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REVIEW 4 major objections 6 minor 31 references

Methods for extending viewing-angle of holographic image by using digital hologram with high numerical aperture

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper argues that the angular field of view of a holographic image is set by the hologram's numerical aperture, not the modulator's pixel pitch, and that high-HNA holograms can widen the view if aliased replicas are suppressed.

desk verdict Plausible HNA-viewing-angle relation, but the wide-angle extension method rests on an unproven alias-removal step and the abstract overclaims. read the letter →

arxiv 1908.09411 v3 pith:5P6VIIXV submitted 2019-08-26 physics.optics eess.IV

Byung Gyu Chae This is my paper · ORCID
classification physics.opticseess.IV
keywords holographicdisplayangularfieldofviewhologramnumericalaperturepixelpitchaliasingviewingangleFresnelspatiallightmodulator
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to overturn a standard assumption in holographic displays: that the viewing angle of a reconstructed image is fixed by the pixel pitch of the spatial light modulator through $\theta = 2\arcsin(\lambda/(2p))$. Its central claim is that the angular field of view is instead governed by the hologram numerical aperture (HNA), the half-angle subtended by the hologram aperture at the image, giving $\Omega = 2\arcsin(\lambda/(2R_{\mathrm{Abbe}})) = 2\arcsin(N\Delta\xi/(2z))$. If true, a fixed-pitch commercial modulator can display a small image with a wide viewing angle by synthesizing the hologram close to the object, as long as the higher-order aliased replicas created by pixel sampling are removed. The paper supports this with Fresnel diffraction analysis, numerical simulations at several synthesis distances, and optical experiments with a phase spatial light modulator showing perspective views at about 7.6 to 7.8 degrees instead of the roughly 3.8-degree pixel-pitch limit. It then proposes enlarging the object during high-HNA synthesis and suppressing aliased images by upsampling the hologram through a binary random mask, which breaks the periodicity of the pixel array.

What carries the argument

The load-bearing object is the hologram numerical aperture, $\mathrm{HNA} = \sin(\Omega/2) = N\Delta\xi/(2z)$, the sine of the half-angle the hologram aperture subtends at the image. The argument runs through the Abbe resolution limit $R_{\mathrm{Abbe}} = \lambda/(2\,\mathrm{HNA})$: because a converging spherical wave from the hologram forms a point image whose diffraction spot has this width, the diverging wave from that image radiates into a cone with full angle $\Omega = 2\arcsin(\lambda/(2R_{\mathrm{Abbe}}))$. The second piece is the Poisson-summation treatment of the pixelated hologram, which separates the finite aperture, which sets the HNA and hence the AFOV, from the periodic pixel lattice, which sets the replica spacing $\lambda z/p$ and the sinc envelope. The identity $\Omega = 2\arcsin(N\Delta\xi/(2z))$ carries the quantitative prediction tested in both simulation and experiment.

What would settle it

Display a high-HNA Fresnel hologram synthesized at $z_1$ with an 8-micrometer-pixel modulator and measure the angular extent over which the reconstructed letter image remains clean before aliased replicas intrude. The paper predicts about 7.6 degrees from $\Omega = 2\arcsin(N\Delta\xi/(2z))$, while the pixel-pitch-only view predicts about 3.8 degrees; if the clean view never exceeds the first-order diffraction zone unless the binary random mask is added, the central claim fails.

