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MINIMUM DETECTION LIMITS (MDL)


             One can readily enough detect any spectral line or band that is approximately as high in the spectrum as the noise level. The RIAS technique used with QASoft can actually detect lines or bands that are below the noise level. For making a conservative tabulation, however, we assume that bands at their detection limit are as high as the noise. Detectability is increased in direct response to reduction of the noise. The noise level is a function of the source intensity, the number of scans, the spectral resolution, the types of optical filters used, the stability of the optical components, and especially the quality of the detector itself. 20 years ago, in an FT-IR experiment at a folded path of several hundred meters, a signal-to-noise ratio of 2,000 was obtained. (Hanst, et al., 1973). With present day equipment and a 100 meter White cell a signal-to-noise ratio of 10,000 is readily obtained.


            There are two ways to lower the detection limit for a given compound: (1) lower the noise level in the spectrum, and (2) increase the size of the absorption features.


            The noise level is made lower by choosing a low noise detector and by bringing to that detector a maximum number of photons, while avoiding detector saturation. The best available detectors today are the photoconductors that operate at liquid nitrogen temperature, like mercury-cadmium-telluride. These detectors usually produce a noise level in the spectrum that is about 100 times lower than the noise level produced by detectors that operate at room temperature. The rate at which photons are delivered to the detector is kept high by having a bright source, an efficient Fourier transform spectrometer and an optical system that conserves the energy. In designing systems for air analysis, this energy conservation factor is sometimes not given enough emphasis.

 

    An additional way to lower the noise level in the spectrum is to use longer measurement times and co-add more interferometer scans. It is difficult to make up for lost photons in this way, however, because the lowering of the noise level is not proportional to the extension of the time. The lowering is only proportional to the square root of the time extension. If for some reason the rate of delivery of photons to the detector is reduced by a factor of 10, the noise level in the spectrum will go up by a factor of 10. If one sought to restore the lower noise level by extending the measurement time, a 100-fold extension would be required, changing a 10 minute measuring time to 17 hours.


            For maximum spectral detail and maximum line heights the spectrometer should fully resolve the spectral lines. When working at one atmosphere total pressure a resolving power of 0.125 cm-1 is a high as one need go because pressure-broadened line widths are about 0.2 cm-1 (full width, half way up the line). For most instruments, however, going to higher resolution increases the noise in the spectrum at a faster rate than it increases the height of the lines. A compromise in the matter of resolution is required. A value of 0.5 cm-1 seems a good choice.


            The main way to increase the size of the spectral features is to lengthen the optical path. The principal limitation on path lengthening is that it should not waste the available photons. There is also an additional problem that when the path gets longer than about 100 meters, absorption by water vapor and carbon dioxide precludes the use of three important bands of air pollutants: the NO2 band near 1600 cm-1, the SO2 band near 1360 cm-1, and the benzene band at 674 cm-1. The importance of these three bands makes it worthwhile to keep the total path at 100 meters or less.


            When the optical path is at 100 meters, the resolution is at 0.5 cm -1, and the spectrum noise level is at 10-4 absorbance units, nearly every important gas can be measured at parts-per-billion levels. Minimum detection limits under these conditions were calculated from our atlas of spectra, and are listed in Table 1.    An important condition for validity of Table 1 is that the water and carbon dioxide lines must be subtracted from the spectrum without introducing noise. In the past this condition was almost impossible to meet, but now it can be met. The modern software has made it possible to match the line positions and line widths of two spectra with a high degree of precision. The software also has made it possible to create reference spectra that show deviations from the absorbance law that are the same as the deviations in the sample spectrum.


            The table of minimum detection limits (MDL's) shows that under the conditions discussed, most compounds are detectable down to the parts-per billion level. Some compounds have MDL'S much below one part-per-billion. Note the extemely low numbers for CF4 and SF6.


            Some of the strongest bands of the compounds have not been used in preparing the table because of interferences from water or carbon dioxide. All the carbonyl bands in the region 1800 to 1700 cm-1 have been left out, for example, because of water vapor interference.


            In the table a narrow and intense spectral feature has been designated "spike". These features occur in the majority of the spectra and they are the main reason for the specificity and sensitivity of the infrared method of measurement. It is the families of spikes and families of lines that give us confidence that a spectrum can be identified and measured when the maximum absorbance is equal to the peak-to-peak noise level.


