Working Group on Infrared Astronomy
Groupe de Travail pour Astronomie Infrarouge

A. T. Young¹, E. F. Milone², and C. R. Stagg²

[1] Astronomy Department, San Diego State University, San Diego, CA 92182, USA and European Southern Observatory, Garching-bei-M\o'"u'nchen, FRG

[2] Department of Physics and Astronomy, University of Calgary, 2500 University Drive, N. W., Calgary, Alberta, Canada T2N 1N4

Abstract

In response to recommendations made by a Working Group on Infrared Extinction and Standardization of IAU Commission 25, we have compared the past and present versions of the passbands in the Johnson JHKLMNQ broadband photometric system used at a number of observatories with the atmospheric window transmissions calculated by MODTRAN. The existing passbands are very diverse; contrary to a widespread misperception, there is no semblance of a standard set in use.

We have used a family of solar-composition model stellar fluxes from Kurucz (1991 private communication) to model the atmospheric extinction under different water-vapor, height, and airmass conditions. Thus, we have simulated extinction curves for the infrared passbands used at several observatories.

A figure of merit related to the curvature of the extinction line describes the sensitivity of each response function to variations in water-vapor extinction. All the existing wideband infrared systems are severely compromised by curve-of-growth effects in the Earth's atmosphere. On the basis of the simulations and the figure of merit, we recommend the improved set of passbands described in Table 3, which are optimized for reproducibility and transformability of photometric results. These have similar effective wavelengths to the existing systems, but are slightly narrower, greatly reducing the effects of molecular absorptions, and allowing the use of a linear extinction curve with much smaller errors.

Finally, we discuss the effects of aurorae, airglow and thermal emission on the passbands. The improved passbands are less affected by atmospheric thermal emission than existing ones, and should provide similar signal/noise ratios.

Correction for atmospheric extinction is difficult in infrared photometry, notwithstanding the apparently linear form of the extinction curve at airmasses greater than 1 in some bandpasses, chiefly because of the strong and variable effects of water-vapor absorption. The extra-atmospheric flux of a star cannot be obtained simply by extrapolating a line fit to the magnitude as a function of airmass. The situation is reviewed in Milone (1989).

More recently, Cohen et al. (1993) have compared existing infrared flux calibrations, and have concluded that extinction correction is so inaccurate for existing systems that a better flux scale can be determined by using theoretical stellar-atmosphere models to set the scale. Obviously, this means that the models themselves cannot be tested for accuracy observationally. This is an unsatisfactory state of affairs.

In spite of the difficulty in correcting for extinction, several infrared astronomers have persevered to produce the best that can be achieved under present circumstances; Bessell and Brett (1989) summarize work done by others to standardize infrared photometry as it is currently practiced. The problem can be minimized by reducing, as far as possible, the response of the instrument to wavelengths where water absorbs strongly. However, a compromise must be struck between the need to minimize the influence of water vapor, and the desire to maximize the measurable signal. This dilemma is not as severe as it might appear, because not much light is transmitted in the water bands. Giving up only a small part of the available signal can reduce the extinction problem by a large factor, as we show below.

To some extent, this problem has been tacitly recognized by observers, who have generally used filters somewhat narrower than Johnson's original ones. However, each observer seems to have chosen a different set of bands; and this variation, together with the rather loose tolerances that have been used in specifying filters, has led to actual passbands at different observatories that bear little relation either to each other or to the original set used by Johnson. Contrary to a widespread misperception that some set of "standard" passbands exists, we have found that the bands in use at different observatories resemble each other in name only.

The diversity of nominally similar passbands certainly has contributed to the difficulty of reproducing measurements at different observatories, and complicated the problem of transforming measurements to any common basis. The transformation problem has been made worse because of the common practice of using quasi-rectangular filter profiles. As pointed out by Young (1974), this is the worst possible form, from the point of view of reproducibility.

Further constraints are imposed by the properties of manufacturable interference filters in the infrared. Conversations with filter manufacturers indicate that conventional filters tend to have large ripples within the passband, and rather steep sides. Gentler slopes seem to be possible, and should improve the accuracy of transformations, as explained by Young (1974).

In this paper, we shall deal primarily with the extinction problem, which is quite serious in broadband systems such as the Johnson JHKL bands. We also take account of real-world constraints in recommending a set of filters that should allow infrared photometry of improved accuracy.

In broadband photometry, the extinction line is always more or less curved, because those wavelengths whose monochromatic extinction coefficients are largest are removed from the stellar spectrum at small air masses, leaving primarily the wavelengths with smaller extinction coefficients at larger air masses. Thus, the slope of the line continuously decreases with increasing airmass. This effect, which is very pronounced in the infrared (Manduca and Bell 1979, Volk et al. 1989), was discovered by J. D. Forbes (1842) and usually bears his name.

In the visible, the monotonic run of extinction with wavelength produces a correlation between effective extinction coefficients and stellar colors. The Forbes effect can then be regarded as a progressive decrease in extinction coefficient due to the increasing atmospheric reddening at large air masses (King 1952; Young 1974, 1988). In the infrared, no such simple picture can be drawn, because large and small monochromatic extinction coefficients are intermixed quasi-randomly by quantum-mechanical interactions within the water molecule that distribute its line positions and strengths irregularly.

In both the visible and the infrared, the Forbes effect can be regarded as a curve-of-growth effect due to the progressive alteration of the transmitted stellar spectrum. In the visible, the effect is small, and can be described by a single parameter (essentially the product of the color coefficient in the extinction with the reddening per unit air mass). But in the infrared, the best we have done so far is to describe the shape of the curved part of the extinction line, which requires at least three parameters. These could be the initial and asymptotic slopes of the curve, and a parameter that specifies the airmass at which their mean is reached. More physically, the three parameters could be maximum and minimum monochromatic extinction coefficients within the instrumental passband, and a parameter that tells how much of the passband has "large" and how much has "small" monochromatic extinction coefficients. Young (1989) suggested a particular parameterization of the curve, which we discuss below.

It would be convenient to have a single parameter to describe the severity of the Forbes effect -- preferably, one equally applicable to the visible and the infrared. Such a parameter should describe how severely the extinction at the zenith mutilates the transmitted spectral irradiance. If we adopt the point of view proposed by Young (1974), the theory of functional analysis provides a suitable parameter.

