1. Introduction
The O2 A-band has a long history in optical remote sensing of the atmosphere from space. It has been used to determine cloud heights (beginning with Hanel 1961 and reviewed by O’Brien and Mitchell 1992), cloud optical properties (Asano et al. 1995), and aerosol optical thickness (Badayev and Malkevich 1978). These applications required high radiometric precision but normally did not need to resolve individual O2 absorption lines. However, this situation is changing. As technology improves and higher demands are placed on remote sensing, there is increasing interest in the possibility of combining high radiometric precision with high spectral resolution in the next generation of spaceborne instruments, not only in the O2 A-band but also in other regions of the visible and infrared spectrum. This paper examines one such application: the measurement of surface pressure, to highlight the technical issues and to show that they are not insuperable.
One technique proposed by Mitchell and O’Brien (1987) for measuring surface pressure from space involves high-precision measurements of the O2 A-band spectrum of sunlight reflected from the surface in clear sky conditions. Observations at selected frequencies allow the integrated column of O2 to be determined using standard techniques of differential absorption. Surface pressure follows easily because O2 is well mixed. In practice, the application is very demanding, because the accuracy of pressure measurements must approach 0.1% if the results are to be usefulfor meteorology. The principal difficulty is that the detected radiance is not only reflected from the surface but also scattered by the atmosphere, so the mean photon path depends upon the distribution of aerosols and haze, quantities that are poorly known. However, the radiance spectrum depends weakly on the level at which scattering occurs in the atmosphere; for example, if two frequencies are chosen, one lying between the two absorption lines comprising one of the doublets of the O2 A-band spectrum (Fig. 1) and the other lying in a region of high transmittance between two doublets, then the ratio of the radiances is a good indicator of the mean scattering level in the atmosphere. Consequently, the additional information in high-resolution spectra helps resolve the ambiguity between reflected and scattered radiance. In particular, observations at frequencies where O2 absorption is high are dominated by radiance scattered by the atmosphere, rather than radiance reflected from the surface, thereby providing a quantitative estimate of the degree of scattering by the atmosphere. Although the changes in the shape of the spectrum are second-order effects, they allow the accuracy of pressure retrievals to be improved from 1% to 0.1% (or 1 to 0.1 kPa in absolute terms), thereby reaching the accuracy required if pressure data are to have a positive impact on forecasting skill in numerical weather prediction.
Any attempt at high-precision, high-resolution spectroscopy from space will encounter two sources of noise. The first lies in the instrument, through detector noise and through degradation of the spectrum by mechanical deformations of the spectrograph. The second is the atmosphere itself, through subvisual haze, temperature fluctuations, turbulence, and nonuniformity of sunlight reflected from the sea. It is not clear a priori whether high-precision, high-resolution spectroscopy is possible in the presence of these noise sources, with either present or future technology. This paper addresses some of these issues, through both analysis and experiments, and attempts to identify the fundamental limitations. The context will be O2 A-band spectra recorded by a grating spectrograph with a silicon photodiode detector array, although many of the results do not depend on the details of the optical configuration. The specifications will be those required for useful measurement of surface pressure, typically 0.1% radiometric error and 1-cm−1 spectral resolution. This paper addresses the following issues.
We examine the factors that limit the signal-to-noise ratio, including detector performance and mechanical and thermal stability. Tolerances are determined using a model of the optical system.
To demonstrate that atmospheric turbulence is not a limiting factor, we describe an experiment that shows that high-resolution O2 A-band spectra can be used to track the mass of O2 along the path of the solar beam with rms error less than 0.1% as the sun moves across the sky.
Last, we describe an experiment to test the sensitivity of measurements to changes in surface pressure. The experiment involves extending the optical path from the sun to the spectrograph with an O2 absorption cell, whose pressure is modulated to simulate changes in atmospheric pressure. Changes as small as 0.1 kPa can be detected clearly.
