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Orbit Determination of the Lunar Reconnaissance Orbiter: Status After Seven Years

The Lunar Reconnaissance Orbiter (LRO) has been orbiting the Moon since 2009, obtaining unique and foundational datasets important to understanding the evolution of the Moon and the Solar System. The high-resolution data acquired by LRO benefit from precise orbit determination (OD), limiting the need for geolocation and co-registration tasks. The initial position knowledge requirement (50 m) was met with radio tracking from ground stations, after combination with LOLA altimetric crossovers. LRO-specific gravity field solutions were determined and allowed radio-only OD to perform at the level of 20 m, although secular inclination changes required frequent updates. The high-accuracy gravity fields from GRAIL, with <10 km spatial resolution, further improved the radio-only orbit reconstruction quality (<10 m). However, orbit reconstruction is in part limited by the 0.3-0.5 mm/s measurement noise level in S-band tracking. One-way tracking through Laser Ranging can supplement the tracking available for OD with 28-Hz ranges with 20-cm single-shot precision, but is available only on the nearside (the lunar hemisphere facing the Earth due to tidal locking). Here, we report on the status of the OD effort since the beginning of the mission, a period spanning more than seven years. We describe modeling improvements and the use of new measurements. In particular, the LOLA altimetric data give accurate, uniform, and independent information about LRO's orbit, with a different sensitivity and geometry which includes coverage over the lunar farside and is not tied to ground-based assets. With SLDEM2015 (a combination of the LOLA topographic profiles and the Kaguya Terrain Camera stereo images), another use of altimetry is possible for OD. We extend the 'direct altimetry' technique developed for the ICESat mission to perform OD and adjust spacecraft position to minimize discrepancies between LOLA tracks and SLDEM2015. Comparisons with the radio-only orbits are used to evaluate this new tracking type, of interest for the OD of future lunar orbiters carrying a laser altimeter. LROC NAC images also provide independent accuracy estimation, through the repeated views taken of anthropogenic features for instance.

Erwan Mazarico

Enceladus Vent Explorer Concept

Our concept, Enceladus Vent Explorer (EVE), is a robotic pathfinder mission to enter these doors. EVE's goals are to descend into erupting conduits up to ~2 km deep, characterize the unknown interior structure of the vent-conduit system, assess the accessibility to the subsurface ocean through the vent-conduit system, potentially reach the liquid interface, and perform astrobiology and volcanology observations in the vent-conduit system. EVE sends two types of modules: Surface Module (SM) and Descent Module (DM). SM is a lander that stays on the surface, while tens of small (~3 kg, 10 cm in width and 30 cm in length) DMs separate from SM, move to a vent, and descend into it. DMs rely on a power and communication link provided by SM through a cable. As the payload volume of DM is extremely limited, each DM can carry only a single miniaturized instrument. This limitation is complemented by heterogeneity. There are several types of DMs, all of which share the common mobility system but carry different instruments. For example, a "scout DM" creates a 3-D map of the geyser system with its stereo cameras and structured light. A "sample return DM" collects particles and ice cores in the vent and deliver them to the mass spectrometer in the SM. An "in-situ science DM" carries science instruments, such as a microscopic imager and a microfluidics chip for biosignature detection. DMs are sent either sequentially or in parallel.

Enceladus

Planetary Rover Localization Within Orbital Maps

This paper introduces an advanced rover localization system suitable for autonomous planetary exploration in the absence of Global Positioning System (GPS) infrastructure. Given an existing terrain map (image and elevation) obtained from satellite imagery and the images provided by the rover stereo camera system, the proposed method determines the best rover location through visual odometry, 3D terrain and hori- zon matching. The system is tested on data retrieved from a 3 km traverse of the Basalt Hills quarry in California where the GPS track is used as ground truth. Experimental results show the system presented here reduces by over 60 the localization error obtained by wheel odometry.

localization

Overview and Initial Results of SAND-E: Semi-Autonomous Navigation for Detrital Environments

