Measurement of the surface profile of a curved optical surface with rotation phase-shifting lateral shear cyclic path optical configuration

Chatterjee, Sanjib; Kumar, Y. Pavan

doi:10.1364/ao.50.002823

Cited by 7 publications

(8 citation statements)

References 20 publications

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“…[12,13] and the LTP [3] would be evident from the following considerations. Generally, for high-brightness SR beam lines, the tangential radii of curvatures are in kilometers.…”

Section: Resultsmentioning

confidence: 93%

“…Reference [12] discusses a rotation phase-shifting SI-based LSI setup for surface profile measurement of long-radius spherical and cylindrical mirrors. A self-referenced polarization phase-shifting SI-based technique for the measurement of the tangential surface profile of TMs is discussed in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…[13]. In the lateral shearing technique [12,13], an interference field with optical path difference (OPD) variation proportional to surface slopes, i.e., a first differential of the height variation, is produced and for long tangential radius of curvature, which is generally in kilometers, the interference field has large fringe spacing and the sensitivity of measurement is quite poor.…”

Section: Introductionmentioning

confidence: 99%

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Determination of the tangential surface profile of Toroidal beam line mirrors with polarization phase-shifting Twyman–Green interferometer

Chatterjee

Kumar

2015

Appl. Opt.

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A new technique for the measurement of the tangential surface profile of Toroidal mirrors (TMs) used in synchrotron radiation beam lines is proposed. A cylindrical lens placed in the collimated input (He-Ne laser) beam of a polarization Twyman-Green interferometer (TGI) forms line foci in the reference and test arms. The effect of the sagittal curvature of the TM is eliminated by adjusting a line focus on the surface of the TM, along the central tangential section. Thus, a toric test wavefront (TTW) with sagittal curvature identical to that of the incident cylindrical wavefront and tangential curvature with slope twice that of the TM, is produced along the reflection direction. The TTW interferes with a reference cylindrical wavefront, generated by retroreflecting the incident cylindrical wavefront from a reference plane mirror in the reference arm of the TGI and having identical curvature in the sagittal direction. Polarization phase-shifting interferometry has been applied to obtain the tangential surface profile of the test TM. Results are compared with other methods. The advantages of the technique are that only a plane reference mirror is needed to generate the reference beam, and the technique is suitable for TMs with long tangential radii of curvature in the kilometer regime.

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“…[12,13] and the LTP [3] would be evident from the following considerations. Generally, for high-brightness SR beam lines, the tangential radii of curvatures are in kilometers.…”

Section: Resultsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Determination of the tangential surface profile of Toroidal beam line mirrors with polarization phase-shifting Twyman–Green interferometer

Chatterjee

Kumar

2015

Appl. Opt.

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“…In our earlier work [11], we had used the lateral shearing, rotation phase shifting SI for the measurement of tangential surface profile of curved mirrors using He-Ne laser source. Later, we applied the technique for white light, reflection DIC microscope [8].…”

Section: Discussionmentioning

confidence: 99%

Un-polarized light transmission DIC microscope

Chatterjee

Kumar

2015

J Opt

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A new technique for creating Differential Interference Contrast (DIC) images of transparent specimens, using un-polarized, white light is discussed. A Sagnac interferometer (SI) is used in the image space of a transmission DIC microscope to produce small/differential laterally sheared, coherent beam components that interfere to form DIC images. Phase shifts between the exit beam components are introduced by applying small angular rotation of the SI in its own plane. Results obtained for a transparent watermark on a glass slide are presented. Most important advantage of the technique is that the birefringence of a test specimen does not affect the DIC images as un-polarized light is used.

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“…A cyclic path optical configuration (CPOC) has been used extensively to measure many physical quantities in many scientific and technological fields . Typical schemas of a CPOC have principally been carried out in lateral shearing interferometry (LSI) [3][4][5][6][7][8] (figure 1(a)) and radial shearing interferometry (RSI) [9][10][11][12][13][14][15] (figure 1(b)). These kinds of setups contain few elements and are relatively insensitive to the external mechanical vibrations that result from the beams travelling along the same optical circuit.…”

Section: Introductionmentioning

confidence: 99%

Carrier fringes and a non-conventional rotational shear in a triangular cyclic-path interferometer

Kantun-Montiel¹,

Meneses-Fabian²

2015

J. Opt.

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This work presents a method for generating carrier fringes and a nonconventional rotational shear in a triangular cyclic-path interferometer, while simultaneously suppressing the presence of typical lateral and radial shearing. To carry out this method, a 4f optical system is implemented into the cyclic interferometer. The most important contributions of this paper are its demonstration of the linear dependence of the movable mirror displacement with the carrier frequency introduced, and the realization of a nonconventional rotational shearing interferometer. Additionally, we think that one of its possible potential applications is the observation of the angular derivative of parallel projections of a phase object placed at the output plane, generating a great advantage in edge-enhancement optical tomography. In this paper, we develop a theoretical model and show experimental results.

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Measurement of the surface profile of a curved optical surface with rotation phase-shifting lateral shear cyclic path optical configuration

Cited by 7 publications

References 20 publications

Determination of the tangential surface profile of Toroidal beam line mirrors with polarization phase-shifting Twyman–Green interferometer

Determination of the tangential surface profile of Toroidal beam line mirrors with polarization phase-shifting Twyman–Green interferometer

Un-polarized light transmission DIC microscope

Carrier fringes and a non-conventional rotational shear in a triangular cyclic-path interferometer

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