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Journal articles on the topic 'Apodization function'

Author: Grafiati

Published: 5 June 2025

Last updated: 24 June 2025

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1

Alsharef, Mohammad1, S. Alzaidi1 Mohammed, M. A. Eid1 Mahmoud, et al. "First order surface grating fiber coupler under the period chirp and apodization functions variations effects." Indonesian Journal of Electrical Engineering and Computer Science 25, no. 2 (2022): 1020–29. https://doi.org/10.11591/ijeecs.v25.i2.pp1020-1029.

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The paper has demonstrated the first order surface grating fiber coupler under the period chirp and apodization functions variations effects. The Fiber coupler transmittivity/reflectivity, the fiber coupler grating index change and the fiber coupler mesh transmission cross-section are clarified against the grating length with the quadratic/cubic root period chirp and Gaussian/uniform apodization functions. The fiber coupler delay and dispersion are simulated and demonstrated with grating wavelength with quadratic/cubic root period chirp and Gaussian/uniform apodization function. As well as the fiber coupler output pulse intensity is simulated against the time period with the quadratic/cubic root period chirp and Gaussian/uniform apodization function. The fiber coupler peak intensity variations against the transmission range variations is also demonstrated by OptiGrating simulation software.

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2

Andra, Naresh Kumar Reddy, Udaya Laxmi Sriperumbudur, and Karuna Sagar Dasari. "Corollaries of Point Spread Function with Asymmetric Apodization." International Journal of Optics 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/1347071.

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Primary energy based corollaries of point spread function with asymmetric apodization using complex pupil function have been studied in the case of three-zone aperture. Merit function like semicircled energy factor, excluded semicircled energy, and displaced semicircled energy were analyzed with respect to Airy case in terms of phase and amplitude apodization. Analytical results have been presented for the optimum parameters of phase and amplitude asymmetric apodization.

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3

Mohammad, Alsharef, Mohammed S. Alzaidi, Mahmoud M. A. Eid, et al. "First order surface grating fiber coupler under the period chirp and apodization functions variations effects." Indonesian Journal of Electrical Engineering and Computer Science 25, no. 2 (2022): 1020. http://dx.doi.org/10.11591/ijeecs.v25.i2.pp1020-1029.

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<p>The paper has demonstrated the first order surface grating fiber coupler under the period chirp and apodization functions variations effects. The Fiber coupler transmittivity/reflectivity, the fiber coupler grating index change and the fiber coupler mesh transmission cross-section are clarified against the grating length with the quadratic/cubic root period chirp and Gaussian/uniform apodization functions. The fiber coupler delay and dispersion are simulated and demonstrated with grating wavelength with quadratic/cubic root period chirp and Gaussian/uniform apodization function. As well as the fiber coupler output pulse intensity is simulated against the time period with the quadratic/cubic root period chirp and Gaussian/uniform apodization function. The fiber coupler peak intensity variations against the transmission range variations is also demonstrated by OptiGrating simulation software.</p>

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4

James, D. I., W. F. Maddams, and P. B. Tooke. "The Use of Fourier Deconvolution in Infrared Spectroscopy. Part I: Studies with Synthetic Single-Peak Systems." Applied Spectroscopy 41, no. 8 (1987): 1362–70. http://dx.doi.org/10.1366/0003702874447374.

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Studies with synthetic single-peak systems have provided information on a range of factors capable of limiting the utility of Fourier deconvolution for peak finding in vibrational spectra. The merits of six apodization functions for controlling Gibbs oscillations resulting from truncation and background effects have been determined. The triangularsinc and triangular-squared functions are the most effective, and the Gaussian function is the least satisfactory. The presence of asymmetry and a degree of Gaussian character in the band shape should not prove a serious limitation for most qualitative and quantitative applications. The peak heights following deconvolution are linear functions of the resolution enhancement factor, K, the constant of proportionality being determined by the particular apodization function employed. By contrast, the areas of deconvoluted bands are sensibly independent of the apodization function. This factor opens the way to quantitative studies on deconvoluted band systems.

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5

Kaesar Abdul Hassan Abbas, Ghada Sabah Karam, and Ziad M. Abood. "Effect of Variable Apodization Functions on the Image Quality of Optical System." International Journal of Scientific Research in Science, Engineering and Technology 12, no. 1 (2025): 148–52. https://doi.org/10.32628/ijsrset25121159.

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Apodization of pupil with various amplitude filters have been investigated for altering the point spread function for diffraction-limited optical systems' pictures of point objects by employing various filters, such as connes and tringle filters. We have shown that, for different levels of amplitude apodization, the lower values. An observation that these filters give good results for lower values of the apodization parameter. (FWHM) Full width at half maximum of the point spread function (PSF) is smaller than the Airy PSF, improving the performance of the optical system.

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Shailaja, P., D. Karuna Sagar Rao, and S. Venkateshwara Rao. "Studies On Point Spread Function With Three Zone Complex Pupil Function." IOSR Journal of Applied Physics 16, no. 5 (2024): 27–30. http://dx.doi.org/10.9790/4861-1605012730.