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Extended reading notes

Core claim

The central claim is that the AFOV of a holographic image is fundamentally determined by the hologram numerical aperture, not by the diffraction angle of the pixel pitch. The paper derives this from treating the sampled hologram as a continuous finite aperture plus a periodic sampling structure: the pixel grid only creates a periodic set of diffraction zones, with replica spacing $\lambda z/p$, while the image inside the first-order zone is formed by the whole finite hologram aperture. For a point object the reconstructed spot has the Abbe-limited width $R_{\mathrm{Abbe}} = \lambda/(2\,\mathrm{HNA})$, and by mirror symmetry the diverging wave from that spot fills a cone whose full angle is $\Omega = 2\arcsin(\lambda/(2R_{\mathrm{Abbe}}))$. In discrete Fresnel holograms this becomes $\Omega = 2\arcsin(N\Delta\xi/(2z))$, so moving the object closer to the hologram raises the viewing angle while shrinking the image. Numerical simulations for conventional Fresnel holograms show about 7.62 degrees at $z_1 = z_0/2$ versus about 4 degrees at $z_0$, and optical experiments with two stacked letter objects at $z_1$ show perspective views estimated at 7.8 degrees, exceeding the 3.8-degree pixel-pitch diffraction angle. The paper then shows that a high-HNA hologram can be made from a larger object by upsampling, and that a binary random mask on the upsampled hologram suppresses the high-order aliased replicas, which is how the wider viewing angle would be secured on a present-day modulator.

Load-bearing premise

The argument depends on the unproven premise that aliasing caused by undersampling the rapidly oscillating fringes of a high-HNA hologram at the modulator's pixel pitch can be compensated during reconstruction or removed with an upsampling plus random mask; Section 2.3 explicitly defers this analysis to later work, and the random-mask demonstration is only a simulation. If that premise fails, a high-HNA hologram on a fixed-pitch modulator just produces overlapping aliased replicas and no clean wide viewing angle.

Editorial extensions

If this is right

  • For a fixed pixel pitch, reducing the synthesis distance increases the hologram numerical aperture and raises the viewing angle $\Omega = 2\arcsin(N\Delta\xi/(2z))$, while shrinking the reconstructed image.
  • Conventional Fresnel holograms synthesized at the Nyquist distance $z_0$ give a viewing angle close to the pixel-pitch diffraction angle, while holograms synthesized at half that distance give approximately double the angle, as shown by simulations and by the optical perspective-view experiment.
  • Upsampling a hologram fringe does not by itself enlarge the viewing angle; it only enlarges the total diffraction zone, because the hologram numerical aperture is unchanged.
  • Holograms synthesized by the convolution method have a viewing angle fixed by the object resolution and hologram pixel pitch, independent of synthesis distance, matching the formula $\Omega = 2\arcsin(\lambda/\Delta\xi)$ when the resolution is held constant.
  • If the aliased high-order replicas can be removed, for example by upsampling the hologram through a binary random mask, a high-HNA hologram loaded on a standard 8-micrometer-pixel modulator can produce a viewing angle of about 7 degrees instead of the usual 3.8-degree pixel-pitch limit.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: If the paper's claim is right, the pixel-pitch diffraction angle is not a hard physical ceiling but a periodicity constraint, so aperiodic pixel layouts or random masks could push the clean viewing field beyond $2\arcsin(\lambda/(2p))$ without spatial or temporal multiplexing.
  • Editorial inference: A direct quantitative test of the paper's formula would be to vary only the synthesis distance on one spatial light modulator and check whether the measured clean viewing angle follows $\Omega = 2\arcsin(N\Delta\xi/(2z))$; the paper's data at $z_1$ and $z_0$ are a start, but a systematic scan would settle it.
  • Editorial inference: The proposed method trades image size for viewing angle, so its practical value depends on whether the deferred analysis of aliasing compensation can recover the missing high-frequency fringes well enough to avoid the image contraction; that later work, not this paper, is the evidence that would make or break the application.
  • Editorial inference: If de-aliased high-HNA holograms become reliable, wide-angle holographic displays could be built with existing modulators and without the enormous data capacity required by tiled or multiplexed SLM arrays, but that consequence is the editor's projection rather than a claim the paper itself makes.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper argues that the angular field of view (AFOV) of a holographic image is determined by the hologram numerical aperture (HNA) rather than by the pixel pitch of the spatial light modulator, with the viewing angle given by Eq. (25) as Ω = 2 arcsin(NΔξ/(2z)). It presents numerical simulations for holograms synthesized by the Fresnel transform and the convolution method, optical experiments using a phase SLM, and a proposed method for extending the viewing angle by increasing the object size during high-HNA synthesis and removing high-order aliasing images with a binary random mask. The central difficulty is that the high-HNA holograms used in the demonstrations have fringe frequencies that approach or exceed the Nyquist limit of the 8-μm SLM, and the alias-compensation mechanism is explicitly deferred to an unpublished follow-up reference.

