Photogrammetric Surveying

Contents

**Recall the Basic Principle of Photo Theodolite** 1

**Describe the working of Photo Theodolite** 2

**Recall the Elevation of Point by Photographic Measurement** 4

**Recall the Components of Aerial Camera** 5

**Derive an expression for Scale of Vertical Photograph** 6

**Define the following terms: i. Datum Scale ii. Average Scale** 7

**Compute the Length of Line between Point of Different Elevations** 7

**Determine Height of Lens for a Vertical Photograph** 8

**Describe the concept of Scale of a Tilted Photograph** 9

**Derive the expression for Length calculation of a Line between two points using Tilted Photograph** 10

**Determine the Flying Height for a Tilted Photograph** 11

**Recall the concept of Tilt Distortion** 11

**Recall the concept of Relief displacement on a Tilted Photograph** 12

**Recall the concept of Flight Planning** 12

**Describe the Effective coverage of Photograph** 12

**Derive an expression for the Determination of Number of Photographs** 13

**Define the following terms: i. Crab ii. Drift** 14

**Describe the Radial Line Methods of Plotting** 14

**Classify the Clue to Depth Perception** 16

**Describe the Purpose of Stereoscope and its types** 17

**Recall Algebraic definition of Parallax** 18

**Describe Parallax Equations for the Determination of Elevation and Ground Co-ordinates** 19

**Describe the Difference in Elevation by the Stereoscopic Parallax** 20

**Recall the Basic Principle of Photo Theodolite**

A photo theodolite is an instrument used in surveying to measure both horizontal and vertical angles. The basic principle of a photo theodolite involves the use of optics and a sighting mechanism to measure the angles between points in the field.

The main components of a photo theodolite include:

- Telescope: The telescope is used to magnify and focus on the points being measured.
- Angle Measurement Mechanism: The angle measurement mechanism is used to measure the horizontal and vertical angles between the points being measured. This mechanism usually consists of two graduated circles, one for horizontal and one for vertical measurements.
- Sighting Mechanism: The sighting mechanism is used to align the photo theodolite with the points being measured. This mechanism usually consists of crosshairs or a laser that is used to aim the instrument at the point being measured.

The basic principle of a photo theodolite involves sighting on two points, measuring the horizontal and vertical angles between them, and then using trigonometry to calculate the distance and direction between the two points. This information is used in surveying to accurately measure and map the layout of a construction site or other physical location.

In summary, the basic principle of a photo theodolite involves the use of optics, angle measurement mechanism, and sighting mechanism to accurately measure the angles between points in the field. This information is then used to calculate distances and direction between points and map the layout of a construction site or other physical location.

**Describe the working of Photo Theodolite**

A photo theodolite is an instrument used in surveying to measure both horizontal and vertical angles. The working of a photo theodolite involves several components and steps to accurately measure and determine the angles between points in the field.

- Setting Up the Photo Theodolite: The photo theodolite is set up on a tripod or other stable platform and levelled to ensure accurate measurements. The sighting mechanism is then aligned with the first point being measured.
- Measuring Horizontal and Vertical Angles: The horizontal and vertical angles between the first and second points are measured using the angle measurement mechanism, which consists of two graduated circles, one for horizontal and one for vertical measurements. The horizontal angle is measured by rotating the instrument until the crosshairs or laser is aligned with the second point, and reading the angle on the horizontal circle. The vertical angle is measured in a similar manner, by tilting the instrument until the crosshairs or laser is aligned with the second point, and reading the angle on the vertical circle.
- Calculating Distance and Direction: The horizontal and vertical angles are used in conjunction with trigonometry to calculate the distance and direction between the two points. This information is used to determine the exact location of the second point relative to the first point, and to map the layout of a construction site or other physical location.
- Photo Theodolite Surveying: The photo theodolite can be used to survey an entire construction site by measuring the angles between multiple points and using the information to map the layout of the site. The photo theodolite is often used in conjunction with other surveying instruments, such as a total station or GPS, to provide a more accurate and comprehensive survey of the site.

In summary, the working of a photo theodolite involves several components and steps, including setting up the instrument, measuring horizontal and vertical angles, calculating distance and direction, and using the information to map the layout of a construction site or other physical location. The photo theodolite is an important tool in surveying and construction, providing accurate and detailed measurements of the angles between points in the field.