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The point spread function of a complex three-zone pupil function is analyzed in the presence of primary spherical aberration and defocus. The second zone is phase-shifted by -π/5, and the third zone by +π/7. Apodization is applied using three filters: a Bartlett amplitude filter for the inner zone, a shaded amplitude filter for the second zone, and a Hanning amplitude filter for the third zone. The primary goal is to enhance the central maximum's intensity, eliminate side lobes, and reduce the radius of the first dark ring. A notable increase in the central maximum occurs when the apodization parameter is set to β = 1.0, and minimized the first dark ring's radius under high spherical aberration and defocus

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7

Qin, Yusheng, Xiangxian Li, Xin Han, Jingjing Tong, and Minguang Gao. "Research on Spectral Restoration and Gas Concentration Inversion Accuracy Based on Quasi-Trapezoidal Window." Photonics 9, no. 11 (2022): 885. http://dx.doi.org/10.3390/photonics9110885.

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The Fourier transform is a popular method for analyzing and processing interference data in which spectrum leakage occurs. Generally, window function (also called apodization function) weighting is employed to limit spectrum leakage. A rectangular window with optimal main-lobe performance and the Rife-Vincent (R-V) window were introduced to improve the window function performance, resulting in the establishment of a quasi-trapezoidal window function. Based on the experimental interference data, the quasi-trapezoidal window function was used in the spectral restoration process. The experimental results show that when the apodization degree of the quasi-trapezoidal window was 1.06, the spectral resolution was improved by 17.46% compared with that of the Hanning window; when the apodization degree was 2.71, the spectral signal-to-noise ratio (SNR) was improved by 130.09% compared with that of the Blackman-Harris window function. In the propane (C3H8) and ethylene (C2H4) gas concentration inversion experiment, when the apodization degree was increased from 1.06 to 2.58, the inversion precision was increased by 6.94% for C3H8 gas and 23.93% for C2H4 gas. Through the parameter adjustment, the quasi-trapezoidal window may achieve a high SNR or high-resolution spectral restoration, which can improve the accuracy of gas concentration inversion to some extent.

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Khonina, Svetlana N., Sergey G. Volotovskiy, Alexey P. Dzyuba, Pavel G. Serafimovich, Sergey B. Popov, and Muhammad A. Butt. "Power Phase Apodization Study on Compensation Defocusing and Chromatic Aberration in the Imaging System." Electronics 10, no. 11 (2021): 1327. http://dx.doi.org/10.3390/electronics10111327.

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We performed a detailed comparative study of the parametric high degree (cubic, fourth, and fifth) power phase apodization on compensation defocusing and chromatic aberration in the imaging system. The research results showed that increasing the power degree of the apodization function provided better independence (invariance) of the point spread function (PSF) from defocusing while reducing the depth of field (DOF). This reduction could be compensated by increasing the parameter α; however, this led to an increase in the size of the light spot. A nonlinear relationship between the increase in the DOF and spot size was shown (due to a small increase in the size of the light spot, the DOF can be significantly increased). Thus, the search for the best solution was based on a compromise of restrictions on the circle of confusion (CoC) and DOF. The modeling of color image formation under defocusing conditions for the considered apodization functions was performed. The subsequent deconvolution of the resulting color image was demonstrated.

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Toto, Saktioto, Ramadhan Khaikal, Soerbakti Yan, Fadli Syahputra Romi, Irawan Dedi, and Okfalisa. "Apodization sensor performance for TOPAS fiber Bragg grating." TELKOMNIKA (Telecommunication, Computing, Electronics and Control) 19, no. 6 (2021): 1982–91. https://doi.org/10.12928/telkomnika.v19i6.21669.

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Optical sensors have more capabilities than electronic sensors, and therefore provide extraordinary developments, including high sensitivity, non-susceptibility to electromagnetic wave disturbances, small size, and multiplexing. Furthermore, fiber Bragg grating (FBG) is an optical sensor with a periodically changing grating refractive index, susceptible to strain and temperature changes. As a sensor, FBG’s performance required to optimize and improve the numerical apodization function and affect the effective refractive index is considered. The grating fiber’s apodization function can narrow the full width half maximum (FWHM) and reduce the optical signal’s side lobes. In all the apodization functions operated by FBG, Blackman has the highest sensitivity of 15.37143 pm/°C, followed by Hamming and Gaussian, with 13.71429 pm/°C and 13.70857 pm/°C, respectively, and Uniform grating fiber with the lowest sensitivity of 12.40571 pm/°C. Hamming, Uniform, and Blackman discovered the sensitivity for a strain to be 1.17, 1.16, and 1.167 pm/microstrain, respectively. The results obtained indicated that apodization could increase FBG’s sensitivity to temperature and strain sensors. For instance, in terms of other parameters, FWHM width, Hamming had the narrowest value of 0.6 nm, followed by Blackman with 0.612 nm, while Uniform had the widest FWHM of 1.9546 nm.

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Saktioto, T., K. Ramadhan, Y. Soerbakti, D. Irawan, and Okfalisa. "Integration of chirping and apodization of Topas materials for improving the performance of fiber Bragg grating sensors." Journal of Physics: Conference Series 2049, no. 1 (2021): 012001. http://dx.doi.org/10.1088/1742-6596/2049/1/012001.

