Differentiable holography

Laser & Photonics Reviews, 2023


We present differentiable holography that takes optical system imperfections (Fig. 1) into account in inverse holographic imaging, demonstrated by successful auto-focused complex field imaging from a single-shot inline hologram obtained with various setups.

Fig. 1: Numerical modeling of a typical computational holography system, parameterized by several realistic setup factors.

(1) We incorporate system imperfections into the imaging modeling with $f(x, \theta)$, where $x$ is the target and $\theta$ is a collection of imperfection parameters. (2) The challenging inversion of the forward model is solved with differentiable optimization algorithm. With this we can achieve complex field imaging from single-shot inline holograms without the use of additional hardware.

Experimental results

Holography type I: Plane illumination II: Spherical illumination III: Lensless holography IV: with fiber bundle1
Fig. 2: Various inline holography systems that used to test the proposed differentiable holography: Inline holography with (I) plane wave illumination and (II) spherical wave illumination, (III) lensless holography, and (IV) inline holography with fiber bundle setup.

data setup type hologram BP Our method
KAUST logo I
particle I
ruler3 II
Fig. 3: Amplitude-object imaging compared to back-propagation (BP).

data setup type hologram amplitude (ours) phase (ours) amplitude (MP) phase (MP)
tilia root I
Fig. 4: Complex fields imaging compared to multi-plane (MP) phase retrieval with 5 holograms.

data setup type hologram amplitude (ours) phase (ours) amplitude (DCOD)4 phase (DCOD)4
cheek cell4 III
Fig. 5: Complex fields imaging compared to DCOD.

data setup type hologram amplitude (ours) phase (ours) amplitude (BP) phase (BP)
balser5 II
blood cell4 III
Fig. 6: Complex fields imaging compared to back propagation (BP).

method image size iteration time cost workstation
DCOD 512 $\times$ 512 30000 ~40 miniutes Nvidia Tesla k80 GPU
Ours 512 $\times$ 512 2500 ~36 seconds Nvidia GTX 1080 GPU
Ours 1024 $\times$ 1024 2500 ~113 seconds Nvidia GTX 1080 GPU
Fig. 7: Computational Efficiency compared to the state-of-the-art learning-based method (DCOD).


title  = {Differentiable holography},
author = {Ni Chen and Congli Wang and Wolfgang Heidrich},
year   = {2022},
month  = {June},
doi    = {10.1002/lpor.202200828},
url    = {},


  1. M. R. Hughes, “Inline holographic microscopy through fiber imaging bundles,” Appl. Opt. 60, A1-A7 (2021).  2

  2. W. Zhang, et. al., “Twin-Image-Free Holography: A Compressive Sensing Approach”, Phys. Rev. Lett. 121, 093902, 2018. 

  3. https://github.com/microcombustion/Holography 

  4. F. Niknam, et. al., Holographic optical field recovery using a regularized untrained deep decoder network. Sci Rep 11, 10903 (2021).  2 3 4 5

  5. F. Momey, et. al., “From Fienup’s phase retrieval techniques to regularized inversion for in-line holography: tutorial,” J. Opt. Soc. Am. A 36, D62-D80 (2019).