Empirical Line Calibration Research Articles

Radiometric calibration of UAV multispectral images under changing illumination conditions with a downwelling light sensor

AbstractUnmanned aerial vehicle (UAV)‐acquired multispectral images commonly suffer from radiometric inaccuracies due to changing illumination produced by intermittent cloud cover. This study addressed cloud shadow effects by integrating direct irradiance measurements from a downwelling light sensor into reflectance calculations. Two reflectance calibration methods were proposed as follows: (1) use of a single calibration reference panel for all images (Method 1) and (2) employment of a minimum distance classifier to assign color‐graded in‐field reflectance calibration targets to individual images based on their proximity in irradiance levels (Method 2). Images were acquired from 30 and 75 m flight altitudes with fixed‐exposure and auto‐exposure settings. Conventional photogrammetric calibration of UAV multispectral images inadequately addressed cloud shadows, resulting in orthomosaics with poor to moderate spatial uniformity (R2 = 0.70–0.92) and high mean absolute percentage error (MAPE = 13.52%–49.18%). The proposed calibration methods improved radiometric accuracy, yielding average R2 = 0.99 and 0.98 at 30 and 75 m images, respectively. Method 1 showed superior performance on the red‐edge and near infrared bands, and Method 2 worked best in the blue, green, and red bands. Post‐processing empirical line calibration of orthomosaics from Methods 1 and 2 reduced MAPE in reflectance estimation by at least 50% compared to conventional calibration. The clear sky reference histograms had lower Jensen–Shannon distance, higher Pearson's correlation, and improved intersection ratios with the histograms from the proposed methods, implying high similarity. Vegetation indices calculated with the proposed methods closely matched those from the reference orthomosaic, exhibiting significantly lower MAPE than conventionally calculated vegetation indices.

Bio-Optical Properties near a Coastal Convergence Zone Derived from Aircraft Remote Sensing Imagery and Modeling

Bio-optical and physical measurements were collected in the Mississippi Sound (Northern Gulf of Mexico) during the spring of 2018 as part of the Integrated Coastal Bio-Optical Dynamics project. The goal was to examine the impact of atmospheric and tidal fronts on fine-scale physical and bio-optical property distributions in a shallow, dynamic, coastal environment. During a 25-day experiment, eight moorings were deployed in the vicinity of a frontal zone. For a one-week period in the middle of the mooring deployment, focused ship sampling was conducted with aircraft and unmanned aerial vehicle overflights, acquiring hyperspectral optical and thermal data. The personnel in the aircraft located visible color fronts indicating the convergence of two water masses and directed the ship to the front. Dye releases were performed on opposite sides of a front, and coincident aircraft and unmanned aerial vehicle overflights were collected to facilitate visualization of advection/mixing/dispersion processes. Radiometric calibration of the optical hyperspectral sensor was performed. Empirical Line Calibration was also performed to atmospherically correct the aircraft imagery using in situ remote sensing reflectance measurements as calibration sources. Bio-optical properties were subsequently derived from the atmospherically corrected aircraft and unmanned aerial vehicle imagery using the Naval Research Laboratory Automated Processing System.

Uncrewed aerial vehicle radiometric calibration: A comparison of autoexposure and fixed‐exposure images

AbstractRemote sensing with uncrewed aerial vehicles (UAVs) is increasingly being used in agriculture to provide data on the physical characteristics of plants under field conditions. Data accuracy is critical for decision making with a high degree of confidence. In this work, we compared two multispectral camera calibration methods for image data collected with a UAV: (1) an autoexposure method that relies on a single calibration panel and a post hoc calibration, and (2) a fixed‐exposure system that uses three in‐field gray calibration panels using the empirical line calibration method. Both methods were compared to reflectance data from (a) four ground calibration targets measured with a spectroradiometer and (b) a single manned aircraft image calibrated with commercial calibration tarps. In a band‐by‐band comparison, the autoexposure method produced almost twice as much radiometric error on average compared with fixed exposure. Because remote sensing data are commonly converted to spectral indices, the calibration methods were also evaluated by calculating the visible atmospherically resistant index (VARI) and comparing the resulting data to the manned aircraft image. Similarly, the autoexposure method in this case produced twice the error of the fixed‐exposure method. The effect of the error was considered in a production agriculture context by simulating a remote sensing‐based prescription map for pesticide application in a cotton (Gossypium) field and calculating the number of mislabeled management zones. The simulation showed that the autoexposure method would be more costly to the farm because of its higher error, roughly $8.00/ha based on the assumptions made.

