Advances in freeform optical design methods for imaging applications

Student thesis: Doctoral Thesis


For decades, well-established manufacturing techniques for precision optics were restricted to rotationally symmetric surfaces. Recent advances in manufacturing allow increasingly precise fabrication of lenses and mirrors with almost any shape, hence the name "freeform" optics. Including freeform components in optical systems provides numerous opportunities for enhanced performance and compact and lightweight packaging.
Given the very large number of parameters needed to describe freeform surfaces, the multi-parametric optimization based approach that is commonly used by optical designers faces considerable challenges. The results obtained by optimization algorithms are highly dependent on the initial designs and cannot guarantee to find qualified solutions.
In this PhD thesis, I have developed two new methods to enhance and facilitate the design of freeform optical systems for a wide range of real-world imaging applications. In contrast to the conventional optimization-based method, a direct optical design approach is a mathematical procedure that delivers the optical surface equations (or point clouds) for a prescribed design problem with no or few iterations. Notwithstanding the success of few existing direct design methods, their usage was limited to perfectly imaging two or three discrete fields with two freeform surfaces. Besides, these methods typically do not include a pupil which is important for correcting off-axis aberrations. To
tackle these two issues, I have developed a new "multi-fields direct design method" that incorporates an entrance pupil in the design procedures, and provides a well-balanced performance over a wide field of view. A key feature of this method is the partial imaging of many more than just two or three fields for a two-surface system in both two and three dimensions. In addition, the method also shows better practicability since it requires less initial parameters to begin with. In order to demonstrate its effectiveness, I have designed a barcode scanner and a wide field line-imaging objective, both achieving superior performance when compared to their rotationally symmetric counterparts.
As a proof of concept for seamless transition from design to prototype, I have applied the multi-fields method to design two freeform mirrors as an ultrashort throw accessory for an off-the-shelf projector. The system has an extremely large field of view to realize the ultrashort effect, which in case of an all-lens design would require many well-corrected lenses with large magnification. Other emerging designs use rotationally symmetric aspherical mirrors/lenses as an accessory to correct distortion. What is more, the designed freeform mirrors have further enhanced the performance in well-matched mapping relation to the rectangular screen, outperforming all preceding rotationally symmetric designs. In addition, I have analyzed the tolerances of the two freeform mirrors,
demonstrating the feasibility of manufacturing. A prototype with a single freeform mirror has been fabricated to demonstrate all essential steps from design to prototype and to ultimately validate the design approach.
Typically, many mainstream compact and portable optical devices are consisting of more than two (freeform) surfaces, for example head mounted displays, which the stateof- the-art direct design methods are incapable of designing. To tackle this issue, I have investigated an alternative promising design strategy by using paraxial aberration theory to generate good starting points for multiple freeform surfaces systems. Two- and threemirror Seidel aberration equations have been deduced for a wide-field convexly curved imaging system. To illustrate the potential of this design strategy, I have calculated and optimized a non-scanning corneal imaging system comprising three freeform mirrors. In
contrast to most existing techniques based on a slower point-, slit-, or annular- scanning, such a device allows imaging the full cornea and sclera with a single snapshot in realtime. My novel strategy also has the potential to design other imaging systems where more than three freeform surfaces are required with specialty constraints.
Date of Award17 Jan 2018
Original languageEnglish

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