1. Introduction

Air temperature, density and pressure are crucial flight-safety-relevant air data. Their accurate and precise determination in all environmental conditions is essential for aircraft control. Due to their working principle and way of integration into the aircraft, conventionally used air data probes can suffer mechanical damage or impairment in harsh environment. A novel active optical remote-sensing technique based on the analysis of Raman and elastic radiation has already been introduced together with performance simulations being capable of supplementing those conventional probes in a redundant way [1]. The measurement concept is a further development of techniques known from lidar for atmospheric observation [2–9]. It comprises four interference-filter-based measurement channels to detect elastic and Raman backscatter from air. In addition to air temperature, molecular number density and pressure, the measurement apparatus is capable of measuring air moisture, particle backscatter as well as volcanic ash independently of assumptions on the atmospheric state. Research activities funded by the European Commission including flight experiments measuring the air velocity vector and air turbulences using direct as well as coherent optical detection have already been successfully carried out [10–13]. Together with these systems, the presented technique will form a fully optical air data system. The whole laboratory measurement system, including optical, mechanical and electronic core components as interference filters and photo detectors, was designed and custom-made based on the specifications resulting from computational simulations [1]. The main apparatus components are a pulsed 532 nm laser, a four-channel receiver including data acquisition electronics and an atmospheric simulation chamber system (atmospheric simulator) for the generation of atmospheric states with regard to air temperature, pressure and moisture. In this paper, the first laboratory test measurements of the system are described and the feasibility of the concept is demonstrated. The evaluation of the air data measurement performance is driven by error requirements specified in the aviation standard AS8002 [14] from The Engineering Society For Advancing Mobility Land Sea Air and Space. The maximally allowable error for air temperature measurements is directly extracted from AS8002 and amounts to ΔT_max = 1.5 K for all measurement altitudes. The one for air pressure measurements is obtained by converting the accuracy requirements for altitude measurements specified in AS8002 with the help of the International Standard Atmosphere (ISA) model [15] and is Δp_max = 0.1% for 0 m and 0.5% for 13000 m. Because density is no parameter directly measured by conventional air data systems, a similar error specification is not defined for density measurements. Nevertheless, the experimental errors for density, as being a parameter directly optically measured by the constructed apparatus, are mentioned as well. It is furthermore noteworthy, that the data set measured by the instrument is not only interesting for application in aviation safety, but likewise capable of providing a new data set for atmospheric science.

2. Measurement methodology

In the airborne implementation, the laser will emit pulses into the atmosphere from inside the aircraft through a window integrated into the aircraft fuselage. The receiver will detect the light signals backscattered from a defined region just outside the disturbed area of the fuselage air flow. In the laboratory setup, the measurement volume is located within an atmospheric simulator. With this simulator, the air inside the measurement volume can be controlled precisely. The comparison of the known thermodynamic state of the air inside the measurement volume with the data measured by the prototype yields precise information on its experimental performance.

The interaction of the emitted laser light with atmospheric air, mainly composed of O₂ and N₂ being in a certain thermodynamic state, generates amongst others a pure rotational Raman (RR) spectrum. The backscattered RR spectrum is shown in Fig. 1. The characteristic intensity distribution of the RR spectral lines reflects the occupation probabilities of the rotational states of the air molecules. These occupation probabilities follow a Boltzmann distribution and are temperature dependent; i.e. the RR spectra at either side of the excitation wavelength change with temperature.

 

Fig. 1 Calculated backscatter coefficients of the pure rotational Raman spectrum for a laser wavelength of 532.07 nm and air consisting of the relevant nitrogen and oxygen spectral lines. The coefficients are plotted for an air temperature of 295 K and air density present at sea level, together with the spectral transmission curves of the manufactured filters RR1 and RR2. The filter central wavelengths (CWLs) in this Fig. are 531.2 nm and 528.9 nm, respectively. The Raman radiation spectral data are taken from [2].

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With two interference-filter-based optical receiver channels, different spectral portions are extracted from the anti-Stokes side of the rotational Raman backscatter. Although the Stokes side of the RR spectrum is somewhat intenser, the RR filters are placed on the anti-Stokes side, in order to avoid risk of interference with fluorescence of glass components or airborne aerosol. The transmission pass-band of the interference filter inside the channel named RR1 is adjusted on the higher wavelength edge of this spectrum. The pass-band of the filter inside the channel named RR2 is placed on the lower wavelength edge. Thus, signals with intensities of opposite temperature dependences are extracted. The transmission pass-bands of the manufactured interference filters in RR1 and RR2 are exemplarily shown in Fig. 1 as well. With the channels RR1 and RR2 air temperature, molecular number density and pressure are measured.

