Extreme shearing interferometry: Theoretical limits with practical consequences

Servı́n, Manuel; Cywiak, Moisés; Dávila, A.

doi:10.1364/oe.15.017805

Cited by 28 publications

(11 citation statements)

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“…The theoretical limits of LSI were analyzed from the frequency response point of view. [ 89 ] Technologies capable of capturing multiple shearing interferograms simultaneously have been developed to improve the accuracy of wavefront reconstruction. Ling et al.…”

Section: Interferometric Areal Measurementmentioning

confidence: 99%

Measurement of Freeform Optical Surfaces: Trade‐Off between Accuracy and Dynamic Range

Chen

Xue

Zhai

et al. 2020

Laser & Photonics Reviews

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Freeform optical surfaces are advantageous to optical designers, as they provide additional degrees of freedom for optimization. The loss of rotational symmetry, however, makes measurement of freeforms more challenging. Herein, advances in interferometric areal measurement of freeform optical surfaces, including null tests, non-null tests, near-null tests, and adaptive null tests, are reviewed. Some new developments, in the Hartmann test, deflectometry, and phase retrieval, as representatives of non-interferometric areal measurement, are then presented. Overall, the focus is on single-point-probe-based profilometry categorized into coordinate measurements and slope-or curvature-based measurements. Innovative measurement technology is trying to bridge the gap between high accuracy and high dynamic range as freeform optical surfaces are finding more applications in visible and shorter-wavelength optics.

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Section: Interferometric Areal Measurementmentioning

confidence: 99%

Measurement of Freeform Optical Surfaces: Trade‐Off between Accuracy and Dynamic Range

Chen

Xue

Zhai

et al. 2020

Laser & Photonics Reviews

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“…Shearing interferometers have a non-uniform spatial frequency response that is well understood [16]. The sampling of the phase difference between two points on the wavefront is insensitive to spatial fluctuations with an integer number of cycles within the shear distance.…”

Section: Sensitivity and Resolutionmentioning

confidence: 99%

“…If the wavefront distortion is attributable to the deformation of a mirror and a reference wavefront φ r free of the effects of the mirror deformation is known, the components of the surface deformation gradient are found from 2∇h = ∇φ d − ∇φ r (16) and equation 13 and have their mean value subtracted (equivalent to removing any tilt of the wavefront). The arrays containing ∂h( r)/∂x and ∂h( r)/∂y are then shifted by an amount corresponding to the average lateral displacement of the interfering beams, − s/2.…”

Section: Interferogram Processing and Wavefront Reconstructionmentioning

confidence: 99%

Measurement of thermo-elastic deformation of an optic using a polarization-based shearing interferometer

Beyersdorf¹,

Cordier²

2012

Appl. Opt.

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A shearing interferometer is presented which uses polarization control to shear the wavefront and to modulate the interference pattern. The shear is generated by spatial walk-off in a birefringent crystal. By adjusting the orientation of the birefringent crystal, the components of the wavefront gradient can be independently measured to allow determination of the full wavefront vector gradient as well as reconstruction of the wavefront. Further, the monolithic nature of the crystal used for shearing allows the interferometer to be setup without need for precise alignment of any components. An algorithm incorporating homodyne detection is presented whichanalyzes the modulated interferograms to determine the components of the wavefront gradient, from which the wavefront is reconstructed. The thermal deformation of a mirror subject to heating from absorption of a Gaussian pump beam was accurately observed with a sensitivity better than λ/160. We show that this sensitivity is scale invariant, and present a method to account for the nonuniform spatial frequency response of the interferometer.

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“…Shearing interferometers have a non-uniform spatial frequency response that is well understood [23]. The sampling of the phase di↵erence between two points on the wavefront is insensitive to spatial fluctuations with an integer multiple of cycles within the shear distance, so surface features smaller than the shear distance can not be resolved.…”

Section: Sensitivity and Resolutionmentioning

confidence: 99%

“…23) which all occur at di↵erent center frequencies in spatial frequency space, allowing us to isolate the desired low spatial frequency phase information contained in U and U ⇤ at frequencies upshifted and downshifted by the modulation frequency K c from the low frequency background intensity centered around zero frequency as shown in the top graph ofFigure 4.4.…”

mentioning

confidence: 99%

Measurement of Laser-Induced Thermo-Elastic Deformation In an Optic Using Polarization-Based Lateral Shearing Interferometry

Cordier¹

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A polarization-based shearing interferometer is presented that is capable of measuring the thermal deformation of a mirror subject to heating from absorption of a Gaussian laser beam. The shear is generated by spatial walk-o↵ in a birefringent crystal. By adjusting the orientation of the crystal, the components of the wavefront gradient can be independently measured to allow determination of the full wavefront vector gradate as well as reconstruction of the wavefront. Furthermore, the monolithic nature of the birefringent crystal allows non-critical alignment of the interferometer's components. The interferogram is modulated, and a homodyne detection algorithm analyzes the modulated interferograms to extract the components of the wavefront gradient from which the wavefront is reconstructed. The thermal deformation of the laser-heated mirror was accurately observed with a sensitivity better than /160. The sensitivity of this interferometer is scale invariant, and we present a method to account for the non-uniform spatial frequency response of the interferometer.

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Extreme shearing interferometry: Theoretical limits with practical consequences

Cited by 28 publications

References 0 publications

Measurement of Freeform Optical Surfaces: Trade‐Off between Accuracy and Dynamic Range

Measurement of Freeform Optical Surfaces: Trade‐Off between Accuracy and Dynamic Range

Measurement of thermo-elastic deformation of an optic using a polarization-based shearing interferometer

Measurement of Laser-Induced Thermo-Elastic Deformation In an Optic Using Polarization-Based Lateral Shearing Interferometry

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