High Spectral Resolution Lidar Research Articles

Technical realization and system simulation of ultraviolet multi-mode high-spectral-resolution lidar for measuring atmospheric aerosols

Multi-mode high-spectral-resolution lidar is a new concept of high-spectral-resolution lidar, which uses the multiple-longitudinal-mode pulsed laser rather than the single frequency laser. In this paper, we analyze the multiple longitudinal mode and its spectral distribution of a typical Nd:YAG laser, and calculate its corresponding Mie scattering and Rayleigh scattering spectra, which are a convolution between the spectral distribution of multiple-longitudinal-mode laser pulse and that of the Mie and Rayleigh scattering excited by a single frequency laser pulse. According to the spectral analyses of the elastic lidar returns, we design an ultraviolet multi-mode high-spectral-resolution lidar, in which a high-power non-seeded Nd:YAG pulsed laser at the third harmonic 355 nm wavelength is used as a transmitter, and a Cassegrain telescope serves as a receiver. In the polychromator, a narrow band interfering filter is selected to block the solar background, and a tunable Mach-Zehnder interferometer (MZI) is designed to separate the aerosol Mie scattering signals from the molecular Rayleigh scattering signals excited by the multi-mode pulsed laser. The MZI is composed of a roof mirror mounted on a piezoelectric ceramic and two beam splitters. The optical path difference of the MZI can be adjusted by the piezoelectric ceramic, while its optimum value should make the correspondence between the free spectral range of MZI and the interval between longitudinal modes of Nd:YAG pulsed laser. The photomultiplier tube is selected as a detector, whose output is the convolution between the transmission function of MZI and the Mie and Rayleigh signals excited by the multi-longitudinal mode laser pulse. In the practical experiment, the optimal optical path difference of MZI can be determined by using envelope analysis. For the transmitter laser, when one channel has a maximum output signal and the other has a minimum output, the center wavelength of each longitudinal mode of laser is locked in the optimal optical path difference. The channel of MZI with the maximum output is to pass the Mie scattering signal, while the channel with the minimum output is to block the Mie scattering signal. The aerosol optical characteristics are retrievable by using the complementary properties of the two output channels of MZI. In order to verify the feasibility of the multi-mode high spectral resolution lidar, the system simulation is carried out by using the real atmospheric model and the designed lidar system parameters. The simulation results show that the designed ultraviolet multi-mode high-spectral-resolution lidar can realize the accurate measurement of aerosol within a height of 10 km.

High spectral resolution lidar based on quad mach zehnder interferometer for aerosols and wind measurements on board space missions

We present the measurement principle and the optical design of a Quad Mach Zehnder (QMZ) interferometer as HSRL technique, allowing simultaneous measurements of particle backscattering and wind velocity. Key features of this concept is to operate with a multimodal laser and do not require any frequency stabilization. These features are relevant especially for space applications for which high technical readiness level is required.

Creating Aerosol Types from CHemistry (CATCH): A New Algorithm to Extend the Link Between Remote Sensing and Models

AbstractCurrent remote sensing methods can identify aerosol types within an atmospheric column, presenting an opportunity to incrementally bridge the gap between remote sensing and models. Here a new algorithm was designed for Creating Aerosol Types from CHemistry (CATCH). CATCH‐derived aerosol types—dusty mix, maritime, urban, smoke, and fresh smoke—are based on first‐generation airborne High Spectral Resolution Lidar (HSRL‐1) retrievals during the Ship‐Aircraft Bio‐Optical Research (SABOR) campaign, July/August 2014. CATCH is designed to derive aerosol types from model output of chemical composition. CATCH‐derived aerosol types are determined by multivariate clustering of model‐calculated variables that have been trained using retrievals of aerosol types from HSRL‐1. CATCH‐derived aerosol types (with the exception of smoke) compare well with HSRL‐1 retrievals during SABOR with an average difference in aerosol optical depth (AOD) <0.03. Data analysis shows that episodic free tropospheric transport of smoke is underpredicted by the Goddard Earth Observing System‐ with Chemistry (GEOS‐Chem) model. Spatial distributions of CATCH‐derived aerosol types for the North American model domain during July/August 2014 show that aerosol type‐specific AOD values occurred over representative locations: urban over areas with large population, maritime over oceans, smoke, and fresh smoke over typical biomass burning regions. This study demonstrates that model‐generated information on aerosol chemical composition can be translated into aerosol types analogous to those retrieved from remote sensing methods. In the future, spaceborne HSRL‐1 and CATCH can be used to gain insight into chemical composition of aerosol types, reducing uncertainties in estimates of aerosol radiative forcing.

