This document provides an introduction to photometry and radiometry, which are the sciences of measuring light. It defines key concepts including:
- Radiant energy, which is the total amount of electromagnetic energy.
- Radiant flux (radiant power), which is the time rate of flow of radiant energy and is measured in watts.
- Radiant flux density, which is the radiant flux per unit area. When the flux is arriving at a surface it is called irradiance, and when leaving a surface it is called radiant exitance.
- Radiance, which is the amount of radiant flux in an elemental cone and provides a measure of the apparent brightness of a surface
Polarization and it's application in OphthalmologyRaju Kaiti
Polarization, types of polarization, mechanisms to produce polarization, Applications of polarization, precautions with polarizing sunglasses, ophthalmic uses of polarization
Polarization and it's application in OphthalmologyRaju Kaiti
Polarization, types of polarization, mechanisms to produce polarization, Applications of polarization, precautions with polarizing sunglasses, ophthalmic uses of polarization
Polarization of Light and its Application (healthkura.com)Bikash Sapkota
Download link ❤❤https://healthkura.com/eye-ppt/29/❤❤
Dear viewers Check Out my other piece of works at ❤❤❤ https://healthkura.com/eye-ppt/ ❤❤❤
polarization of light & its application.
PRESENTATION LAYOUT
Concept of Polarization
Types of Polarization
Methods of achieving Polarization
Applications of Polarization
POLARIZATION
Transforming unpolarized light into polarized light
Restriction of electric field vector E in a particular plane so that vibration occurs in a single plane
Characteristic of transverse wave
Longitudinal waves can’t be polarized; direction of their oscillation is along the direction of propagation.............
For Further Reading
•Optics by Tunnacliffe
•Optics and Refraction by A.K. Khurana
•Principle of Physics, Ayam Publication
•Internet
Dual Nature of Light, Wave nature of light,Young's double slit experiment, Reflection, Refraction of light, Polarization, Particle Nature of Light, Photoelectric Effect of light ..
This PPT gives an elementary idea about dispersion. The dispersion through prism is discussed in some details & combination of prisms are made to make either dispersion or deviation to be equal to zero.
This article describes the principle and phenomenon of polarization of light. This article also illustrates on Birefringence, Dichroism and crossed polarizers.
Malu's Law is elaborated here as prerequisite to understand Polarization along with Brewster's Angle. Polarization by reflection and polarization by refraction are also discussed here for quick comprehension of the readers.
What is Polarization?
Types of polarized light
Few related terms
Few laws related to polarization
Applications
FOR MORE VISIT: https://tariqalfayad.blogspot.com/
The chapter gives knowledge about the fundamentals, theory and applications of optical fiber for the first year Engineering level students. The material is most suitable for the students of first year B.E. and B.Tech.
In this presentation on Radiometry and Photometry we will look at Radiometry, the detection and measurement of radiation across the full electromagnetic spectrum, including ultraviolet, visible and infrared radiation. Photometry is concerned only with the visible portion of the spectrum, from about 380 to 780 nanometers.
Polarization of Light and its Application (healthkura.com)Bikash Sapkota
Download link ❤❤https://healthkura.com/eye-ppt/29/❤❤
Dear viewers Check Out my other piece of works at ❤❤❤ https://healthkura.com/eye-ppt/ ❤❤❤
polarization of light & its application.
PRESENTATION LAYOUT
Concept of Polarization
Types of Polarization
Methods of achieving Polarization
Applications of Polarization
POLARIZATION
Transforming unpolarized light into polarized light
Restriction of electric field vector E in a particular plane so that vibration occurs in a single plane
Characteristic of transverse wave
Longitudinal waves can’t be polarized; direction of their oscillation is along the direction of propagation.............
For Further Reading
•Optics by Tunnacliffe
•Optics and Refraction by A.K. Khurana
•Principle of Physics, Ayam Publication
•Internet
Dual Nature of Light, Wave nature of light,Young's double slit experiment, Reflection, Refraction of light, Polarization, Particle Nature of Light, Photoelectric Effect of light ..
