Fringe Intensity Research Articles

Gamma Correction and Absolute Coordinate Residual Compensation for Triangular Patterns Phase Shifting Profilometry

Triangular patterns phase shifting profilometry is a method of structured light whose three-dimensional reconstructions are susceptible to error from gamma distortion. In practice, the luminance nonlinearity caused by the gamma distortion effect of a digital projector and a digital camera yields undesired fringe intensity changes, which substantially reduce the measurement accuracy, and while the effects of the gamma distortion diminish with an increasing number of employed phase-shifted patterns. A gamma correction method based on the pre-coding of projected grating is proposed to reduce the measurement error caused by the gamma distortion. By applying an appropriate pre-coding value to the projected patterns, the gamma distortion effect is attenuated and the accuracy is enhanced. The linear least square is compensated the absolute coordinate residuals still existing after gamma correction. To verify the presented method in this paper, a 3D shape measurement experimental system is constructed using digital video projector and CCD camera. The experiment results shown that, the gamma pre-coding correction reduce the maximum residuals error of absolute coordinate by 72.2%. After the linear least square compensation, the maximum absolute coordinate residual is only 6.1% of without any correction or compensation. The reconstruction surface of a complex curve surface is hardly any waviness, which is clearly noted in the reconstruction of the same tested object without any correction or compensation.

Processing and phase analysis of fringe patterns with contrast reversals

A method for demodulating fringe patterns containing contrast reversals is proposed. It consists of two steps. First, the absolute value of the fringe intensity distribution with its background removed is calculated. Then, two dimensional continuous wavelet transform with enhanced ridge extraction algorithm is applied to extract the fringe phase map. Proposed approach allows to dispose of phase jumps along the contrast reversal bands. The method requires only one image and has no special demands concerning the fringe pattern design. Method validity and robustness is confirmed using experimentally acquired time-averaged interferograms of vibrating silicon micromembranes.

Nonlinear formation of hot image and double intense image for gain-typed wirelike scatterers

The propagation of high-power laser beams modulated by gain-typed small-scale wirelike scatterer through a Kerr medium slab and free spaces is investigated. The formation of intense hot image is proved by analytical study and computer simulation. Moreover, the formation of double intense images is revealed by computer simulation. It is found that the double intense images are in a plane dozens of centimeters ahead the hot image plane and that the intensities of them are almost directly proportional to the intensity gain of the scatterer. The double intense image intensity and the hot image intensity have the similar variation tendency as the scatterer size increases, but the scatterer size difference between the maximums of them is dozens of micrometers. Moreover, interestingly, the distance between the two fringes for the double intense images has a relation with wavelength, similar to that for the distance between the fringes in single slot diffraction. Besides, the effect of object distance on the formation of double intense images is discussed. • The formations of hot image and double intense image are presented. • The double intense image plane is about 40 cm ahead the hot image plane. • The distance between the double intense image fringes increases as the wavelength increases. • The hot image and the double intense image peak at different scatterer size.

Laser feedback interferometry based on high density cosine-like intensity fringes with phase quasi-quadrature

A novel laser feedback interferometry based on high-order feedback is presented and realized for the first time. The interferometer uses a birefringence dual frequency laser and a tilted feedback mirror with high amplitude reflectivity to generate high density cosine-like optical fringes. These optical fringes have nanoscale resolution. Particularly, phase quasi-quadrature between the dual frequency fringes is obtained because of the phase shift caused by the changes of external optical path length. This phase characteristic can be used to distinguish the direction of movement easily. Under typical room conditions, the system's resolution is 0.51nm in 850μm range, and its 2 min displacement accuracy is 5nm.

Photoelastic Analysis on Different Retention Methods of Implant-Supported Prosthesis.

The aim of this study was to evaluate the stress distribution of different retention systems (screwed, cemented, and mixed) in 5-unit implant-supported fixed partial dentures through the photoelasticity method. Twenty standardized titanium suprastructures were manufactured, of which 5 were screw retained, 5 were cement retained, and 10 were mixed (with an alternating sequence of abutments), each supported by 5 external hexagon (4.0 mm × 11.5 mm) implants. A circular polariscope was used, and an axial compressive load of 100 N was applied on a universal testing machine. The results were photographed and qualitatively analyzed. We observed the formation of isochromatic fringes as a result of the stresses generated around the implant after installation of the different suprastructures and after the application of a compressive axial load of 100 N. We conclude that a lack of passive adaptation was observed in all suprastructures with the formation of low-magnitude stress in some implants. When cemented and mixed suprastructures were subjected to a compressive load, they displayed lower levels of stress distribution and lower intensity fringes compared to the screwed prosthesis.

