Question 1

Spherical astronomy basics — meridian, altitude, and zenith distance Which of the following statements about an observer’s meridian plane and star altitude are correct?

Accepted Answer

Introduction / Context: Field astronomy in surveying uses celestial sphere concepts to determine direction, latitude, and time. Key angles include altitude, azimuth, and zenith distance, and the meridian plane defines reference directions. Given Data / Assumptions: Observer’s local vertical (through zenith) and celestial pole are known constructs. Angles are measured at the station. Concept / Approach: The observer’s meridian is the great circle through the zenith and celestial poles. Altitude is the angle above the horizon; equivalently, the angle between the star’s projection in the vertical and horizontal directions at the observer. Zenith distance equals 90° minus altitude. Step-by-Step Solution: Define meridian → plane through zenith and poles → (a) correct.Define altitude → angle above horizon → (b) restates it → correct.Zenith distance = 90° − altitude → (c) correct. Verification / Alternative check: Standard surveying/astronomy texts present these definitions consistently. Why Other Options Are Wrong: The combined option is most accurate since each statement is true. Common Pitfalls: Confusing azimuth (bearing in the horizontal plane) with altitude (elevation). Final Answer: All of the above.

Question 2

Circumpolar stars — observable behavior for a given latitude Which statement best characterizes circumpolar stars as seen from mid and high latitudes in the Northern Hemisphere?

Accepted Answer

Introduction / Context: Circumpolar stars are important in navigation and surveying because they never set; their apparent motion provides useful reference directions throughout the night. Given Data / Assumptions: Northern Hemisphere observer; analogous statements apply in the south with the south celestial pole. “Circumpolar” defined relative to observer’s latitude. Concept / Approach: A star is circumpolar if its declination satisfies conditions that keep its diurnal circle entirely above the horizon for that observer. Such stars circle the celestial pole without ever setting, thus are always visible (weather permitting). Step-by-Step Solution: Define circumpolar → star never dips below horizon.Hence, the key property is continuous visibility above the horizon.Therefore (c) is the most defining statement. Verification / Alternative check: Diurnal circles drawn on the celestial sphere for high declinations show continuous paths above the horizon. Why Other Options Are Wrong: (a) and (b) describe rotation about a pole but do not uniquely define “circumpolar”. (d) is incorrect; many circumpolar stars are indeed near Polaris. Common Pitfalls: Assuming circumpolar status is global; it depends on latitude and star declination. Final Answer: They remain always above the horizon for the observer.

Question 3

Field astronomy in surveying — what is actually observed? In routine field astronomy applied to surveying, the directly observed quantities are primarily:

Accepted Answer

Introduction / Context: Field astronomy provides direction, time, and latitude/longitude control for geodetic work. Theodolites and total stations are employed to sight celestial targets and measure angular relationships precisely. Given Data / Assumptions: Classical astronomical surveying with optical instruments. Derived quantities (time, position) come from angular measurements and known ephemerides. Concept / Approach: Observers measure horizontal and vertical angles to stars or the Sun (e.g., altitude and azimuth), then compute positions or time. Lengths and heights are not measured directly by astronomical observation; they are derived via geometry, leveling, or distance measurements unrelated to celestial sighting. Step-by-Step Solution: Identify instrument capability → precise angle measurement.Relate angles + time/ephemerides → compute geodetic quantities.Therefore, the observed quantity is angles. Verification / Alternative check: Methodologies such as Laplace azimuths, astronomical latitude by meridian altitude, and time determinations all center on angles. Why Other Options Are Wrong: Lengths and heights may be outcomes of separate surveying operations, not of astronomical observations themselves. Common Pitfalls: Confusing theodolite angle observations with EDM distance measurements; the latter are not “astronomy”. Final Answer: Angles.