**Define the following terms: i. Camera Axis and Picture Plane ii. Principle Point and Nodal Point iii. Focal Length and Focal Plane iv. Fiducial Mark and Axis v. Film Base**

i. Camera Axis and Picture Plane: The camera axis is the line connecting the optical center of the lens to the center of the image sensor in a photo theodolite. The picture plane is the plane perpendicular to the camera axis, where the image of the object being captured is focused.

ii. Principle Point and Nodal Point: The principle point is the point where the camera axis intersects the image plane in a photo theodolite. The nodal point is the point where the light rays entering the lens converge, forming a single point in the image plane. The principle point and nodal point are used to calculate the perspective distortion in a photo theodolite.

iii. Focal Length and Focal Plane: The focal length is the distance from the nodal point to the image plane in a photo theodolite. The focal plane is the plane perpendicular to the camera axis, at a distance equal to the focal length from the nodal point. The focal length and focal plane are used to determine the size and perspective of the image being captured.

iv. Fiducial Mark and Axis: A fiducial mark is a reference point in a photo theodolite, used to align the camera axis with the object being captured. The axis is the line connecting the nodal point to the fiducial mark, used as a reference for aligning the camera axis with the object being captured.

v. Film Base: The film base is the flat surface of a film used in a photo theodolite, on which the image is captured. The film base is positioned parallel to the image plane, and is used to accurately capture the image of the object being measured. The film base is a critical component in a photo theodolite, as it provides a stable surface for capturing the image and helps to ensure accurate measurements.

**Describe the following: i. Determination of Horizontal and Vertical Angle ii. Determination of Horizontal Position of a Point iii. Determination of Focal Length of Lens**

i. Determination of Horizontal and Vertical Angle: The horizontal and vertical angles of a point in a photo theodolite can be determined by aiming the instrument at the point and measuring the angles with the theodolite’s built-in angular measurement system. This measurement system typically consists of a spirit level and an angular measurement device, such as a micrometer or vernier scale, which allow for precise angular measurements to be made. The horizontal angle is the angle between the plane of the instrument and the line connecting the instrument to the point, measured in the plane perpendicular to the vertical plane. The vertical angle is the angle between the plane of the instrument and the line connecting the instrument to the point, measured in the vertical plane.

ii. Determination of Horizontal Position of a Point: The horizontal position of a point in a photo theodolite can be determined by measuring the horizontal and vertical angles of the point, as described above. These angles, along with the distance between the instrument and the point, can then be used to calculate the horizontal position of the point using trigonometry. The horizontal position of the point is the location of the point in the plane perpendicular to the vertical plane.

iii. Determination of Focal Length of Lens: The focal length of a lens in a photo theodolite can be determined by measuring the distance between the lens and the image plane, when an object is in focus. This measurement can be made by adjusting the focus of the lens until an object at a known distance is in focus, and then measuring the distance between the lens and the image plane. The focal length of the lens is the distance between the lens and the image plane, when the lens is in focus. This measurement is important in determining the perspective and size of the image captured by the photo theodolite, as well as for calculating the size of objects in the image.

**Recall the Elevation of Point by Photographic Measurement**

The elevation of a point can be determined by photographic measurement using a photo theodolite. This involves taking a photograph of the point using theodolite, and then measuring the angles and distances in the photograph to determine the elevation of the point.

The process of determining the elevation of a point by photographic measurement typically involves the following steps:

- Set up the photo theodolite at a known location and orientation, with the camera axis perpendicular to the ground plane.
- Aim the photo theodolite at the point of interest, and take a photograph.
- Measure the horizontal and vertical angles of the point in the photograph, using the theodolite’s built-in angular measurement system.
- Measure the distance between the photo theodolite and the point, using a tape measure or other distance measuring device.
- Use the measured angles and distances to calculate the elevation of the point using trigonometry.

By accurately measuring the angles and distances in the photograph, it is possible to determine the elevation of a point with high precision. This method is particularly useful in cases where it is not possible or practical to measure the elevation of a point directly, such as when the point is located on a steep slope or in a remote location.

