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 new laser differential reflection-confocal focal-length measurement (DRCFM) method is proposed for the high-accuracy measurement of the lens focal length. DRCFM uses weak light reflected from the lens last surface to determine the vertex position of this surface. Differential confocal technology is then used to identify precisely the lens focus and vertex of the lens last surface, thereby enabling the precise measurement of the lens focal length. Compared with existing measurement methods, DRCFM has high accuracy and strong anti-interference capability. Theoretical analyses and experimental results indicate that the DRCFM relative measurement error is less than 10 ppm.

Laser differential reflection-confocal focal-length measurement

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.

We present a technique for the focal length measurement of lenses applying Newton's method, using a cyclic path optical configuration (CPOC) and a wedge shear plate (WSP). Two point sources of orthogonal linearly polarized light waves that have a known longitudinal separation between them are generated using CPOC. Selecting a particular state of polarization (s or p), the corresponding point source is made to coincide with the back focal point of the test lens (TL). The collimation of the output beam from TL is tested using the WSP. With a change in the state of polarization, a spherical wavefront would emerge from TL because the corresponding point source is situated slightly away from the focal plane of TL. The radius of curvature of the emerging spherical wavefront from TL approximated as image distance is evaluated by analyzing the shear fringes produced by WSP. Appropriate formulae for the determination of the focal length of TL, from the image distance and known longitudinal separation between the sources, are derived using Newton's method. Results obtained for a positive doublet lens of nominal focal length of 500.0 mm is presented.

Application of Newton's method to determine the focal length of lenses using a lateral shearing interferometer and cyclic path optical configuration setup

A new (to our knowledge) technique for the generation of white light Young's type fringes using a cyclic path optical configuration is presented. The effect of the size of an incoherent broadband light source on the fringe visibility is discussed. Applications and advantages of the technique are described.

Simple technique for the generation of white light Young's fringes with a cyclic optical configuration

We present a technique for the measurement of longitudinal displacement using a lateral shearing cyclic path optical configuration (CPOC) setup and phase shifting interferometry. In the technique, a plane mirror mounted on a linear translation stage, placed slightly away from the focal plane of a lens, introduces a longitudinal focal shift to the incident focusing beam. The resulting spherical wavefront emerging from the lens is sheared into two orthogonally polarized beams using the CPOC setup. By applying polarization phase shifting interferometry (PPSI), the longitudinal focal shift of the beam focus is calculated by determining the slope of the optical path difference variation between the sheared beams. Similarly, the additional focal shift introduced due to longitudinal translation of the mirror, by an unknown amount, is determined using PPSI. Half of the difference between the two longitudinal focal shifts measured gives the longitudinal displacement of the mirror. The technique can be used for an extended range of distance measurement. The novelty of the technique is the introduction of CPOC for the distance measurement. The advantages of the technique compared to other related methods are discussed.

Measurement of longitudinal displacement using lateral shearing cyclic path optical configuration setup and phase shifting interferometry

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

Sanjib Chatterjee

Papers

Application of Newton's method to determine the focal length of lenses using a lateral shearing interferometer and cyclic path optical configuration setup

Simple technique for the generation of white light Young's fringes with a cyclic optical configuration

Measurement of longitudinal displacement using lateral shearing cyclic path optical configuration setup and phase shifting interferometry

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