For air temperature measurements, the ratio Q to be calibrated is defined [2]:

In the case of air molecular number density measurements, a parameter S is defined, which is directly proportional to the air density [1]:

In addition to the pure rotational Raman channels RR1 and RR2, two further interference-filter-based channels are employed to correct potential systematic measurement errors mostly present in extreme atmospheric conditions: The filter in the third channel, named CP (for Cabannes-Particle), is located at the elastic backscatter line (which equals the laser excitation wavelength). With the signal from this channel, elastic radiation leaking to the RR channels as well as atmospheric extinction in clouds can be taken into account. The filter in the fourth channel, named H₂O, extracts the vibrational-rotational Raman backscatter of water vapor (red-shifted from the excitation wavelength by around 128 nm for the excitation wavelength of 532 nm) in order to also the measure air density of moist air. A more detailed description of the measurement theory for molecular and particle backscatter is given in [1], also including results and discussion of computational simulations dealing with the minimization of systematic errors using channel CP and H₂O. With the four channels, measurements of other relevant parameters like relative humidity, particle backscatter coefficient, particle backscatter ratio as well as detection of volcanic ash and an estimation of its mass density are also provided. In the experiments described below, the measurements were concentrated on temperature, density and pressure of dry air, thus the use of channel CP and H₂O was not necessary. Details on measurements with these channels can be found in [16].

3. Experimental laboratory setup

The laboratory temperature, density and pressure measurements were performed using a frequency-doubled Nd:YAG laser, a receiver for the collection of the light scattered inside the measurement volume, and an atmospheric simulator. A computer-controlled USB-oscilloscope and a PC are connected to the receiver to record and analyze the data. As being decisive for the performance of the measurement system, the interference filters form the core part of the receiver.

3.1 Laser source

For the laboratory experiments, a frequency doubled, pulsed (10 Hz, 10 ns) Nd:YAG laser from BigSky (now Quantel) operating at 532.07 nm is used as light source. In this first laboratory prototype setup, the flash-lamp-pumped water-cooled laser is neither actively stabilized nor seeded, generating multimode light emission with a linewidth of < 0.057 nm. Pulsed laser operation is not required in principle, but raises significantly the signal-to-noise ratio. The linewidth as well as the geometrical features of the laser beam within the measurement volume are taken into account by the calibration. They are of minor importance for the measurement performance as long as they remain stable. The pulse energy of the laser beam within the measurement volume is 118 mJ. The pulse energy stability is 6% (peak-to-peak). For the measurement of air density and pressure, a normalization of received light signals to the laser output is necessitated. This is done by using a reference photodiode.

3.2 Receiver

The receiver is set up of four identical measurement channels RR1, RR2, CP and H₂O to be seen in Fig. 2. An appropriately designed interference filter is the differing core part in each channel. The relevant properties of the RR interference filters are listed in Table 1. Each interference filter is mounted on a rotary stage to allow for the adjustment of the angle of incidence φ of the radiation and thus the central wavelength (CWL) of the spectral transmission pass-band. The choice of the CWLs of the two RR interference filters is particularly important for the minimization of the statistical measurement uncertainties. The optimum CWLs pose the best trade-off between filtered signal intensity and signal temperature dependency for the measurement apparatus. The optimum CWL values were found by experimentally determining the temperature, density and pressure measurement uncertainties as a function of the CWLs of filter RR2 within an interval ranging from 527.8 nm to 529.0 nm. The optimum CWL of filter RR1 was directly chosen to be 531.1 nm, because, first, the potentially optimum CWLs of RR1 are much less temperature sensitive than the ones of RR2 giving little margin for uncertainty improvement. Second, the important blocking of elastically scattered radiation of filter RR1 is very susceptible to CWL changes due to the proximity of this filter to the elastic wavelength and does not permit a presumably advantageous CWL red-shift without increasing the amount of leaked elastic radiation. The experiments yielded optimum CWLs of 531.1 nm for filter RR1 and 528.6 nm for filter RR2, which were then selected inside the receiver. With regard to elastic signal leakage, a further key property of the RR interference filters is the high out-of-band optical density, which is >6 (10 designed) for both RR filters. Despite this high value and the small spectral bandwidth of 0.54 nm (RR1) and 1.20 nm (RR2), the filters have a peak transmission of as high as 73% (RR1) and 85% (RR2), respectively.