OpenHSI: A Complete Open-Source Hyperspectral Imaging Solution for Everyone

OpenHSI is an initiative to lower the barriers of entry and bring compact pushbroom hyperspectral imaging spectrometers to a wider audience. We present an open-source optical design that can be replicated with readily available commercial-off-the-shelf components, and an open-source software platform openhsi that simplifies the process of capturing calibrated hyperspectral datacubes. Some of the features that the software stack provides include: an ISO 19115-2 metadata editor, wavelength calibration, a fast smile correction method, radiance conversion, atmospheric correction using 6SV (an open-source radiative transfer code), and empirical line calibration. A pipeline was developed to customise the desired processing and make openhsi practical for real-time use. We used the OpenHSI optical design and software stack successfully in the field and verified the performance using calibration tarpaulins. By providing all the tools needed to collect documented hyperspectral datasets, our work empowers practitioners who may not have the financial or technical capability to operate commercial hyperspectral imagers, and opens the door for applications in new problem domains.

Machine Learning-Based Approaches for Predicting SPAD Values of Maize Using Multi-Spectral Images

Precisely monitoring the growth condition and nutritional status of maize is crucial for optimizing agronomic management and improving agricultural production. Multi-spectral sensors are widely applied in ecological and agricultural domains. However, the images collected under varying weather conditions on multiple days show a lack of data consistency. In this study, the Mini MCA 6 Camera from UAV platform was used to collect images covering different growth stages of maize. The empirical line calibration method was applied to establish generic equations for radiometric calibration. The coefficient of determination (R2) of the reflectance from calibrated images and ASD Handheld-2 ranged from 0.964 to 0.988 (calibration), and from 0.874 to 0.927 (validation), respectively. Similarly, the root mean square errors (RMSE) were 0.110, 0.089, and 0.102% for validation using data of 5 August, 21 September, and both days in 2019, respectively. The soil and plant analyzer development (SPAD) values were measured and applied to build the linear regression relationships with spectral and textural indices of different growth stages. The Stepwise regression model (SRM) was applied to identify the optimal combination of spectral and textural indices for estimating SPAD values. The support vector machine (SVM) and random forest (RF) models were independently applied for estimating SPAD values based on the optimal combinations. SVM performed better than RF in estimating SPAD values with R2 (0.81) and RMSE (0.14), respectively. This study contributed to the retrieval of SPAD values based on both spectral and textural indices extracted from multi-spectral images using machine learning methods.

Surface reflectance calculation and predictive models of biophysical parameters of maize crop from RG-NIR sensor on board a UAV

Unmanned aerial vehicles (UAVs) present themselves as an alternative to overcome the limitations of satellite sensors in monitoring agricultural crops, motivating many studies with UAVs. They can carry sensors, which need studies for better understanding. The present study aimed to vicariously calibrate a Red-Green-Near infrared (RG-NIR) low-cost sensor on board a UAV, and to develop predictive models of biophysical parameters for a maize crop. To achieve this purpose, 15 sets of images were captured over 61 days after emergence (DAE) of the maize crop plantation. Each set of images was mosaicked and had their digital numbers (DN) converted to reflectance. After calibration, normalized difference vegetation index (NDVI) and cumulative NDVI (cNDVI) were calculated to serve as an independent variable in the models for estimating crop parameters. In the field, 54 plants were collected and evaluated for height, leaf area and dry biomass. It was observed that the NIR band had an influence on the red band, but this influence was attenuated with the empirical line calibration. NDVI was able to detect seasonal and spatial variations in maize. The NDVI model obtained on the collection day to estimate the total dry above ground biomass had better results, generating RMSE of 68.68 g m−2 and R2 of 0.81, in comparison with cNDVI. For productivity, the result was satisfactory with cNDVI, showing RMSE of 134.00 g m−2 and R2 of 0.63. Calibration of the sensor was shown to be important to attenuate influence between bands.

