Interferometric microscopes are used to measure surface roughness, from which the computed power spectral density function can be used to extract bandwidth-limited values of the various surface properties, such as root-mean-square (rms) height and slope errors. Measurements with a microscope equipped with different objectives that have an overlapping spatial frequency range usually give different rms results over the common frequency bandwidth. This is a result of different instrument transfer functions (ITFs) that attenuate spatial frequencies by different amounts over the overlapping range. We report on the use of binary pseudo-random array (BPRA) standards to characterize the ITF of an interferometric microscope with the various objectives. We use a simple model of a 1D binary Results show that the spectrum for an undersampled array is a cosine function, rather than a straight line, constant white noise spectrum. We have an analytical model of the ITF that includes the effects of an obscured aperture and defocus, in addition to the usual parameters of numerical aperture, wavelength, and sampling period. In addition, the model includes the effect of aliasing of spatial frequency components beyond the Nyquist back into the sub-Nyquist region. We compare the model PSD predictions to the measurements performed with different objectives. Departures of the measured PSDs from the model predictions indicate that there are higher-order ITF corrections yet to be identified and included in the model.

High-accuracy surface metrology is vitally important in manufacturing ultra-high-quality free-form mirrors designed to manipulate x-ray light with nanometer-scale wavelengths. The current and potential capabilities of x˗ray mirror manufacturing are limited by inherent imperfections of the integrated metrology tools. Metrology tools are currently calibrated with super-polished flat test-standard/reference mirrors. This is acceptable for fabrication of slightly curved x-ray optics. However, for even moderately curved aspherical x-ray mirrors the flat-reference calibration is not sufficiently accurate. For micro-stitching interferometry developed for surface measurements with curved x-ray mirrors, the tool aberration errors are known to be transferred into the optical surface topography of x-ray mirrors. Our approach to improving metrology is to thoroughly calibrate the measuring tool and apply the results of the calibration to deconvolution of the measured data. Here we explore the application of a recently developed technique for calibrating the instrument transfer function (ITF) of 3D optical surface profilers to metrology with significantly curved x-ray optics. The technique, based on test standards patterned with two-dimensional (2D) binary pseudo-random arrays (BPRAs), employs the unique properties of the BPRA patterns in the spatial frequency domain. The inherent 2D power spectral density of the pattern has a deterministic white-noise-like character that allows direct determination of the ITF with uniform sensitivity over the entire spatial frequency range and field of view of an instrument. The high efficacy of the technique has been previously demonstrated in application to metrology with flat and slightly curved optics. Here, we concentrate on development of an efficient fabrication process for production of highly randomized (HR) BPRA test standards on flat and 500-mm spherical optical substrates. We also compare and discuss the results of the ITF calibration of an interferometric microscope when using the HR BPRA standards on flat and curved substrates.

Recently, a technique for calibrating the modulation transfer function (MTF) of a broad variety of metrology instrumentation has been demonstrated. This technique is based on test samples structured as one-dimensional binary pseudo-random (BPR) sequences and two-dimensional BPR arrays (BPRAs). The inherent power spectral density of BPR gratings (sequences) and arrays has a deterministic white-noise-like character that allows direct determination of the MTF with uniform sensitivity over the entire spatial frequency range and field-of-view of an instrument. As such, the BPR samples satisfy the characteristics of a test standard: functionality, ease of specification and fabrication, reproducibility, and low sensitivity to manufacturing error. Here we discuss our recent developments directed to the optimization of the sample design, fabrication, application, and data processing procedures, suitable for thorough characterization of large aperture optical interferometers. Compared with the previous coded-aperture based design, the improved, 'highly randomized' BPRA pattern of the new test standard provides better accuracy and reliability of instrument MTF and aberration characterization, and enables operation optimization of large aperture optical interferometers. We describe the pattern generation algorithm and tests to verify the compliance to desired BPRA topography. The data acquisition and analysis procedures for different applications of the technique are also discussed.

Accurate topography measurements of engineered surfaces over a wide range of spatial frequencies are required in many applications. The instrument transfer function (ITF) of the microscope used to characterize the surface topography must be taken into consideration to ensure that the height, or depth, of features with higher spatial frequency content is not underestimated. This applies especially when comparing surface topography measurements made by different types of microscopes. We discuss ITF measurements of a confocal microscope and an interferometric microscope using a binary pseudo-random array (BPRA) standard. BPRA standards are surfaces designed to have constant inherent power spectral density (PSD) over the spatial frequency passband of a microscope. The ITF of a microscope can thus be derived from a PSD measurement of a BPRA standard in a straight-forward manner. We further show how BPRA standards can be used as efficient diagnostic tools to characterize aspects of the imaging performance of topography-measuring microscopes.