We recall briefly some facts of functional analysis; the reader unfamiliar with the necessary mathematics may turn to Oden (1979), or to Kolmogorov and Fomin (1968), among other sources. The L₂ norm of a square-integrable function f(x) defined on the interval (0, ) is

(1)

(Notice that all stellar spectral irradiances I() and all physically realizable instrumental spectral response functions R() are such functions.) The inner product of two functions f₁ and f₂ is defined as

(2)

Furthermore, any such function can be represented by a point in Hilbert space, or by the vector from the origin to this point. As suggested by Young (1974), we use these vectors to describe our functions. Then the L₂ norm || f || is just the length of the vector corresponding to the function f; for any positive scalar a, || af || = a || f ||. Furthermore, the angle between two vectors f₁ and f₂ is given by

(3)

If the inner product (f₁, f₂) = 0, then = 90; such functions are said to be orthogonal to one another.

The angle  provides the measure of similarity we need. If two functions are identical (apart from a scale factor), then cos = 1 and = 0. If the functions have slightly different shapes,  is a small angle.

We note that if || f₁ || = 1, then

(4)

then the inner product is simply the projection of f₂ on f₁. But the quantity measured by a photometer is simply the inner product

(5)

so we can regard it geometrically as the projection of the spectral irradiance vector I() on the (normalized) response function R(). As pointed out by Young (1974), two systems can be transformed accurately only if their response functions span the same subspace; so we can expect fairly accurate transformations only if the angles between corresponding response functions in the two systems are small.

For example, in the UBV system, the angle between the extra-atmospheric B band that appears in the (B-V) color index and the intra-atmospheric B that appears in the (U-B) index (Azusienis & Straizys 1966a,b; 1969) is only about 4 degrees. (The latter B is intra-atmospheric because Johnson chose to ignore atmospheric reddening in reducing his ultraviolet colors.) Typically, the B extinction coefficient varies by about 0.03 mag/airmass per unit of color index. As is well known, this effect of atmospheric reddening in B can be removed quite accurately, using a small linear color term. However, the correlation with color is much weaker in the infrared, so we cannot expect to be able to remove such effects as fully there.

Because the Chappuis bands of ozone almost exactly compensate for the wavelength dependence of Rayleigh scattering across the V band, the extinction is practically constant across V. This means that no color term is usually required for V: the atmosphere simply scales the V vector, without changing its direction. This is the situation we would like to have everywhere; in general, it is impossible to achieve in broadband photometry.

For another simple example, consider two rectangular passbands of equal width. If their central wavelengths differ by a small fraction of their width, their vectors make a small angle with each other. If they overlap for nine tenths of their width, cos = 0.9 and   27. Such a displacement is similar to those typically found between nominally similar realizations of a photometric system. In this case, transformation errors of a few per cent often occur, even after the systematic effects correlated with color indices are removed.

In the infrared, where color is a much weaker correlate of atmospheric effects, we expect to meet considerable difficulty at such large angles. If the correlation between monochromatic extinction and wavelength (and hence the correlation between effective extinction coefficient and stellar color) is small, little of this vector rotation can be transformed away with the usual color terms. Then the IR transformation errors may remain nearly as large as the raw differences between instrumental and standard systems in the visible before color-term transformation, and we can expect systematic errors on the order of a tenth of a magnitude between stars with different spectra.

We can now use the angle through which the atmosphere rotates the passband's Hilbert-space vector as a measure of the Forbes effect. If this angle is small -- say a few degrees at most -- we can expect minimal difficulty. If the angle is more than 20, we can expect substantial problems, as the simulations described below demonstrate. We shall try to choose band profiles that keep the atmospheric effect down to a few degrees, but that also provide maximum transformability while retaining a respectable degree of throughput.

We have used the AFGL program MODTRAN (Berk et al., 1989) to tabulate typical atmospheric transmission values t( , M ) at 1 cm^-1 intervals, and combined these with model-atmosphere fluxes I() kindly supplied by Kurucz. MODTRAN is a higher-resolution successor to the better-known program LOWTRAN (hence the name, which stands for "MODerate-resolution LOWTRAN"). Although the various versions of LOWTRAN, from LOWTRAN 2 to LOWTRAN 7, have been the standard means of calculating atmospheric transmission from models in the atmospheric-optics community for more than 20 years, they seem to be less well known to astronomers. Therefore, we briefly summarize some of their features.

LOWTRAN was invented about 1970 to provide a quicker but reasonably accurate low-resolution (20 cm^-1) alternative to line-by-line calculations based on the Air Force Geophysics Laboratory database of molecular absorption parameters, which in turn is based on the best data from laboratory spectroscopy. Originally, LOWTRAN was designed to calculate atmospheric transmission at intervals of 5 cm^-1, with a resolution of 20 cm^-1. Both atmospheric transmittance and atmospheric radiance can be calculated, over a variety of atmospheric optical paths, including paths from ground to space and (for an observer above the ground) paths extending below the astronomical horizon; zenith distance is an input parameter that can run from zero to beyond 90 degrees. The geometrical part of the model includes refraction and curvature effects. Molecular absorptions due to water, carbon dioxide, nitrous oxide, methane, ozone, nitric acid, and other infrared-active gases are included, as well as the pressure-induced nitrogen continuum. The model contains Rayleigh scattering, and several aerosol models are also available. Any of several standard atmospheric models can be selected, or the user can read in any desired model atmosphere. In short, it is a comprehensive effort to model the optical effects of the atmosphere in the infrared, and represents over a hundred man-years of work.

Numerous comparisons with direct observations of atmospheric transmittance have been made over the last two decades, with generally satisfactory results; over this period of time, the model has been improved continuously to give better agreement with observation. Some of the comparisons have involved high-resolution spectra of the setting Sun, observed both from the ground and from high-altitude balloons. Because of the Air Force's interest in observing objects in space from the ground, the database and the programs that use it have been extensively checked in observational conditions similar to those employed in astronomical observations. Several such comparisons have been reproduced in the manuals that accompany the various versions of LOWTRAN.

MODTRAN employs the same molecular-line database as LOWTRAN 7, but uses a newer band-model approximation, which gives better agreement with observations made at higher resolution. We therefore believe it is more than adequate for our purposes. Because its transmission values are much more finely spaced than either the fluxes or the tabulated response functions, we have interpolated everything else to the 1 cm^-1 tabular interval of the transmissions, and done the summations in frequency rather than wavelength space.

The transmittance values, and hence the integrand values used, are equally spaced in frequency. For this reason, it is convenient to display some of the accompanying figures in frequency units, which are customary in infrared spectroscopy. We also note that reciprocal wavelengths occur naturally in the design of interference filters. Astronomers unaccustomed to reciprocal centimeters should simply remember that 1 micron corresponds to 10000 cm^-1. Thus, 2 microns is 5000 cm^-1; 5 microns is 2000 cm^-1; 10 microns is 1000 cm^-1; and so on. Astrophysicists will be satisfied that frequency is proportional to photon energy; we do not wish to revive a religious dispute over the "proper" way to display spectra, which has wasted so much time at IAU General Assemblies in the past.

