1. Abstract
2. Introduction
3. The Mathematics of Color
4. Visualization of Spectra
5. The Black Body Spectrum
6. The Solar Spectrum
7. The Planckian Locus
8. Element Emission Spectra
9. Element Emission Colors
10. Possible NIST Inaccuracies
11. Lamp Engineering
12. The Mercury Discharge
13. Phosphors for Mercury
14. The Metal Halide Discharge
15. The Sodium Discharge
16. The Xenon Discharge
17. The Spectral Line Profile in High Pressure Discharges
18. Lamp Chromaticity Table
19. Optimal Lamp Selection
20. Data Analysis
21. Conclusions
22. "Full-Spectrum" Lamps
23. Lamp Testing
24. References

In this article the author uses the spectral distribution data of the elements from NIST ([6]), simulates the emission spectra of some typical lamps and finally derives several interesting conclusions about some lighting engineering applications which use these lamps. The conclusions are reached entirely theoretically. That is, although some data comes from published sources which contain experimental data, this article contains no physical experimentation data. All processing and all graphical visualization is done by a computer program. The reached conclusions are in general agreement with commercially published sources, such as those of lamp manufacturers and lighting engineers. CAUTION: Note that the accuracy of the conclusions on this article depends upon [6]'s published spectral distribution data and the assumptions made in sections 13 and 14, therefore it is advisable to read section Possible NIST Inaccuracies carefully and the author's Copyright & Disclaimer before perusing any of the data below. Atomic elements with a question mark next to their names are (obvious) suspects for inaccuracies.

The best light for general and specific illumination is sunlight and daylight. Whenever such light is not available, lighting engineers strive to create light sources which mimic daylight or light sources with light as close to daylight as possible (or with other different attributes, depending on the application). Because the perception of color of light sources is subjective, lighting engineers usually characterize the "appearance" of light sources based on their chromaticity. To help understand chromaticity, color science and illumination in general better, in 1931 the International Commission on Illumination (CIE) introduced one of the first mathematically defined color spaces, the CIE x,y chromaticity diagram.

CIE x,y chromaticity diagram, generated with Maple.

Chromaticity for light sources is generally defined in two ways: by Correlated Color Temperature (CCT) (related to the color produced by a Black Body radiator), or by their CIE x and y coordinates. These two methods give a measure of the color appearance of the source itself. By using this diagram as a reference, many aspects of color become clarified and lighting engineers can investigate various light sources. Usually the major lamp manufacturers publish both definitions in order to give the consumer an idea of how well the lamp performs. Another key notion which lately is also published by manufacturers is the Color Rendering Index (CRI), which gives a measure of how well colors appear under light from a given light source. The relationship between all three factors, chromaticity, CCT and CRI is very complex. In general chromaticity does not relate directly to CRI. Light sources with similar chromaticities may have greatly different color rendering properties and vice versa. Light engineering is a fascinating science, perhaps the most important science after mathematics, because it is ultimately connected with our ability to process data around us using vision, which is the most important human sense. Without it we would not be able to do our work during the day in places which are not reached by natural light and during the night when there is no strong natural illumination. Because light engineering is tied to color perception, extensive research in various interconnected branches such as physics, spectroscopy, chemistry, the science of color and psychology has been performed and continues being performed. Light engineering is and will continue to be an active research area pursued aggressively by most major lamp manufacturers, because very few (if any) people have no need for artificial light sources.

A preliminary mathematical analysis which explains the first part of the mapping between signals in the time domain and human brain processing, is presented in [42]. The rest of this document analyzes the second part of the visual mapping, that between brain and actual color sensation. To visualize the spectral distributions and colors of all the elements and of various light sources, the author has created a Maple program which inputs a spectral distribution of arbitrary resolution and automatically generates a visual distribution with 1nm resolution like the one to the right on the table below. For lines closer than 1nm together in the input data the author simply added their respective relative intensities, since this is pretty much what happens with visual spectroscopes as well. The program calculates several additional useful parameters, such as the source's CCT in Kelvins (when applicable), CIE coordinates x,y and Photoshop R,G,B coordinates for the source used and a Full-Spectrum index, FS (see [34] and [35]). The R,G,B Photoshop values were used to render the source hues of the color squares, left of the corresponding spectra. The color rendering algorithms were based on [1] and [11], but adjusted to use [31]'s CIE 1931 2-deg XYZ Color Matching Function table with a 1nm resolution:

CIE 1931 color matching functions x(λ), y(λ), z(λ).

The CCT algorithm was based on [2] and [10]. The author chose the CIEsystem in [1] with a γ=2.5 because it gave the best colors on his LCD laptop screen. Element spectral distribution data was taken from [6]. Other data was based on the rest of the references and on extensive discussions with engineering specialists and Maple experts which have taken place in the usenet newsgroups sci.engr.lighting and comp.soft-sys.math.maple, in which the author participates often. The program can additionally display custom distributions, distributions of combinations of elements with different contributions, distributions with a maximum from 0-100%, UV and IR distributions and chromaticity diagrams. Emissions in the UV and IR whenever shown are shown as grey. For most distributions, the author chose the range 380nm to 700nm, because most people are not able to discern colors outside this range and additionally outside this range the computer cannot represent colors accurately. Furthermore, the XYZ Color Matching Functions used, have values very close to zero for wavelengths outside this range. All the diagrams on this page were created by the program automatically.

Generally speaking there are two ways to visualize spectra: By using one-dimensional representations/photographs or by using two dimensional plots. Each has advantages and disadvantages over the other. One-dimensional representations/photos are simply linear scans through the required spectral area with (R_λ,G_λ,B_λ) being the color at wavelength λ. This representation suffers from the fact that stronger lines need to be represented by brighter colors and/or wider lines, in order to give an indication of their strength relative to weaker lines. It is however closer to true images of spectra as seen through spectroscopes. Two-dimensional plots are often created by professional spectrographs and have the spectrum plotted as a histogram consisting of the data points (λ,f(λ)), where λ is the wavelength and f(λ) is the relative intensity (or the energy in mW/nm) of the lines. This has the advantage that the relative strength is shown easily and the resolution stays constant as lines close together don't merge. Two-dimensional plots are always linear with respect to wavelength, whereas real photos can be either linear or non-linear. If the spectroscope uses a prism for example, the resulting spectrum will be non-linear. If it uses a grating, the spectrum will be linear. In this document the author renders two-dimensional representations of spectra, primarily because the author has already devoted considerable time photographing real one-dimensional spectra in [25]. If you want to see more interesting one-dimensional renderings, see [40]. Here is the spectrum of a high pressure mercury lamp using the two different methods. The real spectrum (on the left) is non-linear with respect to wavelength, as it was produced by a prism. On this spectrum the two yellow lines of mercury merge together, because the camera does not have enough resolution to separate them.

One-dimensional Spectrum	Two-dimensional Spectrogram

Generally speaking, the "friendliest" light to human vision is light produced by incandescent matter or as engineers call it, light emitted by Black Body radiators. This is no coincidence: First, the sun is a Black Body radiator so natural sunlight is such light. Second, primitive man had only fire at his disposal which again emits such light. Unfortunately man-made Black Body radiators (such as fire or candle flames) cannot reach temperatures comparable to that of the sun. So, although technically their light is pleasing and warm, it lacks severely in the blue and violet part of the visual spectrum. As a result, blue and violet colors are not rendered correctly under such man-made lights and appear dull and dark. Fortunately, fire and candles are examples at the extreme end of the spectrum (literally!). Newer man-made light sources, such as incandescent lamps are Black Body radiators which operate at higher temperatures and are able to render colors better. A measure of how well Black Body radiators render colors, is their actual radiating temperature, which is usually denoted in degrees Kelvin. Candle flames and fire radiate approximately at T=1020K. Incandescent light bulbs operate at around 2100K to 2700K depending on Wattage. Halogen incandescent lamps operate at still higher temperatures, sometimes reaching 3100K. Although all incandescent lamps produce very pleasing light to the eye, most of their energy is radiated in the infrared part of the spectrum. This can be explained theoretically by looking at Planck's Law and Wien's Displacement Law for Black Bodies, which shows where the maximum of emission occurs. Specifically for the temperatures of most man-made Black Body light sources (with the exception of nuclear explosions!), the maximum occurs at infrared. Here are then some examples of spectra produced by Black Body radiators, for different temperatures. The table below is sorted numerically by Black Body temperature for convenience. It consists of four columns: A column showing the Black Body temperature in Kelvins, a column showing the source's chromaticity CIE coordinates and CCT in Kelvins, a column showing the approximate color of the source in Photoshop R,G,B and a final column showing the visible spectral distribution. The CCT is shown as calculated by the Maple program. Theoretically CCT=T for Black Bodies, however programmatically these are not always in agreement, so they may display some minor disagreement. Note that when T is small (<~4000) the maximum emission occurs in the infrared. As T increases, the maximum moves into the visible and then into UV, so the overall source color changes from red-orangish to white and finally bluish-white. When T becomes very large (which for practical purposes can be taken as infinity) the color shifts to bluish.

T (K)	CIE chromaticity CCT (K)	Source Color	Spectral Distribution
1000 (~candle/fire [32])	x=0.65083 y=0.34631 CCT:N/A
2000	x=0.52592 y=0.41383 CCT:2009
3000 (tungsten halogen lamp)	x=0.43644 y=0.40430 CCT:3010
4000	x=0.37988 y=0.37681 CCT:4016
5000	x=0.34416 y=0.35137 CCT:5035
6000	x=0.32054 y=0.33099 CCT:6079
7000	x=0.26011 y=0.32647 CCT:7165
8000	x=0.29214 y=0.30243 CCT:8308
9000	x=0.28310 y=0.29233 CCT:9521
10000	x=0.27607 y=0.28410 CCT:10824
∞	x=0.076966 y=0.23344 CCT:N/A

The best quality light is of course daylight. Although the sun is a Planckian radiator, its spectrum is not continuous. The sun's photosphere emits a continuous Black Body spectrum at T~5785 but the chromosphere contains many elements which absorb several discrete wavelengths according to their emission spectrum below and Kirchhoff's Law, so the spectrum of the light that reaches us is an absorption spectrum. The most prominent elements in the chromosphere are H, Na, O, Fe, Mg and Ca. The ratio of the elements in the program was adjusted to simulate absorption lines of approximately the correct intensity. The sun's spectrum along with the sun's chromaticity and color are given in the following table. The CCT calculated by the Maple program is slightly different than the sun's T=5785, because the absorption lines are taken into account.

T (K)	CIE chromaticity CCT (K)	Source Color	Spectral Distribution
5785	x=0.32551 y=0.33513 CCT:5822

Black Body radiators are also called Planckian radiators (because of Planck's Law). As T increases continuously, the chromaticity coordinates x,y of a Planckian radiator form a certain curved locus on the CIE diagram, called The Planckian Locus. This locus in shown in grey superimposed on the CIE diagram below. The leftmost point of the locus corresponds to T=infinity.

