An analysis of methods for aberrated spot diagram center evaluation

The paper considers spot diagram center evaluation methods and errors depending on aberration type and value. The authors present the modified center of mass method which provides higher accuracy of center evaluation for spot diagram with coma. Error estimation methods involved using simulated spot diagram with symmetrical and non-symmetrical aberrations of the third and fifth order and their combinations. The error of center evaluation by the maximum value method and center of mass method is analyzed. The proposed modified center of mass method gives higher weight for pixels with higher intensity that leads to better sensitivity of the method and it is compared with other methods. The center of mass method can evaluate accurate center position only for coma-free spot diagram. The maximum value method cannot evaluate accurate center position for spot diagram with coma either and for coma-free spot diagram it can also produce larger errors than the center of mass method. The modified center of mass method is more robust and evaluates center for spot diagram with coma and other aberrations more accurately. The modified center of mass method shows higher accuracy while evaluating center of spot diagram with aberration, and hence higher accuracy of modulation transfer function evaluation by spot diagram. The precise evaluation of spot diagram center will also increase the convergence of the phase retrieval method with parametric optimization techniques.