Fringe Plane Research Articles

Development of tilted fibre Bragg gratings using highly coherent 255 nm radiation

This paper reports the study on development of tilted fibre Bragg gratings using highly coherent 255 nm radiation, obtained from the second harmonic generation (SHG) of copper vapour laser (CVL). The transmission and reflection spectra of the tilted fibre Bragg gratings (TFBG) were studied for the tilt angles of 0° (normal FBG), 1°, 3° and 4° between the fibre axis and the interference fringe plane. It was observed that as the angle of fibre axis and phase mask increased, the main Bragg peak shifted towards the higher wavelength and transmission dip decreased. The transmission dip of the cladding mode first increased and then decreased after reaching a maximum with the increase in the tilt angle.

Axial resonance of periodic patterns by using a Fresnel biprism

This paper proposes a method for the generation of high-contrast localized sinusoidal fringes with spatially noncoherent illumination and relatively high light throughput. The method, somehow similar to the classical Lau effect, is based on the use of a Fresnel biprism. It has some advantages over previous methods for the noncoherent production of interference fringes. One is the flexibility of the method, which allows the control of the fringe period by means of a simple axial shift of the biprism. Second is the rapid axial fall-off in visibility around the high-contrast fringe planes. And third is the possibility of creating fringes with increasing or with constant period as the light beam propagates. Experimental verifications of the theoretical statements are also provided.

Projection angle for C-arm-assisted insertion of posterior acetabular column screws

Objective To explore the optimal projection angle when cannulated screws are placed into the posterior acetabular column under the help of a C-arm fluoroscopic unit. Methods Twenty acetabular sides in 10 corpses were scanned with CT to find the scan plane which contained the maximum cross section of the femoral head. On this scan plane, we measured angle α which was between the posterior surface of the posterior column and the coronal plane, and angle β which was between the posterior surface of the posterior column and the acetabular fringe plane. Results Angle α was 28. 2°± 2. 3° and angle β was 95.4°± 5.3°. Conclusions When the projection direction is paralleled with the posterior surface of the posterior column, the angle between the bulb and the coronal plane is about 30°, 15° more than the obturator oblique view. Compared with the obturator oblique view, 30° can show more exactly the spatial relation between the screw and the posterior surface of the posterior column. The direction perpendicular to the acetabulum fringe plane can also be considered for projection. Key words: Surgical procedures, minimally invasive; Tomography, spiral computed; Tomography, X-ray computed; Bone nails

An Alternative Approach for Imaging in Optical Interferometry

We describe a mathematical formalism for the teaching optical interferometer concept developed by P. Lawson. In this experiment, the co-addition of several interferometric fringe patterns obtained for different baselines between individual telescopes is the image of the source, for the simple reason that the fringe patterns build up the image of the observed source through a convolution product. This basic principle is of interest since it allows one to tackle the image reconstruction for optical long-baseline interferometry through an approach which is complementary to the use of the Fourier plane. Thus, image reconstruction can be thought of in the fringe plane. It allows a better understanding of the fundamental limits of the image dynamical range.

Optoelectronic moire projector for real-time shape and deformation studies of the tympanic membrane

Moire´ topography is a valuable technique for studying the shape and deformation of delicate biological structures such as the tympanic membrane. A projection moire´ method is described that can produce both shape and deformation fringes in real time, at a rate of 25 interferograms per second. The apparatus is based on electronic subtraction of the projected grating line image of the object and a reference grating line image stored in digital memory. The image field and fringe plane distance can be adjusted to the object dimensions. Using a fringe plane distance of 82 mm, a precision of 5 mm over a measuring depth of 0.4 mm is demonstrated by measurements on a spherical calibration object. The application to in vitro shape and deformation measurements of the gerbil tympanic membrane is demonstrated.

Design of a static Fourier-transform spectrometer with increased field of view

We present several novel designs of static Fourier-transform spectrometers based on Wollaston prisms. By numerical modeling we show the increased field of view that can be obtained when an achromatic half-wave plate is included between the prisms or when prisms fabricated from positive and negative birefringent materials are combined. In addition, we model how a single Wollaston prism with an inclined optic axis produces a fringe plane localized behind its exit face, thus enabling the design of a static Fourier-transform spectrometer based on a single Wollaston prism.

