Rethinking the Photometric Data File Format

Three Decades Later

Ian Ashdown, P. Eng., FIES

Senior Scientist, Lighting Analysts Inc. / SunTracker Technologies Ltd.

[Please send all comments to]

If you perform lighting design calculations today, you can thank the efforts of the IES Computer Committee (IESCC) some thirty years ago. Its members recognized an industry need, and so developed and published IES LM-63-86, IES Recommended Standard File Format for Electronic Transfer of Photometric Data. With the growing popularity of the IBM Personal Computer for business applications, it was an idea whose time had come.

The need was clear: Lighting Technologies (Boulder, CO) had released its Lumen Micro lighting design and analysis software product in 1982, and luminaire manufacturers needed to provide photometric data for their products. For them, IES LM-63 was a god-send in that it established an industry-standard file format7.

In keeping with the technology of the time, the file format was human-readable ASCII text, something that could be printed with a dot-matrix printer. It also resulted in files of only a few kilobytes, a definite advantage when data files were transferred by mail on 5-1/4 inch floppy diskettes capable of holding 360 kilobytes of data. The file format itself revealed something of its origins by limiting line lengths to 80 characters – the width of an IBM Hollerith punch card in the 1960s (FIG. 1).

FIG. 1 – IBM Hollerith 80-character punch cards (Source: Wikimedia Commons)

Thirty years later, our personal computers are one thousand times faster, with one million times the memory capacity and ten million times more data storage capacity. Data is transferred by fiber optic cable and satellite links at gigahertz rates … and we are still using IES LM-63 photometric data files!

The “we,” of course refers mostly to North America. In Europe, the equivalent file format is EULUMDAT, which was introduced in 1990 for use with Microsoft’s MS-DOS 3.0 operating system14. Again, in keeping with the technology of the time, it was also human-readable ASCII text.

It is a testament to something – exactly what is unclear – that these two file formats have met the lighting industry’s needs for so long. Coming from an era of floppy diskettes and dial-up modems with acoustic couplers (FIG. 2), they should have become extinct decades ago. (The Chartered Institute of Building Services Engineers in the United Kingdom introduced its CIBSE TM14 file format specification in 1988, but it has since slipped into obscurity2.)

FIG. 2 – Modern communications technology circa 1986 (Source: Wikimedia Commons)

To be fair, LM-63 was revised in 1991, 1995, and 2002. These revisions, however, at best tweaked the file format specification to resolve various ambiguities and add a few minor features. What we have today is basically what was published in 1986, a time when the pinnacle of lamp technology was the compact fluorescent lamp with an electronic ballast.

If the LM-63 file format has an advantage, it is that it is an ANSI/IES standard that is maintained by an internationally recognized standards organization. EULUMDAT, on the other hand, is a de facto standard that has been essentially frozen in time since its publication in 1990[‡]. Without the authority of a standards organization such as ANSI/IES or CEN (European Committee for Standardization) to maintain the file format, it can never be revised.

The problem is that while LM-63 and EULUMDAT are still useful in terms of characterizing architectural and roadway luminaires, the lighting industry has moved beyond luminous intensity distributions. As professional lighting designers, we now have to consider color-changing luminaires, theatrical lighting, human-centric lighting, horticultural lighting, ultraviolet sterilization units, radiant heating devices, and more. We need to consider spectral power distributions, radiant intensity, photon intensity, S/P ratios, melanopic lumens, color rendition metrics … the list goes on and on.

The LM-63 and EULUMDAT file formats are clearly incapable of characterizing light sources and luminaires for these applications. It is therefore time, indeed well past time, to rethink the photometric data file format.

Standards Development

In September 2016, the IESCC initiated a project to develop a new photometric data format from first principles. As is often the case with such projects, one or two members write an initial draft based on their expertise and knowledge. This draft document is reviewed, edited numerous times, and voted upon by the committee members. If approved as a project, the proposed project is again reviewed and voted upon by the IES Board of Directors. In January 2017, technical committee project IES TM-xx, Standard Format for the Electronic Transfer of Luminaire Optical Data, was officially approved (FIG. 3).

FIG. 3 – IESCC project summary

Luminaire Component Data

Some readers may recognize this proposed standard from a previous incarnation known as IESNA LM-74-05, Standard File Format for the Electronic Transfer of Luminaire Component Data8. The IESCC worked on the development of this document for nearly a decade prior to its publication in 2005. It was ambitious effort to combine all aspects of luminaires into a single file, including far-field photometry, lamp and ballast information, physical geometry, construction materials and finishes, CAD drawings and photographs, and more.

Unfortunately, it was too ambitious. Despite the first release being focused on lamp data, the standard was never adopted by its intended audience of luminaire manufacturers, architects and engineers, lighting product specifiers, photometric testing laboratories, and lighting software developers. To the frustration of the IESCC members, the lighting industry at the time did not see a need for such a standard.

