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Sharpness of range focus in the Fresnel region for a linear aperture.

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Title: Sharpness of range focus in the Fresnel region for a linear aperture.
Authors: Cox, Henry1 (AUTHOR) harry.cox@lmco.com
Source: Journal of the Acoustical Society of America. May2025, Vol. 157 Issue 5, p3604-3609. 6p.
Subjects: Fresnel function, Depth of field, Nonlinear functions, Integral functions, Physical constants
Abstract: Large aperture arrays, designed for greater angular resolution and beamforming gain, require focusing in the Fresnel region for some applications in acoustics, seismics and electromagnetics. An important characteristic is the sharpness of the range-response around the focal range. It can be quantified by the "M-dB depth of field" defined as the range window around the focal range for which the loss magnitude is less than M decibels. Similarly, "focal range mismatch loss" is defined as the number of decibels the response is below its peak at the focal range. The response of a focused linear aperture vs range can be expressed as a function of Fresnel integrals. This paper introduces a simple and accurate approximation that quantifies the range response around the focal range to an accuracy of a small fraction of 1 dB, down to the −10 dB level. The non-linear function of Fresnel integrals is replaced by a simple algebraic expression that relates performance measures, focal range mismatch loss, and depth of field, to the physical parameters, array length, wavelength, focal range, and direction. Results, presented in terms of dimensionless ratios of physical quantities, are shown to be valid for all steering angles, not limited to broadside. [ABSTRACT FROM AUTHOR]
Copyright of Journal of the Acoustical Society of America is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 185593258
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PubType: Academic Journal
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  Data: Sharpness of range focus in the Fresnel region for a linear aperture.
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  Data: <searchLink fieldCode="AR" term="%22Cox%2C+Henry%22">Cox, Henry</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> harry.cox@lmco.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+the+Acoustical+Society+of+America%22">Journal of the Acoustical Society of America</searchLink>. May2025, Vol. 157 Issue 5, p3604-3609. 6p.
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  Data: <searchLink fieldCode="DE" term="%22Fresnel+function%22">Fresnel function</searchLink><br /><searchLink fieldCode="DE" term="%22Depth+of+field%22">Depth of field</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+functions%22">Nonlinear functions</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+functions%22">Integral functions</searchLink><br /><searchLink fieldCode="DE" term="%22Physical+constants%22">Physical constants</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Large aperture arrays, designed for greater angular resolution and beamforming gain, require focusing in the Fresnel region for some applications in acoustics, seismics and electromagnetics. An important characteristic is the sharpness of the range-response around the focal range. It can be quantified by the "M-dB depth of field" defined as the range window around the focal range for which the loss magnitude is less than M decibels. Similarly, "focal range mismatch loss" is defined as the number of decibels the response is below its peak at the focal range. The response of a focused linear aperture vs range can be expressed as a function of Fresnel integrals. This paper introduces a simple and accurate approximation that quantifies the range response around the focal range to an accuracy of a small fraction of 1 dB, down to the −10 dB level. The non-linear function of Fresnel integrals is replaced by a simple algebraic expression that relates performance measures, focal range mismatch loss, and depth of field, to the physical parameters, array length, wavelength, focal range, and direction. Results, presented in terms of dimensionless ratios of physical quantities, are shown to be valid for all steering angles, not limited to broadside. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Journal of the Acoustical Society of America is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1121/10.0036692
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      – Code: eng
        Text: English
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        PageCount: 6
        StartPage: 3604
    Subjects:
      – SubjectFull: Fresnel function
        Type: general
      – SubjectFull: Depth of field
        Type: general
      – SubjectFull: Nonlinear functions
        Type: general
      – SubjectFull: Integral functions
        Type: general
      – SubjectFull: Physical constants
        Type: general
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      – TitleFull: Sharpness of range focus in the Fresnel region for a linear aperture.
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            – D: 01
              M: 05
              Text: May2025
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              Y: 2025
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