Integrating-bucket Method Research Articles

Image Quality Analysis of X-ray Grating Interferometer Using Integrating-bucket Method

Abstract Grating-based x-ray phase-contrast imaging has the potential to enhance image quality and provide inner structure details non-destructively. In this work, using grating-based x-ray phase-contrast imaging system and employing integrating-bucket method, the quantitative expressions of signal-to-noise ratios due to photon statistics and mechanical error are analyzed in detail. Photon statistical noise and mechanical error are the main sources affecting the image noise in x-ray grating interferometry. Integrating-bucket method is a new phase extraction method translated to x-ray grating interferometry; hence, its image quality analysis would be of great importance to get high-quality phase image. The authors’ conclusions provide an alternate method to get high-quality refraction signal using grating interferometer, and hence increases applicability of grating interferometry in preclinical and clinical usage.

Scale factor calibration method for integrating-bucket sinusoidal phase shifting interferometry

In order to recover the phase map φ(x, y) from sinusoidally phase-shifted interferograms obtained with the integrating-bucket method, two images Ψs and Ψc should be calculated first which are proportional to sin(φ) and cos(φ) respectively, and one of them needs to be scaled by a scale factor before they are used to solve the phase with the arctangent function. Because parameters deciding the scale factor such as the sinusoidal phase modulation amplitude and initial phase are difficult to be set accurately, miscalibration of it can always happen and result in significant error in the phase demodulation. Therefore, in this paper we propose a simple scale factor calibration method which performs the calibration directly with the phase-shifted interferograms and avoids the need for accurate parameter setting. First, we introduce high-density fringes to the interferograms; then, we construct a new image variable Γ with the squares of Ψs and Ψc; last, we find the value of the scale factor by minimizing the second harmonic amplitude in Γ’s spatial spectrum. Simulation results show that the proposed method is robust against noise and fringe distortion, and it was tested in a fiber-optic fringe projection profilometer.

Post-Processing Method for Image Reconstruction Enhancement in Integrating-Bucket-Based Full-Field Optical Coherence Tomography

An integrating-bucket method is widely used as a reconstruction tool for full-field optical coherence tomography (FF-OCT). However, it requires high-precision adjustments of the phase modulation parameters. If the parameters are not optimal, the reconstructed tomogram will incur severe artifacts. We propose a post-processing method for removing or reducing such artifacts by utilizing a correction factor extracted from a pre-reconstructed tomogram. FF-OCT imaging created using a coin verifies the effectiveness of the method not only for a single en face image but also for an entire 3-D image. It is expected that the proposed method will expand the application of FF-OCT from biomedical imaging to semiconductor wafers or display panel inspections.

Simple and fast scattering information in X-ray grating-based phase-contrast imaging

X-ray grating-based phase-contrast imaging is a potential imaging method with pre-clinical and clinical applications because it has the possibility of a large field of view and is compatible with X-ray tube sources. However, in X-ray grating-based phase-contrast imaging extraction methods have great importance to retrieve and separate information enabling high acquisition speed, reduced exposure dose and improved mechanical stability. Phase-stepping is a widely used extraction method in X-ray grating-based phase-contrast imaging. However, its discontinuous mode of acquisition leads to worse mechanical stability, exposure dose is generally high, which limits clinical applications significantly. In this work, the integrating bucket method is translated from visible light to X-ray regime, to extract scattering information of the investigated object. Both theoretical derivations with numerical simulation and experiments were performed to confirm the veracity and feasibility of the proposed method. In addition, we present the advantages of the proposed method over the phase-stepping method.

Integrating-bucket phase stabilization method for fiber-optic fringe projector

Ac phase tracking technique (PTAC) is an established and effective method for phase stabilization of fiber-optic fringe projectors (FoFP), but it may reduce the fringe visibility owing to the introduction of an extra sinusoidal phase modulation. In this paper we propose an integrating-bucket method to stabilize the phase of FoFPs which is applicable to both linear phase shifting (LPS) profilometry and sinusoidal phase shifting (SiPS) profilometry. The method requires no extra modulation of the interference phase; instead, it divides the interference signal period into N (N > 2) episodes with equal time intervals and directly integrates these episodes to obtain N discrete data. By manipulating these data the interference phase can be calculated and accordingly phase disturbance can be eliminated by the feedback loop. The proposed method is as effective as the PTAC technique but at the same time more computationally efficient because the operations involved are merely add, subtraction and arctangent solution. We built a digital phase controller with the proposed method, and managed to restrict the maximum phase drift of an FoFP to within 15 mrad in 5 min for both LPS and SiPS, which is similar to the result obtained with the PTAC technique. What’s more, we measured the mean value variation of the recovered phase map of a stabilized FoFP profilometer, and results are 30 mrad for LPS and 50 mrad for SiPS in 5 min.