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Abstract The discovery of the fiber Bragg grating (FBG) is an early milestone in developing optical fiber technology, such as optical communication to monitoring material health structures as sensors. For optical communication, the FBG components are capable of filtering functions. As a sensor, it has a high sensitivity immune to electromagnetic wave interference, is small in size, and is resistant to extreme environmental conditions. The sensitivity of the FBG sensor is obtained from the shift in the peak wavelength of each of the temperature and strain quantities. However, the performance of the FBG sensor can be improved by engineering the distribution of the refractive index on the grid with the apodization and chirp functions. Apodization is a technique to improve the performance of the FBG to eliminate noise, narrow the full width half maximum, lower the side lobes of the main lobe, and improve the spectrum ripple factor. Apart from apodization, the chirp function also affects the sensor sensitivity and the refractive index distribution on the grid. Numerical experiments were carried out in designing the FBG component as a sensor using Gaussian apodization and Topas (cyclic olefin copolymer) for several chirp functions. The results show that the Gaussian apodization Topas for all chirp functions as a strain sensor has the same sensitivity, namely 0.84 pm/μstrain while for temperature sensors with the highest sensitivity is obtained at cubic root chirp of 13.82857 pm/°C followed by square root chirp of 13.74286 pm/°C, quadratic chirp 13.71429 pm/°C, and linear chirp 13.4 pm/°C. The Bragg wavelength shift was greater for 1 °C than for the 1 μstrain.

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11

Müller, M., and G. J. Brakenhoff. "Apodization and the point-spread autocorrelation function." Applied Optics 36, no. 13 (1997): 2755. http://dx.doi.org/10.1364/ao.36.002755.

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12

Guo, Qi, Zhongming Zheng, Bo Wang, et al. "Femtosecond Laser Fabricated Apodized Fiber Bragg Gratings Based on Energy Regulation." Photonics 8, no. 4 (2021): 110. http://dx.doi.org/10.3390/photonics8040110.

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In this paper, an energy regulation method based on the combination of a half-wave plate (HWP) and a polarization beam splitter (PBS) is proposed for the fabrication of apodized fiber gratings, which can effectively improve the side lobe suppression ratio of high-reflectivity fiber Bragg gratings (FBGs) fabricated by femtosecond laser. The apodized FBGs prepared by this method has good repeatability and flexibility. By inputting different types of apodization functions through the program, the rotation speed of the stepping motor can be adjusted synchronously, and then the position of the HWP can be accurately controlled so that the laser energy can be distributed as an apodization function along the axial direction of the fiber. By using the energy apodization method, the gratings with a reflectivity of 75% and a side lobe suppression ratio of 25 and 32 dB are fabricated in the fiber with a core diameter of 9 and 4.4 μm, respectively. The temperature and strain sensitivities of the energy-apodized fiber gratings with a core diameter of 4.4 μm are 10.36 pm/°C and 0.9 pm/με, respectively. The high-reflectivity gratings fabricated by this energy apodization method are expected to be used in high-power narrow-linewidth lasers and wavelength division multiplexing (WDM) systems.

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13

Venkanna, M., N. Sabitha, and D. K. Sagar. "Engineering of Aberrated PSF by Asymmetric Apodization with the Complex Shaded Aperture." Journal of Scientific Research 15, no. 1 (2023): 121–29. http://dx.doi.org/10.3329/jsr.v15i1.60366.

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The point spread function (PSF) produced by a coherent optical system under the influence of defocus, coma, and primary spherical aberration (PSA) is examined in this work. This paper deals with asymmetric apodization and pupil engineering to control monochromatic aberrations. To reduce the influence of monochromatic aberrations on the diffracted PSF, this approach uses amplitude and phase apodization. Analytical investigations on intensity PSF are carried out with varying amounts of aberrations and degrees of amplitude and phase apodization. Computed central peak intensity and full width at half maxima (FWHM) and analyzed. The resolution of a diffraction-limited optical imaging system is improved by using an asymmetric optical filter that minimizes the effect of defocus.

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14

Compaleo, Jacob, and Inder J. Gupta. "Spectral Domain Sparse Representation for DOA Estimation of Signals with Large Dynamic Range." Sensors 21, no. 15 (2021): 5164. http://dx.doi.org/10.3390/s21155164.

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Recently, we proposed a Spectral Domain Sparse Representation (SDSR) approach for the direction-of-arrival estimation of signals incident to an antenna array. In the approach, sparse representation is applied to the conventional Bartlett spectra obtained from snapshots of the signals received by the antenna array to increase the direction-of-arrival (DOA) estimation resolution and accuracy. The conventional Bartlett spectra has limited dynamic range, meaning that one may not be able to identify the presence of weak signals in the presence of strong signals. This is because, in the conventional Bartlett spectra, uniform weighting (window) is applied to signals received by various antenna elements. Apodization can be used in the generation of Bartlett spectra to increase the dynamic range of the spectra. In Apodization, more than one window function is used to generate different portions of the spectra. In this paper, we extend the SDSR approach to include Bartlett spectra obtained with Apodization and to evaluate the performance of the extended SDSR approach. We compare its performance with a two-step SDSR approach and with an approach where Bartlett spectra is obtained using a low sidelobe window function. We show that an Apodization Bartlett-based SDSR approach leads to better performance with just single-step processing.