**Recall the Components of Aerial Camera**

An aerial camera is a specialised type of camera that is designed for use in aerial photography. The main components of an aerial camera include:

- Lens: This is the main optical component of the aerial camera and is used to focus light from the scene onto the film or digital sensor. The lens is typically mounted to a lens board that can be rotated to adjust the focus.
- Shutter: The shutter is used to control the amount of light that enters the camera and reaches the film or digital sensor. The shutter typically has adjustable speed settings that allow for different exposure times.
- Film or Digital Sensor: This component is used to capture the light from the scene and record the image. In traditional aerial cameras, this component is a roll of film that must be loaded into the camera. In digital aerial cameras, this component is a digital sensor that records the image electronically.
- Image Formatting: Aerial cameras typically have a standardised image format, such as the 6 x 6 cm format used by many traditional aerial cameras. This ensures that the images produced by different aerial cameras are compatible with each other.
- Camera Body: The camera body contains the lens, shutter, film or digital sensor, and other mechanical components of the camera. The camera body is typically mounted to a mount that allows it to be positioned and rotated as needed.
- Mount: The mount is used to secure the aerial camera to the aircraft and position it in the correct orientation for photography. The mount must be sturdy and stable, as vibrations and movements of the aircraft can affect the quality of the images.
- Control System: Some aerial cameras have a control system that allows for remote control of the camera from the aircraft. This system can be used to adjust the focus, exposure, and other camera settings, as well as to trigger the camera to take a photograph.

**Derive an expression for Scale of Vertical Photograph**

The scale of a vertical photograph refers to the ratio of the size of the object in the photograph to its actual size in the real world. This ratio can be expressed as an expression, which can be derived using the following steps:

- Define the parameters: Let h be the height of the aerial camera above the ground and f be the focal length of the camera lens. Let x be the distance between the camera and the object in the photograph, and let y be the height of the object above the ground.
- Determine the scale of the photograph: The scale of the photograph can be determined using the equation:

scale = h / (h + y)

This equation takes into account the perspective distortion caused by the height of the camera above the ground. The higher the camera, the lower the scale of the photograph, and the greater the perspective distortion.

- Derive an expression for the scale: To derive an expression for the scale, we can substitute the equation for x in terms of h and y into the equation for scale. We can use the similar triangles formed by the camera, the ground, and the object in the photograph to find x:

x = (h * y) / (h + y)

Substituting this equation into the equation for scale, we get:

scale = h / (h + y) = h / (h + y) * (h * y) / (h * y) = (h * y) / (h^{2} + hy)

This expression represents the scale of the photograph in terms of the height of the camera, the height of the object, and the focal length of the camera lens. By understanding the scale of a vertical photograph, you can determine the accuracy and usefulness of aerial photographs for a wide range of applications.

**Define the following terms: i. Datum Scale ii. Average Scale**

The following terms are related to the scale of aerial photographs:

i. Datum Scale: The datum scale is the scale of the photograph at the point where the camera is directly over the datum (reference point) on the ground. This scale is usually expressed as a ratio, such as 1:10,000, which means that 1 unit in the photograph represents 10,000 units in the real world. The datum scale is important because it is used as a reference for all other measurements in the photograph.

ii. Average Scale: The average scale is the average of the scale at different points in the photograph. This is an important measure of the overall accuracy of the photograph, as it takes into account any variations in the scale due to changes in the height of the camera or the distance to the objects in the photograph. The average scale is usually calculated as the mean of the scales at a number of points in the photograph, or as the average of the scales at the four corners of the photograph.

It’s important to note that the datum scale and the average scale are not always the same, and the difference between them can indicate potential errors in the photograph. By understanding these concepts, you can better evaluate the accuracy and usefulness of aerial photographs for various purposes.

**Compute the Length of Line between Point of Different Elevations**

To compute the length of a line between two points of different elevations, you need to take into account the vertical difference in height between the two points, as well as the horizontal distance between them. This can be done using basic trigonometry, as follows:

- Determine the horizontal distance (d) between the two points. This can be measured directly on the aerial photograph or calculated using the known scale of the photograph.
- Determine the vertical difference in elevation (h) between the two points. This can also be measured directly on the photograph or calculated from the known elevation of one of the points.

