Foundations of Optical System Analysis and Design

Lakshminarayan Hazra

• Publisher: CRC Press
• Year: 2022
• Print ISBN: 9781498744928
• eBook ISBN: 9780429531415
• Topic: Sciences physiques
• Subtopic: Ingénierie de l'électricité et des télécommunications

Since the incorporation of scientific approach in tackling problems of optical instrumentation, analysis and design of optical systems constitute a core area of optical engineering. A large number of software with varying level of scope and applicability is currently available to facilitate the task. However, possession of an optical design software, per se, is no guarantee for arriving at correct or optimal solutions. The validity and/or optimality of the solutions depend to a large extent on proper formulation of the problem, which calls for correct application of principles and theories of optical engineering. On a different note, development of proper experimental setups for investigations in the burgeoning field of optics and photonics calls for a good understanding of these principles and theories.

With this backdrop in view, this book presents a holistic treatment of topics like paraxial analysis, aberration theory, Hamiltonian optics, ray-optical and wave-optical theories of image formation, Fourier optics, structural design, lens design optimization, global optimization etc. Proper stress is given on exposition of the foundations.

The proposed book is designed to provide adequate material for 'self-learning' the subject. For practitioners in related fields, this book is a handy reference.

Foundations of Optical System Analysis and Synthesis provides

• A holistic approach to lens system analysis and design with stress on foundations
• Basic knowledge of ray and wave optics for tackling problems of instrumental optics
• Proper explanation of approximations made at different stages
• Sufficient illustrations for facilitation of understanding
• Techniques for reducing the role of heuristics and empiricism in optical/lens design
• A sourcebook on chronological development of related topics across the globe

This book is composed as a reference book for graduate students, researchers, faculty, scientists and technologists in R & D centres and industry, in pursuance of their understanding of related topics and concepts during problem solving in the broad areas of optical, electro-optical and photonic system analysis and design.

1Introduction

DOI: 10.1201/9780429154812-1

1.1 An Early History of Optical Systems and Optics

The history of optical systems can be traced back to the Palaeolithic Age, or old Stone Age, starting around 40,000 bce, when, it can only be surmised, human beings would be surprised and intrigued by observing the images formed by some naturally occurring surfaces.

1.1.1 Early History of Mirrors

In the Palaeolithic Age (around 40,000-10,000 bce) and the Mesolithic Age (10,000–8000 bce), the mirrors used by humans were most likely surfaces of lakes or pools of still water. In the early Neolithic age (8000–3000 bce), the surface of water collected in a primitive vessel of some sort might have acted as a mirror, but historical evidence suggests that the formal manufacture of mirrors took place sometime in that age. The earliest manufactured mirrors were pieces of polished stone, e.g., obsidian, a naturally occurring volcanic glass. Some of the obsidian mirrors excavated by archaeologists at Çatal Höyük, located in Anatolia within the Konya Plain (modern day Turkey), have been dated to around 6000 bce [1–3].

Mirrors of polished copper were crafted in Mesopotamia from 4000 bce, and in ancient Egypt from around 3000 bce. Polished bronze mirrors were made by the Egyptians from 2900 bce.

On the Indian subcontinent, manufacture of bronze mirrors goes back to the time between 2800 bce and 2500 bce, during the Indus valley civilization [4–5]. Bronze mirrors, in general, are of low tin content (usually less than 10 percent). However, historical evidence exists of use of bronze mirrors with a much higher content of tin in different parts of India from an early period. A high-tin metal alloy mirror of high reflectance, known as ‘Aranmula’ mirror, manufactured in the state of Kerala in South India, continues to be made even now [6–7].

Some of the earliest examples of Chinese copper and bronze mirrors belonged to the late Neolithic Qijia culture from around 2000 bce [8]. In Europe, bronze mirrors from the Bronze Age have been discovered from various places, including Britain and Italy. Polished stone and pyrite mirrors from different parts of central and south America have been found, dating from 2000 bce [9]. Interestingly, the oldest mirrors from the Inca period (in Peru) predate the Olmec mirrors (in Mexico) by about 800 years [10].

1.1.2 Early History of Lenses

In comparison with mirrors, the known history of lenses is shorter by several millennia. The earliest lenses, discovered in Egypt, are dated between 2600–2400 bce [11]. These lenses were found in the eyes of Egyptian statues. A set of lenses of larger diameter has been discovered in Troy (now Western Turkey) dating from 2200 bce, whilst another set of lenses of the Minoan era were discovered in Crete and dates from 1500 bce. The very good optical quality of these lenses prompted some scholars to argue that there was widespread use of lenses in antiquity, spanning several millennia [12–13]. Recently discovered ancient artificial eyes have been dated to 3000 bce (for one discovered in Iran), and 5000 bce (for one discovered in Spain) [14].

The ‘Nimrud’ lens, also known as ‘Layard’ lens, in memory of Austin Henry Layard who discovered it in 1850 ce, was unearthed at the Assyrian palace at Nivedeh, near the river Tigris in modern day Iraq [15–17]. It is dated around 1000 bce, and credited by many as the earliest known manufactured lens for use either as a magnifying lens or as a burning lens to start fire by concentrating sunlight. It should be noted that all these early lenses were made of rock crystal, which is pure transparent crystalline quartz (SiO₂), i.e., silica.