Question 4

Photogrammetry — flying height from parallax difference and mean photo base A stereo pair taken from flying height H shows a parallax difference of 0.8 mm for two points whose elevation difference is 100 m. If the mean photo base (distance between p…

Accepted Answer

Introduction / Context: In stereophotogrammetry, the relation between stereoscopic parallax and object height allows height determination. Conversely, if height difference and parallax difference are known, one can infer flying height when the mean photo base is given. Given Data / Assumptions: Elevation difference Δh = 100 m. Parallax difference dp = 0.8 mm (on photos). Mean photo base b = 95.2 mm. Small-relief approximation and mean terrain level near datum so higher-order terms are negligible. Concept / Approach: For small relief, a useful approximation relates parallax difference to height difference via the mean photo base and flying height: dp ≈ b * (Δh / H). This follows from p = (B f)/(H − h) with b = (B f)/H and linearization for small Δh relative to H. Step-by-Step Solution: Use dp ≈ b * (Δh / H)Rearrange → H ≈ b * Δh / dpCompute ratio b/dp = 95.2 / 0.8 = 119Hence H ≈ 119 * 100 m = 11,900 m ≈ 12,000 m Verification / Alternative check: A more exact relation from p = (B f)/(H − h) and b = (B f)/H gives p = b / (1 − h/H). Differencing and linearizing for small Δh leads to dp ≈ b * Δh / H, confirming the approximation. Why Other Options Are Wrong: 8,000 m and 10,000 m underpredict H for the given dp. 14,000 m overpredicts H; the computed value is near 12,000 m. Common Pitfalls: Confusing ground air base B with photo base b; here b is already given in mm on the photographs. Final Answer: 12,000 m.

Question 5

Geographical sign conventions — identify the incorrect longitude sign Which of the following statements about the signs of latitude and longitude is incorrect?

Accepted Answer

Introduction / Context: Mapping and GPS computations adopt a consistent sign convention for latitude and longitude. Misunderstanding the sign can flip hemispheres and lead to large positional errors. Given Data / Assumptions: Standard geodetic convention is used. Positive and negative refer to numerical signs. Concept / Approach: The usual convention assigns: latitude north positive, latitude south negative; longitude east positive, longitude west negative. Therefore, statements claiming east is negative or west is positive are incorrect. Step-by-Step Solution: Check (a) → true.Check (b) → true.Check (c) → false (east is positive).Check (d) → false (west is negative).Thus (e) properly identifies incorrect statements. Verification / Alternative check: Most GIS and GPS data formats (e.g., WGS84) follow this convention; some local systems may adopt alternatives but are rare. Why Other Options Are Wrong: (a) and (b) are correct statements and not “incorrect”. Common Pitfalls: Confusing the sign convention with Easting/Northing coordinates in projected systems. Final Answer: Both (c) and (d) of the above.

Question 6

Photogrammetric parallax — contributors to measured parallax on a photograph The stereoscopic parallax of a point measured on overlapping aerial photographs is influenced by which factors?

Accepted Answer

Introduction / Context: Parallax is the apparent displacement of image points between two overlapping photos and is central to height determination in photogrammetry. Given Data / Assumptions: A standard vertical aerial photography setup with overlap. Rigid camera geometry with known focal length. Concept / Approach: Parallax p is commonly related by p ≈ (B f)/(H − h), where B is air base, f is focal length, H is flying height above datum, and h is ground elevation. Thus, each listed factor directly influences measured parallax values. Step-by-Step Solution: Increase h (higher ground) → denominator decreases → parallax increases.Increase H → denominator increases → parallax decreases.Increase B or f → numerator increases → parallax increases. Verification / Alternative check: Analytical stereotriangulation models and mapping camera geometry yield the same dependencies. Why Other Options Are Wrong: Each single factor is indeed influential; the comprehensive option is therefore correct. Common Pitfalls: Confusing photo base (on image) with air base (in space); both relate via scale. Final Answer: All of the above.

Question 7

Tilted photograph geometry — distance from principal point to plumb point For a tilted aerial photograph with lens focal length f and tilt angle θ, the distance of the plumb point from the principal point is:

Accepted Answer

Introduction / Context: On a tilted photograph, the plumb point is the foot of the vertical (nadir) on the photo plane. Its location relative to the principal point depends on the tilt angle and focal length. Given Data / Assumptions: Small-angle central projection from a calibrated camera. Single-axis tilt for simplicity. Concept / Approach: Consider the right triangle formed by the optical axis, the vertical line through the exposure station, and the photo plane. The offset between principal and plumb points equals the distance along the photo plane corresponding to the tilt: offset = f * tan θ. Step-by-Step Solution: Define tilt θ between optical axis and vertical.Projection on the image plane gives offset = f * tan θ.Thus, choose f * tan θ. Verification / Alternative check: Photogrammetry texts derive this from perspective geometry of a tilted frame. Why Other Options Are Wrong: fsinθ or fcosθ represent other legs of the triangle; f*secθ is not the planar offset. Common Pitfalls: Confusing principal point (intersection of optical axis) with nadir/plumb point. Final Answer: f * tan θ.