2. Experimental configuration
The configuration used in the experiments is shown in Fig. 2. The solar beam is directed into the laboratory by a heliostat located on a tripod outside the laboratory. The heliostat consists of a mirror platform driven by zenith and azimuth stepper motors, a four-quadrant photodiode sun sensor, and a PC that digitizes the sun sensor output, computes corrections to the mirror position, andcontrols the steppermotors. The software algorithm determines the adjustments of the mirror platform from the time of day and error signals from the sun sensor. The PC updates the position of the heliostat approximately every 500 ms. When the system is correctly aligned, the jitter in the position of the solar beam at a distance of 3 m from the heliostat mirror is less than 1 mm, corresponding to an angular stability of δθ ≈ 0.02°. Because the beam is passed through a diffuser in order to simulate reflected light at the entrance port of the spectrograph, the effect of the jitter is reckoned to be negligible.
The spectrograph is a grating instrument used in the Littrow configuration (Born and Wolf 1975) with focal ratio f# = 2.3 and focal length 500 mm (Fig. 3). The focal ratios of the telescope and Petzval objective lens are matched to conserve flux. The grating, used in second order, has 900 lines per millimeter and dimensions 220 mm × 200 mm. Although many other optical configurations are possible, the throughput and signal-to-noise ratio will be approximately the same for all; the benefits of sophisticated optical design are small reductions in both system focal ratio and optical aberrations. The detector is a 512-element Reticon photodiode array (RL512S) whose pixels have 100:1 aspect ratio, matching the entrance slit of the spectrograph. The detector is cooled by nitrogen gas boiled from a LN2 dewar. The spectrograph is mounted in a vacuum tank, whose temperature is regulated above ambient (typically 38°C) by heater mats that cover approximately 40% of the area of the tank. The temperature of the detector array and the tank are regulated with a precision of approximately 0.1°C. The instrument must be left for approximately 24 h to stabilize before observations can commence. All functions of the instrument are controlled by multitasking software running on a 486 PC. Details of the optical design, mechanical stability, software, and detector electronics can be found in papers by Wilson (1989), Petkovic (1989), Jones (1993), Capizzi (1993b), Da Costa (1993), and English (1993).
The decision to use a detector array, rather than scanning the spectrum across a fixed detector, is a complex one. A detector array eliminates the need for mechanical motion of any of the optical elements and allows simultaneous observation of all channels. When high precision is required, the reproducibility of mechanical scanning becomes an important issue. Likewise, in an airborne or spaceborne instrument, sequential scanning of channels means that the channels sample different footprints, with different illumination and cloud contamination, and this may lead to unacceptably large errors. The prime disadvantage of a detector array is the requirement for stigmatic imaging of the entrance aperture over the full area of the detector. In practice, the focal length of a spectrograph with a detector array will be longer than for an instrument with a single detector and mechanical scanning. Longer focal lengths lead to higher mass and greater sensitivity to thermal gradients in the spectrograph.
The solar beam was directed into the laboratory through a 3-m length of 100-mm-diameter PVC pipe. The pipe contained three annular baffles, located at the ends and the center, manufactured from 100-mm aluminium disks with 50-mm holes punched in their centers. The interior of the pipe and the baffles were coated with matt black paint in order to minimize reflections. The baffling reduced the field of view of the spectrograph to a cone centered on the line to the sun. The half-angle θ at the vertex of the cone (defined by tanθ = 50/3000) wasθ ≈1.0°. It will be shown below that the baffling reduced the contribution of scattered radiance entering the spectrograph to a negligible level. For the sensitivity experiments, the light baffle was replaced by an O2 absorption cell whose pressure could be modulated to simulate small changes in atmospheric pressure.
3. Signal-to-noise ratio
The spectrograph described in this paper was designed for airborne operation, although this paper presents only results from preliminary laboratory experiments. In this section we consider the issues of signal-to-noise ratio (SNR) and mechanical stability required for airborne applications.
a. Detector noise
Although the optical system might appear to contain many degrees of freedom, in fact there are very few. The responsivity of Si is fixed, and the saturation charge typically is proportional to the detector area, so the ratio qD/AD is also a fixed property of the detector. The situation is not improved by detectors with higher gain, such as photomultipliers, because the quantum efficiency of Si is already high and because the dominant noise source is shot noise, associated with the random arrival of photons. The quest for high-precision and high-resolution spectroscopy from space inevitably leads to long integration times. Herein lies a dilemma for remote sensing applications that require high accuracy; long integrations lead to large footprints through motion of the satellite, but the spatial variability within large footprints introduces yet another form of noise, thereby limiting the achievable accuracy. Time delay integration or counterrotating scanners to freeze the footprint during the integration can alleviate (but not eliminate) this problem.
