Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry: comparisons of existing algorithms

Dai, Fengzhao; Tang, Feng; Wang, Xiangzhao; Sasaki, Osami; Feng, Peng

doi:10.1364/ao.51.005028

Cited by 87 publications

(18 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The angle of incidence equals the angle of reflection when light coming from the screen goes into the camera after the reflection on the specular surface as depicted in Figure 1 Unlike the classical PMD that calculates the slopes from the fringe phases with pre-known or roughly known height values and then integrates slopes to get the resultant height distribution, the proposed method reconstructs both height and slopes at the same time. The modal wavefront reconstruction method [26][27][28] which could be time consuming, the shape models are defined in the normalized camera…”

Section: Principlementioning

confidence: 99%

Modal phase measuring deflectometry

Huang¹,

Xue²,

Gao³

et al. 2016

Opt. Express

View full text Add to dashboard Cite

In this work, a model based method is applied to phase measuring deflectometry, named modal phase measuring deflectometry. The height and slopes of the surface under test are represented by mathematical models and updated by optimizing the model coefficients to minimize the discrepancy between the reprojection in ray tracing and the actual measurement. The pose of the screen relative to the camera is pre-calibrated and further optimized together with the shape coefficients of the surface under test. Simulations and experiments are conducted to demonstrate the feasibility of the proposed approach.

show abstract

Section: Principlementioning

confidence: 99%

Modal phase measuring deflectometry

Huang¹,

Xue²,

Gao³

et al. 2016

Opt. Express

View full text Add to dashboard Cite

show abstract

“…But in fact, the columns of the orthonormal slope polynomials matrix lose their orthogonality because the number of discrete sampling points is finite. As a result, the expansion coefficientα is not independent and cross-coupling appears because of the lack of orthogonality [21][22][23].…”

Section: Cross-couplingmentioning

confidence: 99%

Modal wavefront reconstruction from slope measurements for rectangular apertures

Zhang

et al. 2015

J. Opt. Soc. Am. A

View full text Add to dashboard Cite

We present a modal wavefront reconstruction from slope measurements for rectangular optical components of high-power laser systems. Wavefront reconstruction with slope data is an important approach used for wavefront control or correction in high-power systems. In this work, we derive a complete set of orthonormal wavefront slope polynomials for rectangular apertures and describe the modal method for obtaining wavefront representation with the aberration balancing property. Error propagation properties for the modal method are evaluated and compared with the Southwell method. The cross-coupling error is also discussed. Numerical experiments are conducted to illustrate that the modal method can achieve a higher accuracy than the Southwell method. In addition, we also investigate the influence of noise on the modal method compared with that of the Southwell method.

show abstract

“…Moreover, the computational complexity of modal methods is significantly reduced when compared with piecewise methods. The commonly used polynomials basis set includes Zernike polynomials [11,12], Legendre polynomials [13], and Chebyshev polynomials [14][15][16]. The corresponding coefficients of each polynomial mode are obtained by linear equations, which are consisted of the gradient of the polynomials and the measured slope data.…”

Section: Introductionmentioning

confidence: 99%

Modal shape reconstruction method for deflectometry based on deep learning

Guan¹,

Li²,

Xi³

2022

Optical Metrology and Inspection for Industrial Applications IX

View full text Add to dashboard Cite

Deflectometry is a slope-based technique to measure specular surfaces. Modal reconstruction methods fit the surface shape with a certain mathematical model based on expansion polynomials and their coefficients. The coefficients are obtained by linear equations, which are consisted of the gradient of the polynomials and the measured slope data. Nevertheless, computing the large linear equations is time-consuming work and the noises and outliers will decrease the reconstruction accuracy. This paper uses the Chebyshev polynomials as the basis set and proposes a modal reconstruction method based on the deep convolutional neural network to directly output the corresponding Chebyshev coefficients. Compared with the conventional modal reconstruction method, the results demonstrate that the reconstruction accuracy and the computational efficiency are improved effectively using the proposed method.

show abstract

Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry: comparisons of existing algorithms

Cited by 87 publications

References 28 publications

Modal phase measuring deflectometry

Modal phase measuring deflectometry

Modal wavefront reconstruction from slope measurements for rectangular apertures

Modal shape reconstruction method for deflectometry based on deep learning

Contact Info

Product

Resources

About