Assessing the Performance of a Low-Cost Thermal Camera in Proximal and Aerial Conditions

The development of low-cost miniaturized thermal cameras has expanded the use of remotely sensed surface temperature and promoted advances in applications involving proximal and aerial data acquisition. However, deriving accurate temperature readings from these cameras is often challenging due to the sensitivity of the sensor, which changes according to the internal temperature. Moreover, the photogrammetry processing required to produce orthomosaics from aerial images can also be problematic and introduce errors to the temperature readings. In this study, we assessed the performance of the FLIR Lepton 3.5 camera in both proximal and aerial conditions based on precision and accuracy indices derived from reference temperature measurements. The aerial analysis was conducted using three flight altitudes replicated along the day, exploring the effect of the distance between the camera and the target, and the blending mode configuration used to create orthomosaics. During the tests, the camera was able to deliver results within the accuracy reported by the manufacturer when using factory calibration, with a root mean square error (RMSE) of 1.08 °C for proximal condition and ≤3.18 °C during aerial missions. Results among different flight altitudes revealed that the overall precision remained stable (R² = 0.94–0.96), contrasting with the accuracy results, decreasing towards higher flight altitudes due to atmospheric attenuation, which is not accounted by factory calibration (RMSE = 2.63–3.18 °C). The blending modes tested also influenced the final accuracy, with the best results obtained with the average (RMSE = 3.14 °C) and disabled mode (RMSE = 3.08 °C). Furthermore, empirical line calibration models using ground reference targets were tested, reducing the errors on temperature measurements by up to 1.83 °C, with a final accuracy better than 2 °C. Other important results include a simplified co-registering method developed to overcome alignment issues encountered during orthomosaic creation using non-geotagged thermal images, and a set of insights and recommendations to reduce errors when deriving temperature readings from aerial thermal imaging.

Mapping the Bathymetry of Melt Ponds on Arctic Sea Ice Using Hyperspectral Imagery

Hyperspectral remote-sensing instruments on unmanned aerial vehicles (UAVs), aircraft and satellites offer new opportunities for sea ice observations. We present the first study using airborne hyperspectral imagery of Arctic sea ice and evaluate two atmospheric correction approaches (ATCOR-4 (Atmospheric and Topographic Correction version 4; v7.0.0) and empirical line calibration). We apply an existing, field data-based model to derive the depth of melt ponds, to airborne hyperspectral AisaEAGLE imagery and validate results with in situ measurements. ATCOR-4 results roughly match the shape of field spectra but overestimate reflectance resulting in high root-mean-square error (RMSE) (between 0.08 and 0.16). Noisy reflectance spectra may be attributed to the low flight altitude of 200 ft and Arctic atmospheric conditions. Empirical line calibration resulted in smooth, accurate spectra (RMSE < 0.05) that enabled the assessment of melt pond bathymetry. Measured and modeled pond bathymetry are highly correlated (r = 0.86) and accurate (RMSE = 4.04 cm), and the model explains a large portion of the variability (R2 = 0.74). We conclude that an accurate assessment of melt pond bathymetry using airborne hyperspectral data is possible subject to accurate atmospheric correction. Furthermore, we see the necessity to improve existing approaches with Arctic-specific atmospheric profiles and aerosol models and/or by using multiple reference targets on the ground.

A simple model for PIFs extraction at digital change detection approach

The radiometric normalization using pseudo-invariant features (PIFs) is one of the best methods of image-based atmospheric correction. However, one of the main challenges of this approach is the correct selection of PIFs. So far many efforts have been made to automate radiometric correction using PIFs, although the capability of all these automated methods has been proven in various studies, their application requires intermediate to advanced statistical and computational knowledge and their application is beyond the reach of most conventional remote sensing users. Therefore, in this research, a straightforward simple method is proposed based on the definition of PIFs that automatically identifies these areas and uses them on a regression procedure for automatic normalization. The study area is Hara Protection Area (the Hara international wetland), which has sub-tropical climate and due to surface homogeneity of its mangrove forests can be used as a pilot for natural, and homogeneous ecosystems such as forested areas. To create an automatic PIFs extraction in this area, initially, we masked areas that should not be in the PIFs by applying some thresholds. At this stage, water, vegetation and mountainous areas were filtered. Then, the radiometric resolution of the two different sensor images was identical, and using the differential histogram shape of the two images, unvaried areas were extracted. To validate the accuracy of the proposed method, absolute radiometric correction using atmospheric and topographic correction (ATCOR), fast line-of-sight atmospheric analysis of hypercubes (FLAASH) and atmospheric correction (ATMOSC) methods, and relative radiometric correction using both empirical line calibration method and dark object subtraction method and automatic radiometric correction using QUick atmospheric correction (QUAC) and autonomous atmospheric correction (IMAGINE AAIC) were applied on the data. The output of all atmospheric correction methods and the proposed method was applied in the image algebra change detection in the form of a difference and with a threshold of twice the standard deviation from the mean to be checked by 219 points. The results of validation and qualitative studies of the histogram comparisons proved the proper functioning of the proposed method (κ greater than 0.8), and using cross tables, the performance of the proposed method is similar to that of the empirical line calibration method (more than 76%). Finally, a few unique features in the current research proposal, including simplicity, automation, negligible systematic error, the possibility of using in a biomarker degradation warning system, the independence on the type of sensor used, distinguish it from other radiometric correction methods.