Significance. If established, the HNA-based viewing-angle formalism would provide a useful design rule for holographic displays and would partially decouple the AFOV from the SLM pixel pitch. The geometric derivation leading to Eq. (25) is simple and plausible, and the numerical simulations show the expected trend when the hologram is band-limited. The manuscript also includes a rare attempt to address the trade-off between image size and viewing angle by proposing a random-mask approach. However, the central claim for pixelated modulators rests on an unproven alias-compensation premise, and the current optical evidence does not isolate a clean wide-angle reconstruction; the wide-angle views are consistent with overlapping high-order replicas. The proposed extension method is validated only in simulation and without quantitative metrics.

major comments (4)
  1. [§2.3] The manuscript explicitly defers the analysis of aliasing compensation to Ref. [26], stating: "The aliasing error generated from the hologram synthesis can be compensated in the reconstruction process. The detailed analysis is out of present research scope, which will be clarified in the subsequent research [26]." This premise is load-bearing: the high-HNA holograms used in Figs. 6, 12, and 13 have fringe frequencies that approach or exceed the Nyquist limit of the 8-μm SLM, so the claimed viewing angles and the proposed extension method depend on a compensation mechanism that is neither derived nor demonstrated in this paper. The simulation in Fig. 13(c)-(d) shows aliasing noise overlapping the reconstructed image and admits that the high-order aliasing is "not completely removed," so the paper does not provide even numerical evidence for the premise.
  2. [§4, Fig. 12] The optical experiment estimates the viewing angle (7.6–7.8°) from perspective views that appear only in the adjacent (replicated) images. The text acknowledges this directly: "Only the diffraction angle of a pixel pitch obstructs to secure an observable viewing window without the superposition of aliased images." Thus the experiment demonstrates overlapping diffraction orders rather than a clean wide-angle reconstruction from a single image order. This does not support the abstract's claim that the HNA-dependence is "proved ... by ... optical experiments."
  3. [§5, Fig. 14] The binary random mask is presented as the key enabler of the viewing-angle extension, but the result is simulation-only, uses a 4-μm mask with a 90% opening ratio, and provides no quantitative evaluation of the reconstructed image quality (e.g., SNR or correlation with the ideal image) and no optical validation. Moreover, the mask is amplitude-only and cannot restore the high-frequency phase content that is lost when a high-HNA hologram is sampled at 8-μm pitch; it can only scramble the aliased replicas into broadband noise, which may still degrade the desired image. The claim that the method "could be a useful tool" is therefore unsupported.
  4. [§3.1, Fig. 6] The numerical viewing angles are measured from the growth rate of the "active diffraction fringe" in the propagated field. For synthesis distances below the Nyquist condition (e.g., z1 in Fig. 6(a)), the hologram fringes are undersampled, as stated in §2.3. Consequently, the measured angular spread may be inflated by aliasing artifacts rather than representing the first-order diffraction component. A control test with a strictly bandlimited hologram—for instance, one synthesized with the angular spectrum method and then resampled to the SLM pitch—is needed to isolate the HNA effect from the alias effect.
minor comments (6)
  1. [Eq. (15)] Equation (15) is garbled in the present text ("z N Ω 2 sin HNA HNA ξ ξ Δ = =") and should be rewritten as a clear mathematical expression relating HNA, N, Δξ, and z.
  2. [Eq. (22)] The notation around Eq. (22) is confusing: the text appears to define HNA in terms of Ω, but the relation between HNA and the half-angle should be stated explicitly and consistently with Eq. (15).
  3. [§3.1] The simulation parameters for the different holograms (N, Δx, z, Δξ, object size) are presented piecemeal across Figs. 5–9; a summary table of these parameters would greatly improve readability and help the reader verify the Nyquist conditions.
  4. [§4] In the optical experiment, the values z0 = 259.8 mm and z1 = 129.9 mm should be explicitly derived from the SLM pixel pitch, wavelength, and chosen object pixel sizes via Eq. (19), to make it clear why the HNA is doubled for the z1 hologram.
  5. [Ref. [26]] The load-bearing claim about alias compensation is deferred to the author's own unpublished manuscript [26]. A journal paper should not rest its central argument on a non-archived reference; the relevant analysis should be included in this paper, or the claim should be substantially weakened.
  6. [§5] The phrase "random sampling deteriorates a periodicity of the pixel structure" is vague; please specify the statistical effect on the diffraction orders and how the mask parameters (e.g., opening ratio, pixel size) affect the suppression of aliasing.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: HNA viewing-angle formula is an independent aperture-geometry result, with the only self-citation being a deferred, non-load-bearing aliasing-compensation claim.