Data Processing of the Middle and Upper Atmospheric Wind Retrieval Based on the Fabry‐Perot Interferometer

Abstract:Since the Doppler shifts of airglow orauroralemission lines due to neutral winds are extremely small, it is essential to determine the center position and radius of fringes with the uppermost accuracy. In this paper, a new method is presented for the center position and radius determination of incomplete interference fringes of Fabry‐Perot Interferometer (FPI). Due to the data noise comes from FPI instrument and space environment, the data pre‐processing was firstly carried out including mean filtering and wiener weightingadaptive filtering. Then, according to the Gauss distribution of fringe intensity, interference fringe peak coordinates were derived from both radius obtained using Gaussian fitting and fringe center coordinates. Subsequently, based on the peak coordinates, new center position and radius were estimated by using circular coordinate fitting with the least square method. Finally, the center coordinate and radius were determined by using the iterative operation between Gaussian fitting and circular coordinate fitting. The new method was applied to Fabry‐Perot interferometer data processing for wind velocity estimation of the middle and upper atmosphere. The retrieval results are 96.9537 m/s (actual wind velocity ∼100 m/s) and 7.5282 m/s (actual wind velocity ∼10 m/s), lower by 2.977 m/s and 2.465 m/s, respectively. Compared with theoretical values, both of them are less than 3 m/s, which suggests a tentatively reliable and practicable method of circle center and radius determination for wind retrieval of the middle and upper atmosphere.

Spatial coherence measurement of polychromatic light with modified Young’s interferometer

Partial spatial coherence is a fundamental concept in optical systems. Theoretically, the normalized mutual coherence function gives a quantitative measure for partial spatial coherence regardless of the spectral nature of the radiation. For narrowband light the degree of spatial coherence can be measured in terms of the fringe modulation in the classic Young's two-pinhole interferometer. Though not commonly appreciated, with polychromatic radiation this is not the case owing to the wavelength dependence of diffraction. In this work we show that with a modified two-beam interferometer containing an achromatic Fresnel transformer the degree of spatial coherence is again related to the visibility of intensity fringes in Young's experiment for any polychromatic light. This result, which is demonstrated both theoretically and experimentally, thus restores the usefulness of the two-pinhole interferometer in the measurement of the spatial coherence of light beams of arbitrary spectral widths.

Nonlinear imaging properties under the coeffect of two wirelike opaque scatterers

Nonlinear imaging in the propagation of a flat-topped circular Gaussian beam under the coeffect of two parallel wirelike opaque scatterers is investigated through computer simulation. The formation of hot images of each scatterer is proved. Moreover, the formations of two other kinds of intense images are found; one is called interference hot image and the other is called pseudo-second-order hot image. The former corresponds to one intense image fringe whose in-beam position is at the middle point between those of the two scatterers. This image fringe is in the plane a quarter of an object distance away from the exit surface of the Kerr medium slab, and its intensity is found comparable to that of the hot image. The latter corresponds to two intense image fringes in a plane near the second-order hot-image plane predicted for single phase-typed scatterer cases. The respective in-beam positions of these image fringes are close to the respective in-beam positions of the scatterers. Interestingly, the intensities of both kinds of images are found primarily determined by the copresence rather than the in-beam positions of the scatterers. Besides, though the hot-image intensity can be lower than the corresponding single opaque scatterer case, the maximum intensity inside the Kerr medium slab increases more quickly and thus is much higher at the exit surface. This is another threat to the safe running of the Kerr media for high-power laser systems.

A comparative study of one and two-dimensional wavelet-based techniques for noisy fringe patterns analysis

Today, more severe industrial constraints of realization require frequently a measurement and control techniques. The optical metrology methods allow a non-destructive control of a wide range of parameters (deformations, displacements…), with a very high accuracy. The phase retrieval is a successful measurement technique which allows the reconstruction of 3D images of physical parameters from the intensity fringe patterns. This research work articulates around the phase retrieval from a single fringe pattern using the wavelet-based techniques. We present here a comparative study of the phase retrieval algorithms based on the one and two-dimensional continuous wavelet transforms for getting access to the phase distribution via local analysis of a noisy fringe patterns. An evaluation through numerical simulations was conducted to prove the validity and the performance of the algorithms. The main advantage of these techniques is their ability to offer a metrological solution adapted to the dynamic analysis needs in disruptive environments.

