As a practical application of the inverse problem consider the periodic structure above.

The desired geometry consists of vertical walls (a=0^o). In manufacturing a may not equal zero. To assure quality control one needs to do testing on samples.

Typical testing involves destroying the samples. Application of the inverse problem can eliminate this problem. A laser is applied to the periodic structure and the resulting diffraction pattern is measured. Using this information, we apply the inverse process we developed to determine a.

No simple relationship exists between a and the resulting diffraction patterns (see some typical results in the next slide).

Solutions to inverse problems may be non-unique.

Numerical modeling of diffraction structures may not be a straightforward process.