Question 8

Human stereoscopic acuity — smallest discernible depth from geometry of vision Assuming normal vision with viewing distance 25 cm, smallest resolvable angular disparity of about 20 arcseconds, and interocular distance 6.5 cm, what is the smallest de…

Accepted Answer

Introduction / Context: Stereoscopic vision detects depth from the small angular difference (binocular disparity) of the lines of sight from the two eyes. The fineness of depth perception is important in stereoscopic plotting and 3D visual interpretation. Given Data / Assumptions: Viewing distance s = 25 cm = 0.25 m. Interocular distance i = 6.5 cm = 0.065 m. Smallest angular disparity α = 20 arcseconds. Small-angle approximations apply. Concept / Approach: For small disparities, geometric relations give approximately: α ≈ i * Δz / s^2, where Δz is the smallest discernible depth difference at range s. Rearranging yields Δz ≈ α * s^2 / i. Convert α to radians for computation. Step-by-Step Solution: Convert α: 20″ = 20 * (π / 648000) ≈ 9.696 × 10^-5 rad.Compute s^2: 0.25^2 = 0.0625 m^2.Apply Δz ≈ α * s^2 / i = (9.696 × 10^-5) * 0.0625 / 0.065 ≈ 9.3 × 10^-5 m.Convert to mm: 9.3 × 10^-5 m ≈ 0.093 mm ≈ 0.1 mm. Verification / Alternative check: The order-of-magnitude (tenths of a millimeter at 25 cm) aligns with psychophysical measurements of stereoacuity under good illumination and contrast. Why Other Options Are Wrong: 0.5 to 1.1 mm are larger than the theoretical threshold and would be easily discerned at the given geometry. Common Pitfalls: Using degrees instead of radians in the formula leads to large errors. Confusing viewing distance with interocular distance in the relation. Final Answer: 0.1 mm.

Question 9

Meridians on a sphere — distance between longitudes at higher latitudes If the separation between two meridians measured along the equator is 100 km, what will be the horizontal distance between the same two meridians measured along the parallel of …

Accepted Answer

Introduction / Context: In geodesy and plane surveying, distances between meridians (lines of longitude) vary with latitude. Along the equator, meridians are farthest apart; toward the poles they converge. This question tests the fundamental cosine scaling that converts an equatorial spacing to the spacing along any parallel (line of latitude). Given Data / Assumptions: Equatorial distance between two meridians = 100 km. Required distance is along the parallel of latitude 60°. Idealized spherical Earth and small-arc approximation so linear scaling by cos(latitude) applies. Concept / Approach: At latitude φ, the radius of the parallel equals Earth radius * cos φ. Hence any arc length between the same longitudes at latitude φ equals the corresponding equatorial arc multiplied by cos φ. Therefore, distance at latitude φ = (equatorial distance) * cos φ. Step-by-Step Solution: Given equatorial spacing = 100 km.Latitude φ = 60°.Use scaling: distance_φ = distance_equator * cos φ.Compute cos 60° = 0.5.Therefore distance at 60° = 100 * 0.5 = 50 km. Verification / Alternative check: At 0° (equator), cos 0° = 1, so spacing is unchanged; at 90° (pole), cos 90° = 0, so meridians meet (distance becomes 0). The computed 50 km at 60° matches this trend. Why Other Options Are Wrong: 100 km and higher values ignore the cosine reduction with latitude. 150 km, 400 km, 500 km would imply spacing grows toward the pole, which is physically impossible. Common Pitfalls: Confusing the longitude degree-length (which varies with latitude) with the latitude degree-length (nearly constant); forgetting to multiply by cos φ when converting equatorial spacing to spacing on a parallel. Final Answer: 50 km

Question 10

Photogrammetry and stereoscopy — standard value of human eye base In stereoscopic plotting and visual perception calculations, what average interpupillary distance (eye base) is typically assumed for a normal adult observer?