Today, we might look upon LM-74-05 as being an early example of a specialized building information management (BIM) schema, one that focused on a small subset of typically much larger datasets. (A document schema is conceptually equivalent to a file format.) The Green Building XML Schema (gbXML) for BIM applications provides an excellent example. Quoting from the gbXML Web site:

“The Green Building XML schema, or “gbXML”, was developed to facilitate the transfer of building information stored in CAD-based building information models, enabling interoperability between disparate building design and engineering analysis software tools. This is all in the name of helping architects, engineers, and energy modelers to design more energy efficient buildings.”

Unfortunately for lighting design professionals, the gbXML schema has an XML “element” (see below) called “Photometry,” whose description reads:

“This element has been left open for use with other photometry definitions. Photometric data is required for various forms of lighting analysis. This tag provides a way for the photometric data to be passed. Since this can be done in a variety of ways (iesna LM-63, cibse TM14, ELUMDAT, etc.) a specific format is not being specified.”

Defining a new luminaire optical data format that is compatible with the gbXML schema therefore serves a clear and present need.

Understanding XML

The advantage of gbXML is that it is based on the international data exchange standard XML (eXtensible Markup Language)15. The details of this standard are complex and exhausting, but basically every XML document consists of text strings called “elements” such as:

where the data is surrounded by begin and end “tags.”.

These elements can be arranged in a hierarchy, such as:

In this example, the <person> element is the “parent,” and any elements within it are its “children.”

Building on this simplest of representations, virtually any type of data can be unambiguously represented within an XML document. If a person or computer program reading an XML document encounters an unknown element tag, the element and its children (if any) can simply be ignored.

This, of course, is the problem with including LM-63 or EULUMDAT text files verbatim (i.e., as a multiline text string) within gbXML or similar BIM documents. Yes, it can be done, but the computer program reading the document needs to be able to somehow identify and read these files. Designing IES TM-xx as an XML document resolves this problem.

Having chosen a suitable representation for TM-xx, we can now consider what it needs to represent.

Luminaire Optical Data

IES TM-xx represents the luminaire optical data in four sections:

  1. Header
  2. Luminaire
  3. Equipment
  4. Light source


The header section includes information that is currently available in LM-63 and EULUMDAT files:

  • Manufacturer
  • Catalog number
  • Description
  • Test laboratory
  • Report number
  • Report date
  • Document creator
  • Document creation date
  • Unique identifier
  • Comments

Most of these elements are self-explanatory, with the exception of the “unique identifier” element. One of the problems with current photometric data files is that there is no version control. If a company reissues photometric data for a product, there is no way of distinguishing between files other than their file creation dates. If the files are copied for any reason, these dates can change.

The unique identifier element is a “universally unique identifier” (UUID) that uniquely identifies the TM-xx document, regardless of whether it has been copied as a file. While it does not prevent someone from intentionally modifying the document data, it at least solves the problem of multiple files with the same name.

The IESCC is currently considering the addition of search terms and possibly CAD symbols to the header section. These and other details may therefore result in changes to the draft release of TM-xx, but the basic structure discussed here will remain.


TM-xx represents the luminaire as a rectangular box or cylinder. The luminaire section therefore lists the dimensions of these geometric objects as length, width, and height. In addition, each face may include an emission area. These areas are useful for calculating visual glare metrics such as the CIE Unified Glare Rating (UGR)5, and also for modeling the luminaire as one or more area sources or arrays of point sources for lighting calculations and visualization.

The luminaire section also includes the light center position with respect to the geometric center of the luminaire. (The light center represents the fixed position about which the goniometer rotates while performing intensity distribution measurements.)


The equipment section describes the laboratory equipment used to perform the luminaire optical data measurements. These can include:

  • Goniometer (intensity measurements)
  • Integrating sphere (flux measurements)
  • Spectroradiometer (spectral power distribution measurements)

and detailed information specific to these instruments.

Light Source

Photometric data files assume that the luminaire includes one or more removable lamps, but this concept does not apply to solid state lighting, which may have removable LED modules or non-removable LED arrays. For the purposes of TM-xx, these are collectively referred to as “light sources.” Following LM-63 and EULUMDAT, the information pertaining to them may include (as applicable):

  • Quantity
  • Description
  • Catalog number
  • Rated lumens
  • Input wattage
  • Tilt angle

In addition, the information may include correlated color temperature (CCT) values, color rendering metric values (Ra and R9 for CIE Colour Rendering3 and Rf and Rg for IES Color Rendition11), and scotopic-to-photopic lumens (S/P) ratios9. (Note that these values may need to be expressed as ranges for variable color temperature light sources.)

There are actually 14 CIE Colour Rendering Special Indices (R1 to R14), which may be required for special purposes. These can either be calculated by the user from the measured spectroradiometric data for the light source (see below), or represented by custom XML elements.

Spectroradiometric Data

A key requirement of the light source section is to represent the spectral power distribution (SPD) of the light source. Following IES TM-27-14, IES Standard Format for the Electronic Transfer of Spectral Data10, the measured spectral radiant flux is reported for each wavelength.