b. Mechanical stability
For our situation, the most stringent requirement on the spectrograph is not detector noise but mechanical stability. Because the absorption coefficient of the O2 A-band changes so rapidly near the absorption lines, any movement of the spectrum relative to the detector will manifest itself as noise. If only low radiometric precision is required, thermal drift of the detector relative to the spectrum can be corrected during analysis by identifying spectral lines and interpolating the measured spectrum. However, when high precision is required, errors introduced by interpolation generally will be unacceptably large. If the absorption lines are symmetric about their centers (and remain so for all atmospheric conditions), then dithering the spectrum by driving the slit position with a piezoelectric transducer, followed by phase sensitive detection, might allow an absolute frequency calibration. In this paper we report on the feasibility of a simpler alternative, namely, designing an instrument so stable that mechanical deformations caused by vibration or thermal gradients do not lead to errors in the spectrum exceeding a specified tolerance ε (equal to 0.1% in our application).
1) Mechanical displacement model
In the optical system shown in Fig. 3, light from the entrance slit is collimated by the objective lens, so the grating is illuminated by a parallel beam. Consequently, it is the orientation and not the position of the grating that is critical. A complete stability analysis of the optical system calls for a finite element analysis, but as an economical first approximation we represented vibration and thermal drift as acombination of two effects:
displacement of the spectrum due to perturbations of the orientation of the grating, and
displacement of the detector in the plane of the spectrum.
Rather than present the details of the model, we simply list the underlying assumptions.
The fold prism, grating, and components of the objective lens move independently. However, the model lumps these motions into an equivalent rotation of the grating and assumes that the other components remain fixed. Although this clearly is an approximation, the estimates for grating stability will provide general estimates for the stability of the fold prism and the elements of the objective lens.
Rotation of the grating about its normal causes misalignment of the slit and the rulings on the grating. This effect is modeled in a simple way by assuming that the image of the slit is also rotated. The magnitude of the rotation is determined by computing the images of the top and midpoints of the slit and by computing the angle between the vertical and the line joining the images. Because the grating is mounted in a way designed to minimize rotations about its normal, the error is expected to be small.
No account has been taken of defocusing of the image, primarily because ray tracing shows that focus is the least critical of the spectrograph adjustments.
Diffraction is assumed to follow the grating equation, and aberrations have been neglected.
2) Model results
Figure 2 shows the atmospheric transmittance in the O2 A-band along a vertical path from the surface to space for the U.S. standard atmosphere. Data for the O2 absorption lines are taken from the HITRAN database (Rothman et al. 1987). Figure 4 shows the percentage change in the transmittance for a translation of the detector relative to the spectrum by 50 nm, the latter figure chosen because the corresponding error is approximately equal to the required accuracy (0.1%). Because the width of each detector pixel is 25 μm, we refer to this displacement as 2 millipixels. The relative error obviously increases where the absorption is high and the signal is low. Sensitivity to displacements in the orthogonal dimension is much lower. Table 2 lists the maximum displacements Δx, Δy of the detector; the maximum rotations Δθ, Δϕ of the normal to the grating; and the maximum rotation Δψ in the plane of the grating that can be tolerated if the relative error ε in radiance is not to exceed approximately 0.1% for all pixels where the signal level is at least 10% of saturation. The x and y axes are aligned with the spectral dimension and the entrance slit, respectively. These tolerances are very tight, but nevertheless are achievable, as we will show later. It is clear that precision of 0.1% in radiance will require stability of the detector to approximately 2 milli-pixels.
