Zero transmittance

Set a suitable flame photometer to a wavelength of 589 nm. Adjust the instmment to zero transmittance against water, and then adjust it to 100.0% transmittance with an aqueous solution containing 200 pig/mL of sodium, in the form of the chloride. Prepare and read the percent transmittance of three other solutions containing 50, 100, and 150 xg/mL each of sodium, and plot the standard curve as percent transmittance versus concentration of sodium... 

CiUoff fillers have transmillances of nearly l(X)% over a portion of the visible spectrum but then rapidly decrea.se to zero transmittance over the remainder. A narrow spectral band can be isolated by coupling a cutoff filter with a second filter (sec Figure 7-17). 

The signal corresponding to zero transmittance (with the lamp shutter closed) is measured. The measuring cycle (Fig. 2) is started either by a teletype command or by a logic input switch. 

Measurement of the zero level is not as simple as one might expect. The complication arises from the inherent lack of energy of a doublebeam optical null system at zero transmittance, where both beams are blocked. Under these conditions it is possible for the optical attenuator to drift or coast below its zero position, since the system has no means of returning the errant attenuator to the true zero. In a well-operating instrument there are three potential causes for fallacious zero reading a too rapid approach to zero, an improper electrical balance, and scattered radiation. 

Spectral filters often are assumed to have zero transmittance outside their pass-band. This assumption may introduce a substantial error. The need for more careful measurements may be checked easily by calculating the effect of a 0.2% out-of-band transmittance. If this effect is large, you had better verify the out-of-band transmittance with a measurement accuracy of 0.2% of better. Review of articles describing problems encountered with cold spectral filters (Stierwalt, 1974 Stierwalt and Eisen-man, 1978) will give the experimenter a healthy respect for potential difficulties ... 

Desired Spectral Rejection. The near-zero transmittance of Ge and Si in the visible and ultraviolet can be used to advantage to protect InSb and lead salt detectors from undesirable effects of exposure to UV. 

Pressure Zero shift, air leaks in signal lines. Variable energy consumption under temperature control. Unpredictable transmitter output. Permanent zero shift. Excessive vibration from positive displacement equipment. Change in atmospheric pressure. Wet instrument air. Overpressure. Use independent transmitter mtg., flexible process connection lines. Use liquid filled gauge. Use absolute pressure transmitter. Mount local dryer. Use regulator with sump, slope air line away from transmitter. Install pressure snubber for spikes. 

Flow Low mass flow indicated. Mass flow error. Transmitter zero shift. Measurement is high. Measurement error. Liquid droplets in gas. Static pressure change in gas. Free water in fluid. Pulsation in flow. Non-standard pipe runs. Install demister upstream heat gas upstream of sensor. Add pressure recording pen. Mount transmitter above taps. Add process pulsation damper. Estimate limits of error. 

The presence of a non-zero dark reading, E0, will, of course, cause an error in the value of r computed. However, this is a systematic error and therefore is of no interest to us here we are interested only in the behavior of random variables. Therefore we set E0s and Eqj. equal to zero and note, if T as described in equation 41-1 represents the true value of the transmittance, then the value we obtain for a given reading, including the instantaneous random effect of noise, is... 

We note that, since by assumption Er is non-zero, and AEt is non-zero and independent of Et, the first term of equation 41-11 is non-zero. The value of the second term of equation 41-11, however, will depend on the value of Es, that is on the transmittance of the sample. 

Next we note further, and this is probably contrary to most spectroscopist s expectations, that the noise of the transmittance spectrum is not constant, but depends on the transmittance of the sample, being higher for highly transmitting samples than for dark samples. Since T can vary from 0 (zero) to 1 (unity), the noise level can vary by a factor of the square root of two, from a relative value of unity (when T = 0) to 1.414... (when T = 1). This behavior is shown in Figure 41-1. 

This is a transcendental equation, which is not easily solved by ordinary methods. Nowadays, however, computers make the solution of such equations by successive approximations easy. In this case, again using EXCEL , we find that the value of T that makes the left-hand side of equation (42-50) become zero, which thus gives the value corresponding to the transmittance corresponding to minimum relative error, is 0.32994, rather than the previously accepted value of 0.368... 

It is even possible for an individual noise pulse to exceed — ET so that a negative reading of Ex will be obtained. This happens in the real world and therefore must be taken into account in the mathematical description. This is a good place to also note that since the transmittance of a physical sample must be between zero and unity, Es must be no greater than If, and therefore when If is small an individual reading of Es can also be negative. Therefore it is entirely possible for an individual computed value of T to be negative. 

The noise of the transmittance thus becomes directly proportional to T and inversely proportional to Er. Under these conditions the noise of the transmittance approaches infinite values as E, approaches zero, even as the expected value of the transmittance approaches zero, as we saw in Chapter 43 [4],... 

Since EJEt is the true transmittance of the sample, the value of T for a given sample is constant, and therefore the variance of that term is zero, resulting in ... 

From Figure 47-17 we note several ways in which the behavior of the transmittance noise for the Poisson-distributed detector noise case differs from the behavior of the constant-noise case. First we note as we did above that at T = 0 the noise is zero, rather than unity. This justifies our earlier replacement of E0 by E0 for both the sample and the reference readings. 

When the noise is small the multiplication factor approaches unity, as we would expect. As we have seen for the previous two types of noise we considered, the nonlinearity in the computation of transmittance causes the expected value of the computed transmittance to increase as the energy approaches zero, and then decrease again. For the type of noise we are currently considering, however, the situation is complicated by the truncation of the distribution, as we have discussed, so that when only the tail of the distribution is available (i.e., when the distribution is cut off at +3 standard deviations), the character changes from that seen when most of the distribution is used. 

Figures 7.5 and 7.6 give the measured spectral reflectances and transmittances of fabrics. It is clear from Figure 7.5 that color (6,white 7,black 1,yellow) has a significant effect in reflecting solar irradiance, and also we see why these colors can be discriminated in the visible spectral region of 0.6 pm. However, in the spectral range relevant to fire conditions, color has less of an effect. Also, the reflectance of dirty (5a) or wet (5b) fabrics drop to <0.1. Hence, for practical purposes in fire analyses, where no other information is available, it is reasonable to take the reflectance to be zero, or the absorptivity as equal to 1. This is allowable since only thin fabrics (Figure 7.6) show transmittance levels of 0.2 or less and decrease to near zero after 2 pm.

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