## Introduction to the Series

Welcome to the * SPIE Field Guides*—a series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the

*is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series.*

**SPIE Field Guides**Each * SPIE Field Guide* addresses a major field of optical science and technology. The concept of these

*is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights, and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each*

**Field Guides***provide additional information such as related material outside the main scope of the volume, key mathematical relationships, and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field.*

**Field Guide**The * SPIE Field Guides* are intended to be living documents. The modular page-based presentation format allows them to be updated and expanded. We are interested in your suggestions for new

*topics as well as what material should be added to an individual volume to make these*

**Field Guide***more useful to you. Please contact us at fieldguides@SPIE.org.*

**Field Guides**John E. Greivenkamp, **Series Editor**

College of Optical Sciences

The University of Arizona

## The Field Guide Series

*:*

**SPIE Field Guides**, Second Edition, Robert K. Tyson and Benjamin W. Frazier**Adaptive Optics**, Christoph U. Keller, Ramon Navarro, and Bernhard R. Brandl**Astronomical Instrumentation**, Second Edition, Larry C. Andrews**Atmospheric Optics**, Paul R. Yoder, Jr. and Daniel Vukobratovich**Binoculars and Scopes**, Ashok K. Batra and Mohan D. Aggarwal**Crystal Growth**, Yakov G. Soskind**Diffractive Optics**, Bernard Kress**Digital Micro-Optics**, Jonathan D. Ellis**Displacement Measuring Interferometry**, William Spillman, Jr. and Eric Udd**Fiber Optic Sensors**, John E. Greivenkamp**Geometrical Optics**, Pierre-Alexandre Blanche**Holography**, Angelo Arecchi, Tahar Messadi, and R. John Koshel**Illumination**, Khan M. Iftekharuddin and Abdul Awwal**Image Processing**, Arnold Daniels**Infrared Optics, Materials, and Radiometry**, Eric P. Goodwin and James C. Wyant**Interferometric Optical Testing**, Rüdiger Paschotta**Laser Pulse Generation**, Rüdiger Paschotta**Lasers**, Julie Bentley and Craig Olson**Lens Design**, Paul McManamon**Lidar**, J. Scott Tyo and Andrey S. Alenin**Linear Systems in Optics**, Tomasz S. Tkaczyk**Microscopy**, Alan Symmons and Michael Schaub**Molded Optics**, Peter E. Powers**Nonlinear Optics**, Ray Williamson**Optical Fabrication**, Rüdiger Paschotta**Optical Fiber Technology**, Chris A. Mack**Optical Lithography**, Ronald R. Willey**Optical Thin Films**, Katie Schwertz and James H. Burge**Optomechanical Design and Analysis**, Daniel G. Smith**Physical Optics**, Edward Collett**Polarization**, Larry. C. Andrews and Ronald L. Phillips**Probability, Random Processes, and Random Data Analysis**, Barbara G. Grant**Radiometry**, Larry C. Andrews**Special Functions for Engineers**, David W. Ball**Spectroscopy**, Créidhe M. O’Sullivan and J. Anthony Murphy**Terahertz Sources, Detectors, and Optics**, Jim Schwiegerling**Visual and Ophthalmic Optics**

## Field Guide to Infrared Systems, Detectors, and FPAs, Third Edition

The amount of new material that was added to the second edition of the * Field Guide to Infrared Systems, Detectors, and FPAs* (2010) was rather extensive. As a result, this third edition is accompanied by a “companion” publication, the

*.*

**Field Guide to Infrared Optics, Materials, and Radiometry**These Field Guides cover a broad range of technical topics necessary to understand the principles of modern infrared technology. They combine numerous engineering disciplines that are essential for the development of infrared systems. The mathematical equations and physical concepts in these Field Guides are in sequence. Therefore, although these publications are sold separately, it is highly recommended that readers acquire the two books as a set.

This third edition of the * Field Guide to Infrared Systems, Detectors, and FPAs,* is devoted to fundamental background issues for optical detection processes. It compares the characteristics of cooled and uncooled detectors with an emphasis on spectral and blackbody responsivity, and detectivity, as well as the noise mechanisms related to optical detection. This edition introduces the concepts of barrier infrared detector technologies and encompasses the capabilities and challenges of third-generation infrared focal plane arrays as well as the advantages of using dual-band technology.