This PPT gives an elementary idea about dispersion. The dispersion through prism is discussed in some details & combination of prisms are made to make either dispersion or deviation to be equal to zero.
This article describes the principle and phenomenon of polarization of light. This article also illustrates on Birefringence, Dichroism and crossed polarizers.
Malu's Law is elaborated here as prerequisite to understand Polarization along with Brewster's Angle. Polarization by reflection and polarization by refraction are also discussed here for quick comprehension of the readers.
What is Polarization?
Types of polarized light
Few related terms
Few laws related to polarization
Applications
FOR MORE VISIT: https://tariqalfayad.blogspot.com/
The chapter gives knowledge about the fundamentals, theory and applications of optical fiber for the first year Engineering level students. The material is most suitable for the students of first year B.E. and B.Tech.
In this presentation on Radiometry and Photometry we will look at Radiometry, the detection and measurement of radiation across the full electromagnetic spectrum, including ultraviolet, visible and infrared radiation. Photometry is concerned only with the visible portion of the spectrum, from about 380 to 780 nanometers.
A Novel Method to Improve Measurement Results of Flame Photometry Using Image...CSCJournals
The estimation of alkali metals in clinical chemistry has many parameters which can influence the result. A novel method to improve the measurement parameters of the Flame Photometer is presented. The improvement of accuracy and reliability is achieved through image processing Change Detection technique using Wiener Filter. The proposed method can be used in low cost Medical Equipment with improved measurement parameters performance.
ASSA imaging group DSLR Photometry Talk 27 Nov 2015Dave Benn
These are the slides for a talk I gave to the imaging group of the Astronomical Society of South Australia about DSLR photometry of variable stars on November 27 2015.
INTERIOR LIGHTING DESIGN A STUDENT'S GUIDEno suhaila
This guide on lighting design is intended for students who have no prior knowledge of lighting and also for those who are experienced but would like to bring themselves up to date with developments in lamp and luminaire design, modern design theory, European Standards and the CIBSE code for Interior Lighting 1994.
It develops the basic principles of lighting science but then goes on to provide a modern design perspective for both artificial lighting and day lighting which will be useful to experienced designers.
These lecture has prepared for postgraduate student (Ophthalmology) according to the curriculum of Bangladesh College of Physician and Surgeons (BCPS) and Bangabondhu Sheikh Mujib Medical University (BSMMU) Bangladesh
These lectures has prepared for postgraduate student (Ophthalmology) according to the curriculum of Bangladesh College of Physician and Surgeons (BCPS) and Bangabondhu Sheikh Mujib Medical University (BSMMU) Bangladesh
This presentation talks about the basic terms and terminologies related to Radiometry and Photometry. Their definitions.
This article also highlights the different theories about Light. It provides a rudimentary and comprehensive idea about light and its nature.
Role of electromagnetic Radiation in Remote SensingNzar Braim
Role of electromagnetic Radiation in Remote Sensing
It should be clear by now that the electromagnetic waves are originator and
carrier of information in Earth observation. The information content of the products delivered by a given type of sensor is essentially related to the parameters, mainly frequency (or wavelength) and polarization, characterizing the observing system, including the geometry at which data are acquired. Therefore, the specifications of an EO system, which include the type of sensor, the band of operation, the observation angle, etc.
Chapters
Reminders: light
speed of light in a vacuum
A brief historical reminder of the speed of light
Invariance of the speed of light in a vacuum
Influence of the propagation medium
Speed or celerity?
Speed, distance traveled, and duration
Relations including the speed of light
Faster than light?
Speed of light: did you know?