Unmanned aerial systems (UAS) and automated terrain analysis for science and navigation are new technologies for planetary exploration. The Mars Helicopter will fly with the Mars2020 rover, the Dragonfly quadcopter will explore Titan, and Soil Properties and Object Classification (SPOC) software will be used for path planning and navigation on the Mars2020 rover. Using an Argo J5 rover instrumented with stereo cameras and Autonomous Soil Assessment System (ASAS) software, and an off the shelf quadcopter, SAND-E tested the use of automated terrain analysis and UAS data for science operations in a Mars-analog environment in Iceland during July of 2019. Scientifically, we sought to determine changes in the physical and chemical properties of sediments along a glacial-fluvial-aeolian transport pathway. Operationally, we tested rover mission-like scenarios that included UAS images and classified terrain images. Here, we present the initial results for both the operations and science elements of the study. Site Selection: A goal of SAND-E is examine sorting and alteration of sediments in fluvial and aeolian environments in both mineral-dominated and glass-dominated basaltic settings. During the first year of the project we focused on a mineral-dominated environment. Selection of the location was based on prior publications that indicated our selected region had a greater abundance of crystalline sediments than other areas fluvial-aeolian settings in Iceland. Other criteria included the presence of both fluvial and aeolian landforms along a transport pathway such that the sediments in transport could be linked to their source rocks. We chose the Skjaldbreidauhraun glacial outwash plain, which sits at the base of Thórisjökull glacier. The site is 30 km north of Thingvellir National Park and ~2 hours from Reykjavik. The outwash plain is fed by two small catchments that drain from the base of the glacier and cut through hyaloclastite and shield volcano bedrock. The drainage progresses from steep alluvial fans near the glacier into a low-sloping fluvial braidplain that becomes confined by the Skjaldbreidur shield volcano and creates a shallow canyon cut into lava bedrock. The fluvial system was a typical braided alluvial environment composed pebble- and cobble-bedded longitudinal bars and sandy channel beds. The river remained active and fluctuated in response to diurnal runoff cycles near the glacier before disappearing into the sandy substrate downstream. The high concentration of suspended sediment in the river was evident by the cloudy water and the silt and clay-sized sediments that draped the channel beds after abandonment and created playas in the lowest sloping areas of the catchment. The entire fluvial system was affected by the winds generated by frontal systems and katabatic flows descending the glacier. This resulted in the formation of aeolian lag deposits and a wind-deflation plain where the fluvial system was not active. Wind ripples and drifts formed in abandoned fluvial channels from aeolian reworking of the sand-sized fluvial sediments. The silt- and clay-sized sediments found in fluvial channels, bar tops, and playas generated dust plumes during high wind events. Our operation sought to capture the variability in this system by sampling from the range of fluvial and aeolian features 6.3 km (proximal), 11.3 km (medial), and 14.4 km (distal) along the river from its origin at the base of glacier.

Ewing, R. C.

Point-to-CAD 3D registration algorithm for relative navigation using depth-based maps

This paper presents an end-to-end 3D registration algorithm for relative navigation between known objects based on a point-to-CAD iterative closest point (ICP) principle. The objective of this method is to take in a measured point cloud extracted from a depth or disparity map – such as the ones obtained from stereo cameras, time-of-flight cameras, LiDARs, or depth from defocus sensors – and calculate the rigid body transformation that best aligns the measured data with a corresponding 3D CAD model.

Setterfield, Timothy P.

Hybrid CFD Engineering Model of Plume Induced Erosion and Crater Formation During Descent of Lunar Landers

With rapidly increased worldwide interest in landing on the moon, the issue of Plume Surface Interactions (PSI) is gaining attention. Hazards posed by lander plume induced dust and debris, as well as landing site deformation can be mitigated when better understood through predictive simulations. As simulation enabling computational power continues to increase, hybrid Computational Fluid Dynamics (CFD)/Engineering models provide the immediate ability to conduct parametric/trade studies driving design decisions for landers. Reduced order erosion engineering models apply correlations of the surface erosion rate to the plume induced surface forces with the correlations anchored to flight observations from Apollo LM landings. The MSFC propulsion fluid dynamics branch has developed such a hybrid model for predicting the plume induced viscous erosive regression of the Lunar surface beneath a landing vehicle. The (Descent Interpolated Gas Granular Erosion Model) DIGGEM was originally implemented as a post processing tool to calculate induced erosion rates through vehicle descent using CFD solutions of the vehicle plume at several fixed altitudes. This capability has since been advanced in the Loci/Chem-DIGGEM model to allow transient, moving vehicle, fully coupled viscous erosion modeling of vehicle descent PSI. This model has recently been used to make preflight predictions of the erosive regression of the ground beneath a Commercial Lunar Payload Services (CLPS) vehicle in support of measurements to be made by the Stereo Cameras for Lunar Plume Surface Studies (SCALPSS) instrument.

Plume Surface Interaction

Hybrid CFD Engineering Model of Plume Induced Erosion and Crater Formation During Descent of Lunar Landers

With rapidly increased worldwide interest in landing on the moon, the issue of Plume Surface Interactions (PSI) is gaining attention. Hazards posed by lander plume induced dust and debris, as well as landing site deformation can be mitigated when better understood through predictive simulations. As simulation enabling computational power continues to increase, hybrid Computational Fluid Dynamics (CFD)/Engineering models provide the immediate ability to conduct parametric/trade studies driving design decisions for landers. Reduced order erosion engineering models apply correlations of the surface erosion rate to the plume induced surface forces with the correlations anchored to flight observations from Apollo LM landings. The MSFC propulsion fluid dynamics branch has developed such a hybrid model for predicting the plume induced viscous erosive regression of the Lunar surface beneath a landing vehicle. The (Descent Interpolated Gas Granular Erosion Model) DIGGEM was originally implemented as a post processing tool to calculate induced erosion rates through vehicle descent using CFD solutions of the vehicle plume at several fixed altitudes. This capability has since been advanced in the Loci/Chem-DIGGEM model to allow transient, moving vehicle, fully coupled viscous erosion modeling of vehicle descent PSI. This model has recently been used to make preflight predictions of the erosive regression of the ground beneath a Commercial Lunar Payload Services (CLPS) vehicle in support of measurements to be made by the Stereo Cameras for Lunar Plume Surface Studies (SCALPSS) instrument.

Plume Surface Interaction

Evaluation of a Laser-Dot Grid-Projection System for Lunar Lander Crater-Shape and Ejecta-Sheet Measurements

Development, testing, and evaluation of an active-illumination laser-dot grid-projection system was performed to evaluate its potential inclusion on an upcoming uncrewed lunar lander mission to the south pole region of the moon. Active illumination may be required for this mission due to the shallow angle of the sun at the landing location, which may cast shadows in the landing region, hindering the stereo camera imaging system’s ability to determine the pre-and post-landing lunar surface/crater shape. Testing includes characterization of the diffractive optical elements used for the grid projection, single-camera tests to determine the imaged laser dot intensity as a function of camera exposure and imaging angle relative to the laser grid projection, laser dot brightness/saturation impact on depth map calculations, angle of imaged laser grid impact on depth map calculations for steep crater edges, impact of density gradients on the depth map calculations, and the feasibility of making measurements of the ejecta sheet.

