Classical field curvature theory emphasizes the Petzval theorem, which models field curvature aberration to the 4th order. However, modern lens designs use aspheric surfaces. These surfaces strongly induce higher order field curvature aberration which is not accounted for Petzval field curvature. This dissertation focuses on developing higher order field curvature theories that are applied to highly aspheric designs. Three new theories to control field curvature aberration are discussed. Theory 1: an aspheric surface that is close to the image and has two aspheric terms sharply reduces field curvature by 85%. Theory 2: an aspheric surface that is farther from the image plane induces astigmatism to balance Petzval field curvature. Theory 3: oblique spherical aberration can be induced to balance Petzval field curvature. All three theories are applied to real design examples including the following lenses: cellular phone, wide angle, fast photographic, and zoom lenses. All of the analyses results are consistent with the theories. Moreover, two types of novel aspheric surfaces are proposed to control field curvature. Neither of the surfaces are polynomial-type surfaces. Examples show that the novel aspheric surfaces are equivalent to even aspheric surfaces with two aspheric coefficients in terms of field curvature correction. The study on field curvature correction using aspheric surfaces provides an alternative method to use when aspheres are accessible. Overall, this dissertation advances the theory of field curvature aberration, and it is particularly valuable to evaluate highly aspheric designs when Petzval theory is inapplicable.

Measurement of the quality and performance of soft contact lenses is not new and is continually evolving as manufacturing methods develop and more complicated contact lenses become available. Qualification of soft contact lenses has not been a simple task since they are fundamentally difficult to measure. The shape of the lens is extremely sensitive to how the lens is supported and the material properties can change quickly with time. These lenses have been measured in several different ways, the most successful being non-contact optical methods that measure the lens while it is immersed in saline solution. All of these tests measure the lens in transmission and do not directly measure the surface structure of the lens. The reason for this is that the Fresnel reflectivity of the surface of a contact lens in saline solution is about 0.07%. Surface measurements have been performed in air, but not in saline. The lens needs to be measured in solution so that it can maintain its true shape. An interferometer is proposed, constructed, verified, and demonstrated to measure the aspheric low reflectivity surfaces of a contact lens while they are immersed in saline solution. The problem is extremely difficult and requires delicate balance between stray light mitigation, color correction, and polarization management. The resulting system implements reverse raytracing algorithms to correct for retrace errors so that highly aspheric, toric, and distorted contact lens surfaces can be measured. The interferometer is capable of measuring both surfaces from the same side of the contact lens as well as the lens thickness. These measurements along with the index of refraction of the lens material are enough build a complete 3D model of the lens. A simulated transmission test of the 3D model has been shown to match the real transmission test of the same lens to within 32nm RMS or 1/20th of a wave at the test wavelength.