The Science of Color, the Emission Spectra of the Elements and Some Lamp Engineering Applications

Version 1.8.3 of 10/12/2008-4:00 a.m.


  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. Lamp Chromaticity Table
  18. Optimal Lamp Selection
  19. Data Analysis
  20. Conclusions
  21. "Full-Spectrum" Lamps
  22. Lamp Testing
  23. References

Abstract

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.


Introduction

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.jpg
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.


The Mathematics of Color

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:

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

The CCT algorithm was based on [2] and [10]. The author chose the CIEsystem in [1] with a =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.


Visualization of Spectra

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,G,B) being the color at wavelength . 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 (,f()), where is the wavelength and f() 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
HPM2.jpg
scalevis.jpg
HPM.jpg

The Black Body Spectrum

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
bb1000K.jpg bb1000K.jpg
2000 x=0.52592
y=0.41383
CCT:2009
bb2000K.jpg bb2000K.jpg
3000
(tungsten halogen lamp)
x=0.43644
y=0.40430
CCT:3010
bb3000K.jpg bb3000K.jpg
4000 x=0.37988
y=0.37681
CCT:4016
bb4000K.jpg bb4000K.jpg
5000 x=0.34416
y=0.35137
CCT:5035
bb5000K.jpg bb5000K.jpg
6000 x=0.32054
y=0.33099
CCT:6079
bb6000K.jpg bb6000K.jpg
7000 x=0.26011
y=0.32647
CCT:7165
bb7000K.jpg bb7000K.jpg
8000 x=0.29214
y=0.30243
CCT:8308
bb8000K.jpg bb8000K.jpg
9000 x=0.28310
y=0.29233
CCT:9521
bb9000K.jpg bb9000K.jpg
10000 x=0.27607
y=0.28410
CCT:10824
bb10000K.jpg bb10000K.jpg
x=0.076966
y=0.23344
CCT:N/A
bbINF.jpg bbINF.jpg

The Solar Spectrum

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
D.jpg D.jpg

The Planckian Locus

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.

PlanckianCIE.jpg
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.


Emission Spectra of the Elements

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

Element Emission Colors

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

H.jpg He.jpg
Li.jpg Be.jpg B C.jpg N.jpg O.jpg F.jpg Ne.jpg
Na.jpg Mg.jpg Al.jpg Si.jpg P.jpg S.jpg Cl.jpg Ar.jpg
K.jpg Ca.jpg Sc.jpg Ti.jpg V.jpg Cr.jpg Mn.jpg Fe.jpg Co.jpg Ni.jpg Cu.jpg Zn.jpg Ga.jpg Ge.jpg As.jpg Se.jpg Br.jpg Kr.jpg
Rb.jpg Sr.jpg Y.jpg Zr.jpg Nb.jpg Mo.jpg Tc.jpg Ru.jpg Rh.jpg Pd.jpg Ag.jpg Cd.jpg In.jpg Sn.jpg Sb.jpg Te.jpg I.jpg Xe.jpg
Cs.jpg Ba.jpg * Hf.jpg Ta.jpg W.jpg Re.jpg Os.jpg Ir.jpg Pt.jpg Au.jpg Hg.jpg Tl.jpg Pb.jpg Bi.jpg Po.jpg At Rn.jpg
Fr Ra.jpg ** Rf etc.
* La.jpg Ce.jpg Pr.jpg Nd.jpg Pm.jpg Sm.jpg Eu.jpg Gd.jpg Tb.jpg Ty.jpg Ho.jpg Er.jpg Tm.jpg Yb.jpg Lu.jpg
** Ac.jpg Th.jpg Pa.jpg U.jpg Np.jpg Pu.jpg Am.jpg Cm.jpg Bk.jpg Cf.jpg Es.jpg Fm Md No Lr

Possible NIST Inaccuracies

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 and 2 above appear contradictory. In 1 [6] says: "...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..." while in 2 it says: "...most relative intensities are not corrected for spectral sensitivity of the measuring instruments (spectrometers, photomultipliers, photographic emulsions)...". The two cannot be true simultaneously, so to be on the safe side the author later assumes that the relative intensities of lines in distributions coming from a single citation are likely accurate. On the other hand, source [5] reports for some of [6]'s distributions:
  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.


Lamp Engineering

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.

elementsCIE.jpg
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 (40C).
  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.