Planckian Locus and isothermal lines for different T (in 10³ Kelvin)

The proximity of a source's chromaticity to the Planckian Locus is a fairly good indicator of a light source's overall color quality. If a source's chromaticity coordinates x,y fall close to the Planckian Locus, this indicates that the source's color is close to the color of a Black Body radiator of a certain T, corresponding to the point on the locus in a certain direction from the source's chromaticity coordinates. This direction is usually indicated by a line which crosses the locus, called an isothermal line (also called a Judd line. See [8]). For an artificial light source or a non-Planckian radiator, this T is defined to be the CCT of the source. In general, the closer a source's chromaticity to the Planckian Locus, the more accurate the correspondence between it and a Planckian radiator of temperature T=CCT is. Two sources lying on the same isothermal line have the same CCT, however the source which lies closer to the Planckian Locus between the two approximates a Black Body radiator better. If the chromaticity lies far way from the locus, such a correspondence is fairly meaningless. To make sure that this correspondence makes sense, in addition to the CCT, engineers also publish the source's CRI. Without the CRI, the CCT may exist but it may make little sense, as one can see later.

Because engineers cannot construct Planckian radiators of temperatures close to that of the sun, alternative approaches have been considered, which essentially rely on exploiting the non-equilibrium electromagnetic radiation emitted by various elements when these are excited electrically. Since the main energy source we have is electricity, the latter is used to power artificial light sources which contain trace quantities of selected elements. The selection and suitability of these elements is a science in and of itself, often involving physics, quantum mechanics, chemistry, electromagnetism and spectroscopic analysis. Contrary to Black Bodies whose emission spectrum is continuous (because it is a probability distribution) and characterized only by their temperature T, the elements have characteristic and unique emission spectra, with discrete emission lines. Below you see a table with the emission spectra of all the elements. Elements which are missing either do not exist in sufficient quantities to warrant spectral examination or do not display emission lines in the range used in this document (380nm-700nm). All elements are normalized with respect to their strongest line which is shown as 100% (in some cases the maximum emission occurs near the edges of visibility, so the rest of the spectrum appears suppressed). The table below is sorted alphabetically for convenience. It consists of four columns: A column showing the standard element name, a column showing the source's chromaticity CIE coordinates and CCT in Kelvins, a column showing the approximate color of the source in Photoshop R,G,B and a final column showing the visible spectral distribution. The author stresses again that the results depend on [6]'s published data. See section Possible NIST Inaccuracies.

Element	CIE chromaticity CCT (K)	Source color	Spectral Distribution
Ac(?)	x=0.20202 y=0.03128 CCT:N/A
Ag	x=0.20673 y=0.57568 CCT:8015
Al	x=0.29828 y=0.56321 CCT:6150
Am	x=0.34847 y=0.21336 CCT:2774
Ar	x=0.30165 y=0.14112 CCT:N/A
As	x=0.16085 y=0.74540 CCT:7865
Au	x=0.28176 y=0.21370 CCT:52792
Ba	x=0.40594 y=0.29390 CCT:2465
Be	x=0.65307 y=0.28337 CCT:N/A
Bi	x=0.13799 y=0.08132 CCT:N/A
Bk(?)	x=0.25865 y=0.48376 CCT:7372
Br	x=0.42538 y=0.17141 CCT:N/A
C	x=0.48870 y=0.40603 CCT:2310
Ca	x=0.30381 y=0.25900 CCT:8820
Cd	x=0.42421 y=0.34372 CCT:2671
Ce	x=0.37811 y=0.51844 CCT:4673
Cf(?)	x=0.22770 y=0.36738 CCT:10822
Cl	x=0.33398 y=0.14900 CCT:5924
Cm(?)	x=0.33030 y=0.13171 CCT:5453
Co	x=0.16760 y=0.09322 CCT:N/A
Cr	x=0.15269 y=0.18140 CCT:N/A
Cs	x=0.43610 y=0.24066 CCT:N/A
Cu	x=0.22108 y=0.47286 CCT:8660
Dy	x=0.18242 y=0.04908 CCT:N/A
Er	x=0.24165 y=0.15290 CCT:N/A
Es(?)	x=0.13603 y=0.77698 CCT:8096
Eu	x=0.21064 y=0.17438 CCT:N/A
F	x=0.70108 y=0.29868 CCT:N/A
Fe	x=0.16540 y=0.23953 CCT:N/A
Ga	x=0.71666 y=0.28028 CCT:N/A
Gd	x=0.17851 y=0.11031 CCT:N/A
Ge	x=0.31803 y=0.37803 CCT:6033
H	x=0.36142 y=0.17779 CCT:1800
He	x=0.40332 y=0.30023 CCT:2593
Hf	x=0.22803 y=0.21893 CCT:N/A
Hg	x=0.22581 y=0.17240 CCT:N/A
Ho	x=0.21480 y=0.11149 CCT:N/A
I	x=0.44470 y=0.45205 CCT:3230
In	x=0.15847 y=0.02011 CCT:N/A
Ir	x=0.18189 y=0.10689 CCT:N/A
K	x=0.24400 y=0.41540 CCT:8644
Kr	x=0.31527 y=0.25843 CCT:7358
La	x=0.32204 y=0.48980 CCT:5755
Li	x=0.65307 y=0.28337 CCT:N/A
Lu	x=0.23161 y=0.22856 CCT:N/A
Mg	x=0.22430 y=0.38397 CCT:10422
Mn	x=0.17279 y=0.07516 CCT:N/A
Mo	x=0.24775 y=0.30775 CCT:12498
N	x=0.50463 y=0.41109 CCT:2182
Na	x=0.56646 y=0.42639 CCT:1784
Nb	x=0.18991 y=0.14174 CCT:N/A
Nd	x=0.23373 y=0.24045 CCT:276889
Ne	x=0.32614 y=0.300694 CCT:5874
Ni	x=0.17530 y=0.29671 CCT:51135
Np	x=0.58908 y=0.39726 CCT:N/A
O	x=0.56255 y=0.38729 CCT:N/A
Os	x=0.18210 y=0.07952 CCT:N/A
P	x=0.37811 y=0.58559 CCT:4817
Pa(?)	x=0.65398 y=0.29507 CCT:N/A
Pb	x=0.24353 y=0.12610 CCT:N/A
Pd	x=0.18926 y=0.18234 CCT:N/A
Pm	x=0.21557 y=0.12110 CCT:N/A
Po	x=0.18962 y=0.16608 CCT:N/A
Pr	x=0.26716 y=0.34978 CCT:8796
Pt	x=0.208396 y=0.21666 CCT:N/A
Pu(?)	x=0.33160 y=0.30768 CCT:5531
Ra(?)	x=0.30080 y=0.47820 CCT:6277
Rb	x=0.29209 y=0.19641 CCT:N/A
Re	x=0.19441 y=0.18127 CCT:N/A
Rh	x=0.18520 y=0.09060 CCT:N/A
Rn	x=0.18304 y=0.03589 CCT:N/A
Ru	x=0.16337 y=0.076314 CCT:N/A
S	x=0.39692 y=0.30582 CCT:2806
Sb	x=0.39856 y=0.55907 CCT:4452
Sc	x=0.30733 y=0.29512 CCT:7263
Se	x=0.17640 y=0.18539 CCT:N/A
Si	x=0.53341 y=0.42437 CCT:2013
Sm	x=0.16931 y=0.15183 CCT:N/A
Sn	x=0.57260 y=0.40128 CCT:N/A
Sr	x=0.18553 y=0.20712 CCT:N/A
Ta	x=0.33978 y=0.26127 CCT:4750
Tb	x=0.17519 y=0.06473 CCT:N/A
Tc	x=0.17048 y=0.13381 CCT:N/A
Te	x=0.51420 y=0.45161 CCT:2354
Th	x=0.22492 y=0.21358 CCT:N/A
Ti	x=0.16351 y=0.15584 CCT:N/A
Tl	x=0.19299 y=0.78151 CCT:7247
Tm	x=0.19167 y=0.09032 CCT:N/A
U	x=0.25803 y=0.13296 CCT:N/A
V	x=0.21169 y=0.07884 CCT:N/A
W	x=0.21324 y=0.28430 CCT:27407
Xe	x=0.46306 y=0.36183 CCT:2266
Y	x=0.21561 y=0.14833 CCT:N/A
Yb	x=0.22844 y=0.28922 CCT:19073
Zn	x=0.28944 y=0.19738 CCT:N/A
Zr	x=0.21275 y=0.13814 CCT:N/A

Here are all the element colors arranged into a periodic table (idea and html code for table courtesy of Matt Roberds).

B

*

At

Fr

**

Rf

etc.

*

**

Fm

Md

No

Lr

All the spectrum renderings and color hues above depend on [6]'s published data. It seems that sometimes the data published contain subtle inaccuracies so things are not as simple as picking the data and plugging them in the program. For example, [6] warns about some of the dangers here. Similarly, source [4] brought to the author's attention the following excerpts from [6]:

1. There is no common scale for relative intensities. The values in the database are taken from the values given by the authors of the cited publications. Since different authors use different scales, the relative intensities have meaning only within a given spectrum; that is, within the spectrum of a given element in a given stage of ionization.
2. The relative intensities are most useful in comparing strengths of spectral lines that are not separated widely. This results from the fact that most relative intensities are not corrected for spectral sensitivity of the measuring instruments (spectrometers, photomultipliers, photographic emulsions).
3. The relative intensities for a spectrum depend on the light source used for the excitation. These values can change from source to source, and this is another reason to regard the values as being only qualitative.

