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Optical Interference Filters Using MATLAB
Author(s): Scott W. Teare
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Book Description

Optical Interference Filters Using MATLAB® provides a foundation for the development of MATLAB code for simulating the performance of thin-film optical structures that can be combined to make interference filters. MATLAB has excellent calculation and visualization capabilities that together are well aligned to the matrix methods commonly used for thin-film calculations. The simulations developed in this book begin with filters based on simple dielectric materials both with and without dispersion. Building on the discussion of these simple filters, simulations are next developed for metal-layer-based induced-transmission filters, and finally for complete thin-film interference filters. Readers ranging from students to practicing scientists and engineers will find that these simulations work well in conjunction with other textbooks in the field, or they can stand alone. The ability to generate custom programs and tune them to explore specific features of optical interference filters is anticipated to enhance the designer’s understanding and appreciation of the subtleties involved in filter design.

Book Details

Date Published: 17 January 2019
Pages: 194
ISBN: 9781510623125
Volume: PM299

Table of Contents
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Table of Contents

List of Notation

1 Introduction
1.1 Optical Filters
1.2 Interference Filters
1.3 Bandpass Filters
1.4 Induced-Transmission Filters
1.6 Summaries of the Chapters

2 Light: Reflection and Transmission
2.1 Light: Reflection and Transmission
2.2 Total Internal Reflection and Brewster's Angle
2.3 Fresnel Equations
2.4 Light Waves at Thin Dielectric Layers
2.5 Antireflection Coatings
2.6 Matrix Methods for Thin Films

3 Complex Index of Refraction in Optical Materials
3.1 Complex Index of Refraction
3.2 Absorbance in Optical Materials
3.3 Wavelength Dependence of the Refractive Index
3.4 Wavelength Dependence of Thin-Film Layers
3.5 Reflection, Transmission, and Absorption from a Metal Layer

4 Optical Admittance Matching
4.1 Impedance and Admittance
4.2 Admittance for Quarter-Wavelength-Thick Layers
4.3 Admittance Diagram
4.4 Broadband Antireflection Coating

5 Dielectric Thin-Film Structures
5.1 Transmission Profile Simulator
5.2 Spike Structure
5.3 Blocking Structure
5.4 Bandpass Filters: Stacked Filters
5.4 Non–QWOT Layers

6 Maximum Potential Transmittance for Induced-Transmission Filters
6.1 Maximum Potential Transmittance
6.2 Constructing the Induced-Transmission Filter
6.3 Peak Shape
6.4 Multiple-Metal-Cavity Filters

7 Offband Effects in Induced-Transmission Filters
7.1 Metal k/n Ratio
7.2 Potential Transmittance of Al, Ag, and Au
7.3 Long-Wavelength Suppression
7.4 Admittance-Matching Metal Layers

8 Enhancing Bandpass Filters
8.1 Multiple-Component Bandpass Filters
8.2 Design File and Calculation Engine: Spike Structure
8.3 Improving the Spike Filter: Multicavity
8.4 Improving the Spike Filter: Increased HL Pairs
8.5 Improving the Spike Structure: Thick Cavity
8.6 Other Structures
8.7 The Multicomponent Filter
8.8 Specifying a Filter for Manufacturing

9 Interference Filter Applications
9.1 Setting Up for Synthesis
9.2 Antireflection of a Lens
9.3 Antireflection of Photodiodes
9.4 Dual-band System
9.5 Near-Infrared Filter
9.6 Well-Blocked Filter

10 From Simulations to Functional Filters
10.1 Measuring the Transmission Profile
10.2 Thickness Monitoring
10.3 Other Thin-Film Materials
10.4 Deposition Techniques
10.5 Stresses in Thin-Film Stacks
10.6 Is Thin-Film Research a Dead Topic?
10.7 All-In-One Filter
10.8 Angle-of-Incidence Variation
10.9 Back to the Standards



Most optical systems benefit from the use of coating technologies to improve the throughput of light, and many optical systems could not work without the advantages of optical coatings. Optical designers and engineers often need to understand and select optical coatings for their systems, balancing cost and performance of available optical coatings in their designs. This means that a good understanding of optical coating design, performance, and limitations is an important asset for optical designers.

Optical interference coatings are made from numerous thin-film layers and can be used to make reflectors and antireflectors as well as bandpass, absorbing, and high- and low-pass filters, to name a few. Modern optical systems make use of a large number of optical elements, typically with each surface coated in order to meet the needed performance. This has resulted in the topic of thin-film interference coatings being an integral part of an optical engineering education that is often supported by introducing students to sophisticated commercially available computer programs. Alternatively, professors and students can use the topic of optical coatings to explore the underlying physics of thin-film coatings and learn the basics of programming by developing their own custom programs. This approach is well supported by the versatility and visualization capabilities of MATLAB, which can be used to explore the full range of designing, evaluating, and tuning optical filters.

My work with optical thin films began as a graduate student with Dr. Charles W. Fischer in the Physics Department at the University of Guelph, Canada. There we used a variety of metal coatings that were thermally evaporated onto semiconductor and glass substrates to investigate interface changes due to high electric fields during anodic oxidation using Rutherford backscattering and other surface physics techniques. Our work was often interrupted by the need to rebuild the oil-diffusion-pump–based deposition system which, greatly improved my skills in rebuilding vacuum systems. This early experience served me well for coating large telescope mirrors at Mount Wilson Observatory in support of laser guide star adaptive optics work with Dr. Laird A. Thompson of the University of Illinois at Urbana-Champaign. This adaptive optics project used the 100-in. telescope for the full-aperture broadcast ultraviolet laser light and to collect Rayleigh backscattered light from a 20-km focus, requiring that high mirror reflectivity be maintained throughout the optical chain. The Mount Wilson Observatory coating system was originally built by Dr. J. Strong and is still in use today with its cast-iron 2.5-m vacuum chamber, a 16-in. diffusion pump, and 72 deposition sources. On coming to New Mexico Tech, I collaborated with Dr. Stanley L. Bryn on novel thin-film optical filter designs, many of which included induced transmission filters.

Optical Interference Filters Using MATLAB® comprises 10 chapters that guide the reader through topics of interest related to thin-film optical coatings, many of which are supported by MATLAB scripts. The book was designed so that the reader can progress through the book and construct optical coating simulators that can be revised to explore particular filter design tasks of interest. If you are familiar with MATLAB, it will be easy to use the programs to better understand optical coatings; if you are already familiar with optical coatings, you can expand your capabilities with MATLAB. If you are already using MATLAB and are well familiar with optical coatings, you might find that this book consolidates many of the ideas you are already comfortable with but have not had a chance to explore in detail.

I appreciate all of the help and support of many individuals who have shared their knowledge and expertise with me over the years. Should errors be found in this text, I would appreciate receiving any comments and corrections. Please direct your correspondence to the author c/o New Mexico Tech, Electrical Engineering Department, Socorro, NM 87801, USA, or email me at

I am most grateful for the support of SPIE for their interest in publishing this work as part of the Monograph Series and, in particular, the efforts of Senior Editor Dara Burrows for putting this work into its final form.

Scott W. Teare
Socorro, New Mexico
January 2019

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