            It is found that the MDL's in the table are similar to those published 20 years ago by Hanst, et al. (1973). The eason for this is that the calculations then and now were based on similar experimental results obtained with an FT-IR spectrometer system, mercury-cadmium-telluride detector and multiple-pass cell. The main difference between then and now is that formerly we could not properly subtract the interferences but now we can.


            The MDL's in our table are some 10 to 100 times lower than the MDL's recently published by Grant, Kagann and McClenny (1992) for an FT-IR system working over an open-air doubled long path totaling 400 meters. The main source of the differences is the two different spectrum noise levels--1.3 x 10-3 absorbance units for Grant, et al., and 1 x 10-4 absorbance units for us. The reason for the two different noise estimates it that they were derived from experience with two radically different optical systems. The simple fact is that our measurement system with the multiple-pass cell is a high throughput (low noise) system while their measurement system with the long path retro-reflector technique is a low throughput (high noise) system.


            An additional advantage for us it that we calculate for only a 100 meter path in air. This lets us consider some important absorption bands that are not accessed in a 400 meter path. This includes strong bands of NO2, SO2 and benzene. Finally, we have said that we can recognize a line or band when its height is equal to the peak-to-peak noise level in the spectrum, while they assumed their detectable band height to be 3.3 times greater than the noise.


            Measurements made with the RIAS technique have confirmed many of the detection limits in the table and have even shown that some can be surpassed. These measurements were done by combining the database spectra, appropriately reduced, with noise spectra and then running RIAS.



TABLE 1. MINIMUM DETECTION LIMITS WHEN MEASURING IMPURITIES IN AIR, for compounds in the Infrared Analysis, Inc. atlas of digitized quantitative reference spectra.


M.D.L. is the Minimum Detection Limit in parts-per-billion (10-9 atmospheres), when resolution is 0.5 cm-1, optical path is 100 meters and spectrum noise level is at 10-4 absorbance units (logarithm, base 10).


                                                      Frequency               M.D.L.

  Compound                                     (cm -1)                   (PPB)                       Remarks


Acetaldehyde                                2900-2600               6.0                          Broad band with some fine structure;

                                                                                                                        structure; open region.

Acetic acid                                     642                       1.0                          Spike.

Acetone                                          1218                      4.0                          Broad band with some                                                                                                                         structure.

Aceto nitrile                                  1080-1010               30.0                         Array of lines.

Acetyl chloride                              1130-1090               1.0                          Band with spikes.

Acetylene                                       739                       0.15                        Spike.

Acrolein                                         959                       5.0                          Spike.

Acrylic acid                                    640                       0.5                          Spike.

Acrylo nitrile                                  954                       3.0                          Spike.

Ammonia                                       970-920                  1.0                          Two bundles of lines.

Analine                                           782                       10.0                         Spike.

Arsine                                             2126                      2.0                          Spike.

Benzene                                          674                       0.6                          Sharp line; CO 2 must

                                                                                                                        be subtracted.

Boron trichloride                            970-940                  0.2                          Strong band.

Bromoform                                    1150                      2.0                          Smooth band.

Bromo methane                             1030-900                 15.0                         Array of lines.

1,3 Butadiene                                 908                       1.0                          Spike.

Butane                                            2968                      1.5                          C-H band; has a spike.

2-Butanone                                     1171                      3.0                          Band about 40 cm -1 wide.

Carbon dioxide                               2363                      0.4                          M.D.L. is 0.4 PPB if no

                                                                                                                        other CO 2 is present.

                                                                                                                         In air, the minimum

                                                                                                                        detectable change in CO 2

                                                                                                                        would be about 50 PPB.

Carbon monoxide                          2200-2100               2.0                          Array of lines.

Carbon tetra-chloride                     800-790                  0.2                          Very strong band.

Carbonyl sulfide                            2080-2030               0.3                          Broad band.

Chloro benzene                              741                       0.8                          Spike.

Chloro difluoro                              809                       0.5                          Spike.

methane

Chloro ethane                                 995-950                  9.0                          Band with P-Q-R structure.