Accepted Answer

Introduction / Context: In air-photo interpretation and stereoscopic vision, the eye base (interpupillary distance) is used when relating stereo parallax to perceived depth. A standard average value allows consistent calculations for stereoscopes and ergonomic setup of plotting instruments. Given Data / Assumptions: Question asks for the typical average eye base used in practice. Normal adult population; specialized clinical variations are ignored. Conventional photogrammetric assumptions are applied. Concept / Approach: The interpupillary distance in adults commonly ranges from roughly 58 mm to 70+ mm. For design and calculation purposes, most photogrammetry texts take a representative mean value near the center of this range. The widely adopted standard is approximately 62 mm, which is used to model comfortable stereo viewing geometry and to scale stereo parallax–depth relations in simple calculations. Step-by-Step Solution: Identify typical adult IPD range (about 58–70 mm).Select the mid-range representative value used in photogrammetry.Adopt the conventional standard: 62 mm. Verification / Alternative check: Manufacturers of stereoscopes and training manuals often cite 62–65 mm as practical settings, with 62 mm being the canonical default for calculations. Why Other Options Are Wrong: 58 mm, 60 mm, 64 mm, 72 mm are plausible individual IPDs but are not the typical standard assumption used in stereoscopic calculation references. Common Pitfalls: Confusing a device's adjustable eyepiece spacing with the standard value used for theoretical calculations; using an extreme IPD that does not represent the average observer. Final Answer: 62 mm

Question 11

Astronomical surveying — multiple equivalent definitions of geographic latitude Which statements correctly describe the latitude of an observer's position on Earth?

Accepted Answer

Introduction / Context: Geographic latitude is a fundamental coordinate in astronomical and geodetic surveying. There are several equivalent ways to define it, each useful for different observational procedures, reductions, or conceptual explanations involving the celestial sphere and the local horizon system. Given Data / Assumptions: Observer at a point on Earth with a well-defined local meridian. Standard celestial sphere relations hold. Any small deflection of the vertical is neglected for basic definitions. Concept / Approach: For an observer in the northern hemisphere, the altitude of the elevated pole (near the pole star Polaris) equals the local geographic latitude. The zenith's declination is also numerically equal to the latitude because the zenith lies along the observer's meridian at an angular distance from the celestial equator equal to the observer's latitude. Fundamentally, latitude is the angular distance along the meridian between the equator and the observer's position, reckoned north or south according to hemisphere. Step-by-Step Solution: Relate pole altitude: altitude of elevated pole = φ (latitude).Relate zenith coordinates: declination of zenith = φ.Geometric definition: angular distance along meridian from equator to the observer = φ.Assign sign: north or south depending on hemisphere. Verification / Alternative check: Simple star-altitude observations (e.g., Polaris) confirm that measured pole altitude equals local latitude to first order, matching these equivalent definitions. Why Other Options Are Wrong: Options (a)–(d) are all correct statements. Therefore, the comprehensive choice is (e). Common Pitfalls: Confusing astronomical declination (celestial coordinate) with terrestrial latitude, although they are numerically equal for the zenith; neglecting the small corrections due to atmospheric refraction and local vertical deflection in precise work. Final Answer: All of the above

Question 12

Solar declination and seasons — identify the event with maximum north declination The Sun's apparent north declination attains its maximum positive value once each year. What is this position/event called in positional astronomy and surveying practi…