3) Vibration tests
The spectrograph was designed for airborne rather than laboratory use and so had to be able to withstand the vibration levels in the Fokker F27 research aircraft used by CSIRO. A testflight was conducted in which the vibration spectrum was measuredat the planned instrument location in the F27 under a wide range of throttle conditions (Vethecan 1992). The dominant modes were the engine fundamental frequency at 20 Hz, the propeller blade pass frequency at 80 Hz, and harmonics of both. To verify the stability of the spectrograph, it was placed on a shaker table and subjected to both vertical and lateral vibrations similar to those measured in the F27 (Capizzi 1993a). Fixed sine wave, swept sine wave, and random frequency excitations were used. Accelerometers were placed near the grating, the detector, and at various points on the vibration isolation system in order to measure the attenuation between the supporting frame attached to the shaker table and the spectrograph. In addition to the accelerometers, the spectrograph was illuminated with a Kr spectral lamp, which has strong emission lines at 13 151.5 and 13 008.2 cm−1, and spectra were logged continuously while the spectrograph was shaken. The analysis focused on the stronger line at 13 151.5 cm−1. For every spectrum, a Gaussian curve was fitted to pixels falling on the line. The center of the Gaussian was taken as a good measure of the position of the spectrum relative to the detector. Table 3 lists representative results from the vibration tests. Generally the spectral shift so determined is less than 1 millipixel. Not shown in the table are systematic drifts caused by temperature gradients, because the spectrograph was not thermally stable for the duration of the shaker tests. These figures show that even though stability at 1-millipixel accuracy is extremely tight, it can be achieved in applications from an airborne platform. The stability of the detector mount owed much to the cylindrical geometry used in its design. The detector was mounted on a cylindrical copper block, through which the cooling gas circulated, and the block was brazed to a disk of stainless steel. The disk in turn was mounted on a Delrin cylindrical support in order to thermally isolate the cold detector assembly from the warm body of the spectrograph. With the detector located at the axis of the cylindrical structure, radial strains were minimized, thereby leading to an exceptionally stable mount.
c. Thermal stability
Thermal stability is much more difficult to achieve, particularly for the spectrograph used in the experiments. A weakness in the design of the spectrograph was the use of cold N2 gas boiled from a dewar of LN2 to cool the detector. The gas was circulated via flexible plumbing through a copper block bonded to the detector. The plumbing provided a mechanical link between the spectrograph and the vacuum tank within which it was mounted. Furthermore, the link was directly to the detector, so differential expansion of the vacuum tank relative to the spectrograph led to forces applied directly to the detector, the most sensitive component. Apart from the plumbing, the spectrograph was attached to the vacuum tank through torsion mounts that allowed expansion of the spectrograph with respect to the vacuum tank without distortion. With hindsight it is clear that radiative cooling of the detector would have been preferable.
Despite these limitations, the spectrograph approached the required stability. Tests were conducted in a large thermal chamber whose temperature was cycled, as shown in Fig. 5. The temperature profile was intended to simulate changes in operating conditions inside the research aircraft as it climbed from a warm surface at 27.5°C to the operating height where the temperature typically would be 15°C, followed by descent to the surface after two hours of data acquisition. As in the vibration tests, the position of the detector was monitored by locating prominent Kr spectral lines that fall within theO2 A-band. Twofragments of the temperature record are shown in the upper panels of Figs. 6 and 7. The first fragment (Fig. 6) shows the response of the detector position to cycling associated with the temperature regulation of the thermal chamber. The response time of the detector cooling system is too slow to correct the vagaries of the chamber temperature, so the detector temperature tracks the chamber temperature. The detector position changes by about 17 millipixels when the chamber temperature varies by about 2°C, so the sensitivity to these rapid fluctuations is approximately 8 millipixels per degree Celsius. The other prominent feature in Fig. 6 is the slow upward drift of the detector position. The mean temperatures of the chamber, detector, and vacuum tank are stable in this period but the spectrograph temperature is slowly ramping upward, allowing us to conclude that the sensitivity of the detector position to changes in spectrograph temperature is approximately 5 millipixels per degree Celsius. In Fig. 7, the ambient temperature is falling rapidly, but the mean values of the other temperatures are relatively steady. When differential expansion occurs between the vacuum tank and the spectrograph, stresses are transmitted to the detector via the cooling pipes bonded to the detector. Hence, the sensitivity to chamber temperature through this mechanism is approximately 15 millipixels per degree Celsius.
