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I present a novel optical device capable of faithfully reproducing arbitrary images and image sequences by utilizing the interplay between mirrors and colored surfaces acting as interactive mosaics. My main contribution is describing a method for pre-computing the mirror lattice configuration and mirror orientation as well as a ways of finding the corresponding diffuse color pattern in the spatio-temporal domain.  The method is fast enough to allow rapid iteration by enabling physically based light ray simulation ahead of fabrication.I demonstrate the effectiveness of my method in a wide range of image and image sequence scenarios as well as multiple device configuration variants.

Deformable mirrors (DMs) are needed in optical systems for compensation of aberrations using a control technique known as adaptive optics (AO). DMs are generally comprised of a mirror face sheet supported by an array of underlying actuators that can shape the face sheet with nanometer-scale precision. A challenge in fabrication of such devices is that the adhesive assembly process that is generally used to attach surface-normal actuators to the face sheet results in undesirable stress and strain, leading to uncorrectable deformation of the face sheet. The work described in this dissertation presents an innovative mechanical design that effectively solves that problem. The dissertation details design, fabrication, assembly, and control of an electromagnetically actuated DM comprised of a bulk-micromachined single crystal silicon face sheet, an array of single crystal silicon posts that are integrally attached to the face sheet, and an electromagnetic actuation system. Actuation is achieved using an array of fixed permanent magnets adhesively attached to the distal ends of the posts, which are attracted to or repelled by an array of fixed electromagnetic coils, each of which can be independently controlled. An analysis of the stress-reducing mechanical design for DM assembly is described, along with simulations and experimental results. The approach entails a direct application of St. Venant’s Principle to transform the complex and elevated stress state at the adhesion interface between magnet and post to a smaller and simpler and stress state at the face sheet, resulting in more than an order of magnitude reduction in stress-induced deformation. Two electro-magnetic actuation approaches were explored. The first uses a surface micromachined and then electroplated planar copper coil array, while the second uses an array of three-dimensional coils made from precision wound copper wire, assembled in an aluminum housing. Multiple DMs based on these designs were produced in a design and assembly process that precisely attached magnets to posts, aligned that subassembly with the actuator array, and controlled the gap between the magnets and the actuation coils. An electronic driver circuit was developed to control the actuator array using a commercial DM driver and a custom designed voltage-to-current amplifier array. Measurements of static and dynamic performance of the DM in response to actuation were made using a partitioned aperture wavefront (PAW) surface mapping microscope and a high bandwidth single point fiber-optical displacement probe. The prototype DMs had 19 actuators spaced 1.5 mm apart, supporting a 12 mm diameter, 10 µm thick face sheet. Actuation of up to +/-10 µm was achieved and dynamic performance was evaluated. This new DM design and shows promise in applications of optical aberration correction and high-power laser beamforming. / 2025-05-23T00:00:00Z

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QC 351 A7 no. 61 / In an attempt to design a three -mirror aspheric camera, a procedure was developed to arrive at a design with a minimum obscuration ratio. It was found that, in some cases, the sky baffling became the diffracting obscuration rather than the obscuration caused by the secondary. The procedure allowed for this and was able to select a system with the smallest diffracting obscuration in the pupil. Initially, two designs were selected and optimized through the use of aspheric surfaces. The designs represented two extremes in that one had much faster surfaces than the other. The fast mirror system was easier to optimize, performed better, and had the shorter over -all length. Further, evaluation of manufacturing errors on the fast mirror design showed that an acceptable level of performance could be expected if the errors were kept small. The maximum errors are spacing errors ±0.0005 in. tilt of surface errors ±0.001 /D in. radii of curvature errors ±0.125 in. where D is the diameter of the mirror surface.

We study mirror symmetry via Fourier-Mukai-type transformations, which we call SYZ mirror transformations, in view of the ground-breaking Strominger-Yau-Zaslow Mirror Conjecture which asserted that the mirror symmetry for Calabi-Yau manifolds could be understood geometrically as a T-duality modified by suitable quantum corrections. We apply these transformations to investigate a case of mirror symmetry with quantum corrections, namely the mirror symmetry between the A-model of a toric Fano manifold X¯ and the B-model of a Landau-Ginzburg model (Y, W). Here Y is a noncompact Kahler manifold and W : Y → C is a holomorphic function. We construct an explicit SYZ mirror transformation which realizes canonically the isomorphism QH*X&d1; ≅Ja cW between the quantum cohomology ring of X¯ and the Jacobian ring of the function W. We also show that the symplectic structure oX¯ of X¯ is transformed to the holomorphic volume form eWOY of ( Y, W). Concerning the Homological Mirror Symmetry Conjecture, we exhibit certain correspondences between A-branes on X¯ and B-branes on (Y, W) by applying the SYZ philosophy. / Chan, Kwok Wai. / Adviser: Nai Chung Conan Leung. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3536. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 52-56). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

The construction introduced by Gross, Hacking and Keel in [28] allows one to construct a mirror family to (S, D) where S is a smooth rational projective surface and D a certain type of Weil divisor supporting an ample or anti-ample class. To do so one constructs a formal smoothing of a singular variety they call the n-vertex. By arguments of Gross, Hacking and Keel one knows that this construction can be lifted to an algebraic family if the intersection matrix for D is not negative semi-definite. In the case where the intersection matrix is negative definite the smoothing exists in a formal neighbourhood of a union of analytic strata. A proof of both of these is found in [GHK]. In our first project we use these ideas to find explicit formulae for the mirror families to low degree del Pezzo surfaces. In the second project we treat the remaining case of a negative semi-definite intersection matrix, corresponding to S being a rational elliptic surface and D a rational fibre. Using intuition from the first project we prove in the second project that in this case the formal family of their construction lifts to an analytic family.

Landau-Ginzburg mirror symmetry predicts isomorphisms between graded Frobenius algebras (denoted A and B) that are constructed from a nondegenerate quasihomogeneous polynomial W and a related group of symmetries G. In 2013, Tay proved that given two polynomials W1, W2 with the same quasihomogeneous weights and same group G, the corresponding A-models built with (W1, G) and (W2, G) are isomorphic. An analogous theorem for isomorphisms between orbifolded B-models remains to be found. This thesis investigates isomorphisms between B-models using polynomials in two variables in search of such a theorem. In particular, several examples are given showing the relationship between continuous deformation on the B-side and isomorphisms that stem as a corollary to Tay's theorem via mirror symmetry. Results on extending known isomorphisms between unorbifolded B-models to the orbifolded case are exhibited. A general pattern for B-model isomorphisms, relating mirror symmetry and continuous deformation together, is also observed.

I am learning through these lessons. The following document includes my convoluted musings about my work, making process, and body leading up to my thesis exhibition, Avoidance Kitchen. My struggle with my reflected image comes from my struggle with my self-perceived physical image. What does it mean for a piece to disappear, only to find the reflection of someone else's work or body in its place? Is my craft rendered obsolete if all you want to do is take a funny selfie? Is my work unacknowledged if all you see is the sculpture across the room, in reverse? What happens when an object or installation is elevated and ignored within the same space?

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