Sanjib Chatterjee

Abstract: We present what we believe is a new technique for the focal-length measurement of positive lenses using Fizeau interferometery. The technique utilizes the Gaussian lens equation. The image distance is measured interferometrically in terms of the radius of curvature of the image-forming wavefront emerging from the lens. The radii of curvature of the image-forming wavefronts corresponding to two different axial object positions of known separation are measured. The focal length of the lens is determined by solving the equations obtained using the Gaussian lens equation for the two object positions. Results obtained for a corrected doublet lens of a nominal focal length of 200.0 mm with a measurement uncertainty of ±2.5% is presented.

Abstract: We present a measurement technique to determine the thickness of a transparent glass plate (GP) by using a lateral shearing cyclic path optical configuration (CPOC) setup and polarization phase shifting interferometry (PPSI). In the technique, the GP introduces a longitudinal shift in the focus of the beam and, as a result, a spherical wavefront emerges from the lens, which is otherwise set for producing a collimated beam. Using CPOC, two laterally sheared orthogonally polarized beams are generated from the incident spherical wavefront. By applying PPSI, the slope of the optical path difference variation between the laterally sheared interfering beams is evaluated, and the radius of the spherical wavefront and the longitudinal shift of the beam focus are calculated. The thickness of the GP is determined from the standard relation between the longitudinal shift of the focus introduced by the GP and the thickness of the GP. Results obtained for a GP of 9.810mm thickness are presented.

Abstract: We present a technique for the measurement of roll angular displacement of a rotary stage using a lateral shearing cyclic path optical configuration (CPOC) setup and polarization phase shifting interferometry (PPSI). The CPOC setup, aligned on the rotary stage, laterally shears the input plane polarized spherical beam into a pair of orthogonally polarized beams, which when brought to the same state of polarization by a polarizer produce interference fringes similar to Young's fringes. Rotation of the CPOC setup in its plane introduces a phase change between the orthogonally polarized lateral sheared beams due to the change in angle of incidence of the input beam. The change in the phase results in spatial displacement of the interference fringes. Using PPSI, the phase, or the optical path difference change between the laterally sheared beams that is related to the rotation angle of the CPOC setup, is measured.

Abstract: We present a simple technique for simultaneous determination of refractive index and thickness of moderately thick plane-parallel transparent glass plates (GPs) using a cyclic path optical configuration (CPOC) setup and a wedge shear plate as lateral shearing interferometer. The CPOC setup is used to simultaneously focus the counterpropagating converging beams at a common point at its hypotenuse arm. The apparent thickness and real thickness of the test GP are determined by observing three retrocollimation positions of the GP surfaces with respect to the common focus point. The RI is obtained by dividing the real thickness with apparent thickness of the GP. Presented in this paper are the results obtained for a test GP with a thickness of 14.983 mm and a RI of 1.515.

Abstract: We present a new technique for the simultaneous measurement of refractive index and wedge angle of optical windows using Fizeau interferometry and a cyclic path optical configuration (CPOC). Two laterally separated beams are obtained from an expanded collimated beam using an aperture containing two rectangular openings. The test wedge plate is placed in one of the two separated beams. Using CPOC, these two beams are made to overlap and interfere, producing interference fringes in the overlapping region. The beams reflected from the front and back surfaces of the test wedge plate interfere and produce Fizeau fringes. The refractive index is related to the spacing of the above two beam fringes. The wedge angle is determined from the evaluated values of the refractive index and Fizeau fringe spacing. The results obtained for a BK-7 optical window are presented.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.