The Mercury Discharge

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:

HgUVIR.jpg
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
Hg.jpg HgUV.jpg
High Pressure x=0.31996
y=0.38645
CCT:5942
HPM.jpg HgHPUV.jpg

Phosphors for Mercury

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, Fluorescence>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
HgLP.jpg HgLP.jpg
Triphosphor Fluorescent
2700K
x=0.46632
y=0.42547
CCT:2724
CFL27K.jpg CFL27K.jpg
Triphosphor Fluorescent
4000K
x=0.37820
y=0.37264
CCT:4031
CFL4K.jpg CFL4K.jpg
Clear
Mercury Vapor
x=0.31996
y=0.38645
CCT:5942
HgHP.jpg HgHP.jpg
Color Corrected
Mercury Vapor
x=0.40288
y=0.39424
CCT:3582
HgHPFL.jpg HgHPFL.jpg
Blended Light x=0.41436
y=0.39733
CCT:3362
BL.jpg BL.jpg

The Metal Halide Discharge

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 700C. 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
MHE.jpg MHE.jpg
Sodium/Scandium
metal halide
(American)
x=0.35185
y=0.32282
CCT:4575
MHA.jpg MHA.jpg
Dysprosium/Thallium
/Thulium/Caesium
"daylight"
(European)
metal halide
x=0.30179
y=0.35347
CCT:6855
MHD.jpg MHD.jpg
Plant growing
metal halide
x=0.36054
y=0.27794
CCT:3629
Planta.jpg Planta.jpg
Blue colored
metal halide
x=0.21958
y=0.15021
CCT:N/A
Blau.jpg Blau.jpg
Green colored
metal halide
x=0.26600
y=0.57411
CCT:6748
Grun.jpg Grun.jpg
Iron/Cobalt diazo
metal halide
x=0.29973
y=0.28898
CCT:8051
DIAZ1.jpg DIAZ1.jpg
Lead/Gallium diazo
metal halide
x=0.2953
y=0.27545
CCT:9022
DIAZ2.jpg DIAZ2.jpg

The Sodium Discharge

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 265C 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 700C. However the temperature of the hottest spot on the discharge tube can reach temperatures of 1200C. 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
NaLP.jpg NaLP.jpg
High Pressure
(source [19])
x=0.50257
y=0.39664
CCT:2104
HPS.jpg HPS.jpg

The Xenon Discharge

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
XeLP.jpg XeLP.jpg
Medium pressure
High voltage
Low amperage
(Xe I-V, Flash tube)
x=0.28998
y=0.28435
CCT:9185
FLASH.jpg FLASH.jpg
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
HPX.jpg HPX.jpg

Lamp Chromaticity Table

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

lampsCIE.jpg
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=CCTL. 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:

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

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:

PCCT=100*(1-|CCT-TD|/(CCTmax-TD)) PLB=100*(1-LB/LBmax) PLD=100*(1-LD/LDmax)
PLE=100*LE/LEmax PLT=100*LT/LTmax PLC=100*(1-LC/LCmax)

Accordingly then, PCCT is the proximity of the lamp/light's calculated CCT relative to TD=5785K, PLB is the proximity of the lamp/light to a Black Body of T=CCT relative to LBmin, PLD is the proximity of the lamp/light to D relative to LDmin, PLE is the lamp/light efficiency relative to LEmax, PLT is the lamp/light lifetime relative to LTmax, PLC is the lamp/light cost relative to LCmin and PFS 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 PLB 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:

Key Light CCT (K) PCCT(1) PLB PLD LE (lm/W)(2) PLE LT (kh)(3) PLT(4) LC (/100W)(5) PLC(6) PFS(7)
TH Tungsten Halogen 3310 41.3 99.7 57.4 24 13.3 2 2.2 15 96.2 81.2
D Daylight 5822 99.1 99.3 100 98 54.4 100 0 100 99.4
CFL27K Triphos. Fluor. 2700K 2724 27.3 +93.2 35 65 36.1 12 13.6 80 80 35
CFL4K Triphos. Fluor. 4000K 4031 58.3 98.7 74.9 75 41.6 12 13.6 80 80 63.4
HPM Mercury Vapor 5942 96.2 +78.9 79.9 52 28.8 24 27.3 25 93.7 49
HPMC Mercury Vapor Corrected 3582 47.7 +97.5 62.2 58 32.2 24 27.3 25 93.7 58.2
BL Blended Light 3362 40.8 +99.1 56.3 18 10 6 6.8 18 95.5 71.1
MHE European Metal Halide 4366 66.3 +82.9 65.3 78 43.3 18 20.5 120 70 51.1
MHA American Metal Halide 4575 71.2 -84.8 88.7 85 47.2 20 22.8 120 70 42.6
MHD Daylight Metal Halide 6855 74.6 +85.8 88.3 74 41.1 10 11.4 120 70 62.8
PLANT Plant Metal Halide 3629 48.8 -55.3 73.9 62 34.4 4 4.5 130 67.5 66.5
BLAU Blue Metal Halide ∞+ 0 41.1 17.2 20 11.1 2 2.2 130 67.5 8.8
GRUN Green Metal Halide 6748 77.1 0 4.4 88 48.8 6 6.8 130 67.5 0
DIAZ1 Diazo 1 Metal Halide 8051 46.2 -94.1 79.4 25 13.8 0.6 0.6 140 65 10.8
DIAZ2 Diazo 2 Metal Halide 8377 38.5 -79.4 66.3 23 12.7 1 1.1 140 65 0
LPS Low Pressure Sodium 1784 5 +90.6 0 180 100 12 13.7 100 75 0
HPS High Pressure Sodium 2104 12.6 -91.4 27.2 100 55.5 22 25.1 140 65 4.6
FLASH Xenon Flash 9050 22.5 -95.8 76.3 25 13.8 50 57 200 50 94.6
HPX High Pressure Xenon 6225 89.5 -93.6 90.3 40 22.2 2 2.2 400 0 75.5

