A laboratory experiment was devised to measure transmission at fine spectral resolution through thick, high-quality samples of CO2 ice over an extended wavelength range. The absorption coefficient throughout the ultraviolet and near-infrared spectral ranges 0.174–1.8 μm (5555–57,470 cm−1 in wave number) is presented here. CO2 ice samples were grown at a temperature of 150 K, typical of the Martian polar caps. The path length of the samples varied from 1.6 to 107.5 mm, allowing the measurement of absorption from <0.1 to 4000 m−1. The experiment used both a grating monochromator (with spectral resolution 0.1–0.3 nm) and a Fourier transform spectrometer (with an effective resolution of <1.0 cm−1). The transmission data for five thicknesses are used to estimate both the scattering losses for each sample and the absorption coefficient at each wavelength. The uncertainty in the most transparent wavelength regions (<10 m−1) is due to scattering extinction. Measurement noise and data scatter produce significant uncertainty only where absorption coefficients exceed 1000 m−1. Between 1.0 and 1.8 μm there are several weak to moderate absorption lines. Only an upper limit to the absorption can be determined in many places; e.g., the absorption from ∼0.25 to 1.0 μm is below the detection limit. The estimated visible absorption, ∼10–2 m−1, is a factor of 1000 smaller than the values reported by Egan and Spagnolo, which have been used previously to compute albedos of CO2 snow. The new results should be useful for studies of the seasonal polar caps of Mars.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
 Carbon dioxide is a significant component of the atmospheres and near-surface regions of the terrestrial planets, and exists in smaller quantities in the atmospheres and surfaces of some of the icy bodies in the outer solar system. Carbon dioxide ice is the major condensate in the seasonal polar caps on Mars, identified by its infrared absorptions in astronomical spectra [Larson and Fink, 1972] and spacecraft spectra [Herr and Pimentel, 1969; Pimentel et al., 1974]. Condensed CO2 also persists in the residual south polar cap throughout the southern summer [Paige et al., 1990; Kieffer, 1979; Bibring et al., 2004]. The narrow near-infrared absorption lines of solid CO2 have now been seen for the first time in spacecraft spectra returned by the Mars Express mission [Bibring et al., 2004, 2005] (unpublished reports from the SPICAM instrument [Bertaux et al., 2005]). Solid CO2 has also been detected or inferred to occur with an abundance of a few percent on the surface of comets [Delsemme, 1988] and has been spectrally identified through its near-infrared lines on the Uranian satellite Ariel [Grundy et al., 2003], and the large satellite of Neptune, Triton [Cruikshank et al., 1993; Quirico et al., 1999]. However, at such small abundances, CO2 ice does not affect the spectra of these bodies except in the strongest absorption bands.
 The optical constants of CO2 ice are needed for radiative transfer models of surface deposits or clouds that contain CO2 ice. The optical constants are the real and imaginary parts of the complex index of refraction ñ = n + ik which is a function of wavelength, λ. The imaginary part of the index of refraction is related to the Lambert absorption coefficient α (units of inverse length) by the expression α = 4πk/λ. CO2 ice absorbs strongly only in a few narrow bands in the near infrared and has very weak absorption in the spectral intervals between these bands. If there are abundant particles of solid CO2 more than a few micrometers in size, as in the Martian seasonal polar caps, the solar reflectivity and thermal emissivity of the surface becomes strongly dependent on grain size in the weak absorption regions between the strong bands. This paper presents absorption measurements for solid CO2 in the ultraviolet (UV) to near-infrared wavelengths 0.174–1.8 μm. Measurements using this same equipment and methods in the spectral range 1.8–333 μm have been reported by Hansen [1997a], hereafter referred to as Paper 1. Preliminary reductions of the ultraviolet to near-infrared data were also presented in graphical form by Hansen [1997b].
Warren  reviewed the previous measurements of the optical constants of CO2 ice over all ranges of absorption and wavelength. More recent measurements of thin films and thick samples of pure CO2 ice in the spectral region discussed here have been made by Quirico and Schmitt  from 1 to 5 μm at 21 K (thin film) and 180 K (thick sample). The only earlier measurements in the moderate- and weakly absorbing wavelengths of the ultraviolet to near-infrared with samples more than a millimeter thick were made by Egan and Spagnolo  (0.3–1.0 μm). Egan and Spagnolo used a 10-mm thick sample of commercial dry ice at 197 K, clarified by the addition of water and oil, to measure the absorption and real refractive index at visible wavelengths. Fink and Sill  also measured the strong, narrow absorption line (maximum absorption 1300 m−1) at 6971 cm−1 (1.4345 μm) in a thin film of CO2. The results of Egan and Spagnolo and Fink and Sill were incorporated in Warren's compilation. Larson and Fink , Fink and Sill , and Calvin  also made spectral measurements of CO2 frosts, which revealed the position and relative strength of many narrow lines in the near infrared, including a quartet between 6000 and 6500 cm−1 (1.54–1.67 μm) and a doublet near 8200 cm−1 (1.21 μm). The strongest of these lines are also seen in the thin film measurement of Quirico and Schmitt . The line structure in the CO2 solid in this spectral range is mostly in a one-to-one relationship to the well known overtone transitions of CO2 gas. The assignment of the strongest lines is given in Table IX in Quirico and Schmitt.
 The measurements described here were undertaken to obtain more accurate absorption coefficients of pure CO2 ice in the weakly absorbing wavelength regions by means of transmission spectroscopy on millimeter- to centimeter-thick samples of clear ice. This was done using five sample thicknesses between 1.6 and 107.5 mm, and employing both a grating monochromator and a Fourier Transform Spectrometer (FTS). The important advantages of this data over earlier data are (1) the absorption measured from a sample more than 10 cm thick, which reveals weak features not readily visible in thinner samples, but visible in coarse-grained frosts, and (2) operation at the finest possible spectral resolution to access the natural line widths and strengths of the many narrow absorption lines. This paper will provide only a brief summary of the experimental techniques and setup, and data reduction processes used to derive the new absorption coefficients for CO2 ice, since these subjects are covered in detail by Paper 1. The only experimental details found here relate to the use of the monochromator, the data from which was not used for the longer wavelengths. A more detailed description of the equipment and the experimental procedures is given by Hansen . To derive the real and imaginary indices of refraction needed for many models, spectral data from thin-film samples is needed in addition to the absorption measurements here. That analysis is outside the scope of this paper, and must be addressed later.
