APPENDIX A
DETERMINATION OF Q SETTING TABLES FOR STANDARD WAVELENGTHS
The settings of Q chosen for the ozone observations depend on the absorption coefficients of ozone and on the character of the solar spectrum; e.g., it is clearly undesirable to choose a setting at a place where a small change in Q makes a large change in spectrophotometer dial reading. For all instruments to make observations on the exact wavelengths selected as described above, the corresponding value of Q1 must be accurately determined to within ±0.20 degree for each instrument.
Two basic methods are available for determining Q settings for the standard wavelength pairs, A, B, C and D. The first method, described in Section 1 below, entails making special spectrophotometer measurements on the clear zenith sky near noon with high sun. (A variation of this method is described elsewhere by Dobson (1957b, Test 15.3). This method is especially suited for determining Q settings for A and D wavelengths, but is less satisfactory for B and C wavelengths. The preferred method, described in Section 2, involves the use of a series of spectral discharge lamps.
1. Determination of Q for Standard Wavelengths A, B, C, and D from Observations on the Clear Zenith
The procedure is to
plot curves of Dobson instrument R-dial readings against Q, using the clear
zenith sky near noon.
(a) Allow the instrument to reach a steady temperature.
(b) Set Q1 = Q2 to a value 5 degrees lower than the value expected for the particular wavelength.
(c) Obtain a preliminary R-dial balance and adjust instrument sensitivity, etc.
(d) Read the instrument temperature.
(e) Make an observation of 20 sec duration.
(f) Advance Q1 = Q2 by 1 degree and make the next observation.
(g) Proceed in this way until a value of Q1 = Q2 is reached that is 5 degrees higher than the expected value.
(h) Repeat the above steps with Q1 = Q2 decreasing.
(i) Read the instrument temperature.
(j) Plot the data as shown in Figure 1, and extract pertinent Q values for A, B, C, and D wavelengths as indicated.
The method described above yields the correct Q settings for, say, D wavelengths at one temperature only; e.g., Q1 is 108.3 at 18.1 °C. To determine the variations of Q1 with temperature, similar tests may be conducted at other instrument temperatures covering a range of at least 15°C. Care must be taken to ensure that the temperature in each case is steady; otherwise, the thermometer may not indicate the true temperature of the optical components. A best-fitting straight line is then drawn through the plot of the Q1 points vs. temperature, and a Q-setting table for D wavelengths is drawn up for routine use during ozone observations.
A simpler procedure is the following. Determine accurately the temperature coefficient of Q1 for the particular instrument under test for the Hg-3129 line only. (Note that this coefficient must be known accurately at all times for an instrument if mercury lamp test data are to be interpreted meaningfully.) Again, a range of at least 15°C must be covered during tests with the mercury lamp, and care must he taken to ensure that instrument temperature is steady during each test. The temperature coefficient for the Hg-3129 line will usually he a value between 0.10 °Q/°C and 0.20 °Q/°C say 0.17 °Q/°C. To determine the instrument temperature coefficients for A, B, C, and D wavelengths, multiply this value by the temperature factors given in the table below.
Table 1. Temperature Factors for A and D Wavelengths
Wavelength Wavelength Temperature
Slit Pair in A.U. Factor
S2 A 3054.8 0.67
S2 B 3087.8 0.87
S2 C 3114.6 0.99
S2 D 3175.8 0.97
Using this value, it is possible to draw on a graph a straight line having a slope of 0.16 °Q/°C and passing, e.g., through the point Q1 = 108.3 at 18.1 °C from which a Q-setting table for D wavelengths is then drawn up. Q-setting tables for A, B, and C wavelengths are established in a similar manner.
2. Determination of Q for Standard Wavelengths by Discharge Lamps
The settings of Q may be determined by using a set of discharge lamps. For this purpose, lamps having envelopes transparent to ultraviolet radiation and containing zinc, helium, and cadmium, in addition to the ordinary mercury lamp, are required. Lamps containing indium and thallium are also desirable, though not essential. They may be mounted vertically and the light thrown onto the G.Q.P. by the sun-director. The wavelengths of the lines used are given in Table 2. These lines will fall on slit S2 at approximately the setting of the Q1 lever given under the heading QS.
Table 2 Element Wavelength QS Temp. Factor, f
Hg 3021.5 A.U. 38.20° 0.58 In 3039.4 44.05 0.61 Zn 3075.3 57.90 0.79 Hg 3129.6 84.10 1.00 Cd 3133.2 86.10 1.00 He 3187.7 112.75 0.92 Th 3229.8 128.35 0.76 In 3256.1 135.90 0.68 Cd 3259.9 136.85 0.67
The measurements are made in exactly the same way as for the routine mercury lamp test. The values found for Q1 should next be corrected to a temperature of 15 °C using the temperature factors, f, of Table 2 and the temperature coefficient for the mercury line 3129.6 A.U. (The temperature coefficient of Q1 for the particular instrument under test for the Hg 3129 line is determined by performing a large number of routine mercury lamp tests at various constant instrument temperatures. A range of at least 15 °C must be covered during tests.) The observed values of Q1 are next subtracted from the average values given under QS and the differences plotted against wavelength as shown in Fig. 2 where a smooth curve is drawn through the points. Finally the values of Qobs - QS for the A, B, C, and D wavelengths are read off the curve and added to the values of QS shown in Table 3 to give the value of Q for these wavelengths at 15 °C.