Accepted Answer

Introduction / Context: Seasonal changes are governed by Earth's axial tilt and its orbit around the Sun. Surveyors and astronomers use standard terms to describe key instants of the Sun's apparent motion on the celestial sphere, which affect day length, solar altitude, and declination used in observations and reductions. Given Data / Assumptions: Declination is measured positive north of the celestial equator and negative south. The Sun's declination varies approximately sinusoidally over the year. We refer to the northern hemisphere seasonal naming convention. Concept / Approach: At the two equinoxes (vernal and autumnal), the Sun's declination is approximately 0°, and day and night are nearly equal. At solstices, the magnitude of declination is maximal: about +23.44° at the June (summer) solstice and about −23.44° at the December (winter) solstice. Therefore, the event when the Sun's north declination is maximum is the summer solstice (around June 21). Step-by-Step Solution: Recall annual cycle: declination ranges from −23.44° to +23.44°.Identify maximum positive (north) value: +23.44° at June solstice.Name of event: summer solstice. Verification / Alternative check: Solar ephemerides and almanacs list declination values peaking in June for the northern hemisphere, confirming the choice. Why Other Options Are Wrong: Vernal/Autumnal equinox: declination ≈ 0°, not maximum. Winter solstice: declination is at its most negative (south) value, not north maximum. Common Pitfalls: Mixing hemisphere conventions; forgetting that “north declination maximum” corresponds to midsummer in the northern hemisphere. Final Answer: Summer solstice

Question 13

Photogrammetry — name of the orthogonal projection of the perspective centre on a tilted photograph In a tilted aerial photograph, what is the point called that is obtained by dropping a perpendicular from the camera perspective centre to the photog…

Accepted Answer

Introduction / Context: Several special points are defined on aerial photographs to aid in interior orientation, exterior orientation, and mapping geometry. On tilted photographs, distinguishing the principal point, nadir (plumb) point, and isocentre is fundamental for geometric constructions and relief displacement analysis. Given Data / Assumptions: Photograph is tilted; the camera perspective centre is not directly above the principal point in plan. Standard photogrammetric definitions apply. Concept / Approach: The principal point is defined as the foot of the perpendicular from the perspective centre onto the photograph plane, regardless of tilt. The nadir (plumb) point is the intersection with the photo plane of the vertical line through the perspective centre (direction of gravity). The isocentre lies midway between the principal point and the nadir point on a tilted photo. Therefore, the orthogonal projection of the perspective centre on the photograph plane is the principal point. Step-by-Step Solution: Identify required projection: perpendicular from centre to photo plane.Match with definition: principal point = orthogonal projection.Differentiate: nadir/plumb is vertical projection; isocentre is the midpoint of principal and nadir points. Verification / Alternative check: Standard interior orientation procedures locate the principal point via fiducial marks; constructions to locate isocentre use the midpoint of principal and nadir, reinforcing the distinct definitions. Why Other Options Are Wrong: Nadir/plumb: vertical (gravity) projection, not orthogonal to the photo plane. Isocentre: midpoint of principal and nadir; not itself a projection from the centre. None of these: incorrect because the correct term is principal point. Common Pitfalls: Interchanging principal point with nadir on vertical photos (they coincide only when tilt is zero), leading to confusion on tilted imagery. Final Answer: Principal point

Question 14

Triangulation terminology — station with no direct observations In a triangulation series, what is the station called where no angles are actually observed, yet the station is included in computations using adjoining observed angles?

Accepted Answer

Introduction / Context: Triangulation networks use a hierarchy of stations: main, subsidiary/satellite, and sometimes computed points used for geometric continuity. Understanding the roles and naming conventions helps in reading specifications and processing angle observations correctly. Given Data / Assumptions: A triangulation series where some stations may not be occupied for angle measurement. Classical nomenclature from geodetic surveying texts. Concept / Approach: A main station is fully observed and forms the backbone of a series. Subsidiary or satellite stations are auxiliary, often established near a main station to avoid obstacles or to observe specific lines. A pivot station (also termed “station of no observations” in many texts) is included in the series for geometric continuity, but no angles are directly measured there; instead, the adjoining observed angles at other occupied stations define the geometry through it. Step-by-Step Solution: Identify the defining property: no angles measured at the station itself.Match terminology: pivot station / station of no observations fits this description.Differentiate from satellite/subsidiary (which are observed) and main stations (primary observed). Verification / Alternative check: Adjustment descriptions often list stations of no observations and constrain them via observed sides/angles from adjacent occupied stations, confirming the usage of “pivot” terminology. Why Other Options Are Wrong: Satellite and subsidiary stations are established for observation, usually near a main station. Main station is an observed principal point of the network. “None of these” is incorrect since a standard name exists. Common Pitfalls: Assuming every named station must be occupied; misunderstanding that some stations are computed for closure and geometry without direct angular observations. Final Answer: Pivot station (station of no observations)