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Bowie, Bryan T., and Peter R. Griffiths. "Determination of the Resolution of a Multichannel Raman Spectrometer Using Fourier Transform Raman Spectra." Applied Spectroscopy 57, no. 2 (2003): 190–96. http://dx.doi.org/10.1366/000370203321535114.

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The resolution of a grating polychromator for Raman spectroscopy has been simulated by measuring spectra on a Fourier transform (FT) Raman spectrometer and selecting the FT of the apodization function so that the instrument line shape function mimics the triangular spectral slit function of the polychromator. To this end, FT-Raman spectra measured with a nominal resolution of 0.5 cm−1 were modified through the application of sinc2 apodization functions of various widths to simulate spectra measured on a polychromator at lower resolution. The success of this approach was validated using the 1085 cm−1 band of calcite. When the modified FT-Raman spectra were compared with spectra measured on a grating polychromator equipped with slits of widths 100 and 150 μm, the resolution of the polychromator was estimated to be 6.3 and 7.8 cm−1, respectively. This conclusion was verified experimentally by measuring the separation of two bands in the Raman spectrum of BaSO4 at ∼460 cm−1

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Gaskins, Weston P., and Kevin J. Haworth. "Investigating the change in point spread function and resolution of random apodization passive cavitation images." Journal of the Acoustical Society of America 153, no. 3_supplement (2023): A268. http://dx.doi.org/10.1121/10.0018807.

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Passive cavitation imaging is an important technique in measuring cavitation dynamics, localizing concomitant bioeffects, and guiding various ultrasound therapies. The canonical algorithm for passive cavitation imaging operates via a delay, sum, and integrate method. With standard diagnostic arrays, this method yields poor axial resolution. We hypothesized that using a random apodization, minimum projection compounding technique could overcome this limitation. The random apodization approach randomly selected only half of the elements to be included in the delay, sum, and integrate algorithm to form a PCI. This process was repeated 30 times using the same data set but a different random subset of half the elements to create 30 images. The final image was obtained via a minimum intensity projection across the 30 images. The improvement of image quality can be tracked by comparing the point spread function (PSF), and the distance at which two cavitation sources can still be resolved, relative to when using the standard algorithm. The PSF reduced by 86% ± 9% when the random apodization was applied. Lateral and axial resolution exhibited qualitative changes associated with a lower PSF, but no quantitative change in resolution, based on the Rayleigh criteria, was observed.

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Salkapuram, Vidya Rani, Anitha Padamuttum, Sabitha Nampally, and Karuna Sagar Dasari. "Effects of Aberrations on Point Spread Function of Three Zone Aberrated Optical Imaging System with Variable Apodization." Photonics Letters of Poland 15, no. 1 (2023): 10–12. http://dx.doi.org/10.4302/plp.v15i1.1199.

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Presence of optical aberrations degrades the performance of the optical system. These effects can be reduced by inserting proper amplitude filters. In the current study, suitable amplitude-apodization pupils have been used for tailoring the point spread function (PSF), in order to attain full-width at half-maximum (FWHM) and suppressed side lobes. Intensity profiles for the unapodized and variable apodized cases have been considered. By comparing and analyzing the various PSFs, the effects induced by monochromatic aberrations such as defocusing effect, and the primary spherical aberration have been controlled for various degrees of apodization parameter β. The proposed apodizer is very effective in increasing the resolution of the optical systems. Full Text: PDF References A.N.K. Reddy, D. Karuna Sagar, Pramana, "Half-width at half-maximum, full-width at half-maximum analysis for resolution of asymmetrically apodized optical systems with slit apertures", J. Phys. 84, 117 (2015). CrossRef A.N.K Reddy, D. Karuna Sagar, "Spherical Aberration of Point Spread Function with Asymmetric Pupil Mask", Adv. Opt. Technol. 2016, 1608342 (2016). CrossRef W. Yang, A.B. Kotinski, "One-sided Achromatic Phase Apodization for Imaging of Extrasolar Planets", The Astrophys. J. 605, 892 (2004). CrossRef M. Kowalczyk, C.J. Zapata-Rodriguez, M. Martinez-Corral, "Asymmetric apodization in confocal scanning systems", Appl. Opt. 37, 8206 (1998). CrossRef S.C. Biswas, A. Boivin, "Influence of Spherical Aberration on the Performance of Optimum Apodizers", Opt. Acta 23, 569 (1976). CrossRef A.N.K. Reddy, S.N. Khonina, "Analysis of electronic parameters and frequency-dependent properties of Au/NiO/n-GaN heterojunctions", Appl. Phys. B. 124, 1 (2018). CrossRef D. Karuna Sagar, G. Bikshamaiah, S.L. Goud, "Defect of focus in two-line resolution with Hanning amplitude filters", J. Mod.Opt. 53, 2011 (2006). CrossRef M. Ruphy, O.M. Ramahi, "Spherical aberration in electrically thin flat lenses", J. Opt. Soc. Am. A 33, 1531(2016). CrossRef A.N.K. Reddy, M. Hashemi, D.K. Sagar, "Effects of aberrations on the point spread function and the two-point resolution with versatile apodization pupils", Pramana J. Phy. 94, P. 1 (2020). CrossRef A.N.K. Reddy, D.K. Sagar, "Two-point resolution of asymmetrically apodized optical systems", Optica Pura y Aplicada 46, 215 (2013). CrossRef

