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.

A new technique for producing a white light differential interference contrast (DIC) image using a lateral shearing, rotation phase shifting Sagnac interferometer (SI) is proposed. The SI, placed in the image space after the tube lens of a microscope system with spatially coherent white light Kohler illumination, splits the image forming beam into coherent components with small lateral shear. Phase shifts, between the interfering components, which can be considered as biased phase difference (BPD), are introduced by applying small angular rotation of the SI in its own plane. This variable BPD between the interfering white light components produces a uniform intensity colored background. The object related phase shift, due to the height difference between two close points on the object surface with separation on the order of least resolvable separation of the microscope objective, in addition to the BPD would produce a change in intensity/hue/color against a uniform background due to the BPD. Thus a DIC image is formed and the variable BPD provides an excellent means of improving the contrast of the image.

White light differential interference contrast microscope with a Sagnac interferometer

A new technique, using a cyclic path optical configuration, for generating two coherent, virtual point sources at the back focal plane of a corrected telescope objective, for producing a pair of mutually tilted collimated beams with linear orthogonal polarizations in a Fizeau interferometer cavity is presented. The orthogonal linear polarization components reflected from the reference and the test surfaces are utilized for introducing polarization phase shift between the reference and test waves. A method for elimination of the residual instrumental aberration due to a slight departure from strict on-axis operation is discussed. The result for a plane optical surface is presented. Because, in polarization phase shifting, it is possible to capture all the necessary phase-shifted interferograms simultaneously, the vibration susceptibility can be minimized and the present system could be applied for dynamic interferometry.

Polarization phase-shifting Fizeau interferometer with a cyclic path optical configuration

A new technique for external measurement of dihedral right angles is presented. An expanded, collimated, and linearly polarized He-Ne laser beam (632.8 nm) from a Fizeau interferometer is launched into a cyclic path optical configuration (CPOC) in which the counterpropagating p and s polarization components traverse the same optical path in opposite directions. A right-angled component (RAC), with its plane surfaces forming the right angle, is set to externally reflect the counterpropagating p and s components of the CPOC in nearly the same directions but with a lateral separation. In a plane normal to the right-angle edge of the RAC, the laterally separated collimated beams have angular separation, which is equal to twice the error in the dihedral right angle. Another CPOC setup is used to recombine the beams by reducing the lateral shear to zero. Error in right angle is calculated from the spacing of the resulting two-beam Fizeau fringes. Methods for overcoming the restriction of measurement accuracy due to beam aperture limitation and the effects of the positional tilt of the RAC have been discussed. Results of validation experiments are presented.

External measurement of dihedral right angles with cyclic optical configuration

A new technique for the measurement of centering error (CE) of a lens using a cyclic path optical configuration (CPOC) is presented. The test lens (TL) is placed in the CPOC, adjusted for zero lateral shear. The mechanical axis (MA) of the TL holder is prealigned along the direction of the central ray (CR) of the counterpropagating collimated beams of the CPOC. A pencil beam is also set along the CR outside the CPOC. If the TL is free from CE, then its optical axis (OA) would coincide with the MA and the CR. The focal points F1 and F2, formed by the TL, and the center of the Haidinger-type fringes, due to interference of the light from F1 and F2 (which is along the line joining F1 and F2), would also lie on the CR. In the presence of CE, F1 and F2 would be laterally displaced from the CR and the fringe center (FC) suffers a deviation from the CR. Adjustments in the angular and lateral positions of the TL necessary to align the OA along the CR, as can be ensured from the coincidence of the FC with the CR, give a measure of the CE.

Measurement of centering error of a lens with cyclic optical configuration

We present a new (to our knowledge) technique for introducing phase shifts between the laterally sheared emergent beam components of a cyclic path optical configuration (CPOC). The phase shifts are introduced by applying a small change in the angle of incidence of the incident beam due to the small angular rotation of the CPOC setup. Phase-shifting interferometry has been applied along with this phase-shifting technique for a CPOC with lateral shear to find the surface slope/profile of curved optical surfaces. Results for a spherical optical surface have been discussed. An optical setup for measurement of the surface profile of toroidal beam line mirrors of synchrotron radiation sources is proposed.

Sanjib Chatterjee

Papers

White light differential interference contrast microscope with a Sagnac interferometer

Polarization phase-shifting Fizeau interferometer with a cyclic path optical configuration

External measurement of dihedral right angles with cyclic optical configuration

Measurement of centering error of a lens with cyclic optical configuration

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