Automatic Design: Artificial and Natural
I was one of forty physicists, chemists, and engineers in the Research Department of my company, the Perkin-Elmer Corporation. We were supposed to develop new technology and new optical-electronic instruments. Our company had us working on research to stay in the vanguard of technology. The top rewards were reserved for the researcher who invented a new solution to some technical problem. Hopefully many potential customers had the problem, because then they would need the solution. Our company sought an exclusive patent on any new device. Once the design was safe from imitation, the Marketing Department would bring out a new product incorporating the invention. Ideally the product would be so superior to others that everyone would buy from our company. The company could charge whatever it wanted for the product and would soon be very rich. This dream has motivated many businessmen to hire researchers. Nevertheless, good ideas are scarce.
Our company specialized in electro-optical instruments like reconnaissance cameras. One that was recently declassified was the Keyhole Camera of the Hexagon program, a space-borne telescope used to observe military and industrial activities in closed countries. Almost all optical instruments use lenses.
The Automatic Lens-Design Program
We can make a lens out of many materials and in many ways. We can vary the curvature of each surface and the distance between the surfaces. Each surface may be flat, spherical, parabolic, elliptical, hyperbolic, or some other form. A camera lens usually consists of several optical elements. The elements may be cemented together in close contact or separated by any distance.
No one knows the best design for any given application. Lens design is very complicated. When a new instrument needed a lens, members of the Optical Physics Group took charge of its design. They chose among known lens designs the one that seemed best for the application.
Then they entered the design parameters in a computer. The program had all the mathematical formulas pertinent to lens design.
The program was a jealously guarded company secret. It had a pretentious name, “Automatic Lens Design.” A programmer was in charge of keeping the program up to date with all improvements in lens design.
The program traced light rays through the lens using mathematical formulas incorporated in the program and sought the focal point of the image. The usual result was that not all of the rays focused on the same point. This design fault is called “aberration.” Lens designers have classified six aberrations that constantly plague their lenses.
Company Top Secret
At this point the secret part of the program entered into play, the part that the company defended against industrial espionage.
Any automatic design program must have some criterion for evaluating the result of the small changes so it can decide to continue making changes of the same kind or try something else. The criterion is usually a number called the “figure of merit” for the design. The higher the number is, the better the design. The figure of merit may be how fast an airplane will fly with an engine of given power. It may simply be the smallest size of some arrangement, like a way of packing suitcases into a car’s trunk. For optical design it was the least aberration because that would produce the clearest image. The program’s task is to find the design with the best figure of merit.
First, the automatic lens design program calculated the amount of aberration, using a special function. The function was called the “merit function.” The smaller the aberration, the greater the value the function returned, and the higher the merit of the design.
Second, the program made small, systematic variations, one by one, of all the parameters and variables of the design. For each variation the program took note of the increase or reduction of the total aberration as the merit function measured it and recorded the results. Each variable that reduced the aberrations was marked positive. If a variable increased the aberrations, that variable was marked negative, under the supposition that a variation in the other direction would have reduced the aberrations.
Finally, the program used known mathematical formulas to calculate a composite variation made up of all the parameters. The composite variation was the combination of all the variations that would produce the greatest reduction in all the aberrations. The formulas used guaranteed this result. The guarantee, nevertheless, was only for small variations. A small variation could only produce a small improvement.
Once the program had gone through one of these cycles of calculations and found the first small improvement in the design, it repeated the process of finding small improvements endlessly. The lens designers believed that, if the original design was sufficiently close to the optimum design, the series of small variations would lead from the original rough design to the optimum design. The series would be a path of constant improvement in the merit function, up to the point where the function would reach its peak, at the best design.
Big steps would have skipped around from one class of design to another, without leaving a clear trail to follow and reach the optimum. Small steps were necessary to avoid losing the path. The path might be long and tortuous, but eventually the designers thought it would arrive at the goal. The designer only had to wait, observe how the design developed automatically, and stop the process when the design stopped developing. At that point the convergence on the best design would be perfect.
Our company specialized in electro-optical instruments like reconnaissance cameras. One that was recently declassified was the Keyhole Camera of the Hexagon program, a space-borne telescope used to observe military and industrial activities in closed countries. Almost all optical instruments use lenses.
The Automatic Lens-Design Program
We can make a lens out of many materials and in many ways. We can vary the curvature of each surface and the distance between the surfaces. Each surface may be flat, spherical, parabolic, elliptical, hyperbolic, or some other form. A camera lens usually consists of several optical elements. The elements may be cemented together in close contact or separated by any distance.
No one knows the best design for any given application. Lens design is very complicated. When a new instrument needed a lens, members of the Optical Physics Group took charge of its design. They chose among known lens designs the one that seemed best for the application.
Then they entered the design parameters in a computer. The program had all the mathematical formulas pertinent to lens design.
The program was a jealously guarded company secret. It had a pretentious name, “Automatic Lens Design.” A programmer was in charge of keeping the program up to date with all improvements in lens design.
The program traced light rays through the lens using mathematical formulas incorporated in the program and sought the focal point of the image. The usual result was that not all of the rays focused on the same point. This design fault is called “aberration.” Lens designers have classified six aberrations that constantly plague their lenses.
Company Top Secret
At this point the secret part of the program entered into play, the part that the company defended against industrial espionage.
Any automatic design program must have some criterion for evaluating the result of the small changes so it can decide to continue making changes of the same kind or try something else. The criterion is usually a number called the “figure of merit” for the design. The higher the number is, the better the design. The figure of merit may be how fast an airplane will fly with an engine of given power. It may simply be the smallest size of some arrangement, like a way of packing suitcases into a car’s trunk. For optical design it was the least aberration because that would produce the clearest image. The program’s task is to find the design with the best figure of merit.
First, the automatic lens design program calculated the amount of aberration, using a special function. The function was called the “merit function.” The smaller the aberration, the greater the value the function returned, and the higher the merit of the design.
Second, the program made small, systematic variations, one by one, of all the parameters and variables of the design. For each variation the program took note of the increase or reduction of the total aberration as the merit function measured it and recorded the results. Each variable that reduced the aberrations was marked positive. If a variable increased the aberrations, that variable was marked negative, under the supposition that a variation in the other direction would have reduced the aberrations.
Finally, the program used known mathematical formulas to calculate a composite variation made up of all the parameters. The composite variation was the combination of all the variations that would produce the greatest reduction in all the aberrations. The formulas used guaranteed this result. The guarantee, nevertheless, was only for small variations. A small variation could only produce a small improvement.
Once the program had gone through one of these cycles of calculations and found the first small improvement in the design, it repeated the process of finding small improvements endlessly. The lens designers believed that, if the original design was sufficiently close to the optimum design, the series of small variations would lead from the original rough design to the optimum design. The series would be a path of constant improvement in the merit function, up to the point where the function would reach its peak, at the best design.
Big steps would have skipped around from one class of design to another, without leaving a clear trail to follow and reach the optimum. Small steps were necessary to avoid losing the path. The path might be long and tortuous, but eventually the designers thought it would arrive at the goal. The designer only had to wait, observe how the design developed automatically, and stop the process when the design stopped developing. At that point the convergence on the best design would be perfect.