Estimation of inter-modal cross talk in a modal wavefront sensor

Abstract

A modal wavefront sensor provides a direct way of measuring the presence of a given type of aberration in the incident beam and is less computationally intensive compared to a zonal wavefront sensor. Such a sensor is particularly useful when the incident beam is aberrated with a limited number of lower order aberrations. The modal wavefront sensor has found applications in diverse areas and research is on to further improve the performance of the sensor. However, one major issue of the modal wavefront sensor is the inter-modal cross talk, that is the effect on the sensor output due to the presence of other aberration modes present in the beam. Although inter-modal cross talk is an inherent phenomenon in a modal wavefront sensor, so far there has not been any comprehensive study on the same in general. Besides there does not exist a model for quick numerical evaluation of the inter-modal cross talk in a modal wavefront sensor. In this paper we develop the theoretical expressions to define an inter-modal cross talk co-efficient and further expand it to a polynomial form. The polynomial form provides a quick way to calculate the effect of inter-modal cross talk. The correctness of the polynomial form thus developed is demonstrated by comparing the results with those obtained using the basic theory and the experimental implementation of a modal wavefront sensor. The polynomial form of the cross talk co-efficient is further used to investigate the effect of inter-modal cross talk in the sensing of a few important low order aberrations.