Reminders: light
Light is an electromagnetic wave, consisting of a magnetic field and an electric field oscillating perpendicular to each other in a plane perpendicular to the direction of propagation of the light wave. In a vacuum, light travels in a straight line at the speed of light noted c.
speed of light in a vacuum
Exact value
The exact value of the speed of light was fixed in 1983 by the Bureau of Weights and Measures at c = 299 792 458 m/s or c = 2.99792458 x 10 8 m/s, using the units of the international system. It can also be expressed in kilometers per hour by multiplying the value in m/s by 3.6: c = 1,079,252,848.8 km/h or c = 1.0792528488 x 10 9 km/h. This value, which represents a fundamental constant of physics, can be used for calculations requiring great precision. It is also used to define the meter in the international system of units: one meter corresponds to the length traveled in a vacuum by light for a duration of 1/299,792,458 seconds.
A brief historical reminder of the speed of light
The first conception concerning light suppose that it can be either present in a space, or absent: the light would therefore be instantaneous. The Arab scholar Alhazen (965-1039) was interested in optics and wrote reference treatises. He is the first to have the intuition that the appearance of light is not instantaneous, that it has a speed of propagation, but he cannot prove it.
Galileo (1564-1039) tries to measure the propagation time of light between two hills using two people a few kilometers apart and equipped with clocks. He fails to measure the speed of light (which, in the context of this experiment, takes 10 -5 seconds to travel the previously defined distance, not measurable for the time) and deduces from the failure of this experiment that the speed of propagation of light is very high.
Cassini (1625-1712) speculated that the irregularity in the movement of Io, a satellite of Jupiter, could come from a delay in the arrival of light from the satellite, "such that it takes 10 or 11 minutes for it travels a distance equal to the radius of the Earth's orbit". Römer (1644-1710) explains the discrepancy between the eclipses of Io (a satellite of Jupiter) and Cassini's predictions by assuming that light has a speed of propagation. It is the first to give an order of magnitude of the speed of light.
Bradley (1693-1762) confirms Römer's hypothesis and proposes a first estimate of the speed of light at approximately 10188 times that of the rotation of the Earth around the Sun, the latter being however poorly known. His discovery is linked to the aberration of light,
Telescope history
&facts,
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualityInflectra
In this insightful webinar, Inflectra explores how artificial intelligence (AI) is transforming software development and testing. Discover how AI-powered tools are revolutionizing every stage of the software development lifecycle (SDLC), from design and prototyping to testing, deployment, and monitoring.
Learn about:
• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
Whether you're a developer, tester, or QA professional, this webinar will give you valuable insights into how AI is shaping the future of software delivery.
2. A rigorous and exact description of electromagnetic radiation and its behavior requires a thorough
knowledge of quantum electrodynamics and Maxwell’s electromagnetic field equations.
Similarly, a complete understanding of how we perceive the light our eyes see delves deeply into
the physiology and psychology of the human visual system. There is an enormous body of
literature related to the physical aspects of light as electromagnetic radiation (e.g., Hecht and
Zajac 1987) and an equally enormous amount devoted to how we perceive it (e.g., Cornsweet
1977). Fortunately, our interests are extremely modest. We simply want to measure what we see
and perceive.
3. Radiometry
Radiometry is the science of measuring light in any portion of the electromagnetic spectrum. In
practice, the term is usually limited to the measurement of infrared, visible, and ultraviolet light
using optical instruments.
There are two aspects of radiometry: theory and practice. The practice involves the scientific
instruments and materials used in measuring light, including radiation thermocouples,
bolometers, photodiodes, photosensitive dyes and emulsions, vacuum phototubes, charge-coupled
devices, and a plethora of others. What we are interested in, however, is the theory.
Radiometric theory is such a simple topic that most texts on physics and optics discuss it in a few
paragraphs. Unfortunately, they rarely discuss the topic in enough detail to be useful. Shorn of
convoluted mathematics and obtuse definitions, radiometric theory is simple and easily
understood.
3.1 Radiant Energy
Light is radiant energy. Electromagnetic radiation (which can be considered both a wave and a
particle, depending on how you measure it) transports energy through space. When light is
absorbed by a physical object, its energy is converted into some other form. A microwave oven,
for example, heats a glass of water when its microwave radiation is absorbed by the water
molecules. The radiant energy of the microwaves is converted into thermal energy (heat).