MODTRAN provides a great variety of elaborate aerosol models. However, aerosol extinction is quite small in the infrared, and (more to the point) varies very little across each photometric band. On the other hand, molecular absorption is important, varies rapidly with wavelength, and the water vapor in particular depends strongly on season and height above sea level. To reduce the size of the parameter space to explore, we have omitted aerosol extinction entirely, and concentrated on models with different water contents. For each model, we computed the transmission, t, at every half airmass between 1.0 and 3.0.

To keep the amount of computing to a manageable level, we selected only the stellar-atmosphere models with log g = 0.0 and 4.0, and ten temperatures from 3500 K to 35000 K, plus the solar and Vega models, from Kurucz's extensive tabulation. The fluxes, as well as typical infrared photometric response functions R(), such as those tabulated by Johnson (1965), were interpolated to 1 cm^-1 resolution. Then the three functions were multiplied together, and the products summed to approximate the wavelength integral

(6)

These signals were converted to magnitudes, in preparation for plotting extinction curves and numerical analysis. To model the extinction curves, the rational expression used by Young (1989) must first be converted to a more practical form. If we rewrite his Equation (3) as

(7)

we see that a now represents the extra-atmospheric magnitude. When M  1/d, the initial (and unobservable) slope at zero airmass is just (b-ad). For M  1/d, the constant terms are negligible compared to those involving M, and the asymptotic line has the equation

(8)

However, we expect the extrapolated intercept b/d to be only a few tenths of a magnitude larger than a in Eq. (7). Thus, it is reasonable to set

(9)

where b' depends on the atmospheric transmission and on the stellar flux distribution, and a is independent of the atmosphere. Equation (9) may be rewritten as

(10)

The transition between the two limits occurs near Md = 1, and 1/d is approximately the airmass at the "corner" of the curve. Note that the vertical asymptote of Eq. (7) is at M = - 1/d; in fact, 1/d corresponds exactly to M₀ in Young's (1989) Eq. (3).

In the large-airmass limit, the slope approaches the smallest monochromatic extinction coefficient within the instrumental spectral passband. Thus we expect c/d to be independent of the stellar spectrum. On the other hand, the parameters b' and d depend on the relative weighting of different wavelengths by the stellar spectral irradiance, and thus should depend on stellar properties. For example, if the molecular absorption is stronger in the blue wing of the passband than the red one, the Forbes effect will be stronger for blue stars than for red ones. Then the parameters b' and d will be larger for blue stars, and the coefficients of their color dependences will be negative.

Crudely, we may arbitrarily assume b' and d depend linearly on stellar color; the simulations show that this is not a bad approximation. Therefore, a reasonable equation of condition to fit the magnitudes calculated from the numerical integrations is

(11)

where a is still the extra-atmospheric magnitude; b in Eq. (7) has been replaced by Eq. (10), where both b' and d have been separated into terms that depend linearly on color and terms that are independent of color; C is a suitable color index; and c'd has replaced c, so that c' = c/d is independent of color, as discussed above. Only a and C vary from star to star; the other parameters are fixed for a given passband and atmospheric model. We have used the program GaussFit (Jefferys et al. 1988) to fit Eqs. (7) and (11) to the simulated observational data, which extend from 0.0 to 3.0 airmasses. Typical residuals are a millimagnitude or less; the maximum residuals do not exceed 0.01 mag.

The residuals are larger for Eq. (11) than for Eq. (7), partly because the linear functions of color neglect higher-order effects, and partly because ordinary color indices undersample the spectrum, and are therefore only a crude substitute for the gradients across each band that we really need (Young, 1988, 1992). Fortunately, most stellar features are weaker in the infrared than in the visible, which keeps these aliasing errors small except for the coolest stars.

One should not be misled by the good fits into thinking that this is a practical way to model infrared extinction for the usual broad infrared bands. Figures 1--3 show extinction curves for Johnson's original J, K, and M bands and the U. S. Standard Atmosphere model, available in MODTRAN. Calculations have been done for sites 1, 1.8, 2, and 4.2 km above sea level, but most of the results described in this section are done for an observatory 2 km above sea level, which is near the heights of Kitt Peak, Palomar, CTIO, ESO, and many other places where good photometry is commonly done. Evidently, most of the harm is done high in the atmosphere, at less than 1 air mass. Indeed, d is typically about 2 (cf. Table 1); the corner occurs near M = 0.5. As pointed out by Young (1989) and by Volk et al. (1989), it is unreasonable to expect to extrapolate the large curvature between 0 and 1 air masses from the nearly straight portion accessible to observation, for most broad-band IR filters. Furthermore, the different parameters vary with water content in different and nonlinear ways; we cannot even expect to reduce the number of free parameters by exploiting correlations among them.

If b' were independent of color, we could neglect the curvature and reduce all data to the zenith (M = 1), letting the changes with water content appear as a fictitious zero-point drift. Unfortunately, b' depends on both the color of the star and the amount of water vapor in the vertical column (see Table 1). This means that the apparent difference in magnitude or color between two stars with different spectra changes from night to night, even at the zenith, as the water abundance changes. The only way to obtain reproducible data, given the changing water-vapor content of the atmosphere, is to reduce everything to outside the atmosphere. But this appears impossible in practice with the original Johnson bands, or anything like them.

The problem is simply that the original Johnson infrared bands are so broad as to include much strong water-vapor absorption; see Figs 4--6. These spectral regions become nearly black high in the atmosphere, so there is no information left in them at air masses greater than 1. Consequently, the passbands available to observation are badly mutilated versions of the inherent instrumental bands. Table 2 shows the angles through which the atmosphere rotates the instrumental response vectors; they are on the order of 20 even at the zenith. Obviously, these large angles mean that transforming from inside to outside the atmosphere is very difficult.

It is sometimes supposed that the transition from opaque to transparent at the edges of the water bands is so abrupt that these can be allowed to define the instrumental passband edges. But Table 2 shows that even for a fixed atmosphere, going from 1 to 2 airmasses causes an additional rotation of 4 or 5 degrees. We know from the example of the B band of UBV that this is already an effect of several hundredths of a magnitude, which is by no means negligible. But in B we have the advantage that the effects are well-correlated with color index, and so can be removed; we lack this leverage in the infrared.

Furthermore, the water content of the atmosphere is highly variable. Figure 7 shows the amount of precipitable water above various heights for the six standard atmospheric models built into MODTRAN. At a given height, the range is about a factor of ten. The seasonal range from summer to winter is about a factor of 3 at mid-latitudes, and about 5 at high latitudes. There is an additional substantial factor of about 5 over the range of heights of astronomical observatories, due to the small effective scale height of water vapor; the range of water-vapor .I absorptions exceeds this, because variations in pressure broadening are important and add to the scale-height effect. Finally, these are merely representative values, and do not display the real variations of the atmosphere from night to night.

