(

**a**) Overlapping object points after reconstruction of each layer in the hologram, and (

**b**) the optical setup for the proposed system (adapted from [39]).

**Figure 21.**Reconstructed images for cell with (

**a**) 2 layer, (

**b**) 4 layer, (

**c**) 6 layer, and (

**d**) 8 layer holograms (adapted from [39]).

**Figure 22.**Recorded images with a (

**a**) 2 step phase fringe = 0, π/2 (left-top); (

**b**) 4 step phase fringe = 0, π/2, π/4, 7π/4 (right-top); (

**c**) 6 step phase fringe = π/4, 7π/4, 3π/8, 13π/8, π/8, 15π/8, 0, π/2 (left-bottom); and (

**d**) 8 step fringe with phase = 3π/8, 13π/8, π/8, 15π/8, 0, π/2, π/4, 7π/4 (right-bottom). Reconstructed images of the living cell B16F10 with a (

**e**) 2 step phase fringe (top), (

**f**) 6 step phase fringe (middle) and (

**g**) 8 step phase fringe (bottom).

**Figure 23.**3D localization of a single 0.1 µm fluorescent bead. (

**a**) Histograms of 68 localizations in x, y, and z of one single 0.1 µm red (580/605) fluorescent bead on a coverslip. The standard deviations of the measurements are ${\sigma}_{x}={\sigma}_{y}=5\mathrm{nm}$, and ${\sigma}_{z}=40\mathrm{nm}$. (

**b**) Representative hologram of a single bead acquired in one 50 ms exposure. Scale bar is 50 µm. (

**c**) Scatter plot of localizations. Reprinted with permission from [40].

**Figure 24.**Schematics of the IHLLS systems with one diffractive lens of focal length, f

_{SLM}= 400 mm (IHLLS 1L) and two diffractive lenses with focal lengths f

_{d1}= 220 mm and f

_{d2}= 2356 mm (IHLLS 2L). A collimated 30 Bessel beam is focused by an excitation objective lens which generates a lattice light sheet. It excites fluorophores in the focal plane and in/off the focal plane of the detection objective lens, which is a water immersed microscope objective MO (Nikon 25X, NA 1.1, WD 2 mm). The detection system also includes two pairs of lenses for beam size adjustment to fit the size of the SLM active area, L

_{1}= L

_{4}with focal lengths 175 mm, L

_{2}= L

_{3}with focal lengths 100 mm; mirrors M

_{1}, M

_{2}, M

_{3}; polarizer P; 40 nm band pass filter BPF centered on the 520 nm wavelength, spatial light modulator SLM, and CMOS camera. While the z-galvo and z-piezo are moved along the z axis to acquire stacks in LLS and IHLLS 1L

**,**in IHLLS 2L only the z-galvo is moved at various z positions (Visualization 1 [41]). The diffraction mask in the excitation path was positioned for all experiments on the anulus of 0.55 outer NA and 0.48 inner NA. The detection magnification ${M}_{T-LLS}$ = 62.5 and the illumination wavelength ${\lambda}_{illumination}$ = 488 nm. The width of the light sheet in the center of the FOV is about 400 nm.

**Figure 25.**IHLLS 2L imaging of a lamprey spinal cord ventral horn neuron with dendrites; (

**a**) Amplitude reconstruction of a neuronal cell at three z-galvo positions: (

**a**) +30 µm, (

**b**) 0 µm, (

**c**) −30 µm, and (

**d**) the superposition of all three; Phase reconstruction of a neuronal cell at z-galvo positions: (

**e**) +30 µm, (

**f**) 0 µm, (

**g**) −30 µm, and (

**h**) the superposition of all three. (Images are taken from [41] with permission).

**Figure 26.**Schematic of CCS. (

**a**) A self-interference digital holography system with CCS and FINCH. (

**b**) Image-reconstruction procedures.

**Figure 27.**Experimental results. Reconstructed images at wavelengths of (

**a**) 618, (

**b**) 530, and (

**c**) 455 nm. (

**d**) Photograph of the specimen and (

**e**) color-synthesized image generated from (

**a**–

**c**). Plots of borderlines in (

**d**,

**e**) along groups (

**f**) 7, (

**g**) 8, and (

**h**) 9. Red lines in (

**d**,

**e**) indicate the locations where the plots are selected. In (

**e**), the white balance was calculated during synthesis. Red and blue lines in (

**f**–

**h**) indicate the results obtained from (

**d**,

**e**), respectively.

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**MDPI and ACS Style**

Rosen, J.; Alford, S.; Anand, V.; Art, J.; Bouchal, P.; Bouchal, Z.; Erdenebat, M.-U.; Huang, L.; Ishii, A.; Juodkazis, S.;
et al. Roadmap on Recent Progress in FINCH Technology. *J. Imaging* **2021**, *7*, 197.
https://doi.org/10.3390/jimaging7100197

**AMA Style**

Rosen J, Alford S, Anand V, Art J, Bouchal P, Bouchal Z, Erdenebat M-U, Huang L, Ishii A, Juodkazis S,
et al. Roadmap on Recent Progress in FINCH Technology. *Journal of Imaging*. 2021; 7(10):197.
https://doi.org/10.3390/jimaging7100197

**Chicago/Turabian Style**

Rosen, Joseph, Simon Alford, Vijayakumar Anand, Jonathan Art, Petr Bouchal, Zdeněk Bouchal, Munkh-Uchral Erdenebat, Lingling Huang, Ayumi Ishii, Saulius Juodkazis,
and et al. 2021. "Roadmap on Recent Progress in FINCH Technology" *Journal of Imaging* 7, no. 10: 197.
https://doi.org/10.3390/jimaging7100197