Ex situ metrology of x-ray diffraction gratings Valeriy V. Yashchuk n , Wayne R. McKinney, Nikolay A. Artemiev Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA 94720, USA article info Available online 10 November 2012 Keywords: Optical metrology Diffraction grating Groove density Interferometric microscope Power spectral density abstract 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 TM -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 75%. 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. & 2012 Elsevier B.V. All rights reserved. 1. Introduction In the present work we consider metrology of x-ray gratings with interferometric microscopes. These gratings are the main elements of x-ray spectrometers and monochromators. There has been constant development of this instrumentation by improve- ment of grating fabrication and by simultaneous tightening of the requirements for the shape (groove distribution and profile) and fabrication tolerances of the gratings, associated with correspond- ing strengthening of requirements of the dedicated metrology. A revolution in both concept and implementation of mono- chromators for soft x-ray wavelengths was begun with the seminal paper of Petersen [1]. The novel design separates the focusing and diffracting modalities allowing for better focusing performance over a wider x-ray energy range than spherical grating monochromators (SGM) where both functions are com- bined in a single optic. It also allows the monochromator to operate in the angular range where the efficiency of the grating is a significant fraction of the maximum attainable. The design [1] incorporates a unique patented mechanism that permits a single carefully selected rotation axis just behind the grating to maintain the focal properties when the grating and plane pre-mirror are rotated as a unit [2]. A systematic review of the new design compared to the classical SGM has been published in Ref. [3], 12 years after the original paper. Concurrently with these revolutionary developments, Harada, Hettrick and their collaborators pioneered both the design and mechanical fabrication of new designs by the ruling and usage of varied line space (VLS) gratings [4,5]. It was only natural for the original idea and VLS to be combined and modified in various new ways [6–9]. For example, VLS gratings were made by interfero- metric methods [6], or the original concept of Ref. [1] was modified to use the grating in collimated light [10]. Recently, for undulator beams which naturally have quite small numerical apertures of emission, the use of this general approach has been further broadened by retaining the elegant single rotation of the pre-mirror/grating combination, but placing all of the focusing into the varied line space nature of the grating [11]. Even the shaping of the mirrors by heat loading from absorption of the beams may be taken into account [11]. A typical optical schematic of such a monochromator utilizing a VLS grating is shown in Fig. 1. In this case, the VLS groove density function g(w) is specified by a polynomial: gðwÞ¼ g 0 þ g 1 w þ g 2 w 2 þ ::: ð1:1Þ where w is the distance along the grating parallel to the optical path (w ¼ 0 is the grating center), g 0 is the groove frequency at the center of the grating, g 1 allows a linear variation of the groove frequency, and g 2 allows a quadratic variation of the groove frequency. The grating equation in groove frequency units: Sin a þ Sinb ¼ mlg 0 ð1:2Þ Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/nima Nuclear Instruments and Methods in Physics Research A 0168-9002/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2012.10.109 n Corresponding author. Tel.: þ1 510 495 2592; fax: þ1 510 486 7696. E-mail address: vvyashchuk@lbl.gov (V.V. Yashchuk). Nuclear Instruments and Methods in Physics Research A 710 (2013) 59–66