Table 3 Slit Wavelength Wavelength QS Temp. factor, f Pair
S2 A 3054.8 A.U. 49.65° 0.67 S2 B 3087.8 63.40 0.87 S2 C 3114.6 76.35 0.99 S2 D 3175.8 107.45 0.97
The following measurements made on one instrument are given as an example:
Line Qobs Obs. Temp. DeltaQ Q15°C QS Q15°C - QS
Hg 37.48° 10.9O° .38° 37.86° 38.20° -0.34° Zn 57.95 14.65 .04 57.99 57.90 +0.09 Hg 84.40 10.95 .65 85.05 84.10 +0.95 Cd 86.90 14.60 .06 86.96 86.10 +0.86 He 112.80 11.10 .57 113.37 112.75 +0.62 Tl 128.85 14.90 .01 128.86 128.35 +0.51 Cd 137.05 14.60 .04 137.09 136.85 +0.24
For the particular instrument, the temperature coefficient for the Hg-3129 line was 0.16 °Q/°C. Thus, for the Hg-3021 line the DeltaQ = 0.38 value was obtained by multiplying the differences between the observed and 15°C temperatures by 0.16 x 0.58. The standard wavelength settings at 15°C then follow.
Wavelengths Qobs - QS QS Q15°C
A -0.15° 49.65° 49.50° B +0.25 63.40 63.65 C +0.75 76.35 77.10 D +0.75 107.45 108.20
The instrument temperature coefficients for the A, B, C and D wavelengths are determined by multiplying the temperature factors given in Table 3 in turn by the instrument temperature coefficient for the line Hg 3129. Thus, in the example given above for A wavelengths, say, the instrument temperature coefficient is 0.16 °Q/°C x 0.67 = 0.11 °Q/°C. A straight line of slope 0.11 °Q/°C and passing through the point Q1 = 49.50 at 15°C is now drawn on graph paper from which a Q-setting table for A wavelengths is established. Tables of Q-settings vs. temperature for the B, C, and D wavelengths are determined in a similar manner. A sample Q setting table for A, B, C, and D wavelengths is shown in Table 4.
| TABLE OF SETTINGS OF Q | ||||||||||||||
| BOULDER, COLORADO INST. NO. 76 MARCH 18, 1980 |
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(82 TEMP. COEFF. DEG. Q / DEG. C : A: 0.93 B: 0.000 C: 0.138 D: 0.135 HG3129: 0.139 ) |
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| TEMP | A | C | D | HG | TEMP | A | C | D | HG | TEMP | A | C | D | HG |
| -5.0 | 46.85 | 72.65 | 103.75 | 80.35 | 10.0 | 48.25 | 74.70 | 105.75 | 82.40 | 25.0 | 49.65 | 76.75 | 107.80 | 84.50 |
| -4.5 | 46.90 | 72.70 | 103.80 | 80.40 | 10.5 | 48.30 | 74.75 | 105.85 | 82.50 | 25.5 | 49.70 | 76.85 | 107.85 | 84.60 |
| -4.0 | 46.95 | 72.80 | 103.90 | 80.50 | 11.0 | 48.35 | 74.85 | 105.90 | 82.55 | 26.0 | 49.70 | 76.90 | 107.90 | 84.65 |
| -3.5 | 47.00 | 72.85 | 103.95 | 80.55 | 11.5 | 48.35 | 74.90 | 105.95 | 82.65 | 26.5 | 49.75 | 76.95 | 108.00 | 84.70 |
| -3.0 | 47.00 | 72.90 | 104.00 | 80.60 | 12.0 | 48.45 | 75.05 | 106.10 | 82.75 | 27.0 | 49.80 | 77.05 | 108.05 | 84.80 |
| -2.5 | 47.05 | 73.00 | 104.10 | 80.70 | 12.5 | 48.45 | 75.05 | 106.10 | 82.75 | 27.5 | 49.85 | 77.10 | 108.15 | 84.85 |
| -2.0 | 47.10 | 73.05 | 104.15 | 80.75 | 13.0 | 48.50 | 75.10 | 106.15 | 82.85 | 28.0 | 49.90 | 77.20 | 108.20 | 84.95 |