If we are to have a system that is reproducible despite the large variations in water absorption from place to place and from hour to hour, we must have bands that are minimally affected by water under typical clear conditions with average moisture. Fortunately, Figs. 4--6 suggest that bands about half as wide as the original Johnson passbands can, indeed, be very much freer of water absorption. This does not even mean giving up a factor of 2 in signal, as the parts we must reject are the parts most obscured, in which there is little signal anyway. The water bands are regions of variable systematic error, the worst kind of error. Without them, we can have a system that should allow much more accurate measurements. Nevertheless, to maximize throughput, we have widened the passbands as much as possible, consonant with our avowed aims.

The best way to do this is to find passbands that are minimally disturbed by molecular absorptions. The Hilbert-space approach described earlier has the additional property that the projection of one vector onto another is actually the least-squares approximation of the first vector by the second. And in fact the residual vector, which is orthogonal to the least-squares approximation, is proportional to the sine of the angle between the two vectors.

When the two vectors represent the instrumental function inside and outside the atmosphere, the residual vector represents information removed by the atmosphere. To keep this information loss small, we must keep the angle small; a small angle between the intrinsic and atmospherically perturbed response functions means the intra-atmospheric response is not very different from that outside the atmosphere.

This means we should choose response functions that are large only in regions where the atmosphere is fairly uniformly transparent, and allow only a little response where the atmosphere absorbs a lot. The general rule for selecting filters, therefore, is that we should allow only a few narrow regions of deep absorption within the main part of the response. The deep, dense portions of the water bands must be scrupulously avoided. Thus a first approximation to the bands we need can be obtained simply by adopting the lower envelope of the transmission window between water bands, if we choose an atmospheric model with somewhat more water than is practical, at present, to observe through.

Figure 7 shows that there are about 1.8 cm of precipitable water above 1 km in the mid-latitude summer model atmosphere. The usual rule of thumb is not to observe through more than 1 precipitable cm, so this seems a reasonable limit. The JHKLMNQ passband windows in Figures 8--24 are shown for this relatively wet model; note the reduction in transmission, compared to Figs. 4--6. The windows, with superimposed passband profiles, have been calculated for other models too, and are available on request. If, as a first approximation, we pick the half-peak transmission points of these windows as the half-power points of our filters, we should be able to get fairly satisfactory results for drier conditions -- i.e., any conditions in which a reasonable observer is likely to attempt infrared photometry.

We must also bear in mind the properties and limitations of actual filters. Most infrared filters must be cooled to minimize thermal radiation to the detector; cooling shifts the passband, because both the refractive indices and thicknesses of the layers used are temperature-dependent. Therefore it is essential to specify to the filter manufacturer the temperature at which the filters will actually be used (which, because of heat-transfer problems, may be considerably warmer than the temperature of the coolant used).

Furthermore, filters cannot have transmission functions with arbitrary shapes. The possible shapes depend on the design and on manufacturing tolerances, which vary somewhat from one maker to another. A rough rule is that filters with fractional passbands narrower than a few per cent of the central wavelength can be made with simple resonant cavities, as solid-state Fabry-Perot etalons. Such filters have fairly simple passband shapes, and are fairly symmetrical. Wider filters, on the other hand, are made by combining a cut-off filter with a cut-on filter. These filters have considerable ripple within their passband, and may also have large ripples (leaks) in their stopband.

The crossover between the two designs comes at widths between about 2% and 10% of the central wavelength, depending on the manufacturer and on other specifications. Thus, the JHKLMN series of filters, with passbands of 10 to 15%, are generally made as combinations of edge filters. This design allows approximately rectangular profiles; however, transformation difficulties increase as the sides get steeper, because the mean-square difference between two similar filters with slightly different edge placement is directly proportional to the edge steepness. This is confirmed by experiment, as we note below.

>From discussions with filter manufacturers, a reasonable specification seems to be that the slope from 5% transmission to 80% of peak transmission should span about 5% of the central wavelength. A transition width as narrow as 2% or 3% is possible, and would be a slightly better match to some window edges; but this steeper transition causes greater difficulties with transformation errors, and should be avoided. Conventional filter designs achieve good out-of-band blocking by superimposing two or more similar dielectric mirrors; as the number of layers goes up, the edge slope and blocking increase together. However, it may be possible to de-tune the edges slightly to achieve gentler slopes without sacrificing blocking.

A tolerance of 1% on central, cutoff, and cut-on wavelengths seems to be the best current choice: looser tolerances do not make the filters much cheaper, and tighter ones rapidly increase the price. If the 5%-to-80% slope covers only 2% of the wavelength, a 1% error in edge placement produces transmission differences between individual filters of 37.5%. But if the slope extends over 5% of the wavelength, the 1% error in wavelength placement produces only a 15% transmission error at a fixed wavelength. Of course, the price to be paid for reduced errors in transmittance (and hence reduced errors in transformations) is some loss of throughput in the shoulders of the band. This cannot reach the factor of 2 difference between a triangular and a rectangular band with the same base; the conventional filter already loses about half as much as the proposed profile, so the actual cost of decreasing transformation errors a factor of 2 is about 25% reduction in throughput.

These comments assume a rigorous degree of blocking both to short and to long wavelengths; experience among the Working Group suggests that blocking by more than a factor 10^-5 is required, and for certain filters, higher still; serious leaks will compromise and may vitiate the improvements we seek.

Finally, we note that the more gently sloping profiles that we are proposing are less sensitive to detector spectral sensitivity variation and to sharp astrophysical features at the bandpass edges than are conventional filters. Bearing in mind the somewhat conflicting requirements for optimum bandpasses, we now consider each of the principal windows in turn.

Figures 8 and 9 show that there are really two separate windows here, each fairly clear. Johnson's original band (see Fig. 4) included all of the longer-wavelength window, but also included the 8800 cm^-1 (1.14 m) water band, and had high response at the 7200 cm^-1 (1.39 m) band. This is most undesirable; even at the zenith, the fairly wet atmosphere used for Figs. 8 and 9 rotates the Johnson J by 30. Because Johnson J overlaps the 1.4 m water band so strongly, the situation is hardly better even with a dry atmosphere at a high site: if we adopt the Tropical atmosphere model at 4.2 km as typical of Mauna Kea, we still find 20 of atmospheric rotation.