Section 2 describes the sample chamber, the spectrometers, the techniques for measuring and calibrating the spectral transmission, and the properties of the CO2 ice samples. Section 3 details the analysis procedures used to extract absorption coefficients from transmission measurements. Section 4 presents the absorption coefficients and their uncertainties over the full wavelength range, including the joining of wavelength segments and with previous data.
2. Experimental Apparatus and Methods
2.1. Sample Chamber, Temperature Control, and Optical Setup
 The sample chamber was made of fused quartz, so the sample could be easily viewed, and a nylon plug allowed the attachment of the chamber to the copper refrigerator tip. Cooling was supplied to the top of the sample and to the window frames through copper spacers. The windows were mounted on tubes which could be sealed into five different positions against the spacers. The aperture of the windows was 12.7 mm in diameter. A cross-section drawing of the chamber is shown in Figure 1 of Paper 1. The beam of the monochromator and FTS was focused near the middle of the chamber, so that little light was lost due to vignetting by the windows. The path lengths available in this chamber were 1.6, 4.6, 13.8, 41.3, and 107.5 mm. Paper 1 describes the constraints for the minimum and maximum path lengths and how they were measured, the temperature sensors and radiation shield. All the measurements shown here were made using calcium fluoride (CaF2) chamber windows, except for a handful of ultraviolet measurements that used fused quartz or sapphire windows. The experimental transmission of these few samples was “converted” to that for CaF2 windows, using the known real indices of refraction for these materials. The vacuum, refrigeration, and temperature control systems are described in Paper 1. The vacuum system was modified by a tube used to evacuate the monochromator when it was in use. The CO2 supply tubing during most of the monochromator measurements with the 41.3-mm path was made of Teflon, and enough atmospheric H2O diffused through it during the typical sample growth period of 30 hours to coat the windows with a layer of H2O ice. This caused problems of excessive scattering extinction in most of the samples. The best samples transmitted 70–80% (similar to most samples using copper tubing in the FTS experiment), and other measurements were normalized to that level for analysis.
 The optical alignment of the FTS system is described in Paper 1 and shown in Figure 2 of Paper 1. Carbon dioxide ice is not birefringent and its optical properties are not sensitive to the polarization of incident light [Warren, 1986, and references therein], so variable polarization introduced by the optical components was not considered.
2.2. Fourier Transform Spectrometer
 The general properties and operation of the FTS are described in Paper 1. The FTS measurements in the spectral region considered here used a CaF2 beamsplitter, a Tungsten or Globar source, and a photovoltaic indium antimonide (InSb) detector. The FTS measurements with the CaF2 beamsplitter contained data from about 1850–10000 cm−1 (1.0–5.4 μm), but the only data processed here was in the range 5400–10000 cm−1 (1.0–1.85 μm), just to provide a small overlap with the earlier analysis (Paper 1). These spectra were calculated using Norton-Beer Medium apodization [Norton and Beer, 1976].
Appendix A contains a detailed description of the processing of the near-infrared FTS spectra, including the removal of alias spectra, short- and long-period fringes, and other artifacts, all of which had amplitudes of 10% or more of the peak signal. After removal of the alias signal, the spectra were found to have signal down to about 1.1 μm (9000 cm−1) with the Tungsten source, and only to 1.25 μm (8000 cm−1) with the globar source, even though the free spectral range of the measurement extended to 0.6 μm. This appendix also contains a description of the wave number calibration (with an accuracy of better than 0.1 cm−1 in regions of high signal), and of the spectral resolution (approximately 1 cm−1 at these wave numbers).
2.3. Grating Monochromator
Appendix B contains a detailed description of the operation and properties of the monochromator. This includes a discussion of sources, detectors, and amplifiers. From 0.3 μm through the near infrared, spectral resolutions of 0.1–0.3 nm were used, while the shortwave ultraviolet was measured at 0.5–3.0 nm resolution, depending on the detector used. The appendix also describes in detail the wavelength calibration method, which results in a wavelength calibration accurate to about 0.03 nm. It also details the various methods (normal, free-running, and single-step) used to measure long, high resolution infrared spectra.
2.4. Transmission Spectra and CO2 Ice Samples
 The measurement of transmission spectra from blank, sample, and reference paths is described in detail in Paper 1. After the CO2/blank ratios were calculated, further processing for the FTS spectra was performed as described in Appendix A. For the monochromator data, the spectral ratios were put on a calibrated wavelength scale, and for wavelengths >1.4 μm, fringes were removed in a similar way as described for the FTS data, except that the sine function was sampled at the wavelengths and using the instrument function of the monochromator. Fringes could not be effectively removed from any of the spectra that had coarse and variable wavelength sampling, except in limited regions where the sampling was fine enough to resolve the fringes. Then the available data for each spectral order and sample thickness were combined, using the free-running spectra to define the general level and shape, but scaled to the typically highest transmission of the experiment (about 0.80–0.85). All data sets were normalized locally to this level, and a smooth line was traced through the data in a manner similar to that described in Paper 1 for the FTS data.
 Large samples of clear CO2 ice were grown slowly (30–50 hours) in an environment where the gas pressure was in equilibrium with the ice. A detailed discussion of the samples and their quality is given in Paper 1. All samples used a refrigerator temperature between 145 and 150 K, except for some of the ultraviolet samples that were measured at higher temperatures (up to ∼160 K), needed to drive off ultraviolet-absorbing condensates that formed on the outside of the chamber windows. Paper 1 describes a pressure oscillation in the 41.3-mm samples with a period of ∼25 min, which produced 5% oscillations in the sample transmission. This oscillation in time became an oscillation in wavelength with the scanning monochromator. For scans shorter than 2 hours, 6–8 measurements could be used to define an envelope, or they could be averaged to remove most of the oscillation. This technique was used at wavelengths <500 nm. For longer infrared scans, the alternate sample and reference measurements were abandoned to make quick open-loop scans of sample and reference sequentially as described previously. These fast scans defined the overall level of the spectrum, while slower stepped spectra provided better wavelength certainty.
