We report the first observation of interference in the light scattered from two trapped atoms ({sup 198}Hg{sup +} ions localized in a linear Paul trap). The visibility of the interference fringes can be explained in the frame-work of Bragg scattering by a harmonic crystal, but with important differences compared to the case of a large crystal. Comparison of the experimental data with theory shows that the interference pattern offers another method to determine ion temperatures and separations. Furthermore, by exploiting the atom`s internal structure we have found a way to obtain {open_quotes}which path{close_quotes} information without invoking the position-momentum uncertainty relation. If the light scattered by the atoms is detected in a polarization-sensitive way, then it is possible to selectively demonstrate either the particle-nature or the wave-nature of the scattered photons.

Young`s interference experiment with light scattered from two atoms

We present a quick, simple and accurate digital holographic characterization of the Bessel beams produced by polymeric microaxicons. This technique allows the numerical reconstruction of both intensity and phase of the beam at whichever point starting from a single acquired hologram. From these data, it is possible to go back to the axicon structure, and to gather information about their characteristics. In particular, the focal length and the depth of focus of the axicon lens are experimentally measured, and the full width at half maximum of the beam is obtained too. The depth of focus, very large for a Bessel beam with respect to a Gaussian one, is successfully exploited for optical trapping of micrometric objects.

https://iopscience.iop.org/article/10.1088/0957-0233/23/6/065204/pdf

Characterization of Bessel beams generated by polymeric microaxicons

A compact, fiber-coupled, six degree-of-freedom measurement system which enables fast, accurate calibration, and error mapping of precision linear stages is presented. The novel design has the advantages of simplicity, compactness, and relatively low cost. This proposed sensor can simultaneously measure displacement, two straightness errors, and changes in pitch, yaw, and roll using a single optical beam traveling between the measurement system and a small target. The optical configuration of the system and the working principle for all degrees-of-freedom are presented along with the influence and compensation of crosstalk motions in roll and straightness measurements. Several comparison experiments are conducted to investigate the feasibility and performance of the proposed system in each degree-of-freedom independently. Comparison experiments to a commercial interferometer demonstrate error standard deviations of 0.33 μm in straightness, 0.14 μrad in pitch, 0.44 μradin yaw, and 45.8 μrad in roll.

Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology

A ring-shaped random laser in momentum space is designed by directly coupling a random laser with a commercial optical fiber. By using a simple approach of selectively coating the random gain layer on the surface of the fiber, red and yellow random lasers are respectively achieved with low threshold values and a good emission direction due to the guiding role of optical fibers. The unique coupling mechanism leads to a random laser with a ring shape in momentum space, which is an excellent illuminating source for high-quality imaging with an extremely low speckle noise. More importantly, a triple-state color-switchable random laser with yellow, red and yellow-red dual-colors can be flexible, and is obtained by simply moving the pump position. The results may promote the practical applications of random lasers in the fields of sensing, in vivo biological imaging, and high brightness full-field illumination.

A ring-shaped random laser in momentum space.

A simple measurement technique for the thickness distribution of transparent plates is proposed by using the sampling moire method. The thickness distribution is automatically analyzed by measuring the phase difference of the moire fringe obtained from a single image, consistent with light refraction. The relationship between the actual thickness and phase difference of the moire fringe is calibrated by using glass plates of known thicknesses. The thickness measured by the present method was found to be in agreement with measurements using a digital micrometer. In our experiment, the average error in glass plate thickness was 1.9% over a 3.5 mm measurement range. Experimental results indicate that the present method can be useful for nondestructive measurements of the thickness distribution of various transparent plates.

https://iopscience.iop.org/article/10.1088/0957-0233/21/2/025305/pdf

A simple technique for measuring thickness distribution of transparent plates from a single image by using the sampling moiré method

We present a Twyman–Green interferometer (TGI)-based polarization phase-shifting shearing interferometric technique for testing the conical surface of an axicon (AX) lens. In this technique, the annular beam generated due to the passing of an expanded collimated laser beam traveling along the axis of revolution of the transparent glass AX element is split up into its reflected and transmitted components, having the plane of polarization in the orthogonal planes, by the polarization beam splitter (PBS) cube of the TGI-based optical setup. The split-up components are made to travel unequal paths along the two arms of the TGI and are recombined by the PBS. Because of the difference in path lengths traveled by the annular conical beams, a linear shear is introduced along the radial direction between the interfering components. Thus, the resulting interference pattern gives a map of the optical path difference (OPD) between two successive close points along a radial direction on the conical surface of the AX lens. The OPD map along radial directions, and hence the slopes/profiles of the conical surface, are obtained by applying polarization phase-shifting interferometry. Results obtained for an AX lens are presented.