(1): with CCTmax=10000K assigned to BLAU.
(2): does not include support gear power losses.
(3): To 50% survival.
(4): relative to LTmax=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.


Optimal Lamp Selection

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 Fn(m) associated with each item m and each objective n, and looks at the consumer/user/application preferences. These preferences correspond to n weights wn which assign each objective n an "importance" factor. Then the researcher, for each item m tries to maximize S(m)=∑k=1..nwk*Fk(m). It is immediately obvious that while each Fn(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 wn. In general Fn(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≤Fn(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 wn and look at the ratios S(m)/Smax. 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:

L/A CCT LB LD LE LT LC FS
TH 43.9 (12) 95.6 (2) 57.6 (13) 20.1 (15) 12.9 (14) 92 (2) 79.1 (3)
D 100 (1) 100 (1) 100 (1) 64 (2) 99.9 (1) 100 (1) 99.9 (1)
CFL27K 30.1 (15) 88.6 (9) 36.7 (15) 40.3 (9) 20.2 (10) 76.4 (7) 36.9 (13)
CFL4K 59.7 (8) 95.4 (3) 73.8 (8) 47.6 (7) 23.3 (8) 78.3 (6) 64.1 (7)
HPM 93.8 (2) 78.2 (15) 78.7 (5) 36.1 (12) 35.2 (3) 91 (4) 51.8 (11)
HPMC 50.1 (9) 94.2 (5) 62.5 (12) 38.6 (11) 34.1 (4) 90.2 (5) 59.2 (9)
BL 43.2 (13) 94.9 (4) 56.6 (14) 16.8 (18) 16.3 (12) 91.1 (3) 69.9 (5)
MHE 66.3 (7) 81 (14) 64.8 (10) 48.6 (6) 28 (7) 69 (11) 52.5 (10)
MHA 71.2 (6) 83.1 (13) 85.9 (3) 52.9 (4) 30.7 (5) 69.5 (9) 45.4 (12)
MHD 74.2 (4) 84 (12) 85.7 (4) 47.3 (8) 21.5 (9) 69.5 (9) 63.6 (8)
PLANT 49.7 (10) 55.6 (17) 71.7 (9) 39.3 (10) 13.6 (13) 65.9 (12) 65.4 (6)
BLAU 2.69 (19) 39.3 (18) 17.9 (17) 13.4 (19) 6.02 (19) 62.3 (16) 10.5 (15)
GRUN 72.4 (5) 3.71 (19) 7.58 (18) 50.2 (5) 11.3 (16) 63.2 (13) 3.71 (19)
DIAZ1 46.8 (11) 89.1 (8) 75.6 (6) 19.1 (16) 9.29 (17) 63 (14) 15.2 (14)
DIAZ2 39 (14) 75.2 (16) 63.4 (11) 17.1 (17) 8.33 (18) 62.1 (17) 4.76 (18)
LPS 9.67 (18) 85.5 (11) 5.11 (19) 99.9 (1) 19.2 (11) 71.3 (8) 5.14 (17)
HPS 16.4 (17) 86.2 (10) 29.2 (16) 57.9 (3) 28.4 (6) 62.5 (15) 9.18 (16)
FLASH 27.4 (16) 92.5 (6) 74.7 (7) 21 (14) 58.3 (2) 51.5 (18) 91.4 (2)
HPX 86.4 (3) 89.8 (7) 86.5 (2) 28.2 (13) 12.4 (15) 6.74 (19) 73.7 (4)