1. Silver: I have seen silver arcs in sparking switch contacts and I have seen the spectrum. The color I remember being more bluish. I suspect the roughly 470 and roughly 490 nm features were stronger.
2. Aluminum: In my experience with arcs, the borderline-violet-UV feature dominates the spectrum more than is shown and the source color is close to pure white or slightly violetish white.
3. Argon: The color looks roughly right to me. However, what I think that one needs is for the spectral lines to be scaled upwards (author: The lines are suppressed because a feature near 700nm is at 100).
4. Barium: I think it would look more "correct" to me if lines get scaled down with the exception of: The the strongest ones around 450, 490, 550, the two around 610, and the one around 650.
5. Calcium: I think the spectrum is normally dominated by a resonance line around 420 nm and maybe one or a few red lines. I have seen it add a red coloration to flames, though in an arc without oxygen I suspect it could produce mainly the resonance line.
6. Cadmium: I have struck small arcs on cadmium-plated hardware and found a greenish blue color, with the blue lines being stronger and the red line being weaker (The author tends to agree).
7. Copper: I have struck copper arcs. I think the lines other than green ones are weaker than shown and the color is more greenish than shown (The author agrees, with the exception of the features near 400nm).
8. Iron: I think the green and greenish lines are weaker than shown. (Or, maybe scale up lines other than green/greenish ones.) In my experience, iron arcs are a bluish-violet-white color.
9. Gallium: When I see spectral tables, I usually see two extremely strong lines near 400 nm (The two features are there, but are greatly suppressed).
10. Hydrogen: Sometimes glows the color shown, sometimes glows more red.
11. Helium: I have seen the color of helium glowing in a spectrum tube and it is more orangish, almost the color of HPS or a little less white and more orangish than a very warm color fluorescent. I find the line near 450 nm weaker than shown and the yellow one stronger than shown.
12. Mercury: I would scale up the green line and scale down the violet and blue lines a little for low pressure. I have always seen low pressure mercury glow a more greenish, less violetish shade of light blue than shown.
13. Indium: I would take down the 410 nm or so line a little. I also think that some lines other than the two shown exist weakly.
14. Potassium: I think the green and blue-green lines should be weaker than shown. I have always seen its flame coloration to be a whitish purple.
15. Krypton: I think the bluish lines other than the two shortest wavelength ones should be weaker and two around 420-430 nm should be stronger. The color I do find accurate at least sometimes however.
16. Lithium: You show the spectrum having only lines around 610 and 670 nm, but the color to be slightly whitish. I would either show other spectral lines or make the color a more saturated slightly orangish shade of red. I have seen the flame coloration, and found it to be more saturated. It may not be saturated in an arc (author: There are some additional features in the distribution which are suppressed, but may contribute to the color because of the eye's sensitivity in that area).
17. Magnesium: I have seen the flame color - slightly more saturated shade of green. I don't know what color it usually glows in an arc however.
18. Nitrogen: I find it to glow a little less yellowish and more whitish-pinkish. I also see in its spectrum (my experience) a series of bands in the yellow through red that I think are molecular rather than atomic in origin.
19. Sodium: Looks OK to me! But I did check the RGB in the color, and saw b=27. I think the b value should be lower, as in the color being more saturated (for low pressure sodium).
20. Neon: In my experience, the lines shorter than the roughly 535-540 nm green ones are nearly nonexistent, the green lines should be a little weaker, and the lines from yellow through red should be stronger. I think we have all seen the color, so I think the color shown is obviously not typical real-world for neon! (author agrees).
21. Radium: I have not seen it glowing, but I do know that one of those blue-green lines is a resonance line, and lines other than that one would probably be weaker in a flame and in an arc lamp.
22. Scandium: Where did those huge deep red lines around 660-670 nm come from? (author: from NIST!!) In a lamp, it glows more bluish. I have heard of it in arcs other than in metal halide lamps it glows more bluish still. In addition, I think the line clusters around 470 nm and 510 nm should be stronger, based on how I see the spectra of metal halide lamps.
23. Strontium: May be reasonably accurate. However, the blue line around 460 nm is a resonance line, and I suspect in arc lamps lines other than that one are likely to be weaker.
24. Thallium: The only inaccuracy I can see is the color, and that I can blame on the color gamut limitations of computer monitors. I would show the green color as being less bluish.
25. Xenon: I think the color and spectrum are both inaccurate. At low intensity, I have seen the main features being the two blue lines around 460-470 nm, after that some green lines around 530 nm, and a fair amount of continuum, with the color being bluish white. In some situations (flashlamp with lower xenon pressure, lower capacitance, higher voltage) I see the lines of singly ionized xenon being prominent. The color is a slightly greenish bluish white. I think the red lines near and over 620 nm are shown stronger than I usually see them.
26. Zinc: In my experience with arcs using a couple to a few amps, the color is a slightly greenish whitish blue, with the red line being weaker than shown (author agrees).

In view of the above comments, the reader should expect several color rendering inaccuracies above, when [6] cites more than one source in the corresponding spectral distributions or when the element's lines are of equal intensity (as in radioactive elements with a question mark next to them). The author chose to keep the NIST distributions as they are, in order to have a single consistent source of data. Should a better source come along, the author will recalculate all the results.

The main problem with the elements when engineers consider them as artificial light sources, is that their spectra do not contain all the wavelengths in the visual spectrum, so adjustments need to be made, by utilizing combinations of elements or fluorescence. What's worse, not only they do not contain all the wavelengths of a continuous spectrum, they have wildly varying CCTs and CRIs and the emission spectrum may change when the discharge temperature or pressure is changed. Assuming NIST's data come from a non-specialized standard low pressure element discharge, the following figure shows the distribution of all the elements' chromaticities plotted against the CIE diagram and gives a general idea of how useful their emission spectrum is.

Chromaticity distribution of element spectra

In general the physics of lamp discharges is extremely complicated, so selecting elements as discharge ingredients for lamps is hard science! First, from the above diagram for example, it is fairly obvious that most elements make bad candidates for light production, because of bad CCTs/CRIs. As far as chromaticity is concerned there are some good candidates: O, C, N, P, Xe, Na, W and Sc among others. It turns out however that this is only one of the factors that determine discharge element suitability. Other factors such as heat conductivity, vapor pressure, corrosiveness of hot vapor and toxicity are very important and usually limit the choices of lighting engineers even more. For example, the selection of the discharge tube material which is used to confine the discharge in a lamp in an efficient way is extremely important. It requires very advanced material technology because many elemental vapors at high temperature will corrode the confining discharge tube very fast, making practical lamp construction impossible. The two most used elements in lamp discharges are mercury, which is the main ingredient in fluorescent lamps, mercury vapor lamps and metal halide lamps, and sodium, which is the main ingredient in low and high pressure sodium lamps. The most often used material for discharge tubes is fused quartz and aluminum oxide. Mercury for example is relatively inert and when it is the main ingredient in a discharge, its vapor won't corrode quartz. Other elements are not this friendly to quartz. Hot sodium will corrode quartz tubes, so high pressure sodium lamp discharge tubes are made of translucent aluminum oxide (polycrystalline alumina). This material has a lower transparency than quartz (~95%) but withstands the hot sodium vapor. Other materials such as zirconium or sapphire have been considered but were abandoned because they were expensive. The advantages of using mercury and sodium (which often are not found in other elements) are:

Mercury (source [4]):

1. Liquid at room temperature, so it can provide a reservoir of mercury vapor.
2. Optimum vapor pressure over liquid at convenient temperature (40°C).
3. Resonance line(s) at convenient wavelength for fluorescence.
4. Most of the energy in the low pressure discharge can be dissipated by the 254nm resonance line.
5. Most of the energy in the high pressure discharge can be dissipated by the 365nm line and by the visible lines.
6. Does not react with glass, phosphor, metals used for electrodes or emission mix used on electrodes.
7. Is cheap.
8. Can be used as a buffer gas which has low pressure and density at room temperature yet high pressure and density at high temperature.
9. Large atoms with low thermal conductivity.
10. Low reaction rate with air, making manufacturing easy.

Sodium (source [4]):

1. Resonance lines in visible near peak of eye response curve, implying very high efficiency.
2. Relatively large fraction of energy delivered to the discharge is dissipated by the two resonance lines at 589 and 589.6nm.

Other elements (source [5]):

1. Xenon is a good candidate, although full concentration in the arc tube occurs when the arc tube is cold and that means very high starting voltages. It has been explored as a significant ingredient in high pressure sodium lamps and as a standalone gas with xenon flash lamps (because the Xenon I-V spectrum has a very good daylight quality color with a CCT of around 6000K-9000K (see [3] and The Xenon Discharge)) and xenon short-arc lamps (because under high pressure its spectrum is almost continuous, also with a very good daylight quality color with a CCT of around 5600K-6300K (see [3] and The Xenon Discharge)). Its efficiency is low, however.
2. CO₂ has some serious strong points and the light is of superb golden-white color with a CCT of around 6500K. But, as a fill gas, it is far from inert. It oxidizes incandescently hot iron in mere seconds. CO may be an improvement in terms of corrosion, but lower molecular weight means smaller size molecules which will have high heat conduction losses.
3. Thallium is a candidate although vapor pressure in the atmospheric range requires some temperature much higher than the boiling point of sodium. Also, its spectrum is virtually monochromatic, with only one emission line at 535nm. Although green metal halide lamps with thallium exist, they are mostly used for decorative applications and lighting effects. It is used however in combination with other elements in some metal halide lamps of European technology where the arc tube vapor content is mainly mercury. Finally, it is toxic, so its use is limited.
4. Indium has two strong and easily broadened emission lines in the deep blue and in the violet, but worse than thallium, for vapor pressure in the atmospheric range it requires temperatures hotter than regular quartz arc tubes can withstand. It is also used in combination with other elements in metal halide lamps of European technology.
5. Other metals in this region of the periodic table are even harder to vaporize and/or have strong UV emissions worse than that of mercury or both.
6. Red-hot sulfur rapidly oxidizes any metal more reactive than platinum or gold. This limits sulfur to electrodeless lamps, generally powered by microwave generators. The idea has been explored with the sulphur lamp, but eventually it was booted.
7. Another set of ingredients with low heat conduction loss and easily vaporizable would be potassium, rubidium, and caesium. The big problems with these are chemical reactivity like that of sodium but worse, and very strong and easily-broadened main emission spectral lines in the infrared. Francium falls in this class also, with the additional disadvantage of being radioactive with its longest-lived isotope having a half-life of 21 minutes.
8. Alkaline earth metals may be candidates somewhat, although none of them vaporize nearly as easily as sodium. Strontium has its main emission line around 461 nm in the blue and barium has its main emission line in the yellow-green. Calcium, magnesium and beryllium have even lower vapor pressures at a given temperature and main emission in the UV. Radium has its main emission in the blue-green and is highly radioactive.
9. Lithium has more heat conductivity than sodium and its main and easily broadened emission line at 671 nm, is deep red with low luminous efficacy. It is used infrequently in certain specialty magenta metal halide lamps.
10. Other metals besides those mentioned above generally have their main emission in the UV or have very bad CCTs/CRIs in addition to being much more difficult to vaporize than sodium. Most also have vapor with higher heat conductivity than that of mercury. Tungsten, for example has an excellent spectrum, but it has the highest melting point of all the elements, so it's practically useless as an ingredient in discharges. It is no coincidence that the electrodes of most discharge lamps are made of tungsten.
11. Scandium is a good candidate and is in fact used as a partial ingredient along with sodium and mainly mercury in metal halide lamps of American technology.
12. Iron and cobalt are sometimes used in some rare diazo metal halide lamps because their spectra are relatively rich with decent CCTs/CRIs.
13. Radon is an improvement over xenon, except that it is radioactive and its longest-lived isotope has a half-life a little less than 4 days.
14. Halogens are corrosive (iodine will even corrode quartz over 10,000's of hours at typical arc tube temperatures, others except short-life-radioactive astatine are even worse) and badly impair starting and impair stability of arcs receiving AC or pulsating DC. Metal halide lamps even require extra ballast open-circuit voltage compared to mercury just because of maybe at most a few Torr of iodine vapor quenching the arc between half-cycles until the vapor is dense enough to be hot enough to maintain some ionization between half-cycles.
15. Heat conduction of lighter atomic/molecular weight gases (compared to xenon or mercury) is a problem in HID lamps if used as a majority ingredient.
16. Compounds such as organic gases, boranes, and some inorganic fluorides have impressively low heat conductivity.