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ZHANG Peng, 张鹏, and 张志辉 ZHANG Zhihui. "A Novel Apodization Function of Single Sided Interferogram." ACTA PHOTONICA SINICA 41, no. 7 (2012): 878–82. http://dx.doi.org/10.3788/gzxb20124107.0878.

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ZHANG Peng, 张鹏, and 张志辉 ZHANG Zhihui. "A Novel Apodization Function of Single Sided Interferogram." ACTA PHOTONICA SINICA 41, no. 7 (2012): 878–82. http://dx.doi.org/10.3788/gzxb20124107.878.

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Buslov, D. K., N. A. Nikonenko, and R. G. Zhbankov. "Digital-filter apodization-function approximation in spectrum deconvolution." Journal of Applied Spectroscopy 56, no. 4 (1992): 397–401. http://dx.doi.org/10.1007/bf00665039.

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Deng Jinglan, 邓竞蓝, 童晶晶 Tong Jingjing, 高闽光 Gao Minguang, et al. "Improved Triangular Window Apodization Function Based on Zero-Order Bessel Function." Acta Optica Sinica 40, no. 3 (2020): 0307001. http://dx.doi.org/10.3788/aos202040.0307001.

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22

Sumi, Chikayoshi. "Determination of Lateral Modulation Apodization Functions Using a Regularized, Weighted Least Squares Estimation." International Journal of Biomedical Imaging 2010 (2010): 1–7. http://dx.doi.org/10.1155/2010/635294.

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Recently, work in this group has focused on the lateral cosine modulation method (LCM) which can be used for next-generation ultrasound (US) echo imaging and tissue displacement vector/strain tensor measurements (blood, soft tissues, etc.). For instance, in US echo imaging, a high lateral spatial resolution as well as a high axial spatial resolution can be obtained, and in tissue displacement vector measurements, accurate measurements of lateral tissue displacements as well as of axial tissue displacements can be realized. For an optimal determination of an apodization function for the LCM method, the regularized, weighted minimum-norm least squares (WMNLSs) estimation method is presented in this study. For designed Gaussian-type point spread functions (PSFs) with lateral modulation as an example, the regularized WMNLS estimation in simulations yields better approximations of the designed PSFs having wider lateral bandwidths than a Fraunhofer approximation and a singular-value decomposition (SVD). The usefulness of the regularized WMNLS estimation for the determination of apodization functions is demonstrated.

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González-Acuña, Rafael G. "Stigmatic singlet with a user-defined apodization pupil function." Journal of the Optical Society of America A 39, no. 2 (2022): 213. http://dx.doi.org/10.1364/josaa.447689.

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Reddy, A. N. K., D. K. Sagar, and S. N. Khonina. "ASYMMETRIC APODIZATION FOR THE COMMA ABERRATED POINT SPREAD FUNCTION." Computer Optics 41, no. 4 (2017): 484–88. http://dx.doi.org/10.18287/2412-6179-2017-41-4-484-488.

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Takeuchi, Akihisa, Kentaro Uesugi, Yoshio Suzuki, Seiichi Itabashi, and Masatoshi Oda. "Fresnel zone plate with apodized aperture for hard X-ray Gaussian beam optics." Journal of Synchrotron Radiation 24, no. 3 (2017): 586–94. http://dx.doi.org/10.1107/s1600577517003289.

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Fresnel zone plates with apodized apertures [apodization FZPs (A-FZPs)] have been developed to realise Gaussian beam optics in the hard X-ray region. The designed zone depth of A-FZPs gradually decreases from the center to peripheral regions. Such a zone structure forms a Gaussian-like smooth-shouldered aperture function which optically behaves as an apodization filter and produces a Gaussian-like focusing spot profile. Optical properties of two types of A-FZP, i.e. a circular type and a one-dimensional type, have been evaluated by using a microbeam knife-edge scan test, and have been carefully compared with those of normal FZP optics. Advantages of using A-FZPs are introduced.

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Gregory, Philip C. "Bayesian Planet Searches for the 10 cm/s Radial Velocity Era." Proceedings of the International Astronomical Union 11, A29A (2015): 205–7. http://dx.doi.org/10.1017/s1743921316002817.