Most SPDs are reported with constant wavelength intervals (e.g., 5 nm), but TM-xx does not impose such a restriction. Consequently, both continuous and line emission spectral features can be represented with arbitrary wavelength precision.

Intensity Data

With photometric data files, most of the data represents the luminous intensity measurements for vertical and horizontal angles. The same is true for TM-xx documents in the light source section except that, depending on the application, the intensity measurements may be based on luminous flux, radiant flux, photon flux[§], or spectral radiant flux.

Luminous intensity distributions are expressed in lumens per steradian (i.e., candela), and are most useful for architectural and roadway lighting applications.

Radiant intensity distributions are expressed in watts per steradian, and are most useful in characterizing ultraviolet and infrared radiation sources for applications such as UV sterilization and radiant heating.

Photon intensity distributions are expressed in micromoles per steradian per second, and are most useful for horticultural lighting applications1.

Both radiant and photon intensity are measured over a specified range of wavelengths. When photon intensity is measured over the range of 400 nm to 700 nm, it is equivalent to photosynthetically active radiation (PAR)1.

Spectral radiant intensity distributions assign an SPD to each measurement for vertical and horizontal angles. Expressed in watts per steradian per nanometer, they are useful for representing the variation in color over viewing angle, such as occurs with phosphor-coated white light LEDs.

Finally, each intensity measurement is expressed as (for example):

By explicitly expressing the vertical and horizontal angles for each measurement, there is no requirement for the data to be organized as a two-dimensional array of vertical angles and horizontal planes. This is important because some robotic goniometers are capable of measuring angular positions on a geodesic sphere and other complex angular patterns.


IES TM-xx differs from its predecessor LM-74-05 in that it focuses exclusively on luminaire optical data. This necessarily excludes other luminaire components and characteristics, including:

  • Detailed physical dimensions
  • Mechanical and structural data
  • Materials and finishes
  • Building code certifications
  • CAD drawings
  • Photographs and renderings
  • Electronic ballasts and drivers
  • Lighting controls and sensors

It would certainly be possible to include this information, but it comes at a price. Every time a component option is added to a product, it increases the number of product variations exponentially. If, for example, a lighting control has four ordering options, this potentially results in 16 different TM-xx documents.

With this, the design philosophy for TM-xx follows what Albert Einstein purportedly once said: “Everything should be made as simple as possible, but no simpler.” Given the purposeful extensibility of XML, it is always possible to add elements with custom tags for specific purposes. To avoid conflicts with identical tag names being used by other companies, an XML namespace can be used to uniquely identify the custom tags. With this, TM-xx is being designed to be “as simple as possible but no simpler.”

This design philosophy also extends to the intensity data. TM-xx optionally reports luminous, radiant, photon, and spectral radiant intensity, but not, for example, melanopic intensity that is useful in human centric lighting applications13. The reason is that if you report melanopic intensity, you should arguably also report cyanopic, chloropic, erythropic, and rhodopic intensity to represent to the responsivity of short-wavelength, (blue), medium-wavelength (green), and long-wavelength (red) cones and rods respectively in the human retina. (Melanopic intensity represents the responsivity of intrinsic retinal ganglion cells, or ipRGCs, to retinal irradiance.) This is, of course, an extreme example, but it illustrates the complexities that can arise in trying to satisfy every requirement.

Luminous, radiant, photon, and spectral radiant intensity are optionally reported because they are the most commonly used metrics in architectural, roadway, and horticultural lighting applications. All other intensity metrics can be calculated, if necessary, by appropriately weighting the spectral radiant intensity data.

Files versus Documents

Thirty years ago, almost all data was stored on magnetic media – floppy disks, hard disks, and magnetic tape. Data, whatever its form, was organized in the form of files. It therefore made sense to refer to photometric data files and file formats.

Today, data is stored on a variety of media, including magnetic, optical, solid state, and holographic devices. Long-term storage of data still requires data files and file formats, such as the default NTFS file system used by Microsoft Windows operating systems. However, the data itself has become somewhat more amorphous. How it is organized better described as a document, a symbolic representation of the data.

Using gbXML as an example, an architect or engineer may assemble a temporary BIM document by linking together information from various manufacturers. The BIM program sends requests to the manufacturers’ servers, which may in turn assemble BIM documents to be returned as XML documents. The documents are compressed for transmission, so that the document format is converted into a more compact representation. More to the point, the document may never exist as a physical file.

With this, TM-xx defines a standard format for XML documents. The term “file” is properly relegated to the era of floppy disks and acoustic modems.

Why Not JSON?

Computer-savvy readers may well ask, “Why XML and not JSON?” After all, JSON is an alternative computer markup language that is widely used to exchange data between browsers and servers12. Compared to XML, it is a much simpler and less verbose language that typically results in smaller documents. It also natively supports two-dimensional data (i.e., matrices) such as luminous intensity distributions, which are more difficult to represent in XML.