Although mercury ended up as being one of the best candidate for lamps, in a low pressure discharge it emits most of its radiation in the UV:

Spectrum of a low pressure mercury lamp from 100nm to 2000nm

Most of the energy (~78%) is radiated at the resonance line at 253.7nm. The discharge also radiates significant energy at 365nm, at 184.9nm and at various other UV lines. These lines are usually utilized by various lamp manufacturers for different reasons. The 253.7nm line for example is strongly bacteriocidal, so low pressure mercury lamps with a clear glass with very low iron oxide content, which allow this line to pass through are used as germicidal lamps in hospitals, warehouses, barbershops and wherever else bacterial disinfection is required, such as for water purification and disinfection. The 184.9nm line converts O₂ to O₃, more commonly known as ozone, so low pressure mercury lamps which allow this line through are used to sanitize air. Although ozone is toxic in high concentrations, the concentrations achieved by small ozone lamps are usually not high enough to become toxic. In general caution should be exercised with high concentrations of ozone.

When the pressure in a mercury vapor discharge increases, the spectrum of the mercury discharge is altered significantly: The maximum emission moves from the 253.7nm resonance line to the 365nm ³P°-³D non-resonance line. The 253.7nm line becomes greatly suppressed and approximately half the energy is now radiated at the 365nm line. The intensities of the visible lines increase and they contribute to the visible spectrum with different ratios than when under low pressure. There is also broadening of the spectral lines and emission of some continuum (sources [23], [25], [30]) Consequently the efficiency and color temperature of the discharge are changed dramatically. The efficiency changes from a mere 10-12 lm/W to a decent 52 lm/W, so a lamp employing a high pressure mercury discharge becomes practical as a source for general illumination. The source's new chromaticity allows for a determination of CCT which is around 6000K-7000K (sources [3], [7], [16], [18], [19], [30]) and the source shifts its color from blue to greenish white moving closer to the Planckian Locus. However, although the CCT is good, the CRI of a high pressure mercury vapor lamp is not very good and reds are muted appearing as dull browns/greys because the spectrum lacks in red emissions. Here is a comparison between the two types of discharges in the range 150nm to 700nm. The data was based on [9], [19] and [23], although the data in [9] is conflicting with the data in the other two references. [19] lists a CCT of 6300K and (x,y)=(0.315,0.385) for its 1000 Watt clear mercury vapor lamp, which are close to what the program calculated for the high pressure distribution.

Discharge Type	CIE chromaticity CCT (K)	Source Color	Spectral Distribution
Low Pressure	x=0.22581 y=0.17240 CCT:N/A
High Pressure	x=0.31996 y=0.38645 CCT:5942

Because most of the energy with both low and a high pressure mercury lamps is radiated in the UV, engineers harness the two lines, the 253.7nm line in low pressure and the 365nm line in high pressure to increase the efficiency of lamps which use these two types of discharges. Harnessing the 253.7nm line in a low pressure lamp results in the fluorescent lamp. Harnessing the 365nm line results in the color corrected mercury vapor lamp. In both technologies, UV high energy photons excite special phosphors which absorb those photons and then re-emit photons of lower energy in the visible by fluorescence, improving the CCT of the source in both cases. Generally there are three types of phosphors: Halophosphate phosphors and triphosphors used with fluorescent lamps and mercury vapor color correction phosphors.

1. Halophosphate phosphors were the earliest kind used with the very first fluorescent lamps. Usually they employ some kind of crystalline lattice which fluoresces, for example crystalline ores of manganese with impurities or calcium halophosphate activated with bismuth and manganese. Employing a crystalline lattice allows for broader light emission zones, the spectral distribution of which depends on the centers which emit and the atoms which surround them, with the crystal impurities playing the role of local imperfections of the crystalline lattice. The electrons of the crystal structure can freely move around into certain "energy zones" in which the energy remains constant. UV stimulation in this case (by the 253.7nm line) simply displaces the electrons from one zone to another. As the possible combinations for such transitions are many, the fluorescent emission centers cannot be pinpointed down as of being of a specific wavelength, therefore the spectral distribution of the fluorescence is broad and usually results in the emission of a continuous distribution (source [23]). Employing different impurities and ratios of materials in the crystal lattices allows for a range of CCTs approximately between 2300K and 7000K. The older common "daylight" halophosphate fluorescents in use before triphosphor fluorescents came about were of this kind.
2. Triphosphors are three color component phosphors which are the result of more recent technology. They also utilize the 253.7nm resonance line but re-emit molecular bands at specific wavelengths related to the transitions of ions of terbium and europium. The terbium ions usually produce fluorescent molecular bands in the blue and green while the europium ions produce fluorescent bands in the red (source [25], [27]). By altering the ratio of terbium to europium ions in the phosphor and by doping the phosphor with various other ions, many different CCT ranges can be achieved. The first triphosphor fluorescent lamps (which are also the commonest kind) had a CCT of 2700K. Newer technology allowed for raised CCTs with ranges from 2700K to 17000K.
3. Phosphors for mercury vapor lamps try to harness mainly the 365nm line and secondarily the 300-313nm cluster of lines where most of the energy is radiated by mercury vapor in high pressure. Generally, the two most common types which were in use in the past and are used today are fluorescent powders of magnesium fluoroarsenate/fluorogermanate (activated with manganese) and yttrium vanadate phosphate. Magnesium fluoroarsenate was eventually replaced by magnesium fluorogermanate because it was toxic. These powders generally deliver two-three specific fluorescent peaks around 611nm-650nm, depending on type. Their emissions therefore have specific wavelengths in the red part of the spectrum which increase the overall efficiency of the mercury vapor lamp. Mercury vapor lamps employing such phosphors are termed "color-corrected" mercury lamps and have CCTs in the range 3000K-5000K. For an extensive reference of mercury vapor phosphors consult [3] (specifically this subpage).

Considerable improvement also occurs when the light of mercury lamps or color corrected mercury lamps is combined with a planckian radiator's light. This is the main principle behind blended light lamps, which use an incandescent filament in series with the mercury burner to simultaneously limit the current of the lamp and provide warm planckian radiation at around 2500K (sources [22], [30]). As these lamps do not require any support gear, they are often used as retrofit lamps in regular incandescent installations with excellent results, replacing the relatively yellowish light of regular incandescents with crisp, whiter light, although the combined efficiency of both radiators is relatively low, so their use is somewhat sparse.

In all cases above where fluorescence occurs, Stokes' Shift is applicable. This means, λ_Fluorescence>λ_Stimulation. Here then is a comparative table for the two types of mercury discharge in the visible range 380nm to 700nm, employed by the popular triphosphor fluorescents, the color corrected mercury vapor lamps and the blended light lamps, with spectra simulated by adjusting the line intensity of all sources using the Maple program:

Lamp Type	CIE chromaticity CCT (K)	Source Color	Spectral Distribution
Low Pressure Mercury	x=0.22581 y=0.17240 CCT:N/A
Triphosphor Fluorescent 2700K	x=0.46632 y=0.42547 CCT:2724
Triphosphor Fluorescent 4000K	x=0.37820 y=0.37264 CCT:4031
Clear Mercury Vapor	x=0.31996 y=0.38645 CCT:5942
Color Corrected Mercury Vapor	x=0.40288 y=0.39424 CCT:3582
Blended Light	x=0.41436 y=0.39733 CCT:3362

The technological descendant of the mercury discharge is the metal halide discharge. In this discharge halides of selected metals are added to the mercury discharge to improve the quality of generated light by shifting the chromaticity of the corresponding lamp closer to the Planckian Locus. The halides are easy to vaporize and this generally guarantees relatively high source efficiencies. During normal operation the discharge reaches temperatures of around 700°C. At this temperature the vapor pressure of the halides is a few milligrams of mercury. Close to the discharge axis the halides break down to their corresponding constituent metal and halogen and the metal vapor enters the arc stream where it participates in light production. Away from the discharge axis and close to the tube walls the metals recombine with halogen and again form halides which condense there in liquid form. This mechanism ensures two good things: That the corresponding metals in the halides participate almost exclusively in the light production (which would be impossible if they were put in the discharge tube in pure form) and that the discharge tube is not chemically attacked by them. Because the electrodes need to also be chemically unaffected by the halides, they are often constructed from metals which are immune to chemical attacks (such as thorium oxide). The previous fact along with the facts that there's always trace quantities of hydrogen in the tube (halides are hygroscopic) and that the electron emission rate of such electrodes is lower than that of tungsten electrodes, necessitate much higher starting voltages than regular mercury vapor lamps. As a result their support gear is relatively expensive and these lamps either require a separate thyristor ignitor or ballasts which deliver higher peak voltages, depending on type (source [23]). Two main halide technologies exist, the European technology and the American technology:

1. The European halide technology focused on halides of sodium, thallium and indium. This technology arose as a result of extended research by PHILIPS in 1962, targeting the need to find a suitable light source which could be used with good results for color television broadcasts of major sporting events in stadiums. Color television broadcasts mainly in three bands (red, green and blue), so the result was a lamp which has emission peaks in all three areas. Sodium gives a peak at orange red, thallium a peak at green and indium at blue, therefore these elements were deemed most suitable (source [19]). European technology alternatively also focused on halides of dysprosium and thallium (and optionally on thulium and caesium). Original research by OSRAM produced a metal halide lamp which simulates daylight very effectively with a high CCT of around 5000K-6000K (depending on type) and a CRI close to 95 (see [3]), because dysprosium, caesium and thulium have relatively rich spectral distributions.
2. The American halide technology focused on halides of scandium, it being one of the best candidates in terms of CCT (see Lamp Engineering, above). Sodium halide is also added to the discharge to lower scandium's relatively high CCT of around 7300K and to stabilize the discharge arc. The scandium spectrum is also relatively rich so scandium/sodium metal halides in general have decent CRIs around 65-70. The result is a lamp with very good chromaticity and a CCT of around 4000K (source [18]).
3. In addition to the above two main technologies many other halide lamps have been constructed. By adding other halides or by combining the previous ones in different ways, metal halide lamps for specific applications such as diazo reprographic processes, sun-tanning and colored light have been made possible. Such metal halides usually have relatively short lifetimes to be of any practical use for general illumination (see Lamp Engineering).