High-contrast epi-fluorescence wide-field imaging of biological cells using integrating-bucket method

We present an optical lock-in detection scheme, called the integrating-bucket technique, as a signal-to-background ratio enhancement method for wide-field fluorescence imaging of biological cells. The proposed method uses sinusoidally modulated illumination light and captures four frames of fluorescence images, one per each quarter of the modulation period, by integrating the fluorescence intensity signal. The capability of this technique is demonstrated by imaging fluorescent bead solutions as well as labeled cells. The results show that the method yields a 4–10dB higher signal contrast than conventional fluorescence microscopy, and a background-free fluorescence image can be extracted within a sub-second time scale. Our findings indicate that the proposed method could be advantageous for the long-term study of live cells.

Sinusoidal phase-modulating fiber-optic interferometer fringe with a feedback control system.

A displacement measurement system using a fiber-optic interferometer fringe projector with a feedback control system is presented and demonstrated. The system utilizes the integrating bucket method to detect the desired phase or the displacement and Fresnel reflection signal to realize measurement of the disturbance and feed it back to the modulated signal of the laser at the same time. The continuous signal truly reflects the error information, as the output light and reflected light share the same optical path. Practical experiments validate the feasibility of this method.

Fiber-optic interferometer fringe projection using integrating bucket modulation

A new fiber-optic interferometer fringe projection with the integrating bucket method is presented. This method is based on the sinusoidal phase-modulating technique and makes use of Mach-Zehnder interferometer structure and Young's double pinhole interference principle to achieve interference fringe projection. Here, we consider the modulated signal with the modulation intensity of laser (companion amplitude modulation) m in the calculation directly, adjust the optimal value of z to accommodate different m, and calculate the initial phase with phase generated carrier technology at the same time. Preliminary results from the optimum phase modulation z and initial phase φ(0) are discussed.

Full-field surface plasmon resonance sensor for high resolution refractive index measurement using common-path heterodyne interferometer

This study presents a full-field surface plasmon resonance (SPR) sensor induced by attenuated total reflection (ATR)-couple for liquid refractive index measurement. The system adopts a common-path heterodyne interferometer to measure the phase difference between P- and S-wave after passing through the SPR sensor. In order to realize the full-field measurement, it adopts a three-frame integrating-bucket method. The experimental results show great consistency profile between single point and full-field liquid refractive index measurement from 1.330 to 1.340 RIU. It shows that the best sensitivity and resolution of a single pixel in charge couple device (CCD) for liquid refractive measurement are 3.3 × 10 4 (deg/RIU) and 3.53 × 10 −6 (RIU), respectively. As compared with traditional single-point method, the proposed method with a regular CCD has no degradation. Therefore, the system has many applications in chemistry and biology.

2D full-field measurement of oxygen concentration based on the phase fluorometry technique that uses the four-frame integrating-bucket method

A modulation system for the phase-resolved two-dimensional fluorescence phase imaging of a planar optical oxygen sensor is presented. The proposed system is based on the phase fluorometry technique and uses the four-frame integrating-bucket method. Integrating buckets with multiple frames are achieved using a complex programmable logic device to provide an external trigger to the charge coupled device (CCD). The oxygen-sensitive film is based on microporous film prepared using a sol–gel process with a Pt(II) complex, platinum tetrakis pentafluorophenyl porphine (PtTFPP); the film can be efficiently excited by a laser diode with a central wavelength of 405 nm. The experiment results show that the maximum phase difference between 0% and 100% gaseous oxygen is 22°. The 2D full-filed O 2 distribution imaging was found to be the most sensitive between 0% and 20% O 2. The combination of optical sensor technology and phase-resolved imaging allows the determination of the distribution of chemical or physical parameters in heterogeneous systems, making the proposed system a powerful testing tool for screening and mapping applications.

