High-resolution shape measurements with phase-shifting Schlieren (PSS)

Joannes, Luc; Beghuin, Didier; Ligot, Renaud; Farinotti, S.; Dupont, Olivier

doi:10.1117/12.545536

Cited by 1 publication

(1 citation statement)

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“…For the purpose of emphasizing the advantage of the compressive sensing method, we shall briefly explain the existing method. For a detailed description of the same, the interested readers can consult [31,30]. The system is configured to work using several phase shifted sinusoidal patterns (for modulation) in order to measure deflections and this configuration is named Phase Shifting schlieren (PSS).…”

Section: Phase Shifting Schlierenmentioning

confidence: 99%

Compressive Imaging and Characterization of Sparse Light Deflection Maps

Sudhakar¹,

Jacques²,

Dubois³

et al. 2015

SIAM J. Imaging Sci.

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Light rays incident on a transparent object of uniform refractive index undergo deflections, which uniquely characterize the surface geometry of the object. Associated with each point on the surface is a deflection map (or spectrum) which describes the pattern of deflections in various directions. This article presents a novel method to efficiently acquire and reconstruct sparse deflection spectra induced by smooth object surfaces. To this end, we leverage the framework of Compressed Sensing (CS) in a particular implementation of a schlieren deflectometer, i.e., an optical system providing linear measurements of deflection spectra with programmable spatial light modulation patterns. In particular, we design those modulation patterns on the principle of spread spectrum CS for reducing the number of observations. Interestingly, the ability of our device to simultaneously observe the deflection spectra on a dense discretization of the object surface is related to a particular Multiple Measurement Vector (MMV) model. This scheme allows us to estimate both the noise power and the instrumental point spread function in a specific calibration procedure.We formulate the spectrum reconstruction task as the solving of a linear inverse problem regularized by an analysis sparsity prior using a translation invariant wavelet frame. Our results demonstrate the capability and advantages of using a CS based approach for deflectometric imaging both on simulated data and experimental deflectometric data.Finally, the paper presents an extension of our method showing how we can extract the main deflection direction in each point of the object surface from a few compressive measurements, without needing any costly reconstruction procedures. This compressive characterization is then confirmed with experimental results on simple plano-convex and multifocal intra-ocular lenses studying the evolution of the main deflection as a function of the object point location.

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Section: Phase Shifting Schlierenmentioning

confidence: 99%