Fluxo de Trabalho para a Calibração de Imagens Espectrais Obtidas emAeronaves Remotamente Pilotadas (ARPs) pelo Método da Linha Empírica

O uso de Aeronaves Remotamente Pilotadas (ARPs) em estudos ambientais aumentou nos ultimos anos devido a possibilidade de se realizar a aquisicao de imagens aereas por um baixo custo. No entanto, esses estudos geralmente precisam extrair informacoes fisicas sobre as condicoes espectrais de um determinado alvo. Este artigo tem como objetivo descrever alguns dos passos fundamentais na aquisicao de imagens e a sua calibracao utilizando o metodo da linha empirica. Um fluxo de trabalho foi gerado, e um estudo de caso aplicando a calibracao por linha empirica em imagens obtidas com o auxilio de ARP e discutido. Esperamos que o fluxo de trabalho sirva como um guia para os usuarios de ARPs durante o planejamento de campo e o processamento das imagens, a fim de ajuda-los a padronizar e sistematizar a aquisicao e correcao dos dados.

Challenges and Best Practices for Deriving Temperature Data from an Uncalibrated UAV Thermal Infrared Camera

Miniaturized thermal infrared (TIR) cameras that measure surface temperature are increasingly available for use with unmanned aerial vehicles (UAVs). However, deriving accurate temperature data from these cameras is non-trivialsince they are highly sensitive to changes in their internal temperature and low-cost models are often not radiometrically calibrated. We present the results of laboratory and field experiments that tested the extent of the temperature-dependency of a non-radiometric FLIR Vue Pro 640. We found that a simple empirical line calibration using at least three ground calibration points was sufficient to convert camera digital numbers to temperature values for images captured during UAV flight. Although the camera performed well under stable laboratory conditions (accuracy ±0.5 °C), the accuracy declined to ±5 °C under the changing ambient conditions experienced during UAV flight. The poor performance resulted from the non-linear relationship between camera output and sensor temperature, which was affected by wind and temperature-drift during flight. The camera’s automated non-uniformity correction (NUC) could not sufficiently correct for these effects. Prominent vignetting was also visible in images captured under both stable and changing ambient conditions. The inconsistencies in camera output over time and across the sensor will affect camera applications based on relative temperature differences as well as user-generated radiometric calibration. Based on our findings, we present a set of best practices for UAV TIR camera sampling to minimize the impacts of the temperature dependency of these systems.

Maximizing the quantitative utility of airborne hyperspectral imagery for studying plant physiology: An optimal sensor exposure setting procedure and empirical line method for atmospheric correction

