Fermat principle based reflector design for fast and contactless freeform optical component inspections

We propose a well-designed reflector, based on the Fermat principle, that is placed on a transmitted optical path to reflect the impinging light on the surface so that the null testing of the interference inspection for the freeform lens can be realized. The design methodology of such a reflector for a freeform lens with rotational symmetry is given and a reflector designed for a high-order aspheric surface is manufactured. Our investigations show that the theoretical accuracy of such an interference inspection can be up to 10(-7)  mm with the designed reflector. We fabricated the designed reflector by a single point diamond turning machine and a high-order aspheric lens was measured with our methods, showing a good agreement with conventional interference inspection approaches. This might open a way to the fast inspection of freeform surfaces and thus improve the efficiencies of optical testing.