Joshua M. Weisberger

Autonomous Ocean World Exploration: Advancement of a Virtual Testbed

The search for life (extinct or extant) and potentially habitable bodies in our solar system and beyond is one of the 12 priority science questions outlined in the National Acadamies’ 2022 decadal survey [5]. Extraterrestrial destinations containing liquid water present an opportunity to search for life as we know it, and in recent years an increasing number of such locations have been discovered within our solar system. Several Jovian moons—Europa, Ganymede, and Callisto [10]—and the Saturnian moons Enceladus [8] and Titan [9] are known or suspected to harbor massive subsurface oceans. Of these "ocean worlds", Europa is the focus of at least one planned NASA orbiter mission, Europa Clipper [4], and an early lander mission concept, the Europa Lander [2, 3]. Whereas most robotic missions to the Moon and Mars (e.g. orbiters, rovers, landers) to date have had ground controllers on Earth tightly involved in mission operations, missions to more distant worlds will require a high degree of onboard autonomy due to long communication lags and blackouts, harsh environments (radiation, cold), and more limited battery and hardware life. The past decade has seen great advances in both AI technologies and computing scalability and performance that offer promising solutions for spacecraft autonomy and motivate the software system and research programs described in this paper. The Ocean Worlds Autonomy Testbed for Exploration, Research, and Simulation (OceanWATERS) [1], which has been in development at the NASA Ames Research Center since 2018, is a virtual environment for testing lander autonomy solutions. It is built on the Robot Operating System (ROS), runs on consumer-grade Linux workstations, and was released as open source in 2020. OceanWATERS provides a physical and visual simulation of a prototypical lander in a Europa-like environment (Figure 1). The lander was modeled after requirements and specifications made in JPL’s Europa Lander Study of 2016 [3]. Simulated lander systems include stereo cameras and spotlights mounted on an antenna mast that pans and tilts, a 6 degrees of freedom (DoF) robotic arm with a force-torque sensor and two interchangeable end effectors, and a battery pack power system. The environment consists of multiple terrain models including a highly detailed model sourced from the FROST dataset [11], simulation of surrounding planetary bodies based on an ephemeris model, and lighting from the sun with associated surface illumination, reflectance, and shadows. Operations supported by OceanWATERS include panoramic and directed imaging of the environment and lander workspace, Cartesian and joint-level arm commanding, grinding of the terrain surface (e.g. digging a trench), and scooping of ground material (Figure 2) which can be discarded or collected as science samples in a receptacle that can be emptied (science operations themselves are not simulated). These operations are realized as ROS Actions and are complimented by a wide selection of telemetry that is continually produced by each lander subsystem. The power system model is driven by the open-source Generic Software Architecture for Prognostics (GSAP) [11] that predicts the battery’s remaining useful life and other characteristics. As a testbed for high-level autonomy, OceanWATERS provides an execution framework based on PLEXIL [12], an open-source plan specification language and execution engine developed largely at Ames. NASA's initial development of OceanWATERS, as well the Ocean Worlds Lander Autonomy Testbed (OWLAT) [6], a complimentary physical testbed developed at JPL, was the first step in a plan for realizing candidate onboard autonomy solutions for such planetary landers. In 2020 NASA solicited applications for its Autonomous Robotics Research for Ocean Worlds (ARROW) program, and in 2021 the similar Concepts for Ocean worlds Life Detection Technology (COLDTech) program. Collectively six research teams, based in universities and companies across the United States, were awarded grants to develop and demonstrate autonomy solutions on OceanWATERS and OWLAT. These 1–2-year projects have now finished or are nearing completion, and a wide variety of autonomy challenges in ocean world surface missions were addressed. Prototyped and demonstrated solutions have included autonomous discovery, response and adaptation to system faults and unexpected environmental events, world model synthesis through perception, plan synthesis using learned models, methods to optimize sample target selection and prioritize science data transmission, extension of PLEXIL for stochastic decision-making, and an integration of a model of JPL’s mission-ready COLDArm [7]. Technologies used in these projects include many forms of machine learning, causal reasoning, automated planning, Markov decision processes, formal methods, and other advanced techniques. A more detailed summary of the ARROW and COLDTech projects is given herein. OceanWATERS has had significant enhancements since its open-source release in 2020. Many of its new features were driven or shaped by feedback from the ARROW and COLDTech teams and requirements of their projects. In support of enabling autonomous adaptation to spacecraft faults (a specific capability solicited by both programs), a fault injection and detection framework was developed that supports a wide and growing range of fault types such as locked joints, image loss, and battery failures. The power system model was completed and integrated into the simulator, starting as a single-cell battery model and later upgraded to a multi-cell model with associated faults such as cell disconnection. Arm/terrain interaction was improved by adding a force-torque sensor and associated faults, and an analytic dig force model based on the Balovnev bucket force equations. Environment fidelity was increased by modeling terrain deformation resulting from digging and scooping; visual improvements were made in textures, lighting, and shadows. To facilitate interoperation with OWLAT, a unified command and telemetry interface between the testbeds was developed at the ROS level, along with a PLEXIL interface. The number of lander operations was greatly expanded (e.g. with Cartesian-based arm and antenna movement), and a framework was designed for users to build their own lander actions. A GUI for PLEXIL plan selection was created (Figure 3), and an expansive set of plans were added, such as those that illustrate patterns for fault handling. This paper provides a self-contained high-level description of OceanWATERS, focusing on more detailed coverage of the aforementioned enhancements. It provides a high-level summary of the projects undertaken by participants in the ARROW and COLDTech programs and how these efforts have helped shape OceanWATERS. Finally, potential future work and directions for the testbed are listed, as likely informed by the recent planetary science decadal survey [5].