By combining the corresponding element distributions, it's possible to simulate the most common metal halide discharge spectra. Here's a comparative table of some metal halide lamp spectra rendered with the Maple program. For the visualization and all subsequent calculations and sections the author assumed the following:

1. That the relative intensity of the mercury lines is approximately equal to the intensity ratios found in a high pressure mercury lamp, so the author uses the high pressure mercury spectral distribution found in [19] (also used in section The Mercury Discharge). Source [4] confirms this: Both high pressure mercury and metal halide lamps have lower electron temperatures than low pressure mercury lamps, and both high pressure mercury and metal halide lamps have much higher mercury resonance line trapping rates than low pressure mercury lamps, so the assumption is on the reasonable side. In true reality the relative intensities of mercury lines in a metal halide discharge may be different from both the low and high pressure spectrum, so the previous is overall an untested assumption.
2. That the intensities of all the lines of each element mixed in are directly proportional to the element's contribution ratio in the discharge. This seems to be a reasonable assumption and is supported by [22], where an example of quantitative spectroscopy is given.
3. That the vapor pressure of the metals in metal halide lamps is approximately equal to the vapor pressure of the same metal in the discharge data found in [6]. This is probably a wrong assumption since it is very likely that the vapor pressure of an element in a metal halide discharge is likely higher than the vapor pressure of the corresponding discharge source [6] used to acquire its spectral data (for example, in [19], the 670nm-690nm scandium red lines are present in the corresponding metal halide spectrum but are much more suppressed). As a result the intensity ratios of the lines of each element may be slightly different in reality. This should affect the elements with rich spectra such as scandium, dysprosium, thulium, iron and cobalt and not the elements with a few lines such as sodium, thallium, gallium and lead.
4. That [6]'s relative line intensities in the spectral distributions of Sc, Dy, Ho, Th, Cs, In and Tl are relatively accurate within each spectrum. The author checked the above elements in [6] and found that at most two different sources were cited in each respective spectral distribution (see section Possible NIST Inaccuracies).
5. That phenomena such as pressure and/or thermal broadening and/or self-absorption of element lines don't occur. We simply use the line's relative intensity at its 1nm central wavelength bin as it is given by [6]. This seems to also be a reasonable approximation, since when such phenomena occur (with sodium and indium for example), one can simply intensify the central emission wavelength of the un-broadened line appropriately to simulate the total energy when broadening occurs.

To conclude: Although the results of section Element Emission Spectra may contain inaccuracies, the assumptions on this and the subsequent sections seem to generally be on the safe side. This side seems to be partially supported by the fact that there existed specific ratios of the elements which gave the required chromaticities and CCTs for all the combinations below (therefore the assumptions must indeed have been accurate). The results for the calculations of CCTs and chromaticities in general agree with the published data the author has at his disposal (such as [3], [15]-[19], [22]-[23] and [25]), so the program can conceivably be used as a predictor for the efficiency of various discharges. Alternatively, custom spectral distributions of halides (at the correct vapor pressure) may be entered giving even better results. Some rather rare metal halide types are shown towards the bottom of the table. On some spectra the author has suppressed the maximum intensity shown, in order to show the weaker lines.

Lamp Type	CIE chromaticity CCT (K)	Source Color	Spectral Distribution
Sodium/Thallium/Indium metal halide (European)	x=0.37426 y=0.41000 CCT:4366
Sodium/Scandium metal halide (American)	x=0.35185 y=0.32282 CCT:4575
Dysprosium/Thallium /Thulium/Caesium "daylight" (European) metal halide	x=0.30179 y=0.35347 CCT:6855
Plant growing metal halide	x=0.36054 y=0.27794 CCT:3629
Blue colored metal halide	x=0.21958 y=0.15021 CCT:N/A
Green colored metal halide	x=0.26600 y=0.57411 CCT:6748
Iron/Cobalt diazo metal halide	x=0.29973 y=0.28898 CCT:8051
Lead/Gallium diazo metal halide	x=0.2953 y=0.27545 CCT:9022

Sodium is the second most important candidate for light production. An electrical discharge through sodium vapor is generally quite efficient because sodium has its resonance lines in the visible, at D₁=589nm and D₂=589.6nm. Such a discharge can take generally two forms, depending on pressure. Under low pressure (0.004 milligrams of mercury) and when the tube wall temperature is approximately 265°C most of the energy is dissipated at the D lines, so such a source has very high efficiency (180-210 lm/W for the highest Wattages available (source [30])), because the wavelengths of the D line are close to the wavelength where the eye has its maximum sensitivity (555nm). Under high pressure things are much more complex. Generally the optimal pressure of sodium in a high pressure discharge is around 100-200 millimeters of mercury, when the temperature of the coldest spot in the discharge tube is around 700°C. However the temperature of the hottest spot on the discharge tube can reach temperatures of 1200°C. At such high temperatures, sodium corrodes most available materials that try to contain it, so the technology that allowed mass construction and use of high pressure lamps took a while to emerge. The breakthrough came with the creation and testing of a polycrystalline alumina (see Lamp Engineering), which was impervious to hot sodium corrosion. Under high pressure, the sodium D lines suffer thermal/pressure broadening and the D line suffers self-absorption. In addition, additional energy is radiated at several other secondary lines which in a low pressure discharge are very weak (the intensity ratio between the second strongest sodium line and D is roughly 0.7%, see [25]). This transforms the spectrum from a virtually monochromatic source under low pressure to a non-monochromatic source, therefore minor perception of color is possible. The majority of the radiation however is still produced by the self-reversed D line's "wings" (the wavelengths around the absorption feature which produce continuous radiation), so the discharge attains a golden-yellow color. Although the CCT of a low pressure discharge is essentially meaningless because its light is monochromatic, the high pressure discharge attains a CCT of 1800K-2500K depending on Wattage and pressure. Color rendering is generally bad, since most colors past green are muted. The efficiency is lower than that of the low pressure discharge and is in the vicinity of 100-110 lm/W. The two types of the sodium discharge are simulated below. The high pressure discharge has been approximated using a Lorentzian distribution, which usually describes thermally broadened lines quite accurately. The intensities of all lines other than D have been increased to account for thermal/pressure broadening. As such they appear more intense than in the distributions found in [16],[18] and [19].

Lamp Type	CIE chromaticity CCT (K)	Source Color	Spectral Distribution
Low Pressure	x=0.56646 y=0.42639 CCT:1784
High Pressure (source [19])	x=0.50257 y=0.39664 CCT:2104

Xenon is the third most important candidate for light production. Generally the xenon discharge takes three different forms depending on the power load used to excite the gas. Under low to medium pressure with low voltage and amperage its spectrum is rich but contains many lines in the red which lowers its CCT to non-acceptable levels for general illumination. Considerable improvement occurs when xenon at medium pressure is discharged with high voltage, in which case ions II and III (and possibly IV and V depending on voltage) participate in the light production by producing hundreds of new lines which raise the CCT of the discharge, shifting the color of the source towards cool daylight. Because the spectrum of xenon from this type of discharge is well-balanced and has a high CCT and CRI, it is used in flash tubes to mimic daylight when taking photographs. The third type of xenon discharge manifests when xenon has a pressure between 30 and 100 atmospheres and is discharged with a high current density. Xenon lamps employing this kind of discharge have very short arcs, operate on regulated DC and have extremely high brightness (100k cd/cm² at wattages higher than 6 kW). Their CCT in the neighborhood of 5600K-6300K is excellent (sources [3], [15]) and their spectrum is almost continuous. Their efficiency is around 40 lm/W, but the advantage of having a very good daylight spectrum and a good CCT overweighs this shortcoming, as a result they are employed in large cinema projectors (replacing the now obsolete carbon arc lamps), in search beacons and display spotlights, whenever light of very high quality is required. However they are expensive, their support gear is complicated and they are also dangerous because they operate under very high pressures, so they are usually operated only in enclosed fixtures and only by qualified personnel.

Lamp Type	CIE chromaticity CCT (K)	Source Color	Spectral Distribution
Low pressure Low voltage Low amperage (Xe I)	x=0.46306 y=0.36183 CCT:2266
Medium pressure High voltage Low amperage (Xe I-V, Flash tube)	x=0.28998 y=0.28435 CCT:9185
High pressure Low voltage High amperage (Short arc) (data from [29], and [33] mathematically weighed by the author)	x=0.31971 y=0.31096 CCT:6225

As stated in the abstract, the calculations in this document assume a fairly naive interpretation of [6]'s published spectral distribution data and the assumptions made in sections 13 and 14, therefore it is advisable to read again section Possible NIST Inaccuracies. That is: that the energy dissipated in all low pressure spectra is concentrated according to relative line strength. Further, most of the high pressure discharge spectral profiles described in the sections above for Mercury, Metal Halide, Sodium and Xenon, take for granted that the majority of the lines in the corresponding spectra are infinitely thin even at high pressures and temperatures. While the former (energy dissipated in proportion to line strength) is a tacit assumption that works fairly well with the subsequent engineering calculations, the latter should not be and needs to be detailed further. The line profile of most lines in element spectra changes drastically under conditions of higher temperature and pressure. The most important change occurs because of thermal/pressure broadening and self-absorption.

When these changes are taken into account, we obtain a much more accurate spectral profile for the lamps involved, which can be used to aid in further chromaticity calculations. To avoid unnecessary complication, we will concentrate on only thermal broadening and self-absorption. Since pressure (P) is proportional to temperature (T) in an ideal gas chamber of fixed volume V in thermal equilibrium - like the discharge burner of high pressure lamps, we can just assume only changes in T and see how these affect the lines' profile. The first modification therefore is to change the overall profile of all lines in the high pressure spectra into having a Lorentzian profile or even better a Voigt profile. For simplicity with calculations, we choose Lorentzian. A preliminary analysis for this is considered in the self-absorption for Sodium, which takes into account heat dissipation as a function of distance from the center of the arc in the arc tube. For further simplicity, we drop the heat dissipation function (the distance between center arc gas and arc wall gas is small) and we add one more assumption to the theory behind this change, which has been validated by experimental spectroscopy: That lines of higher intensity, degenerate faster into their high T Lorentzian profiles than low intensity lines at the same T(1). That is, intense lines are more prone to thermal pressure broadening and self-absorption, so we also change the sensitivity of lines to self-absorption: Experimental evidence suggests that lines of lower (relative) intensity suffer self-absorption at lower T rates than lines of higher sensitivity. We therefore denote as T1(3) the temperature of the discharge arc itself (in ° C), T2(2) the temperature of the arc discharge tube burner and T3 the radiation temperature (in ° K) of the blackbody contribution of the hot arc (denoted as K(°Celcius) below).