Demonstration of a diode-laser-based high spectral resolution lidar (HSRL) for quantitative profiling of clouds and aerosols.

We present a demonstration of a diode-laser-based high spectral resolution lidar. It is capable of performing calibrated retrievals of aerosol and cloud optical properties at a 150 m range resolution with less than 1 minute integration time over an approximate range of 12 km during day and night. This instrument operates at 780 nm, a wavelength that is well established for reliable semiconductor lasers and detectors, and was chosen because it corresponds to the D2 rubidium absorption line. A heated vapor reference cell of isotopic rubidium 87 is used as an effective and reliable aerosol signal blocking filter in the instrument. In principle, the diode-laser-based high spectral resolution lidar can be made cost competitive with elastic backscatter lidar systems, yet delivers a significant improvement in data quality through direct retrieval of quantitative optical properties of clouds and aerosols.

Spectral analysis made by Mach–Zehnder interferometer for atmospheric backscattering

The ability to analyze the spectra of 532 nm/354.7 nm backscatter signal of atmosphere for Mach-Zehdner interferometer is demonstrated. The Mach-Zehdner interferometer accepts return signal. The phase difference and interference contrast are measured, which are formed by the interferometer’s double arm, polarization and quadro-channels, and Doppler frequency shift of atmosphere and backscatter ratio of aerosol backscatter to molecular backscatter are derived. Transmitter laser can operate with multi-longitudinal mode, and Mie backscattering and Rayleigh backscattering analysis spectrograph is free from locking to laser frequency. Analysis method of simultaneous measurements atmosphere aerosol backscattering ratio profile and wind profile are also discussed. If Mach-Zehnder interferometer is employed as atmospheric backscatter signal’s frequency spectrum analyzer, this high spectral resolution lidar will become an atmosphere analysis instrument with excellent performance and anticipant prospect.

Measurement method of high spectral resolution lidar with a multimode laser and a scanning Mach-Zehnder interferometer.

A simple high spectral resolution lidar technique using a multi-longitudinal mode laser is proposed for measuring aerosol extinction and backscattering coefficients. A scanning interferometer having the same free spectral range as the mode spacing of the laser is used to separate Rayleigh from Mie scattering. Scanning the interferometer in the span of one fringe, the lidar signals at the minimum and maximum Mie-scattering transmission are measured. The Rayleigh scattering signal is analyzed from these signals, and the aerosol extinction coefficient is derived. The interferometer transmittance for Mie scattering is calibrated with the reference signals taken with a portion of the transmitted laser beam.

Design of iodine absorption cell for high-spectral-resolution lidar.

Iodine absorption cells are extensively employed by high-spectral-resolution Lidars (HSRLs) for aerosol optical properties and atmosphere state parameters profiling. To the best of our knowledge, the optimal design of the parameters of iodine cells has not been talked about systematically. In this paper, a heuristic method based on multi-objective concept is proposed for the design of iodine cells employed in HSRLs for aerosol profiling, and the method can be also applied to different types of HSRLs. The bi-objective model is established based on the retrieval error analysis of HSRL and then the Pareto optimal solutions are obtained through the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The performance of different absorption lines are compared according to the Pareto solution sets, and the stability of transmittance characteristics of different absorption lines are discussed through sensitivity analysis. The results are expected to provide guidance for the design of HSRLs based on iodine absorption filters.

Current Research in Lidar Technology Used for the Remote Sensing of Atmospheric Aerosols

Lidars are active optical remote sensing instruments with unique capabilities for atmospheric sounding. A manifold of atmospheric variables can be profiled using different types of lidar: concentration of species, wind speed, temperature, etc. Among them, measurement of the properties of aerosol particles, whose influence in many atmospheric processes is important but is still poorly stated, stands as one of the main fields of application of current lidar systems. This paper presents a review on fundamentals, technology, methodologies and state-of-the art of the lidar systems used to obtain aerosol information. Retrieval of structural (aerosol layers profiling), optical (backscatter and extinction coefficients) and microphysical (size, shape and type) properties requires however different levels of instrumental complexity; this general outlook is structured following a classification that attends these criteria. Thus, elastic systems (detection only of emitted frequencies), Raman systems (detection also of Raman frequency-shifted spectral lines), high spectral resolution lidars, systems with depolarization measurement capabilities and multi-wavelength instruments are described, and the fundamentals in which the retrieval of aerosol parameters is based is in each case detailed.

