Odak contains essential ingredients for research and development targeting Computer-Generated Holography.
We consult the beginners in this matter to Goodman's Introduction to Fourier Optics
book (ISBN-13: 978-0974707723) and Principles of optics: electromagnetic theory of propagation, interference and diffraction of light
from Max Born and Emil Wolf (ISBN 0-08-26482-4).
This engineering note will provide a crash course on how light travels from a phase-only hologram to an image plane.
As depicted in above figure, when such holograms are illuminated with a collimated coherent light (e.g. laser), these holograms can reconstruct an intended optical field at target depth levels.
How light travels from a hologram to a parallel image plane is commonly described using Rayleigh-Sommerfeld diffraction integrals (For more, consult Heurtley, J. C. (1973). Scalar Rayleigh–Sommerfeld and Kirchhoff diffraction integrals: a comparison of exact evaluations for axial points. JOSA, 63(8), 1003-1008.
).
The first solution of the Rayleigh-Sommerfeld integral, also known as the Huygens-Fresnel principle, is expressed as follows:
where field at a target image plane,
where A represents the spatial distribution of amplitude and Sypek, Maciej. "Light propagation in the Fresnel region. New numerical approach." Optics communications 116.1-3 (1995): 43-48.
).
There are multiple variants of this simplified approach:
Matsushima, Kyoji, and Tomoyoshi Shimobaba. "Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields." Optics express 17.22 (2009): 19662-19673.
,Zhang, Wenhui, Hao Zhang, and Guofan Jin. "Band-extended angular spectrum method for accurate diffraction calculation in a wide propagation range." Optics letters 45.6 (2020): 1543-1546.
,Zhang, Wenhui, Hao Zhang, and Guofan Jin. "Adaptive-sampling angular spectrum method with full utilization of space-bandwidth product." Optics Letters 45.16 (2020): 4416-4419.
In many cases, people choose to use the most common form of h described as
where z represents the distance between a hologram plane and a target image plane. Note that beam propagation can also be learned for physical setups to avoid imperfections in a setup and to improve the image quality at an image plane:
Peng, Yifan, et al. "Neural holography with camera-in-the-loop training." ACM Transactions on Graphics (TOG) 39.6 (2020): 1-14.
,Chakravarthula, Praneeth, et al. "Learned hardware-in-the-loop phase retrieval for holographic near-eye displays." ACM Transactions on Graphics (TOG) 39.6 (2020): 1-18.
,Kavaklı, Koray, Hakan Urey, and Kaan Akşit. "Learned holographic light transport." Applied Optics (2021).
.
For more engineering notes, follow: