Gregory R. Brady

Nonlinear optimization algorithm for retrieving the full complex pupil function.

Techniques for retrieving the phase of an optical field typically depend on assumptions about the amplitude of the field in a desired plane, usually a pupil plane. We describe an approach that makes no such assumptions and is capable of retrieving both the amplitude and phase in the desired plane. Intensity measurements in two or more planes are used by a nonlinear optimization algorithm to retrieve the phase in the measurement planes. The complex field (amplitude and phase) in the desired plane is then computed by simple propagation. We show simulation results and examine the convergence of the algorithm.

Optical wavefront measurement using phase retrieval with transverse translation diversity

We demonstrate the use of transverse translation-diverse phase retrieval as a method for the measurement of wavefronts in situations where the detected intensity patterns would be otherwise undersampled. This technique involves using a smaller moving subaperture to produce a number of adequately sampled intensity patterns. The wavefront is then retrieved using an optimization jointly constrained by them. Expressions for the gradient of an error metric with respect to the optimization parameters are given. An experimental arrangement used to measure the transmitted wavefront of a plano-convex singlet using this technique is described. The results of these measurements were repeatable to within approximately lambda/100 RMS.

Phase retrieval as an optical metrology tool; Technical Digest

Phase retrieval can be useful in the measurement of optical surfaces and systems. It distinguishes itself through the simplicity of the experimental apparatus, just a detector array which collects light near a focal plane. Aspherics can be measured without null optics. The challenging part of the method is the estimation of the wavefront from the near-focus intensity measurements to reconstruct the wavefront.

Effect of broadband illumination on reconstruction error of phase retrieval in optical metrology

Phase retrieval is a promising method for optical system and surface metrology that makes use of intensity measurements of diffraction patterns. An iterative algorithm is used to solve the inverse problem to find the phase of the field producing the measured intensity distributions. For practical reasons, such as the reduction of coherent artifacts or to improve the signal-to-noise ratio of the measured data, it is often desirable to measure intensity distributions using broadband illumination. It is possible to perform phase retrieval with broadband data by incorporating a broadband model of the system into the phase retrieval algorithm. To do this, the system is modeled at several discrete wavelengths and the results from each are summed incoherently to produce a broadband result. This significantly increases the computational load. We show here that when aberrations are small, accurate estimates of the OPD distribution, on the level of &lgr;/1000 RMS error, can be achieved using data with bandwidth up to about 10% as the input to a phase retrieval algorithm that assumes monochromatic data.

Measurement of an Optical Surface Using Phase Retrieval

We describe the experimental measurement of a concave spherical mirror using a phase retrieval algorithm. Estimates of the resulting phases using different data sets agree to within about three thousandths of a wave RMS.

Broadband Phase-Diverse Phase Retrieval in Systems with Chromatic Aberration

We describe a phase retrieval method capable of recovering different phase distributions for each wavelength forming a polychromatic intensity distribution. Simulation results show reconstruction errors of a few thousandths of a wave RMS.

Phase Retrieval with Transverse Translations for X-ray and Optical Wavefront Sensing

Phase sensing has led to advances in X-ray beam characterization and cellular microsurgery.