Thin ice clouds in the Arctic: cloud optical depth and particle size retrieved from ground-based thermal infrared radiometry

Abstract. Multiband downwelling thermal measurements of zenith sky radiance, along with cloud boundary heights, were used in a retrieval algorithm to estimate cloud optical depth and effective particle diameter of thin ice clouds in the Canadian High Arctic. Ground-based thermal infrared (IR) radiances for 150 semitransparent ice clouds cases were acquired at the Polar Environment Atmospheric Research Laboratory (PEARL) in Eureka, Nunavut, Canada (80° N, 86° W). We analyzed and quantified the sensitivity of downwelling thermal radiance to several cloud parameters including optical depth, effective particle diameter and shape, water vapor content, cloud geometric thickness and cloud base altitude. A lookup table retrieval method was used to successfully extract, through an optimal estimation method, cloud optical depth up to a maximum value of 2.6 and to separate thin ice clouds into two classes: (1) TIC1 clouds characterized by small crystals (effective particle diameter ≤ 30 µm), and (2) TIC2 clouds characterized by large ice crystals (effective particle diameter > 30 µm). The retrieval technique was validated using data from the Arctic High Spectral Resolution Lidar (AHSRL) and Millimeter Wave Cloud Radar (MMCR). Inversions were performed over three polar winters and results showed a significant correlation (R2 = 0.95) for cloud optical depth retrievals and an overall accuracy of 83 % for the classification of TIC1 and TIC2 clouds. A partial validation relative to an algorithm based on high spectral resolution downwelling IR radiance measurements between 8 and 21 µm was also performed. It confirms the robustness of the optical depth retrieval and the fact that the broadband thermal radiometer retrieval was sensitive to small particle (TIC1) sizes.

Vertically- resolved phytoplankton carbon and net primary production from a high spectral resolution lidar.

Passive ocean observing sensors are unable to detect subsurface structure in ocean properties, resulting in errors in water column integrated phytoplankton biomass and net primary production (NPP) estimates. Active lidar (light detection and ranging) sensors make quantitative measurements of depth-resolved backscatter (bbp) and diffuse light attenuation (Kd) coefficients in the ocean and can provide critical measurements for biogeochemical models. Sub-surface phytoplankton biomass, light, chlorophyll, and NPP fields were characterized using both in situ measurements and coincident airborne high spectral resolution lidar (HSRL-1) measurements collected as part of the SABOR (Ship-Aircraft Bio-Optical Research) field campaign. We found that depth-resolved data are critical for calculating phytoplankton stocks and NPP, with improvements in NPP estimates up to 54%. We observed strong correlations between coincident HSRL-1 and in situ IOP measurements of both bbp (r = 0.94) and Kd (r = 0.90).

Retrieving the seawater volume scattering function at the 180° scattering angle with a high-spectral-resolution lidar.

A high-spectral-resolution lidar (HSRL) is proposed to retrieve the seawater volume scattering function at the 180° scattering angle βπ without the assumption of the lidar extinction-to-backscatter ratio. A field-widened Michelson interferometer is employed as the ultra-narrow spectral discriminator to reject particulate scattering and molecular Rayleigh scattering but transmit molecular Mandelshtam-Brillouin scattering. The theoretical framework to retrieve βπ is presented in detail based on a dual-channel HSRL configuration. Simulation on the retrieval and error estimation shows that, the proposed oceanographic HSRL based on the ship or aircraft can perform well to extract the profile of βπ and has a real potential in the oceanographic remote sensing.