Use the Pythagorean theorem to calculate the length of the line:

- L = √(d
^{2}+ h^{2})

This formula gives the actual length of the line on the ground, taking into account both the horizontal distance and the vertical difference in elevation between the two points. This information can be useful for a variety of purposes, such as planning a road or a pipeline, or estimating the length of a slope or a contour line. By understanding and applying this formula, you can effectively use aerial photographs to calculate the length of lines between points of different elevations.

**Determine Height of Lens for a Vertical Photograph**

The height of the lens, or camera, is an important factor in determining the scale of a vertical photograph. To determine the height of the lens for a vertical photograph, you need to consider the following:

- The focal length of the lens: The focal length of the lens is the distance between the lens and the image plane when the lens is focused at infinity. This value is typically given by the manufacturer of the lens and is an important factor in determining the scale of the photograph.
- The scale of the photograph: The scale of the photograph is the ratio of the distance on the ground to the distance on the photograph. In a vertical photograph, the scale is determined by the relationship between the height of the lens and the focal length of the lens.
- The height of the terrain: The height of the terrain is the distance from the ground to the lens. To determine the height of the lens, you need to know the height of the terrain.

To determine the height of the lens, you can use the following formula:

h = (f * S) / (1 + S)

where:

h is the height of the lens

f is the focal length of the lens

S is the scale of the photograph

By using this formula, you can calculate the height of the lens for a given vertical photograph, taking into account the focal length of the lens, the scale of the photograph, and the height of the terrain. This information is useful for a variety of purposes, such as determining the relative heights of different features in the photograph or estimating the accuracy of the photograph for a given height of lens.

**Describe the concept of Scale of a Tilted Photograph**

The scale of a tilted photograph is a measure of how much an object appears distorted or enlarged in a photograph that is taken at an angle, as opposed to a photograph that is taken vertically. When a photograph is taken at an angle, objects that are further away from the camera appear smaller and more compressed, while objects that are closer to the camera appear larger and more distorted. The scale of a tilted photograph is influenced by the angle at which the photograph is taken, as well as the height of the camera and the focal length of the lens.

To understand the concept of scale in a tilted photograph, it is helpful to consider the following:

- The viewing angle: The viewing angle refers to the angle at which the camera is positioned relative to the ground. A larger viewing angle will result in a larger amount of distortion in the photograph, while a smaller viewing angle will result in less distortion.
- The height of the camera: The height of the camera is an important factor in determining the scale of a tilted photograph. The higher the camera is positioned, the smaller the objects in the photograph will appear.
- The focal length of the lens: The focal length of the lens determines how much an object is enlarged in the photograph. A longer focal length will result in a larger amount of enlargement, while a shorter focal length will result in less enlargement.

In general, the scale of a tilted photograph is determined by the relationship between the viewing angle, the height of the camera, and the focal length of the lens. The scale of a tilted photograph can be calculated using mathematical formulas that take into account these factors.

It is important to understand the concept of scale in a tilted photograph in order to accurately interpret the information that is captured in aerial photography and to use this information in various applications, such as surveying, mapping, and resource management.

** ****Derive the expression for Length calculation of a Line between two points using Tilted Photograph**

The scale of a tilted photograph is different from that of a vertical photograph, as it depends on the tilt angle of the camera relative to the ground. The expression for the length calculation of a line between two points using a tilted photograph involves the determination of the tilt angle of the camera and the determination of the elevation difference between the two points.

To derive the expression, the following steps can be taken:

- Determine the tilt angle: The tilt angle of the camera can be determined by taking two vertical photographs of two known points, and then using photogrammetric techniques to calculate the tilt angle.
- Determine the elevation difference: The elevation difference between two points can be determined by taking a vertical photograph of one point, and then using photogrammetric techniques to calculate the elevation of the other point.
- Calculation of length: Once the tilt angle and the elevation difference are known, the length of the line between the two points can be calculated using the following formula:

Length = (Elevation Difference) / (Scale * tan (Tilt Angle))

Where “Scale” is the scale of the tilted photograph, and “Tilt Angle” is the tilt angle of the camera relative to the ground.

