Design and development of compact optical systems

Tesis Doctoral

Autor: Jiayao Liu

Director: Juan Carlos Miñano

We will consider optical design from two points of view: imaging optics and
nonimaging optics. Imaging optics focuses on the imaging of the points of the object.
Nonimaging optics arose from the development of concentrators and illuminators,
focuses on the transfer of light energy, and has wide applications in illumination and
concentration photovoltaics.
In general, compact optical systems are necessary for both imaging and nonimaging
designs. For nonimaging optical systems, compact optics use to be important for reducing
cost. The reasons are twofold: (1) compact optics is small in volume, which means less
material is needed for mass-production; (2) compact optics is small in size and light in
weight, which saves cost in transportation. For imaging optical systems, in addition to the
above advantages, compact optics increases portability of devices as well, which
contributes a lot to wearable display technologies such as Head Mounted Displays (HMD).
This thesis presents novel design approaches of compact optical systems for both imaging
and nonimaging applications.
Collimator is a typical application of nonimaging optics in illumination, and can be
used in concentration photovoltaics as well due to the reciprocity of light. There are
several approaches for collimator designs. In general, all of these approaches have an
aperture diameter to collimator height not greater than 2. In order to reduce the height of
the collimator while maintaining the illumination area, a multichannel design is presented
in this thesis.
In imaging optics, aspheric and freeform surfaces are useful in controlling image
aberrations and reducing the number and size of optical elements. Due to the rapid
development of digital computing systems, ray tracing can be easily performed to
evaluate the performance of optical system. This has led to the modern optical designs
created by using different multi-parametric optimization techniques. These techniques
require a good initial design to be a starting point so that the final design after optimization
procedure can reach the optimum solution. This requires a direct design method for
aspheric and freeform surface close to the optimum. A differential equation based design
method is presented in this thesis to obtain single freeform and double aspheric surfaces.
The thesis comprises of five chapters.
In Chapter 1, basic concepts of imaging and nonimaging optics are presented and
typical design techniques are introduced. Readers can obtain an understanding for the
following chapters.
Chapter 2 describes the design of ultra-compact collimator. The ultra-low aspect
ratio of this collimator is achieved by using a multichannel structure. Its design procedure
is presented together with a prototype and its evaluation. The ultra-compactness of the
device has been approved.
Chapter 3 describes the main concepts of optimizing optical systems: merit function
and Damped Least-Squares method. The importance of a good starting point is
demonstrated by presenting an example through different design approaches. The
differential equation method is introduced as an ideal tool to obtain a good starting point
for the final solution. Additionally, different interpolation and representation techniques
for aspheric and freeform surface are presented for optimization procedure.
Chapter 4 describes the application of differential equation method in the design of
single freeform surface optical system. Basic concepts of differential geometry are
presented for understanding the derivation of partial differential equations. A numerical
solution procedure is also presented. The initial condition is chosen as an additional
freedom to control the image surface. Based on this approach, anastigmatic designs can
be readily obtained and is used as starting point for a single reflective surface HMD design
example. After optimization, the evaluation shows better MTF.
Chapter 5 describes the differential equation method extended to double aspheric
surface designs. For single optical surface designs, neither image surface nor the mapping
from object to image can be prescribed. With one more surface added, the image surface
can be prescribed. This leads to a set of three implicit ordinary differential equations.
Numerical solution can be obtained by MATLAB and its procedure is also explained. An
anastigmatic lens is derived from this design method and compared with an aplanatic lens.
The anastigmatic design converges much faster in optimization and the final solution
shows better performance.