Determining stages of cirrus evolution: a cloud classification scheme

Abstract. Cirrus clouds impose high uncertainties on climate prediction, as knowledge on important processes is still incomplete. For instance it remains unclear how cloud microphysical and radiative properties change as the cirrus evolves. Recent studies classify cirrus clouds into categories including in situ, orographic, convective and liquid origin clouds and investigate their specific impact. Following this line, we present a novel scheme for the classification of cirrus clouds that addresses the need to determine specific stages of cirrus evolution. Our classification scheme is based on airborne Differential Absorption and High Spectral Resolution Lidar measurements of atmospheric water vapor, aerosol depolarization, and backscatter, together with model temperature fields and simplified parameterizations of freezing onset conditions. It identifies regions of supersaturation with respect to ice (ice-supersaturated regions, ISSRs), heterogeneous and homogeneous nucleation, depositional growth, and ice sublimation and sedimentation with high spatial resolution. Thus, all relevant stages of cirrus evolution can be classified and characterized. In a case study of a gravity lee-wave-influenced cirrus cloud, encountered during the ML-CIRRUS flight campaign, the applicability of our classification is demonstrated. Revealing the structure of cirrus clouds, this valuable tool might help to examine the influence of evolution stages on the cloud's net radiative effect and to investigate the specific variability of optical and microphysical cloud properties in upcoming research.

Optimization design of spectral discriminator for high-spectral-resolution lidar based on error analysis.

Accurate aerosol optical properties could be obtained via the high spectral resolution lidar (HSRL) technique, which employs a narrow spectral filter to suppress the Rayleigh or Mie scattering in lidar return signals. The ability of the filter to suppress Rayleigh or Mie scattering is critical for HSRL. Meanwhile, it is impossible to increase the rejection of the filter without limitation. How to optimize the spectral discriminator and select the appropriate suppression rate of the signal is important to us. The HSRL technology was thoroughly studied based on error propagation. Error analyses and sensitivity studies were carried out on the transmittance characteristics of the spectral discriminator. Moreover, ratwo different spectroscopic methods for HSRL were described and compared: one is to suppress the Mie scattering; the other is to suppress the Rayleigh scattering. The corresponding HSRLs were simulated and analyzed. The results show that excessive suppression of Rayleigh scattering or Mie scattering in a high-spectral channel is not necessary if the transmittance of the spectral filter for molecular and aerosol scattering signals can be well characterized. When the ratio of transmittance of the spectral filter for aerosol scattering and molecular scattering is less than 0.1 or greater than 10, the detection error does not change much with its value. This conclusion implies that we have more choices for the high-spectral discriminator in HSRL. Moreover, the detection errors of HSRL regarding the two spectroscopic methods vary greatly with the atmospheric backscattering ratio. To reduce the detection error, it is necessary to choose a reasonable spectroscopic method. The detection method of suppressing the Rayleigh signal and extracting the Mie signal can achieve less error in a clear atmosphere, while the method of suppressing the Mie signal and extracting the Rayleigh signal can achieve less error in a polluted atmosphere.

Information content of bistatic lidar observations of aerosols from space.

We present, for the first time, a quantitative retrieval error-propagation study for a bistatic high spectral resolution lidar (HSRL) system intended for detailed quasi-global monitoring of aerosol properties from space. Our results demonstrate that supplementing a conventional monostatic HSRL with an additional receiver flown in formation at a scattering angle close to 165° dramatically increases the information content of the measurements and allows for a sufficiently accurate characterization of tropospheric aerosols. We conclude that a bistatic HSRL system would far exceed the capabilities of currently flown or planned orbital instruments in monitoring global aerosol effects on the environment and on the Earth's climate. We also demonstrate how the commonly used a priori "regularization" methodology can artificially reduce the propagated uncertainties and can thereby be misleading as to the real retrieval capabilities of a measurement system.

Summertime tropospheric ozone enhancement associated with a cold front passage due to stratosphere‐to‐troposphere transport and biomass burning: Simultaneous ground‐based lidar and airborne measurements

