This project is funded by the National Science Foundation.
The Question
Is it possible to enumerate all feasible designs of opto-mechanical
devices from the specification of its desired input-output behavior and
knowledge of available primitive components?
Approach
We introduce a new, systematic and complete compositional technique
for conceptual design of imaging optical systems from behavioral
specifications. There are two key ideas: (1) modeling the structure
and behavior of optical components using affine transformations, and
(2) using a systematic search algorithm integrated with a powerful
algebraic constraint solver to compute three-dimensional layouts of
optical components in the design. By embedding our tool in a
constraint programming environment, we are able to automate the
conceptual design of optical imaging systems --- a step performed
manually by human designers until now. We demonstrate the power of
the method by recreating several designs for imaging systems of
copiers.
Summary of results
First, our layout synthesis algorithm is grounded in the laws of
optics with optical components represented as linear transformations
on object and image configurations. Second, our algorithm is
complete; if enumerates all feasible design families that implement a
given specification. Since our algorithm explores designs in
increasing order of complexity as specified by the number of primitive
components, we can guarantee minimality for the designs produced.
Third, our algorithm computes key constraints on positions and
orientations for all components in the design. These can then be
instantiated further for input into a detailed design program for
further optimization and analysis. Our approach allows for rapid
generation of conceptual design sketches that can be refined with
further computation. Fourth, even though we work from first principles
in optics, we can obtain real-time generation of alternative design
topologies. Our synthesis algorithm is fully implemented in
Mathematica, and all of the examples presented below are the
output of our design system rendered using the Optica application.
- An imaging system that transforms an object at (0,0,0) into a
real image of the same size at (1,1,0) rotated by 180 degrees about
the z axis with respect to the object. Here is the top view and here is the 3-D arrangement of components.
- An imaging system for the Xerox 914 copier designed by our
synthesis program. Here is the top view
and here is the 3-D arrangement
of components. The system transforms an object at (0,0,0)
oriented along the x-axis into a real image of the same size at
(4,0,0) oriented along the x-axis.
- An imaging system for the Xerox 4000 copier designed by our
synthesis program. Here is the top view
and here is the 3-D arrangement
of components. The system transforms an object at (0,4,0)
oriented along the x axis into a real image of the same size at
(2,0,0) also oriented along the x axis.
Papers
- A compositional theory of opto-mechanical
synthesis (submitted to Research in Engineering Design),
November 2001 (with R. Goldman).
- Kinematic synthesis
using configuration spaces, Research in Engineering Design,
7:193-213, 1995 (with Ed Wang).
- Intelligent tools for conceptual design
and simulation of opto-electro-mechanical devices,
Proceedings of the NSF Design and Manufacturing Grantees
Conference, ASME Press, 1994 (with Ed Wang).
- Artificial
intelligence and conceptual design, Proceedings of IJCAI
(invited paper), pp 800-809, 1993.
-
Constraint-based kinematic synthesis, Proceedings of the 7th
International Workshop on Qualitative Reasoning about Physical
Systems, pp 228-239, 1993 (with Ed Wang).
- Conceptual synthesis of mechanisms
from qualitative specifications of behavior , Technical report,
1992 (with Ed Wang, Scott Stoller and Arjun Kapur).