With this acquired background, the last chapter considers the systems design aspects of infrared imagers. Figures of merit such as MTF, NETD, and MRTD of starring arrays are examined for the performance metrics of thermal sensitivity and spatial resolution of thermal imaging systems. The parameter λ(* F*/#)/

*, motion MTF, and atmospheric MTF are included in this third edition. It also includes an overview of the targeting task performance (TTP) metric.*

**d**I would like to acknowledge and express my gratitude to my professor and mentor Dr. Glenn Boreman for his guidance, experience, and friendship. The knowledge that he passed on to me during my graduate studies at CREOL ultimately contributed to the creation of this book.

I extend my sincere appreciation to Dr. Mel Friedman, NVESD, who took on the onerous task of improving and clarifying the TTP metric concepts and its contents. I would also like to thank Mr. Thomas Haberfelde for his efforts in reviewing the drafts of the manuscripts as well as Alexander Daniels and Dara Burrows for their skillful editing assistance.

Above all, I voice a special note of gratitude to my kids Becky and Alex, and my wife Rosa for their love and support.

Lastly, I would particularly like to thank you, the reader, for selecting these books and taking the time to explore the topics related to this motivating and exciting field. I trust that the contents of these Field Guides will prove interesting and useful to engineers and scientists working in one of the various infrared fields.

These Field Guides are dedicated to the memory of my father and brothers.

**Arnold Daniels**

September 2018

#### Glossary of Symbols

**a**

Size of airborne particles

**A**

Area

**A**_{d}

Detector area

**A**_{obj}

Area of an object

**A**_{opt}

Area of an optical component

**A**_{s}

Area of a source

**B**

3-db bandwidth

B-B

Bound-to-bound

B-C

Bound-to-continuum

B-QB

Bound-to-quasi-bound

BLIP

Background-limited infrared photodetector

**c**

Speed of light in vacuum

**C**_{d}

Detector capacitance

**C**_{th}

Thermal capacitance

${C}_{n}^{2}$

Refractive index structure constant

CQWIP

Corrugated quantum-well infrared photodetector

CTE

Coefficient of thermal expansion

CTF

Contrast transfer function

CTF_{eye}

Contrast threshold function of the eye

CTF_{n}

Contrast threshold function in the presence of external noise

CTF_{sys}

Contrast threshold function of a system

**d**

Detector size

**d**_{diff}

Diameter of a diffraction-limited spot

**d**_{h}

Detector size in the horizontal direction

**d**_{v}

Detector size in the vertical direction

**D**

Electrical displacement

**D ^{*}
**

Normalized detectivity of a detector

${D}_{\mathrm{BF}}^{*}$

Background fluctuation D-star

${D}_{\mathrm{BLIP}}^{*}$

D-star under BLIP conditions

${D}_{\mathrm{TF}}^{*}$

Temperature fluctuation D-star

**D ^{**}
**

Angle-normalized detectivity

**D**_{in}

Input diameter

**D**_{lens}

Lens diameter

**D**_{opt}

Optics diameter

**D**_{out}

Output diameter

e

Energy-based unit subscript

**E**_{bkg}

Background irradiance

**E**_{source}

Source irradiance

ESF

Edge spread function

$\mathcal{E}$

Energy of a photon

${\mathcal{E}}_{\mathrm{gap}}$

Energy gap of a semiconductor material

**f**

Focal length

**f**_{0}

Center frequency of an electrical filter

**f**_{eff}

Effective focal length

* f* (

*,*

**x***)*

**y**Object function

**F**

Finesse

* F*(ξ,η)

Object spectrum

FOR

Field of regard

FOV

Full-angle field of view

FPA

Focal plane array

* F*/#

F-number

* g*(

*,*

**x***)*

**y**Image function

**G**

Gain of a photoconductive detector

* G*(ξ,η)