2.5. Preparing and Combining Spectral Data
 The spectral data obtained in this wavelength range are depicted in Figure 1. Data from all five available path lengths were obtained for 1.1–1.8 μm, although the 41.3-mm samples were measured only with the monochromator, where ∼0.3 nm was the finest resolution measured over this range. The 107.5-mm samples were measured using both instruments, the monochromator at 0.1-nm resolution to ∼1.605 μm, and the FTS from ∼1.3 (8000 cm−1) to >1.8 μm (5555 cm−1), although the quality of the FTS data is quite poor below ∼1.4 μm (7150 cm−1). Since the instrumental function is quite different between these methods, comparison of the monochromator and FTS measurements revealed much about the natural line widths of the near infrared lines. The spectral region between 0.3 and 1.1 μm exhibited very little or no absorption. Only three weak narrow lines between 1.0 and 1.1 μm and a possible very weak ultraviolet roll-off appeared in the two longest paths (41.3 and 107.5 mm) in this range. These features were too weak to be reliably seen through thinner samples. In the ultraviolet, only the four outer path lengths were measured as a compromise due to the lack of available time.
 The smoothed FTS infrared measurements all exhibited slopes or curves across the 1.1–1.8 μm range. It was judged that the multiple thickness analysis would work better with the spectra “flattened” over this range. The monochromator averages were assembled with scaling to a selected high transmission level at each wavelength, and so were already very level. The absorption between the narrow lines and features below 1.4 μm was not measurable, and beyond that, was not measurable in the two thinnest samples between the narrow lines across most of the range, so a level spectrum is natural. The leveled spectra were scaled to the average transmission of the original spectra, except for the 107.5-mm path spectra, which was scaled by ∼0.81 so it could be combined with the monochromator measurements for that path length. The original data and leveled and scaled FTS data are shown in Figure 2.
 The monochromator and FTS measurements of the 107.5-mm sample overlapped between 1.25 and 1.605 μm. For this analysis, a combined spectrum from the two data sets was needed. The monochromator spectra were measured at a finest resolution of 0.1 nm, comparable to or better than the corresponding resolution of the FTS (especially if the degradation due to finite field of view is considered). When comparing with the spectra from all path lengths, the 107.5-mm FTS data were found to have severely distorted spectral lines below 1.4 μm, so the monochromator data were used exclusively in this region. Beyond this, the two spectra were combined in various ratios at various wavelengths guided by 41.3-mm spectrum when necessary. Between 1.4 and 1.5 μm, the combined data consisted of 50–100% monochromator data in the absorption lines and typically 100% FTS data in the weakly absorbing continuum regions. From 1.5 to 1.6 μm, the combined spectrum was 50–100% FTS data in the absorption lines and close to 100% FTS data in the continuum regions. The spectrum between 1.52 and 1.57 μm is shown in Figure 3, illustrating the two data sets and the adopted values for this region.
 To enable the 41.3-mm measurements to be compared to the other thicknesses measured at finer resolutions, a process was developed to “sharpen” the 41.3-mm spectrum in 16 selected narrow lines (<0.3–0.4 nm wide) where the data were found to disagree. The process started with a line profile from a higher resolution measurement and an assumed instrument function for the monochromator with 0.3–0.4 nm resolution. A minimization was used to adjust the starting spectrum to match the measured 41.3-mm spectrum using the given instrument function. For each line, a resolved spectrum was calculated for both 0.3-nm and 0.4-nm resolutions. One of these models was chosen in each wavelength interval, based on comparisons with the finer-resolution data from other path lengths. This process is illustrated in Figure 4.
3. Determining Absorption Coefficients and Their Uncertainty
 The calculation of absorption coefficients α and their uncertainty is treated in detail in Paper 1. In the absence of scattering, the absorption can be determined by the least squares solution of a set of linear equations in α and the logarithm of transmission. The expected maximum transmission Tmax of the CO2/blank ratios can be calculated (Paper 1, equation (2)) using the known refractive indices of the windows and the real index of CO2 ice, while ignoring the CO2 absorption. This is a function with weak wavelength dependence that exceeds 1.0 because the reflection loss at the CO2-window interface is less than that for a vacuum-window interface. The samples rarely exhibited Tmax > 1, indicating that the experimental transmission had been considerably reduced by scattering. In fact, if one assumes no scattering for the thickest sample, the calculated absorption will indicate greater and greater scattering for successively shorter path lengths. The level of maximum transmission reduced by scattering, lying between Tmax and the highest parts of the spectra is termed Tscatt, and this value must be included in the equations as a variable. One can now calculate a least squares solution for a set of consistent Tscatt's for the path lengths available. When Tscatt for one thickness is changed, a new least squares absorption coefficient and a set of Tscatt's for the other thicknesses are generated. Using this method, a family of self-consistent solutions can be arrived at, with a wide range of Tscatt's for the longest path (not all the way up to Tmax, since it is not reasonable for the thickest sample to have significantly less scattering than the thinner samples), and narrower ranges for shorter paths. This range of variation gives a range of absorption coefficients which can be construed as upper an lower limits (in the final analysis, the minimum α is set to 0 whenever the lower limit is below 10−3 m−1). The data are divided into several spectral segments in which Tscatt is represented by second-order polynomials in wavelength, and constrained to lie below Tmax.
 The coefficients of these polynomials, plus the absorption coefficients α(ν) for the segment, are adjusted to minimize the variance of the fit (χ2) between the model transmission mi and the measurement Mi. In the spectral region considered here, CO2 ice is very transparent, and requires, for models evenly spaced in log α space, a finely detailed logarithmic spacing of Tscatt in transmission space. For this reason, the offset of the Tscatt polynomial for the thickest sample was not allowed to vary. Also, for the 5 segments from 5555 to 9000 cm−1 (1.1–1.8 μm) the Tscatt's for the thickest sample were constrained to be continuous by reducing the degrees of freedom in the polynomials. In the ultraviolet region, as discussed below, it was not possible to obtain a good result with quadratic polynomials because of a power law increase of scattering with wavelength. Here, high-order polynomial fits were used, with the only free parameters being the Tscatt level for other than the thickest sample. Other “costs” were used in the minimizations, including for large slope and/or curvature of the Tscatt polynomials. Since the gradients of the cost function could be calculated, a gradient-search method was used. A family of valid solutions is found starting with different Tscatt levels, which have nearly equal minimum χ2.