Proper calibration of airborne hyperspectral imagery is essential for maximizing the quantitative utility of remotely-sensed imagery, especially when distinguishing subtle changes in spectral curves related to specific plant physiological properties (e.g. chlorophyll and water). Many studies use the empirical line approach with reference reflectance taken from dark and bright targets to calibrate airborne images. However, few have paid attention to the issue of sensor oversaturation due to the exposure setting of the imaging sensor, and no studies have investigated the effects this has placed on image calibration. With limited radiometric resolution, a sensor would become saturated by energy reflected from bright targets when its exposure is set to maximize signals reflected from a feature of interest, for example vegetation. This would result in large bias in the reflectance calibration process, and should be addressed for enormous amounts of high spatial and spectral resolution data that have been increasingly taken by manned or unmanned aircraft. In this study, we test the exposure setting of a hyperspectral sensor for maximizing vegetation signal and investigate potential reference targets in an airborne scene, and propose a more suitable airborne hyperspectral imaging and an empirical line atmospheric correction procedure by taking into account: 1) imaging sensor exposure setting, 2) spectral extrapolation, 3) sensor saturation of targets’ signal, and 4) optimal materials and grey levels for field reference reflectance for the empirical line method. The imaging experiment was conducted over a grassland field with the Micro-Hyperspec VNIR sensor. Using field hyperspectral data to validate the calibration results, we found that our proposed empirical line calibration approach improved the reflectance accuracy significantly. Vegetation indices calculated from the calibrated spectra were able to estimate chlorophyll content with success. Our work offers insights into image calibration and describes a feasible method to maximize quantitative utilities of airborne Hyperspectral imagery for vegetation studies.

Simultaneous and Constrained Calibration of Multiple Hyperspectral Images Through a New Generalized Empirical Line Model

The empirical line (EL) calibration method is commonly used for atmospheric correction of remotely sensed spectral images and recovery of surface reflectance. The current EL-based methods are applicable to calibrate only single images. Therefore, the use of the EL calibration is impractical for imaging campaigns, where many (partially overlapped) images are acquired to cover a large area. In addition, the EL results are unconstrained and an undesired reflectance with negative values or larger than 100% can be obtained. In this paper, we use the standard EL model to formulate a new generalized empirical line (GEL) model. Based on the GEL, we present a novel method for simultaneous and constrained calibration of multiple images. This new method allows for calibration through multiple image constrained empirical line (MIcEL) and three additional calibration modes. Given a set of images, we use the available ground targets and automatically extracted tie points between overlapping images to calibrate all the images in the set simultaneously. Quantitative and visual assessments of the proposed method were carried out relatively to the off-the-shelf method quick atmospheric correction (QUAC), using real hyperspectral images and field measurements. The results clearly show the superiority of MIcEL with respect to the minimization of the difference between the reflectance values of the same object in different overlapping images. An assessment of the absolute accuracy, with respect to 11 field measurement points, shows that the accuracy of MIcEL, with an average mean absolute error (MAE) of ~11%, is comparable with respect to the QUAC.

A Simplified Empirical Line Method of Radiometric Calibration for Small Unmanned Aircraft Systems-Based Remote Sensing

The use of small unmanned aircraft systems (sUAS) to acquire very high-resolution multispectral imagery has attracted growing attention recently; however, no systematic, feasible, and convenient radiometric calibration method has been specifically developed for sUAS remote sensing. In this research, we used a modified color infrared (CIR) digital single-lens reflex (DSLR) camera as the sensor and the DJI S800 hexacopter sUAS as the platform to collect imagery. Results show that the relationship between the natural logarithm of measured surface reflectance and image raw, unprocessed digital numbers (DNs) is linear and the y-intercept of the linear equation can be theoretically interpreted as the minimal possible surface reflectance that can be detected by each sensor waveband. The empirical line calibration equation for every single band image can be built using the y-intercept as one data point, and the natural log-transformed measured reflectance and image DNs of a gray calibration target as another point in the coordinate system. Image raw DNs are therefore converted to reflectance using the calibration equation. The Mann-Whitney U test results suggest that the difference between the measured and the predicted reflectance values of 13 tallgrass sampling quadrats is not statistically significant. The method theory developed in this study can be employed for other sUAS-based remote sensing applications.

The selection of appropriate spectrally bright pseudo-invariant ground targets for use in empirical line calibration of SPOT satellite imagery