Phase shift calibration based on Fresnel diffraction from phase plates

When a transparent plane-parallel plate is illuminated at a boundary region by a parallel monochromatic beam of light, Fresnel diffraction occurs because of the abrupt change in phase imposed by the finite change in refractive index at the plate boundary. The intensity of the diffraction fringes varies periodically with changes in the optical path difference of the light passing through the plate edge. The optical path difference depends on the incident angle of the light, the refractive index of the plate and surrounding medium, and the wavelength of the light. Plotting the intensity of the diffraction fringes versus optical path difference provides a general phase shift method for phase change measurement, in which the phase shift is made by changing the incident angle. Using this technique we have measured the phase change imposed by the refractive index profile of a single mode optical fiber.

Phase Tuning Characteristics of a Double-Longitudinal-Mode He-Ne Laser with Optical Feedback

The phase tuning characteristics of a double-longitudinal-mode He-Ne laser with optical feedback are demonstrated. The phase behaviors of the two adjacent longitudinal modes are studied with different laser cavity lengths at the weak feedback level, and it is found that the phase difference of the two modes can be 0 to 180° along with the changing of the length of external cavity. The high-density intensity fringes are obtained with asymmetric feedback cavity at a strong feedback level. In particular, the phase difference is also observed between the two high-density fringes of adjacent modes, which have the potential to develop a direction sensitive laser feedback interferometer with high resolution. A simple theoretical analysis is presented, which fits well with the experimental results.

Analysis on the effect of UV beam intensity profile on the refractive index modulation in phase mask based fiber Bragg grating writing

This paper presents an analytical study on the role of intensity profile of writing UV beam on fringe intensity distribution and its effect on the refractive index modulation of fiber Bragg gratings (FBGs) written by the phase mask technique. It is shown that during FBG inscription, the induced average refractive index and refractive index modulation profiles in the photosensitive fiber changes by the continuous exposure of UV fringes of non-uniform intensity distribution. This is explained on the basis of non-linear growth of refractive index and its saturation at different sections of the grating occurring at different irradiation times. The evolutions of refractive index modulation of FBGs written at different distances from the phase mask are also different. Effect of varying refractive index modulation profiles on evolution of reflection spectra of fiber Bragg gratings are discussed. Controlled UV fringe exposure times for FBG fabrication and fringeless UV exposure for post-fabrication processing are discussed in view of grating apodisation.

Effect and suppression of secondary fringes in FATWindII

By considering the instrument as a complex operator on the incident electric field, a model to calculate secondary fringes of the Field-widened, Achromatic, Temperature-compensated Wind Imaging Interferometer (FATWindII) has been built. The distribution of secondary fringes on a charge coupled device detector has been plotted. The effects of secondary fringes on inversion errors of temperature and wind velocity have been presented. The results show that antireflection coating on the air/glass interface cannot meet the accuracy requirement of FATWindII. A theoretical method for calculating the optimal wedge angles of compensating glasses is derived to suppress the secondary fringes while preserving the primary ones. By adopting both methods, coating with antireflection film and shaping wedge compensating glasses, the relative intensity of secondary fringes is reduced to below 2.5% and the inversion errors of temperature and wind velocity introduced by the effects of secondary fringes can be minimized to about 0.05 K and 0.045 ms(-1), respectively.

High dynamic range fringe acquisition: A novel 3-D scanning technique for high-reflective surfaces

This paper presents a novel 3-D scanning technique for high-reflective surfaces based on phase-shifting fringe projection method. High dynamic range fringe acquisition (HDRFA) technique is developed to process the fringe images reflected from the shiny surfaces, and generates a synthetic fringe image by fusing the raw fringe patterns, acquired with different camera exposure time and the illumination fringe intensity from the projector. Fringe image fusion algorithm is introduced to avoid saturation and under-illumination phenomenon by choosing the pixels in the raw fringes with the highest fringe modulation intensity. A method of auto-selection of HDRFA parameters is developed and largely increases the measurement automation. The synthetic fringes have higher signal-to-noise ratio (SNR) under ambient light by optimizing HDRFA parameters. Experimental results show that the proposed technique can successfully measure objects with high-reflective surfaces and is insensitive to ambient light.

Squeezing bandwidth controllable twin beam light and phase sensitive nonlinear interferometer based on atomic ensembles

We review our recent experimental progress in quantum technology employing amplification effect of four-wave mixing in a rubidium vapor. We have produced an intensity difference squeezed light source at frequencies as low as 1.5 kHz which is so far the lowest frequency at which squeezing has been observed in an atomic system. Moreover, we find that the bandwidth of our squeezed light source can be controlled with light intensity pumping. Using our non-classical light source, we have further developed a nonlinear Mach-Zehnder (MZ) interferometer, for which the maximum fringe intensity depends quadratically on the intensity of the phase-sensing field at the high-gain regime, leading to much better sensitivity than a linear MZ interferometer in which the beam splitters have the same phase-sensing intensity. The quantum technologies developed by our group could have great potential in areas such as precision measurement and quantum information.

