Computer-Generated Holography¶
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).
In the rest of this document, you will find engineering notes and relevant functions in Odak that helps you describing complex nature of light on a computer.
Note that, the creators of this documentation are from Computational Displays domain, however the provided submodules can potentially aid other lines of research as well, such as Computational Imaging or Computational Microscopy.
Engineering notes¶
| Note | Description |
|---|---|
Holographic light transport |
This engineering note will give you an idea about how coherent light propagates in free space. |
Optimizing phase-only single plane holograms using Odak |
This engineering note will give you an idea about how to calculate phase-only holograms using Odak. |
Learning the model of a holographic display |
This link navigates to a project website that provides a codebase that can learn the model of a holographic display using a single complex kernel. |
Optimizing three-dimensional multiplane holograms using Odak |
This link navigates to a project website that provides a codebase that can help optimize a phase-only hologram representing multiplanar three-dimensional scenes. |
odak.learn.wave¶
This submodule is based on torch, therefore the functions provided here are differentiable and can be used with provided optimizers in torch.
| Function | Description |
|---|---|
| odak.learn.wave.adjust_phase_only_slm_range | Adjust the range of a spatial light modulator. |
| odak.learn.wave.band_limited_angular_spectrum | Optical beam propagation with bandlimited angular spectrum. |
| odak.learn.wave.calculate_amplitude | Calculate amplitude of a complex field. |
| odak.learn.wave.calculate_phase | Calculate phase of a complex field. |
| odak.learn.wave.custom | Optical beam propagation with a custom complex kernel. |
| odak.learn.wave.generate_complex_field | Generate a complex field from an amplitude and a phase value. |
| odak.learn.wave.gerchberg_saxton | Phase-only hologram optimizasion using Gerchberg-Saxton algorithm. |
| odak.learn.wave.gradient_descent | Phase-only hologram optimizasion using Gradient-Descent algorithm. |
| odak.learn.wave.impulse_response_fresnel | Optical beam propagation with impulse response fresnel. |
| odak.learn.wave.linear_grating | One or two axis linear grating. |
| odak.learn.wave.phase_gradient | Regularization function to measure the variation of the phase. |
| odak.learn.wave.point_wise | Phase-only hologram optimization using point wise integration method. |
| odak.learn.wave.prism_phase_function | Prism phase function, a prism. |
| odak.learn.wave.produce_phase_only_slm_pattern | Produce phase-only hologram for a spatial light modulator with given phase range. |
| odak.learn.wave.propagate_beam | General function for optical beam propagation. |
| odak.learn.wave.quadratic_phase_function | Quadratic phase function, a lens. |
| odak.learn.wave.set_amplitude | Set amplitude of a complex field. |
| odak.learn.wave.shift_w_double_phase | Shift a phase-only hologram by propagating the complex hologram and later apply double phase principle. |
| odak.learn.wave.speckle_contrast | Regularization function to measure the speckle contrast. |
| odak.learn.wave.stochastic_gradient_descent | Phase-only hologram optimization using Stochastic Gradient Descent optimization. |
| odak.learn.wave.transfer_function_kernel | Optical beam propagation with transfer function kernel. |
| odak.learn.wave.wavenumber | Wave number. |
odak.wave¶
This submodule is based on Numpy. This submodule existed much before odak.learn.wave. Though this submodule contains more functions than odak.learn.wave, it does not provide the flexibility in optimization provided by differentiation support of torch.
| Function | Description |
|---|---|
| odak.wave.adaptive_sampling_angular_spectrum | Propagate coherent beams with adaptive sampling angular spectrum method. |
| odak.wave.angular_spectrum | Optical beam propagation with angular spectrum. |
| odak.wave.add_phase | Add a given phase to a given complex field. |
| odak.wave.add_random_phase | Add a random phase to a given complex field. |
| odak.wave.adjust_phase_only_slm_range | Adjust the range of a spatial light modulator. |
| odak.wave.band_extended_angular_spectrum | Optical beam propagation with band extended angular spectrum. |
| odak.wave.band_limited_angular_spectrum | Optical beam propagation with bandlimited angular spectrum. |
| odak.wave.calculate_amplitude | Calculate amplitude of a complex field. |
| odak.wave.calculate_intensity | Calculate intensity of a complex field. |
| odak.wave.calculate_phase | Calculate phase of a complex field. |
| odak.wave.double_convergence | Provides an initial phase for beam shaping. |
| odak.wave.electric_field_per_plane_wave | Return the state of a plane wave at a particular distance and time. |
| odak.wave.fraunhofer_equal_size_adjust | Match physical size of field with simulated. |
| odak.wave.fraunhofer_inverse | Adjoint model for Fraunhofer beam propagation. |
| odak.wave.generate_complex_field | Generate a complex field from an amplitude and a phase value. |
| odak.wave.gerchberg_saxton | Phase-only hologram optimization using Gerchberg-Saxton algorithm. |
| odak.wave.gerchberg_saxton_3d | Phase-only hologram optimization using Gerchberg-Saxton algorithm for three-dimensional reconstructions. |
| odak.wave.impulse_response_fresnel | Optical beam propagation with impulse response fresnel. |
| odak.wave.linear_grating | One or two axis linear grating. |
| odak.wave.prism_phase_function | Prism phase function, a prism. |
| odak.wave.produce_phase_only_slm_pattern | Produce phase-only hologram for a spatial light modulator with given phase range. |
| odak.wave.propagate_beam | General function for optical beam propagation. |
| odak.wave.propagate_field | Propagate a given array of spherical sources to given set of points in space. |
| odak.wave.propagate_plane_waves | Propagate a given plane wave in space and time. |
| odak.wave.quadratic_phase_function | Quadratic phase function, a lens. |
| odak.wave.rayleigh_resolution | Calculate Rayleigh resolution limit. |
| odak.wave.rayleigh_sommerfeld | Optical beam propagation with Rayleigh-Sommerfeld integral. |
| odak.wave.rotationspeed | Calculate rotation speed of a wave. |
| odak.wave.set_amplitude | Set amplitude of a complex field. |
| odak.wave.transfer_function_kernel | Optical beam propagation with transfer function kernel. |
| odak.wave.wavenumber | Wave number. |