An Introduction to Sonar Systems Engineering

Table of Contents

Preface xiii

1.1 Coupling Transmitted and Received Electrical Signals

to the Fluid Medium 1

1.1.1 Transmit Coupling Equation 1

1.1.2 Receive Coupling Equation 4

1.2 The Near-Field Beam Pattern of a Volume Aperture 6

1.2.1 Transmit Aperture 6

1.2.2 Receive Aperture 21

1.3 The Far-Field Beam Pattern of a Volume Aperture 28

1.3.1 Transmit Aperture 28

1.3.2 Receive Aperture 33

Problems 35

Appendix 1A 36

Appendix 1B Important Functions and their Units at a Transmit

and Receive Volume Aperture 39

2.1 The Far-Field Beam Pattern of a Linear Aperture 41

2.2 Amplitude Windows and Corresponding Far-Field Beam Patterns 44

2.2.1 The Rectangular Amplitude Window 45

2.2.2 The Triangular Amplitude Window 48

2.2.3 The Cosine Amplitude Window 52

2.2.4 The Hanning, Hamming, and Blackman Amplitude

Windows 57

2.3 Beamwidth 63

2.4 Beam Steering 70

2.5 Beamwidth at an Arbitrary Beam-Steer Angle 73

2.6 The Near-Field Beam Pattern of a Linear Aperture 81

2.6.1 Aperture Focusing 84

2.6.2 Beam Steering and Aperture Focusing 85

Problems 86

Appendix 2A Transmitter and Receiver Sensitivity Functions

of a Continuous Line Transducer 90

Appendix 2B Radiation from a Linear Aperture 92

Appendix 2C Symmetry Properties and Far-Field Beam Patterns 98

Appendix 2D Computing the Normalization Factor 100

Appendix 2E Summary of One-Dimensional Spatial Fourier

Transforms 102

3 Complex Aperture Theory – Planar Apertures 103

3.1 The Far-Field Beam Pattern of a Planar Aperture 103

3.2 The Far-Field Beam Pattern of a Rectangular Piston 106

3.3 The Far-Fiel