AbstractStratosphere‐to‐troposphere transport (STT) and biomass burning (BB) are two important natural sources for tropospheric ozone that can result in elevated ozone and air‐quality episode events. High‐resolution observations of multiple related species are critical for complex ozone source attribution. In this article, we present an analysis of coinciding ground‐based and airborne observations, including ozone lidar, ozonesonde, high spectral resolution lidar (HSRL), and multiple airborne in situ measurements, made on 28 and 29 June 2013 during the Southeast Nexus field campaign. The ozone lidar and HSRL reveal detailed ozone and aerosol structures as well as the temporal evolution associated with a cold front passage. The observations also captured two enhanced (+30 ppbv) ozone layers in the free troposphere (FT), which were determined from this study to be caused by a mixture of BB and stratospheric sources. The mechanism for this STT is tropopause folding associated with a cutoff upper level low‐pressure system according to the analysis of its potential vorticity structure. The depth of the tropopause fold appears to be shallow for this case compared to events observed in other seasons; however, the impact on lower tropospheric ozone was clearly observed. This event suggests that strong STT may occur in the southeast United States during the summer and can potentially impact lower troposphere during these times. Statistical analysis of the airborne observations of trace gases suggests a coincident influence of BB transport in the FT impacting the vertical structure of ozone during this case study.

Generalized high-spectral-resolution lidar technique with a multimode laser for aerosol remote sensing.

High-spectral-resolution lidar (HSRL) is a powerful tool for atmospheric aerosol remote sensing. The current HSRL technique often requires a single longitudinal mode laser as the transmitter to accomplish the spectral discrimination of the aerosol and molecular scattering conveniently. However, single-mode laser is cumbersome and has very strict requirements for ambient stability, making the HSRL instrument not so robust in many cases. In this paper, a new HSRL concept, called generalized HSRL technique with a multimode laser (MML-gHSRL), is proposed, which can work using a multimode laser. The MML-gHSRL takes advantage of the period characteristic of the spectral function of the interferometric spectral discrimination filter (ISDF) thoroughly. By matching the free spectral range of the ISDF with the mode interval of the multimode laser, fine spectral discrimination for the lidar return from each longitudinal mode can be realized. Two common ISDFs, i.e., the Fabry-Perot interferometer (FPI) and field-widened Michelson interferometer (FWMI), are introduced to develop the MML-gHSRL, and their performance is quantitatively analyzed and compared. The MML-gHSRL is a natural but significant generalization for the current HSRL technique based on the IDSF. It is potential that this technique would be a good entrance to future HSRL developments, especially in airborne and satellite-borne aerosol remote sensing applications.

Design and analysis of high-spectral resolution lidar discriminator

An accurate aerosol optical property can be obtained by a high spectral resolution lidar (HSRL) technique, which employs a narrow spectral filter to suppress Mie scattering in the lidar return signal. The ability for filter to suppress Rayleigh scattering is critical for the HSRL. In the HSRL system, Rayleigh scattering signal is obtained and aerosol scattering is suppressed at least by a factor of 10-5 through using the narrow filter. Usually, an atomic absorption filter can reach this level. While, the gaseous absorption lines do not exist at many convenient laser wavelengths, thus restricting the development of multi-wavelength HSRL instrument. A new and practical filtering method is proposed to realize the precise detection of atmospheric optical parameters by using the reflection field of Fabry-Perot (FP) interferometer. An optical splitting system with high spectral resolution is designed and its spectral characteristics are analyzed. Based on the characteristic of hyper-spectral lidar detection signal, the variations of spectral separation ratio and Rayleigh signal transmittance with reflectivity and cavity length are discussed. Spectral separation ratio is the transmittance ratio of aerosol scattering signal to molecular scattering signal through the spectral filter. With the increases of FP cavity length and surface reflectivity, the spectral separation ratio decreases and the Rayleigh signal transmission increases. The high spectral separation ratio and Rayleigh signal transmittance can be achieved by the reflection field of FP interferometer when the FP cavity length and reflectivity parameter can be chosen reasonably. We design an FP interferometer with a cavity length of 36 mm and reflectivity of 0.4. Its spectral separation ratio is affected by the echo divergence and incidence angle. The spectral separation ratio keeps unchanged when the beam divergence angle is within 3 mrad and the incident angle of the beam is within 0.5 mrad. In addition, a simulation analysis model is established based on the error propagation. An observed actual Mie-scattering profile is used for analyzing the errors. Moreover, the influences of the divergence angle and the incident angle of the echo beam on detection results are also discussed. The results show that the proposed FP interferometer can achieve fine spectral separation of Mie and Rayleigh scattering signal, and the error of detection result is not sensitive to laser divergence angle. Fine aerosol optical parameters can be achieved when the divergence and incidence angles are controlled within 10 mrad and 1.5 mrad, respectively.