Similarly, visible light causes an electric current to flow in a photographic light meter when its
radiant energy is transferred to the electrons as kinetic energy.
Radiant energy (denoted as Q) is measured in joules.
3.1.1 Spectral Radiant Energy
A broadband source such as the Sun emits electromagnetic radiation throughout most of the
electromagnetic spectrum, from radio waves to gamma rays. However, most of its radiant energy
is concentrated within the visible portion of the spectrum. A single-wavelength laser, on the other
hand, is a monochromatic source; all of its radiant energy is emitted at one specific wavelength.
From this, we can define spectral radiant energy, which is the amount of radiant energy per unit
wavelength interval at wavelength λ. It is defined as:
Qλ = dQ dλ (1)
Spectral radiant energy is measured in joules per nanometer.
A-2
3. 3.2 Radiant Flux (Radiant Power)
Energy per unit time is power, which we measure in joules per second, or watts. A laser beam, for
example, has so many milliwatts or watts of radiant power. Light “flows” through space, and so
radiant power is more commonly referred to as the “time rate of flow of radiant energy,” or
radiant flux. It is defined as:
Φ = dQ dt (2)
where Q is radiant energy and t is time.
In terms of a photographic light meter measuring visible light, the instantaneous magnitude of the
electric current is directly proportional to the radiant flux. The total amount of current measured
over a period of time is directly proportional to the radiant energy absorbed by the light meter
during that time. This is how a photographic flash meter works -- it measures the total amount of
radiant energy received from a camera flash.
The flow of light through space is often represented by geometrical rays of light such as those
used in computer graphics ray tracing. They can be thought of as infinitesimally thin lines drawn
through space that indicate the direction of flow of radiant energy (light). They are also
mathematical abstractions -- even the thinnest laser beam has a finite cross section. Nevertheless,
they provide a useful aid to understanding radiometric theory.
Radiant flux is measured in watts.
3.2.1 Spectral Radiant Flux (Spectral Radiant Power)
Spectral radiant flux is radiant flux per unit wavelength interval at wavelength λ. It is defined as:
Φ λ = dΦ dλ (3)
and is measured in watts per nanometer.
3.3 Radiant Flux Density (Irradiance and Radiant Exitance)
Radiant flux density is the radiant flux per unit area at a point on a surface, where the surface can
be real or imaginary (i.e., a mathematical plane). There are two possible conditions. The flux can
be arriving at the surface (Fig. 1a), in which case the radiant flux density is referred to as
irradiance. The flux can arrive from any direction above the surface, as indicated by the rays.
Irradiance is defined as:
E = dΦ dA (4)
where Φ is the radiant flux arriving at the point and dA is the differential area surrounding the
point.
The flux can also be leaving the surface due to emission and/or reflection (Fig. 1b). The radiant
flux density is then referred to as radiant exitance. As with irradiance, the flux can leave in any
direction above the surface. The definition of radiant exitance is:
M = dΦ dA (5)
where Φ is the radiant flux leaving the point and dA is the differential area surrounding the point.
A-3
4. dA dA
Figure 1a Irradiance Figure 1b Radiant exitance
The importance of a “real or imaginary” surface cannot be overstated. It means that radiant flux
density can be measured anywhere in three-dimensional space. This includes on the surface of
physical objects, in the space between them (e.g., in air or a vacuum), and inside transparent
media such as water and glass.
Radiant flux density is measured in watts per square meter.
3.3.1 Spectral Radiant Flux Density
Spectral radiant flux density is radiant flux per unit wavelength interval at wavelength λ. When
the radiant flux is arriving at the surface, it is called spectral irradiance, and is defined as:
Eλ = dE dλ (6)
When the radiant flux is leaving the surface, it is called spectral radiant exitance, and is defined
as:
Mλ = dM dλ (7)
Spectral radiant flux density is measured in watts per square meter per nanometer.
