A novel algorithm for the retrieval of the spatial mutual coherence function of the optical field of a light beam in the quasimonochromatic approximation is presented. The algorithm only requires that the intensity distribution is known in a finite number of transverse planes along the beam. The retrieval algorithm is based on the observation that a partially coherent field can be represented as an ensemble of coherent fields. Each field in the ensemble is propagated with coherent methods between neighboring planes, and the ensemble is then subjected to amplitude restrictions, much in the same way as in conventional phase recovery algorithms for coherent fields. The proposed algorithm is evaluated both for one- and two-dimensional fields using numerical simulations.

We propose a method to narrow the gap between the rigorous methods for the propagation of partially coherent light, which require excessive computational capacity, and the numerical methods used in practical engineering applications, where it is not clear how to handle spatial and temporal coherence in a statistically correct manner. As is the case for the latter methods, the numerical method described can deal with fields with a large spatial and temporal extent, which is necessary in practical applications such as laser fusion or optical lithography. However, the method also takes a few steps toward a more rigorous, yet efficient, representation of the optical field, which depends on detailed specified coherence properties of the radiation. The described method uses a set of independent monochromatic fields at different oscillation frequencies. The frequencies are chosen such that the statistical properties of the integrated intensity closely resemble those from a full-time trace treatment. Finally, we demonstrate the capabilities and limitations of the method with a few numerical examples of the propagation of a large field with a specified spatial and temporal coherence.

The intensity probability distribution as well as the cross-spectral density of partially coherent optical fields generated through high-numerical-aperture illuminations are analyzed, and novel effects, not apparent in paraxial optical fields, are described. It is shown that the intensity probability distribution significantly differs from what can be expected from a small-angle analysis, and the number of degrees of freedom for the distribution is higher. It is further shown that the cross-spectral density of a high-angle optical field is a function of the coordinate difference along the propagation direction of the field.

LER (line edge roughness) is becoming increasingly critical for manufacturers and efforts to understand and control it have given disappointing results. We propose that LER is due to a combination of coherent optical effects, mask LER, and chemical processes during exposure, PEB (post exposure bake) and development. Different sources of LER have similar scaling laws and PSD (Power spectral density) distribution, and the causes of LER are easily misidentified. High sensitivity, thin resist, and low image log-slope generally give more LER. No single-effect model is going to be adequate to give quantitative predictive guidance how to reduce LER. Since LER is shared between chemistry, optics and metrology, a cross-disciplinary model is needed. We propose such an LER budget model with a unified analysis of the metrology and consequences of LER, but with models for source effects plugged in by experts from the relevant domains.

We present a fast and general iterative design method for both diffractive and nondiffractive two-dimensional optical elements. The method is based on a finite-thickness model in combination with the Yang-Gu phase-retrieval algorithm. A rigorous electromagnetic analysis (boundary element method) is used to appraise the designed results. We calculate the transverse-intensity distributions, diffraction efficiency, and spot size of the designed microlenses at the focusing plane for microlenses designed using the presented method and the conventional zero-thickness model. The main findings show the superiority of the presented method over the conventional method, especially for nondiffractive optical elements.