Dynamic tracking down-conversion signal processing method based on reference signal for grating heterodyne interferometer

Traditional displacement measurement systems by grating, which purely make use of fringe intensity to implement fringe count and subdivision, have rigid demands for signal quality and measurement condition, so they are not easy to realize measurement with nanometer precision. Displacement measurement with the dual-wavelength and single-grating design takes advantage of the single grating diffraction theory and the heterodyne interference theory, solving quite well the contradiction between large range and high precision in grating displacement measurement. To obtain nanometer resolution and nanometer precision, high-power subdivision of interference fringes must be realized accurately. A dynamic tracking down-conversion signal processing method based on the reference signal is proposed. Accordingly, a digital phase measurement module to realize high-power subdivision on field programmable gate array (FPGA) was designed, as well as a dynamic tracking down-conversion module using phase-locked loop (PLL). Experiments validated that a carrier signal after down-conversion can constantly maintain close to 100 kHz, and the phase-measurement resolution and phase precision are more than 0.05 and 0.2 deg, respectively. The displacement resolution and the displacement precision, corresponding to the phase results, are 0.139 and 0.556 nm, respectively.

Single high-order round-trip feedback effects in orthogonally polarized dual frequency laser

We present the effects of single high-order round-trip feedback in orthogonally polarized dual frequency laser. The high quality intensity fringes of two orthogonally polarized lights are obtained, which are cosine-like. The fringe frequency of a single high-order round-trip feedback is five times that of the conventional optical feedback. Even higher frequencies are possible with this setup. Particularly, there is a phase difference between two orthogonal polarized lights in single high-order round-trip feedback and the phase difference is determined by the feedback order, the length of the external cavity, and the frequency difference of the two orthogonal polarized lights. A theoretical analysis based on a compound cavity model of a dual frequency laser agrees well with the experimental results. These results provide a potential application in precision measurement with both directional discrimination and high optical resolution.

High density fringes and phase behavior in birefringence dual frequency laser with multiple feedback

The high density intensity fringes and phase behavior in birefringent dual frequency laser with multiple feedback are studied for the first time. It was discovered that the fringes of output intensity are made of bipolar pulses with symmetric external cavity feedback and the fringe density is as high as compared to the conventional feedback. The high density cosine-like fringes are obtained with asymmetric external cavity feedback by adjusting the tilt angle of the feedback mirror and the fringe density is about 22 times higher compared to the conventional feedback. Moreover, there is a phase difference between the two cosine-like fringes and the phase difference is varied with the change of the external cavity length. The experimental results and a theoretical analysis are presented in this work. These results offer a large increase in the resolution for the optical feedback interferometer with the birefringence dual frequency laser.

Research of secondary fringes in field-widened achromatic, temperature-compensated wind, imaging interferometer (FATWindII)

The accurate method to calculate secondary fringes of field-widened, achromatic, temperature-compensated wind imaging interferometer (FATWindII) is presented, and the distribution of secondary fringes on instrument detector is simulated. The effects of secondary fringes on inversion errors of temperature and wind velocity are calculated. The formulas of modulation functions and phase shifts are derived when the wedge compensating glasses with arbitrary tilt angles, and the optimal tilt angles of wedge compensating glasses are obtained in FATWindII. By adopting antireflection film and wedge compensating glasses, the relative intensity of secondary fringes is reduced to below 2.5%, and the inversion errors of temperature and wind velocity introduced by the effects of secondary fringes can be minimized to about 0.05 K and 0.045 m·s-1 respectively. The research has important theoretical significance and practical guidance for the FATWind instrument design, fabrication and calibration.

Technology of polarization interference imaging spectral based on pupil division and angle shear

With the combination of pupil division, Wollaston prism angle shear and Savart plate lateral shear interference, a new technology that can aquire the message of imaging, polarization and spectrum simultaneously is presented. The system works at the pushing mode with neither mechanical movable nor electrically tunable device, and four quarters of the single charge-coupled device can get four interferograms of different polarization states (two polarization-difference spectral imagings). The device is discussed in detail, and the relationship between azimuth of the prism principal cross section and the output light intensity is analyzed, and then system parameters are optimized. In the paper, we derive the interference fringe intensity distribution formula, use computer numerical simulation to verify the feasibility and accuracy of this method, and thus provide an important theory basis and the practice instruction for designing a new type of imaging spectrometer and its engineering applications.