title: Problems in the application of a null lens for precise measurements of aspheric mirrors.
abstract: Problems in the application of a null lens for surface shape measurements of aspherical mirrors are discussed using the example of manufacturing an aspherical concave mirror for the beyond extreme ultraviolet nanolithographer. A method for allowing measurement of the surface shape of a sample under study and the aberration of a null lens simultaneously, and for evaluating measurement accuracy, is described. Using this method, we made a mirror with an aspheric surface of the 6th order (i.e., the maximum deviation from the best-fit sphere is 6.6 μm) with the parameters of the deviations from the designed surface PV=5.3  nm and RMS=0.8  nm. An approximation of the surface shape was carried out using Zernike polynomials {Z(n)(m)(r,φ),m+n≤36}. The physical limitations of this technique are analyzed. It is shown that for aspheric measurements to an Angstrom accuracy, one needs to have a null lens with errors of less than 1 nm. For accurate measurements, it is necessary to establish compliance with the coordinates on the sample and on the interferogram.
authors.forename: N I
authors.initials: NI
authors.lastname: Chkhalo
authors.forename: I V
authors.initials: IV
authors.lastname: Malyshev
authors.forename: A E
authors.initials: AE
authors.lastname: Pestov
authors.forename: V N
authors.initials: VN
authors.lastname: Polkovnikov
authors.forename: N N
authors.initials: NN
authors.lastname: Salashchenko
authors.forename: M N
authors.initials: MN
authors.lastname: Toropov
authors.forename: A A
authors.initials: AA
authors.lastname: Soloviev