Programmable phase fresnel lenses and other diffractive elements by pixelated liquid crystal displays

Resumen

In this dissertation, we have addressed a range of motivated research objectives related to the use of commercial spatial light modulators based on pixelated liquid crystal devices to reproduce diffractive optical elements, particularly, programmable lenses, holograms, and combinations of both. To the necessary characterization of the optical response of the different transmissive and reflective SLMs used in this work, we have set the programmable variables that allow us to control the operation mode and have measured the dynamic ranges of such variables. We have also taken into account the inherent distortion of reflective parallel aligned SLMs, measuring it and calculating the compensation, not only for the backplane curvature but also for other possible nonuniformities caused by thickness variations of the liquid crystal layer across the aperture. We have defined a grid of cells onto the SLM aperture and developed a multipoint calibration. Additionally, we have analyzed the time response of a reflective SLM for different frame rates. Since its modulation capability in static configuration exceeds 2¿ radians, we have also developed a dynamic LUT that enhances the efficiency of the phase modulation in high frequency configurations. We have estimated the potential applicability of the analyzed SLMs to the generation of different type of lenses, from monofocal to bifocal and multifocal lenses. From the technical characteristics and constraints of the modulator, we have calculated the range of powers and available apertures for feasible lenses, in such a way that a subsampling of the phase function by the pixels of the lens aperture has been avoided. We have obtained the minimum focal length for the programmable lens as function of the pixel pitch, lens aperture, and illuminating wavelength, and also analyzed the influence of the focal shift in low power lenses acting as imaging systems. We have proposed three different ways to compensate the notorious chromatic aberration of a programmable diffractive phase Fresnel lens working under polychromatic illumination. These proposals are based on a multiplexing of lenses, designed with the same focal length for a set of wavelengths, and a spectral filtering of the light that impinges each sublens. Since each sublens operates as a channel for a given wavelength, the combination of sublenses results in an achromatic multichannel phase Fresnel lens that would allow one to use such a diffractive lens for high quality polychromatic imaging purposes. In addition to this, we have drastically reduced the transversal chromatic aberration of the Point Spread Function in the central order by properly adjusting the pupil size of each sublens. Finally, as experimental implementation, We have developed a set-up to reconstruct color Fresnel holograms, where we have decomposed the image in several amplitude distribution, one per wavelength, adding the phase distribution of the lens, with the same focal length, optimized for each wavelength, and finally multiplexing the intensity distributions of the focal plane.