# Breaking of Wavelength-Dependence in Holographic Wavefront Sensors Using Spatial-Spectral Filtering

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Experimental Demonstration

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## 4. Results and Discussion

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## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Geary, J.M. Introduction to Wavefront Sensors, 1st ed.; SPIE: Bellingham, WA, USA, 1995. [Google Scholar]
- Platt, B.C.; Shack, R. History and Principles of Shack-Hartmann Wavefront Sensing. J. Refract. Surg.
**2001**, 17, S573. [Google Scholar] [CrossRef] [PubMed] - Primot, J. Theoretical description of Shack–Hartmann wave-front sensor. Opt. Commun.
**2003**, 222, 81–92. [Google Scholar] [CrossRef] - Roddier, F. Curvature sensing and compensation: A new concept in adaptive optics. Appl. Opt.
**1988**, 27, 1223–1225. [Google Scholar] [CrossRef] [PubMed] - Ragazzoni, R.; Diolaiti, E.; Vernet, E. A pyramid wavefront sensor with no dynamic modulation. Opt. Commun.
**2002**, 208, 51–60. [Google Scholar] [CrossRef] - Esposito, S.; Riccardi, A. Pyramid Wavefront Sensor behavior in partial correction Adaptive Optic systems. Astron. Astrophys.
**2001**, 369, L9–L12. [Google Scholar] [CrossRef] - Neil, M.A.A.; Booth, M.J.; Wilson, T. New modal wave-front sensor: A theoretical analysis. J. Opt. Soc. Am. A
**2000**, 17, 1098–1107. [Google Scholar] [CrossRef] - Khonina, S.N.; Karpeev, S.V.; Porfirev, A.P. Wavefront Aberration Sensor Based on a Multichannel Diffractive Optical Element. Sensors
**2020**, 20, 3850. [Google Scholar] [CrossRef] - Venediktov, V.Y.; Gorelaya, A.V.; Krasin, G.K.; Odinokov, S.B.; Sevryugin, A.A.; Shalymov, E.V. Holographic wavefront sensors. Quantum Electron.
**2020**, 50, 614. [Google Scholar] [CrossRef] - Caulfield, H.J. Handbook of Optical Holography, 1st ed.; Academic Press: Cambridge, UK, 1979. [Google Scholar]
- Orlov, V.V.; Venediktov, V.Y.; Gorelaya, A.V.; Shubenkova, E.V.; Zhamalatdinov, D.Z. Measurement of Zernike mode amplitude by the wavefront sensor, based on the Fourier-hologram of the diffuse scattered mode. Opt. Laser Technol.
**2019**, 116, 214–218. [Google Scholar] [CrossRef] - Andersen, G.P.; Dussan, L.C.; Ghebremichael, F.; Chen, K. Holographic wavefront sensor. Opt. Eng.
**2009**, 48, 085801. [Google Scholar] - Ghebremichael, F.; Andersen, G.P.; Gurley, K.S. Holography-based wavefront sensing. Appl. Opt.
**2008**, 47, A62–A69. [Google Scholar] [CrossRef] [PubMed] - Booth, M.J. Direct measurement of Zernike aberration modes with a modal wavefront sensor. In Proceedings of the Advanced Wavefront Control: Methods, Devices, and Applications, San Diego, CA, USA, 6–7 August 2003. [Google Scholar]
- Collier, R.J.; Burckhardt, C.B.; Li, L.H. Optical Holography, 1st ed.; Academic Press: New York, NY, USA, 1971. [Google Scholar]
- Neil, M.A.A.; Booth, M.J.; Wilson, T. Closed-loop aberration correction by use of a modal Zernike wave-front sensor. Opt. Lett.
**2000**, 25, 1083–1085. [Google Scholar] [CrossRef] [PubMed] - Changhai, L.; Fengjie, X.; Haotong, M.; Shengyang, H.; Zongfu, J. Modal wavefront sensor based on binary phase-only multiplexed computer-generated hologram. Appl. Opt.
**2010**, 49, 5117–5124. [Google Scholar] [CrossRef] [PubMed] - Lee, W.H. III Computer-Generated Holograms: Techniques and Applications. Prog. Opt. PROG
**1978**, 16, 119–232. [Google Scholar] - Dallas, W.J. Computer-Generated Holograms. In Digital Holography and Three-Dimensional Display, 1st ed.; Springer: New York, NY, USA, 2006; pp. 1–49. [Google Scholar]
- Neff, J.A.; Athale, R.A.; Lee, S.H. Two-dimensional spatial light modulators: A tutorial. Proc. IEEE
**1990**, 78, 826–855. [Google Scholar] [CrossRef] - Waller, L.; Situ, G.; Fleischer, J. Phase-space measurement and coherence synthesis of optical beams. Nat. Photon.
**2012**, 6, 474–479. [Google Scholar] [CrossRef] - Kueny, E.; Meier, J.; Levecq, X.; Varkentina, N.; Kärtner, F.X.; Calendron, A.L. Wavefront analysis of a white-light supercontinuum. Opt. Express
**2018**, 26, 31299–31306. [Google Scholar] [CrossRef] - Stsepuro, N.; Kovalev, M.; Zlokazov, E.; Kudryashov, S. Wavelength-Independent Correlation Detection of Aberrations Based on a Single Spatial Light Modulator. Photonics
**2022**, 9, 909. [Google Scholar] [CrossRef] - Kovalev, M.S.; Krasin, G.K.; Odinokov, S.B.; Solomashenko, A.B.; Zlokazov, E.Y. Measurement of wavefront curvature using computer-generated holograms. Opt. Express
**2019**, 27, 1563–1568. [Google Scholar] [CrossRef] - Ruchka, P.A.; Verenikina, N.M.; Gritsenko, I.V.; Zlokazov, E.Y.; Kovalev, M.S.; Krasin, G.K.; Odinokov, S.B.; Stsepuro, N.G. Hardware/Software Support for Correlation Detection in Holographic Wavefront Sensors. Opt. Spectrosc.
**2019**, 127, 618–624. [Google Scholar] [CrossRef] - Goodman, J.W. Introduction to Fourier Optics, 4th ed.; W.H. Freeman: New York, NY, USA, 2017. [Google Scholar]
- Krasin, G.; Kovalev, M.; Stsepuro, N.; Ruchka, P.; Odinokov, S. Lensless Scheme for Measuring Laser Aberrations Based on Computer-Generated Holograms. Sensors
**2020**, 20, 4310. [Google Scholar] [CrossRef] [PubMed] - Lakshminarayanan, V.; Fleck, A. Zernike polynomials: A guide. J. Mod. Opt.
**2011**, 58, 545–561. [Google Scholar] [CrossRef] - Calero, V.; García-Martínez, P.; Albero, J.; Sánchez-López, M.M.; Moreno, I. Liquid crystal spatial light modulator with very large phase modulation operating in high harmonic orders. Opt. Lett.
**2019**, 38, 4663–4666. [Google Scholar] [CrossRef] - Fuentes, J.L.M.; Fernández, E.J.; Prieto, P.M.; Artal, P. Interferometric method for phase calibration in liquid crystal spatial light modulators using a self-generated diffraction-grating. Opt. Express
**2016**, 24, 14159–14171. [Google Scholar] [CrossRef] [PubMed]