 

Fig. 2 Concept of the laboratory emitter and receiver system. A pulsed laser emits light into the atmosphere. Four channels detect and spectrally filter the light backscattered from the measurement volume at distances between around 0.4 m and 0.83 m.

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Table 1. Optical properties of the RR interference filters. The values put into brackets are the correspondent angles of incidence φ.

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All receiver channels are built symmetrically around a hollow construction rail encircling the emitted laser beam. Each channel forms a bistatic configuration with the laser. To maximize the detected optical backscatter, the receiver channels are built as close as possible to the construction rail. The distance of the channel optical axes to the laser beam axis amounts to only d = 81 mm.

The geometrical form factor and the measurement volume are set by the overlap of the central laser beam with the receiving volume of each channel, defined by the optical properties of the components in each channel and by their alignment with respect to each other. All optics have a diameter of 2 inch and are appropriately anti-reflection coated. Each channel comprises two wedge prisms, a collection lens of 600 mm focal length, an imaging lens of 40 mm focal length, and a photo detector with an active area diameter of 3 mm. The wedges are used to refract the collected light by 8.1° in the direction of the channel axis. The field of view of each channel amounts to FOV = 83 mrad and allows for efficient collection of radiation, resulting in a measurement volume of around 430 mm length centered at a distance of about 550 mm in front of the receiver. The measurement volume ranges thus from 0.4 m to 0.83 m.

For channel RR1 and RR2, respectively, temperature stabilized photo detectors based on avalanche photo diodes (APDs; of the manufacturer Laser Components: SAR3000) together with custom-made transimpedance amplification electronics are used. The detection bandwidth of these APD detectors is limited to frequencies of around 350 MHz. The choice of this detector type is a result of optimization calculations with the aim of maximizing the signal-to-noise ratio [1]. The detectors are plugged to an USB-oscilloscope (PicoTechnology: PicoScope 6000 series), which has a frequency bandwidth of 350 MHz, a real time sampling rate of 5 giga-samples / s (corresponding to 1.25 giga-samples / s per channel), and a resolution of 8 bits. A simple PIN photodiode detector (Thorlabs: DET10A) is employed to monitor the shot-to-shot change of the laser pulse energy. The total receiver arrangement of the prototype comprising all channels is about 200 mm long and has a diameter of 230 mm. This receiver could be integrated behind an aircraft window with a diameter of 200 mm.

3.3 Atmospheric simulator

In order to simulate the earth atmosphere with regard to air temperature, density and pressure encountered by an aircraft at various altitudes according to the ISA model [15], an atmospheric simulator consisting of two chambers was set up. This chamber system consists of a cylindrical vacuum tube being fully located inside a bigger temperature test chamber. Both chambers are equipped with windows to allow for the transmission of the laser radiation and the backscattered light. The windows have a broad-band anti-reflection coating specifically designed for the relevant radiation wavelengths. The laser beam passes the cylindrical vacuum tube on its axis. With the surrounding temperature test chamber, the temperature T_chamber of the vacuum tube and thus the air being enclosed in the tube can be homogenously adjusted from around 230 K to 330 K. With the vacuum tube, the air pressure p_chamber can be controlled from around 100 hPa to 1000 hPa. The atmospheric simulator is located directly in front of the receiver, so that the emitted laser radiation can be guided through the vacuum tube and the backscatter can be detected from its inside. Light shielding elements and the geometrical configuration of the atmospheric simulator and the receiver ensure, that all detected radiation is really scattered inside the vacuum tube. Detection of direct stray light coming from the tube windows is not possible. To avoid aerosols and moisture inside the measurement volume at this stage, the vacuum tube is multiply purged with clean air with a dew point below −60°C prior to every experiment. The presented experiments have been performed in a dark laboratory in order to guarantee equal and reproducible experimental conditions. However, laboratory background radiation did not measurably deteriorate the measurement uncertainties obtained with the pulse energies of the used laser (118 mJ). This low susceptibility to background noise are in agreement with results of computational simulations [1].

