William H. Southwell

Wave-front estimation from wave-front slope measurements

The problem of wave-front estimation from wave-front slope measurements has been examined from a least-squares curve fitting model point of view. It is shown that the slope measurement sampling geometry influences the model selection for the phase estimation. Successive over-relaxation (SOR) is employed to numerically solve the exact zonal phase estimation problem. A new zonal phase gradient model is introduced and its error propagator, which relates the mean-square wave-front error to the noisy slope measurements, has been compared with two previously used models. A technique for the rapid extraction of phase aperture functions is presented. Error propagation properties for modal estimation are evaluated and compared with zonal estimation results.

Coating design using very thin high- and low-index layers

Any arbitrary generalized gradient-index interference coating (including homogeneous and inhomogeneous layers) possesses a digital configuration (sequence of thin high- or low-index layers), which is spectrally equivalent at all wavelengths. Such digital configurations are found directly from arbitrary-index profiles by using a prescribed two-layer high-low equivalent to a thin layer of arbitrary index. Digital configurations may be designed directly from given spectral requirements by using a flip-flop optimization scheme.

Antireflection surfaces in silicon using binary optics technology

Binary optics processing methods were applied to a silicon substrate to generate an array of small pillars in order to enhance transmission. The volume fraction of the silicon in the pillars was chosen to simulate a single homogeneous antireflection layer, and the pillar height was targeted to be a quarter-wave thickness. A mask was generated, using a graphics computer-aided design system; reactive-ion etching was used to generate the pillars. An improvement in long-wavelength infrared transmission is observed, with diffraction and scattering dominating at shorter wavelengths.

Using apodization functions to reduce sidelobes in rugate filters

Appending gradient-index matching regions and apodization, which is an amplitude modulation of the rugate sinusoidal index profile, are two effective means to reduce and nearly eliminate the sidelobes. When a combination of these methods is used in the rugate design, the resulting filter will have good sidelobe suppression both near to and far from the stopband and will have high reflectance in the stopband.

Validity of the Fresnel approximation in the near field

By direct numerical-integration comparisons, it is established that the Fresnel approximation for collimated propagation is quite good (within about 2% in amplitude and 0.02 rad in phase) in every case, including that with the limit of a high Fresnel number. Moreover, the Fresnel approximation begins to break down in phase for spherical-wave propagation for beams faster than about f/12. It has been discovered, however, that if one also invokes the paraxial approximation, that is, replaces the spherical wave by a quadratic phase front, then the Fresnel approximation becomes valid for expanding (or diverging) beams as well. This result is substantiated through the use of stationary-phase arguments.

Spectral response calculations of rugate filters using coupled-wave theory

A closed-form solution for the reflectivity of an optical coating with a sine-wave index profile (rugate) is derived by using coupled-wave theory. Reflectance is calculated for such coatings on arbitrary substrates and incident media. A vector formalism is used that produces results for both s- and p- polarization components.

Codeposition of continuous composition rugate filters.

Rugate filters are optical thin film interference structures with sinusoidal refractive index profiles. Two-wavelength reflection filters have been fabricated by codeposition of SiO(2) and TiO(2). Composition modulation was monitored and controlled using quartz crystal rate controllers. The resulting filters exhibited two well-defined stopbands. Microscopic examination revealed that the structure is glasslike without pronounced thin film microstructure.

Rugate filter sidelobe suppression using quintic and rugated quintic matching layers

Sine wave rugate index profiles may be superimposed on a slowly varying average index in such a way as to reduce sidelobes over broad spectral regions and at the same time maintain the strength of the stopband reflectance.

Broadband gradient-index antireflection coating for ZnSe

A gradient-index antireflection coating spanning the 0.6–12.6-μm wavelength range for a ZnSe substrate was designed, fabricated, and tested. The index profile used was a fifth-order polynominal that smoothly matches the substrate. The coating was fabricated using a discrete layer approximation for the gradient-index design using ZnSe and CaF2 deposited by laser-assisted evaporation. Total thickness of the coating was 3 μm. Transmission measurements show good agreement with calculated performance. Reflectivity per surface is <3% (compared with 17% for uncoated ZnSe) in the wavelength band encompassing 4.5 octaves from 0.6 to 12.6 μm.

Wave-front analyzer using a maximum likelihood algorithm

A technique is described wherein the pupil phase profile is obtained from the image irradiance or point spread function. Results of numerical examples are shown that illustrate the procedure on spread functions with large aberrations and on irradiance measurements containing noise.