Suppressing carrier removal error in the Fourier transform method for interferogram analysis

Fan, Qi; Hongru, Yang; Li, Gaoping; Zhao, Jianlin

doi:10.1088/2040-8978/12/11/115401

Cited by 19 publications

(5 citation statements)

References 14 publications

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“…There are different tools available to transform the time series into these components including the Fourier and Wavelet transformations. The Fourier transformation requires the stationarity of the data [ 47 ] whereas the macroeconomic variables are less likely to be integrated of order zero (i.e., stationary). To explore the scale-dependent causal linkages between inflation and policy rate, we employ Wavelet transformation to decompose the series into various frequency scales.…”

Section: Methodsmentioning

confidence: 99%

Inflation targeting: A time-frequency causal investigation

Islam,

Ahmed

2023

PLoS ONE

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The enduring discourse regarding the effectiveness of interest rate policy in mitigating inflation within developing economies is characterized by the interplay of structural and supply-side determinants. Moreover, extant academic literature fails to resolve the direction of causality between inflation and interest rates. Nevertheless, the prevalent adoption of interest rate-based monetary policies in numerous developing economies raises a fundamental inquiry: What motivates central banks in these nations to consistently espouse this strategy? To address this inquiry, our study leverages wavelet transformation to dissect interest rate and inflation data across a spectrum of frequency scales. This innovative methodology paves the way for a meticulous exploration of the intricate causal interplay between these pivotal macroeconomic variables for twenty-two developing economies using monthly data from 1992 to 2022. Traditional literature on causality tends to focus on short- and long-run timescales, yet our study posits that numerous uncharted time and frequency scales exist between these extremes. These intermediate scales may wield substantial influence over the causal relationship and its direction. Our research thus extends the boundaries of existing causality literature and presents fresh insights into the complexities of monetary policy in developing economies. Traditional wisdom suggests that central banks should raise interest rates to combat inflation. However, our study uncovers a contrasting reality in developing economies. It demonstrates a positive causal link between the policy rate and inflation, where an increase in the central bank’s interest rates leads to an upsurge in price levels. Paradoxically, in response to escalating prices, the central bank continues to heighten the policy rate, thereby perpetuating this cyclical pattern. Given this observed positive causal relationship in developing economies, central banks must explore structural and supply-side factors to break this cycle and regain control over inflation.

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Section: Methodsmentioning

confidence: 99%

Inflation targeting: A time-frequency causal investigation

Islam,

Ahmed

2023

PLoS ONE

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“…To eliminate the carrier and background phase quickly and accurately, the algorithms with aid of the utilization of specimen-free holograms have been presented [14,19]. In contrast to fitting techniques or special compensation methods [22][23][24][25][26], the algorithms can remove the background phase without complex processes and high computation cost. Assuming specimen-free holograms with intensity distributions H 1 ʹ and H 2 ʹ are captured with the same phase shift Δθ, their retrieved complex result can be obtained as:…”

Section: Phase Retrievalmentioning

confidence: 99%

Slightly off-axis flipping digital holography using a reflective grating

Bai

Min

Yang

et al. 2020

J. Opt.

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A slightly off-axis digital holography is proposed using the flipping interferometry with a reflective grating to obtain the quantitative phase distribution. The setup is established based on a modified 4f optical system using an improved flipping module with a reflective grating and a retro-reflector made of a two-mirror construction. The input plane of the system is divided into two windows: one for object beam and the other for reference beam. Employing the flipping module, the interference patterns can be obtained by flipping the images of the object and reference beams. By translating the +1 diffraction order of the reflective grating, two carrier holograms with a phase shift between them can be obtained in two exposures. The reconstructed quantitative phase distribution of a specimen can be acquired with a simple slightly off-axis retrieval method aided by specimen-free holograms. Many measurements on both thick and thin phase specimens are performed to prove the validity of our method.

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“…In order to obtain the correct spectrum centering, some scholars have developed the research on the carrier frequency elimination methods. In 2010, Fan et al [61] analyzed that if the carrier frequencies were not an integer multiple of the frequency interval, the peak coordinates of C and C* in Equation 13would not be equal to the carrier frequencies. Aimed at the problem, a carrier frequency judgment method by means of a spectral centroid was presented to suppress the carrier removal error.…”

Section: Tilt Phase Error Compensationmentioning

confidence: 99%

Recent Progress on Aberration Compensation and Coherent Noise Suppression in Digital Holography

Liu

Wang

2018

Applied Sciences

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Digital holographic microscopy (DHM) is a topographic measurement technique that permits full-field, nondestructive, dynamic, quantitative amplitude, and phase-contrast imaging. The technique may realize the lateral resolution with submicron scale and the longitudinal resolution with subnanometer scale, respectively. Improving imaging quality has always been the research focus in DHM since it has a direct effect on the precise topographic measurement. In this paper, the recent progress on phase aberration compensation and coherent noise suppression is reviewed. Included in this review are the hologram spectrum's centering judgment methods of side band in tilt phase error compensation, the physical and numerical compensation methods in phase aberration compensation, and the single-shot digital process methods in coherent noise suppression. The summaries and analyses for these approaches can contribute to improving the imaging quality and reducing the measurement error of DHM, which will further promote the wider applications of DHM in the topographic measurement fields, such as biology and micro-electro mechanical systems.

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Suppressing carrier removal error in the Fourier transform method for interferogram analysis

Cited by 19 publications

References 14 publications

Inflation targeting: A time-frequency causal investigation

Inflation targeting: A time-frequency causal investigation

Slightly off-axis flipping digital holography using a reflective grating

Recent Progress on Aberration Compensation and Coherent Noise Suppression in Digital Holography

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