The temperature distribution inside the vacuum tube is monitored with four PT100 Class 1/10 DIN B probes, together with a data acquisition module (Omega: PT-104A). The pressure is monitored with a temperature-stabilized capacitance diaphragm vacuum gauge (Oerlikon Leybold Vacuum: Ceravac CTR 101) located outside the chamber system and connected to the vacuum tube. The pressure sensor is connected to a control and data display unit (Vacom: MVC-3 C). The precision of the temperature measurement electronics (sensor plus data acquisition) of the atmospheric simulator under the laboratory experimental conditions according to the data sheet is better than 0.01 K for the whole measurement range of interest. The precision of the pressure measurement electronics is better than 0.01% (1000 hPa) to 0.05% (200 hPa). The precisions of the reference equipment are thus better than the precisions of the expected optical temperature and pressure measurements. The absolute accuracy of the temperature measurement electronics is of minor importance, because generated systematic measurement deviations stay the same and can be considered in the calibration. The absolute accuracy of the pressure measurement electronics (gauge plus control unit) of the atmospheric simulator is better than 0.25% (at 1000 hPa) to 0.65% (at 200 hPa) of the measured pressure value, when used at common laboratory temperatures. The absolute accuracy of the pressure measurement system is essential for the assessment of the linearity of the APD detectors of the channels RR1 and RR2 and thus of the systematic errors of the optical measurements. With this reference measurement equipment, which is used for the calibration of the measurements, the errors of the calibration coefficients, except for the linearity factor a in Eq. (4), are negligible.

4. Experimental results

4.1 Processing of raw data

The determination of the exact optical energy of the scattered and detected signal pulses is a key to accurate and precise air data measurements. The photons, which are scattered from inside the atmospheric simulator, are collected by the receiver optics, converted into electrical signals by the APD detectors and sampled and quantized by the oscilloscope. An example for the APD detector output signals is given in Fig. 3(a). Around 25 samples are taken within each single of the ≈10 ns long electrical pulses. As to be seen in Fig. 3, both APD detectors generate negative voltage undershoots. These undershoots are caused by a 10 MHz high-pass filter being an unavoidable feature inherent to the APD detector electronics. The substructures within the signals, like the dips close to the signal maxima, are generated by the flash-lamp pumped laser and are changing from shot-to-shot. After recording, the signals are post-processed with a 50 MHz digital low-pass-filter. The effect of the post-processing can be seen in Fig. 3(b). Thus, the substructures are eliminated and noise, like e.g. the quantization noise of the oscilloscope, is reduced. The energy of the detected optical pulses is identified with the peak of the post-processed electrical signal pulses. These signal peaks are then normalized with the output of the laser monitoring PIN diode. The output of the monitoring diode is post-processed in the same way as the RR signals. The post-processing of the signals in the described manner reduces the standard deviation of the determined pulse energy distribution in a series of recorded signal pulses by a factor of 3 to 10, dependent on the absolute signal amplitude to be measured. The post-processed signal pulse peaks are named U_RR1 in channel RR1 and U_RR2 in channel RR2. U_RR1 and U_RR2 are also shown in Fig. 3(b).

 

Fig. 3 Typical signal pulses recorded with the APD detectors in channel RR1 and RR2 from air at a temperature of T_chamber = 238 K and a pressure of p_chamber = 946 hPa. (a) Direct APD detector outputs. (b) Digitally filtered with a 50 MHz low-pass filter and normalized to the laser output pulse energy. The post-processed signal pulse peaks U_RR1 and U_RR2 relevant for the air data analysis are marked.

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4.2 Calibration and systematic measurement errors

The temperature and density measurements are calibrated using Eq. (2) and Eq. (4), respectively. For the determination of the calibration constants, 1000 post-processed signal pulses U_RR1 and U_RR2 are recorded and averaged at a constant air pressure p_chamber = 946 hPa inside the vacuum tube and at 8 different air temperatures T_chamber between 235 K to 305 K. The systematic temperature errors are defined as the deviations of the air temperatures recorded with the reference equipment of the atmospheric simulator from the optically measured temperatures obtained after calibration. This definition represents thus the measurement accuracy of the prototype. The experimentally obtained systematic temperature measurement errors are only < 0.05 K. This is close to the value of < 0.02 K, which is obtained from the computational performance model adapted for this measurement scenario [1]. Analogously, for air molecular number density measurements, the systematic deviations of the reference densities from the optically measured densities are < 0.07%. The error values of the performance model are < 0.03% and thus close to the experimental ones as well. The systematic pressure measurement deviations are < 0.06%. Although pressure is calculated from temperature and density via the ideal gas equation and the errors of both parameters contribute to the error of pressure, the latter is found to be always slightly smaller. This is due to an anti-correlation of the single deviations of the temperature and density measurements, leading to a partial error compensation for the pressure measurements.