Chloroform                                    780-760                  0.5                          Wide band, but strong.

Chloro methane                              732                       5.0                          Spike.

Chloro trifluoro                              1107                      0.7                          Spike.

methane

Crotonaldehyde                             2900-2600               10.0                         Broad bands in unique                                                                                                                         position.

Cyclo hexane                                  2934                      0.5                          Spike in C-H band.

Cyclo hexene                                  2936                      1.0                          Spike in C-H band; also

                                                                                                                        spikes in region 1160                                                                                                                         to 650.

Cyclo pentene                                698                       1.2                          Spike.

Cyclo propane                                3101                      1.0                          Sharp spike in C-H band.

1,2 Dibromo ethane                       1195-1180               2.5                          Band with characteristic                                                                                                                         shape.

m-Dichloro benzene                       800-770                  1.5                          Band with spike.

o-Dichloro benzene                        749                       1.5                          Spike.

p-Dichloro benzene                        820                       1.5                          Spike.

Dichloro difluoro                           1161                      0.2                          Strong spike.

methane

1,1 Dichloro ethane                        1060                      3.0                          Spike.

1,2 Dichloro ethane                        740-710                  2.0                          Broad band.

cis-1,2 Dichloro ethylene               696                       0.6                          Spike.

Dichloro methane                           770-740                  1.3                          Band with some structure.

1,2 Dichloro                              1250-800                 0.7                          Group of strong bands.

tetrafluoro ethane

Diethyl amine                                1130-1160               3.0                          Broad band.

Diethyl ether                                 1150-1120               1.0                          Smooth band.

Di-isopropyl ether                         1400-1000               2.0                          Group of bands.

Dimethyl ether                               1179                      2.5                          Band with P-Q-R structure.

1,1 Dimethyl hydrazine                 2814, 2775              4.0                          Spikes.

Dimethyl sulfide                           2980-2900               8.0                          Structure in C-H band.

Dinitrogen                                      1240, 740               1.0                          Two strong bands.

pentoxide

Ethane                                           3050-2880               1.5                          Structure in C-H band.

Ethanol                                          1090-1020               4.0                          Broad band with some structure.

Ethyl acetate                                  1270-1225               0.5                          Broad band.

Ethyl acrylate                                1210-1180               0.5                          Broad band.

Ethyl benzene                                 698                        4.0                          Spike.

Ethyl formate                                1210-1150               0.5                          Broad band with some structure

Ethylene                                         950                        1.0                          Spike.

Ethylene oxide                               3066                       0.5                          Spike.

Ethyl vinyl ether                            1230-1200               2.0                          Wide band with some structure.

Fluoro benzene                               754                        0.5                          Spike.

Formaldehyde                               2711, 2779              3.0                          Two sharp spikes.

Formic acid                                    1105                       0.8                          Spike.

Furan                                              744                        0.2                          Spike.

n-Hexane                                        2970                       1.0                          C-H band not specific; total

                                                                                                                        hydrocarbon is often quoted

                                                                                                                        in hexane equivalents.

Hydrazine                                      1000-890                 4.0                          Band with complex fine structure

Hydrogen bromide                        2700-2400               8.0                          Array of lines.

Hydrogen chloride                        3050-2700               1.5                          Array of lines.

Hydrogen cyanide                          712                        0.4                          Q branch.

Hydrogen fluoride                         4200-3700               1.0                          Array of lines.

Hydrogen sulfide                           1300-1200               400                         Many lines, but extremely weak.

Isobutane                                        2967                       1.0                          Spike in C-H band.

Isobutanol                                     1060-1030               3.0                          Broad band.

Isobutylene                                     890                        1.5                          Spike.

Isoprene                                          900                        1.5                          Two distinctive spikes near 900.

Isopropanol                                   1420-900                 7.0                          Group of bands.

Mesitylene                                      836                        3.0                          Spike.

Methane                                         3018                       2.0                          Spike and fine structure                                                                                                                         in C-H band.

Methanol                                        1033                       1.5                          Spike.

Methyl acetate                               1265-1230               1.0                          Broad band with some                                                                                                                         structure.

Methyl acrylate                             1220-1180               1.0                          Broad band with some                                                                                                                         structure.