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:

L/A Home Work Street Cinema Public Alert Growth Astro Diazo Photo Overall
TH 81.7 (3) 72 (5) 40 (14) 60 (10) 70.5 (9) -75.1 (11) 76.2 (3) 74.6 (8) -33.9 (13) 69.8 (6) 59.9 (9)
D 100 (1) 99.6 (1) 99.9 (1) 100 (1) 99.9 (1) -112 (17) 99.9 (1) 93.5 (2) -99.5 (17) 100 (1) 99.9 (1)
CFL27K 73 (7) 52.4 (14) 53.8 (11) 34.1 (15) 49.8 (15) -19 (5) 51.8 (13) 78.4 (5) -27.6 (11) 35.2 (14) 49.1 (13)
CFL4K 79.9 (6) 73.5 (4) 60.6 (5) 68.4 (6) 78.4 (6) -72.4 (9) 67.3 (6) 66 (11) -17.7 (8) 69 (7) 66.1 (4)
HPM 80.3 (5) 71 (6) 58.9 (8) 76.6 (4) 77.1 (7) -121 (18) 59 (10) 79.6 (4) -123 (18) 64.2 (9) 69.6 (2)
HPMC 83.1 (2) 70.4 (7) 60.2 (7) 58.3 (11) 70 (10) -62.9 (6) 69.3 (4) 84.9 (3) -20.3 (9) 60.2 (11) 64.2 (6)
BL 81.3 (4) 69.4 (9) 38.5 (15) 56.8 (12) 68.4 (11) -77.4 (12) 68 (5) 76.5 (7) -28.2 (12) 64 (10) 58.3 (10)
MHE 71 (10) 63.7 (11) 60.3 (6) 62.5 (9) 68.2 (12) -67.9 (7) 56.9 (11) 60.6 (12) -68.6 (15) 58.1 (12) 61.3 (8)
MHA 72.8 (8) 70.4 (7) 65.4 (4) 73.3 (5) 80.2 (4) -87.4 (14) 54.6 (12) 60.6 (12) 6.86 (7) 64.8 (8) 65.6 (5)
MHD 72.6 (9) 73.9 (3) 57.8 (9) 78.8 (3) 83.4 (3) -96.8 (15) 63 (8) 52.4 (16) -23.3 (10) 75.2 (4) 66.5 (3)
PLANT 53.9 (17) 62.6 (12) 49.4 (12) 65.8 (8) 66.1 (13) -67.9 (7) 76.3 (2) 50.9 (17) 35.3 (4) 70 (5) 53.8 (12)
BLAU 39.9 (18) 26.4 (18) 27.9 (18) 11.3 (18) 21.2 (18) -5.07 (3) 39.5 (15) 69 (10) 46 (4) 12.8 (17) 22.7 (19)
GRUN 30.8 (19) 14.9 (19) 56 (10) 21.4 (16) 8.71 (19) -13.2 (4) 47.3 (14) 73.8 (9) -270 (19) 2.92 (18) 31.4 (18)
DIAZ1 69.4 (11) 58.1 (13) 33.1 (16) 54.6 (13) 71.6 (8) -96.8 (16) 17.2 (17) 53.9 (15) 84.8 (2) 43.7 (13) 47.5 (14)
DIAZ2 61.6 (15) 48.4 (15) 31.5 (17) 43.4 (14) 58.7 (14) -79.6 (13) 15.7 (18) 58.5 (14) 78 (3) 31.8 (15) 40.3 (17)
LPS 68.1 (13) 34.2 (17) 96.8 (2) 2.61 (19) 24.6 (17) 100 (1) 60.9 (9) 100 (1) -46.4 (14) 0.3 (19) 43.5 (15)
HPS 66.9 (14) 42 (16) 66.5 (3) 19 (17) 40.1 (16) 21.4 (2) 36.5 (16) 78 (6) 22.5 (6) 15.6 (16) 43.2 (16)
FLASH 69.3 (12) 77.3 (2) 44 (13) 68.1 (7) 79.7 (5) -74 (10) 64 (7) 35 (18) 99.9 (1) 85.6 (2) 62.9 (7)
HPX 56.2 (16) 67 (10) 23.3 (19) 86.6 (2) 88.9 (2) -133 (19) 11.9 (19) -31.4 (19) -88.2 (16) 82.7 (3) 57.3 (11)