Detection linearity is a very important demand for accurate air data measurements: In order to maintain calibration and obtain accurate air data at different flight altitudes, the measured signal amplitudes in each RR channel must be proportional to the optical input signal energies. However, the responses of the used APD detectors are not exactly linear, but rather exponential with a deviation of up to 5% from linearity. This has been proven by measurements performed at air pressures varying from 200 hPa to 950 hPa and constant air temperature of 298.95 K. Thus, the responses of the APDs are linearized using correction functions after signal processing for each RR channel, respectively, and the calibration is always performed using the correction functions. With this linearity correction, the residual measurement errors sourcing in nonlinear response of the experimental hardware made within the range of possible optical signal energies are reduced from around 5.5 K to 0.22 K for temperature measurements, from around 0.9% to 0.36% for density measurements, and from around 1.25% to 0.31% for pressure measurements.

4.3 Statistical measurement uncertainties as function of altitude

Statistical measurement uncertainties are a consequence of inherent noise present within the recorded signals. The measurement uncertainties for temperature, density and pressure are determined by the standard deviation – either 1-σ or 3-σ – of the distributions of a series of measured signals U_RR1 and U_RR2. The measurement uncertainties are regarded as a measure for the repetitiveness of a parameter value (temperature, density or pressure) in subsequent measurements in the sense of a measurement precision. Systematic errors like those discussed in sect. 4.2 are not included. The different noise sources and the reduction of noise have been discussed in [1] in detail on the basis of the computational performance model set up for the described measurement system. The central wavelengths (CWLs) of the spectral transmission pass-bands of the interference filters in the two RR channels are important for the minimization of measurement uncertainties.

The optical measurement uncertainties are dependent on the thermodynamic state of the atmosphere and thus on the measurement altitude as well as on the emitted laser pulse energy. The influence of both parameters was quantified in experiments. Different atmospheric states were generated with the atmospheric simulator. The vacuum tube air temperature T_chamber and air pressure p_chamber were changed corresponding to ISA altitudes [15] ranging from 500 m to 10300 m. At each virtual flight altitude 1000 values of U_RR1 and U_RR2 were recorded for laser pulse energies E_L varying from 12 mJ (10% of the maximum laser output pulse energy) to 118 mJ (100%). The different values of E_L were obtained via a set of neutral density filters in front of the laser beam. First, the temperature, density and pressure measurements were calibrated with the recorded data. With the calibration functions, the statistical measurement uncertainties ΔT, ΔN / N and Δp / p defined as the standard deviations of subsequent temperature, density and pressure measurements, respectively, were determined both as a function of altitude and as a function of the laser pulse energy. ΔT, ΔN / N and Δp / p were determined for the analysis of single pulses as well as for the analysis of the averages of blocks of every 10 or 100 consecutive pulses. The 1-σ uncertainties for the 100-pulse-average detection are illustrated for a measurement example in Fig. 4 and the further analysis is concentrated on the 100-pulse-average detection. The graphs for the uncertainties for single-pulse-detection and for 10-pulse-average detection are not shown. However, because the uncertainties are proportional to 1 / √n, with n being the number of averaged pulses, the uncertainty values for single-pulse-detection and 10-pulse average detection can easily be calculated, which corresponds very well to the results of the measurements. The altitude dependency curves of the uncertainties shown in Fig. 4 are not smooth. This is caused by slightly different positions of the neutral density filters in the beam path for each measurement altitude. On the other hand, the measurement conditions, like e.g. the laboratory temperature, and thus hardware properties varied relative strongly due to the long duration of the whole experiment, which was more than 12 hours.

 

Fig. 4 Results of the measurements performed with the atmospheric simulator. The plots illustrate the statistical measurement uncertainties ΔT (top), ΔN / N (center) and Δp / p (bottom) as a function of measurement altitude for different laser pulse energies at 532.07 nm (100% Α 118 mJ). The 1-σ uncertainties for 100-pulse-average detection are shown. For temperature and pressure measurements, the requirements set by the aviation standard AS8002 (sect. 1) are indicated by black lines. For density measurements, no requirements are specified in the aviation standard. The air temperatures and pressures adjusted inside the atmospheric simulator are specific for the shown altitudes according to the ISA model [15].

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The measurement error requirements to be met by air data systems used for aircraft control are defined in the aerospace standard AS8002 (sect. 1). The upper error limits ΔT_max and Δp_max for temperature and pressure, respectively, as a function of altitude extracted from this standard are shown in Fig. 4 (bold black lines).