 Starting points were typically determined by selecting a constant Tscatt for the longest path length sample, deriving the required absorption coefficient at wavelengths where the sample transmission is >0, then deriving the required Tscatt in that wave number range for the next shorter path length. This Tscatt is then fitted with a second-order polynomial. This process is continued down to the thinnest sample, yielding a second-order Tscatt polynomial for each thickness. A trial absorption coefficient is then calculated for each of the path lengths using the initial Tscatt functions. These agreed with each other as well as the second-order fits allowed. The initial absorption coefficient was derived from the thickest sample estimate; narrow regions of higher absorption were then replaced with data from shorter path lengths. A set of eleven Tscatt levels was designed to provide absorption coefficients in the most transparent wavelengths that varied linearly over 3–4 orders of magnitude around the adopted value (the uncertainty in Tscatt is by far the largest source of uncertainty in most of the UV to near-IR wavelengths). The Tscatt for the thickest sample is varied to about half the distance to Tmax, at which level it is comparable to or larger than the Tscatt of the sample with the highest measured transmission.
 The uncertainty in absorption coefficient due to scattering uncertainty was significant only for α < 10 m−1. In regions of higher absorption, other sources of error, such as measurement noise or sample thickness uncertainty, were much larger. Uncertainties from noise, and from measurement scatter due to uncertain thickness or other effects, were quantified. Even when sample thicknesses were modified to get the best mutual fit between all the sample spectra, there remained a significant disagreement in the strength of many of the narrow absorption lines (up to ±10%). This data scatter uncertainty is weighted by spectral signal-to-noise, which results in discounting measurements near 0 or 100% transmission. This uncertainty is larger than any others at the tops of many lines and in a few other places like the UV edge near 200 nm. The measurement noise is 0.1–0.2% in the infrared, except for FTS measurements >7000 cm−1 (<1.4 μm), where the noise level increases to over 0.5%. The UV noise varies from 0.5 to 2.0%, with the maximum near 190–200 nm. The noise level is translated to absorption, and the minimum noise envelope (from the sample which best measures each region) is determined. This noise-uncertainty dominates where the absorption is large and the data scatter is small.
4. Absorption Coefficients
4.1. Near-Infrared Measurements With Five Thicknesses (1.1–1.8 μm)
 The smoothed, flattened spectra in this region are displayed in Figure 5. Included here are the sharpened grating spectra for the 41.3-mm thickness described in section 2, and the combined FTS and grating measurement for the 107.5-mm thickness also described in section 2. The other three thicknesses are from FTS measurements. The absorption of solid CO2 across most of this wavelength region is very small, and is defined by the measurements of the two largest thicknesses, while the definition of four strong lines required spectra from the thinner samples.
 The number of spectral points in the combined data was over 10,000, and it was necessary to break the spectra into five segments in order to complete the minimization, each part a separate process for all five spectra and a set of Tscatt transmission functions. The minimizations were designed so that the Tscatt level for the 107.5-mm sample was continuous over the five segments, this so that the derived absorption coefficient would be nearly continuous (in practice, there remained small discontinuities in the absorption data that were smoothly connected for the adopted absorption coefficient only). The free parameters in the minimization were the polynomial coefficients for quadratic Tscatt functions (constrained on the thickest sample to preserve level and continuity) and the logarithm of the absorption coefficient (this prevented negative absorption coefficients). The minimization was initialized at each level by simple scaling of the previous level, but the starting level (smallest absorption) had to be worked on at some length to get the best results.
 Eleven starting Tscatt levels were used in this region. These are illustrated in Figure 6, which shows the first, fifth, and 11th levels above the 107.5-mm spectrum and the calculated Tmax. The maximum Tscatt level is only halfway between the spectrum and Tmax, but this was considered sufficient, since it implies already 2–3 times more scattering for the 107.5-mm sample than for the 13.8-mm sample. The absorption coefficients calculated using these Tscatt levels give the maximum and minimum α due to Tscatt uncertainty. The adopted absorption is from Tscatt number 5, which lines up well with the previous longwave FTS data near 1.8 μm [Hansen, 1997b] (see Figure 7).
 The other error sources (data scatter and measurement noise) were each measured relative to the adopted absorption coefficients, weighted according to the measurement signal-to-noise, then added in quadrature. The resulting uncertainties are larger than the Tscatt uncertainty in most of the strongly absorbing regions, with the noise varying smoothly while the scatter is much larger in certain places. The three sources of error are illustrated in Figure 7, shown as minimum and maximum uncertainty on the same scale as the adopted absorption and separately as a fractional error (e.g., [maximum - mean]/mean) in the lower panel that illustrates the level of error in the narrow lines, which cannot be easily seen in the upper panel. Where the minimum value was less than 10−3 m−1, it was set to zero (and the fractional error to one).
4.2. Near-Infrared Measurements With Two Thicknesses (1.0–1.1 μm)
 The spectra from the 107.5-mm and 41.3-mm thicknesses in this region are shown in Figure 8. In this region only three narrow weak lines were found, all with strengths of less than 2% for the 41.3-mm sample. None of these features would likely have been resolved in thinner sample spectra. The minimizations in this region were designed so that the Tscatt level for the 107.5-mm sample was set to be equal to the levels on the adjoining end of the previous 1.1–1.8 μm segment. The free parameters in the minimization were the polynomial coefficients for quadratic Tscatt functions (constrained for the thickest sample to preserve level) and the logarithm of the absorption coefficient. The absorption coefficient was initialized using the 107.5-mm spectrum.
 Eleven starting Tscatt levels were used in this region. These are illustrated in Figure 9, which shows the first, fifth, and 11th levels above the 107.5-mm spectrum and the calculated Tmax. The maximum Tscatt level is only halfway between the spectrum and Tmax, following the previous segment. The absorption coefficients calculated using these Tscatt levels give the maximum and minimum due to Tscatt uncertainty. The adopted absorption is again from Tscatt number 5, which lines up well with the previous data near 1.1 μm. The uncertainties from data scatter and measurement noise are comparable to the Tscatt uncertainties only in the lower limit absorption near the tops of the absorption lines. The absorption coefficient and its uncertainties are shown in Figure 10.