Question 15

Aerial survey line planning — spacing between parallel flight lines on map An area 30 km wide is to be covered by 16 parallel flight lines run perpendicular to the width. What will be the spacing between adjacent flight lines as measured on a photog…

Accepted Answer

Introduction / Context: Flight line spacing determines overlap/sidelap and coverage uniformity when planning aerial photography. Converting ground distances to map distances requires careful use of the representative fraction (RF) of the map scale. Given Data / Assumptions: Total coverage width perpendicular to flight lines = 30 km. Number of flight lines = 16. First and last flight lines coincide with the two edges, so spacing = width/(n − 1). Map scale = 1:50,000. Concept / Approach: Compute ground spacing between adjacent lines, then convert to map distance using the scale RF. For n lines spanning a fixed width, there are (n − 1) equal intervals between edges. Step-by-Step Solution: Ground spacing = 30 km / (16 − 1) = 30/15 = 2 km.Convert 2 km to centimeters: 2 km = 2000 m = 200,000 cm.Apply map scale 1:50,000: map distance = 200,000 / 50,000 = 4 cm.Therefore, spacing on the map = 4 cm. Verification / Alternative check: Reverse check: 4 cm on map at 1:50,000 represents 4 * 50,000 cm = 200,000 cm = 2 km on ground, consistent with the computation. Why Other Options Are Wrong: 1 cm, 2 cm, 3 cm, 5 cm correspond to ground spacings of 0.5, 1, 1.5, and 2.5 km respectively at this scale, none of which match 2 km. Common Pitfalls: Using n instead of (n − 1) intervals; unit conversion errors (km → m → cm); misreading the map scale RF. Final Answer: 4 cm

Question 16

Homologous points in photogrammetry — identifying corresponding pairs Which of the following pairs are homologous points (i.e., correspond to the same object point in the ground–image relationship)?

Accepted Answer

Introduction / Context: In photogrammetry, a “homologous” pair comprises an image-space point and its corresponding point defined in object space (ground) under the imaging geometry. Recognizing homologous feature pairs supports orientation, calibration, and quality control of aerial photographs. Given Data / Assumptions: Standard definitions of principal point, isocentre, and plumb (nadir) point. Well-defined camera geometry and ground reference framework. Concept / Approach: The photo principal point corresponds to the ground principal point; likewise, the photo isocentre corresponds to its ground counterpart; and the photo plumb point corresponds to the ground plumb point. Each pair refers to the same conceptual entity in image and ground spaces and is therefore homologous. Step-by-Step Solution: Match each photo-defined control point to its ground-defined counterpart.All listed pairs represent the same physical/geometry-based feature in their respective domains.Hence, choose “All of the above.” Verification / Alternative check: Orientation procedures treat these control points as conjugate entities when transforming between image and object spaces, confirming their homologous nature. Why Other Options Are Wrong: Rejecting any single pair would contradict standard photogrammetric definitions. Common Pitfalls: Confusing homologous points with conjugate image points between left and right photos; here, the pairing is between photo and ground, not between two photos. Final Answer: All of the above

Question 17

Apparent motion of Polaris — direction at eastern elongation At the instant of eastern elongation in its small diurnal circle around the north celestial pole, in which direction does the pole star (Polaris) appear to move?

Accepted Answer

Introduction / Context: Stars appear to move in circles around the celestial poles due to Earth’s rotation. Polaris lies close to the north celestial pole and traces a small circle (of radius ≈ 1°) about it. Understanding instantaneous motion at elongation points helps in precise astronomical observations and instrument checks. Given Data / Assumptions: Northern hemisphere perspective with counterclockwise apparent rotation about the pole. Eastern elongation is the point of the small circle farthest to the east of the pole. Concept / Approach: At the easternmost point of a counterclockwise circular path, the instantaneous motion is tangential and directed upward on a standard sky diagram, that is, toward the north (increasing altitude) for Polaris. Conversely, at western elongation, the motion is toward the south (decreasing altitude). “Eastward” or “westward” at elongations would imply radial motion toward/away from the pole, which is not correct for the tangential diurnal motion. Step-by-Step Solution: Model the small circle around the pole; identify the easternmost point.With counterclockwise motion, the tangent at the east point points northward.Therefore, Polaris moves northward at eastern elongation. Verification / Alternative check: Star-trail diagrams and planetarium software confirm the motion sense: northward at eastern elongation and southward at western elongation for Polaris. Why Other Options Are Wrong: Eastward/westward: do not represent the tangent direction at elongation. Southward: applies at western elongation, not eastern. Common Pitfalls: Confusing cardinal directions on the sky dome with azimuthal directions on the ground; forgetting the counterclockwise sense around the north pole. Final Answer: Northward