The target stability of 2 millipixels requires temperature stability of approximately 0.1°C. Because the detector temperature could be regulated much more closely with a small heater close to the detector and radiative cooling to the environment, we believe that these figures are excessively tight and reflect the vagaries of the design of the instrument used for these experiments.
d. Nonuniform illumination
In an ideal spectrograph, all light in narrow frequency intervals Δν falling on the entrance aperture would be collected by the appropriate detector element, so the spatial distribution of the light on the entrance aperture would not affect the detector output. With some solid-state detector arrays, this happy state of affairs does not occur because the response functions of adjacent pixels overlap. For example, Fig. 8 shows the response of the RL512S detector quoted by Reticon (1991). Each pixel has a sensitive P-type region, separated from its neighbors by an N-type region. Light falling between pixels produces a response in both, with the strength of the response varying linearly with distance from the edge of the pixel. Because the telescope focuses an image of the footprint onto the entrance aperture and the spectrograph focuses the entrance slit onto the detector, spatial nonuniformity of the footprint illumination will affect the apparent spectral composition. For example, if all the available energy were to fall on one side of the entrance aperture, pixels n − 1 and n would be illuminated, but if the energy were on the opposite side of the entrance aperture, then pixels n and n + 1 would respond. Thus, the inherent limit to the spectral shift is one pixel. To overcome this problem, pixels must be binned in groups of three, so that the total of the light falling on the sum of the pixels is insensitive to the distribution of energy on the entrance aperture. The immediate penalty of so binning the pixels is a threefold reduction in spectral resolution. All data presented in this paper have been binned.
A second effect concerns illumination varying from top to bottom of the entrance aperture. If the responsivity of each detector pixel is not spatially uniform, then changing illumination can lead to an apparentsource of noise. Fortunately, this effect is small for silicondetectors in the near-infrared; at thermal wavelengths with HgCdTe detectors, the effect would be more important.
4. Sun tracking test
The first test to which the O2 A-band spectrograph was subjected involved tracking the optical thickness of the atmosphere along the line of sight to the sun as the sun moved across the sky. The goal was to predict the air mass with an accuracy equivalent to 0.1% in surface pressure. The experiment was designed to eliminate scattered radiance, thereby simplifying analysis of the data. Although others have tracked the sun with low-resolution radiometers (Grechko and Dianov-Klokov 1981, 1983; Barton and Scott 1986), this was an important test of the noise and stability of the grating spectrograph. The test also demonstrated that atmospheric turbulence should not be a limiting factor in such high-resolution spectroscopic measurements.
a. Procedure
The instrument was left to stabilize thermally for approximately 24 h prior to the test. Spectra were acquired in cycles of 10, the first 9 of the sun and the last of a quartz halogen calibration lamp. Before each solar or calibration spectrum, a dark integration was performed with the same integration time (1.4 s). The dark spectra were subtracted from the solar and calibration spectra during analysis to cancel dark current and fixed pattern noise. After each solar or calibration spectrum, a second dark integration was performed with the same integration time, followed by 20-s wait time. During the wait time, the array was flushed at 100-ms intervals to ensure that the detector pixels were fully charged prior to the next integration. Without this precaution, the detector–amplifier combination may exhibit a long memory of previous integrations (Vogt et al. 1978).
b. Solar aureole
At the time of the experiments, the solar aureole was particularly bright, caused by local pollution in Melbourne and stratospheric aerosols from the eruption of Mount Pinatubo in the Philippines. However, we will show in this section that the contribution of the aureole to the flux density at the entrance aperture of the spectrograph was less than 0.1% of the direct solar beam and therefore may be ignored in the analysis.
At 13 102 cm−1, the center of the A-band, the Rayleigh optical thickness of the molecular atmosphere (labeled by i = 0) is τ0 = 0.023. The Rayleigh phase function has Φ0(1) = 3/2. For a cone with vertex half-angle of 1°, the solid angle is Ω = 9.6 × 10−4 sr. Thus, A0 = 2.6 × 10−6 and the Rayleigh aureole is totally negligible in comparison with the direct beam.