4.3. Ultraviolet Measurements With Four Thicknesses (0.174–0.3 μm)
 The measurements in the visible to ultraviolet showed smooth reductions in transmission shortward of 0.5 μm. Originally this was interpreted as absorption [Hansen, 1997b], but careful inspection of the data argues otherwise. Figure 11 shows the spectrum of the two thickest samples between the UV and 0.5 μm (nothing but flat, featureless spectra were measured between 0.5 and 1.0 μm). The 41.3-mm spectrum was measured from samples with greater visible window scattering and water contamination. It shows a much greater UV roll-off than the 107.5-mm spectrum measured from a much clearer sample. Assuming that the thickest clean sample represents only absorption (level Tscatt in Figure 11), then the corresponding Tscatt for the 41.3-mm spectrum must be 20% lower at 0.2 μm than at 0.5 μm, verifying that the observed roll-off in that spectrum is all, or almost all, scattering extinction. Given the probable sub-micron nature of the scattering defects on the window-CO2 interfaces and within the solid ice, it is reasonable to assume that all the weak reductions in transmission toward the UV could be caused by scattering rather than absorption.
 The spectra from all four thicknesses measured in the first order (0.16–0.31 μm) are displayed in Figure 12a. They show differing amounts of spectral roll-off between 0.3 μm and the sharp UV edge near 0.18 μm. This behavior can be approximately modeled by scaled extinction varying as λ−4 (shown in Figure 12b), consistent with scattering in the Rayleigh limit by objects much smaller than the wavelength. Three of the spectra are normalized and plotted in Figure 13, where the average reduction is shown to be about 4% (dashed line). This plot illustrates the strategy for choosing Tscatt: The 4.6-mm spectrum was adjusted to have the same slope as the 107.5 mm spectrum (by raising it to a power) and then scaled to the 107.5 mm spectrum. This curve was used to estimate a high-order curve for Tscatt (107.5 mm). The resulting curve separates from the 107.5-mm spectrum at about 0.24 μm, implying weak absorption starting at that wavelength, and getting much stronger below 0.2 μm. The 107.5-mm spectrum deviates from the λ−4 fit in Figure 12b in the same way. Using the absorption coefficients from this calculation, the Tscatt's for the other three thicknesses were estimated. In all cases, because of the spectral curvature and weak absorption, the Tscatt curves were much higher order than quadratic, implying that the minimization procedure used in the infrared had to be modified. The Tscatt's were shifted up and down, accordingly, for the initial condition, and only the absorption coefficients were adjusted in the minimization. The thicknesses of the two thinnest spectra were increased to ∼2.0 and >6 mm to get better agreement with each other and the thicker spectra where they overlapped in the highly absorbing regions.
 There were eleven logarithmically spaced starting Tscatt levels used in this region as in the infrared. The Tscatt levels were typically high-order polynomials or other functions that provided an acceptable match to the spectrum at the lowest Tscatt level (providing the lowest absorption coefficient). These are illustrated in Figure 14, which shows the first, fifth, 9th, and 11th levels above the 107.5-mm spectrum and the calculated Tmax. The maximum Tscatt level is well below Tmax on the two thickest spectra, but it was near to or even greater than Tmax on the other thicknesses. A close-up of a portion of the 4.6-mm spectrum is shown in Figure 15, along with some Tscatt levels and Tmax. Since the noise level of this spectrum is 0.5–1%, the spectrum and most of the Tscatt levels are within the noise level of Tmax. However, the top two Tscatt's are well above Tmax for more than 20 nm, so these models were excluded from the subsequent error analysis. The absorption coefficients calculated using these Tscatt levels give the maximum and minimum due to Tscatt uncertainty. The adopted absorption is from Tscatt number 5, which agrees well with the previous data near 1 μm (see Figure 7).
 The uncertainties due to data scatter and measurement noise are comparable to or smaller than the Tscatt uncertainty in the weakly absorbing regions above 0.2 μm, while all three sources are comparable between 0.19 and 0.2 μm, and the noise uncertainty dominates below 0.19 μm. The combined sources of error are illustrated in Figure 16, shown as minimum and maximum uncertainty on the same scale as the adopted absorption and separately as a fractional error in the lower panel that illustrates the level of uncertainty in the UV cutoff, which cannot be easily seen in the upper panel. Where the minimum value was less than 10−3 m−1, it was set to zero (and the fractional error to one).
4.4. Joining the Segments of New Spectrum
 In addition to joining the five segments of the 1.1–1.8 μm data, the new absorption coefficients need to be joined to the data of Hansen [1997a, 1997b] that begin near 1.8 μm (5555 cm−1). This is illustrated in Figure 17, where all of the 1997 spectra agree near 1.84 μm (5435 cm−1). A line from there is merged smoothly into the new data below 1.83 μm (5465 cm−1) and follows the new data to 1.80 μm, the beginning of the 1997 data. All of the Hansen [1997b] data and most of the Hansen [1997a] data lie within the uncertainties of the new spectrum. The joints at 1.1 μm and between 0.3 μm and 1.0 μm and their uncertainty envelopes are joined by straight lines. All of the data presented in this paper are plotted together with uncertainties in Figure 18. A computer readable file of these new coefficients and their uncertainties, including the modification to match them to previous data, is available as auxiliary material from AGU.
 The measurement of large, clear samples of solid CO2 ice has provided the absorption coefficient and an estimate of its uncertainty for the wavelength range 0.174–1.8 μm. The largest uncertainty occurs at the wavelengths of strongest and weakest absorption, the former due to the noise and scatter of the measurements of the thinner samples, and the latter due to the uncertainty in the scattering extinction in the thickest samples.
 The places where this new compilation can be compared to the review by Warren  are in the visible (0.3–1.0 μm) where he used data from Egan and Spagnolo , and the strong, narrow line near 6970 cm−1 (1.435 μm) where he used data from Fink and Sill . The ends of the visible data are plotted in Figure 18 (the center is in not shown in the axis gap between ∼0.33 and 0.8 μm). The Egan and Spagnolo absorption level is more than ten times our upper limit and three orders of magnitude above the adopted level in this region. Egan and Spagnolo could not have possibly measured the absorption of CO2 ice in the visible using their contaminated 1-cm thick sample; all of their assumed absorption must be due to scattering extinction. Radiative transfer predictions of the albedo of CO2 snow, which used Egan and Spagnolo's absorption spectrum, are therefore too low [Warren et al., 1990].