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AbstractA new apodized Keplerian model is proposed for the analysis of precision radial velocity (RV) data to model both planetary and stellar activity (SA) induced RV signals. A symmetrical Gaussian apodization function with unknown width and center can distinguish planetary signals from SA signals on the basis of the width of the apodization function. The general model for m apodized Keplerian signals also includes a linear regression term between RV and the stellar activity diagnostic In (R'hk), as well as an extra Gaussian noise term with unknown standard deviation. The model parameters are explored using a Bayesian fusion MCMC code. A differential version of the Generalized Lomb-Scargle periodogram provides an additional way of distinguishing SA signals and helps guide the choice of new periods. Sample results are reported for a recent international RV blind challenge which included multiple state of the art simulated data sets supported by a variety of stellar activity diagnostics.

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Proença, Maria da Conceição. "Two-dimensional Kaiser apodization function for interferometric radiometry from space." Optical Engineering 46, no. 3 (2007): 036201. http://dx.doi.org/10.1117/1.2713801.

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Kim, Jin. "TRANSMIT APODIZATION USING A SINC FUNCTION IN AN ULTRASOUND SYSTEM." Journal of the Acoustical Society of America 131, no. 4 (2012): 3205. http://dx.doi.org/10.1121/1.4707527.

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Spencer, Lynne R., and Daniel D. Traficante. "New Window Function for Very Short Acquisition Times." Applied Spectroscopy 52, no. 1 (1998): 139–42. http://dx.doi.org/10.1366/0003702981942474.

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An apodization function, the sinc-TRAF function (S-TRAF), has been developed for application to exponentially decaying data sets where the acquisition times ( AT) is less than or equal to one time constant, T2. For heavily truncated time-domain signals, S-TRAF is able to remove sinc ripple with only minor losses in linewidth (LW) and signal-to-noise ratio (S/N). Ripple removal achieved with the application of S-TRAF rivals that observed from use of the “ultimate ripple-free resolution enhancement” function (URFRE) for AT as low as 0.3 T2*. S-TRAF maintains LW and S/N better than URFRE for all acquisition times examined.

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Schwiegerling, Jim. "Relating wavefront error, apodization, and the optical transfer function: general case." Journal of the Optical Society of America A 34, no. 5 (2017): 726. http://dx.doi.org/10.1364/josaa.34.000726.

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Ferry, A., and P. Jacobsson. "Curve Fitting and Deconvolution of Instrumental Broadening: A Simulated Annealing Approach." Applied Spectroscopy 49, no. 3 (1995): 273–78. http://dx.doi.org/10.1366/0003702953963643.

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A curve-fitting procedure based on the simulated annealing algorithm has been developed for the analysis of spectral Raman data. By the inclusion of a priori information about the instrumental broadening in the definition of the cost function that is minimized, effects of the finite instrumental resolution are eliminated from the resulting fit. The ability of the method to reproduce original band shapes is tested on synthesized spectra and FT-Raman spectra of diamond recorded at different resolutions with different apodization functions. The procedure yields the global optimum of the fitted parameters and is easily implemented on a personal computer.

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Andra, Naresh Kumar Reddy, and Karuna Sagar Dasari. "Spherical Aberration of Point Spread Function with Asymmetric Pupil Mask." Advances in Optical Technologies 2016 (November 29, 2016): 1–5. http://dx.doi.org/10.1155/2016/1608342.

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Point spread function underneath spherical wave aberration with antiphase apodization has been obtained by one-dimensional pupil mask functions. In the presence of spherical aberration, suppression of optical side-lobes has increased on one side of the point spread function with the width of the periphery strips within the pupil mask. On introducing wave aberration effect, there exists dependence of the lateral resolution of central peak of the asymmetric point spread function on the amount of amplitude masking. However, the magnitude of intensity of central peak is originated be to amplified by the highest degree of amplitude and phase masking. Additionally, for aberrated asymmetric PSF, FWHM increases and it further decreases with the control parameters of amplitude and phase mask. The magnitude of this corollary can quantify the super resolution of diffracted structures under spherical aberration.

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33

Schwiegerling, Jim. "Relating wavefront error, apodization, and the optical transfer function: on-axis case." Journal of the Optical Society of America A 31, no. 11 (2014): 2476. http://dx.doi.org/10.1364/josaa.31.002476.

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Traficante, Daniel D., and Gregory A. Nemeth. "A new and improved apodization function for resolution enhancement in NMR spectroscopy." Journal of Magnetic Resonance (1969) 71, no. 2 (1987): 237–45. http://dx.doi.org/10.1016/0022-2364(87)90053-9.

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35

Xigyu, Yang, Feng Qiyuan, and Li Runlin. "Apodization of the instrumental function curve of sisam with a single grating." Journal of Applied Spectroscopy 60, no. 1-2 (1994): 49–54. http://dx.doi.org/10.1007/bf02606075.

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Yan, Lu, Juan Yang, Feng Xu, and Shengchun Piao. "Low-Sidelobe Imaging Method Utilizing Improved Spatially Variant Apodization for Forward-Looking Sonar." Remote Sensing 16, no. 12 (2024): 2100. http://dx.doi.org/10.3390/rs16122100.