full rationale

The central claim, that the angular field of view is set by the hologram numerical aperture rather than by the pixel-pitch diffraction angle, is derived from the aperture size and the Abbe resolution limit: Eq. (15) defines HNA geometrically, Eq. (16) gives R_Abbe = lambda/(2 HNA), and Eq. (25) then gives Omega = 2 arcsin(N Delta_xi/(2z)). No parameter is fitted to the measured viewing angles. The numerical propagations in Figs. 5-7 are produced with the same discrete Fresnel transform that defines the pixel-resolution relation (Eq. 19), so the agreement with Eq. (25) is a self-consistency check rather than a fitted prediction; the optical experiments in Fig. 12 independently support the HNA dependence (about 7.6-7.8 degrees at z1 versus 3.8 degrees at z0). The one self-citation that could be questioned is Section 2.3's promise that alias errors from under-sampled high-HNA fringes can be compensated, deferred to the author's own follow-up [26]. That claim is not used in the HNA derivation, and the random-mask extension in Section 5 is a self-contained simulation. Thus there is no significant circularity; the score of 2 reflects only the minor deferred self-citation, not a load-bearing circular step.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced. The central claim relies on standard Fourier optics plus two unproven assumptions specific to the proposed method: alias compensation in reconstruction (deferred to [26]) and random-mask alias removal (shown only in simulation).

assumptions (4)
  • standard math Fresnel diffraction and discrete Fresnel transform are valid models for hologram synthesis and reconstruction.
    Used throughout Sections 2 and 3 as the basis for Eqs. (3), (18), (27), and (31).
  • domain assumption Abbe resolution criterion applies to coherent holographic image formation, so R_Abbe = λ/(2 HNA) holds.
    Invoked in Section 2.2 to connect the sinc width of the point image to resolution and viewing angle.
  • ad hoc to paper Aliasing error in under-sampled high-HNA holograms can be compensated in reconstruction.
    Asserted in Section 2.3 and deferred to the author's follow-up [26]; no derivation or experimental support is given in this paper.
  • ad hoc to paper A binary random mask suppresses high-order aliasing without corrupting the desired image.
    Proposed and demonstrated only in simulation in Section 5; no optical validation is provided.

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Cite this review

Pith. "Pith review of Methods for extending viewing-angle of holographic image by using digital hologram with high numerical aperture." pith.science (2026). https://pith.science/paper/5P6VIIXV

@misc{pith2026190809411,
  author       = {Pith},
  title        = {Pith review of: Methods for extending viewing-angle of holographic image by using digital hologram with high numerical aperture},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5P6VIIXV}},
  note         = {Machine review of arXiv:1908.09411}
}
read the original abstract

We investigate the angular field of view (AFOV) of a holographic image reconstructed from the digital Fresnel hologram in holographic display. The theoretical analysis reveals that the AFOV of a holographic image is fundamentally determined by the hologram numerical aperture (HNA) other than a diffraction angle of pixel pitch of a pixelated modulator. This property is proved for various types of the digital holograms by using a numerical simulation and optical experiments. The high-HNA hologram reconstructs the image with a high viewing-angle, although the image contraction is inevitable due to the Nyquist sampling criterion. We propose the method for extending the viewing-angle of a holographic image in the manner of increasing the object size during the high-HNA hologram synthesis and removing the high-order aliasing images.