4.4 General uncertainty functions

The obtained uncertainties for each measured air parameter can be well approximated by a function. The general uncertainty function ΔX_stat of the optical signal X is dependent on the detected optical pulse energy E_det:

With regard to the flight critical air parameters temperature T and pressure p and their experimental measurement uncertainties ΔT and Δp / p, three dependencies were derived:

4.5 Required pulse energies at 532 nm

With the functions ΔX_stat,T and ΔX_stat,p, the exact laser pulse energies E_L,min can be calculated, which are necessary to reduce the temperature and pressure measurement uncertainties below the maximum allowable errors for aviation ΔT_max and Δp_max. The values for E_L,min, if regarding 1-σ measurement uncertainties, are obtained by solving the inequations ΔX_stat,T(E_L,min) < ΔT_max or ΔX_stat,p(E_L,min) < Δp_max, respectively. For 3-σ uncertainties, the following inequations have to be solved: 3∙ΔX_stat,T(E_L,min) < ΔT_max or 3∙ΔX_stat,p(E_L,min) < Δp_max. The results for E_L,min for 100-pulse-average temperature measurements are shown in Fig. 5(a).

 

Fig. 5 (a) Laser pulse energies E_L,min necessary at 532 nm in order to meet the temperature measurement requirements with the measurement apparatus at different measurement altitudes specified for aviation in AS8002 (sect. 1 and Fig. 4). The solid lines show the values obtained with the uncertainty functions ΔX_stat,T (1-σ and 3-σ) when averaging 100 subsequent pulses. Dashed lines indicate the upper (u.b.) and lower bounds (l.b.) for E_L,min, when assuming the fit constants ΔA´_0,T and ΔB´_0,T being erroneous by 20%. (b) The same for air pressure measurements.

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Because ΔT_max = 1.5 K is constant for all measurement altitudes, the necessary laser pulse energies E_L,min increase with altitude being maximum at the highest altitude of 10300 m. Thus, the measurements in high altitudes pose the highest demands for temperature measurements. This is evident, since the measurement uncertainties increase with altitude as well due to decreasing molecular air density. The rising uncertainty has to be countered then by an increase of laser pulse energy. In order to stay below ΔT_max, E_L,min has to be larger than 11 mJ (35 mJ) for 1-σ (3-σ) 100-pulse-averaged measurements. Equivalently, Fig. 5(b) illustrates the necessary values E_L,min for pressure measurements as function of measurement altitude. In contrast to the temperature measurements, the highest pulse energies are needed for measurements close to sea level (highest demands for pressure measurements), since here, the maximally allowable errors are lowest (Δp_max ≈0.1%) and thus most challenging. In order to stay below Δp_max, E_L,min has to be larger than 95 mJ (355 mJ) for 1-σ (3-σ) 100-pulse-averaged measurements. The obtained values for E_L,min are dependent on the mean values of the fit constants ΔA´₀ and ΔB´₀ for temperature and density, respectively. These mean values, however, are determinable from experiment with an error of about 20% resulting in upper and lower bounds for E_L,min for temperature and pressure measurements, respectively. The bounds are illustrated as dashed lines in Fig. 5.

4.6 Required pulse energies at UV wavelengths

The resulting values for E_L,min, which refer to the utilization of the prototype apparatus including the laser with an emission wavelength of λ_L = 532.07 nm are relatively large, especially for pressure measurements. This changes when the same measurement apparatus, but a laser with shorter emission wavelength λ_L is used. The usage of shorter wavelengths is advantageous due to higher RR backscatter cross-sections [2]. For the extrapolation of the uncertainties to UV wavelengths, this 1/λ_L⁴ dependency of the detected signal power has to be accounted for in ΔX_stat,T and ΔX_stat,p. This is done by substituting n_E in Eq. (7) by n_E ∙ n_σ ∙ n_n. The factor n_σ = (532 nm)⁴ / λ⁴_L is the ratio of the RR backscattering cross-sections at 532 nm with regard to λ_L. n_n = λ_L / 532 nm is the ratio of the photon numbers at 532 nm with regard to λ_L for equal pulse energies at the two wavelengths. For all considered laser wavelengths, equal detector quantum efficiencies as at 532 nm are assumed. This assumption is only true by approximation, but makes the results comparable regardless of changing state-of-the-art photo detector technology and material.

