Study of triplicator diffraction gratings and holograms displayed onto spatial light modulators
- Autores: Shang Gao
- Directores de la Tesis: Maria del Mar Sánchez López (dir. tes.), Ignacio Moreno Soriano (codir. tes.)
- Lectura: En la Universidad Miguel Hernández de Elche ( España ) en 2025
- Idioma: español
- Tribunal Calificador de la Tesis: Germán Torregrosa Penalva (presid.), Ángel Lizana Tutusaus (voc.), Elisabet Pérez Cabré (voc.)
- Programa de doctorado: Programa de Doctorado en Bioingeniería por la Universidad Miguel Hernández de Elche
- Materias:
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- Resumen
Summary This thesis comprises the design of phase-only triplicator diffraction gratings and computer-generated holograms (CGHs) and their encoding on phase-only liquid-crystal spatial light modulators (SLMs). Polychromatic CGHs are also developed, where the colour reconstructions are successfully realized by implementing chromatic dispersion control in the hologram design and synchronizing a high-speed SLM with and RGB laser.
SLMs are programmable optoelectronic liquid-crystal microdisplays that allow the shaping of light beams, in amplitude, phase and polarization, with high spatial resolution and in real time, thus opening up a wide range of possibilities for bioengineering applications. Here we focus on displaying phase-only functions, since they have ideally 100% diffraction efficiency. However, the performance of SLMs is affected by their pixelated structure and other deletory effects, like phase flicker, refresh rate and light efficiency, that must be taken into account. Therefore, this thesis addresses both the design and characteristics of phase-only diffractive optical elements and the principal aspects that affect the ideal SLM performance, which must be properly evaluated and compensated.
Triplicator gratings are 1x3 fan-out elements that generate three equally intense 0th and ±1st diffraction orders. The optimum triplicator phase design has received renewed attention for the implementation of trifocal diffractive intraocular lenses. Also, combined with a spiral phase function, it has served to generate arrays of vortex beams. In this thesis we extend the triplicator phase profile to triplicator holograms, where we are able to obtain the target image on the triplicator orders: direct and inverted image on the ±1st orders, and a delta function on the zero-order. In this way, we can realize an optical convolver and correlator by adding the hologram of the target image to the triplicator holograms. This optical element keeps the high efficiency of the optimum phase triplicator, what is of interest given the essential tool of correlators to check the likeness between two light patterns.
This thesis is presented in the conventional mode of a doctoral thesis report and comprises two parts. The first part is devoted to the materials and methods employed: liquid-crystal (LC) on silicon SLMs and Fourier optics theory. When illuminated with linearly polarized light parallel to the LC director, LC-SLMs modulate the phase of input light by addressing them from a computer with a gray level pattern displayed on the device pixelated screen. The displayed pattern then diffracts the incoming light beam and reconstructs the desired optical wavefront. Three different phase-only SLMs are employed in this work; their characteristics and calibration are described in detail. An automatic calibration method based on a polarization camera is proposed and demonstrated on a monopixel LC retarder. The theoretical methods supporting this thesis rely on Fourier analysis, light diffraction theory and Fourier optics. Fourier analysis (including Fourier series and Fourier transform) is briefly reviewed together with the relevant properties that provide the tools for analysing diffraction gratings, calculating CGHs, and modelling the pixelated structure of SLMs. The optical architectures employed to obtain the optical Fourier transform are introduced using the classical simplest approach of Fourier optics, where light beams are considered within the paraxial approximation and a two-dimensional Fourier relation is obtained for the diffracted field with respect to the field behind the diffractive element.
The second part of the thesis presents the analytical and experimental results, together with the corresponding discussions. First, using the Fourier series analysis, different phase-only triplicator designs are compared, including binary, multilevel and continuous phase profiles. They are implemented on a LC-SLM considering large periods (of 64 pixels) to verify their properties. The condition for generating a triplicator with high efficiency are discussed. The binary Phi phase grating proves to be a feasible option, with a theoretical efficiency not so far from Gori's optimum continuous profile, and also close to the efficiency of the multilevel phase profile that adapts well to the SLM pixelated structure. Interestingly, the large number of pixels available in the device enable us to apply a random multiplexing approach, which provides a triplicator with less efficiency but free of higher harmonic orders. However, the pixels feature a dead zone and a limited effective area, thus resulting in a periodical physical structure of the SLM. We model it as an amplitude grating of period equal to the pixel pitch. Using the Fourier transform approach we demonstrate that this SLM pixelated structure yields diffraction parasite orders with weights given by a sinc envelope. Consequently, this effect will be relevant when encoding on the SLM phase gratings with short periods, particularly at the spatial resolution limit (Nyquist limit), i.e. period of two times the pixel pitch, which must be binary phase profiles. The convolutional Fourier approach gives a clear physical insight into this phenomenon, where the target diffraction pattern is replicated on the SLM parasite orders. Therefore, there is a superposition between orders of the different replicas. Analytical expressions for the diffraction orders' intensities are obtained in terms of the device fill factor and phase level of the binary grating. The triplicator's diffraction efficiency is also derived and verified experimentally for binary gratings with different periods. As the period decreases down to two pixels (Nyquist limit), the fringing field effect cannot be ignored. Therefore, making use of the fact that the fringing effect smooths the phase profile, we build a nonlinear phase profile model that fits the experimental intensity curves and provides the actual distorted phase implemented on the SLM due to fringing.
On the other hand, a systematic study on how to improve the reconstruction quality of phase-only CGHs is done as well. We compute the Fourier transform of the original image and retrieve only the phase (kinoform CGH) to implement it on the SLM, where advantage is taken of fast Fourier transform (FFT) kits in Python. For simple CGH computation, we explore several methods to improve the hologram intensity reconstruction, such as adding amplitude/phase noise to the original field, applying a limit window to the target area, and applying a nonlinear calculation to the original image. All the above methods aim at increasing the weight of the high-frequency component and flattening the intensity distribution in the reconstructed target field with high signal-to-noise ratio. The inverse Fourier transform algorithm (IFTA) is applied. Polychromatic CGHs are presented, where realistic reconstructions can be obtained. Red (R), green (G), and blue (B) lasers are modulated independently and synchronised to a 180 Hz LC-SLM so that, by properly scaling the RGB phase masks, we can compensate for the chromatic dispersion and recover the original colour object.
Finally, the triplicator phase profile is applied to CGHs, leading to the reconstruction of the target image at the customized diffraction orders. This provides simultaneously an optical convolver and a correlator. This is useful because when two identical images (in all aspects) are correlated, a delta function will be shown in the reconstructed field. However, if the two images have any difference, like phase information that is invisible, the profile of the delta function will be broadened.
This doctoral thesis thus contributes to the advance in the proper use of phase-only liquid-crystal SLMs for the accurate implementation of triplicator phase diffraction gratings and computer-generated holograms. Given the growing interest in using such programmable devices in optical imaging techniques, this thesis provides useful tools for bioengineering, telecommunications, or industry applications.