Measurements at CSIRO Division of Atmospheric Research by Young et al. (1992) after the Mount Pinatubo eruption give τ1 ≈ 0.1 for the optical thickness of the Mount Pinatubo aerosol layer (labeled by i = 1). If the aerosol phase function given by McClatchey et al. (1972) is assumed for the volcanic aerosols, then Φ1(1) ≈ 100 and A1 = 760 × 10−6. Although the aureole caused by aerosols is much brighter than the Rayleigh aureole, its contribution to the flux density at the entrance aperture of the spectrograph is still less than 0.1% of the direct solar beam.
These calculations show that the solar aureole can be neglected in the experiments with the cone of acceptance of the instrument defined by baffles as outlined earlier. Multiple scattering will not alter these conclusions substantially.
c. Thermal drift
d. Fourier power spectrum
In practice, only the discrete Fourier transform (DFT) can be computed, and its power spectrum is not invariant under translations in ν. Nevertheless, to the extent that the DFT approximates the Fourier transform, the invariance is approximately true. In practice, the following procedure was adopted.
A section of the P-branch of the O2 A-band spectrum containing 14 prominent doublets was selected.
- The spectrum was multiplied by the functionwhere i denotes pixel index, and i− and i+ denote the minimum and maximum pixels of the selected region of the P-branch.
- The DFT of the sequencehifϕii−ii+was computed. Herefϕifϕνiwhere νi is the central frequency of the ith pixel. Function h decays smoothly to zero at both end points and reduces ringing in the DFT, which otherwise would occur because fϕi is not periodic on [i−, i+].
The discrete power spectrum contains a peak at a frequency of approximately 14 cycles per period. The peak conveys information about the shape of the absorption doublets. A Gaussian was fitted to the peak by adjusting the center (C), width (W), and amplitude (A) of the Gaussian.
Because the optical path and atmospheric transmittance depend on air mass, so too does the amplitude of the power spectrum. However, the shape of the power spectrum also changes, and this is reflected in changes of the position and width of the peak. In fact, the position, width, and amplitude of the peak are almost linear functions of air mass m when surface pressure p is fixed, and linear functions of p with fixed m. In each case, the dependence certainly can be modeled accurately by a low-order polynomial. As one would expect, the amplitude varies more strongly than either the position or width of the peak, but the amplitude is less useful for analysis because it depends on absolute radiances.
Based on these observations, it was decided that air mass would be predicted from the observed spectra and the surface pressure, both of which were logged continuously thoughout the experiment. The analysis began with a calibration phase in which coefficients in a polynomial fit to C as a function of m were determined by empirical calibration of the instrument. Typically, the calibration phase would last for approximately 20% of the experimental run. Thereafter the polynomial relation was inverted to recover m or p from subsequent measured values of C.
e. Sensitivity of spectra to atmospheric temperature
The simulations showed that diurnal temperature variations lead to changes in transmittance (after convolution with the spectrograph transfer function) smaller than 0.1% at frequencies in the wings of O2 A-band absorption lines. At frequencies close to line centers, where atmospheric transmittance is less than 10%, diurnal effects should be taken into account. By excluding such low transmittance data from the analysis, atmospheric temperature variations may be neglected in the experiments. However, data from a satellite instrument would require more sophisticated analysis using frequencies close to line centers, in which case boundary layer temperature variations would have to be taken into account. Such analysis would require as data thesurface temperature, satellite, or radiosonde temperature profile above the boundary layer, a model for the boundary layertemperature profile, and a complete model for the transmittance as a function of temperature.
f. Air mass–pressure relation
In the course of the experiment, both the air mass m and the surface pressure changed. Although the changes in the latter were small (≈0.2 kPa), the effects were not negligible, and so the air mass was corrected for surface pressure variations by the procedure outlined below.
g. Calibration
h. Results
The relation between predicted and observed air mass over a period of 3.5 h is shown in Fig. 11. The correlation is excellent, showing clearly that air mass can be tracked with high precision if scattered radiance is excluded from the entrance beam. In a later paper we will present data to show that similar accuracy can be achieved from an airborne platform. The pressure errors that follow from Eq. (5) are shown in Fig. 12. The pressure error never exceeds 0.1 kPa and the root-mean-square pressure error is 0.032 kPa.