In Fig. 6(a), E_L,min is shown for 100-pulse-averaged temperature measurements as function of the laser wavelength λ_L. The pulse energies necessary at a measurement altitude of 10300 m, which is the worst case scenario for temperature measurements, are taken as a basis for the extrapolation. Considering 1-σ (3-σ) measurement uncertainties, the required laser pulse energy drops to 3 mJ (10 mJ) for 355 nm laser wavelength and even to 1.5 mJ (4 mJ) at 266 nm laser wavelength. However, for measurements with 266 nm laser light, ozone absorption has to be considered, which may reach significant values. Furthermore, Fig. 6(a) also shows the upper and lower bounds for E_L,min values when again assuming both ΔA´_0,T and ΔB´_0,T simultaneously being 20% higher or lower, respectively. In Fig. 6(b), E_L,min for 100-pulse-averaged pressure measurements are illustrated in an analogous way. Here, as opposed to temperature measurements, pulse energies necessary at a measurement altitude at 1500 m were taken as a basis for the extrapolation, since for pressure measurements the accuracy demands are highest at this altitude. Regarding 1-σ (3-σ) measurement uncertainties, E_L,min decreases to 27 mJ (110 mJ) for 355 nm laser wavelength and to 12 mJ (45 mJ) for 266 nm laser wavelength. Table 2 summarizes the requirements with respect to the minimum laser pulse energy E_L,min for 100-pulse-averaged measurements. Additionally, the results for 10-pulse-averaged measurements are listed, which were obtained analogously.

 

Fig. 6 (a) Minimum laser pulse energies E_L,min needed to meet the temperature measurement requirements for aviation (sect. 1 and Fig. 4) when using different laser wavelengths λ_L and analyzing the average of 100 signal pulses. The measurement altitude is 10300 m, which poses the highest demand for temperature measurements. The solid lines describe the values expected to be required with the current measurement apparatus (1-σ and 3-σ). Dashed lines mark the upper (u.b.) and lower bounds (l.b.) for E_L,min, when assuming the fit constants ΔA´_0,T and ΔB´_0,T being erroneous by 20%. (b) The same for air pressure measurements. Here, the measurement altitude is 1500 m, which poses the highest demand for pressure measurements.

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Table 2. Overview of the laser pulse energies E_L,min at different laser wavelengths being necessary to reach the measurement error requirements specified in sect. 1. The values of E_L,min are listed for 10-pulse-average measurements and 100-pulse-average measurements with the current measurement system.

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5. Discussion and conclusions

The qualification of an air data apparatus measuring air temperature and pressure for aircraft control prerequisites the compliance with the error margins set in aviation standards. The margin for temperature measurements at all flight altitudes is 1.5 K. Those for pressure measurements at altitudes from 0 m to 13000 m range from 0.1% to 0.5%, respectively.

The experimental results of temperature, molecular number density and pressure measurements using the constructed prototype and the atmospheric simulator were presented. The systematic measurement errors experimentally obtained from mean values of 1000 signal pulses recorded at different air temperatures varying from 238 K to 308 K but constant air pressure of 946 hPa are < 0.05 K, < 0.07% and < 0.06% for temperature, density and pressure, respectively. These error values meet the aviation requirements. However, they are larger by a factor of about 2-3 than those calculated with the computational model [1], which considers only the errors of the individual calibration functions. Because the obtained experimental errors are very small per se, a clear identification of their sources and separation of error contributions by experimental means is technically intricate. Experimentally, a drift of the laser wavelength on the order of 1 pm could qualitatively be proven by analyzing the emitted radiation by two means: First, by using a high-resolution Fabry-Perot interferometer, second, by using an interference filter with a steep spectral transmission curve. With regard to further error reduction, it will be necessary to use an actively frequency-stabilized laser system stabilizing the emission wavelength to better than 1 pm. This will improve wavelength jitter from shot-to-shot as well as long term wavelength stability. Injection seeding or a master-oscillator-power-amplifier laser configuration could be beneficial with regard to the spectral beam profile. In order to further reduce systematic errors, active thermal control of the used hardware components would be beneficial as well. Thermal drift of the spectral transmission curves of the interference filters has been observed and has minimization potential. Taking the thermal characteristics of the interference filters as a basis, a changing laboratory temperature by up to 2 K is already sufficient to evoke measurement errors of the obtained magnitude. A temperature stabilization of the interference filters by better than 0.5 K, e.g. by means of a thermal housing, needs to be implemented. Amplification change of the highly temperature sensitive APD detectors is a critical issue as well. Here, temperature stability is even more important and has to be better by a factor of about ten, than for the interference filters. All hardware related instabilities lead to decalibration of the system and to inaccurate measurements. A detailed quantitative analysis of measurement errors evoked by instable hardware is found in [16].

