A new data processing method based on orthonormal rectangular gradient polynomials is introduced in this work. This methodology is capable of effectively reconstructing surfaces or wavefronts with data obtained from deflectometry systems, especially during fabrication and metrology of high resolution and freeform surfaces. First, we derived a complete and computationally efficient vector polynomial set, called <strong>G</strong> polynomials. These polynomials are obtained from gradients of Chebyshev polynomials of the first kind – a basis set with many qualities that are useful for modal fitting. In our approach both the scalar and vector polynomials, that are defined and manipulated easily, have a straightforward relationship due to which the polynomial coefficients of both sets are the same. This makes conversion between the two sets highly convenient. Another powerful attribute of this technique is the ability to quickly generate a very large number of polynomial terms, with high numerical efficiency. Since tens of thousands of polynomials can be generated, mid-to-high spatial frequencies of surfaces can be reconstructed from high-resolution metrology data. We will establish the strengths of our approach with examples involving simulations as well as real metrology data from the Daniel K. Inouye Solar Telescope (DKIST) primary mirror.
Dynamic metrology holds the key to overcoming several challenging limitations of conventional optical metrology, especially with regards to precision freeform optical elements. We present two dynamic metrology systems: 1) adaptive interferometric null testing; and 2) instantaneous phase shifting deflectometry, along with an overview of a gradient data processing and surface reconstruction technique. The adaptive null testing method, utilizing a deformable mirror, adopts a stochastic parallel gradient descent search algorithm in order to dynamically create a null testing condition for unknown freeform optics. The single-shot deflectometry system implemented on an iPhone uses a multiplexed display pattern to enable dynamic measurements of time-varying optical components or optics in vibration. Experimental data, measurement accuracy / precision, and data processing algorithms are discussed.
Several next generation astronomical telescopes or large optical systems utilize aspheric/freeform optics for creating a segmented optical system. Multiple mirrors can be combined to form a larger optical surface or used as a single surface to avoid obscurations. In this paper, we demonstrate a specific case of the Daniel K. Inouye Solar Telescope (DKIST). This optic is a 4.2 m in diameter off-axis primary mirror using ZERODUR thin substrate, and has been successfully completed in the Optical Engineering and Fabrication Facility (OEFF) at the University of Arizona, in 2016. As the telescope looks at the brightest object in the sky, our own Sun, the primary mirror surface quality meets extreme specifications covering a wide range of spatial frequency errors. In manufacturing the DKIST mirror, metrology systems have been studied, developed and applied to measure low-to-mid-to-high spatial frequency surface shape information in the 4.2 m super-polished optical surface. In this paper, measurements from these systems are converted to Power Spectral Density (PSD) plots and combined in the spatial frequency domain. Results cover 5 orders of magnitude in spatial frequencies and meet or exceed specifications for this large aspheric mirror. Precision manufacturing of the super-polished DKIST mirror enables a new level of solar science.