3.4 Radiance
Radiance is best understood by first visualizing it. Imagine ray of light arriving at or leaving a
point on a surface in a given direction. Radiance is simply the infinitesimal amount of radiant flux
contained in this ray. Period.
A more formal definition of radiance requires that we think of a ray as being an infinitesimally
narrow (“elemental”) cone with its apex at a point on a real or imaginary surface. This cone has a
differential solid angle dω that is measured in steradians.
We must also note that the ray is intersecting the surface at an angle. If the area of intersection
with the surface has a differential cross-sectional area dA, the cross-sectional area of the ray is
dA cos θ , where θ is the angle between the ray and the surface normal, as shown in Figure 2.
(The ray cross-sectional area dA cos θ is called the projected area of the ray-surface intersection
area dA. The same term is used when referring to finite areas ∆A.)
With these preliminaries in mind, we can imagine an elemental cone dω containing a ray of light
that is arriving at or leaving a surface (Figs. 3a and 3b). The definition of radiance is then:
L = d 2 Φ [dA(dω cos θ )] (8)
A-4
5. n
Φ
θ
Projected area
dAcos θ
dA
Figure 2 A ray of light intersecting a surface
where Φ is the radiant flux, dA is the differential area surrounding the point, dω is the differential
solid angle of the elemental cone, and θ is the angle between the ray and the surface normal n at
the point.
Unlike radiant flux density, the definition of radiance does not distinguish between flux arriving
at or leaving a surface. In fact, the formal definition of radiance (ANSI/IES 1986) states that it
can be “leaving, passing through or arriving at” the surface.
Φ n Φ n
θ θ
dω dω
dA dA
Figure 3a Radiance (arriving) Figure 3b Radiance (leaving)
Another way of looking a radiance is to note that the radiant flux density at a point on a surface
due to a single ray of light arriving (or leaving) at an angle θ to the surface normal is
dΦ (dA cos θ ) . The radiance at that point for the same angle is then d 2 Φ [dA(dω cos θ )] , or
radiant flux density per unit solid angle.
Radiance is measured in watts per square meter per steradian.
3.4.1 Spectral Radiance
Spectral radiance is radiance per unit wavelength interval at wavelength λ. It is defined as:
Lλ = d 3Φ [ dA(dω cos θ )dλ ] (9)
and is measured in watts per square meter per steradian per nanometer.
A-5
6. 3.5 Radiant Intensity
We can imagine an infinitesimally small point source of light that emits radiant flux in every
direction. The amount of radiant flux emitted in a given direction can be represented by a ray of
light contained in an elemental cone. This gives us the definition of radiant intensity:
I = dΦ dω I (10)
where dω is the differential solid angle of the elemental cone containing the given direction. From
the definition of a differential solid angle ( dω = dA r 2 ), we get:
E = dΦ dA = dΦ r 2 dω = I r 2 (11)
where the differential surface area dA is on the surface of a sphere centered on and at a distance r
from the source and E is the irradiance of that surface. More generally, the radiant flux will
intercept dA at an angle θ (Fig. 4). This gives us the inverse square law for point sources:
E = I cos θ d 2 (12)
where I is the intensity of the source in the given direction and d is the distance from the source to
the surface element dA.
n
θ
d
dA
Figure 4 Inverse square law for point sources
We can further imagine a real or imaginary surface as being a continuum of point sources, where
each source occupies a differential area dA (Fig. 5). Viewed at an angle θ from the surface normal
n, the source has a projected area of dA cos θ . Combining the definitions of radiance (Eqn. 8) and
radiant intensity (Eqn. 10) gives us an alternative definition of radiance:
L = dI (dA cos θ ) (13)
where dI is the differential intensity of the point source in the given direction.
Radiant intensity is measured in watts per steradian.
n
dI
θ
dA
Figure 5 Radiance of a point source
A-6
7. 3.4.1 Spectral Radiant Intensity
Spectral radiant intensity is radiant intensity per unit wavelength interval at wavelength λ. It is
defined as:
Iλ = dI dλ (14)
and is measured in watts per steradian per nanometer.