Figures

Figures reproduced from arXiv: 1908.09411 by the authors.

Figure 1
Figure 1. Configuration of digital hologram and objects during the hologram synthesis. The object size decreases at lower distance from the digital hologram, based on the Nyquist criterion, and the angles from the blue lines and red lines mean the values for the numerical aperture of the digital hologram and diffraction zone due to a pixel pitch, respectively. z1 z0 z2 Ω1 Ω0 Ω2 ξ z η y y x x x θ [PITH_FULL_IMAGE:figures/full… view at source ↗
Figure 2
Figure 2. Schematic diagram for the generation of high [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

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Reference graph

Works this paper leans on

31 extracted references · 29 canonical work pages

  1. [26]

    Analysis on image recovery for digital Fresnel hologram with aliased fringe generated from self-similarity of point spread function

    B. G. Chae, “Analysis on image recovery for digital Fresnel hologram with aliased fringe generated from self- similarity of point spread function,” arXiv:1911.07997 (2019)

    work page Pith review arXiv 2019

  2. [1]

    J. W. Goodman, Introduction to Fourier optics (Roberts & Company, 2005)

    work page 2005

  3. [2]

    Viewing-zone scanning holographic display using a MEMS spatial light modulator,

    Y. Takaki and K. Fujii, “Viewing-zone scanning holographic display using a MEMS spatial light modulator,” Optics Express 22(20), 24713-24721 (2014)

    work page 2014

  4. [3]

    Extended viewing angle holographic display system with tilted SLMs in a circular configuration,

    T. Kozacki, M. Kujawińska, G. Finke, B. Hennelly, and N. Pandey, “Extended viewing angle holographic display system with tilted SLMs in a circular configuration,” Appl. Opt. 51(11), 1771-1780 (2012)

    work page 2012

  5. [4]

    Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators,

    J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, “Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators,” Opt. Express 16(16), 12372-12386 (2008)

    work page 2008

  6. [5]

    Space-bandwidth product of optical signals and systems,

    A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, “Space-bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A 13(3), 470-473 (1996)

    work page 1996

  7. [6]

    Electro-holographic display using 15 mega pixels LCD,

    K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 mega pixels LCD,” Proc. SPIE 2652, 15-23 (1996)

    work page 1996

  8. [7]

    Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,

    T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Display Technol. 7(7), 382-390 (2011)

    work page 2011

Show all 31 references
  1. [8]

    Circular holographic video display system,

    F. Yaraş, H. Kang, and L. Onural, “Circular holographic video display system,” Opt. Express 19(10), 9147- 9156 (2011)

    2011

  2. [9]

    Viewing-angle enlargement in holographic augmented reality using time division and spatial tiling,

    Y.-Z. Liu, X.-N. Pang, S. J. Jiang, and J.-W. Dong, “Viewing-angle enlargement in holographic augmented reality using time division and spatial tiling,” Opt. Express 21(10), 12068-12076 (2013)

    2013

  3. [10]

    Digital holographic display system with large screen based on viewing window movement for 3D video service,

    M. Park, B. G. Chae, H. Kim, J. Hahn, H. Kim, C. H. Park, K. Moon, and J. Kim, “Digital holographic display system with large screen based on viewing window movement for 3D video service,” ETRI J. 36(2), 232-241 (2014)

    2014

  4. [11]

    Large holographic display as an alternative to stereoscopic displays,

    R. Haussler, A. Schwerdtner, and N. Leister, “Large holographic display as an alternative to stereoscopic displays,” Proc. SPIE 6803, 68030M-9 (2008)

    2008

  5. [12]