**Figure 2.**Phase function cross section: (

**a**) object wave; (

**b**) reference wave in the hologram recording plane.

**Figure 4.**Distribution of the phase argument of the CGH with the value of the weight coefficient in the reference beam: (

**a**) 0.53λ for grayscale Fourier CGHs; (

**b**) 1.33λ for grayscale Fourier CGHs; (

**c**) 0.53λ for binary Fourier CGHs; (

**d**) 1.33λ for binary Fourier CGHs.

**Figure 5.**Correlation response in the output to the SLM of the grayscale and binary Fourier CGH with the value of the weight coefficient of the Zernike polynomial: (

**a**) 0.53λ for grayscale Fourier CGHs; (

**b**) 1.33λ for grayscale Fourier CGHs; (

**c**) 0.53λ for binary Fourier CGHs; (

**d**) 1.33λ for binary Fourier CGHs.

**Figure 6.**(

**a**) Cross section of the correlation function from the Figure 5a,b; (

**b**) normalized dependences of the amplitude of the maximum correlation response.

**Figure 7.**The normalized amplitude of the maximum of the correlation function depending on various parameters of the SLM for sources with a wavelength: (

**a**) ${\lambda}_{1}=473$ nm; (

**b**) ${\lambda}_{2}=532$ nm; (

**c**) ${\lambda}_{3}=561$ nm; (

**d**) dependence of maximum correlation function on SLM settings related to reference wavelength ${\lambda}_{0}$.

**Figure 8.**Comparison of the dependence of the maximum of the correlation function on the settings of the SLM relative to the reference wavelength λ

_{0}for the grayscale Fourier CGHs and binary at the wavelength: (

**a**) ${\lambda}_{1}=473$ nm; (

**b**) ${\lambda}_{2}=532$ nm; (

**c**) ${\lambda}_{3}=561$ nm.

**Figure 9.**Deviation of the value of the weight coefficient of the Zernike polynomial as a function of the SLM tuning associated with the reference wavelength ${\lambda}_{0}$ for sources with a wavelength: (

**a**) ${\lambda}_{1}=473$ nm; (

**b**) ${\lambda}_{2}=532$ nm; (

**c**) nm; (

**d**) the deviation of the position of the correlation response in the analysis plane.

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**MDPI and ACS Style**

Stsepuro, N.; Kovalev, M.; Zlokazov, E.; Kudryashov, S. Breaking of Wavelength-Dependence in Holographic Wavefront Sensors Using Spatial-Spectral Filtering. *Sensors* **2023**, *23*, 2038.
https://doi.org/10.3390/s23042038

**AMA Style**

Stsepuro N, Kovalev M, Zlokazov E, Kudryashov S. Breaking of Wavelength-Dependence in Holographic Wavefront Sensors Using Spatial-Spectral Filtering. *Sensors*. 2023; 23(4):2038.
https://doi.org/10.3390/s23042038

**Chicago/Turabian Style**

Stsepuro, Nikita, Michael Kovalev, Evgenii Zlokazov, and Sergey Kudryashov. 2023. "Breaking of Wavelength-Dependence in Holographic Wavefront Sensors Using Spatial-Spectral Filtering" *Sensors* 23, no. 4: 2038.
https://doi.org/10.3390/s23042038