Measurement of the surface profile of an axicon lens with a polarization phase-shifting shearing interferometer

A new technique for the measurement of the surface profile of optical surfaces of long radius of curvature is presented. A phase shifting lateral shearing interferometer is used. Laterally sheared wavefronts are generated due to Fresnel reflections of the test wavefront at oblique inci- dence from the (plane parallel and separated) inner surfaces of a pair of glass wedge plates. A pair of matched wedge plates, which together form a parallel plate, whose thickness can be varied by translating one of the wedges, is used to introduce phase shifts between the laterally sheared components.Surfaceslopesandprofilearedeterminedbyapplyingphase shifting interferometry. An optical setup for measurement of surface profile of beam line mirrors of synchrotron radiation sources is proposed. C 2010

Measurement of surface profile of a long-radius optical surface with wedge phase shifting lateral shear interferometer

What we believe to be a new experimental technique for the generation of a plane crystal surface perpendicular to the optic axis direction of a transparent birefringent uniaxial crystal is presented. A simple setup has been described for the initial optic axis alignment of a raw uniaxial crystal blank. Error correction methods have been illustrated. A technique for producing high optical quality surfaces by block polishing plane parallel crystal surfaces normal to the direction of the optic axis, in one setting, is discussed. The block with angular graduations facilitates the correction of angular error. A new conoscopy setup has been coupled to a Fizeau interferometer for high accuracy testing of the optic axis alignment with respect to the surface normal of the relevant polished surface of the uniaxial crystal. The results obtained for a quartz crystal blank are presented.

Simple technique for the generation of plane surface normal to optic axis direction of uniaxial crystal

A new technique for the measurement of surface form error of a test spherical surface with respect to a reference spherical surface, using wedge phase shifting Fizeau interferometer, is presented. A two stage measurement method is discussed. The individual surface form error of the test and reference spherical surfaces along with the residual wave front aberration introduced by the common optical elements in the Fizeau cavity are measured with respect to a plane reference surface using phase shifting interferometry. Finally, data subtraction is used to eliminate the effect of the residual wave front aberration introduced by common optical elements and thereby transforming the result as the surface form error of the test spherical surface with respect to the reference spherical surface. Results obtained for a test spherical surface is presented.

Measurement of the surface form error of a spherical surface with a wedge phase shifting Fizeau interferometer

Thickness measurement of an opaque optics using a cyclic path optical configuration (CPOC) setup and polarization phase shifting interferometry (PPSI) is presented. The CPOC setup is used to simultaneously focus two orthogonally polarized counterpropagating converging beams at its hypotenuse arm. The opaque optics is placed at the hypotenuse arm of the CPOC setup such that one of its surfaces reflects back one of the counterpropagating focusing beams. Because of the thickness of the opaque optics, the other focusing beam suffers a longitudinal shift in the beam focus. Applying PPSI, the longitudinal shift in the beam focus which is twice the thickness of the opaque optics is determined. The results obtained for a silicon plate of thickness 0.660 mm with a measurement uncertainty of 0.013 mm are presented.

Y. Pavan Kumar

Papers

Measurement of the surface profile of an axicon lens with a polarization phase-shifting shearing interferometer

Measurement of surface profile of a long-radius optical surface with wedge phase shifting lateral shear interferometer

Simple technique for the generation of plane surface normal to optic axis direction of uniaxial crystal

Measurement of the surface form error of a spherical surface with a wedge phase shifting Fizeau interferometer

Opaque optics thickness measurement using a cyclic path optical configuration setup and polarization phase shifting interferometry