K Michael Dalal

Analysis of faults and pit chains in Noctis Labyrinthus: Implications for early extension and possible magmatic plumbing

Noctis Labyrinthus has been a region of disputed origin due to its complexity and poor understanding of how various processes and mechanisms may have combined to form it. The surface is an integrated record of intensive tectonic activity expressed by a multiple extended sets of dip-slip faults oriented in different directions, and thought to have acted on this region over its history. These faults are always coalescent to pits and pit chains displaying a complicated geological history in the region. To understand this geological history, we mapped the surface features in Noctis Labyrinthus using the High-Resolution Stereo Camera (HRSC) onboard Mars Express ND2 nadir channel basemaps, and we adapted the Digital Terrain Map (DTM) from the Mission Experiment Gridded Data Record (MEGDR) of Mars Orbiter Laser Altimeter (MOLA) onboard Mars Global Surveyor (MGS) for the topography. We have investigated the spatial distribution and trend of fault systems, the pit chains' morphology, and the correlation between these two types of features. Our results show three fault systems: i) NS and NNE-SSW, ii) EW and ENE-WSW, and iii) NNW-SSE and NW. The analysis of the faults trending, cross-cutting correlation and the superimposition led to identify multiple intersections between these faults that have been alongside with the reactivations of some inherited faults. We interpreted the first system of fault to be related to coeval lateral extension, generated by regional stress tensor, which is probably related to the slight bending of Valles Marineris within two phases of bidirectional extension. The second system of faults has been generated by the radial oblate stress tensor related to the formation of the small shield volcanoes in Syria Planum. However, the third system is likely related to the external driving process, probably in the Tharsis province. We classified pits in four evolutionary stages based on their morphometric attributes. We believe that the formation of the pit chains in Noctis Labyrinthus is related to a surface collapse after a pressure drop related to the magma chamber deflation associated with Syria Planum volcanic province. We propose a deformational model based on early extension and magmatic plumbing as driving processes for the formation of Noctis Labyrinthus.

Mayssa El Yazidi

Dramatic Improvements to Feature Based Stereo

The camera registration extracted from feature based stereo is usually considered sufficient to accurately localize the 3D points. However, for natural scenes the feature localization is not as precise as in man-made environments. This results in small camera registration errors. We show that even very small registration errors result in large errors in dense surface reconstruction. We describe a method for registering entire images to the inaccurate surface model. This gives small, but crucially important improvements to the camera parameters. The new registration gives dramatically better dense surface reconstruction.

Smelyansky, V. N.

A system for extracting 3-dimensional measurements from a stereo pair of TV cameras

Obtaining accurate three-dimensional (3-D) measurement from a stereo pair of TV cameras is a task requiring camera modeling, calibration, and the matching of the two images of a real 3-D point on the two TV pictures. A system which models and calibrates the cameras and pairs the two images of a real-world point in the two pictures, either manually or automatically, was implemented. This system is operating and provides three-dimensional measurements resolution of + or - mm at distances of about 2 m.

Yakimovsky, Y.

A system for extracting three-dimensional measurements from a stereo pair of TV cameras

Obtaining accurate three-dimensional (3-D) measurement from a stereo pair of TV cameras is a task requiring camera modeling, calibration, and the matching of the two images of a real 3-D point on the two TV pictures. A system that models and calibrates the cameras and pairs the two images of a real-world point in the two pictures, either manually or automatically, was implemented at JPL. This system is operating and provides three-dimensional measurement resolution of plus or minus 5 mm at distances of about 2 m.

Yakimovsky, Y.

Stereo pair design for cameras with a fovea

We describe the methodology for the design and selection of a stereo pair when the cameras have a greater concentration of sensing elements in the center of the image plane (fovea). Binocular vision is important for the purpose of depth estimation, which in turn is important in a variety of applications such as gaging and autonomous vehicle guidance. We assume that one camera has square pixels of size dv and the other has pixels of size rdv, where r is between 0 and 1. We then derive results for the average error, the maximum error, and the error distribution in the depth determination of a point. These results can be shown to be a general form of the results for the case when the cameras have equal sized pixels. We discuss the behavior of the depth estimation error as we vary r and the tradeoffs between the extra processing time and increased accuracy. Knowing these results makes it possible to study the case when we have a pair of cameras with a fovea.

Chettri, Samir R.

Testbed for remote telepresence research

The paper describes the design and implementation of a telepresence system, as well as its control hardware and software. The mobile omnidirectional robot has three independent degrees of freedom that permit independent control of translation and rotation, thereby simulating a free-flying robot in a plane. The kinematically redundant robot arm has eight degrees of freedom that assist in obstacle and singularity avoidance. The on-board control computers permit control of the robot from the dual hand controllers via a radio modem system. A head-mounted display system provides the user with a stereo view from a pair of cameras attached to the mobile robotics system. The head tracking camera system moves stereo cameras mounted on a three-DOF platform to coordinate with the operator's head movements. This telepresence system provides a framework for research in remote telepresence, and teleoperations for space.

