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Spie Press Book

Modeling the Imaging Chain of Digital Cameras
Author(s): Robert D. Fiete
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Book Description

The process by which an image is formed, processed, and displayed can be conceptualized as a chain of physical events called the imaging chain. By mathematically modeling the imaging chain, we can gain insight into the relationship between the camera design parameters and the resulting image quality. The mathematical models can also be used to optimize and assess the design of a camera for specific applications before expenditures are committed to building hardware.

Modeling the Imaging Chain of Digital Cameras teaches the key elements of the end-to-end imaging chain for digital camera systems and describes how elements of the imaging chain are mathematically modeled using the basics of linear systems mathematics and Fourier transforms. The emphasis is on general digital cameras designed to image incoherent light in the visible imaging spectrum. The reader will learn how digital camera design parameters are related to the elements of the imaging chain and how they influence the resulting image quality. The book also discusses the use of imaging chain models to simulate images from different digital camera designs for image quality evaluations.

Book Details

Date Published: 4 November 2010
Pages: 226
ISBN: 9780819483393
Volume: TT92

Table of Contents
SHOW Table of Contents | HIDE Table of Contents
Preface /xiii
List of Acronyms /xv
1 The Importance of Modeling the Imaging Chain /1
2 The Imaging Chain and Applications /5
2.1 The Imaging Chain /5
2.2 Generating Simulated Image Products Using the Imaging Chain /6
2.3 Applications of the Imaging Chain Model Through a Camera
     Development Model /8
    2.3.1 Imaging system concept /8
    2.3.2 Image product requirements /8
    2.3.3 System requirements /10
    2.3.4 System build /10
    2.3.5 System initialization /10
    2.3.6 System operations and improvement /11
    2.3.7 Verification of imaging chain models /11
2.4 Applying the Imaging Chain to Understand Image Quality /11
    2.4.1 Image quality assurance /12
    2.4.2 Image forgery /12
References /14
3 Mathematics /15
3.1 Fundamental Mathematics for Modeling the Imaging Chain /15
3.2 Useful Functions /15
3.3 Linear Shift-Invariant (LSI) Systems /21
3.4 Convolution /22
3.5 Fourier Transforms /25
    3.5.1 Interpreting Fourier transforms /27
    3.5.2 Properties of Fourier transforms /29
    3.5.3 Fourier transforms of images /32
References /37
4 Radiometry /39
4.1 Radiometry in the Imaging Chain /39
4.2 Electromagnetic Waves /39
4.3 Blackbody Radiation /41
4.4 Object Radiance at the Camera /43
References /47
5 Optics /49
5.1 Optics in the Imaging Chain /49
5.2 Geometric and Physical Optics /49
5.3 Modeling the Optics as a Linear Shift-Invariant (LSI) System /52
5.4 Modeling the Propagation of Light /53
5.5 Diffraction from an Aperture /54
5.6 Optical Transfer Function (OTF) /62
5.7 Calculating the Diffraction OTF from the Aperture Function /65
5.8 Aberrations /68
References /72
6 Digital Sensors /73
6.1 Digital Sensors in the Imaging Chain /73
6.2 Focal Plane Arrays /73
    6.2.1 Array size and geometry /76
6.3 Sensor Signal /79
6.4 Calibration /82
6.5 Sensor Noise /84
    6.5.1 Signal-to-noise ratio /87
6.6 Sensor Transfer Function /88
6.7 Detector Sampling /91
References /97
7 Motion /99
7.1 Motion Blur in the Imaging Chain /99
7.2 Modeling General Motion /99
7.3 Smear /100
7.4 Jitter /104
7.5 Oscillation /106
References /108
8 The Story of Q /109
8.1 Balancing Optics and Sensor Resolution in the Imaging Chain /109
8.2 Spatial Resolution /109
    8.2.1 Resolution Limits /112
8.3 Defining Q /115
8.4 Q Considerations /118
References /126
9 Image Enhancement Processing /127
9.1 Image Processing in the Imaging Chain /127
9.2 Contrast Enhancements /128
    9.2.1 Gray-level histogram /128
    9.2.2 Contrast stretch /130
    9.2.3 Tonal enhancement /134
9.3 Spatial Filtering /137
    9.3.1 Image restoration /138
9.4 Kernels /141
    9.4.1 Transfer functions of kernels /144
    9.4.2 Kernel designs from specified transfer functions /148
    9.4.3 Kernel examples /150
9.5 Superresolution Processing /156
    9.5.1 Nonlinear recursive restoration algorithms /157
    9.5.2 Improving the sampling resolution /158
References /160
10 Display /163
10.1 Display in the Imaging Chain /163
10.2 Interpolation /164
10.3 Display System Quality /168
References /171
11 Image Interpretability /173
11.1 Image Interpretability in the Imaging Chain /173
11.2 The Human Visual System /173
11.3 Psychophysical Studies /177
11.4 Image Quality Metrics /179
    11.4.1 Image quality equations and the National Imagery
     Interpretability Rating Scale (NIIRS) /181
References /186
12 Image Simulations /189
12.1 Putting It All Together: Image Simulations from the Imaging
       Chain Model /189
    12.1.1 Input scene /190
    12.1.2 Radiometric calculation /190
    12.1.3 System transfer function /191
    12.1.4 Sampling /192
    12.1.5 Detector signal and noise /194
    12.1.6 Enhancement processing /195
12.2 Example: Image Quality Assessment of Sparse Apertures /195
References /203
Index /205

To the Reader

This tutorial aims to help people interested in designing digital cameras who have not had the opportunity to delve into the mathematical modeling that allows understanding of how a digital image is created. My involvement with developing models for the imaging chain began with my fascination in the fact that image processing allows us to "see" mathematics. What does a Fourier transform look like? What do derivatives look like? We can visualize the mathematical operations by applying them to images and interpreting the outcomes. It was then a short jump to investigate the mathematical operations that describe the physical process of forming an image. As my interest in camera design grew, I wanted to learn how different design elements influenced the final image. More importantly, can we see how modifications to a camera design will affect the image before any hardware is built? Through the generous help of very intelligent professors, friends, and colleagues I was able to gain a better understanding of how to model the image formation process for digital cameras.

Modeling the Imaging Chain of Digital Cameras is derived from a course that I teach to share my perspectives on this topic. This book is written as a tutorial, so many details are left out and assumptions made in order to generalize some of the more difficult concepts. I urge the reader to pick up the references and other sources to gain a more in-depth understanding of modeling the different elements of the imaging chain. I hope that the reader finds many of the discussions and illustrations helpful, and I hope that others will find modeling the imaging chain as fascinating as I do.

Robert D. Fiete
October 2010

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