The answer is that the electronic exchange of data between computer systems typically involves compressed documents, often with the ZIP file format. In the compression process, the element tags are represented by single symbols, which typically results in document compression ratios of 10:1. More to the point, compressed XML and JSON documents representing the same data are typically the same size. With this, the ability to embed TM-xx documents in XML-based BIM documents outweighs any advantages of JSON.

International Standards

Referring once again to FIG. 3, note the phrase “international standard.” There have been several attempts in the past to develop an international standard for photometric data formats, including CIE 102-1993, Recommended File Format for the Electronic Transfer of Luminaire Photometric Data4 and EN 13032-1:2004+A1:2012, Light and Lighting – Measurement and Presentation of Photometric Data of Lamps and Luminaires – Part 16. Despite being an explicitly international file format developed by representatives of eleven countries, CIE 102 was never adopted for commercial use. Sadly, the same fate seems to have befallen EN 13032-1.

This is, unfortunately, the fate of many standards. Companies and individuals volunteer their time and expertise to develop standards that meet perceived industry needs, but the industry in question is the final arbiter of what its needs are. If existing standards are sufficient, it is often difficult to convince manufacturers to abandon them in favor of a new and untried standard. Good examples of this are CIE 102-1993, EN 13032-1, and IES LM-74-05, but there are many others.

Recognizing this problem, the IES Computer Committee has chosen to work directly with its international colleagues, including lighting software companies, luminaire manufacturers, testing laboratories, lighting professionals, and academia with expertise in both architectural and horticultural lighting. It is further using social media to communicate its activities and invite feedback from several thousand lighting professionals. More than any other standard, TM-xx is being designed by those who will most benefit from its adoption and use.

Finally – and this is perhaps a key point – IES TM-xx has been explicitly designed to be forward compatible with IES LM-63, EULUMDAT, and CIBSE TM14. That is, it will be possible to automatically batch convert previous photometric data files into TM-xx documents with insignificant loss of information. Lighting software companies, luminaire manufacturers, and testing laboratories will therefore be encouraged but not required to transition their workflow and photometric data to TM-xx. In the meantime, lighting design software will be able to seamlessly support both photometric data files and TM-xx documents.


The intent of this article has been to: 1) review the history of photometric data file formats; 2) describe the ongoing efforts of the IES Computer Committee and its partners to develop an international standard for architectural, roadway, and horticultural lighting; and 3) describe both the design philosophy and the international effort behind the development of IES Technical Memorandum TM-xx, Standard Format of the Electronic Transfer of Luminaire Optical Data.

Simply put, the lighting industry currently relies on photometric data file formats that were developed three decades ago. IES TM-xx is being designed for today and the future.


  1. ASABE. 2017. Definition of Metrics of Radiation for Plant Growth (Controlled Environment Horticulture) Applications. St. Joseph, MI: American Society of Agricultural and Biological Engineers. (In press.)
  2. CIBSE. 1988. TM14:1988, CIBSE Standard File Format for the Electronic Transfer of Luminaire Photometric Data. London, UK: Chartered Institution of Building Services Engineers.
  3. CIE 13.3-1995. Method of Measuring and Specifying Colour Rendering Properties of Light Sources. Commission Internationale de l’Eclairage, Vienna, Austria.
  4. CIE 102-1993. Recommended File Format for Electronic Transfer of Luminaire Photometric Data. Commission Internationale de l’Eclairage, Vienna, Austria. (Originally published in CIE Journal 6(1):23-31, 1987.)
  5. CIE 117-1995. Discomfort Glare in Interior Lighting. Commission Internationale de l’Eclairage, Vienna, Austria.
  6. EN. 2012. European Standard EN 13032-1:2004+A1:2012, Light and Lighting – Measurement and Presentation of Photometric Data of Lamps and Luminaires – Part 1: Measurement and File Format. Brussels, Belgium: European Committee for Standardization.
  7. IES LM-63-02. Standard File Format for Electronic Transfer of Photometric Data. New York, NY: Illuminating Engineering Society of North America.
  8. IES LM-74-05. IESNA Standard File Format for the Electronic Transfer of Luminaire Component Data. New York: Illuminating Engineering Society of North America.
  9. IES TM-12-12. Spectral Effects of Lighting on Visual Performance at Mesopic Light Levels. New York, NY: Illuminating Engineering Society of North America.
  10. IES TM-27-14. IES Standard Format for the Electronic Transfer of Spectral Data. New York, NY: Illuminating Engineering Society of North America.
  11. IES TM-30-15. IES Method for Evaluating Light Source Color Rendition. New York, NY: Illuminating Engineering Society of North America.
  12. IETF. 2014. The JavaScript Object Notation (JSON) Data Interchange Format. Request for Comments 7159, Internet Engineering Task Force. (Available from
  13. Lucas, R. J., S. N. Peirson, D. N. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueior, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard. 2013. “Measuring and Using Light in the Melanopsin Age,” Trends in Neuroscience 37(1):1-9.
  14. Stockmar, A. W. 1990. “EULUMDAT – ein Leuchtendatenformat für den europäischen Beleuchtungplaner,” Tagungsband Licht ’90, pp. 641–644.
  15. W3C Extensible Markup Language (XML) 1.0, Fifth Edition (

[‡] The EULUMDAT file format specification is available from

[§] Photon flux, also commonly referred to as quantum flux, is the rate of flow of photons. Radiant flux, by comparison, is the rate of flow of energy. The energy of a photon is inversely proportional to its wavelength, so quantum flux is not directly comparable to radiant flux.