The best thing to do here is restrict a J-like band to the region between about 7650 and 8600 cm^-1 (1.31 and 1.16 m, respectively), and to use the 1.03-m window for a separate band. Such a band is sometimes used, with the name "z" (after the Kodak Z sensitization class, which is useful in this region). Figure 8 suggests that its limits should be near 9100 and 10300 cm^-1 (0.97 and 1.10 m).

We carried out a series of simulations with slightly altered profile parameters for each passband to establish the best placement (see Fig. 10a, for "z"), and the widest FWHM on the toe of the Hilbert rotation plot (Fig. 10b). The 50% transmission points for "z" are optimally located near a center wavelength of 1.03 m. We suggest a relatively narrow FWHM until a suitable detector (i.e., one having a flat response) is available for this region as well as the other near infrared passbands; the fractional bandpass is about 7%. For an improved J band, Fig. 11 shows a central wavelength of 1.24 m and fractional bandpass of about 6%. The optimization data for these two passbands were obtained with the MODTRAN 4.2 km atmosphere model, but the results are nearly the same for the 1 km atmosphere model.

Figure 12 shows this window, which extends from about 5700 to 6600 cm^-1 (1.52 to 1.75 m). Optimization experiments (Figs. 13a and b) suggest a center wavelength of 1.62 m and a fractional bandwidth of about 9% . The pair of carbon-dioxide bands near 6300 cm^-1 (1.59 m) occur in what would otherwise be the clearest part of the window; but they are narrow enough and weak enough not to be a serious problem.

Figure 14 shows that the carbon-dioxide bands near 4850 and 4970 cm^-1 (2.06 and 2.01 m, respectively) are deep enough and broad enough to cause problems here; remember that these transmission spectra refer to the zenith. Because CO₂ is uniformly mixed, it does not decrease with height nearly as fast as does water vapor; even at high-altitude observatories, these bands will be stronger at M = 2 than shown here. Therefore it would be best to place the band edges near 4250 and 4810 cm^-1 (2.08 and 2.35 m). The simulations (Figs. 15) suggest that this can be broadened slightly with little degradation to the 5% limits 2.05 and 2.35 m. With a FWHM of 0.188 m, the minimum angle is found for a peak at 2.22 m and a fractional bandwidth of about 9%.

The water band at the middle of the window near 4600 cm^-1 looks a little worrisome in Fig. 14, but is weak enough that it fades into insignificance under drier observing conditions; in any case, it is difficult to avoid.

Recently two "short K" passbands have been suggested (Skrutskie, private communication, 1992; Wainscoat and Cowie 1992) for imaging work. In both cases, the red edge is close to that of the passband we suggest here; and in both cases the blue edge intrudes into the absorption on the blue side of the window, with the Wainscoat-Cowie filter being much more compromised by water vapor than the Skrutskie filter. Since the avowed purpose of these imaging filters is to minimize the IR atmospheric emission, overlapping with the blue edge of the atmospheric window is not a good idea. Our filter may even provide better S/N than either of these filters at lower-altitude observatories; nevertheless, they both represent an improvement over previous K filters.

Figure 16 shows the L and M windows, which are rather cleanly separated by the 4.3 m CO₂ band. Johnson's original L covered the whole region from about 3.0 to 4.1 m (2440 to 3330 cm^-1). As Fig. 16 clearly shows, the portion between 2400 and 2700 cm^-1 is much cleaner than the higher-frequency region. Thus, some observers have defined a band in the cleaner region, usually called L' . This is clearly a good idea; whereas the atmosphere rotates Johnson's L by 20 -- 30 (cf. Table 2), the L' suffers only 3.8 rotation at the zenith, and 9.4 at M = 3. However, one can do better by avoiding the water-laden region above 2700 cm^-1. The simulations (Fig. 17a) suggest two minima, which we designate "L" and "L' " for present purposes. The (5%) edges of the bluer ("L") passband are at 2964 and 2576 cm^-1 (3.37 and 3.88 m), the central wavelength is about 3.62 m and the fractional bandwidth is about 6%. The FWHM optimization data are plotted in Fig. 17b. The somewhat better passband ("L' ") has 5% limits at 2737 and 2400 cm^-1 (3.65 and 4.16 m) with a central wavelength of 3.90 m and a fractional bandwidth of 7%. The optimization data for this passband are shown in Fig. 17c.

Still better performance is possible with still narrower bands: a UKIRT narrow band devised by Selby (Cohen, private communication, 1992) centered at 3.805 m with a FWHM of 0.144 m is rotated only 1.7 at the zenith, and 3.8 at M = 3 -- as little as L' at the zenith. Such a passband is excellent for calibration work, although it includes very little flux to measure. Extinction curves for such narrow bands are nearly straight lines. However, one must realize that these narrow bands define quite a different system from the original Johnson one: the angle between Johnson's L II and the L' band is 59, and that between L II and the very narrow band is 76. Thus we cannot expect the narrower bands to be transformable to the relatively ill-defined Johnson system; we are dealing with a new system here, though one that is much more reproducible than the Johnson one.

The M window is much more obscured by water vapor than by any we have previously considered. Its use should be restricted to exceptionally dry conditions. Figure 18 shows the zenith transmission for the Tropical atmosphere model at 4.2 km above sea level, which should apply to Mauna Kea. Even here, the M window is not very clear. A fairly narrow band extending from only about 2090 to 2190 cm^-1 (4.56 to 4.78 m) may be fairly satisfactory, if it is used when the precipitable water is less than, say, 0.5 cm. This corresponds to a center wavelength of about 4.68 m and a fractional bandwidth of only 2.4%, much narrower than the previous passbands. A recent attempt to meet these specifications by Barr Associates, Inc., was quite successful; they produced a filter peaking at 4.685 m with only a slightly asymmetric profile and having 50% transmission points at 4.74 and 4.61 m for a fractional width of 2.8% (Heatley 1993, private communication). The optimization data (Figs. 19a and b) indicate that such slight broadening is well within the limits of good performance at an excellent site. Although there is some advantage in keeping to the bluer side of the window, a slightly longer central wavelength than we stipulate yields slightly smaller values of .

Figure 20 shows the very interesting N window near 10 m. The original N window covered the whole region from 7 to 14 m, and thus was not only badly affected by water on the short-wavelength side, but was nearly centered on the 9.6 m ozone band. Because the ozone absorption arises much higher in the atmosphere than the height of any observatory, it is nearly the same for all places, and cannot be reduced much by going to higher sites. The obvious need here is to use the two windows on either side of the ozone band separately.