1.1.3 Early History of Glass Making

The history of glass making dates back to at least 3600 bce in central north Syria, Mesopotamia and Egypt, but manufacturing of glass was not very widespread for a long time. In Mesopotamia, it was revived in 700 bce, and in Egypt in 500 bce. For the next 500 years, Egypt, Syria and other countries along the coast of the Mediterranean Sea were centres for glass manufacturing. In the first century bce, Syrian craftsmen invented the blow pipe, and this made the production of glass easier, faster and cheaper. Glass production flourished in the Roman empire, and spread from Italy to all countries under its rule. From the first century ce onwards, use of magnifying glasses increased, and quality lenses were made from glass throughout the Roman empire [18–21]. In India, development of glass technology began in 1700 bce [22]. In ancient China, glass making had a later start during the Warring States period (475–220 bce).

The brief history of optical systems of the ancient period, as enunciated above, forms an integral part of the history of optics.

1.1.4 Ancient History of Optics in Europe, India and China

In all major civilizations, the ancient history of optics concerned the nature of light [23], and the visual perception [24]. In fifth century bce, the pre-Socratic philosopher, Empedocles argued that vision occurred when light issued from the eyes. This was what is known as the ‘Emission Theory’, or the ‘Extramission Theory’. Plato held this theory, as did Hero, Euclid and Ptolemy in the Hellenistic age. Later, Aristotle, around 350 bce, advocated for a ‘theory of intromission’ by which the eye received rays rather than directed them outward.

A few other theories involved different combinations or modifications of these two approaches. On the nature of light, in ancient India, the philosophical schools of Sāmkhya and Vaiśeşika developed theories of light in the period of the sixth to the fifth century bce [25–27]. The concept of a ray of light was developed in these schools, and the theory of vision in Vaiśeşika school of philosophy comprised of a combination of the theories of extramission and intromission.

For example, below are three Vaiśeşika Sûtras of Kanâda. The first one defines the nature of light, whilst the next two define the nature of darkness. The numbers after each statement refer to the identifying number of the Sûtra in Vaiśeşika philosophy:

1. तेजो रुपस्पर्शबत््् । २/१/३ [Tejo rūpasparśavat//2/1/3//] ‘Fire or light is identifiable by feel and sight’.
2. द्रब्यगुणकर्मनिष्पत्तिबैधर्म्यादभावस्तम: । ५/२/१९ [Dravyaguṇakarmmaniṣpattivaidharāmmyādabhāvastmamaḥ //5/2/19//] ‘Darkness is non-existence, because it is different in its production from substance, attribute and action’.
3. तेजसोद्रब्यान्तरेणावरणाच्च । ५/२/२० [Tejaso dravyāntareṇāvaraṇācca //5/2/20] ‘(Darkness is non-existence), also because (it is produced) from the obscuration of light by another substance’.

It is interesting to note that the concept of a ray as a direction of propagation of light was also developed in the early Hellenic period. A work entitled Optics by Euclid of Alexandria (300 bce), often referred to as the founder of geometry, is the earliest surviving Greek treatise on ‘Geometrical Optics’. It deals with the rectilinear propagation of light, shadows, perspective, parallax, etc [28]. Hero ce of Alexandria (10–70 ce), also known as Heron of Alexandria, is considered the greatest experimenter of antiquity. It is surprising to note that he derived the laws of reflection of light by invoking the stationarity principle. His treatise entitled Catoptrica deals with the progression of light, reflection, and the use of mirrors [29]. Ptolemy (100–170 ce), also of Alexandria, wrote a treatise called Optics that survives in a poor Arabic translation. He wrote about the properties of light, including reflection, refraction, and colour. His works influenced the subsequent investigators significantly [30–31].

A book entitled Catoptrics used to be attributed to Euclid. The book covers mathematical theory of mirrors, particularly the images formed by plane and spherical concave mirrors. However, the authorship of the available version of the book is disputed, and it is argued that it might have been compiled by the fourth century ce mathematician, Theon of Alexandria [32].

It is also noteworthy that, during the Warring States period in China, Mo Zi (385 bce), who established the Mohism school dealing with natural sciences and engineering, deliberated on many phenomena of light in his book [33–34].

1.1.5 Optics Activities in the Middle East in 10th Century ce

After the fourth century ce, there was a lull in investigations in optics and related areas for a few centuries, as evidenced by the absence of any significant report. A revival of activities took place in the middle east in the tenth century ce. Ibn Sahl, a Persian mathematician, developed geometrical treatments for burning mirrors and lenses. Although he did not put forward any formal law of refraction, his analysis was mostly correct [35]. Another Persian mathematician, Al Quhi, developed geometrical treatments for mirrors from different conic sections [36–37]. The well-known Arab scholar, Ibn al-Haytham, also ...

Table of contents

• Cover
• Half-Title Page
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Acknowledgements
• Author Brief Biography
• 1 Introduction
• 2 From Maxwell’s Equations to Thin Lens Optics
• 3 Paraxial Optics
• 4 Paraxial Analysis of the Role of Stops
• 5 Towards Facilitating Paraxial Treatment
• 6 The Photometry and Radiometry of Optical Systems
• 7 Optical Imaging by Real Rays
• 8 Monochromatic Aberrations
• 9 Chromatic Aberrations
• 10 Finite or Total Aberrations from System Data by Ray Tracing
• 11 Hopkins’ Canonical Coordinates and Variables in Aberration Theory
• 12 Primary Aberrations from System Data
• 13 Higher Order Aberrations in Practice
• 14 Thin Lens Aberrations
• 15 Stop Shift, Pupil Aberrations, and Conjugate Shift
• 16 Role of Diffraction in Image Formation
• 17 Diffraction Images by Aberrated Optical Systems
• 18 System Theoretic Viewpoint in Optical Image Formation
• 19 Basics of Lens Design
• 20 Lens Design Optimization
• 21 Towards Global Synthesis of Optical Systems
• Epilogue
• Index