In Search of Luminance

Understanding What We See

Ian Ashdown, P. Eng., FIES

Chief Scientist, Lighting Analysts Inc.

[ Please send comments to ]

The IES Lighting Handbook, Tenth Edition (IES 2010), describes luminance as “perhaps the most important quantity in lighting design and illuminating engineering.” This is an accurate but curious description, as the editors neglected to include an entry for Section 5.7.3, Luminance, in the handbook’s index.

The section itself is a mere five paragraphs long, informing the curious reader that luminance is the “local surface density of light emitting power in a particular direction,” defined mathematically as:

In Search of Luminance - EQN 1

which for most readers will be completely and absolutely … opaque.

This is unfortunate, as luminance is undeniably the most important quantity, and indeed the most fundamental concept, in lighting design and illuminating engineering. More than a mathematical definition, professional lighting designers need to understand what it is that we see.

Luminance Understood

To understand luminance, we begin with a parallel beam of light. Ignore any thoughts of surfaces or light sources; just imagine a beam of light traveling through empty space in a given direction. Imagine also that this beam has a finite width; say, a rectangular beam one meter on a side.

If we take a cross-section of this beam at any point along its length, we can measure so many lumens of light (i.e., photons per second) per unit area. In photometric terms, this is the luminous flux Φ per unit area, or luminous flux density, of the beam. Being parallel, the beam does not diverge or converge, and so the luminous flux density remains constant along the length of the beam.

Now, what happens if the beam illuminates a real or imaginary surface at an angle? We have this:

In Search of Luminance - FIG 1

FIG. 1 – Illuminance of a surface A

The luminous flux per unit area received by the surface A is determined by the cosine of the angle of incidence θ from the surface normal n. Conceptually, as the angle of incidence becomes greater (i.e., more oblique), the illuminance E (lumens per unit area) of the surface decreases. The expression A cos θ represents the projected area of the illuminated surface, and is equal to the cross-sectional area of the beam.

This is nothing more than Lambert’s Cosine Law (Lambert 1760):

In Search of Luminance - EQN 2

If we imagine the area A as being infinitesimally small, we can designate it as dA (for “differential area”). Similarly, the amount of luminous flux Φ within the infinitesimally narrow beam approaches zero, and so we designate it as dΦ. This gives us:

In Search of Luminance - EQN 3

This is basic high school algebra! Ignore the symbols and concentrate on the underlying physical concept.

We can further imagine the beam not as a parallel beam that is infinitesimally narrow, but as an elemental cone whose infinitesimal solid angle we designate as . (See the previous article Solid Angles for an explanation of this concept.)

In Search of Luminance - FIG 2

FIG. 2 – Luminance of a differential surface dA

With this, we have the conceptual framework to understand the formal definition of luminance:

In Search of Luminance - EQN 4

where the factor d2Φ does not mean that the symbol d is being squared. Rather, it simply means that the luminous flux dΦ is being divided by the solid angle of the elemental cone dω and the area dA. Further, the parameter ψ indicates that the luminance may also vary when the beam is rotated horizontally by angle ψ around the surface normal n.

What this equation is saying is that the luminance L of the surface dA is equal to the amount of luminous flux Φ (lumens) leaving dA in the direction θ and contained within the elemental cone (i.e., parallel beam) dω. This is equivalent to the IES Lighting Handbook description of “local surface density of light emitting power in a particular direction.”

There is an important but underappreciated corollary to this definition of luminance. Recalling that the surface can be real or imaginary, we can imagine placing an imaginary surface that is perpendicular to the beam direction (i.e., θ is equal to zero) anywhere along its length. What this means is that the luminance of a parallel beam of light is constant along its length. In other words, luminance is not an intrinsic property of the surface, but of the beam itself. (As an example, the sky has a measurable luminance when viewed from the ground, but it has no real surface.)

Dispensing with the mathematics, we can therefore say:

Luminance is the amount of luminous flux per unit area as measured in a parallel beam of light in a given direction.

Photometry is traditionally taught using the concept that luminance is a property of real or imaginary surfaces. The problem with this approach is that you cannot easily explain why participating media such as the atmosphere, smoke, fog, colloidal suspensions in water, and so forth have measurable luminance. Thinking of luminance as a property of a beam of light rather than of surfaces eliminates this difficulty.

