Modal Data Processing for High Resolution Deflectometry

  • Maham Aftab
  • James H. Burge
  • Greg A. Smith
  • Logan Graves
  • Chang-jin Oh
  • Dae Wook KimEmail author
Regular Paper


In this paper, we present a modal data processing methodology, for reconstructing high resolution surfaces from measured slope data, over rectangular apertures. One of the primary goals is the ability to effectively reconstruct deflectometry measurement data for high resolution and freeform surfaces, such as telescope mirrors. We start by developing a gradient polynomial basis set which can quickly generate a very high number of polynomial terms. This vector basis set, called the G polynomials set, is based on gradients of the Chebyshev polynomials of the first kind. The proposed polynomials represent vector fields that are defined as the gradients of scalar functions. This method yields reconstructions that fit the measured data more closely than those obtained using conventional methods, especially in the presence of defects in the mirror surface and physical blockers/markers such as fiducials used during deflectometry measurements. We demonstrate the strengths of our method using simulations and real metrology data from the Daniel K. Inouye Solar Telescope (DKIST) primary mirror.


Surface measurements, numerical approximation and analysis Instrumentation, measurement, and metrology Information processing Deflectometry Testing 



This material is partly based on work performed for the DKIST. DKIST is managed by the National Solar Observatory, which is operated by the Association of Universities for Research in Astronomy Inc. under a cooperative agreement with the National Science Foundation. Also, it is based in part upon work performed for the “Post-processing of Freeform Optics” project supported by the Korea Basic Science Institute. The deflectometry related software development is partially funded by the II–VI Foundation Block grant.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.College of Optical SciencesUniversity of ArizonaTucsonUSA
  2. 2.Steward Observatory, University of ArizonaTucsonUSA

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