Ex situ metrology of x-ray diffraction gratings

The idea of measurements of groove density distributions of diffraction gratings suggested and first realized in Proceedings of SPIE 5858, (2005) 58580A consists of determination of the spatial frequency of the first harmonic peak appearing in the power spectral density (PSD) distribution of the grating surface profile observed with a microscope. Using a MicroMap™-570 interferometric microscope, it was experimentally proven that this technique is capable of high precision measurements with x-ray gratings with groove densities of about 250 grooves/mm, varying along the grating by ±5%. In the present work, we provide analytical and experimental background for useful application of PSD characterization of groove densities of diffraction gratings. In particular, we analyze the shape of harmonic peaks and derive an analytical fitting function suitable for fitting the PSD peaks obtained with gratings with a variety of groove shapes. We demonstrate the capabilities of the method by application to the groove density distribution measurements with a 300-groove/mm grating suitable for soft x-ray applications.