Luminance Perceived

How do we perceive luminance? Imagine that you are looking at a blank sheet of matte white paper. Being an approximately ideal diffuser (except at very oblique angles), this paper will scatter incident light equally in all directions.

Now, imagine that each point of the paper’s surface is a point source of light. In accordance with the inverse square law, the luminous flux density of this light will decrease with the square of the distance from the point source. That is:

In Search of Luminance - EQN 5

where I is the intensity of the point source, d is the distance from the source, and E is the illuminance of a surface (such as the cornea of your eye) at that distance … so why do we see and measure the luminance of the paper as being constant with distance?

To answer this, we need to look at the eye itself, which basically consists of a lens that focuses images onto the cones and rods of the retina. Each cone and rod has a finite width, and so it receives light from a finite area of the surface of the paper.

In Search of Luminance - FIG 3

FIG. 3 – Eye focusing a parallel beam onto the retina

But wait! This area of the paper is dependent on the distance of the paper from the eye. Moreover, it is proportional to the square of the distance … which exactly cancels out the inverse square law for a single point source. Therefore, we perceive the luminance of a finite area surface as being constant regardless of its distance from the eye.

There is a counterexample that emphasizes this point: the night sky. Even though the actual diameter of a star may be a million miles or so, it is so far away that we perceive its light as a parallel beam that is focused onto a single rod or cone of our retina. The luminance of this beam is constant, and so we see the star as having a specific perceived brightness (or visual magnitude). The inverse square law still applies to the star’s emitted light, however – it is after all a point source – and so its magnitude depends on its distance from the Earth. All other things being equal, more distant stars are inherently fainter.

How the eye sees a parallel beam of light, however, is the key point: wherever we look, we see luminance. We do not see luminous intensity or illuminance; we see the luminance of beams of light. Luminance really is the fundamental concept of lighting design.


A famous 20th-century physicist (whose name I regrettably cannot recall, even with Google’s assistance) once observed that until you can visualize a problem, you cannot truly understand the mathematics that describe it. He was likely referring to quantum mechanics, which nobody yet fully understands, but the observation still applies. In particular, knowing the mathematical definition of luminance is not enough; we must understand the concept of luminance. With this understanding, we can better understand its importance to lighting design and illumination engineering.


IES. 2010. IES Lighting Handbook, Tenth Edition. New York, NY: Illuminating Engineering Society of North America.

Lambert, J. H. 1760. Photometria (in Latin). English translation by D. L. DiLaura, 2001. New York, NY: Illuminating Engineering Society of North America.

Smith, W. 2008. Modern Optical Engineering, Fourth Edition. New York, NY: McGraw-Hill.

Solid Angles

Truly Understanding Luminous Intensity

Ian Ashdown, P. Eng., FIES

Chief Scientist, Lighting Analysts Inc.

[ Please send comments to ]

Do you suffer from math anxiety? A surprising number of us do (e.g., Wigfield 1988). I would tell you the exact numbers, but you would need to understand statistical analysis …

Fortunately, we can mostly muddle through our lives without having to deal with statistics, vector calculus, differential geometry, algebraic topology and all that. As an electrical engineer in the 1980s for example, I never needed anything more than a four-function calculator to do my work designing billion-dollar transportation systems.

Our fear (note the implicit “we”) can, however, disadvantage us in subtle ways. In studiously ignoring the mathematics of a topic, we all too often overlook the underlying concepts that help us better understand what we are interested in.

An example from lighting design: luminous intensity. We measure the luminous intensity of a light source in candela, which is defined as “one lumen per steradian” (IES 2010). A lumen is easy enough to understand, but what the blazes is a “steradian”?

The all-knowing Wikipedia has an answer: it is the measure of a “solid angle.” Going to the Wikipedia definition of this phrase, we see:

Solid Angle Equation

Anxiety? What anxiety?

But now for a trade secret: most mathematicians do not think in terms of equations like these double integrals. Instead, they visualize. Just as lighting designers can look at architectural drawings and imagine lighting designs, mathematicians can look at a set of equations – which are really nothing more than an arcane written language – and visualize new mathematical concepts and proofs.

I learned this from a professor of mine whose specialty was hyperspace geometry – he could “easily imagine” four- and five-dimensional objects by mentally projecting them into three-dimensional shapes and imagining how their shadows changed as he rotated the objects in his mind. Some people …

So, we start by visualizing a circle (FIG. 1):

FIG. 1 - Circle

FIG. 1 – Circle with radius r

If you remember anything at all from mathematics in school, it is that the circumference C of a circle with radius r is equal to two times pi times its radius, or:

C = 2 * pi * r

where pi is approximately 3.14159. (Remember that 1980s-era four-function calculator – it is all you will need for this.)

What this means is that if we take a piece of string with length r, we will need to stretch it by a factor of two pi (6.28328 …) to wrap around the circumference of the circle.