 The 6970-cm−1 line is shown in Figure 19, with the two Fink and Sill  (FS) points and Warren's  curve fit. Also shown are a point representing the maximum absorption and center of the line from Table IX of Quirico and Schmitt  (QS). I find the center of this line to be at about 2 cm−1 lower frequency than FS and 1 cm−1 lower than QS. This may be due to the different temperature and crystallinity of the samples in the three different thin-film measurements. However, the wave number calibration is not discussed in FS and QS, and the amplitude of the field-of-view wave number correction at this wavelength in this experiment was about 1 cm−1. When the four independently calibrated FTS spectra are compared, the standard deviation of the measured line centers of the strongest lines is typically <0.1 cm−1.
 The positions and peak absorptions of the 5 strongest lines in this wavelength region as measured here are compared to the earlier data in Table 1. The uncertainty in peak absorption given by unweighted scatter is given in this table, as well as the formal uncertainty bounds. There are various differences in wave number centers compared to QS Table IX, as large as 3 cm−1 for the weakest line. However, they measured this near-infrared region only using a thin film, where the weak lines are barely discernible, and at 21 K so that the ice was partially amorphous. The centers of their stronger lines are within 1 cm−1 of our measurements, probably within the uncertainties given the difference in the samples. Their thin-film sample spectra were also somewhat underresolved at 2 cm−1. The combination of poor crystallinity and coarse resolution probably results in their consistently low estimates (by factors of 1.5 to 3) of maximum absorption for all five lines compared to this work. The FS peak absorption estimate for the strongest line is from a 69-μm film at 82 K, which would cause ∼7% absorption that could easily be measured to the 15% precision that they present. The ∼40% difference between this work and FS could easily be attributed to the different temperature, since there is evidence that the narrow CO2 absorption lines become even narrower at lower temperatures. If one assumes a constant integrated absorbance for these lines, this implies that the maximum strength increases at lower temperatures.
Table 1. Comparison of Line Positions and Peak Absorptions
 The CaF2 measurements were made using double the normal interferogram sampling rate, yielding a theoretical free spectral range to 0.633 μm (15,798 cm−1). However, the majority of the signal below 1.0 μm (above 10,000 cm−1) was due to an “alias” spectrum probably caused by uneven sampling of the interferogram [see Hansen, 1996, chap. 3]. The alias spectrum is normally a small fraction of the true spectrum reflected around 7899 cm−1 (1.266 μm) added to the true spectrum. A simple analysis shows that the amplitude of the alias spectrum is actually proportional to the wave number, and this behavior is seen when plotting F(ν0 − ν)/F(ν) versus ν where ν is the wave number, ν0 is the free spectral range (15,798 cm−1), and F is the measured spectrum. In regions where the true spectrum is zero, this expression is approximately equal to δ · ν, with δ being the constant of proportionality. The true spectrum is then derived from the measured spectrum by this expression:
This analysis worked well for about half of the measured spectra. When applied to the other spectra, this expression resulted in negative intensities around 1 μm (10000 cm−1). This anomalous behavior was approximately compensated for by subtracting a Gaussian function with fixed position and width from the straight line δ · ν, effectively making δ a function of ν rather than a constant. The corrected spectra extended to a shortwave limit of about 9000 cm−1 (1.1 μm) (with a signal-to-noise (S/N) ratio greater than ∼10) when using the Tungsten source and only to about 8000 cm−1 (1.25 μm) with the globar source.
 The data collected with the CaF2 beamsplitter exhibited very strong channel fringes from the highly polished CaF2 windows. The fringes in the ice sample spectra were smaller and modified in phase compared to the blank spectra, so the CO2 ice/blank ratios still had fringes at a level of several percent or more. To remove the fringes, a relatively simple, but elaborate, technique was developed [see Hansen, 1996, chap. 3]. A model fringe with a single sine frequency (with a period of ∼2.5 cm−1) was divided into 25–50 cm−1 segments of ratio spectrum to get an improved spectrum. By using the short segments and letting the model amplitude and phase vary smoothly across the segment, the fundamental fringe frequency could be completely removed, leaving only fringes with lower and higher frequencies and random noise, all having amplitudes less than 10% of that of the fundamental fringe.
 Another long-period (220 cm−1) fringe was apparent in the CaF2 beamsplitter data, coming from the reference path spectrum (probably from a film on the mirrors). This fringe was most apparent in the shortest wavelengths, where the CO2 spectrum is mostly very smooth, and was easily modeled and removed. Also in the region shortwave of 7000 cm−1 (<1.4 μm) there were curves and steep slopes in the ratio data, presumably resulting from incomplete correction of the alias spectra. These curves were removed as much as possible using, for example, polynomial fits, to make the spectra straight between 1.1 and 1.4 μm.
 The measured wave numbers were corrected for off-axis rays [Bell, 1972, chap. 11] by assuming a correction linear with wave number, νtrue = aνmeas + b, where νtrue is the corrected wave number, νmeas is the measured wave number, and a and b are the slope and offset of the correction (b is usually near zero and can be forced to zero). The slope and offset are determined by a least squares fit to the observed center wave numbers of selected well-isolated absorption lines of H2O, CO, and CO2 visible in spectra, compared to the center wave numbers given in the HITRAN database [Rothman et al., 1992]. The precision of wave number calibration was better than 0.1 cm−1 in regions of high S/N.
