**Photogrammetric Surveying**

**Scale of a Vertical Photograph**

H = height of exposure station (or the airplane) above the mean sea level.

h = Height of ground above MSL

f = Focal length of the camera

- If A and B are two points on the ground having elevations h
_{a}and h_{b}above MSL, then the Average scale of a line joining A and B is given by.

**Datum scale**

**Scale of a photograph**

where l = distance in the photograph

L = distance in ground

**Computation of length of the line between points of different elevations from measurement on a vertical photograph.**

If A and B be two ground points having elevations h_{a }and h_{b} above MSL and coordinates (*X _{a}, Y_{a}*) and (

*X*)

_{b}, Y_{b}Let a and b be the position of corresponding points in the photograph and (*x _{a}, y_{a}*) and (

*x*) be the corresponding coordinates.

_{b}, y_{b}where,

The length between AB is given by

**Relief displacement on a Vertical Photograph**

When the ground is not horizontal the scale of the photograph varies from point to point. The ground relief is shown in perspective on the photograph. Every point on the Photograph is, therefore, displaced from the true orthography position. This displacement is called relief displacement.

aa_{0} is called relief displacement.

aa_{0} = r - r_{o}

from similar triangle.

So relief displacement

So relief displacement

If relief displacement is known then the height of an object is given by,

**Scale of a tilted photograph**

where,

θ = 180-*s*

s = Swing

t = tilt

f = Focal length

H = Flying height above datum

h = high of ground above datum.

It can be seen that the tilt and relief displacements tend to cancel in the upper part of the photograph while they are cumulative to the lower part.

**Overlap in the Photographs**

Longitudinal overlap = 55 to 65%

Lateral Overlap = 15 to 35%

for the maximum rectangular area, to be covered by one photograph, the rectangle should have the dimension in the flight to be one-half the dimension normal to the direction of flight.

W = 2BW = 1.22H W = width of ground % overlap ≈ 60% in longitudinal direction.

**Number of Photographs to Cover a Given Area**

A = Total area to be photographed

a = net ground area covered by each photography

N = number of photographs required.

*a = L×W*

*L = (1-P _{1})s.l.*

*W = (1-P _{w})s.l.*

*a = l.ws ^{2}(1-P_{1})(1-P_{w})*

where, l = length of photograph in direction of flight

W = width of photograph.

P_{l} = % lap in longitudinal direction

P_{w} = lap in longitudinal direction

S = Scale of Photograph

If instead of total area A, the rectangular dimensions L_{1} × L_{2} (parallel and Transverse to flight) are given then, the number of photographs required are given as follows.

Let L_{1} = Dimension of area parallel to the direction flight

L_{2} = Dimension of area Transverse the direction of flight

N_{1} = Number of photographs in each strip

N_{2} = Number of strips required.

N = Total number of photographs to cover the whole area.

**Interval between exposures**

V = ground speed of the airplane in kmph.

L = ground distance covered by each photograph in the direction of flight = (1 – P_{l}) s.l …… in Km

**Photogrammetry**

**(i) Terrestrial photogrammetry: **Photographs are taken from a fixed position on or near the ground.

**(ii) Aerial Photogrammetry: **Photographs are taken from a camera mounted in an aircraft flying over the area.

**Phototheodolite: **It is a combination of “theodolite and a terrestrial camera. Important parts are:

- Camera Box of a fixed focus type.
- The hollow rectangular frame consists of two crosshair.
- Photographic plate
- Theodolite

**Important Definitions**

**(i) Camera Axis: **Line passing through the center of camera lens perpendicular both to camera plate (Negative) and picture plane (photograph).

**(ii) Picture Plane: **Positive plane, perpendicular to the camera axis.

**(iii) Principal point: **K or K’ point on the intersection of camera axis with either picture plane or the camera plate.

**(iv) Focal length (f): **Perpendicular distance from the center of a camera lens to either to picture plane or camera plate. It satisfies the relation.