The clearer window runs from just about 800 to 1000 cm^-1 (i.e., 10.0 to 12.5 m). It is clear that one would do well to cut back on the longer-wavelength side. Indeed, experiments show that decreases monotonically with peak wavelength over the atmospheric window. Our simulations (Figs. 21a and b) suggest that with a bandpass of 1.644 m, the optimum placement is near 11.0 m. However, the center of the window is closer to 11.1 m. At this central wavelength, a satisfactory value of (4.1) is achieved, and little dispersion among stellar atmosphere models is found even at a FWHM of 2.0 m. The optimization data shown in Figs. 21 demonstrate the feasibility of using the N passband successfully at low-altitude sites. The data shown are calculated for a 1-km site under mid-summer, temperate-latitude conditions. A central wavelength of 11.1 m and a fractional bandwidth of 18% still give a very generous bandpass, and still encompass a number of astrophysically interesting spectral features.

Indeed, the proposed N passband filter is still so broad that it could well be divided into two or more parts. This idea is worth trying, because smoother bands can be obtained; and if they overlap adequately, very accurate transformations are possible.

The bluer side of the old passband is suitable for a number of narrower passbands. The optimization data for one of the best of these, which we have designated the "n" passband, are shown in Figs. 22a and b. As designated, it is marginally useful at lower altitude sites; but the 0.323 m FWHM limit should not be greatly exceeded even at high altitude sites, since increases rapidly after this value. We originally designated a FWHM of 0.144 m, but this is excessively restrictive, especially at high altitude sites where it is most likely to be used. Although still relatively narrow, with a fractional bandwidth of 3.6%, this filter is capable of yielding photometric information about the Ar III emission feature, found in some planetary nebulae (Allen 1975), with precision; the feature lies squarely in the middle of the suggested passband. A slightly deeper minimum is found at closer to 9.1 m, but rises rapidly after this value, placing tighter restrictions (and higher cost) on the manufacturing process.

The referees point out that three narrower bands are already used at ESO to measure the silicate-dust feature in this region. However, the ESO bands (N1 at 8.4 m, N2 at 9.69 m, and N3 at 12.9 m) are all seriously affected by telluric absorptions -- particularly N2, which is nearly centered on the ozone band. Perhaps placing two narrow bands in each of the 8- and 11-m windows would offer a cleaner way to obtain this astrophysical information. Designing such a special-purpose system is beyond the scope of our present task, however.

Although this translucent "window" is rather badly obscured, its long wavelength makes it very useful for certain planetary and other studies. Figure 23 shows the zenith transmission in this region for the Tropical model at 4.2 km height. Our optimization experiments (Figs. 24a and b) suggest a placement near 18.08m with 5% power points at 594 and 515 cm^-1 (16.84 and 19.41 m respectively) and a fractional bandwidth of 9%. Even in this improved Q-passband, observations should be attempted only at the highest sites and under the driest possible conditions. A recent comparison of photometry in existing Q-bands clearly demonstrates the need for an improved passband. Although not as good as we would like it to be, the recommended passband is likely to improve agreement among data sets obtained at different times and places, given the same careful attention that observers have had to provide in the past for all IR photometry.

Our simulations have been carried out for several altitudes, with two principal atmosphere models: mid-latitude summer and tropical \(em the latter used only with the 4.2-km Mauna Kea simulation. For the most part, the bands have been optimized for a 1-km site, with mid-latitude summer water-vapor conditions. Consequently, some of the filters (e.g., H) may be narrower than necessary at higher and drier sites; but an important merit of the passbands we have defined is their anticipated reproducibility from all sites. The lack of such reproducibility is at the heart of the 3% transformability limit which currently undermines attempts at accurate photometry in the infrared. Having said this, we note again that M and Q are difficult under any circumstances. Here, selection was based on the optimization for the 4.2-km tropical site alone.

The selection of the final FWHMs requires additional comment, because the variation of the atmosphere-induced angle as a function of FWHM is smooth and for the most part monotonic. How does one select the "best" FWHM under such circumstances? Figs. 10b, 13b, 15b, 17b, 17c, 19b, 21b, and 22b show for bands with different widths in the various windows, as functions of the bands' FWHM. These figures show that the angle is small and very slowly increasing for narrow bands. But at some FWHM, the angle begins to increase much more rapidly. Evidently, this "elbow" is approximately the optimal compromise between increasing signal/noise ratio and increasing transformation difficulty, as the band width increases.

If we try to match the FWHM of the band to the FWHM of the window, we have too much response in the tails of the band, where atmospheric absorption is strong. For the "elbow" width, the instrumental response is typically 0.10 to 0.14 of peak at the "window" edges. A good compromise would put the 50% points of the windows at the points where the filters have about 0.1 of their peak transmission, rather than 50% of peak. This is undoubtedly why the numerically determined optimum FWHM values appear to be narrower than the windows in most cases. We have tried to select FWHM values which are 1-2% smaller than the value at the elbow region, to lessen the effect of manufacturing errors. This applies to all the windows discussed above.

The wavelengths at the 5%, 50%, 80%, and 100% (mid-band) points on the adopted filter profiles are listed in Table 3. The filter designations in Table 3 are prefixed with the letter "i" to avoid confusion with existing passbands. Elsewhere, we have used the Johnson designations for readability, and for easy identification of the atmospheric windows to which they pertain. These bands have profiles that are nearly triangular, or trapezoidal with rather narrow tops, rather than being rectangular. As explained previously, these shapes allow improved transformation accuracy, at some cost, typically 25% in total transmission (but different from passband to passband), compared to conventional filter profiles. The M filter is narrower than we would like, and the simulations show that some broadening is possible (see Fig. 19b) to allow the more gradual slopes we prefer, if the passband is used under the best conditions, and confined to the best sites.

Table 3: Recommended band profiles. All wavelengths (m) have nominal tollerances of 1%
Band	50% points		80% points		5% points		100% peak
iz	0.996	1.069	1.016	1.047	0.970	1.099	1.032
iJ	1.201	1.280	1.225	1.254	1.170	1.315	1.240
iH	1.555	1.707	1.585	1.672	1.514	1.754	1.628
iK	2.100	2.288	2.141	2.240	2.047	2.353	2.196
iL	3.483	3.757	3.554	3.686	3.374	3.882	3.620
iL'	3.763	4.037	3.834	3.966	3.654	4.162	3.900
iM	4.618	4.732	4.652	4.698	4.564	4.784	4.657
in	8.873	9.196	8.968	9.101	8.731	9.339	9.030
iN	10.100	12.100	10.369	11.832	9.756	12.444	11.100
iQ	17.106	18.712	17.439	18.329	16.656	19.231	17.900

The proposed filters have been designed for maximum throughput, consistent with minimum overlap with water-vapor bands, and in the case of the K and L filters, to minimize thermal emission also (as we note below). They must also be blocked, however, both on the short-wavelength side to minimize contamination from the strongly rising stellar flux, and on the long-wavelength side to prevent red leaks.

