Blackbody apertures

We can sample the energy density of radiation p(v, T) within a chamber at a fixed temperature T (essentially an oven or furnace) by opening a tiny transparent window in the chamber wall so as to let a little radiation out. The amount of radiation sampled must be very small so as not to disturb the equilibrium condition inside the chamber. When this is done at many different frequencies v, the blackbody spectrum is obtained. When the temperature is changed, the area under the spechal curve is greater or smaller and the curve is displaced on the frequency axis but its shape remains essentially the same. The chamber is called a blackbody because, from the point of view of an observer within the chamber, radiation lost through the aperture to the universe is perfectly absorbed the probability of a photon finding its way from the universe back through the aperture into the chamber is zero. 

Planck s radiation law determines the power emitted by a small aperture in a cavity, which is at a given equilibrium temperature. The spectral flux emitted by an isotropic blackbody source into a solid angle 2 = 2rr sin 0r (where 9r is the angular radius of the first optical element of the spectrometer) is ... 

A blackbody enclosure at 1000°C has a small aperture into the environment. Determine (i) the blackbody radiation intensity emerging from the aperture, and (ii) the blackbody radiation heat flux from the blackbody. 

Blackbody radiation is achieved in an isothermal enclosure or cavity under thermodynamic equilibrium, as shown in Figure 7.4a. A uniform and isotropic radiation field is formed inside the enclosure. The total or spectral irradiation on any surface inside the enclosure is diffuse and identical to that of the blackbody emissive power. The spectral intensity is the same in all directions and is a function of X and T given by Planck s law. If there is an aperture with an area much smaller compared with that of the cavity (see Figure 7.4b), X the radiation field may be assumed unchanged and the outgoing radiation approximates that of blackbody emission. All radiation incident on the aperture is completely absorbed as a consequence of reflection within the enclosure. Blackbody cavities are used for measurements of radiant power and radiative properties, and for calibration of radiation thermometers (RTs) traceable to the International Temperature Scale of 1990 (ITS-90) [5]. 

FIGURE 7.4 Blackbody characteristics for isothermal enclosures (a) intensity is the same in all directions, and irradiation on any surface inside the enclosure is equal to the blackbody emissive power, and (b) emission through a small aperture approximates that of a blackbody, and the cavity acts as a perfect absorber. 

A blackbody is one that is a perfect absorber of radiation it absorbs all the radiation falling on it, without reflecting any. More relevant for us, the radiation emitted by a hot blackbody depends (as far as the distribution of energy with wavelength goes) only on the temperature, not on the material the body is made of, and is thus amenable to relatively simple analysis. The sun is approximately a blackbody in the lab a good source of blackbody radiation is a furnace with blackened insides and a small aperture for the radiation to escape. In the second half of the nineteenth century the distribution of ... 

A well-defined molecular beam strictly defines the source area and angular range of molecules and restricts the amount of background vapor that reaches the ionizer. Furthermore, by using a small field aperture one can make the source area of the molecular beam smaller than the cross-sectional area of the cell orifice. This definition of the beam effectively removes the effect of the shape of the orifice on the fiux distribution of the molecular beam and makes KEMS measurements independent of orifice shape. This effect is analogous to the requirements of sampling the radiation from fuUy within the blackbody when temperature is measured with a pyrometer. 

For InjO mode reflectometers, a non-Lambertian radiation source may introduce a measurement error. Wood et al. (31) described a typical cavity blackbody source that exhibits a monotonic drop in emitted radiance (52) with angle. The percentage decrease in radiance from the normal incidence value is 3 to 4% at 45° and 6 to 7% at 70°. Beyond 80°, the falloflf is very rapid due to direct viewing of the cavity wall near the exit aperture of the source. If a Lambertian sample is illuminated with radiance having an angular dependence L 6), where L(0) = 1, then the ratio of the measured reflectance to the true reflectance will be given by... 

In this context, the use of synchrotron radiation (SR) as a photon source has been suggested because of its brilliance advantage, namely in the range of two to three orders of magnitude through small apertures at the sample position, over conventional blackbody (Globar) sources that equip most commercial FTIR microscopes. 