Data Analysis

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:

L D HPMC TH BL HPM CFL4K CFL27K MHA MHD MHE DIAZ1 FLASH LPS HPS DIAZ2 HPX PLANT BLAU GRUN
S(D)-S(L) 0 16.9 18.3 18.7 19.7 20.1 27 27.2 27.4 29 30.6 30.7 31.9 33.1 38.4 43.8 46.1 60.1 69.2
[S(D)-S(L)]/
[S(D)-S(HPMC)]
0 1 1.08 1.11 1.17 1.19 1.6 1.61 1.62 1.72 1.81 1.82 1.89 1.96 2.27 2.59 2.73 3.56 4.09

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:

Home
D
HPMC, TH
BL, HPM, CFL4K
CFL27K, MHA, MHD
MHE
DIAZ1, FLASH, LPS
HPS
DIAZ2
HPX
PLANT
BLAU
GRUN

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 TD=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.


Conclusions

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.


"Full-Spectrum" Lamps

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...


Lamp Testing

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 and Technical Literature

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 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.
  8. G. Wyszecki and W. S. Stiles, "Color Science: Concepts and Methods, Quantitative Data and Formulae", Second Edition, John Wiley & Sons, 1982.
  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)
  11. G. Hoffmann, "CIE Color Space". (online)
  12. E.F. Glynn, "Chromaticity Diagrams". (online)
  13. Wikipedia, "The Periodic Table of Elements". (online)
  14. Wikipedia, "Abundances of the elements (data page)". (online)
  15. PHILIPS "Lamp Catalog", 1985. (online)
  16. RADIUM Die Lichtmarke, "Lamp Catalog", 1999. (online)
  17. OSRAM "Outdoor and Indoor Lighting Catalog". (online)
  18. SYLVANIA's Light Sources: Product Information/Engineering Bulletins, 1985. (online)
  19. NORTH AMERICAN PHILIPS CORPORATION, "Guide To High Intensity Discharge Lamps", 1983.
  20. Linos (formerly Spindler & Hoyer), "Optics Catalog", 1999. (online)
  21. C.J. Smith, "A Degree Physics Part III: Optics", Indian Edition 1985, Radha Publishing House.
  22. K.D. Alexopoulos, "General Physics: Optics", 1st Edition, Athens 1966 (in Greek).
  23. D. Eythymiatos, "Technical Constructions: Light And Sound", 2nd Edition, Athens 1985 (in Greek).
  24. G. Bruhat, "Cours De Physique Generale: Optique", Sixieme Edition, Paris 1965 (in French).
  25. This author, "The Double Amici Prism Hand-Held Spectroscope in Practice", 2007. (online)
  26. ADVANCE, "Ballasts for High Intensity Discharge Lamps, H.I.D. Buyer's Guide" No. 6, 1990. (online)
  27. Wikipedia, "Phosphors for Fluorescent Lamps". (online)
  28. GE Lighting, "Specifying Lamp Color". (online)
  29. M. Kofferlein, T. Dohring, Hans D. Payer and H.K. Seidlitz, "Xenon Lighting Adjusted to Plant Requirements". (online)
  30. M.F. Gendre "History, Science and Technology of Light Sources". (online)
  31. "CVRL Color & Vision Research Laboratories" database. (online)
  32. J. Urbas and W. J. Parker, "Surface Temperature Measurements on Burning Wood Specimens in the Cone Calorimeter and the Effect of Grain Orientation", Fire and Materials, Vol. 17, No. 5, 205-208, Sep./Oct. 1993 (online)
  33. H.C. Becker, Assistant Professor of Physical Chemistry at Uppsala University (online)
  34. M. Rea, L. Deng and R. Wolsey, "Full-Spectrum Light Sources". (online)
  35. Rensselaer Polytechnic Institute, "Appendix B: Calculating color rendering metrics". (online)
  36. Lighting Ideas, Inc., Cleveland, Ohio USA. (T. McGowan, FIES, LC)
  37. M. Rea, L. Deng and R. Wolsey, "Light Sources and Color". (online)
  38. J.A. Veitch et al, "Full-Spectrum Lighting". (online)
  39. J.A. Veitch (editor), "Full-Spectrum Lighting Effects on Performance, Mood, and Health". Internal Report, Institute for Research in Construction, (IRC-IR-659) June 1994, 659 pp. (online)
  40. N. Cutic, "Visualization of Element Spectra". (online)
  41. Wikipedia, "Full-Spectrum Light". (online)
  42. This author, "From Mathematics To Color Perception". (online)
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