Image spectrum

**h**

Planck’s constant

**h**_{img}

Image height

**h**_{obj}

Object height

* h*(

*,*

**x***)*

**y**Impulse response

**H**

Heat capacity

* H*(ξ,η)

Transfer function

HIFOV

Horizontal instantaneous field of view

HFOV

Horizontal field of view

**i**

Electrical current

$\stackrel{\u203e}{i}$

Mean current

**i**_{avg}

Average electrical current

**i**_{bkg}

Background rms current

**i**_{dark}

Dark current

**i**_{j}

rms Johnson noise current

**i**_{1/}
**
_{f}
**

rms 1/* f*-noise current

**i**_{nG}
**
_{/}
**

_{R}

Generation–recombination (G/R) noise rms current

**i**_{noise}

Noise current

**i**_{o}

Dark current

**i**_{oc}

Open circuit current

**i**_{pa}

Preamplifier noise rms current

**i**_{ph}

Photogenerated current

**i**_{rms}

rms current

**i**_{sc}

Short circuit current

**i**_{shot}

Shot noise rms current

**i**_{sig}

Signal current

IC

Integrated circuit

IRFPA

Infrared focal plane array

**j**

imaginary number

**J**

Current density

$k$

Boltzmann’s constant

$\mathcal{K}$
(ξ*
_{f}
*)

Spatial-frequency-dependant MRTD proportionality factor

**l**_{w}

Width of a well

$L$

Atmospheric path length

**L**

Radiance

**L**_{bkg}

Background radiance

**L**_{e}

Radiance in energy units

**L**_{p}

Radiance in photon units

**L**_{v}

Visual luminance

**L**_{λ}

Spectral radiance

LPE

Liquid phase epitaxy

LSF

Line spread function

LWIR

Longwave infrared

${m}_{\text{e}}^{*}$

Effective mass of an electron

**M**

Exitance

**M**_{e}

Exitance in energy units

**M**_{meas}

Measured exitance

**M**_{obj}

Exitance of an object

**M**_{p}

Exitance in photon units

**M**_{λ}

Spectral exitance

MRTD

Minimum resolvable temperature difference

MTF

Modulation transfer function

MTF_{aer}

Aerosol MTF

MTF_{d}

Detector MTF

MTF_{linear}

Linear-motion MTF

MTF_{post}

Post-sampled MTF (display, digital processing, and the eye–brain filter)

MTF_{pre}

Pre-sampled MTF (optics detector, and line-of-sight jitter),

MTF_{random}

Random-motion MTF

MTF_{sin}

Sinusoidal-motion MTF

MTF_{sys}

System’s MTF

MTF_{tur}

Turbulence MTF

MWIR

Midwave infrared

$\mathcal{M}$

Magnification

${\mathcal{M}}_{\mathrm{ang}}$

Angular magnification

**n**

Refractive index

**n**_{cycles}

Number of cycles needed to discriminate a target

**n**_{d}

Number of detectors

**n**_{e}

Number of photogenerated electrons

**n**_{lines}

Number of lines

NEI

Noise-equivalent irradiance

NEP

Noise-equivalent power

NETD

Noise-equivalent temperature difference

NETD_{BF}

Background fluctuation NETD

NETD_{BLIP}

NETD under BLIP conditions

NETD_{TF}

Temperature fluctuation NETD

NEΔ**f**

Noise-equivalent bandwidth

OTF

Optical transfer function

p

Photon-based unit subscript

$\mathcal{p}$

Pyroelectric coefficient

**p**

Momentum of an electron

**P**

Magnitude of internal polarization

**P**_{avg}

Average power

**P**_{chance}

Probability of chance

**P**_{measured}

Field-measured probability

**P**_{observer}

Observer’s probability

PSD

Power spectral density

PSF

Point spread function

PV

Photovoltaic (or photodiode)

**r**_{o}

Fried coherence length

**R**

Resistance

**R**_{d}

Detector resistance

**R**_{eq}

Equivalent resistance

**R**_{in}

Input resistance

**R**_{L}

Load resistance

**R**_{out}

Output resistance

**R**_{th}

Thermal resistance

RIIC

Read-in integrated circuit

ROIC

Read-out integrated circuit

RSS

Root sum square

$\mathcal{R}$

Responsivity

$\mathcal{R}$
_{i}

Current responsivity

$\mathcal{R}$
_{υ}

Voltage responsivity

$\mathcal{R}$
(* T*)