Shape Control of Plates using Piezoceramic Elements

the potential error magnitudes associated with angle bias. The effect of turbulence is also shown in comparing Figs. 2a and 2b. As would be expected, the increased turbulence tends to increase the PPD when the mean flow angle is close to parallel to the fringe planes. However, the PPD is slightly reduced when the mean flow angle is close to perpendicular to the fringe planes. Of particular interest are the results shown in Fig. 3, which were obtained using V f / V p = 2. As a rule of thumb, LV users typically use this ratio to ensure uniform instrument response for all flow angles, based on predictions of the Whiffen et al. theory. The data presented in Fig. 3 show that uniform instrument response is not achieved at V//VP = 2. For optical and flow parameters that are representative of those present in this experimental setup, the simulation shows that, for practical limits of Vf/Vp, perfectly uniform response will not be achieved. For example, using these parameter values and Vf/ Vp = 4, the simulation predicts a minimum PPD of 87% at a mean flow angle of 90 deg. Although this PPD is relatively high, it still does not ensure isotropic instrument response. Acknowledgments This work was performed under the auspices of Grant NGT-50868 provided through the NASA Langley Research Center while the first author was in residence at West Virginia University. The authors wish to thank James F. Meyers for suggesting the research presented in this paper.

Aztec surface-relief volume diffractive structure

Surface-relief diffractive optical elements made interferometrically typically are recorded with the off-axis technique, for which the fringe maxima lie on planes that are predominantly perpendicular to the recording surface and with an intensity variation that is sinusoidal. Such a structure can be readily replicated by mechanical means. Volume diffractive elements, on the other hand, which result from beams propagating in opposite directions, have fringe planes that are predominantly parallel to the surface and, as such, cannot be mechanically replicated. A new type of surface-relief diffractive structure called Aztec is discussed here; it combines features of both off-axis and volume recording geometries, with the result being a phase-quantized, or terraced, surface-relief pattern. The groove profile, instead of being sinusoidal, resembles a stepped pyramid. This structure has been replicated by metal mastering and molding into plastic in the same manner as conventional embossed surface-relief elements, but the diffraction characteristics are typical of volume phase reflective structures. Light of a given wavelength is resonantly diffracted from steps that are a half-wavelength apart and with a bandwidth that is inversely proportional to the number of steps. Color control has been achieved by overcoating the step structure with a clear dielectric that shifts the resonant wavelength to a new value, depending on the index of refraction of the dielectric. Information content is less for the single-layered, but stepped, Aztec structure than for the usual multilayered volume diffractive element. Deep Aztec stepped gratings have also been fabricated by optical lithography, using multiple-mask techniques.

Automatic calibration method for phase shift shadow moire interferometry

A new calibration procedure for phase shift moire interferometry is proposed. The method does not ask for a high precision machined calibration object and makes use only of the moire setup itself. The procedure is fast and fully automatic. The fringe plane distance lambda was determined with a precision of 1.3%. We present control measurements on a plane surface and a perfect sphere confirming the value and the precision of lambda.

Speckle photography of out-of-plane motion: effect of multiple-exposures in free space geometry of recording

A theoretical and experimental analysis is carried out of the fringe formation in speckle photography of the out-of-plane motion of a diffuse object. Multiple exposure technique has been used to sharpen the fringes. Intensity distribution at the fringe plane is investigated in case of filtering by collimated beam of light for double and multiple exposures. A good agreement is found between the theoretical and experimental results.

Effect of an angular bias on LDA measurements in supersonic turbulent flow

The problem of a laser Doppler anemometer's statistical response to the velocity direction of particles scattering in space has been studied for many years. This phenomenon introduces a statistical bias distinct from the classical bias related to velocity fluctuations. Though the latter has corrected some controversial application, the only answer found to counter the angular bias remains, for most experimenters, the utilization of Bragg cells. It is not always possible to use such a device, however, and this is particularly true in supersonic flows. The angular bias, inevitable in this case, shows increased effects when the normal to the fringe plane is inclined with respect to the mean velocity direction. Analysis of the phenomenon in the more complex case of a two-component anemometer and a supersonic flow helps to show how measurements of velocity fluctuations in a boundary layer quite close to the wall may include significant errors because of this bias.

