Bironchigram processing method for quantitative evaluation of optical focusing mirrors

Since its proposal the Ronchi “ruling” test has been considered as the most remarkable technique of the Schlieren family. Despite being based on fringe pattern generation and commonly interpreted in a qualitative way, it was capable of achieving outstanding results in the detection of aberrations in optical surfaces. Given its theoretical straightforwardness, experimental simplicity and economic affordability in comparison to other methodologies in the field, in the present work is addressed the lingering issue of how to extract quantitative information from digital captures of this test. Such task was accomplished taking advantage of the improved Ronchi test with a square grid, from which it was possible to develop a mathematical model with foundation in the Fourier theory to describe its observations. Thereupon, it was devised a novel iterative algorithm grounded in Fourier phase measuring able to compute fairly accurate wavefront gradient estimations from a single “bironchigram” sample with grid defocus. This procedure is complemented by a mandatory integration algorithm that is based on the regularization theory. The overall proposed methodology was put to test in a large aspherical mirror, estimating a surface aberration profile with a P-V (peak to valley) ratio of 155 nm, value well in accord with the one reported by the commercial interferometric system used for validation.