Design of multichannel freeform optical systems for imaging applications

The problem of coupling an object to be imaged perfectly through an optic is an ancient one and has evolved through the ages, from Newton´s paraxial formulation to the very recent multi-parametric optimization techniques. This evolution has been constantly aided by developments in fabrication techniques and driven by demands posed by other fields particularly from those arising out of consumer needs and not just strictly research oriented. Initial solutions to these imaging problems were elegant and matched to the needs of specific fields at that point in time. But, with increasing demands to make the resulting systems more and more compact with form factors resembling to those of commonly used consumer devices, solving these problems with trivial solutions no longer seemed to be an option. Advancements in manufacturing techniques first led to the use of non-aspherical or aspherical surface shapes in solving common imaging problems. For example, Schwarzschild analytically proved in 1906 that two aspherical shapes are required to solve the problem of aplanatism. This paved way for more systems employing these aspherical shapes to come up with elegant solutions. With increasing complexity in the system demands and other imaging constraints, additional degree of freedoms were needed by the designer. This could in turn be solved by using more number of surfaces leading to bulkier solutions. Thankfully, with advancements in injection moulding techniques, the use of freeform surfaces seem to be the solution. Freeform surfaces were first made practical with their introduction in solving non-imaging problems where the design constraints are not so strict when compared to their imaging counterpart but was more of a mass transport problem. The resulting freeform systems were compact and thus demonstrated the significance of freeform surfaces in miniaturising optical systems. This also led to many direct design techniques to be formulated for the design of freeform optical surfaces. The next logical step in the optics community was to adapt this introduction of freeform surfaces into imaging problems. The bottleneck in this introduction was the unavailability of systems to be used as a starting point. Thus came the heavy reliance on computer-aided optimization techniques. This led to many investigations into the representations of freeform surfaces shapes which could have direct consequence in fabrication constraints to making the resultant systems more practically realisable. One such direct design method was the Simultaneous Multiple Surface method (SMS), which was initially introduced as a Non-Imaging direct design technique for the design of freeform optical surfaces. This was later extended to imaging applications where it immensely helped the designers in arriving at a good starting point for further optimisation. This thesis tracks this evolution of freeform surfaces and is introduced in Chapter 1 with a basic introduction of optical design as such, along with the metrics used for the quantification of system performance. This chapter also provides a brief introduction of various terminology used with respect to virtual reality optics which forms the main focus of later chapters. Chapter 2 continues with the exploration of the SMS method and its extension in designing three input wavefronts constituting a plane to be coupled onto three output wavefronts constituting a plane. This particular extension of the SMS method can be used as a good direct design technique in designing freeform optical systems. We also demonstrate a simple and a straight forward way of deriving the sine condition under freeform prescription, whose violation will result in systems suffering from aberrations having linear field dependency. Thereafter, we mathematically prove the connection between the SMS method and a classical system free from spherical aberration and coma known as “Aplanatic systems”. This work is one of the first to report formally, the link between SMS method and freeform aplanatic systems. Chapter 3 details extensively with the formulation of three surface aplanatic systems through the use of differential equation formulation and how, in general, three freeform optical surfaces are needed in obtaining freeform aplanatism. This is established through the use of integrability condition to demonstrate how there is no solution when two freeform optical surfaces are used. There is a noticeable exception to this rule of thumb, namely, afocal freeform aplanatic systems where only two freeform surfaces is enough. Chapter 4 introduces the concept of ThinEyes® in the context of virtual reality optical systems. This design strategy is explained in detail with use of a traditional pancake optic and how the use of ThinEyes® technology can significantly increase the apparent image resolution, at the same time without compromising on other system parameters. We also introduce other compact novel multichannel freeform optical design models namely: (a) Hybrid refractive-diffractive two channel freeform optical design (b) Nine fold refractive freeform optical design. Chapter 5 focuses on the design, development and characterization of a two channel freeform optical design to be used for a virtual reality headset. The chapter details extensively, the design rules and also the subsequent characterization of the fabricated optic through experimental determination of the distortion function to be software corrected.