High-precision phase compensation in deflectometry for discrete surfaces

Nansheng Zhang; Shanshan Wang; Shaohui Zhang; Qiudong Zhu

doi:10.1364/AO.589095

High-precision phase compensation in deflectometry for discrete surfaces

Nansheng Zhang
, Shanshan Wang^*
, Shaohui Zhang
, Qiudong Zhu

^*Corresponding author for this work

Beijing Institute of Technology
National Key Laboratory on Near-Surface Detection

Research output: Contribution to journal › Article › peer-review

Abstract

Phase compensation deflectometry enables the rapid assessment of surface figure errors and defects on specular surfaces. This method requires the construction of high-precision compensation fringes, whereas most existing approaches rely on analytical surface models and struggle to handle discrete surfaces. This paper presents a generic geometric modeling and reconstruction method for phase compensation deflectometry on discrete surfaces, overcoming the constraints of conventional height-field models. During ray reconstruction, the method incorporates the Möller–Trumbore algorithm combined with barycentric normal interpolation to accurately compute surface intersection points and normal vectors. Experimental results demonstrate that the Pearson correlation coefficient between the proposed method and interferometer measurements exceeds 0.7. This work provides a versatile and efficient solution for high-precision null testing of discrete surfaces.

Original language	English
Pages (from-to)	3065-3074
Number of pages	10
Journal	Applied Optics
Volume	65
Issue number	9
DOIs	https://doi.org/10.1364/AO.589095
Publication status	Published - 20 Mar 2026
Externally published	Yes

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title = "High-precision phase compensation in deflectometry for discrete surfaces",

abstract = "Phase compensation deflectometry enables the rapid assessment of surface figure errors and defects on specular surfaces. This method requires the construction of high-precision compensation fringes, whereas most existing approaches rely on analytical surface models and struggle to handle discrete surfaces. This paper presents a generic geometric modeling and reconstruction method for phase compensation deflectometry on discrete surfaces, overcoming the constraints of conventional height-field models. During ray reconstruction, the method incorporates the M{\"o}ller–Trumbore algorithm combined with barycentric normal interpolation to accurately compute surface intersection points and normal vectors. Experimental results demonstrate that the Pearson correlation coefficient between the proposed method and interferometer measurements exceeds 0.7. This work provides a versatile and efficient solution for high-precision null testing of discrete surfaces.",

author = "Nansheng Zhang and Shanshan Wang and Shaohui Zhang and Qiudong Zhu",

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T1 - High-precision phase compensation in deflectometry for discrete surfaces

AU - Zhang, Nansheng

AU - Wang, Shanshan

AU - Zhang, Shaohui

AU - Zhu, Qiudong

PY - 2026/3/20

Y1 - 2026/3/20

N2 - Phase compensation deflectometry enables the rapid assessment of surface figure errors and defects on specular surfaces. This method requires the construction of high-precision compensation fringes, whereas most existing approaches rely on analytical surface models and struggle to handle discrete surfaces. This paper presents a generic geometric modeling and reconstruction method for phase compensation deflectometry on discrete surfaces, overcoming the constraints of conventional height-field models. During ray reconstruction, the method incorporates the Möller–Trumbore algorithm combined with barycentric normal interpolation to accurately compute surface intersection points and normal vectors. Experimental results demonstrate that the Pearson correlation coefficient between the proposed method and interferometer measurements exceeds 0.7. This work provides a versatile and efficient solution for high-precision null testing of discrete surfaces.

AB - Phase compensation deflectometry enables the rapid assessment of surface figure errors and defects on specular surfaces. This method requires the construction of high-precision compensation fringes, whereas most existing approaches rely on analytical surface models and struggle to handle discrete surfaces. This paper presents a generic geometric modeling and reconstruction method for phase compensation deflectometry on discrete surfaces, overcoming the constraints of conventional height-field models. During ray reconstruction, the method incorporates the Möller–Trumbore algorithm combined with barycentric normal interpolation to accurately compute surface intersection points and normal vectors. Experimental results demonstrate that the Pearson correlation coefficient between the proposed method and interferometer measurements exceeds 0.7. This work provides a versatile and efficient solution for high-precision null testing of discrete surfaces.

UR - https://www.scopus.com/pages/publications/105033058660

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DO - 10.1364/AO.589095

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VL - 65

SP - 3065

EP - 3074

JO - Applied Optics

JF - Applied Optics

IS - 9

ER -

High-precision phase compensation in deflectometry for discrete surfaces

Abstract

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