But suppose we wrap the string with length r part way around the circle (FIG. 2). The resultant angle is precisely one radian, which is abbreviated rad.

FIG. 2 - One radian

FIG. 2 – One radian

Most of us are used to thinking of angles in terms of degrees – there are 360 degrees in a circle. (The reason for the magic number 360 is lost in history, according to Wikipedia.) This means that one radian is equal to 360 / (2 * pi) = 180 / pi degrees, which is approximately 57.3 degrees. Radians are more useful simply because they are related to the geometry of the circle rather than some magic number – they are easier to visualize and so understand.

Now, imagine a sphere with radius r, and with a cone-shaped section whose base has a surface area of r * r, or r2 (FIG. 3):

FIG. 3 - Solid angle

FIG. 3 – Solid angle

This cone has a solid angle of precisely one steradian (or one “solid radian”), which is abbreviated sr.

No mathematics required – easy.

(To be precise, a solid angle does not need to be a circular cone-shaped section as shown in FIG. 3. The top of the cone can be any shape; all that matters is the ratio of the surface area of the base to the radius r.)

How many “square degrees” in a steradian? That’s also easy: if one radian is equal to 180 / pi degrees, then one steradian is equal to (180 / pi) * (180 / pi), or approximately 3282.8, square degrees.

To be honest, I also suffer from math anxiety when first reading a set of equations. I do not really understand them until I can visualize what they mean. Mathematical equations are just the formal written language we use to express what we have visualized.

… now if only I could understand batting averages in baseball and cricket …


IES. 2010. IES Lighting Handbook, Tenth Edition. New York, NY: Illuminating Engineering Society of North America.

Wigfield, A., and J. L. Meece. “Math Anxiety in Elementary and Secondary School Students,” Journal of Educational Psychology 80(2):210-216.

Mesopic Photometry and Statistics

Ian Ashdown, P. Eng., FIES

Chief Scientist, Lighting Analysts Inc.

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Related Posts

Understanding Mesopic Photometry

One of the joys of statistics is that you can never be proven wrong …

In a previous All Things Lighting article titled “Understanding Mesopic Photometry” (October 8th, 2013), I wrote:

Some publications on mesopic lighting have indicated that the S/P ratio of a lamp can be estimated from its correlated color temperature (CCT), but this is incorrect …

I continued on with an example that compared the spectral power distributions and scotopic-to-photopic (S/P) ratios of a phosphor-coated white light LED:


Fig. 1– Phosphor-coated LED module

and a red-green-blue LED:


Fig. 2 – Red-green-blue LED module

Both lamp modules had the same correlated color temperature (CCT) of 3500K, but their S/P ratios were 1.41 and 2.02 respectively. I concluded that:

Simply put, the only way to accurately determine the S/P ratio of a light source is through calculation using its spectral power distribution.

While this statement is technically correct, it is not particularly useful when you need to know the S/P ratio of a lamp or lamp module for mesopic roadway or area lighting calculations.

Measurements and Equations

One of the publications I chose not to reference was the “City of San Jose Public Streetlight Design Guide” [Anon. 2011]. This report presented a list of eight light sources with their reported S/P ratios, which were derived from [CIE 2010] and [Berman 1992]:

Source S/P Ratio CCT
Low pressure sodium 0.25 1700
High pressure sodium 0.65 2100
Warm white metal halide 1.35 3500
Daylight metal halide 2.45 5500
Warm white fluorescent 1.00 3000
Cool white fluorescent 1.46 3700
Triphosphor fluorescent 1.54 4100
Daylight fluorescent 2.22 7500

Table 1 – S/P Ratio versus CCT [Anon. 2011]

This list is somewhat selective, as Berman reported the S/P ratio versus CCT of sixteen light sources:

FIG. 3

Fig. 3 – S/P Ratio versus CCT [Berman 1992]

The report noted:

Although the S/P ratio is derived from the spectral power distribution of the light source, it approximately corresponds to the correlated color temperature of that source.

However, this was immediately followed by:

To determine the S/P ratio for any given CCT, the following equation can be used:

S/P ratio = -7 * 10-8 (CCT)2 + 0.001 * CCT – 1.3152

While I otherwise agree with the report, I must disagree with this statement. Of the tens of thousands of lamp types that are commercially available, you cannot fit a quadratic curve through a mere eight data points and generalize it to any light source. This is especially true when the light sources include the near-monochromatic spectral power distribution (SPD) of low-pressure sodium (LPS) lamps.

Worse, there is no indication of the expected error with this equation. You may calculate an S/P ratio for a given CCT, but you have no idea whether it is accurate. Is it for example 1.65, 1.6, or somewhere between 1.0 and 2.0?


Based on the work of [Berman 1992], it is evident that the S/P ratio of a white light source “approximately corresponds” to its CCT. However, the evidence in support of this conclusion is statistically weak, and further does not consider today’s phosphor-coated white light LEDs.