Blackbody responsivity

$\mathcal{R}$ (λ)

Spectral responsivity

SCN_{tmp}

Scene contrast temperature

SL

Superlattice

SNR

Signal-to-noise ratio

SR

Strehl-intensity ratio

SRR_{out}

Out-of-band spurious response ratio

**t**

Time

**T**

Temperature

**T**_{bkg}

Background temperature

**T**_{c}

Curie temperature

**T**_{d}

Detector temperature

**T**_{load}

Load temperature

**T**_{source}

Source temperature

**T**_{target}

Target temperature

TRC

Thermal resistance coefficient

VFOV

Vertical field of view

VIFOV

Vertical instantaneous field of view

**x**

Alloy composition or molar fraction ratio

α

Coefficient of absorption

α

Thermal resistance coefficient

Δ**f**

Electronic frequency bandwidth

Δ**t**

Time interval

Δ**T**

Temperature difference

Δλ

Wavelength interval

ε

Emissivity

η

Spatial frequency in the vertical direction

η

Quantum efficiency

η_{scan}

Scan efficiency

θ

Angle variable

θ_{max}

Maximum angle subtense

Θ

Seebeck coefficient

λ

Subscript indicating a spectral radiometric quantity

λ

Wavelength

λ_{cutoff}

Cutoff wavelength

λ_{cuton}

Cuton wavelength

λ_{max}

Maximum wavelength

λ_{max-cont}

Maximum-contrast wavelength

λ_{o}

Fixed wavelength

λ_{peak}

Peak wavelength

Λ

de Broglie wavelength

μ

Vertical sample frequency

ν

Optical frequency

ξ

Spatial frequency in the horizontal direction

ξ_{cutoff}

Spatial cutoff frequency

ξ_{cuton}

Spatial cuton frequency

ξ_{J}

Johnson spatial frequency

ρ

Electric charge

ρ

Reflectance

σ

Standard deviation

σ

Atmospheric extinction coefficient

σ^{2}

Variance

σ_{a}

Random amplitude of the jitter

σ_{e}

Stefan–Boltzmann constant in energy units

σ_{eye}

rms visual noise expressed at a display

σ_{n}

rms noise filtered by a display

σ_{p}

Stefan–Boltzmann constant in photon units

τ

Transmittance

τ_{atm}

Atmospheric transmittance

τ_{dwell}

Dwell time

τ_{external}

External transmittance

τ_{frame}

Frame time

τ_{int}

Integration time

τ_{internal}

Internal transmittance

τ_{line}

Line time

τ_{opt}

Optical transmittance

τ_{peak}

Peak transmittance

τ_{RC}

Electrical time constant

τ_{th}

Thermal time constant

$\mathit{\upsilon}$

Horizontal sample frequency

$\stackrel{\u203e}{v}$

Mean voltage

**v**_{det}

Detector voltage

**v**_{in}

Input voltage

**v**_{j}

Johnson noise rms voltage

**v**_{n}

rms noise voltage

**v**_{oc}

Open-circuit voltage

**v**_{out}

Output voltage

**v**_{sc}

Short-circuit voltage

**v**_{s}

Shot-noise rms voltage

**v**_{scan}

Scan velocity

**v**_{sig}

Signal voltage

φ

Flux

φ_{abs}

Absorbed flux

φ_{bkg}

Background flux

φ_{d}

Detector flux

φ_{e}

Radiant flux in watts

φ_{img}

Flux incident on an image

φ_{inc}

Incident flux

φ_{obj}

Flux radiated by an object

φ_{p}

Photon flux

φ_{sig}

Signal flux

φ_{trans}

Transmitted flux

φ_{λ}

Spectral flux

ψ

Eigenfunction

ω

Angular frequency

Ω

Solid angle

Ω_{bkg}

Background solid angle

Ω_{d}

Detector solid angle

Ω_{opt}

Optical solid angle

Ω_{s}

Source solid angle