A system includes a tool, an input device, a shape sensor system, and a processing unit. The processing unit is configured to determine a state estimate of the input device based on shape information from the shape sensor system, and control the tool based on the state estimate.

A freeform DOE for use in an optical transmitter and a method of designing and manufacturing the DOE are provided. The freeform DOE is capable of achieving the same, or nearly the same, functionality as that of a glass DOE, but has a design that has been transformed to make the surface profile of the DOE compatible with a molding process that can be used to manufacture the DOE with high quality at low costs. The method of designing and manufacturing the DOE includes preselecting a CGH that will obtain a target freeform DOE design, using a preselected smoothing function to smooth the surface profile of the target freeform DOE design to transform the design into a DOE design that is compatible with a molding process, and using a fabrication process to manufacture a freeform DOE that is based on the transformed DOE design.

A freeform DOE for use in an optical transmitter and a method of designing and manufacturing the DOE are provided. The freeform DOE is capable of achieving the same, or nearly the same, functionality as that of a glass DOE, but has a design that has been transformed to make the surface profile of the DOE compatible with a molding process that can be used to manufacture the DOE with high quality at low costs. The method of designing and manufacturing the DOE includes preselecting a CGH that will obtain a target freeform DOE design, using a preselected smoothing function to smooth the surface profile of the target freeform DOE design to transform the design into a DOE design that is compatible with a molding process, and using a fabrication process to manufacture a freeform DOE that is based on the transformed DOE design.