The shape and structure of the HOE is dependent on the piece of hardware it is needed for, and the coupled wave theory is a common tool used to calculate the diffraction efficiency or grating volume that helps with the design of an HOE.
Early concepts of the holographic optical element can be traced back to the mid-1900s, coinciding closely with the start of holography coined by Dennis Gabor.
[1][2][3] The holographic optical element is closely linked to holography (science of making holograms), a term proposed by Dennis Gabor in 1948.
This essentially describes a holographic mirror (one of the first HOEs created) and fixed the issue of overlapping images.
It was not until around the mid-1960s that Densiyuk's proposals resurfaced after some development from Emmett Leith and Juris Upatnieks.
These two associates encoded and reconstructed images with a two step hologram process on photographic transparency.
More experiments for holographic instruments such as the holographic stereogram developed by Lloyd Cross in the 1970s took the imaging process developed by Leith and Uptanieks and arranged them into vertical strips that were curved into a cylinder.
This demonstrates a very simple version of the diffraction concepts that are still utilized in the production of HOEs and a prototype for 3D glasses.
[4] HOEs differ from other optical devices since they do not bend light with curvature and shape.
Some materials that are most commonly used in manufacturing HOEs include silver halide emulsion and dichromate gelatin.
[6][7] In the early 2000s NASA conducted a test known as the Holographic Airborne Rotating Lidar Instrument Experiment(HARLIE) that utilized dichromate gelatin-based volume HOE sandwiched between float glass.
The objective of the test was to find a new method of measuring surface and atmospheric parameters that could reduce the size, mass, and angular momentum of a spaceborne lidar systems.
Additionally, transparency can be achieved due to the selectivity of the volume grating that is used to diffract light at a specific incident angle or wavelength.
[9] This allows for the development of transparent head-up displays that convey information to aircraft pilots and conserves cockpit space.
The spectral and angular Bragg selectivity of the reflective volume hologram makes it particularly well-suited for a combiner using such light sources as RGB LEDs, providing both good see-through quality and good quality of the projected image.
[12][13] One of the goals in the design of an HOE is to try and create 3D visualization and the closest thing to that is augmented reality.
Some examples of this type of display include Microsoft's HoloLens I, II, Google Glass, and Magic Leap.
Items like these are often very expensive due to the high cost of materials used to produce HOEs.
[1][14] There is also a second type of 3D visualization method that looks to replicate 3D objects through the creation of light fields.
This type of visualization is closer to the ones seen in science fiction films or video games.
The proposed technology works by having the MLA type HOE form a spherical wave of arrays.
It was first written about by Herwig Kolgenik in 1969 and contains mathematical models that determine the wavelength and angular selectivity(these factors determine how efficiently something may be able to adjust and transmit light at a certain angle or wavelength) of certain materials.
[16] Several premises are given by the theory: it is valid for large diffraction efficiencies(measures how much optical power is diffracted at a given spot) and its derivation is done on the basis that the monochromatic light incident is near the Bragg angle (a small angle between a light beam and a plane of crystals) and perpendicular to the plane of incidence (a plane that contains both a ray of light and a surface that usually acts as a mirror at a certain point).
Since the HOE works by diffracting light by constructing new waves, trying to get the thick HOE material to diffract light near the Bragg angle will make for more efficient wavefront construction.
as the angular bandwidth at FWHM (full width at half the maximum): Diffraction efficiency equation accounts for
as the diffraction efficiency for TM mode (polarization parallel to the plane of incidence), and
as the propagation constant that is spatially modulated: Lenslet[1] (very small lenses measured in micrometers) shape variation calculations that may help determine the distance, wavelength, and middle-mask aperture that determine HOE output for HOEs acting like a lens.