4. Illumination versus Thermal Engineering
The definitions given above are those commonly used in illumination engineering and are in
accordance with the American National Standard Institute publication Nomenclature and
Definitions for Illuminating Engineering (ANSI/IES 1986). Unfortunately, these definitions differ
somewhat from those used in thermal engineering (e.g., Siegel and Howell 1981). Radiative heat-
transfer theory (i.e., infrared light) does not use the point source concept that is common in
illumination engineering texts. Thermal engineers instead use the term “radiant intensity” to
describe radiance (watts per unit area per unit solid angle).
The different terminology was of little consequence until the computer graphics community
adapted the concepts of radiative heat transfer to create radiosity theory. In the process of doing
so it adopted thermal engineering’s terminology. This is an unfortunate situation, because
computer graphics also relies on the point source concept for ray tracing.
This tutorial defines radiant intensity as “watts per unit solid angle” and radiance as “watts per
unit area per unit solid angle” to maintain consistency between radiosity and ray-tracing theory.
Note, however, that many papers and texts on radiosity theory and some computer graphics texts
define “radiant intensity” as “watts per unit area per unit solid angle.”
5. Photometry
Photometry is the science of measuring visible light in units that are weighted according to the
sensitivity of the human eye. It is a quantitative science based on a statistical model of the human
visual response to light -- that is, our perception of light -- under carefully controlled conditions.
The human visual system is a marvelously complex and highly nonlinear detector of
electromagnetic radiation with wavelengths ranging from 380 to 770 nanometers (nm). We see
light of different wavelengths as a continuum of colors ranging through the visible spectrum: 650
nm is red, 540 nm is green, 450 nm is blue, and so on.
The sensitivity of the human eye to light varies with wavelength. A light source with a radiance
of one watt/m2-steradian of green light, for example, appears much brighter than the same source
with a radiance of one watt/m2-steradian of red or blue light. In photometry, we do not measure
watts of radiant energy. Rather, we attempt to measure the subjective impression produced by
stimulating the human eye-brain visual system with radiant energy.
This task is complicated immensely by the eye’s nonlinear response to light. It varies not only
with wavelength but also with the amount of radiant flux, whether the light is constant or
flickering, the spatial complexity of the scene being perceived, the adaptation of the iris and
retina, the psychological and physiological state of the observer, and a host of other variables.
Nevertheless, the subjective impression of seeing can be quantified for “normal” viewing
conditions. In 1924, the Commission Internationale d’Eclairage (International Commission on
Illumination, or CIE) asked over one hundred observers to visually match the “brightness” of
monochromatic light sources with different wavelengths under controlled conditions. The
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8. statistical result -- the so-called CIE photometric curve shown in Figure 6 -- shows the photopic
luminous efficiency of the human visual system as a function of wavelength. It provides a
weighting function that can be used to convert radiometric into photometric measurements.
1
0.9
0.8
0.7
Photopic 0.6
luminous 0.5
efficiency 0.4
0.3
0.2
0.1
0
390 440 490 540 590 640 690 740
Wavelength (nm)
Figure 6 CIE photometric curve
Photometric theory does not address how we perceive colors. The light being measured can be
monochromatic or a combination or continuum of wavelengths; the eye’s response is determined
by the CIE weighting function. This underlines a crucial point: The only difference between
radiometric and photometric theory is in their units of measurement. With this thought firmly in
mind, we can quickly review the fundamental concepts of photometry.
5.1 Luminous Intensity
The foundations of photometry were laid in 1729 by Pierre Bouguer. In his L’Essai d’Optique,
Bouguer discussed photometric principles in terms of the convenient light source of his time: a
wax candle. This became the basis of the point source concept in photometric theory.