 Off-axis rays also degrade the instrumental resolution with a magnitude comparable to the wave number offset; however, it was not possible to correct for this effect [see Hansen, 1996, Appendix A]. The angular distribution of rays for two samples was determined by fitting an ideal axial model spectrum smeared by the off-axis rays to the measured data in a region of water vapor lines. The weighted mean off-axis beam location was somewhat less than 1 degree, consistent with the shift of center wavelength observed. This distribution was then used to study the degradation of monochromatic and ideal Lorentzian-shaped lines. The result was that the effective resolution at the highest wave numbers is more controlled by the smearing than by the selected maximum path length, with an intrinsic resolution (for a monochromatic line) of ∼1 cm−1 at 1.7 μm (1600 cm−1). At this wavelength, a Lorentzian line of width 1 cm−1 has an instrumental width of ∼1.7 cm−1. The measured widths of many CO2 lines were compared to these model functions to demonstrate that they are resolved (plotting well above the monochromatic line) but have increased widths due to smearing. No effort has been made to correct these widths here, but it is noted that the true widths of the narrowest lines in the near-infrared are probably about 1 cm−1 narrower than the measured data.
 For this data using CaF2 optics, the finest resolution measurements were made at 0.26 cm−1 resolution rather than the finer 0.14 cm−1 resolution that was available. This was judged sufficient, since lines with apparent widths <0.5 cm−1 did not occur at ν > 4000 cm−1 (λ < 2.5 μm). These fine-resolution spectra (few in number because of the time needed to take them) were the main source for the smoothed spectral data presented here. Large averages of spectra at coarser resolutions (0.7 and 3.5 cm−1) were used as a guide in regions of low spectral activity, where their inherent noise was lower than the fine-resolution data.
Appendix B:: Grating Monochromator
 The output of the monochromator was an f/8.7 beam emanating from a slit 3 mm high. The optical system is illustrated in schematic form in Figure B1. The monochromator output entered into an evacuated mirror box where it was reflected by a flat mirror onto a concave mirror which focused an image of the slit at the center of the vacuum chamber. The beam was not occulted by any part of the sample chamber. The reference mirror system was the same as used for the FTS measurements, but was commonly used at each measured wavelength in the monochromator system. The central mirror of the reference system in the back of the chamber maintained the focus of the system by refocusing the slit image that appeared in the incoming beam at the same distance along the outgoing beam. The direct and reference beams entered an evacuated detector box through a 40-mm gate valve, which was used as a dark slide, or as a method for changing the order filter during measurement of a sample. Two detector box designs were used during the experiment, one for the photomultiplier tube (PMT), mounted internally, and one for the silicon detectors and InSb Dewar detector, which were mounted to the vacuum box with a special flanges. The incoming beam was focused by an off-axis parabolic mirror in both boxes.
 The monochromator system used two sources, a 75 W Xenon arc-lamp with optical feedback and a deuterium arc-lamp. The Xenon output is characterized by many pressure-broadened emission lines on top of a smooth continuum running from 0.21 to ∼4 μm, with a maximum output between 0.6 to 1.0 μm. The light from the 30 W cold-cathode deuterium source passed through a magnesium fluoride (MgF2) window, and was bolted directly to the vacuum flange of the monochromator. Its spectral output has a detailed line structure from ∼120 to 170 nm and a continuum beyond 170 nm. The monochromator had no measurable transmission below ∼140 nm.
 The vacuum monochromator had a 0.5-m focal length with Czerny-Turner optics. The slits were adjustable from 5 to 3000 μm allowing for wavelength resolutions according to
where δλ is the resolution (full width at half-height of the instrument response to a monochromatic line), wslit is the slit width, and a is the number of lines per millimeter of the grating (1200 or 600). The instrument response function, as demonstrated when observing the lines of the Mercury-Argon line source used for wavelength calibration, was roughly triangular, as expected for such an instrument operated far from the diffraction limit of resolution. Wavelength scanning was performed by a sine drive mechanism driven by a stepping motor, with gearing such that one step equals 0.025 nm with a 600-mm−1 grating. The three gratings used in this experiment included a 1200 mm−1 blazed at 200 nm, a 600 mm−1 blazed at 400 nm, and a 600 mm−1 blazed at 1000 nm.
 Four long-pass and band-pass order filters were used to isolate the spectral orders of the gratings. The shortest wavelengths were observed with no filter up to twice the spectrometer cut-on (∼300 nm). Five filters were used in these wavelength ranges: 240–470 nm, 330–640 nm, 550–1100 nm, 0.80–1.60 μm, and 1.42–2.40 μm (using the 600-mm−1 grating). The scattered light, undispersed light which escapes the monochromator exit slit, was usually less than one-thousandth of the peak dispersed light.
 There were four detectors used in the monochromator experiment: two for the vacuum ultraviolet, one for the visible and near-infrared, and one for near-infrared. A 9-stage PMT was used in some of the vacuum ultraviolet measurements; it had the highest sensitivity to the weak deuterium lamp signal. The short-wave cutoff from the fused quartz envelope of the tube near 150 nm was of no consequence, since the monochromator did not transmit much light below that wavelength. A silicon X-ray/UV detector was also used, which was windowless and had no short-wave cutoff. This detector was much easier to connect and use, but, even using 10 times lower spectral resolution, had much lower S/N. The X-ray/UV silicon and PMT detectors were only used in the filter-free spectral order, ∼150–300 nm. The wavelengths from 250 to 1100 nm were measured by an ultraviolet-enhanced silicon detector, using the three shortest-range filters. A custom-built transconductance amplifier was used with the PMT and silicon detectors, providing a maximum gain of 109 V/A with a bandwidth >800 Hz. In the infrared beyond 800 nm, the same InSb detector from the FTS experiment was used. It had a built-in transconductance amplifier with a fixed gain (2.2 × 104 V/A for the monochromator and 7.5 × 103 V/A for the FTS). The 0.80-μm and 1.49-μm filters were mounted in a 60° field-of-view cold aperture (to minimize the thermal signal in their cutoff wavelength regions).
 Light choppers are used to modulate the source intensity so that the component of the detected signal from the source can be separated from other components. When measured by a lock-in amplifier, AC components in a narrow range around the chopper frequency are selected, removing any DC components (energy not from the source), and avoiding most of the 1/f noise at low frequencies which arises from semiconductor amplifiers [Wolfe, 1988]. Two choppers were used in this experiment, a variable-speed rotary chopper and a fixed-speed tuning-fork chopper. The rotary chopper was operated at a chopping frequency of ∼270 Hz. The tuning fork chopper operated at 280 Hz and had to be mounted close to the entrance slit to fully modulate the source signal. It was mounted on the slit assembly in vacuum with the Deuterium source, but with the Xenon source it had to be mounted on a special inset flange outside the vacuum because of overheating problems.