In an operational situation with a spectrograph on a satellite, day-to-day stability of the spectrograph would be an importantissue. However, for the proof of concept experiments described here, it was sufficient to recalibrate the spectrograph for each day of observation.
5. Oxygen cell test
In the sun tracking test described above, the changes in air mass were large and followed a predictable path. In contrast, the changes in air mass caused by changes in surface pressure will be small, and it is not clear that they will be detectable in the presence of noise from atmospheric sources. These sources include scattering by aerosols and cloud, whose distribution is highly variable and difficult to predict, and density and refractive-index inhomogeneities caused by turbulence and thermal gradients. This section outlines an experiment conducted to test whether changes in surface pressure as small as 0.1 kPa can be detected against the noisy background of the atmosphere.
The spectrograph was located in the laboratory with its field of view restricted to a narrow cone along the line of sight to the sun, as in the sun tracking test. An absorption cell containing O2 was placed in the optical path just in front of the spectrograph, and the pressure of O2 in the cell was modulated to simulate small changes in atmospheric pressure. The pressure of O2 required in the cell was determined as follows.
Table 5 lists the changes in surface pressure equivalent to the cell pressures listed above. The air masses listed in the table reflect the movement of the sun during the experiment. The interval between spectra was 20 s.P′ = 102, 394, 102, 394, 102, 330, 102, 330, 102, 219 kPa.
Figure 13 shows the changes in equivalent pressure recorded during the experiment. The steps where the O2 pressure was changed are clearly visible, with the exception of the final change that occurred near noon when the alignment of the heliostat was most critical, resulting in a change of illumination of the diffusing screen.
It is important to note that the pressure scale in Fig. 13 is the empirical calibration scale, obtained by matching the instrument response to measured pressure changes. Nevertheless, the magnitudes of the steps in Fig. 13 agree well with the results of the transmittance simulations presented above. The accuracy is limited because the pressure gauge on the O2 cell was not a precision instrument and because the spectrograph had not stabilized thermally. Despite these caveats, the 0.15-kPa pressure step is clearly visible, and steps of one-half that magnitude should be detectable.
6. Conclusions
As we move into an age with evermore demanding applications of remote sensing, there is increasing incentive to move to high-resolution, high-precision spectroscopy from space. However, such a move poses many technical problems, primarily associated with achieving high signal-to-noise ratio when the signal level is low. This paper has examined several of these issues in the context of remote sensing of surface pressure from observations in the O2 A-band. This application is typical of many others.
The instrument consisted of a grating spectrograph with a cryogenically cooled photodiode array as detector. The system performance was found to be limited by shot noise associated with the random arrival of photons. Even more stringent is the limitation imposed by mechanical and thermal stability. The structural model suggested that thermal stability must be maintained to within 0.1°C if thermal drift is to contribute less than 0.1% to the total noise. Temperature control with this precision is challenging; in practice, it might be preferable to attempt wavelength calibration, using either a calibration lamp or identifiable features in the solar spectrum.
The sun tracking test and the O2 absorption cell test showed that the component of atmospheric noise due to turbulence in the lower atmosphere is not a serious limitation. More important limitations in these applications are scattering by aerosols and subvisual cloud. These will be addressed in subsequent papers.
Acknowledgments
We gratefully acknowledge the assistance of mechanical engineers at Vipac Engineers and Scientists Ltd. in both Adelaide and Melbourne who conducted the vibration tests and helped interpret the results. In particular, we thank Vincent Capizzi, Dounia Affnan, and Jerome Vethecan. We also thank Dr. Ross Mitchell at CSIRO Division of Atmospheric Research for many constructive comments.
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Simulated transmittance spectrum of the atmosphere in the O2 A-band along a vertical path from space to the surface. The spectral resolution is 1 cm−1.
Citation: Journal of Atmospheric and Oceanic Technology 14, 1; 10.1175/1520-0426(1997)014<0105:HPHRMO>2.0.CO;2
Experimental configuration for the sun tracking test.