Question 18

Aerial Photogrammetry – Idealized projection model In the context of photogrammetry, an aerial photograph (captured from a finite flying height with a lens of focal length f) is best idealized as which type of geometric projection for mapping and me…

Accepted Answer

Introduction / Context: Aerial photogrammetry relies on understanding how terrain points are projected onto the photo plane. The geometric model used in computations must reflect how a real camera forms images. Recognizing that aerial photos are created by rays passing through a single perspective center is foundational to scale, relief displacement, and orientation concepts. Given Data / Assumptions: A finite focal length camera captures the scene from a finite height above ground. Light rays from ground points pass through a single optical center (perspective center) before reaching the image plane. We are considering the idealized geometric model (ignoring lens distortion and tilt for the core concept). Concept / Approach: In central (perspective) projection, all image-forming rays converge at one point: the camera's perspective center. This contrasts with parallel or orthogonal projection where projectors are mutually parallel and conceptually originate at infinity. Central projection accurately represents how a real lens maps 3D terrain onto a 2D photo, which is why photogrammetric collinearity equations use the perspective center explicitly. Step-by-Step Solution: Identify the imaging geometry of a lens: rays converge at the optical center → perspective mapping.Match this with the projection type → central (perspective) projection.Exclude parallel/orthogonal models because they assume infinite focal distance and do not produce relief displacement or perspective scale changes. Verification / Alternative check: Relief displacement formula d = (r * h) / H and photo scale S = f / H derive from central projection assumptions. These relations would not hold under a parallel projection model. Why Other Options Are Wrong: Parallel/orthogonal projections ignore the finite focal length and perspective center, hence they cannot explain radial displacement. “None of these” is invalid because central projection precisely describes aerial photos. Common Pitfalls: Assuming near-vertical photos behave like maps; maps approximate orthographic views, while photos are central projections that require rectification for planimetric accuracy. Final Answer: Central projection

Question 19

Camera rotations in aerial photography – name the rotation about the vertical (optical) axis During exposure, when the camera undergoes a rotation about its vertical axis (through the perspective center), what is this motion commonly called in photo…

Accepted Answer

Introduction / Context: Orientation of aerial photographs is described using small rotations about three mutually perpendicular axes. Correctly naming these rotations is essential for understanding exterior orientation, image rectification, and error sources in photogrammetry. Given Data / Assumptions: Axes follow photogrammetric convention: two horizontal axes in the image plane and a vertical axis through the perspective center. We consider instantaneous camera attitude at the moment of exposure. Terminology aligns with classical stereoplotter usage (ω, φ, κ or equivalents). Concept / Approach: The three basic rotations are often denoted ω (about x), φ (about y), and κ (about z, the vertical axis). Traditional names are tilt and tip for rotations about horizontal axes, and swing for rotation about the vertical (optical) axis. Swing effectively rotates the image around its nadir/principal point in plan. Step-by-Step Solution: Identify the axis: vertical through the optical center → z-axis.Photogrammetric name for rotation about z-axis → swing (κ).Therefore, select “Swing”. Verification / Alternative check: Stereoplotter controls typically label κ as the swing knob, changing the image's azimuthal orientation without altering tilt magnitude. Why Other Options Are Wrong: Tilt and tip refer to rotations about horizontal axes, affecting apparent photo tilt. “None” is incorrect because a standard term exists. Common Pitfalls: Confusing aircraft yaw with camera swing; while related, photogrammetric naming is determined at the camera perspective center. Final Answer: Swing

Advanced Surveying Questions