We obtain thermal data for calibration of the Lorentzian profile and we finally model the line profiles as LorentzianLine(T1)(broadened emission)-LorentzianLine(T2)(less broad absorption)(2)+Blackbody(T3)(thermal//black body emission) for the line intensities throughout the lamp spectrum. [5] provided the author with some thermal data in private communication along with data for Black body contribution for high temperature Hg, Na and MH hot gas arcs. Combined with data from [3] and [60], we have the following table:

Follow some spectra of the discharge lamps above recalculated using the new data for the Lorentzian line profile and by varying the Ti parameters:

Lamp Type	CIE chromaticity CCT (K)	Source Color	Spectral Distribution
High Pressure Mercury Clear T1=300, T2=180, T3=K(300) [*] Black body contribution (mostly) insignificant Slight broadening of Mercury lines Compare with lamptech and [1.4.1] [*]: T1/T2/T3 in real lamps can vary according to Discharge burner table above) and the calculations in this document are not exactly calibrated for the Ti data provided, so these are only numerically experimental examples indicative of that showing CCT and chromaticities matches only. For updated calculations with calibrated T3, consult MapleSoft where you can find Maple code that generates any of the graphs on this page.	x=0.32175 y=0.40504 CCT:5849
Blended Light (fluorescent) T1=480[2*], T2=200, T3=2800 Black body contribution significant @2800K (raises T1 and T2) More intense thermal broadening of Mercury lines Note improved color relative to Clear Mercury Compare with lamptech and [1.4.5] [2*]: Same note as [*] above. T3 is close to true for the Tungsten filament in series with the arc tube in Blended Light lamps and the Black Body radiation from it is roughly calibrated against the intensity of the Hg lines, based on lamptech's spectrograph.	x=0.38611 y=0.45067 CCT:4289
UHP Mercury T1=1100[3*], T2=250, T3=K(10000) Black body contribution significant @10300K (raises T1 and T2) Most intense thermal broadening of Mercury lines Compare with lamptech [3*]: T1 in real lamps can be anywhere between 2000-10000C (Discharge burner table above) depending on lamp-type and pressure and the calculations in this document are not exactly calibrated for Ti data, so this is only a numerically experimental example.	x=0.28793 y=0.34251 CCT:7713
Tri-band (Na/Tl/In) Metal Halide[4*] T1=380, T2=200, T3=K(380) Black body contribution insignificant Partial thermal broadening of Na/Tl/In lines Compare with lamptech and [1.6.1] [4*]: A more accurate depiction than the one shown in section The Halide Discharge. [3] shows that this Metal Halide often contains Li as well and possibly traces of other elements. The exact amount of Li here was determined by comparing with lamptech and experimenting numerically with the ratios in the mix as shown on top of the spectrum graph.	x=0.37505 y=0.50351 CCT:4689
Na/Sc Metal Halide[5*] T1=350, T2=200, T3=K(350) Black body contribution insignificant Partial broadening of Na D line Compare with lamptech and [1.6.3] [5*]: A more accurate depiction than the one shown in section The Halide Discharge. For Sc, [6] shows several lines around 673-683nm of dubious intensity (see section Possible NIST Inaccuracies). These lines were removed.	x=0.35601 y=0.35204 CCT:4597
Kr/Th Metal Halide[5a*] T1=400, T2=200, T3=K(400) Black body contribution insignificant Partial broadening of Na D line Compare with [1.6.10] [5a*]: Similar to [5*] above, but with additional traces of Kr and Th.	x=0.36482 y=0.34957 CCT:4272
Daylight (Rare Earth) Metal Halide[6*] T1=450, T2=100, T3=K(450) Black body contribution insignificant Partial broadening of Tl line Compare with lamptech and [1.6.4] [6*]: A more accurate depiction than the one shown in section The Halide Discharge. Contents may vary depending on type. [3] reports Dy, Tl and Cs. Other sources have reported Th and Ho as well. Contents and ratios for this one shown on the upper part of the spectrogram. In terms of intensity, compares better with the visual measurement of [1.6.4].	x=0.28292 y=0.44641 CCT:6903
Plant Growing Metal Halide[7*] T1=380, T2=320, T3=K(380) Black body contribution insignificant Partial broadening of Na/In lines and some self-absorption on In lines (reduced peak intensity) [7*]: A more accurate depiction of the one shown in section The Halide Discharge. Contents: Hg, Na, In and Li (but not Tl, as green does not contribute to plant growth). Not in production anymore (RADIUM). In terms of intensity, compares better with the visual measurement of [1.6.8].	x=0.31224 y=0.19496 CCT:N/A
Iron Cobalt Diazo Metal Halide[8*] T1=350, T2=100, T3=K(350) Black body contribution insignificant No significant line broadening [8*]: A more accurate depiction of the one shown in section The Halide Discharge, with higher Ti's taken into consideration. Contents: Hg, Na, Co and Fe. In terms of intensity, compares fairly well with the visual measurement of [1.6.5].	x=0.29897 y=0.31992 CCT:7421
Lead Gallium Diazo Metal Halide[9*] T1=500, T2=350, T3=K(500) Black body contribution insignificant Some Pb lines broadened and self-absorbing [9*]: A more accurate depiction of the one shown in section The Halide Discharge, with higher Ti's taken into consideration, showing thermal broadening and self-absorption of the violet Pb lines. Contents: Hg, Pb and Ga. In terms of intensity, compares fairly well with the visual measurement of [1.6.6].	x=0.27821 y=0.30451 CCT:9440
Blue Metal Halide[10*] T1=500, T2=350, T3=K(500) Black body contribution insignificant In lines broadened and self-absorbing [10*]: A more accurate depiction of the one shown in section The Halide Discharge, with higher Ti's taken into consideration, showing thermal broadening and self-absorption of the blue In lines. Contents: Hg, In and Na. In terms of intensity, compares fairly well with the visual measurement of [1.6.7].	x=0.19816 y=0.11262 CCT:∞+
Green Metal Halide[11*] T1=500, T2=350, T3=K(500) Black body contribution insignificant Tl line broadened and self-absorbing [11*]: A more accurate depiction of the one shown in section The Halide Discharge, with higher Ti's taken into consideration, showing thermal broadening and self-absorption of the green Tl line. Contents: Hg, Tl and traces of Na. In terms of intensity, compares fairly well with the visual measurement of [1.6.9].	x=0.26837 y=0.62300 CCT:6560
Warm White Deluxe Metal Halide[12*] T1=550, T2=300, T3=K(550) Black body contribution mostly insignificant Tl and Na lines broadened and self-absorbing Compare with [1.6.2] [12*] This lamp also emits broadband molecular emissions, which cannot be simulated accurately.	x=0.40833 y=0.50118 CCT:4096
Warm White Deluxe Metal Halide[12.1*] T1=550, T2=300, T3=K(550) Black body contribution mostly insignificant Tl and Sn lines broadened and self-absorbing Compare with lamptech [12.1*] Without Na.	x=0.41979 y=0.47531 CCT:3779
Sodium discharge at medium pressure[13*] T1=500, T2=100, T3=K(500) Black body contribution mostly insignificant Na D line thermally broadened. Secondary lines intensifying Compare with [1.5.4] [13*]: During the warm-up phase of a high pressure discharge, at about half-time to total brightness.	x=0.54799 y=0.42880 CCT:1926
High Pressure Sodium Discharge[14*] T1=1050, T2=900, T3=K(1050) Black body contribution mostly somewhat significant Na D line thermally broadened and self-absorbed. Secondary lines partially broadened Compare with lamptech and [1.5.5] [14*]: After full warm-up to total brightness.	x=0.49294 y=0.44186 CCT:2514
Super High Pressure Sodium White Lamp T1=3150, T2=3000, T3=K(3150) Black body contribution significant Na D line almost totally self-absorbed. All secondary lines broadened Compare with [1.5.6] and lamptech. Differences between spectral distributions due to changed behavior of hot Na gas, which behaves very much like a black body radiator at high temperature, rather than emitting a simple broadband spectrum.	x=0.38960 y=0.43761 CCT:4150
Pulsed Xenon High Pressure discharge T1=2500, T2=500, T3=K(6000) Black body contribution significant Most xe lines broadened Compare with [1.12.3]. Probably the best that can be done given the range of referenced T's in Discharge burner table, above. Using two separate data tables for the lines of Xe, one for low pressure and one for XeI-III, a Color Temperature of ~6300 (lamptech) was achieved at an average arc T1 of 2500 and T2 of 500, which according to [60] are the temperatures of the tip of the (+) electrode and the quartz envelope in these lamps.	x=0.31640 y=0.31976 CCT:6363

Notes:

1. Relative intensity is not a coincidence: It's basically the wavelengths of the transitions that have the highest probabilities of occuring - although the author is not aware of any theoretical research that proves this for all transitions or elements.
2. The exact expression for weaker lines takes r*T2 instead of T2 - where r is the ratio |LineIntensity(nm)|/|LineIntensity_max(nm)|. This is a bit ad-hoc, but it covers sufficiently a different problem that shows up: Different elements need different T's for evolving their Lorentzian profiles. Hence, since spectroscopic samples are quantitative, mixing two or more different elements in different proportions, mimicks the proportions of energy needed to excite the particular element in the sample's proportion.
3. A base T1=265C=Tr(eversal) is taken as a reference for the start of thermal broadening & self-absorption of the Na D line, based on experimental/visual evidence - as the surface T of the inner glass tube of a low pressure Sodium SOX lamp, which operates optimally without showing any signs of self-absorption on this line (The Sodium Discharge). For calculations for spectra with different elements this is a bit ad-hoc, but it's not so far from the truth, particularly when the contents contain traces of Na. That's when the D line will self absorb, so if the elements are ordered according to their content ratios to Na, they will start broadening their lines proportionally to the increased T relative to Na, according to ratio.

NOTE: Calculations & results in all subsequent Sections do NOT take section 17. The Spectral Line Profile in High Pressure Discharges into account. All subsequent calculations are based on the raw (infinitely thin) spectra given in Sections 12. The Mercury Discharge through 16. The Xenon Discharge. The author is planning an update, with all results recalculated including lamps whose spectra feature thermal broadening and self-absorption, but one shouldn't expect too much of a difference (except perhaps for FS indexes), since the chromaticity values and CCTs for the new spectra are fairly close to the ones used in Sections 12.-16.

Here are the chromaticities of all the lamps discussed above plotted against the 1931 CIE diagram:

Chromaticities for some of the lamps discussed above.

We now extract some crucial information from the data above. We consider a lamp L and the Black Body B of T=CCT_L. Such a Black Body will lie exactly at the intersection of the Planckian Locus and the corresponding isothermal line. The geometric distance LB then, gives a measure of how well L approximates a Black Body of temperature equal to the lamp's CCT. On the other hand the distance LD gives a measure of how well L approximates D=Daylight:

Lamps L_i and L'_i have the same CCT (equal to the T of Black Body B_i), but different CRIs.
L₁ appears redder than B₁. L₂ appears greener than B₂. L₃ appears bluer than B₃.
L'_i appears pinker/purpler than B_i.