Citation: Journal of Atmospheric and Oceanic Technology 14, 1; 10.1175/1520-0426(1997)014<0105:HPHRMO>2.0.CO;2
Optical configuration of the spectrograph.
Citation: Journal of Atmospheric and Oceanic Technology 14, 1; 10.1175/1520-0426(1997)014<0105:HPHRMO>2.0.CO;2
Error ε (%) caused by a 50-nm displacement in the x direction of the detector relative to the spectrum.
Citation: Journal of Atmospheric and Oceanic Technology 14, 1; 10.1175/1520-0426(1997)014<0105:HPHRMO>2.0.CO;2
Temperature of the thermal chamber during the stability tests (run 12100751).
Citation: Journal of Atmospheric and Oceanic Technology 14, 1; 10.1175/1520-0426(1997)014<0105:HPHRMO>2.0.CO;2
The upper panel shows the temperatures of the thermal chamber, vacuum tank, detector, and spectrograph during run 12100751 at a time when the mean values of the chamber and the tank temperatures were steady. The tank and detector temperatures have been offset so that all graphs can be plotted on the same scale. The lower panel shows the corresponding thermal drift of the detector in units of millipixels.
Citation: Journal of Atmospheric and Oceanic Technology 14, 1; 10.1175/1520-0426(1997)014<0105:HPHRMO>2.0.CO;2
The upper panel shows the temperatures of the thermal chamber, vacuum tank, detector, and spectrograph during run 12100751 at a time when the chamber temperature is changing rapidly but the mean values of the other temperatures are relatively stable. The lower panel shows the corresponding thermal drift of the detector in units of millipixels.
Citation: Journal of Atmospheric and Oceanic Technology 14, 1; 10.1175/1520-0426(1997)014<0105:HPHRMO>2.0.CO;2
Overlap of the response functions of adjacent pixels in the Reticon RL512S self-scanning photodiode array (Reticon 1991).
Citation: Journal of Atmospheric and Oceanic Technology 14, 1; 10.1175/1520-0426(1997)014<0105:HPHRMO>2.0.CO;2
Apparent shift of the reference pixel (256) as a function of time during run 25080954. Time is measured in hours from switch on and includes the thermal stabilization period. The shift is expressed in units of millipixels.
Citation: Journal of Atmospheric and Oceanic Technology 14, 1; 10.1175/1520-0426(1997)014<0105:HPHRMO>2.0.CO;2
Logarithm of the Fourier transform Fϕ(s) of the optical spectrum fϕ(ν).
Citation: Journal of Atmospheric and Oceanic Technology 14, 1; 10.1175/1520-0426(1997)014<0105:HPHRMO>2.0.CO;2
Correlation between predicted (m̂) and observed (m) air masses in the sun tracking experiment (run 25080954). An empirical instrument calibration has been used.
Citation: Journal of Atmospheric and Oceanic Technology 14, 1; 10.1175/1520-0426(1997)014<0105:HPHRMO>2.0.CO;2
Equivalent pressure errors in the sun tracking test (experimental run 25080954). The pressure units are kilopascals.
Citation: Journal of Atmospheric and Oceanic Technology 14, 1; 10.1175/1520-0426(1997)014<0105:HPHRMO>2.0.CO;2
Equivalentsurface pressure changes recorded in the O2 cell test (experimental run 28081010). The pressure units are kilopascals.
Citation: Journal of Atmospheric and Oceanic Technology 14, 1; 10.1175/1520-0426(1997)014<0105:HPHRMO>2.0.CO;2
Parameters used in the signal-to-noise ratio calculations
Maximum perturbations to the optical system that can be tolerated if the relative error in radiance is not to exceed 0.1% whenever the signal level is at least 10% of saturation.
Vibration levels and consequent displacements of the detector during mechanical tests conducted on a vibration table. The level of excitation of the table was matched to the vibration environment of the research aircraft.
The O2 cell pressure P′ required to simulate a surface pressure change of Δp. The air mass is assumed to be m = 1.64, the average value in the experiment.
Predicted values of Δp for the specific air mass andO2 cell pressures used in the experiment.