The experimental systematic errors for measurements at air pressures varying from 200 hPa to 950 hPa but constant air temperature of 298.95 K are < 0.22 K, < 0.36% and < 0.31% for temperature, density and pressure, respectively. Here, these errors are larger than in the case of measurements at constant air pressure, so that aviation requirements are not met for air pressure measurements. This is due to superimposed non-linearities of the used hardware equipment itself, which generally have a larger impact the more the measured air pressure and the signal amplitudes vary. With regard to error reduction, the non-linear response of each APD detector in the RR channels is minimized by a correction function, respectively. The remaining systematic signal deviations in both RR channels after this linearity correction are correlated and referable to the nonlinearity of the reference pressure measurement system of the atmospheric simulator (sect. 3.3). In further measurement setups, a customized more stable reference vacuum gauge with better linear response and better measurement repeatability will be advantageous for excluding systematic measurement errors having their source in hardware other than the one of the laser and receiver system.

The statistical measurement uncertainties obtained in the experiments are dependent on the pulse energy of the used laser. Because the measurement uncertainties can be reduced by increasing the pulse energy, the aviation standards identify minimum pulse energy values, which are necessary to meet the aviation error requirements. The necessary laser pulse energies for the used measurement apparatus (532 nm) were determined from the experimental data. For 100-pulse-averaged temperature measurements, the energy has to be larger than 11 mJ (35 mJ), when regarding 1-σ (3-σ) uncertainties at all measurement altitudes. For 100-pulse-averaged pressure measurements, the laser pulse energy has to be larger than 95 mJ (355 mJ), when regarding 1-σ (3-σ) uncertainties at all measurement altitudes. For single pulse and for 10-pulse-averaged pressure measurements at 532 nm, the required laser pulse energy values seem non-realistically large for an application in an aircraft. Although no measurable effect on the measurement performance could be asserted, the laboratory background light was reduced to a minimum to establish equal and reproducible measurement conditions. Although computational simulations predict the low susceptibility of the prototype to background light [1], the exact influence of solar background as present in the atmosphere will be experimentally quantified in the future. Here, DC APD detectors in the RR channels will be suited for measuring the amount of detected background light, in order to determine its correlation with the measurement performance.

The utilization of UV laser wavelengths, e.g. 355 nm, instead of 532 nm will significantly reduce the required laser power due to increased RR backscatter cross-sections. Thus, the experimental results concerning the required minimum laser pulse energies were extrapolated from 532 nm to UV wavelengths using a mathematical description for the measurement uncertainties attained with the current measurement setup. With regard to 1-σ (3-σ) temperature uncertainties for 100-pulse-averaged measurements, the required laser pulse energy drops significantly to 3 mJ (10 mJ) at 355 nm and to 1.5 mJ (4 mJ) at 266 nm. Analogously, with regard to 1-σ (3-σ) pressure uncertainties, the required laser pulse energy drops to 27 mJ (110 mJ) at 355 nm and to 12 mJ (45 mJ) at 266 nm. However, in the practical airborne application, ozone absorption has to be considered at 266 nm.

As in the case of the systematic measurement errors, improvements of the measurement hardware have the potential for reducing measurement uncertainties as well. Additionally to the already mentioned improvements of the laser emission characteristics, the employment of a laser with a more stable temporal pulse shape and output pulse energy (here: 6% peak-to-peak) will be beneficial. Furthermore, the incorporated 10 MHz AC high-pass filters inside the APD detectors have to be modified. These filters cut a significant part of signal power from the signal frequency spectrum. A reduction of the high-pass filter cut-off frequency would lead to an increase in detected signal amplitude and thus to smaller measurement uncertainties. Additional noise components are generated by the oscilloscope quantization noise, due to the 8-bit digitizing of the analogue output signals of the APD detectors. These noise components can be reduced by using read-out electronics based on 12-bit analogue-to-digital converters. Beyond that, it was found that the signal output of the APD detector in channel RR1 is noisier compared to the output of the identical APD detector in channel RR2 under equal measurement conditions. Here, a further reduction of the electronic noise is possible.

The next steps concerning the further development of the measurement system consist in modifying the apparatus to UV wavelengths, improving of the mentioned hardware, and evaluating the apparatus performance in a particle-loaded atmosphere. Detailed model simulations concerning measurements in particle-loaded air have been presented in [1]. First air data measurements in moist air will be presented in [16]. The generally better RR signal-to-noise ratios achievable in the UV make the use of UV lasers with lower pulse energy and higher repetition rate possible. Flight tests in different environment will give a final proof of the capabilities of the optical air data system.