Because the actual wavelength tolerance of filter manufacture is about 1%, as we note above, we assume that a 1% tolerance will be specified to the manufacturer for each of the wavelengths defining each filter; extra decimals are given in Table 3 to prevent roundoff error. We realize that a 1% wavelength error may allow filter edges to encroach slightly onto the adjoining water bands, and more significantly, will cause some error in transformations when sharp features in an astronomical source are located at the edges of the passbands. However, because of the rather shallow slopes we have specified, this 1% wavelength error will, at worst, allow the filter to have 25% transmission at the intended 10%-transmission point, where the atmosphere transmits 50% under the worst assumed conditions. As such extreme errors are unlikely to be reached, particularly at both ends of the passband, we believe this is an acceptable deviation from the intended design. In any case, filters made to these specifications will be much more satisfactory than those in use today.

This section deals with what remains undone. We briefly consider detector spectral responses, aerosol effects, thermal and non-thermal background, and nomenclature.

We have ignored the detectors' responses. For the most part, this is justified because they vary only slowly across most of the passbands. If one wishes to use a detector for the "z" passband that is used for the other infrared passbands, difficulties arise, because extremely good blocking is required over a wide wavelength range to remove unwanted long-wavelength radiation. Optical detectors for the far red, such as photocathodes, have cutoffs in or near this region. The S-1 photocathode is fairly flat here, but its quantum efficiency is miserable. Silicon photodiodes and thick CCDs are available, but their sensitivities are also relatively low and falling in this area. Perhaps these difficulties will be overcome with detector or filter developments; as we have argued, the z-window is a superb one in which to observe.

We have ignored aerosols in the MODTRAN models because they produce slowly changing transmission across the bandpass regions. One must remember that total aerosol optical depth in the visible is only a few hundredths of a magnitude per airmass under photometric conditions, and decreases roughly with the reciprocal of the wavelength. Normally, therefore, aerosol extinction is small in the near IR, and practically negligible in the thermal IR. The variation across a photometric passband, which is what contributes to the Forbes effect, is even smaller. The exclusion of aerosol effects seems well justified.

However, since the scattering properties of aerosols can be complicated in the mid-IR (McCartney, 1976), we note the need for more work to be done in this area, especially for the aerosols produced in volcanic eruptions, such as sulfuric acid. Work by Hummel et al. (1988) indicates that fresh volcanic products can produce scattering increases of up to two orders of magnitude in the range 1 -- 20 microns. However, this effect can only be significant for a few weeks after a major volcanic eruption. Even if the volcanic aerosol optical depth were 0.1 at V, the mean aerosol extinction at J would be about 0.04 mag/airmass, and its variation across our proposed J passband would be a few millimagnitudes per airmass. The effects would be still smaller at longer wavelengths.

In addition to atmospheric absorptions, we must also consider the effects of both thermal and nonthermal atmospheric emissions. The latter are especially important for high-geomagnetic-latitude observatory sites. The nonthermal emissions are classified as airglow, which is important from the visible to the intermediate IR, peaks throughout the H-passband, and varies slowly; and aurora, which is capable of large-scale and high-frequency fluctuations. Both phenomena are important in the non-thermal infrared, i.e., out to the K- and L-bandpass regions.

The airglow is a primary concern for photometry that is carried out in the stare mode of imaging detectors, as the slow spatial variations can affect different portions of an image differently, and the temporal variations make sky subtraction difficult. The spatial variations are more serious in wide-angle images. These slow variations are fairly well chopped out in point-detector photometry, where only small angular variations are important. The aurora, on the other hand, can have a major impact on photometry done with chopping systems, because of its high-frequency components (to kHz); and its finer spatial structure makes it more of a problem for imaging work. Both effects are much more serious for observers near the auroral zones.

The principal airglow features are the Meinel OH bands, at 1.00--1.03, 1.02--1.06, 1.08--1.12, 1.14--1.18, 1.20--1.26, 1.29--1.34, 1.38--1.44, 1.42--1.50, 1.51--1.56, 1.58--1.66, 1.67--1.75, 1.76--1.85, 1.87--1.97, 2.00--2.10, 2.15--2.27, 2.80--3.04, 2.94--3.19, 3.09--3.36, 3.32--3.54, 3.35--3.74, 3.55--3.97, 3.78--4.23, 4.04--4.54, and 4.36--4.92 m (Chamberlain 1961, Harrison 1969). Note the considerable overlap between successive bands. The peak emission occurs at about 1.6 -- 1.7 m, with a lesser peak at 2.1 -- 2.2 m (Noxon, Harrison, and Jones 1959). Twilight enhancements in the Meinel bands have been observed also (Berthier, cited in Chamberlain, p. 377). Like starlight, the emissions are best seen in the windows, where atmospheric attenuation is least. Clearly the major impact of the OH bands is in the H and K windows, but none of the near-IR windows fully escapes them. Chamberlain notes that beyond 2.5 m the OH is overwhelmed by thermal emission, but that the result is hardly blackbody. Strong emission features have been seen also at 4.3, 6.3, 9.6, and 15 m, peaking between 7 and 8 m.

More recent work by Ramsay et al. (1992) provides detailed OH emission intensities and spectra for the band features in the J, H, and K atmospheric windows. Their Figure 3 shows the steep rise in thermal emission beginning at about 2.1 m, and already dominating by 2.3 m.

In aurorae, the Meinel N₂+ bands predominate at 1.42 -- 1.63 m (Harrison and Vallance Jones 1959), but strong N₁ and N₂+ structures have been seen at 1.04 and 1.11 m, respectively, and other features such as an O₂ band emission at 1.27 m have been observed too (see Ramsay et al. 1992, Figure 1). Finally, O₂ infrared atmospheric band emission is expected at 1.47 m also. Thus these features affect both J and H windows.

Measured values of the surface brightness of the OH features at 1.6 m have been reported of 100--400 kR, while aurorae have been reported to be even brighter in the J and H windows (Allen 1973). Consequently, one can conclude that it is most difficult to tailor any optimum passbands to minimize airglow and auroral effects, although the latter are less uniformly spread across the windows. Ramsay et al. (1992) and Hodapp et al. (1992) report variations of OH emission on time scales of minutes to hours. Ramsay et al. (1992) performed a two-night experiment with a near-infrared spectrometer and found singly-periodic variations of order 10 minutes with amplitudes of 10% (on one night) as well as multiple periodicities and secular changes showing variation of nearly 50% over a time scale of a few hours (on another night). They also found no evidence of spatial variation along their 30 arcsec slit. Therefore, chopping may be a partial remedy against airglow; it is not clear what can be done against aurorae, except to remove the features before detection. An ingenious scheme devised by T. Maihara (see Iwamuro et al. 1992), brought to our attention by A. Tokunaga, involves the spectral masking of the OH features in a spectrometer. Such a scheme may be even more broadly applicable, but may create some transformation difficulties with some types of objects, such as OH-emission sources.