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For two-dimensional forward-looking sonar imaging, high sidelobes significantly degrade the quality of sonar images. The cosine window function weighting method is often applied to suppress the sidelobe levels in the angular and range dimensions, at the expense of the main lobe resolutions. Therefore, an improved spatially variant apodization imaging method for forward-looking sonar is proposed, to reduce sidelobes without degrading the main lobe resolution in angular-range dimensions. The proposed method is a nonlinear postprocessing operation in which the raw complex-valued sonar image produced by a conventional beamformer and matched filter is weighted by a spatially variant coefficient. To enhance the robustness of the spatially variant apodization approach, the array magnitude and phase errors are calibrated to prevent the occurrence of beam sidelobe increase prior to beamforming operations. The analyzed results of numerical simulations and a lake experiment demonstrate that the proposed method can greatly reduce the sidelobes to approximately −40 dB, while the main lobe width remains unchanged. Moreover, this method has an extremely simple computational process.

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37

Wang, Dai Qiang, Liang Rong Li, Yu Qing Chen, Zu Ming Yao, Hong Gong, and Qiao Liu. "A SAW Filter of Elliptic Structure IDT." Applied Mechanics and Materials 665 (October 2014): 623–28. http://dx.doi.org/10.4028/www.scientific.net/amm.665.623.

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The design uses silicon-AlN thin films as the piezoelectric substrate, Use apo- dization weighting methods to optimize the design of IDT. The improved δ function model was Modeling Tools of Apodization weighted ellipse IDT structure, According to the result of simulation, we designed a layout of SAW band-pass filter and fabricated a sample of it which center frequency is 300MHz and insertion loss is 7dB, The research shows the consistency of simulation results with the experimental results.

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Díaz, José A. "Relating wavefront error, apodization, and the optical transfer function: on-axis case: comment." Journal of the Optical Society of America A 33, no. 8 (2016): 1622. http://dx.doi.org/10.1364/josaa.33.001622.

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Schwiegerling, Jim. "Relating wavefront error, apodization, and the optical transfer function: on-axis case: reply." Journal of the Optical Society of America A 33, no. 8 (2016): 1626. http://dx.doi.org/10.1364/josaa.33.001626.

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40

Traficante, Daniel D., and Dieter Ziessow. "A new apodization function for resolution enhancement with a minimum loss of sensitivity." Journal of Magnetic Resonance (1969) 66, no. 1 (1986): 182–86. http://dx.doi.org/10.1016/0022-2364(86)90121-6.

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Reddy, Andra Naresh Kumar, and Dasari Karuna Sagar. "Point Spread Function of Optical Systems Apodized by Semicircular Array of 2D Aperture Functions with Asymmetric Apodization." Journal of information and communication convergence engineering 12, no. 2 (2014): 83–88. http://dx.doi.org/10.6109/jicce.2014.12.2.083.

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Liu, Juwhan, Antti O. K. Nieminen, and Jack L. Koenig. "Deconvolution of the Chemical Shift Effects in Proton Nuclear Magnetic Resonance Imaging." Applied Spectroscopy 43, no. 7 (1989): 1260–64. http://dx.doi.org/10.1366/0003702894203697.

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When the gradient strength is not strong enough to suppress the chemical shift effects, it is possible to apply a numerical deconvolution technique to remove the chemical shift artifacts. The Wiener filter and an apodization function are combined to produce an effective deconvolution method for the NMR images obtained by standard spin-echo NMR imaging technique. In the deconvolution process, an NMR spectrum is utilized which is taken at the same condition as the NMR image but with the phase encoding and the read gradients off.

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Nadler, T. K., S. T. McDaniel, M. O. Westerhaus, and J. S. Shenk. "Deconvolution of Near-Infrared Spectra." Applied Spectroscopy 43, no. 8 (1989): 1354–58. http://dx.doi.org/10.1366/0003702894204272.

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Deconvolution is a mathematical technique for improving the resolution of spectra. Deconvolution can be done in either signal space or frequency space. Both methods were attempted after special adaptations of the algorithms were carried out in order to make them specific for the near-infrared (NIR) spectrum. Signal-space deconvolution works well when a line is subtracted from the spectrum before a modified Jansson's algorithm is applied. Frequency-space deconvolution requires the addition of a polynomial tail to the spectrum, the addition of a constant to the bandpass divisor, and a Gaussian apodization function.

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Khonina, Svetlana N., and Andrey V. Ustinov. "Thin Light Tube Formation by Tightly Focused Azimuthally Polarized Light Beams." ISRN Optics 2013 (August 19, 2013): 1–6. http://dx.doi.org/10.1155/2013/185495.

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Theoretical and numerical analysis of the transmission function of the focusing system with high numerical aperture was conducted. The purpose of the study was to form a thin light tube in a focal area using the azimuthally polarized radiation. It was analytically shown that, due to destructive interference of two beams formed by two narrow rings, it is possible to overcome not only the full aperture diffraction limit but also the circular aperture limit. In this case, however, the intensity at the center of the focal plane is significantly reduced, which practically leads to the tube rupture. It was numerically shown that long thin one-piece tubes may be formed through the aperture apodization with diffractive axicon phase function or with complex transmission function of Laguerre-Gaussian or Airy-Gaussian beams.