Methyl amine                                 820-720                  2.5                          Band with structure.

2-Methyl-2-butene                         2969                       5.0                          C-H band not specific; use spike

                                                                                                                        at 890 for identification.

3-Methyl-1-butene                         2970                       2.0                          C-H band not specific; use spike

                                                                                                                         at 913 for identification.

Methyl formate                              1210                       1.5                          Spike.

Methyl methacrylate                     1215-1150               1.2                          Two-hump broad band.

Methyl nitrite                                 860-790                  2.0                          Band with structure.

2-Methyl pentane                           2967                      1.0                          C-H band not specific.

3-Methyl pentane                           2967                      1.0                          C-H band not specific.

2-Methyl-1-pentene                       2970                      2.5                          C-H band not specific; use feature

                                                                                                                        at 892 for identification.

2-Methyl-2-pentene                       2973                      2.0                          C-H band not specific.

4-Methyl-2-pentene                       2967                      1.5                          C-H band not specific; use feature

                                                                                                                        at 721 for identification.

Methyl vinyl ether                         1400-800                 1.0                          Five different spikes.

Methyl vinyl ketone                       744                        8.0                          Spike.

Nitric acid                                      896, 879                 2.0                          Spikes.

Nitric oxide                                   1920-1870               4.0                          Array of lines.

Nitro benzene                                 701                        1.0                          Spike.

Nitro ethane                                   900-850                  10.0                         Band with P-Q-R shape.

Nitro methane                                656                        3.0                          Spike.

Nitrogen dioxide                            1600                       2.0                          Several bundles of lines.

Nitrous acid                                    852, 790                 0.5                          Q branches.

Nitrous oxide                                 2210                       1.0                          Array of lines.

Ozone                                             1054                       2.0                          Band with structure.

n-Pentane                                       2966                       1.5                          Difficult to distinguish

                                                                                                                        from other large alkanes.

1-Pentene                                       2968                       2.0                          C-H band strongest but

                                                                                                                        not specific; use feature

                                                                                                                         at 915 for identification

2-Pentene                                       2970                       2.0                          C-H band strongest but

                                                                                                                        not specific; use feature

                                                                                                                        at 961 for identification

Phosgene                                        864-830                  0.3                          Strong band with structure.

Phosphine                                       992                        10.0                         Spike.

Phosphorus                                     515-495                  3.5                          Smooth band.

trichloride

Propane                                          2968                       1.0                          Spike in C-H band.

Propionaldehyde                           2850-2650               8.0                          Broad bands in the open.

Propionic acid                                1144                       2.0                          Band 30 cm -1 wide.

Propylene                                       913                        2.0                          Spike.

Propylene oxide                             3050                       3.0                          Spike.

Styrene                                           695                        2.0                          Spike.

Sulfur dioxide                                1361                       2.0                          Spike; water must be

                                                                                                                        carefully subtracted.

Sulfur hexafluoride                        950-940                  0.04                        Extremely strong band.

1,1,1,2 Tetrachloro ethane             980-700                  1.3                          Group of bands.

Tetrachloro ethylene                      930-900                  0.7                          Smooth band.

Tetrafluoro methane                       1283                       0.03                        Extremely strong spike.

Toluene                                          729, 694                 2.0                          Spikes.

1,1,1 Trichloro ethane                    735-715                  0.5                          Smooth band.

1,1,2 Trichloro ethane                    760-720                  0.8                          Broad band.

Trichloro ethylene                          783                        1.4                          Spike.

Trichloro fluoro methane               855-840                  0.2                          Very strong band.

Trichlorotrifluoro ethane               1240-800                 0.6                          Group of strong bands.

Vinyl acetate                                 1240-1210               0.7                          Broad band.

Vinyl chloride                                942, 896                 2.0                          Two spikes.

Vinylidene chloride                        869                        1.0                          Spike.

Water                                             1700-1400               5.0                          M.D.L. is 5 PPB if no other

                                                                                                                        water is present. In humid air,

                                                                                                                         the minimum detectable change in

                                                                                                                        water content would be 1000 PPB.

m-Xylene                                       768                        2.0                          Spike.

o-Xylene                                        741                        1.0                          Spike.

p-Xylene                                        795                        2.0                          Spike.



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