In the article humorously titled Blackbody, blackbody simulator, blackbody simulator cavity, blackbody simulator cavity aperture, and blackbody simulator aperture are each different from one another, Bartell (1989b) points out important conceptual differences that should be recognized but are generally overlooked when we speak of BBS. A (true) BB is an idealization. The devices in our laboratories that we call BBS are actually blackbody simulators. One type uses an approximately isothermal cavity and a separate aperture. For a well-designed simulator, accurate radiometric calculations can be done by fleating that separate aperture (not the cavity itself, nor the cavity opening) as the IR source. The IR irradiance depends on the distance from the separate aperture. 

TBB Blackbody Tetsperature, deg K TCR Chopper Tenperature, deg R N Nuinber of tooth-slot pairs OCH - Chopper "pitch diaaeter DAP o Blackbody aperture diameter DIST BB aperture to detector distance... 

Bartell (1989b) Blackbody, Blackbody Simulator, Blackbody Simulator Cavity, Blackbody Simulator Cavity Aperture, and Blackbody Simulator Aperture are Each Different from One Another by F. O. Bartell, Proc SPIE, 1110, 183. 

The most common source for IR work is a blackbody, and a blackbody is the obvious choice whenever it will generate acceptable signal levels at obtainable temperatures. A well-made cavity blackbody (technically a blackbody simulator) has an emissiv-ity so close to unity that we can safely assume that value. It requires no calibration except that required for the temperature sensors. Given the cavity temperature and the area of the separated aperture, Planck s radiation law yields the exitance and irradiance - both as a function of wavelength, and integrated over any desired spectral region. These were discussed in Chapter 2. Mounting and calibration of blackbodies is discussed in Section 9.3.1. 

Ease of operation should be considered Can the blackbody aperture plate be moved readily Can the aperture identifiers be read easily How difficult will it be to gain access to parts that need maintenance Can the blackbody cavity be probed conveniently It may be that the various design goals cannot be met, but it is worthwhile for everyone who has an interest in the set to recognize and acknowledge the trade-offs at this stage, rather than being disappointed later. 

We almost always want to take blackbody data on a detector at a given irradiance. Someone needs to determine a combination of spectral filters, field-of-view shields, blackbody temperature, apertures, and distances that will provide the required background and adequate signal-to-noise ratio and allow prediction of the performance at the wavelengths of interest. 

Evidently, we cannot get all of the required background reduction with a cold shield alone, so we will need a spectral filter in conjunction with the cold shield. We pay a penalty for the use of the spectral filter the signal from the blackbody will be reduced. Assume that (like many labs) we have 500 and 800 K blackbodies with apertures that range from 0.050 to 0.500 in diameter, and that total distances from the blackbody aperture to the detector can be as small as 8 . We calculate the irradiance we can expect with three filters, each with a bandpass of 0.2pm, centered at 3, 4, and 5 pm, using two blackbody temperatures (500,800 K) and the two blackbody aperture extremes. Table 9.1 shows the irradiances that we can expect with the 12 different combinations. It also lists the signal-to-noise ratios that we will see, based on the expected NEI. From this table we can pick out the acceptable combinations. 

Table 9.1 shows that we can achieve the desired background with all three of the filters proposed. But with the 5-pm filter, the field-of-view limiting aperture is only 0.23-in. in diameter this is shorter than the length of our array, so it will probably vignette the signal from the blackbody, or at least make careful alignment necessary. If a better solution is not evident, we may try a narrower spectral filter at 5 pm, but set this option aside for the moment. 

The 3.0-pm filter provides the required background with a 2.4-in.-diameter cold aperture the signal-to-noise ratios with the 500 K blackbody are too small, but those with the 800 K blackbody are acceptable. We could certainly get by with a much smaller cold aperture and a much wider spectral filter, but the4-pm filter is probably a better choice because it is nearer the peak wavelength of the detector. 

Blackbody Calibration Radiometric calibration is different from conventional calibration of micrometers and scales. We discuss the radiometric calibration problem in Section 9.6. For now, we discuss the emissivity and the more mechanical parts of blackbody calibration, determination (in a traceable way) of the temperature, and (for cavity type blackbodies) the aperture diameter. 

Measurement of Aperture Diameters The apertures used to define the emitting area of a cavity blackbody are quite small, so we need to know their sizes quite accurately. If we allow a 2% contribution to the error in irradiance due to uncertainties in the diameter of a 0.020-in. aperture, we must know its diameter within 0.0002-in.. This requires careful work. 

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