Problem Given the number of times in which an unknown event has happened and failed: Required the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named. SECTION 1 Definition 1. Several events are inconsistent, when if one of them happens, none of the rest can. 2. Two events are contrary when one, or other of them must; and both together cannot happen. 3. An event is said to fail, when it cannot happen; or, which comes to the same thing, when its contrary has happened. 4. An event is said to be determined when it has either happened or failed. 5. The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon it’s 2 happening.

An essay towards solving a problem in the doctrine of chances. [Facsimil]

The High-Resolution Imaging Camera (HiRIC) is one major payload of China’s first Mars exploration mission, and its main objective is to obtain the detailed observation images of the key areas on the Martian surface. In this paper, the leading group of HiRIC shows a full blueprint of the HiRIC. The HiRIC can achieve a high resolution (0.5 m at an altitude of 265 km) with a wide swath width of 9 km. The HiRIC adopts an Off-Axis Three-Mirror Astigmatic (TMA) optical system with a focal length of 4640 mm, an F-number of 12 and a Field of View (FOV) of 2° × 0.693°. In order to reduce the instrument weight, carbon-based material is widely used in the opto-mechanical structure which is in ultra-lightweight design, thus, a light-weight camera with a total mass of 42 kg is obtained. The Time Delay and Integration (TDI) Charge Coupled Devices (CCDs) and Complementary Metal-Oxide-Semiconductor Transistor (CMOS) detectors are all set on the imaging plane to achieve the push-broom imaging and frame imaging, respectively. And the high Signal-to-Noise Ratio (SNR) >100:1 can achieve in multi observation types for various scientific imaging tasks. After 4-year design and fabricate, the HiRIC has been assembly. The testing results show that the instrument is in good condition, and the Modulation Transfer Function (MTF) can achieve 0.18 at Nyquist frequency. The HiRIC can achieve a well image on China first Mars exploration mission.

High Resolution Imaging Camera (HiRIC) on China’s First Mars Exploration Tianwen-1 Mission

Photoclinometry was used to analyze the small-scale roughness of areas that fall within the proposed Mars Exploration Rover (MER) 2003 landing ellipses. The landing ellipses presented in this study were those in Athabasca Valles, Elysium Planitia, Eos Chasma, Gusev Crater, Isidis Planitia, Melas Chasma, and Meridiani Planum. We were able to constrain surface slopes on length scales comparable to the image resolution (1.5 to 12 m/pixel). The MER 2003 mission has various engineering constraints that each candidate landing ellipse must satisfy. These constraints indicate that the statistical slope values at 5 m baselines are an important criterion. We used our technique to constrain maximum surface slopes across large swaths of each image, and built up slope statistics for the images in each landing ellipse. We are confident that all MER 2003 landing site ellipses in this study, with the exception of the Melas Chasma ellipse, are within the small-scale roughness constraints. Our results have provided input into the landing hazard assessment process. In addition to evaluating the safety of the landing sites, our mapping of small-scale roughnesses can also be used to better define and map morphologic units. The morphology of a surface is characterized by the slope distribution and magnitude of slopes. In looking at how slopes are distributed, we can better define landforms and determine the boundaries of morphologic units.

Meter-scale slopes of candidate MER landing sites from point photoclinometry : Mars exploration rover mission and landing sites

An incomplete airborne lidar survey of Langjokull, Iceland's second largest ice cap ˜900 km2 and the surrounding area was undertaken in August 2007. Elevation data were interpolated between the lidar swaths using the technique of photoclinometry PC, which relates Sun-parallel slope angles to image brightness. A Landsat Enhanced Thematic Mapper Plus ETM+ image from March 2002 was used for this purpose. Different bands and band combinations were assessed and Band 4 760–900 nm was found to be the most appropriate. Parameters in the slope–brightness equation were derived empirically by comparing the image brightness with lidar elevation data in a 4 km × 4 km region in the centre of the ice cap. This relationship was then used to calculate the slopes, and, by integration between tie points of known lidar elevation, the elevations of the 30 m pixels that were not surveyed by lidar. The root-mean-square RMS precision repeatability of lidar elevations was 0.18 m and the accuracy was estimated to be 0.25 m. The 68.3% quantile of absolute difference relative to lidar analogous to root-mean-square error RMSE of all interpolated areas where PC assumptions are met was 5.44 m 4.66 m and 8.73 m for on-and off-ice areas, respectively. Where one or more PC assumptions were not met e.g. self-shading, sensor saturation, the 68.3% quantile of absolute difference relative to lidar was 27.89 m 18.52 m on the ice cap and 32.91 m off-ice. These accuracies were applicable to 63%, 31%, and 6% of the ice cap and 59%, 28%, and 13% of the final digital elevation model DEM, respectively. The area-weighted average 68.3% quantiles were 2.89 m for the ice cap and 6.75 m for the entire DEM. The PC technique applied to satellite imagery is a useful and appropriate method for interpolating a lidar survey of an ice cap.

