We show that, in order to attain complete polarization control across a beam, two spatially resolved variable retardations need to be introduced to the light beam. The orientation of the fast axes of the retarders must be linearly independent on the Poincaré sphere if a fixed starting polarization state is used, and one of the retardations requires a range of 2π. We also present an experimental system capable of implementing this concept using two passes on spatial light modulators (SLMs). A third SLM pass can be added to control the absolute phase of the beam. Control of the spatial polarization and phase distribution of a beam has applications in high-NA microscopy, where these properties can be used to shape the focal field in three dimensions. We present some examples of such fields, both theoretically calculated using McCutchen's method and experimentally observed.

We show that the volumetric field distribution in the focal region of a high numerical aperture focusing system can be efficiently calculated with a three-dimensional Fourier transform. In addition to focusing in a single medium, the method is able to calculate the more complex case of focusing through a planar interface between two media of mismatched refractive indices. The use of the chirp z-transform in our numerical implementation of the method allows us to perform fast calculations of the three-dimensional focused field distribution with good accuracy.

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Accurate simulation of the propagation of light between the spacecraft of the laser interferometer space antenna (LISA) gravitational wave observatory will be a vital tool in determining the optical design of the telescopes used in the constellation. In this work, we examine the methods available for numerical simulation of this propagation, and consider the effect of an aberrated transmitting telescope (Tx) on the light collected by the receiving telescope (Rx). Propagation software has been developed using direct numerical integration methods, and has been validated by comparison to analytical solutions for particular cases. Zernike modal aberrations up to and including primary spherical have been considered in the Tx, and, in particular, the effects of defocus, astigmatism and coma were examined. It was found that minimization of the even radial order aberrations in Tx resulted in a reduced wavefront error at Rx, while odd aberrations such as coma can displace the maximum irradiance away from the optical axis. Thus careful consideration of the impact of telescope aberrations will be required to minimise detrimental effects on the detection of gravitational waves.

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The generalised phase contrast (GPC) method provides versatile and efficient light shaping for a range of applications. We have implemented a generalised phase contrast system that used two passes on a single spatial light modulator (SLM). Both the pupil phase distribution and the phase contrast filter were generated by the SLM. This provided extra flexibility and control over the parameters of the system including the phase step magnitude, shape, radius and position of the filter. A feedback method for the on-line optimisation of these properties was also developed. Using feedback from images of the generated light field, it was possible to dynamically adjust the phase filter parameters to provide optimum contrast.

It is envisaged that future large space telescopes will be lightweight and employ active optics to maintain optical quality throughout the mission lifetime. We have proposed a 4 m, two-mirror space telescope with an active optics system based on reimaging the telescope primary mirror onto a small active mirror (110 mm optical pupil). Using Zemax, we demonstrate the feasibility of using this mirror to correct low-order Zernike aberrations and show that the aberration is well corrected across the 2.5 arcmin field of the telescope, operating at 0.55 μm. We describe the modeling carried out to develop the active mirror design. Using end-to-end modeling, a 25-actuator mirror with polar actuator geometry, and a ratio of mechanical to optical pupil diameter of 2 has been chosen. A single-actuator prototype has been manufactured and used to test stroke, linearity, and hysteresis. Finally, we describe the design of a laboratory breadboard that will image phase screens onto an exact replica of the space active mirror and show the results of measuring the phase screen accuracy.

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