Self-mixing interferometry based on sinusoidal phase modulation and integrating-bucket method

In order to realize real-time displacement measurement with high resolution, sinusoidal phase modulation and integrating-bucket method are introduced in the self-mixing interference (SMI) system firstly. The phase of the laser beam is modulated by an electro-optic modulator (EOM) in the external cavity. Theoretical analysis, simulation results and error evaluation are presented. Experimentally, the micro-displacement of a high-precision commercial PZT is reconstructed and the reconstruction accuracy is on the order of nanometers for displacements of a few micrometers.

A 2-D Heterodyne Polarimeter for the Determination of Parameters in Twisted Nematic Liquid Crystal Cells

In this paper, an experimental method for measuring the 2-D cell parameter distribution of a twisted nematic liquid crystal is presented. Based on phase-sensitive imaging polarimeter with a common-path heterodyne configuration, this study adopts an integrating-bucket method to extract 2-D phase distribution on the detected heterodyne signal for the inverse calculation of the azimuth angle (entrance director angle), twist angle, and cell gap. The advantage of the heterodyne scheme introduces high sensitivity on phase detections, and the multiple parameters could be easily extracted through the genetic algorithm. The measurement range of the azimuth angle is from 0deg to 180deg without ambiguity. By using standard 8-bit gray-level charge-coupled device, the experimental results show that the 2-D standard deviation of 0.4deg, 0.7deg, and 0.032 mum in the measurement of azimuth angle, twist angle, and cell thickness have been obtained.

Full-field and full-range sequential measurement of the slow axis angle and phase retardation of linear birefringent materials

A method is proposed for obtaining full-range sequential measurements of the slow axis angle and phase retardation of linear birefringent materials (LBMs) using a full-field heterodyne interferometer with a charge-coupled device (CCD) camera and an image processing algorithm based on a three-frame integrating-bucket method. The dynamic ranges of the principal axis and phase retardation measurements extend from 0 degrees to 180 degrees and from 0 degrees to 360 degrees , respectively. The proposed method not only enables full-range measurements of the slow axis angle to be obtained, but also allows a decision to be made as to whether the principal axis labeled by the manufacturer is the slow axis or the fast axis. The standard deviations of the slow axis angle and phase retardation measurements are found to be 0.14 degrees and 0.27 degrees, respectively. In addition, it is shown that the noises induced by environmental disturbances are reduced by elimination of the dc component of the output light intensity in the image processing algorithm. We also investigate the sensitivity of the measured error caused by the orientation of LBM.

A Highly Phase-Sensitive Heterodyne Polariscope for the Full-Field Measurement of Twisted- Nematic Liquid Crystal

This study proposes a highly phase-sensitive imaging polariscope with a common-path heterodyne configuration for the mapping of spatially distributed cell gap of a twisted-nematic liquid crystal (TNLC). The polariscope adopts an electrooptic modulator incorporated with a quarter-wave plate to modulate the linear polarized light. By applying an integrating-bucket method, the two-dimensional (2-D) phase distribution of the detected heterodyne signal is extracted for the inverse calculation of the TNLC cell thickness. The proposing system has no need to remove or to rotate any optical elements in the measuring process and makes it possible to perform high-speed 2-D mapping. The dynamic range of retardation is around 0.7 mu m without ambiguity in the proposing method. By using a standard 8-bit gray level charged-coupled device (CCD), the experimental result shows that the standard deviation of 1.8 nm in the 2-D measurement of cell thickness has been obtained. The retardation resolution of 0.5 nm of the proposed method is also achieved and is better than that of the Stokes parameters determination method with high gray level CCD.

Disturbance-free high-speed sinusoidal phase-modulating laser diode interferometer

A surface profiler that incorporates a feedback controller to eliminate external disturbances is proposed and demonstrated. Its overall performance is dependent on the frequency response of the feedback loop. The frequency of the modulating signal strongly influences the response of the feedback controller. When we used the integrating-bucket method, the CCD camera had to be operated at a low-frequency video rate. Our technique uses a CCD camera equipped with an electronic shutter. The shutter function enables us to apply high-speed sinusoidal phase modulation to the conventional integrating-bucket method under the standard video rate.

Two-wavelength laser diode interferometer with time-sharing sinusoidal phase modulation.

We describe an interferometer system that uses two separate wavelengths to measure step height. The overlapping interference images detected by a CCD camera are easily separated by an ordinary integrating-bucket method and time-sharing sinusoidal phase modulation, in which two laser diodes are alternately modulated with a sinusoidal signal. A phase map is obtained only for the laser diode into which the modulation signal is injected. In this instance, a 1-microm step height was accurately detected.