 The AC signal at the detector was measured synchronously by a lock-in amplifier. This amplifier allows selection of pre-amp sensitivity and time constant of the low-pass filter. For this experiment, the output of the lock-in amplifier was digitized (inside or outside the amplifier) for computer storage. The main trade-off in using a synchronous detection system is to use the low-pass filter with the shortest time constant that provides an acceptable noise level. Any changes in the signal due to wavelength change or reference mirror movement were accompanied by a delay time about 10 times the time constant to allow the signal to settle. Therefore measurements using time constants on the order of 1 s or more were only used in special cases. The most common time constant used was 0.1 s.
 Two lock-in amplifiers were used, an analog one wired to the analog-to-digital card of a data acquisition system, and a digital one operable by a computer through a serial port. The data acquisition system or computer also manipulated the monochromator and reference mirror stepper motors through a serial port to the motor drivers. The first lock-in had only manual control of sensitivity and time constant, so these were changed only rarely during measurement. Combined with a lower typical S/N, the lack of detailed sensitivity switching resulted in much poorer quality data available from this amplifier compared to the second one. The second lock-in had a choice of more and steeper cutoff filters, resulting in a typical S/N of several hundred to one. The sensitivity of this amplifier was automatically adjusted during acquisition to keep the output signal between 0.3 and 1 times full scale.
 Wavelength calibration of the monochromator data was done using a low-pressure mercury-argon arc lamp placed behind the chopper near the input slit. When this lamp was measured in the absence of an order filter, lines from higher order grating reflections also appear, increasing the number of lines available for calibration, especially in the infrared beyond 1 μm, where first order emission lines from the lamp are few and weak. To supplement the few infrared lines available, the numerous narrow lines from the CO2 ice itself were used as calibration standards, since they had been measured accurately to ±0.1 cm−1 during the FTS measurements. For the emission lines of the Hg-Ar lamp, the centers of the lines were determined by the intersection of two straight lines fit in the least squares sense to the triangular slopes of the measured lines. Although the accuracy of this method depended on the resolution (0.01–3.0 nm) and S/N (≥10) of the measurement, with the second lock-in amplifier most of the lines could be measured to better than ±0.03 nm. The overall shape of the wavelength calibration curves is characteristic of the sine drive of the monochromator. When a grating was remounted or the wavelength drive motor reset, its calibration was the same as previous calibrations of that grating but with an offset. During a series of measurements with one grating, the motor was kept energized so as not to lose the fine calibration. The calibration curve for each grating needed to be measured accurately across its full range only once; thereafter, only a few strong, well-spaced lines were measured to determine the offset.
 The calibration curves were fitted to a functional form representing a small misadjustment of the wavelength drive [Ando, 1964]. To this function, a sine wave was added that represents errors in the drive screw [Fisher, 1959]. The period and amplitude of this sine wave was observed and measured when the absorption lines of gaseous CO2 at 2.7 μm were used for calibration [see Hansen, 1996, Figure 5–8]. By careful choice of the parameters of the overall function and the phase of the screw error sine, the calibration curve could be fit to most of the measured calibration points within a few hundredths of a nm, comparable to the accuracy with which the lines could be measured. Examples of fits using this functional form are illustrated in Figure B2. Another effect on the accuracy of wavelength determination was the backlash in the grating drive, seen as a difference between calibration data taken in the forward and reverse scanning directions of about 0.4–0.45 nm (for 600-mm−1 gratings). Ultimately, most monochromator measurements were made in the forward scanning direction to avoid the need to make calibration measurements in both directions.
 There were several modes in which measurements were taken. The most accurate in terms of both amplitude and wavelength accuracy was when measurements were taken between alternating motions of the reference mirrors and wavelength scan, so that a measurement of direct and reference paths was taken for each wavelength. At each position, multiple readings (usually 4–6) of the lock-in voltage were taken and averaged together. Allowing for settling times, the measurements at each wavelength took about 15–20 s. The scattered (undispersed) light level, found by scanning the monochromator below the wavelength of the order-filter cut-on, was measured at each sensitivity setting and later subtracted from the measured spectral signals. Even though scans were designed to take as few steps as possible by using a variable step size (sampling resolution) based on the assumed amount of spectral detail, using this method in the near-infrared took 4–7 hours to complete. Typical temporal changes in the optical quality of the ice sample being measured showed up as spectral variation in these cases. This problem was solved by either one of two methods, described in the next paragraph. Both methods required abandoning near-simultaneous measurement of the direct and reference paths, so that scans over the full wavelength range were made with the reference mirrors in one position, followed by another scan with the mirrors in the other position.
 The first method is a “free running” method in which the monochromator is scanned continuously, while the computer makes periodic measurements of the lock-in output. This method is the fastest (15–60 min for an infrared spectrum), but suffers from difficult wavelength calibration, since the loop time of the computer was not constant in time nor consistent between subsequent scans. The wavelengths of these spectra were calibrated by using variable offsets to align the measured spectral features with their locations in stepped spectra. The second method is called “single-step”, because it moves the monochromator by constant small steps, taking 1–4 measurements at each wavelength, allowing for the proper settling time, thus retaining wavelength accuracy. Using this method, it was possible to acquire an entire infrared spectrum at high sampling frequency in about the same time as the standard method (several hours).
 I thank William Smythe for the use of his laboratory space and both him and Robert Carlson for their equipment at the Jet Propulsion Laboratory (JPL), funded primarily by the Galileo Near Infrared Mapping Spectrometer (NIMS) group. The expertise of Vachik Garkanian was invaluable in the design and fabrication of all of the custom mechanical assemblies required for this experiment. Much useful advice was received from William Smythe and Robert Carlson. Purchase of much of the new equipment required for the experiment and support of the author during the experiment was made possible by grants from NASA Planetary Atmospheres, NASA Planetary Geology and Geophysics, the University of Washington Space Grant, the Caltech President's Fund, and the Directors Discretionary Fund at JPL. Data analysis and publication were supported by NSF grant ATM-98-13671 (to Stephen Warren) and the University of Washington Astrobiology Institute. The final manuscript received an extensive and helpful review by Stephen Warren.