**(v) Nodal point: **Nodal point is either of two points on the optical axis of a lens so located that when all object distances are measured from one point, and all image distances are measured from another. They satisfy the simple lens relation.

**(vi) Principal plane: **It is a plane that contains a principal line and optical axis.

**(Vii) Oblique photograph: **Photograph taken from the air with the axis of camera tilted from vertical are called oblique photograph, these are of two type

**Low Oblique photograph:**An oblique photograph that does not show the horizon is called a low oblique photograph.**High Oblique photograph:**If the tilt is more up to such that horizon is shown in the photograph, it is called a high oblique photograph.

**(viii) Convergent photograph: **Low oblique photographs which are taken with two cameras exposed simultaneously at successive exposure stations, with their axes tilted at a fixed inclination from vertical, so that forward exposure of the first station from a stereo pair with backward exposure of next station, these photographs are called ‘Convergent Photographs’.

**Horizontal and Vertical angles from the terrestrial photograph**

Angle *φ*_{1 }is the magnetic bearing of the camera axis (or principal vertical plane.)

Azimuth of line *Ok* = *φ*_{1}

Azimuth of line OA = *φ*_{1 }- α_{a} (OA is left to OK)

Azimuth of line OB = *φ*_{1 }- α_{b} (OA is right to OK)

So, Azimuth of a line = Camera azimuth + α

**Elevation of a point by photographic measurement**

Consider Point A

If V = Elevation of point A above Horizontal plane through camera axis.

From Similar triangle

Elevation of point A.

h = H_{C} + V + C

Where, H_{C} = Elevation of camera

V = Elevation of point A

C = Correction for curvature and refraction.

h = H_{C} + V + C

**Determination of focal length of the lens**

Take two points A and B. Measure angle *θ* very accurately from a theodolite

Quadratic equation in f.

**Aerial Photogrammetry**

Aerial photograph is taken from a fast speed aerial camera which has very high speed and efficient shutter, using high-speed emulsion for the film.

**Important Definitions**

**Vertical photographs:**When a photograph is taken keeping the camera axis vertical, coinciding with the direction of gravity, it is called a vertical photograph.**Tilted Photograph:**camera axis inclined at an angle from vertical.**Exposure station:**Point in space, occupied by camera lens at the time of exposure.**Flying height:**Elevation exposure station above sea level.**Flight line:**Line drawn on the map to represent the track of the aircraft.**Focal length:**distance from front Nodal point of the lens to plane of photograph (OK)**Principal Point:**Point, where perpendicular dropped from the front nodal point, strikes the photograph (K).**Nadir Point:**Nadir point is a point where the plumb line intersects the photograph.**Ground Nadir point:**Point on the ground vertically beneath the exposure station (Point N).**Tilt:**Vertical angle defined by the intersection at the exposure station. ∠*KON = t = tilt***Principal Plane:**Plane defined by lens (O) ground Nadir Point (N) Principal point produced on the ground (K).**Principal Line:**Intersection of the principal plane with the plane of photograph (line NK)**Isocentre:**Isocentre is the point at which the bisector of the angle of tilt meets the photograph.**Swing:**Angle measured in-plane of a photograph from + y-axis clockwise to Nadir point.**Azimuth of principal plane:**Clockwise horizontal angle measured about the ground nadir point from the ground survey north meridian to the principal plane of the photograph.**Horizon point (h):**Intersection of principal line with the horizontal line through the perspective center. Such as point h in the figure is the horizon point.**Axis of Tilt:**Axis of tilt is a line in photograph plane perpendicular to principal line at the isocentre such as i_{1}, i i_{2}in the figure. The plane of the photograph is tilted about the axis.

**Relation between principal point, plumb point, and isocentre**

(i) NK = distance of nadir point from principal point.

(ii) Ki = distance of the isocentre from the principal point.

(iii) Kh = distance of a principal point to horizon point.

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