We then call the lamp efficiency LE, the lamp lifetime LT and the lamp cost LC (sources for lamp efficiencies and lifetimes: [3],[5],[15],[16],[22],[23] and [25]. Source for lamp cost: personal data from lamps acquired). After the suggestion of source [36] the author has also included a lamp Full-Spectrum Color Index FS (see [34] and [37]-[39]). To have a more convenient form of data to work with the author first normalizes all the lamp/light data using the transformations:

Accordingly then, P_CCT is the proximity of the lamp/light's calculated CCT relative to T_D=5785K, P_LB is the proximity of the lamp/light to a Black Body of T=CCT relative to LB_min, P_LD is the proximity of the lamp/light to D relative to LD_min, P_LE is the lamp/light efficiency relative to LE_max, P_LT is the lamp/light lifetime relative to LT_max, P_LC is the lamp/light cost relative to LC_min and P_FS is the lamp/light Full-Spectrum color index relative to an equal energy spectrum which has an index of 100. A plus sign on the P_LB column should be interpreted as redder/greener/bluer than the color of the corresponding Black Body of T=CCT (depending on the source's CCT), while a minus sign should be interpreted as pinker/purpler than the corresponding Black Body, as indicated on the above diagram.

Here is all the data tabulated in order of presentation:

Notes:

1. With CCT_max=10000K assigned to BLAU.
2. Does not include support gear power losses.
3. To 50% survival.
4. Relative to LT_max=10y=87600h.
5. Cost of complete functional unit, with support gear when needed (such as luminaire, ballast, ignitor, etc).
6. Percent of "free".
7. Based on [35] with dw=10nm increments.

Selecting a particular lamp for general or specific lighting is a difficult choice even for professional lighting engineers. There are several factors which come to play and these factors are more or less related to CCT, LB, LD, LE, LT, LC and FS. To make the issue even more confusing, lighting depends on distance, application, space, place, population density and on hundreds of other factors which are usually analyzed extensively in college architecture courses. Architects, additionally, deal with the extra factor of aesthetics which is also important in most public space applications. In general, architectural treatises (such as [23]) separate the course material into a first technical section which is common between them and lighting engineers and describes most known artificial light sources and then delve into the optics and engineering of specific private or public places. In this section the author uses multiple objective optimization to derive some interesting conclusions. This kind of optimization is used whenever there are several conflicting objectives which must be optimized simultaneously. The objectives here are optimal values of CCT, LB, LD, LE, LT, LC and FS. When n different (and possibly) conflicting objectives are present, the researcher examines some value functions F_n(m) associated with each item m and each objective n, and looks at the consumer/user/application preferences. These preferences correspond to n weights w_n which assign each objective n an "importance" factor. Then the researcher, for each item m tries to maximize S(m)=∑_k=1..nw_k*F_k(m). It is immediately obvious that while each F_n(m) may well have a well-defined minimum and maximum for a specific n (when item m varies), S(m) will depend on the weights w_n. In general F_n(m) are normalized so that their ranges are similar, otherwise S(m) may end up biased. In this example, we have n=7 objective functions: F₁(m)=CCT(m), F₂(m)=LB(m), F₃(m)=LD(m), F₄(m)=LE(m), F₅(m)=LT(m), F₆(m)=LC(m) and F₇(m)=FS(m), where m is the lamp/light type. We have normalized the ranges of all the objective functions such that 0≤F_n(m)≤100, via the normalization transforms above, so there is no bias on the objective functions relative to each other. All we need to do now is assign the weights w_n and look at the ratios S(m)/S_max. To save space, we denote the weights for a particular application as the array [w₁,w₂,w₃,w₄,w₅,w₆,w₇]. Here the author chooses seven testing and ten typical applications, along with the overall performance as follows:

1. [50,1,1,1,1,1,1]: CCT: Proximity to CCT=T=5785 matters most, the rest equal.
2. [1,50,1,1,1,1,1]: LB: Proximity to Black Body matters most, the rest equal.
3. [1,1,50,1,1,1,1]: LD: Proximity to Daylight matters most, the rest equal.
4. [1,1,1,50,1,1,1]: LE: Efficiency matters most, the rest equal.
5. [1,1,1,1,30,1,1]: LT: Lifetime matters most, the rest equal.
6. [1,1,1,1,1,50,1]: LC: Cost matters most, the rest equal.
7. [1,1,1,1,1,1,50]: FS: Full-Spectrum matters most, the rest equal.
8. [100,390,5,15,80,250,10]: Home: Proximity to Black Body and cost matter the most. Good CCT is also important. People prefer warm and full lighting in houses and generally don't pay for very expensive lamps unless there is an advantage. They also want to use their house lamps as long as possible so lifetime is also important. Full-Spectrum quality is also somewhat important.
9. [10,220,380,50,80,170,250]: Work: Proximity to Black Body, to Daylight and Full-Spectrum matter the most. Corporations and companies want people to feel more energized and to remind them continuously that the sun is still out, so it's work time. They also don't want to spend a fortune to achieve these results because on average office spaces use a large number of lamps.
10. [1,1,50,550,200,200,1]: Street: Efficiency, lifetime and cost matter the most, because cities need to illuminate extended spaces using the smallest number of lamps.
11. [200,10,400,1,1,1,200]: Cinema/Studio: Excellent CCT, Daylight quality color and Full-Spectrum matter the most, in order for film/camera colors to be reproduced accurately. Lifetime is relatively unimportant, because the total projection/reproduction hours are relatively few. So is cost, because movie business is big business.
12. [30,100,200,1,1,1,50]: Public Gatherings/Sports: Proximity to Daylight and to Black Body matters the most because people tend to become agitated and aggressive in large groups under color-distorted artificial lighting, particularly in stadiums when sporting events take place.
13. [-150,-15,-150,200,1,1,1]: Caution/Alert/Attention/Decor: Lighting which needs to "catch" the eye for various reasons, such as to cause attention, to alert or caution or for unusual decor, needs to be as far away from Daylight as possible and to have high efficiency so that the eye is sensitive to it.
14. [-20,-30,10,40,-1,50,50]: Plant Growth: CCT, proximity to Black body and lamp time don't matter at all, because this is a dedicated application. What matters are proximity to daylight, efficiency, cost and a good Full-Spectrum, with peaks at blue and red to match the photosynthesis curve.
15. [-50,-10,-50,100,100,500,-100]: Astronomical Observatory Lighting: For lighting near professional observatories, nothing matters except lamp life, lamp cost and for the lamp to be as far away from 'Full-Spectrum' as possible. Efficiency matters some, but in general not as much as for street lighting, because observatories are relatively few compared to public streets.
16. [-100,-10,100,1,1,1,-20]: Diazo Replicating Process: For document replicating processes CCT should be very high but the overall color should be bluish and close to the daytime sky. The lamp should radiate mainly in the blue and be away from a Black Body. Cost, efficiency and lifetime do not matter much, because the usable hours are relatively few.
17. [10,1,500,1,1,1,550]: Photography Studio: In photography studios the three factors which matter the most are proximity to daylight, very good CCT and very accurate reproduction of colors, so a Full-Spectrum index should be as high as possible. Cost, efficiency and lifetime do not matter much, because the usable hours are again relatively few and professional photographers as well as movie producers spend a lot of money on dedicated lighting equipment.
18. [1,1,1,1,1,1,1]: Overall: A compromise with all weights equal to see what the average optimal choices are.

Here are then the scores S(L) of lamp/light L the Maple program generated for the test applications A(1)-A(7). The optimal choices for each application are indicated in parentheses, with best=1, worst=18. The top four choices are highlighted in magenta:

Here are also the scores S(L) of lamp/light L the Maple program generated for the actual applications A(8)-A(18). Again, the optimal choices for each application are indicated in parentheses, with best=1, worst=18. The top four choices are highlighted in magenta:

First, although the optimal choices for each application are numbered according to score for convenience, we need to qualify the numbering a bit. Here's a detailed table for the Home application, with the first row being S(D)-S(L), which is the score difference between D and the lamp L, and with the second row being the ratio of this difference to S(D)-S(HPMC), the optimal choice:

The above table gives a measure of how "good" the rest of the choices are, relative to the optimal. For example, the 2700K triphosphor fluorescent, the American metal halide and the daylight metal halide are all roughly 1.6 magnitudes worse a choice than the high pressure mercury color corrected choice. Considering then the above numbers to one decimal place, the final practical ordering becomes:

It's obvious that after a certain point, such as 1.7-1.8 orders of magnitude "worse" than the optimal choice (in this application), the choices displayed don't make very much sense, so all application results above should be interpreted accordingly. With the above assumption, here are the results:

1. CCT: The optimal choices here came out to be the high pressure xenon (which has an excellent CCT), the mercury vapor lamp and the daylight metal halide. Although it is well known that the mercury vapor lamp distorts reds making then look brownish, the result is due to the fact that the corresponding weight for proximity to daylight is low relative to the weight for CCT, so the program's calculated CCT of 5942K for the mercury vapor is very close to T_D=5785K. While with low wattage mercury lamps the measured CCT is closer to 7000K, with wattages in the 1000-2000W range and with super high pressure mercury lamps the CCT is lower, around 5500-6200K, so the result is generally consistent.
2. LB: The optimal choices here are the tungsten halogen and the 4000K triphosphor fluorescent, followed by the blended light mercury vapor. Indeed tungsten halogen lamps are essentially black body radiators and so are blended light lamps, while the 4000K triphosphor fluorescent and the color corrected mercury are also quite close to black bodies, with their fluorescent powders adding important emissions to the relatively barren spectrum of plain mercury, so the result is generally consistent.
3. LD: The optimal choice here is the high pressure xenon which offers the best color approximation of Daylight, followed by the American and Daylight metal halides, so the result is consistent.
4. LE: The optimal choice here is of course the source with the highest efficiency, the low and high pressure sodium lamps, followed by the American metal halide. The result is consistent.
5. LT: If one excludes the xenon flash which is not used for general lighting, the optimal choices are again mercury vapor lamps, and the American metal halide which offer the longest lifetimes.
6. LC: The optimal choice when cost in an issue is of course the tungsten halogen which is the cheapest type of lamp that gives good lighting, followed by mercury vapor lamps and blended light lamps, which are also relatively cheap, so the results are again consistent.
7. FS: The optimal choices when Full-Spectrum is an issue are the xenon flash and the tungsten halogen, followed by the high pressure xenon and the blended light lamp. Indeed, these lamps have the fullest spectra, so the results are consistent.
8. Home: The optimal choices here are the color corrected mercury vapor, the tungsten halogen and the blended light. Although color corrected mercury vapor and blended light lamps are usually not used often for indoor lighting, they are an excellent choice for such lighting. Most people use incandescent/tungsten halogen and 2700K triphosphor fluorescents in their homes. Note however that the 4000K triphosphor fluorescent scores higher than the 2700K triphosphor fluorescent. Indeed, LCD computer screens are back illuminated by such fluorescents, and given the fact that computer people with laptops spend many hours staring at their screens, the choice is not accidental. In general 4000K triphosphor fluorescents generally give a more balanced spectrum than that of the 2700K triphosphor fluorescent (see [25]), so the result is consistent.
9. Work: Excluding again the xenon flash which is not used for general illumination, the optimal choices here are the daylight metal halide followed by the 4000K triphosphor fluorescent and the tungsten halogen. These are indeed the best choices for general lighting in offices and general work-spaces where attention to detail is important.
10. Street: The optimal choices here are the low and high pressure sodium, followed by the American metal halide. These lamps are indeed used mostly for street lighting, with the latter being especially popular in the States on highways.
11. Cinema/Studio: The optimal choices here are the xenon high pressure, the daylight metal halide and the high pressure mercury, followed by the American metal halide. Indeed, these lamps are the lamps of choice for cinema projectionists, although typically mercury vapor lamps used with projectors are of much higher pressure than the ones used for general lighting. In general cost with professional projection services is not an issue, so considerable amounts of money are spent for good daylight-quality color reproduction. The corresponding equipment (which is often quite complicated) is operated by dedicated personnel.
12. Public Gatherings/Sports: The choices here are the high pressure xenon, followed by the Daylight and American metal halides. Usually when large gatherings such as election campaign gatherings and public speeches take place, professional lighting engineers use large xenon spotlights on separate poles or metal halide lamps. On the other hand, sport stadiums usually use Daylight (Europe) or American (States) metal halides.
13. Caution/Alert/Attention/Decor: The optimal choices here are naturally the low pressure sodium followed by the blue and green metal halides. Low pressure sodium lamps are usually used for caution/attention-getting purposes in tunnels, railroad crossings and on generally dangerous places because they increase visual acuity and vision becomes sharper under their light. On the other hand, blue and green metal halides are used more and more often for the decorative lighting of stores, buildings and public monuments and for special effects illumination, so the result is consistent.
14. Plant Growth: The optimal choices are the PLANTA specialized metal halide, followed by the tungsten halogen, the color corrected mercury and the blended light lamp. Although many people who grow plants think that the high pressure sodium lamp is a good choice, the above choices easily outperform it because their spectrum matches the photosynthesis curve better, so there's no need to spend a fortune for plant growing if one knows what to look for (even though the PLANTA metal halide is not that cheap). See also [25].
15. Astronomical Observatory Lighting: The top choices here are the low pressure sodium, followed by the mercury vapor lamps. This shows that these choices are indeed much better than the high pressure sodium, because their spectra contain the fewest number of lines, so they are easy to filter out by the observatory when the need arises. The 2700K triphosphor fluorescents also offer a nice alternative to high pressure sodium lamps which are responsible for most of the existent light pollution present today.
16. Diazo Replicating Process: The top choices here are the xenon flash, the two diazo lamps and the blue colored metal halide. Indeed, for diazo processes, xenon flash lamps and special blue diazo lamps are used which radiate mainly in the blue-violet region of the spectrum, so the result is consistent.
17. Photography Studio: The top choice in photography studios is of course the xenon flash tube, but when the service hours become high, occasionally other high CCT and high color quality sources are used, such as the Daylight metal halide. For cinema shots the high pressure xenon is often used, which has excellent color qualities, so the results are consistent here as well.
18. Overall: On an equal importance basis for all the factors presented above and when a compromise is desired, the result seems to favor the mercury vapor lamp, the Daylight metal halide, followed by the 4000K triphosphor fluorescent, the American metal halide and the Mercury vapor corrected lamps. This result is more or less consistent with the general trend. The best overall performer then seems to be the mercury vapor lamp. That's because it's relatively cheap, requires relatively simple support gear and has a good CCT, although as mentioned above it distorts reds. Excluding the fact that it renders some colors badly, it was the first major step towards high efficiency lighting. In fact, it couldn't have been otherwise, as the high pressure mercury discharge is of fundamental importance to all other discharges and high pressure mercury lamps were the first efficient lamps used for public and highway lighting. Mercury vapor lamps (uncorrected) are still used extensively for highway lighting and for back porch security lighting in the States because they offer good optical control in highway luminares, but in Europe they are somewhat rare. High and super high pressure mercury vapor lamps are still considered efficient competitors in high CCT applications and projection lighting (see [3]'s ME and MD pages for example). The sodium/scandium American metal halide is also a top performer because considerable research has gone into its development and so is the daylight metal halide, which is used more and more often in Europe as it was developed by OSRAM. On the other hand 4000K triphosphor fluorescents are very well balanced chromatically and with an excellent color, so they are gaining in popularity as well for small space illumination. The color corrected mercury vapor is cheap and used very often with generally good color although it does not offer very good optical control. The sodium/thallium/indium European metal halide comes next, which was originally developed for color television broadcasts, but has found its way into sports, airport, shipyard, warehouse and public lighting. Although of lower overall rating than the other two metal halides, it is slightly more popular here in Europe, competing with the Daylight metal halide. The xenon flash which is the choice of professional photographers needs no special introduction and neither does the tungsten halogen which is now produced in small wattages. The popularity of the latter is staying constant, although triphosphor fluorescents are starting to displace it somewhat (see next section). Close to tungsten halogen are blended light lamps which are also good choices whenever quick lighting improvement is required on incandescent installations. The rest of the players are either specialized application lamps or very expensive or lamps which deviate considerably from what the average human calls "normal" light, so they are employed only in specialized applications.

The above analysis uses multiple objective optimization on the seven objectives CCT, LB, LD, LE, LT, LC and FS. The researcher may conceivably consider many more objectives, such as a "security" objective which may be related to how fast the lamps reach their full output, a "power-range" objective which is related to whether the lamp is available at a given wattage, or more specialized objectives such as "aesthetic appeal", "warmth", etc. Such additional objectives will eliminate certain choices which show up with high scores anyway. In the "Cinema/Studio" or "Public Gathering/Sports" applications for example, the objective "power-range" will eliminate triphosphor fluorescents and tungsten halogen lamps, since these either don't exist in sufficiently high powers, or when they do, they are grossly uneconomical to use.

The calculations and results of the above two sections are meant to be taken somewhat liberally. For example, there is no easy way to decide what constitutes a "balanced set" of weights w(n), for the n=1..7 objectives used in the calculations, unless all the weights are equal. For example, when one uses w(i)=200 and w(j)=1, does this really mean that the user/consumer preference for objective i is 200 times "stronger" than for preference j? Not really. What the Maple program shows is that given "sufficient" leverage on the weights to skew the user/consumer preferences sufficiently, the produced results are generally consistent with the general commercial/consuming trend. The general product trend is usually set by the major lamp manufacturers (who in turn rely on lighting engineers for research) and then is passed onto the consumer via appropriate advertising. Whether the trend catches on or gets dropped depends on additional factors, price notwithstanding. To make the issue more confusing, some trends catch on even without offering significant benefits. For example, the 2700K triphosphor compact fluorescent has been marketed as a considerable economical improvement over cheap incandescent lamps. The author hasn't tested ordinary incandescent lamps, but the results above show that the 2700K compact fluorescent is a worse overall performer than tungsten halogen lamps (score 13 vs 9 for tungsten halogen), even in the Home application itself! (score 7 vs 3). A much better overall performer than tungsten halogen lamps is the 4000K compact/triphosphor fluorescent (score 4 vs 9). However the general consumer usually has no idea of the difference, particularly in view of the fact that clueless distributors interchange the two kinds without discrimination. The end result is some consumers being benefited and some being suckered in, depending on which type they accidentally buy. This tends to happen less often with more expensive and larger power lamps, but it happens in this case as well.

People also get suckered in with the notion of "Full-Spectrum" lamp. Ever since the invention of the bi and tri-component phosphors (triphosphors) used in compact fluorescent lamps, hundreds if not thousands of rogue companies usurped the label "Full-Spectrum" for their own selling agendas, without regard to its actual meaning, selling lamps which they themselves call "Full-Spectrum" but which in reality do not differ from non-"Full-Spectrum" ones (see [41]). The latter is a deliberate attempt to con the consumer. It's not easy to calculate the 'Full-Spectrum' index which has been defined in [34] and used here, and under this advanced mathematical definition very few lamps are truly 'Full-Spectrum' lamps. For example and depending what percentage one considers a "cut-off" for "Full-Spectrum", the four winners in the FS column in the above table may safely be considered "Full-Spectrum" (Actual Daylight, Xenon Flash, Tungsten Halogen and High Pressure Xenon). If one lowers the "cut-off" percentage a bit, the Blended Light lamp may also be considered "Full-Spectrum" since one of its internal components is a radiating tungsten filament which is very close to "Full-Spectrum" (see FS index in the above tables and also [25]). The research on this page proves exactly this: That optimal lamp selection is complicated business depending on dozens of factors (the most crucial ones of which are used in the analysis above), best left to professional engineers or architects. If there was such a thing as a truly "Full-Spectrum" lamp, we'd all use that and be done with. As the reader can obviously see, that's not the case. Some lamps are better performers than others. There is no single light source whose light quality outperforms all the rest in all possible lighting applications, except the sun which produces Daylight. Nature has a knack for perfection and optimality...

If you are a private consumer who has been sold a lamp which was claimed to be a good performer for some reason or another or if you are a manufacturer/reseller of a particular lamp which you think is a good performer and you want the lamp to be independently tested and rated mathematically relative to the above lamps, you can email the author for details. You can specify additional criteria or objectives for the author to test, according to your likes, provided they can be mapped to reasonable mathematical values. After the lamp is tested, you can publish the results on your company's website or use them for whatever reason you deem appropriate.

References belong to two categories: Essential theory and advanced theory/applications. Essential theory references are provided in the form of direct links embedded in the text to avoid cluttering this section. The following advanced theory/application references are not sorted in any way of importance. They were simply added in no particular order as the author was building the page. The author is grateful to V.D. Roberts ([4]) for providing reference [7], to D.L. Klipstein ([5]) for T data on discharge tubes, to J.D. Hooker ([3]) for providing reference [8], to T. McGowan ([36]) for providing references [34], [35], [38] and [39] and to M. Rea for providing reference [37].

1. J. Walker, "Color Rendering of Spectra". (online)
2. B. Lindbloom, "XYZ to Correlated Color Temperature". (online)
3. J.D. Hooker "Museum of Historic Discharge Lamps". (online)
4. Roberts Research & Consulting, Inc. (online)
5. D.L. Klipstein "Don's Light, Lamp and Strobe Site!" (online)
6. National Institute of Standards and Technology (NIST), Atomic Spectra Database. (online)
7. W. Elenbaas, "The High Pressure Mercury Vapour Discharge", North-Holland, Amsterdam, 1951, p. 111-129. (online)
8. G. Wyszecki and W. S. Stiles, "Color Science: Concepts and Methods, Quantitative Data and Formulae", Second Edition, John Wiley & Sons, 1982, p. 225-228. (online)
9. J.G. Frayne and C. G. Montgomery, "Variations in the Intensities of Mercury Spectrum Lines with Pressure of the Vapor", Physical Review, Volume 33, April 1929.
10. G. Hoffmann, "Correlated Color Temperature". (online, online 2)
11. G. Hoffmann, "CIE Color Space". (online)
12. E.F. Glynn, "Chromaticity Diagrams". (online)
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