What is needed is a random sampling of many commercial white light sources. Ideally, the work would be done by an independent photometric testing laboratory so as not to inadvertently skew the results towards the products of a single lamp manufacturer.

Having the results for many different light sources serves two purposes. First, it provides enough data points to have confidence that an equation fitted to the data fairly represents most commercial lamps and LED lamp modules.

Second, it provides the all-important confidence interval for any given S/P ratio. That is, given a calculated S/P ratio for a specific CCT, you can have (say) 95% confidence that the value is accurate to within a given range of values.

This is important because photometric measurements and calculations always include implicit confidence intervals. For example, electric lighting calculations are typically accurate to within ±10 percent when compared to careful in situ measurements of the completed project. It makes no sense therefore to perform (for example) mesopic roadway lighting calculations if your assumed S/P ratio varies by ±0.5.


The good news is that we now have the necessary information. LightLab International Inc. ( recently collated the results of some 90 tests of LED-based roadway and area lighting luminaires that they performed for their customers. In accordance with the requirements of LM-79 testing procedures [IESNA 2008], the test reports included spectral power distribution measurements, and with them (although not required by LM-79) calculated S/P ratios.

As you might expect, the lamp CCTs clustered around the industry-standard nominal values:

FIG. 4

Fig. 4 – Lamp CCTs

Perhaps less expected is that they exhibited a reasonably linear relationship between S/P ratio and CCT:

FIG. 5

Fig. 5 – S/P ratio versus CCT

I will not repeat the curve-fitting equation here, as it has a meaningless precision of 15 decimal points. What is important is this table of recommended values (where the 2700K values were extrapolated from the measured data):

CCT S/P Ratio Range
2700K 1.1 – 1.4
3000K 1.2 – 1.5
3500K 1.3 – 1.6
4000K 1.4 – 1.8
5000K 1.6 – 2.0
6000K 1.9 – 2.2

Table 2 – S/P Ratio versus CCT for LED lamps

Note carefully that this table applies to LED-based white light sources only; it does not apply to fluorescent (including magnetic induction) or HID lamps, and certainly not to LPS lamps. (Metal halide lamps in particular as reported in Table 1 are outside of the range of this table.)

Looking at Figure 1, it is perhaps not surprising that LED lamps exhibit a strong correlation between S/P ratio and CCT. Virtually all of today’s high-flux LEDs for roadway lighting applications rely on a blue pump LED (which accounts for the 450 nm peak in Figure 1) and broadband emission phosphors between 500 and 700 nm. With minor differences due to different phosphor combinations, most white light LED SPDs will look something like Figure 1, with the CCT mostly determined by the ratio of the blue peak to the phosphor emissions.

The counterexample of course is the red-green-blue LED SPD shown in Figure 2, with its anomalous S/P ratio of 2.02 for a CCT of 3500K. It is not coincidental that the SPD somewhat resembles that of a triphosphor fluorescent or metal halide lamp.

Ideally, we would have S/P ratio versus CCT data for thousands of white light sources. It is unlikely that the recommended S/P values above would change by more than 0.1 units, but it would improve our statistical confidence in the results.

On the other hand, these results show that the S/P ratio varies by ±0.2 for any given CCT, or about ±10 percent of the median value. This is commensurate with the expected accuracy of most electric lighting applications.

Granted, it would be preferable to have S/P ratios available for every lighting product. (S/P ratios are also integral to IES TM-24-13, Incorporating Spectral Power Distribution into the IES Illuminance Determination System for Visual Task Categories P through Y [IESNA 2013].) As was explained in “Understanding Mesopic Photometry” however, there are practical reasons why this is unlikely to occur.

In retrospect, this likely does not matter.. Lighting designers can rarely assume the use of particular product when performing photometric calculations. With competitive bidding for commercial and government projects, it is best to simply specify luminaires with a given CCT. Given that most new roadway and area lighting installations will involve LED-based luminaires, Table 2 provides lighting designers with the confidence that they can assume a usefully narrow range of S/P ratios for design and specification purposes.


Anonymous. 2011. City of San Jose Public Streetlight Design Guide. Available as

Berman, S. W. 1992. “Energy Efficiency Consequences of Scotopic Sensitivity,” Journal of the IES 21(1):3-14.

CIE. 2010. Recommended System for Mesopic Photometry Based on Visual Performance. CIE Technical Report 191:2010. Vienna, Austria: Commission International de l’Eclairage.

IESNA. 2008. IES LM-79-08. Electrical and Photometric Measurements of Solid-State Lighting Products. New York, NY: Illuminating Engineering Society of North America.

IESNA. 2013. IES TM-24-13. Incorporating Spectral Power Distribution into the IES Illuminance Determination System for Visual Task Categories P through Y. New York, NY: Illuminating Engineering Society of North America.


Thanks to Eric Southgate of LightLab International Inc. ( for sharing the S/P versus CCT data on which this article was based.

Thanks also to Dawn DeGrazio of Lighting Analysts Inc. for invaluable editorial assistance.