slmsuite.holography.algorithms

GPU-accelerated holography algorithms.

This module is currently focused on Gerchberg-Saxton (GS) iterative Fourier transform phase retrieval algorithms via the Hologram class; however, support for complex holography and other algorithms (e.g. gradient descent algorithms) is also planned. Additionally, so-called Weighted Gerchberg-Saxton (WGS) algorithms for hologram generation with or without closed-loop camera feedback are supported, especially for the generation of optical focus arrays, a subset of general image formation. We also support Mixed Region Amplitude Freedom (MRAF) feedback.

Tip

This module makes use of the GPU-accelerated computing library cupy (GitHub) If cupy is not supported, then numpy is used as a fallback, though CPU alone is significantly slower. Using cupy is highly encouraged.

Important

slmsuite follows the shape = (h, w) and vector = (x, y) formalism adopted by the numpy ecosystem. numpy, scipy, matplotlib, etc generally follow this formalism. The shape and indexing of an array or image always uses the inverted (h, w) form, but other functions such as numpy.meshgrid(x, y) (default), scipy.odr.Data(x, y), or matplotlib.pyplot.scatter(x, y) use the standard cartesian (x, y) form that is more familiar to users. This is not ideal and causes confusion, but this is the formalism generally adopted by the community.

Important

This package uses a number of bases or coordinate spaces. Some coordinate spaces are directly used by the user (most often the camera basis "ij" used for feedback). Other bases are less often used directly, but are important to how holograms are optimized under the hood (esp. "knm", the coordinate space of optimization).

Bases used in slmsuite.

Basis	Meaning
"ij"	Pixel basis of the camera. Centered at (i, j) = (cam.shape[1], cam.shape[0])/2. Is in the image space of the camera.
"kxy"	Normalized (floating point) basis of the SLM’s \(k\)-space in normalized units. Centered at (kx, ky) = (0, 0). This basis is what the SLM projects in angular space (which maps to the camera’s image space via the Fourier transform implemented by free space and solidified by a lens).
"knm"	Pixel basis of the SLM’s computational \(k\)-space. Centered at (kn, km) = (0, 0). "knm" is a discrete version of the continuous "kxy". This is important because holograms need to be stored in computer memory, a discrete medium with pixels, rather than being purely continuous. For instance, in SpotHologram, spots targeting specific continuous angles are rounded to the nearest discrete pixels of "knm" space in practice. Then, this "knm" space image is handled as a standard image/array, and operations such as the discrete Fourier transform (instrumental for numerical hologram optimization) can be applied.

See the first tip in Hologram to learn more about "kxy" and "knm" space.

Classes

FeedbackHologram	Experimental holography aided by camera feedback.
Hologram	Phase retrieval methods applied to holography.
SpotHologram	Holography optimized for the generation of optical focal arrays.