Adnan, Sarmad

From Antarctica to space: Use of telepresence and virtual reality in control of remote vehicles

In the Fall of 1993, NASA Ames deployed a modified Phantom S2 Remotely-Operated underwater Vehicle (ROV) into an ice-covered sea environment near McMurdo Science Station, Antarctica. This deployment was part of the antarctic Space Analog Program, a joint program between NASA and the National Science Foundation to demonstrate technologies relevant for space exploration in realistic field setting in the Antarctic. The goal of the mission was to operationally test the use of telepresence and virtual reality technology in the operator interface to a remote vehicle, while performing a benthic ecology study. The vehicle was operated both locally, from above a dive hole in the ice through which it was launched, and remotely over a satellite communications link from a control room at NASA's Ames Research Center. Local control of the vehicle was accomplished using the standard Phantom control box containing joysticks and switches, with the operator viewing stereo video camera images on a stereo display monitor. Remote control of the vehicle over the satellite link was accomplished using the Virtual Environment Vehicle Interface (VEVI) control software developed at NASA Ames. The remote operator interface included either a stereo display monitor similar to that used locally or a stereo head-mounted head-tracked display. The compressed video signal from the vehicle was transmitted to NASA Ames over a 768 Kbps satellite channel. Another channel was used to provide a bi-directional Internet link to the vehicle control computer through which the command and telemetry signals traveled, along with a bi-directional telephone service. In addition to the live stereo video from the satellite link, the operator could view a computer-generated graphic representation of the underwater terrain, modeled from the vehicle's sensors. The virtual environment contained an animate graphic model of the vehicle which reflected the state of the actual vehicle, along with ancillary information such as the vehicle track, science markers, and locations of video snapshots. The actual vehicle was driven either from within the virtual environment or through a telepresence interface. All vehicle functions could be controlled remotely over the satellite link.

Stoker, Carol

Co-registration of Laser Altimeter Tracks with Digital Terrain Models and Applications in Planetary Science

We have derived algorithms and techniques to precisely co-register laser altimeter profiles with gridded Digital Terrain Models (DTMs), typically derived from stereo images. The algorithm consists of an initial grid search followed by a least-squares matching and yields the translation parameters at sub-pixel level needed to align the DTM and the laser profiles in 3D space. This software tool was primarily developed and tested for co-registration of laser profiles from the Lunar Orbiter Laser Altimeter (LOLA) with DTMs derived from the Lunar Reconnaissance Orbiter (LRO) Narrow Angle Camera (NAC) stereo images. Data sets can be co-registered with positional accuracy between 0.13 m and several meters depending on the pixel resolution and amount of laser shots, where rough surfaces typically result in more accurate co-registrations. Residual heights of the data sets are as small as 0.18 m. The software can be used to identify instrument misalignment, orbit errors, pointing jitter, or problems associated with reference frames being used. Also, assessments of DTM effective resolutions can be obtained. From the correct position between the two data sets, comparisons of surface morphology and roughness can be made at laser footprint- or DTM pixel-level. The precise co-registration allows us to carry out joint analysis of the data sets and ultimately to derive merged high-quality data products. Examples of matching other planetary data sets, like LOLA with LRO Wide Angle Camera (WAC) DTMs or Mars Orbiter Laser Altimeter (MOLA) with stereo models from the High Resolution Stereo Camera (HRSC) as well as Mercury Laser Altimeter (MLA) with Mercury Dual Imaging System (MDIS) are shown to demonstrate the broad science applications of the software tool.

Laser

Principles of stereo reconstruction of aerial objects using stationary cameras

An overview is given here of the principles and mathematics of stereo reconstruction of objects in the sky using stationary cameras with an emphasis on meteorological applications. Through its Atmospheric Radiation Measurement program, the Department of Energy has operated stereo-photogrammetric cameras since 2017 as part of an effort to measure the life-cycle properties of clouds. At the core of that technology is stereo reconstruction, which calculates the real-world position of an object from the location of the object’s image in two cameras’ photographs. Here, stereo reconstruction is stripped down to its basic elements and presented using conventions tailored to applications in atmospheric science. In addition, the resulting equations are used to illustrate the high sensitivity of reconstructed cloud positions to errors in the cameras’ Euler angles. The interested reader will find here a self-contained guide to performing stereo reconstructions using distortion-corrected images from a pair of calibrated, stationary cameras, as well as a demonstration of the need for high accuracy in the measurement of camera properties and orientations.

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