Wax candles were used as national light source standards in the 18th and 19th centuries. England,
for example, used spermaceti (a wax derived from sperm whale oil). These were replaced in 1909
by an international standard based on a group of carbon filament vacuum lamps and again in
1948 by a crucible containing liquid platinum at its freezing point. Today the international
standard is a theoretical point source that has a luminous intensity of one candela (the Latin word
for “candle”). It emits monochromatic radiation with a frequency of 540 x 1012 Hertz (or
approximately 555 nm, corresponding with the wavelength of maximum photopic luminous
efficiency) and has a radiant intensity (in the direction of measurement) of 1/683 watts per
steradian.
Together with the CIE photometric curve, the candela provides the weighting factor needed to
convert between radiometric and photometric measurements. Consider, for example, a
monochromatic point source with a wavelength of 510 nm and a radiant intensity of 1/683 watts
per steradian. The photopic luminous efficiency at 510 nm is 0.503. The source therefore has a
luminous intensity of 0.503 candela.
5.2 Luminous Flux (Luminous Power)
Luminous flux is photometrically weighted radiant flux (power). Its unit of measurement is the
lumen, defined as 1/683 watts of radiant power at a frequency of 540 x 1012 Hertz. As with
luminous intensity, the luminous flux of light with other wavelengths can be calculated using the
CIE photometric curve.
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9. A point source having a uniform (isotropic) luminous intensity of one candela in all directions
(i.e., a uniform intensity distribution) emits one lumen of luminous flux per unit solid angle
(steradian).
5.3 Luminous Energy
Luminous energy is photometrically weighted radiant energy. It is measured in lumen seconds.
5.4 Luminous Flux Density (Illuminance and Luminous Exitance)
Luminous flux density is photometrically weighted radiant flux density. Illuminance is the
photometric equivalent of irradiance, whereas luminous exitance is the photometric equivalent of
radiant exitance.
Luminous flux density is measured in lumens per square meter. (A footcandle is one lumen per
square foot.)
5.5 Luminance
Luminance is photometrically weighted radiance. In terms of visual perception, we perceive
luminance. It is an approximate measure of how “bright” a surface appears when we view it from
a given direction. Luminance used to be called “photometric brightness.” This term is no longer
used in illumination engineering because the subjective sensation of visual brightness is
influenced by many other physical, physiological, and psychological factors.
Luminance is measured in lumens per square meter per steradian.
6. Lambertian Surfaces
A Lambertian surface is a surface that has a constant radiance or luminance that is independent of
the viewing direction. In accordance with the definition of radiance (luminance), the radiant
(luminous) flux may be emitted, transmitted, and/or reflected by the surface.
A Lambertian surface is also referred to as an ideal diffuse emitter or reflector. In practice there
are no true Lambertian surfaces. Most matte surfaces approximate an ideal diffuse reflector but
typically exhibit semispecular reflection characteristics at oblique viewing angles. Nevertheless,
the Lambertian surface concept is useful in computer graphics.
Lambertian surfaces are unique in that they reflect incident flux in a completely diffuse manner
(Fig. 7). It does not matter what the angle of incidence θ of an incoming geometrical ray is -- the
distribution of light leaving the surface remains unchanged.
We can imagine a differential area dA of a Lambertian surface. Being infinitesimally small, it is
equivalent to a point source, and so the flux leaving the surface can be modeled as geometrical
rays. The intensity Iθ of each ray leaving the surface at an angle θ from the surface normal is
given by Lambert’s cosine law:
Iθ = In cos θ (15)
where Ιn is the intensity of the ray leaving in a direction perpendicular to the surface.
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10. n
θ
dA
Figure 7 Reflection from a Lambertian surface
The derivation of Equation 15 becomes clear when we remember that we are viewing dA from an
angle θ. For a differential area dA with a constant radiance or luminance, its intensity must vary
in accordance with its projected area, which is dA cos θ . This gives us:
L = dI (dA cos θ ) = dIn dA (16)
for any Lambertian surface.
There is a very simple relation between radiant (luminous) exitance and radiance (luminance) for
flux leaving a Lambertian surface:
M = πL (17)
where the factor of π is a source of endless confusion to students of radiometry and photometry.
