25 October 2011 Obtaining the wavefront in the Ronchi test using only one Ronchigram with random coefficients of aberration
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It is well known that the Ronchi test can be used to measure the derivative of the optical path difference of a wavefront [1]. Therefore when the Ronchi test is used to determine the wavefront of the surface under test, two orthogonal Ronchigrams are required to reconstruct the surface [2]. We present a simple method to recovery the wavefront with one Ronchigram without using polynomial fit or trapezoidal integration. The recovery of the aberration coefficients of third order is achieved by assigning random values but controlled in the equation of the optical path difference (OPD) which is given for a lateral sheared interferometer. Since the Ronchi test can be seen as a variation of this type of interferometer [3], namely, the OPD for the Ronchi test is given by the difference between the original wavefront W(x,y) and the sheared wavefront W(x + Δx,y), resulting in the generation of various Ronchigrams, which are compared with the Ronchigram under analysis. The generated Ronchigram with lower RMS (Root Mean Square) must have the highest correlation with the Ronchigram analyzed, since the RMS is inversely proportional to the correlation. For some simulated Ronchigrams which were generated by introducing Gaussian noise, some results are shown. The proposed method retrieves in a reliable the coefficients of the polynomial of the analyzed Ronchigram in a reliable and accurate way.
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D. Aguirre-Aguirre, D. Aguirre-Aguirre, F. S. Granados-Agustín, F. S. Granados-Agustín, A. Cornejo-Rodríguez, A. Cornejo-Rodríguez, } "Obtaining the wavefront in the Ronchi test using only one Ronchigram with random coefficients of aberration", Proc. SPIE 8011, 22nd Congress of the International Commission for Optics: Light for the Development of the World, 801117 (25 October 2011); doi: 10.1117/12.902606; https://doi.org/10.1117/12.902606

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