Experimental and theoretical evaluation of the efficiency of an off-axis volume holographic lens

The properties of a high-efficiency lens, fabricated in bleached photographic emulsion, are discussed. A symmetric off-axis configuration is adopted, and approximately uniform dielectric-constant modulation is achieved. The lens is tested using a probe beam of small diameter. Experimental results are presented for replay under on- and off-Bragg conditions, both in air and under index-matched conditions. 59±3% efficiency is achieved across the lens aperture. Variations in efficiency are attributed to rotation of fringe planes, and results are compared with local one-dimensional theory.

Fringe shifts in multiple-beam Fizeau interferometry

A computer program was developed to compute the profile of multiple-beam Fizeau fringes and was tested against laboratory observations. By using the program as a tool for studying the behavior of the fringes, a simplified model of the fringe formation process was developed. The shifts of the fringes from their expected locations are caused primarily by a reduction in spatial frequency that is due to the oblique projection of the fringes onto the detector. The angle at which the fringes are inclined to the input beam of the interferometer may be calculated by using a phase law developed by Brossel [ Proc. Phys. Soc.59, 224 ( 1947)] and is independent of the reflectivity of the cavity. Once the orientations of the fringe planes and the detector are known, the fringe shifts may be calculated by using simple trigonometry. Although the absolute shift of a particular fringe may be an appreciable fraction of a fringe spacing, neighboring fringes have nearly identical shifts, making the relative fringe shift inconsequential. The finesse of the fringes may be increased by either tilting the Fizeau cavity or defocusing the detector optics. Unlike the tilt angle required to minimize the fringe shift, the tilt angle that maximizes the finesse is a strong function of the cavity reflectivity.

Two-Component Dual-Scatter Laser Doppler Velocimeter with Frequency Burst Signal Readout

A dual-scatter laser Doppler velocimeter (LDV) system designed for measuring wind tunnel flow velocity is described. The system simultaneously measures two orthogonal velocity components of a flowing fluid at a common point in the flow. Essential single-velocity component dual-scatter concepts are presented to simplify the description of the more sophisticated two-component system. To implement the two-component system three laser beams with a 0 degrees , 45 degrees , and 90 degrees polarization plane relationship are focused to a common point in the flow by the system-transmitting optics. The beams interfere to form two perpendicular sets of interference fringe planes that are orthogonally polarized. The system-receiving optics collect and separate the orthogonally polarized components of laser radiation scattered from micron-size particles moving with the flowing fluid through the ringes. The system requires no artificial seeding, since intrinsic test section aerosols are utilized for radiation scattering. The passage of each scatter particle through the interference fringes simultaneously produces two frequency-burst-type photodetected signals, the frequencies of which are directly proportional to two perpendicular components of particle velocity. The system photodetection, signal-conditioning, and data acquisition instrumentation is specifically designed to process the frequency burst information in the time domain as opposed to spectrum analysis or frequency domain processing. The system was initially evaluated in an AEDC wind tunnel operating over a Mach number range from 0.6 to 1.5. The LDV and calculated wind tunnel mean velocity data agreed to within 1.25%; flow direction deviations of a few milliradians were resolved.

Holographic Optical Element for Visual Display Applications

Off-axis and off-bisector reflection-type holographic visual display elements have been recorded in dichromated gelatin deposited on planar or spherical shell substrates of glass or Plexiglas. A procedure for bonding gelatin to Plexiglas is given. Holographic elements are recorded at the argon wavelength of 514.5 nm and reconstructed with spectral lines from a low pressure mercury arc lamp. Measured image characteristics for a flat substrate hologram agree with ray-tracing calculations. A swelling of the gelatin by approximately 6.6% after processing does not perceptibly affect the dispersion, astigmatism, or distortion in the image, that is, the grating equation depends on the spacing between the fringes on the surface of the gelatin and is not affected by the swelling or shrinking. However, the Bragg equation depends on the distance normal to the fringe planes and is affected by thickness changes of the gelatin. Therefore, this thickness change is taken as an independent parameter and used to adjust the wavelength for maximum diffraction efficiency, without affecting the image angle. Data reveal a near linear relationship between the dichromate concentration of 0.5-10% used to photosensitive the gelatin and the display wavelength of maximum diffraction efficiency. Lateral dispersion is 0.12 +/- 0.01 degrees / nanometer for both planar and spherical shell substrate elements recorded in quite similar geometry, but their astigmatisms are not alike.