Fortunately, there is an intuitive explanation. Suppose we place a differential Lambertian emitter
dA on the inside surface of an imaginary sphere S (Fig. 8). The inverse square law (Eqn. 12)
provides the irradiance E at any point P on the inside surface of the sphere. However,
d = D cos θ , where D is the diameter of the sphere. Thus:
E = Iθ cos θ ( D cos θ ) = Iθ D2 cos θ
2
(18)
n
Sphere S
P
D
θ
θ d
dA
Figure 8 A Lambertian emitter illuminating the interior of a sphere
and from Lambert’s cosine law (Eqn. 15), we have:
E = Iθ cos θ D2 cos θ = In D2 (19)
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11. which simply says that the irradiance (radiant flux density) of any point P on the inside surface of
S is a constant.
This is interesting. From the definition of irradiance (Eqn. 4), we know that Φ = EA for constant
flux density across a finite surface area A. Since the area A of the surface of a sphere with radius r
is given by:
A = 4πr 2 = πD2 (20)
we have:
Φ = EA = πIn D2 D2 = πIn (21)
Given the definition of radiant exitance (Eqn. 5) and radiance for a Lambertian surface (Eqn. 16),
we have:
M = dΦ dA = πdIn dA = πL (22)
This explains, clearly and without resorting to integral calculus, where the factor of π comes
from.
7. What is Radiosity?
ANSI/IES (1986) does not define or even mention the term “radiosity.” This is not unusual --
there are many photometric and radiometric terms whose use is no longer encouraged.
“Illuminance,” for example, used to be called “illumination.” It was changed to “illuminance” to
avoid confusion with “the act of illuminating or the state of being illuminated” (ANSI/IES 1986).
When Moon wrote The Scientific Basis of Illumination Engineering in 1936, luminous exitance
was called “luminosity.” Curiously, there was no equivalent term for “radiant exitance,” so he
coined the term “radiosity” to describe the density of radiant flux leaving a surface.
The illumination engineering community ignored Moon’s proposal. Luminosity was changed to
“luminous emittance” and later to “luminous exitance,” with “radiant exitance” following as a
consequent. Meanwhile, the thermal engineering community adopted “radiosity” (e.g., Siegel and
Howell 1981).
It’s all very confusing. Fortunately, we only need to remember that:
Radiosity is radiant exitance.
This tutorial takes exception, perhaps unwisely, to the computer graphics community’s use of the
term “radiosity” to describe radiant exitance. Whereas it is an accepted term within the thermal
engineering community, it is not acceptable to illumination engineers for a variety of historical
reasons. The computer graphics and illumination engineering communities have many common
interests. If we are to communicate effectively, we must use a common lexicon of definitions.
That lexicon is ANSI/IES (1986).
8. Conclusions
There is much more that we have not covered here, such as reflectance, transmittance, absorption,
scattering, diffraction, and polarization. We have also ignored the interaction of the human visual
system with light, including scoptic and mesopic luminous efficiency, temporal effects such as
flicker, and most important, color perception. The study of light and how we perceive it fills
volumes of research papers and textbooks.
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12. Nevertheless, it begins with an understanding of how we measure light. While there is more to it
than “intensity,” you can see from this tutorial that radiometric and photometric theory is
conceptually simple and easily understood.
9. References
ANSI/IES. 1986. Nomenclature and Definitions for Illuminating Engineering, ANSI/IES RP-16-
1986. New York, NY: Illuminating Engineering Society of North America.
Bouguer, P. 1729. L’Essai d’Optique. Paris.
Cornsweet, T. N. 1977. Visual Perception. Cambridge, MA: Academic Press.
Hecht, E. and A. Zajac. 1987. Optics (2nd ed.) Reading, MA: Addison-Wesley.
Kaku, M. 1994. Hyperspace. Oxford, UK: Oxford University Press.
Moon, P. 1936. The Scientific Basis of Illumination Engineering. New York, NY: McGraw-Hill.
Siegel, R. and J. R. Howell. 1981. Thermal Radiation Heat Transfer. Washington, DC:
Hemisphere Publishing.
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