The suggested passbands may improve S/N in at least some passbands by removing spectral regions of little transparency but large thermal emission. We note that thermal emission from the lower atmosphere is about twice as intense at the long-wavelength edge of L than at its short-wavelength edge, as this band lies in the Wien tail of the Planck function for typical atmospheric temperatures. One might suppose that a substantial improvement in signal/noise ratio could be obtained by trimming L at the long-wavelength side. If we approximate this tail locally by a triangle, we see that its area is proportional to the square of its base (that is, cutting back on the long-wavelength side reduces the height by the same factor as the base), so that reducing the width of L by some factor to reduce the photon noise from the sky reduces the signal strength by the same factor.

If the sky noise is due primarily to emissivity fluctuations rather than to photon noise, a small advantage could be gained by cutting back on the long side of L. However, the gain cannot exceed the factor of 2 mentioned above, and is likely to be much less. We have already removed most of this sky noise by excluding the long-wavelength portion of the window, where water absorption (and hence emissivity) is relatively large. Therefore, it does not seem that further reduction is useful; we recommend the L band described in Table 3. Similar comments apply to the K window, where, however, the thermal emission level is much less. Our recommended passband has a red edge no redder than the recent "short" filter passbands of Skrutskie and of Wainscoat and Cowie, but a blue edge red enough to avoid the blue edge of the atmospheric window. Substantial background improvement has been reported with the use of the Wainscoat-Cowie K' filter, so even more improvement can be expected from the present suggested passband.

Finally, in many telescopes the background emission is dominated by the telescope. If photon noise from the telescope itself is the limitation, reducing the width of a passband by a factor of 2 reduces the photon noise from the telescope by the square root of 2. However, the reductions in passband width we are recommending do not produce such large reductions in stellar signals, because we have primarily removed spectral regions of low atmospheric transmission. Rough estimates indicate that our passbands should give signal/noise ratios only 0.1 or 0.2 mag worse than the original Johnson bands, if the photon noise from the telescope is the main noise source. If sky noise is the main noise source, we should do somewhat better.

The relative importance of telescope noise and sky noise depends on local circumstances, such as the amount of water vapor in the air, the cleanliness of the telescope, and baffling in the instrument. For example, Hodapp et al. (1992) cite a contribution from the telescope of 14.5 mag/(arcsec)² in Wainscoat and Cowie's K'-band, and 14.9 mag/(arcsec)² from the atmosphere, on a particular night. The use of superior filters can therefore help, but attention to telescope cleaning and good photometer design is still required for success in the thermal infrared.

A closely related but still somewhat different question is the overall S/N performance of the proposed passbands. While improved accuracy and precision of infrared photometry have been our primary concerns, we recognize the need to maintain or improve S/N, especially in the thermal IR, where detector sensitivity is low and the background is high. Accordingly, we plan to calculate the expected S/N under a variety of conditions, and to put the simulations to a test with filter field trials over the next year. At this writing, Barr Associates, Inc., are fabricating the intermediate-passband filters and report excellent results thus far. We are looking forward to field-testing these filters.

When we began to collect actual filter profiles from various observatories, we were struck by the wide variations among the filters used at different places (cf. Fig. 25). Even more startling, in the face of this variation, was the insistence on the part of several astronomers that they were using "the" standard passbands. Clearly, there is no standard set of filters in use; nor is any filter set currently in use close to the original Johnson set.

This situation is made more confusing by the widespread use of Johnson's passband notation for bands that differ widely from each other, as well as from Johnson's original profiles. No doubt this has contributed to the difficulty of reproducing standards between observatories. Using identical names for widely divergent passbands is misleading. We urge observers to publish the transmission curves of filters they use, and to refrain from using Johnson's names for passbands that are appreciably different from his.

We hope our proposed filter specifications will introduce some standardization into this chaotic situation. In any case, we believe it is inappropriate to continue using Johnson's names for passbands that are quite different from his. Since it is Commission 25's prerogative to recommend, and the IAU's to accept, recommendations for nomenclature of these passbands, we refrain at present from suggesting names for them. However, to insure that there is no confusion with any existing passbands, we prefix the filter designations in Table 3 with "i" for "improved". Earlier versions of Table 3 which have been circulated, without this notation change, should be discarded.

We thank Bob Kurucz for providing his model-atmosphere fluxes; Jim Chetwynd at AFGL for recommending that we use MODTRAN rather than LOWTRAN 7; P. Zvengrowski and K. Salkauskas, of the Mathematics Department of the University of Calgary, for helpful discussions with ATY of Hilbert space and functional analysis; Ted Ziajka, and Doug Phillips, of the Academic Computer Services of the University of Calgary, for providing ATY with an account on the IBM RS6000, and for recommending the NCAR Graphics package (and instruction in its use), respectively; Barbara McArthur, of the University of Texas, for providing much assistance with the use of .I GaussFit , which was used to model the airmass dependence of extinction; A.W. Harrison and L. Cogger of the Physics and Astronomy Department of the University of Calgary for helpful discussions with EFM on atmospheric emissions; and members of the Working Group on Infrared Extinction and Standardization, particularly Ian McLean for commissioning the WG. Special thanks are due members Bob Kurucz for providing his stellar-atmosphere models; Martin Cohen, Ian Glass, and Alan Tokunaga for forwarding their filter profiles for use in the trials; and D.A. Allen, R. Angione, M.S. Bessell, T.A. Clark, J.H. Elias, R.F. Garrison, B. Jones, A. Moorwood, M. Mountain, G. Rieke, S.J. Schiller, D. Simons, M. Skrutskie, C. Sterken, R.I. Thompson and R.F. Wing for useful discussions. Roger Heatley of Barr Associates, Inc., and Mike Larro of OCLI provided much helpful information about interference filters. Sun Kwok assisted with computer hardware support at the University of Calgary. This project was supported through grants from the University of Calgary Research Grants Committee and the Natural Sciences and Research Council of Canada to EFM, for which we express gratitude. We also thank the Astronomy Department at San Diego State University, the Center for Astrophysics and Space Science of the University of California at San Diego, and the Canada-France-Hawaii Telescope Corporation, Waimea, Hawaii, for hospitality to and use of facilities by EFM, and the European Southern Observatory for their support for ATY.

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