| -1.5 | 47.15 | 73.10 | 104.20 | 80.85 | 13.5 | 48.55 | 75.20 | 106.25 | 82.90 | 28.5 | 49.95 | 77.25 | 108.25 | 85.00 |
| -1.0 | 47.20 | 73.20 | 104.30 | 80.90 | 14.0 | 48.60 | 75.25 | 106.30 | 83.00 | 29.0 | 50.00 | 77.30 | 108.35 | 85.05 |
| -.5 | 47.25 | 73.25 | 104.35 | 80.95 | 14.5 | 48.65 | 75.30 | 106.35 | 83.05 | 29.5 | 50.05 | 77.40 | 108.40 | 85.15 |
| 0.0 | 47.30 | 73.35 | 104.40 | 81.05 | 15.0 | 48.70 | 75.40 | 106.45 | 83.10 | 30.0 | 50.10 | 77.45 | 108.45 | 85.20 |
| .5 | 47.35 | 73.40 | 104.50 | 81.10 | 15.5 | 48.75 | 75.45 | 106.50 | 83.20 | 30.5 | 50.15 | 77.50 | 108.55 | 85.25 |
| 1.0 | 47.40 | 73.45 | 104.55 | 81.15 | 16.0 | 48.80 | 75.55 | 106.55 | 83.25 | 31.0 | 50.20 | 77.60 | 108.60 | 85.35 |
| 1.5 | 47.45 | 73.55 | 104.60 | 81.25 | 16.5 | 48.85 | 75.60 | 106.65 | 83.35 | 31.5 | 50.25 | 77.65 | 108.65 | 85.40 |
| 2.0 | 47.50 | 73.60 | 104.70 | 81.30 | 17.0 | 48.90 | 75.65 | 106.70 | 83.40 | 32.0 | 50.30 | 77.75 | 108.75 | 85.50 |
| 2.5 | 47.55 | 73.65 | 104.75 | 81.40 | 17.5 | 48.95 | 75.75 | 106.80 | 83.45 | 32.5 | 50.35 | 77.80 | 108.80 | 85.55 |
| 3.0 | 47.60 | 73.75 | 104.90 | 81.45 | 18.0 | 49.00 | 75.80 | 106.85 | 83.55 | 33.0 | 50.40 | 77.85 | 108.85 | 85.60 |
| 3.5 | 47.65 | 73.80 | 104.90 | 81.50 | 18.5 | 49.05 | 75.85 | 106.90 | 83.60 | 33.5 | 50.40 | 77.95 | 108.95 | 85.70 |
| 4.0 | 47.70 | 73.90 | 104.95 | 81.60 | 19.0 | 49.05 | 75.95 | 107.00 | 83.70 | 34.0 | 50.45 | 78.00 | 109.00 | 85.75 |
| 4.5 | 47.70 | 73.95 | 105.00 | 81.65 | 19.5 | 49.10 | 76.00 | 107.05 | 83.75 | 34.5 | 50.50 | 78.05 | 109.05 | 85.85 |
| 5.0 | 47.75 | 74.00 | 105.10 | 81.75 | 20.0 | 49.15 | 76.10 | 107.10 | 83.80 | 35.0 | 50.55 | 78.15 | 109.15 | 85.90 |
| 5.5 | 47.80 | 74.10 | 105.15 | 81.80 | 20.5 | 49.20 | 76.15 | 107.20 | 83.90 | 35.5 | 50.60 | 78.20 | 109.20 | 85.95 |
| 6.0 | 47.85 | 74.15 | 105.25 | 81.95 | 21.0 | 49.25 | 76.20 | 107.25 | 83.95 | 36.0 | 50.65 | 78.30 | 109.25 | 86.05 |
| 6.5 | 47.90 | 74.20 | 105.30 | 81.95 | 21.5 | 49.30 | 76.30 | 107.30 | 84.00 | 36.5 | 50.70 | 78.35 | 109.35 | 86.10 |
| 7.0 | 47.95 | 74.30 | 105.35 | 82.00 | 22.0 | 49.35 | 76.35 | 107.40 | 84.10 | 37.0 | 50.75 | 78.40 | 109.40 | 86.20 |
| 7.5 | 48.00 | 74.35 | 105.45 | 82.10 | 22.5 | 49.40 | 76.40 | 107.45 | 84.15 | 37.5 | 50.80 | 78.50 | 109.45 | 86.25 |
| 8.0 | 48.05 | 74.45 | 105.50 | 82.15 | 23.0 | 49.45 | 76.50 | 107.50 | 84.25 | 38.0 | 50.85 | 78.55 | 109.55 | 86.30 |
| 8.5 | 48.10 | 74.50 | 105.55 | 82.20 | 23.5 | 49.50 | 76.55 | 107.60 | 84.30 | 38.5 | 50.90 | 78.60 | 109.60 | 86.40 |
| 9.0 | 48.15 | 74.55 | 105.65 | 82.30 | 24.0 | 49.55 | 76.65 | 107.65 | 84.35 | 39.0 | 50.95 | 78.70 | 109.70 | 86.45 |
| 9.5 | 48.20 | 74.65 | 105.70 | 82.35 | 24.5 | 49.60 | 76.70 | 107.70 | 84.45 | 39.5 | 51.00 | 78.75 | 109.75 | 86.55 |
Return to Table of Contents
Forward to Appendix B. Correcting the Table of Setting of Q