## 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.

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.