基于高光谱分辨率激光雷达的气溶胶分类方法研究

Aerosols play a key role in climate change and air quality. The quantitative analysis of aerosol's contribution relies on accurate measurements of aerosol optical properties and their vertical profiles. The High Spectral Resolution Lidar(HSRL) has the capability of spectrally discriminating molecular backscatter from aerosol backscatter by a narrow-band optical filter. Therefore aerosol extinction coefficient and aerosol backscatter coefficient can be retrieved independently without assumption of the aerosol lidar ratio.The research on aerosol classification method was conducted based on HSRL technique in this paper. According to published results of aerosol classification, a classification method based on aerosol optical properties was given and an aerosol classification look-up table was provided accordingly. Aerosol extinction coefficient, aerosol backscatter coefficient and depolarization ratio measured by HSRL in Qingdao during the spring of 2015 were used to classify aerosol types referring to the established aerosol classification look-up table. The results are consistent with the trajectory model HYSPLIT and aerosol analysis system NAAPS. Results of case studies demonstrate the method in this paper is capable to identify different aerosol types properly.

Aerosol Retrievals from CALIPSO Lidar Ocean Surface Returns

This paper describes approaches to retrieve important aerosol results from the strong lidar return signals that are received by the space-borne CALIPSO lidar system after reflecting off-ocean surfaces. Relations, from which the theoretically expected values of area under ocean surface returns can be computed, are presented. A detailed description of the lidar system response to the ocean surface returns and the processes of sampling and averaging of lidar return signals are provided. An effective technique that reconstructs the lidar response to surface returns—starting from down-linked samples—and calculates the area under it, has been developed and described. The calculated area values are validated after comparing them to their theoretically predicted counterpart values. Methods to retrieve aerosol optical depths (AODs) from these calculated areas are described and retrieval results are presented, including retrieval comparison with independent AOD measurements made by an airborne High Spectral Resolution Lidar (HSRL) that yielded quite good agreement. Techniques and results are also presented on using the spectral ratios of the surface response areas to determine spectral ratios of aerosol round-trip transmission and AOD spectral difference, without need of a specific/accurate ocean-surface reflectance model.

Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 2: simulations with synthetic optical data.

We developed a mathematical scheme that allows us to improve retrieval products obtained from the inversion of multiwavelength Raman/HSRL lidar data, commonly dubbed "3 backscatter+2 extinction" (3β+2α) lidar. This scheme works independently of the automated inversion method that is currently being developed in the framework of the Aerosol-Cloud-Ecosystem (ACE) mission and which is successfully applied since 2012 [Atmos. Meas. Tech.7, 3487 (2014)10.5194/amt-7-3487-2014; "Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas)," in International Laser Radar Conference, July 2015, paper PS-C1-14] to data collected with the first airborne multiwavelength 3β+2α high spectral resolution lidar (HSRL) developed at NASA Langley Research Center. The mathematical scheme uses gradient correlation relationships we presented in part 1 of our study [Appl. Opt.55, 9839 (2016)APOPAI0003-693510.1364/AO.55.009839] in which we investigated lidar data products and particle microphysical parameters from one and the same set of optical lidar profiles. For an accurate assessment of regression coefficients that are used in the correlation relationships we specially designed the proximate analysis method that allows us to search for a first-estimate solution space of particle microphysical parameters on the basis of a look-up table. The scheme works for any shape of particle size distribution. Simulation studies demonstrate a significant stabilization of the various solution spaces of the investigated aerosol microphysical data products if we apply this gradient correlation method in our traditional regularization technique. Surface-area concentration can be estimated with an uncertainty that is not worse than the measurement error of the underlying extinction coefficients. The retrieval uncertainty of the effective radius is as large as ±0.07 μm for fine mode particles and approximately 100% for particle size distributions composed of fine (submicron) and coarse (supermicron) mode particles. The volume concentration uncertainty is defined by the sum of the uncertainty of surface-area concentration and the uncertainty of the effective radius. The uncertainty of number concentration is better than 100% for any radius domain between 0.03 and 10 μm. For monomodal PSDs, the uncertainties of the real and imaginary parts of the CRI can be restricted to ±0.1 and ±0.01 on the domains [1.3; 1.8] and [0; 0.1], respectively.