    Comparative analysis on viewing angle change in Fresnel and Fourier holographic images reconstructed by a tilted plane wave,

    B. G. Chae, “Comparative analysis on viewing angle change in Fresnel and Fourier holographic images reconstructed by a tilted plane wave,” Appl. Opt. 53(15), 3203-3212 (2014). 22

    2014

  6. [13]

    Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields,

    H. Yu, K. Lee, J. Park, and Y. Park, “Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields,” Nat. Photon. 11, 186-192 (2017)

    2017

  7. [14]

    M. K. Kim, Digital Holographic Microscopy (Springer, 2011)

    2011

  8. [15]

    Digital simulation of scalar optical diffraction: revisiting chirp function sampling criteria and consequences,

    D. G. Voelz and M. C. Roggemann, “Digital simulation of scalar optical diffraction: revisiting chirp function sampling criteria and consequences,” Appl. Opt. 48(32), 6132-6142 (2009)

    2009

  9. [16]

    Controlling the aliasing by zero-padding in the digital calculation of the scalar diffraction,

    J.-P. Liu, “Controlling the aliasing by zero-padding in the digital calculation of the scalar diffraction,” J. Opt. Soc. Am. A 29(9), 1956-1964 (2012)

    2012

  10. [17]

    Algorithm for reconstruction of digital holograms with adjustable magnification,

    F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett. 29(14), 1668-1670 (2004)

    2004

  11. [18]

    Magnified reconstruction of digitally recorded holograms by Fresnel- Bluestein transform,

    J. F. Restrepo and J. Garcia-Sucerquia, “Magnified reconstruction of digitally recorded holograms by Fresnel- Bluestein transform,” Appl. Opt. 49(33), 6430-6435 (2010)

    2010

  12. [19]

    Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms,

    P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, “Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms,” Opt. Lett. 29(8), 854-856 (2004)

    2004

  13. [20]

    Analysis of practical sampling and reconstruction from Fresnel fields,

    A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng. 43(1), 239-250 (2004)

    2004

  14. [21]

    Sampling of the diffraction field,

    L. Onural, “Sampling of the diffraction field,” Appl. Opt. 39(32), 5929-5935 (2000)

    2000

  15. [22]

    Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,

    C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 38(22), 4812-4820 (1999)

    1999

  16. [23]

    General theoretical formulation of image formation in digital Fresnel holography,

    P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A 25(7), 1744-1761 (2008)

    2008

  17. [24]

    Inverted Gabor holography principle for tailoring arbitrary shaped three- dimensional beams,

    T. Latychevskaia and H.-W. Fink, “Inverted Gabor holography principle for tailoring arbitrary shaped three- dimensional beams,” Scientific Reports 6, 26312 (2016)

    2016

  18. [25]

    Schnars and W

    U. Schnars and W. Juptner, Digital Holography (Springer, 2005)

    2005

  19. [27]

    T. C. Poon and J. P. Liu, Introduction to Modern Digital Holography with MATLAB (Springer, 2007)

    2007

  20. [28]

    Band-limited angular spectrum method for numerical simulation of free space propagation in far and near fields,

    K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free space propagation in far and near fields,” Opt. Express 17(22), 19662-19673 (2009)

    2009

  21. [29]

    A practical algorithm for the determination of the phase from image and diffraction plane pictures,

    R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237-246 (1972)

    1972

  22. [30]

    Is the Rayleigh-Sommerfeld diffraction always an exact reference for high speed diffraction algorithms ?,

    S. Mehrabkhani and T. Schneider, “Is the Rayleigh-Sommerfeld diffraction always an exact reference for high speed diffraction algorithms ?,” Opt. Express 25(24), 30229-30240 (2017)

    2017

  23. [31]

    Wide viewing-angle holographic display apparatus using high numerical aperture of digital hologram,

    B. G. Chae, “Wide viewing-angle holographic display apparatus using high numerical aperture of digital hologram,” KR patent application 10-2019-0083427 (10 July 2019)

    2019

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