The appropriate utilization of multi-temporal SPOT multispectral satellite imagery in quantitative remote sensing studies requires the removal of atmospheric effects. One widely used and potentially very accurate way of achieving absolute atmospheric correction is the calibration of at-satellite radiance data to field measures of the surface reflectance factor ( ρ s ). There are a number of variations in this technique, which are known collectively as empirical line (EL) approaches. However, the successful application of an EL spectral calibration requires the presence and careful selection of appropriate pseudo-invariant ground targets within each scene area. Real surfaces, even those that are man-made and vegetation-free, display non-Lambertian reflectance behaviour to some extent. Because of the ±31° off-nadir incidence angle range of the SPOT sensors, this is a crucial consideration. In favourable circumstances, it may be possible to utilize a goniometer to collect multiangular ρ s measurements, but for widespread lower cost application of EL approaches currently, the use of a handheld spectrometer to measure nadir only ρ s is a more realistic proposition. In either case, the selection of targets that have more limited and stable multiangular reflectance behaviour is preferable. Details are given of the reflectance properties of a variety of spectrally bright potential calibration surface types, encompassing sands, gravel, asphalts, and managed and artificial grass turf surfaces, measured in the field using the Finnish Geodetic Institute Field Goniospectrometer (FIGIFIGO). Bright calibration site selection requirements for SPOT data are discussed and the physical mechanisms behind the varying reflectance characteristics of the surfaces are considered. The most desirable properties for useful calibration targets are identified. The results of this study will assist other workers in the identification of likely suitable EL calibration sites for medium and high resolution optical satellite data, and therefore help optimize efforts in the time consuming and costly process of measuring ρ s in the field.

Spectral analysis of coastal vegetation and land cover using AISA+ hyperspectral data

This paper describes a spectral analysis of several coastal land cover types in South Padre Island, Texas using AISA+ hyperspectral remote sensing data. AISA+ hyperspectral data (1.5 metre) were acquired throughout the area on 9 March 2005. Data over mangrove areas were converted to percent reflectance using four 8×8 metre reflectance tarps (4%, 16%, 32% and 48%) and empirical line calibration. These data were then compared to percent reflectance values of other terrestrial features to determine the ability of AISA+ data to distinguish features in coastal environments. Results suggest that these data may be appropriate to discriminate coastal mangrove vegetation and provide researchers with high resolution spatial and spectral information to more effectively manage coastal ecosystems.

Empirical versus Model‐based Atmospheric Correction of Digital Airborne Imaging Spectrometer Hyperspectral Data

This paper reports the results of a quantitative comparison of empirical and model based atmospheric correction techniques for the radiometric calibration of a Digital Airborne Imaging Spectrometer (DAIS) 3715 hyperspectral image dataset. Empirical line calibration (ELC) and the radiative transfer based model Atmospheric CORrection Now (ACORN) were applied to transform the hyperspectral dataset from values of radiance to scaled percent reflectance. An additional spectral polishing technique called single spectrum enhancement (SSE) was implemented a posteriori to refine the transformation results. To evaluate the accuracy of the radiometric calibration techniques, spectra extracted from the processed images were analytically compared to spectral measurements collected in situ with a handheld spectroradiometer at 46 sample point locations. Average RMSE errors were as follows: ELC without SSE = 0.1415, ACORN without SSE = 0.0645, ELC with SSE = 0.0345, and ACORN with SSE = 0.0314. Based on the results of this analysis, spectral polishing through the use of SSE appears to introduce the greatest improvement in the removal of deleterious atmospheric effects when compared to in situ data, regardless of the choice of the model (i.e. ACORN or ELC).

Ronda peridotite massif: Methodology for its geological mapping and lithological discrimination from airborne hyperspectral data

The Ronda peridotite massif in the Sierra Bermeja, southern Spain, was imaged in July 1991 by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) during the Europe 1991 Multispectral Airborne Campaign. Principal component analysis was used (i) to extract the most spectrally extreme pixels for empirical line calibration; (ii) to physically interpret the image spectral information; and (iii) to define an optimal endmember selection based on both spatial and spectroscopic characteristics. Two successive spectral mixture analyses that allow one to focus on subtle spectral variations related to bedrock and soil lithology were applied. The first spectral mixture analysis was used to identify the major surface constituents in the image and extract the geological target to be investigated, i.e. the peridotite massif; and the second one was used to model the spectral variability within the designated target. Although mineralogical variations observed in the rocks were at a sub-pixel scale for the airborne survey, spatially organized units could be identified within the major outcrops of the peridotite massif from their spectral variations. A mineralogical interpretation of these spectral variations is proposed in relation with the field observations, in terms of relative abundance variations in the pyroxene/olivine ratio among the pixels. This work demonstrates that the proposed methodology makes possible the spectral distinction of lithological units within an ultramafic body, despite the occurrence of partial vegetation cover and multiple sub-pixel mixtures. Furthermore, it shows that hyperspectral data can provide such information, resulting in a very cost-effective method of petrologic mapping.