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# Parallax limitations in digital holography: a phase space approach

• Light: Advanced Manufacturing  3, Article number: 28 (2022)
• Corresponding author:

Ulf Schnars (schnars@t-online.de)

• These authors contributed equally: Ulf Schnars, Claas Falldorf

• Received: 26 August 2021
Revised: 05 April 2022
Accepted: 20 April 2022
Accepted article preview online: 28 April 2022
Published online: 20 June 2022
• The viewing direction in Digital Holography can be varied if different parts of a hologram are reconstructed. In this article parallax limitations are discussed using the phase space formalism. An equation for the parallax angle is derived with this formalism from simple geometric quantities. The result is discussed in terms of pixel size and pixel number of the image sensor. Change of perspective is demonstrated experimentally by two numerical hologram reconstructions from different parts of one single digital hologram.
•  supplementary_material_video_description.docx film_x.mp4.avi
•  [1] Hariharan, P. Optical Holography: Principles, Techniques and Applications. (New York: Cambridge University Press, 1984). [2] Schnars, U. et al. Digital Holography and Wavefront Sensing. (Heidelberg: Springer, 2015). [3] Kemper, B. & Von Bally, G. Digital holographic microscopy for live cell applications and technical inspection. Applied Optics 47, A52-A61 (2008). [4] Langehanenberg, P., Von Bally, G. & Kemper, B. Autofocusing in digital holographic microscopy. 3D Research 2, 4 (2011). [5] Simic, A. et al. In-line quality control of micro parts using digital holography. Proceedings of SPIE 10233, Holography: Advances and Modern Trends V. Prague: SPIE, 2017, 1023311. [6] Falldorf, C. et al. Reduction of speckle noise in multiwavelength contouring. Applied Optics 51, 8211-8215 (2012). [7] Kujawinska, M. et al. Multiwavefront digital holographic television. Optics Express 22, 2324-2336 (2014). [8] Agour, M., Falldorf, C. & Bergmann, R. B. Holographic display system for dynamic synthesis of 3D light fields with increased space bandwidth product. Optics Express 24, 14393-14405 (2016). [9] Kelly, D. P. et al. Quantifying the 2.5D imaging performance of digital holographic systems. Journal of the European Optical Society 6, 11034 (2011). [10] Kozacki, T. et al. Holographic capture and display systems in circular configurations. Journal of Display Technology 8, 225-232 (2012). [11] Schnars, U. Digitale Aufzeichnung und Mathematische Rekonstruktion von Hologrammen in der Interferometrie. (Duesseldorf: VDI-Verlag, series 8, No 378, 1994). [12] Situ, G. & Sheridan, J. T. Holography: an interpretation from the phase-space point of view. Optics Letters 32, 3492-3494 (2007). [13] Testorf, M. E., Hennelly, B. M. & Ojeda-Castañeda, Phase-Space Optics: Fundamentals and Applications. (New York: McGraw-Hill, 2009). [14] Hennelly, B. M. Digital holography in the light of phase space. Progress in Electromagnetics Research 515 (2010). [15] Kozacki, T. et al. Extended viewing angle holographic display system with tilted SLMs in a circular configuration. Applied Optics 51, 1771-1780 (2012). [16] Arnold, J. M. Rays, beams and diffraction in a discrete phase space: Wilson bases. Optics Express 10, 716-727 (2002). [17] Gabor, D. Theory of communication. Part 1: the analysis of information. Journal of the Institution of Electrical Engineers-Part III:Radio and Communication Engineering 93, 429-441 (1946). [18] Lohmann, A. W. et al. Space–bandwidth product of optical signals and systems. Journal of the Optical Society of America A 13, 470-473 (1996). [19] Bastiaans, M. J. Wigner distribution function and its application to first-order optics. Journal of the Optical Society of America 69, 1710-1716 (1979). [20] Testorf, M. & Lohmann, A. W. Holography in phase space. Applied Optics 47, A70-A77 (2008). [21] Stern, A. & Javidi, B. Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields. Journal of the Optical Society of America A 23, 1227-1235 (2006). [22] Kreis, T. M., Adams, M. & Jueptner, W. P. O. Aperture synthesis in digital holography. Proceedings of SPIE 4777, Interferometry Xi: Techniques and Analysis. Seattle: SPIE, 2002, 69-76.
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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### Research Summary

Digital Holography: Parallax Limitations calculated with a Phase Space Approach

The viewing direction in Digital Holography can be varied if different parts of a hologram are reconstructed. In this article parallax limitations are discussed using the phase space formalism. An equation for the parallax angle is derived with this formalism from simple geometric quantities. The result is discussed in terms of pixel size and pixel number of the image sensor. Change of perspective is demonstrated experimentally by two numerical hologram reconstructions from different parts of one single digital hologram.

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## Parallax limitations in digital holography: a phase space approach

• 1. private, 27628 Hagen im Bremischen, Germany
• 2. BIAS-Bremer Institut für Angewandte Strahltechnik GmbH, Klagenfurter Str. 5, 28359 Bremen, Germany
• ###### Corresponding author: Ulf Schnars, schnars@t-online.de;
• These authors contributed equally: Ulf Schnars, Claas Falldorf

Abstract: The viewing direction in Digital Holography can be varied if different parts of a hologram are reconstructed. In this article parallax limitations are discussed using the phase space formalism. An equation for the parallax angle is derived with this formalism from simple geometric quantities. The result is discussed in terms of pixel size and pixel number of the image sensor. Change of perspective is demonstrated experimentally by two numerical hologram reconstructions from different parts of one single digital hologram.

### Research Summary

Digital Holography: Parallax Limitations calculated with a Phase Space Approach

The viewing direction in Digital Holography can be varied if different parts of a hologram are reconstructed. In this article parallax limitations are discussed using the phase space formalism. An equation for the parallax angle is derived with this formalism from simple geometric quantities. The result is discussed in terms of pixel size and pixel number of the image sensor. Change of perspective is demonstrated experimentally by two numerical hologram reconstructions from different parts of one single digital hologram.

show all
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