Combining airborne lidar and Landsat ETM+ data with photoclinometry to produce a digital elevation model for Langjökull, Iceland

Abstract Orbital observations suggest that Mars underwent a recent ‘ice age’ (roughly 0.4–2.1 million years ago), during which a latitude-dependent ice-dust mantle (LDM) 1,2 was emplaced. A subsequent decrease in obliquity amplitude resulted in the emergence of an ‘interglacial period’ 1,3 during which the lowermost latitude LDM ice 4–6 was etched and removed, returning it to the polar cap. These observations are consistent with polar cap stratigraphy 1,7 , but lower- to mid-latitude in situ surface observations in support of a glacial–interglacial transition that can be reconciled with mesoscale and global atmospheric circulation models 8 is lacking. Here we present a suite of measurements obtained by the Zhurong rover during its traverse across the southern LDM region in Utopia Planitia, Mars. We find evidence for a stratigraphic sequence involving initial barchan dune formation, indicative of north-easterly winds, cementation of dune sediments, followed by their erosion by north-westerly winds, eroding the barchan dunes and producing distinctive longitudinal dunes, with the transition in wind regime consistent with the end of the ice age. The results are compatible with the Martian polar stratigraphic record and will help improve our understanding of the ancient climate history of Mars 9 . 

/pdf/martian-dunes-indicative-of-wind-regime-shift-in-line-with-3tawer8n.pdf

Martian dunes indicative of wind regime shift in line with end of ice age.

The relief of polygonal structures at the Phoenix landing site on Mars has been determined with the improved photoclinometry method from the images acquired with the HiRISE camera on board the Mars Reconnaissance Orbiter. The investigations showed that, within 1 km from the landing site, the topography amplitude of the relief on the surface scales of 5.5–65 m varies within the range of ∼40 to 70 cm. The polygonal structures of 2–6 m across correspond to the small-scale relief with the topography amplitude ranging from 20 to 30 cm and the standard deviation of about 3 cm. Within 1 km from the landing site, the variations of these characteristics are small. For the small polygons that are less than 5.5 m in size, the typical height is 10–15 cm. The polygons of 18–22 m in size are up to 28 cm in height, while the polygons of 60–90 m in size reach about 44 cm in height. The error in determining the relief heights was ±5.5%. The investigations showed that the improved photoclinometry method is promising for the study of small-scale features of the Martian surface.

Topography of polygonal structures at the Phoenix landing site on mars through the relief retrieval from the HiRISE images with the improved photoclinometry method

We discuss the problem of obtaining a diffraction-limited image when an object is observed through a medium with random inhomogeneities of refraction index. A new method for post-detector signal accumulation over a significantly long sequence of instantaneous images is examined. The effectiveness of the method is illustrated by the example of images obtained by computer simulation.

Fourier-component phase accumulation in observation of an object through a turbulent atmosphere: I

We investigate whether it is possible to overcome the limitations on the efficient application of Fourier-component phase accumulation method. We suggest the use of an instrument with a composite aperture for observation. It is shown that, in this case, the limitations are shifted as many times as the subaperture’s size is less than the typical size of atmospheric inhomogeneities. The interferograms obtained by means of a multibeam interpherometer are processed with the help of the total phase accumulation method using a computer model and the results are presented in the paper.

Accumulation of Fourier Component Phases during Object Observation through a Turbulent Atmosphere. II

Improved Photoclinometry Method: Topography of the Lunar Surface Area in Mare Imbrium from a Set of Images

Determination of the Relief and Radiooptical Parameters of a Surface Area by Means of a Synthetic Aperture Radar

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