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Sun, Nai-Hsiang, Min-Yu Tsai, Jiun-Jie Liau, and Jung-Sheng Chiang. "Chebyshev apodized fiber Bragg gratings." Science Progress 104, no. 3_suppl (2021): 003685042210941. http://dx.doi.org/10.1177/00368504221094173.

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In this paper, a new apodized fiber Bragg grating (FBG) structure, the Chebyshev apodization, is proposed. The Chebyshev polynomial distribution has been widely used for the optimal design of antennas and filters, but it has not been used for designing FBGs. Unlike the function of traditional Gaussian-apodized FBGs, the Chebyshev polynomial is a discrete function. We demonstrate a new methodology for designing Chebyshev-apodized FBGs: the grating region is divided by discrete n sections with uniform gratings, while the index change is used to express the Chebyshev polynomial. We analyze the Chebyshev-apodized FBGs by using coupled mode theory and the piecewise-uniform approach. The reflection spectrum and the dispersion of Chebyshev-apodized FBGs are calculated and compared with those of Gaussian FBGs. Moreover, a sidelobe suppression level (SSL), a parameter of the Chebyshev polynomial, along with the maximum ac-index change of FBGs are analyzed. Assume that the grating length is 20mm, SSL is 100 dB, the section number is 40, and the maximum ac-index change is 2 × 10−4. The reflection spectrum of Chebyshev apodized FBGs shows flattened sidelobes with an absolute SSL of −95.9 dB (corresponding to SSL=100 dB). The simulation results reveal that at the same full width at half maximum, the Chebyshev FBGs have lower sidelobe suppression than the Gaussian FBGs, but their dispersion is similar. We demonstrate the potential of using Chebyshev-apodized FBGs in optical filters, dispersion compensators, and sensors; Chebyshev apodization can be applied in the design of periodic dielectric waveguides.

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Zhang, Yancao, Qi Fan, Xinchao Li, Jianjun Shi, and Baiyu Yang. "Optimization of the window function for digital hologram apodization in reconstructing the holographic image." Journal of Optics 15, no. 10 (2013): 105406. http://dx.doi.org/10.1088/2040-8978/15/10/105406.

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Sumi, Chikayoshi. "A case of apodization function using singular-value decomposition: Determination of beamforming parameters by optimization." Acoustical Science and Technology 29, no. 2 (2008): 185–87. http://dx.doi.org/10.1250/ast.29.185.

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48

Shailaja, P., S. V. Rao, D. K. Sagar, and M. Venkanna. "Mitigation of Edge Ringing for the Optimization of Highly Aberrated Coherent Optical Systems." Journal of Scientific Research 15, no. 3 (2023): 595–605. http://dx.doi.org/10.3329/jsr.v15i3.63023.

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The images of straight-edge objects formed by a coherent optical system with a circular aperture apodized with a shaded aperture have been studied. Image quality assessment parameters such as edge-ringing, edge-gradient, and edge-shift of the edge fringes have been investigated as a function of apodization parameters for various degrees of defocus, coma, and primary spherical aberrations. The reduction in the ringing pattern is more effective at the suitable combination of aberrations than the aberration-free cases and attains the minimum value for φd=2π where it is completely balanced with φd. It has been found that the image quality of straight-edge objects can be improved by combining specific aberrations with the appropriate apodizer.

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Kilgour, David P. A., and Steven L. Van Orden. "Absorption mode Fourier transform mass spectrometry with no baseline correction using a novel asymmetric apodization function." Rapid Communications in Mass Spectrometry 29, no. 11 (2015): 1009–18. http://dx.doi.org/10.1002/rcm.7190.

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Skorupski, Krzysztof, Sławomir Cięszczyk, Patryk Panas, and Piotr Kisała. "Numerical and Experimental Analysis of Matched Filter Interrogation of FBG Sensors with Large Side Lobes." Sensors 20, no. 19 (2020): 5522. http://dx.doi.org/10.3390/s20195522.

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This article presents the effect of fiber Bragg gratings side lobes on interrogation systems consisting of sensor and matched filters. The conducted research shows that high-value side lobe structures applied as sensors and/or filters are characterized by some interesting properties. The paper presents both numerical analysis and experimental verification of the fiber Bragg gratings (FBG) interrogation systems with matched filters for gratings containing high side lobes. Numerical modeling of Bragg structures was performed for two different cases: uniform and inverse apodization. Modification of apodization can change the side lobe reflectance level even above levels found in uniform structures. This is a case not described in the literature, especially in terms of possible applications. Transfer characteristics, i.e., the relationship between power intensity as a function of wavelength shift, were determined. A collection of gratings with spectra corresponding to those analyzed in numerical experiments were fabricated. Next, the transfer characteristics of the interrogation systems containing real FBG were determined. The properties of the proposed systems are described. It has been shown that a significant level of sidebands, which is often the subject of many drawbacks in filtering or telecommunications systems, can be an advantage. It has been demonstrated that a high level of side lobes can be used to increase the measurement range of the FBG sensor interrogation systems. It has been determined numerically and confirmed experimentally that from the point of view of the design of sensor interrogation systems, it is beneficial to combine specific pairs of gratings: one with a spectrum characterized by a low side lobe level and a second one in which the spectrum has very high side lobes.

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