** ****Determine the Flying Height for a Tilted Photograph**

The flying height for a tilted photograph is the height of the aerial camera lens above the ground when the photograph is taken. The height is important because it affects the scale of the photograph, which is a measure of the size of features on the ground as they appear on the photograph. The flying height can be determined by considering the tilt angle of the camera, the focal length of the lens, and the scale of the photograph. The tilt angle is the angle between the optical axis of the camera and the ground. The focal length is the distance between the lens and the film or image sensor in the camera. The scale of the photograph is determined by the size of features on the ground as they appear on the photograph. To determine the flying height, these factors must be related using mathematical equations, which take into account the geometry of the camera and the position of the features on the ground.

**Recall the concept of Tilt Distortion**

Tilt distortion is a phenomenon that occurs when an aerial camera is tilted, causing the photograph to have an incorrect representation of size and shape. This occurs because the camera lens is not perpendicular to the ground, and so features on the ground are not captured in their true size and shape. Tilt distortion can cause significant inaccuracies in measurements made from the photograph, particularly for larger features that are farther from the center of the photograph. The extent of tilt distortion depends on the angle of tilt, the focal length of the lens, and the flying height of the camera. To minimize tilt distortion, aerial cameras are typically flown at a high altitude with the lens perpendicular to the ground. When tilt is unavoidable, correction methods can be applied to the photograph to remove or reduce the distortion, but these methods can be complex and time-consuming.

**Recall the concept of Relief displacement on a Tilted Photograph**

Relief displacement on a Tilted Photograph refers to the apparent displacement of objects in a photograph when taken at an angle instead of vertically. This happens due to the change in perspective that results from the tilt. Objects appear to be shifted in relation to one another, making it difficult to accurately measure distances and elevations. The degree of relief displacement is affected by several factors, including the tilt angle, the height of the lens, and the distance between the objects being photographed. Understanding relief displacement is important in aerial photography because it affects the accuracy of measurements and mapmaking. To minimize relief displacement, aerial photographers typically fly at higher altitudes and use larger-format cameras with longer focal lengths.

**Recall the concept of Flight Planning**

Flight planning is the process of determining the most suitable and safe flight path for an aircraft. It involves various steps and considerations, including weather conditions, air traffic control restrictions, the aircraft’s weight and fuel load, available navigation aids, and any other factors that may impact the flight. The flight plan should also take into account any emergency scenarios and have alternative routes in place to ensure the safety of the passengers and crew. Flight planning is critical to the success of any flight, as it helps ensure that the aircraft arrives at its destination on time and in good condition, while minimising the risk of incidents or accidents.

**Describe the Effective coverage of Photograph**

Effective coverage of a photograph refers to the area of ground that is captured in a clear and usable manner in a single aerial photograph. It is determined by factors such as the height of the aerial camera, the focal length of the lens, the flying height, and the tilt angle of the camera. The effective coverage of a photograph is important for determining the number of photos required to cover a certain area and for ensuring that the desired level of detail and accuracy is achieved in the resulting aerial images. Effective coverage can be calculated using mathematical formulas based on the parameters of the aerial camera and the flying conditions. The formula takes into account the scale of the photograph, the size of the film or digital sensor, the size of the ground area that is captured, and the overlap between consecutive photos. The effective coverage of a photograph can be used in flight planning to determine the most efficient way to fly a survey mission, taking into account the desired coverage, the available film or digital storage, and the time and cost constraints.

**Derive an expression for the Determination of Number of Photographs**

The learning outcome requires the derivation of an expression for the determination of the number of photographs required for a certain area.

In aerial photography, the number of photographs required for a certain area is dependent on several factors such as the flying height, the camera lens and its focal length, the film size, and the ground resolution. The ground resolution refers to the minimum size of an object that can be seen on the film.

The expression for the determination of the number of photographs required can be derived by using the following formula:

Number of photographs = Area to be covered / (Film width * Ground resolution)

Where:

- Area to be covered refers to the total area of the ground that needs to be captured in the photographs.
- Film width refers to the width of the film used in the camera.
- Ground resolution refers to the minimum size of an object that can be seen on the film.

By using this formula, the number of photographs required can be determined, which helps in planning the flight and ensuring that all the necessary areas are captured in the photographs.

**Define the following terms: i. Crab ii. Drift**

i. Crab – Crab is a term used in aerial photography that refers to the lateral offset or deviation of the aerial camera from the flight path. It occurs when the aerial camera is not aligned with the flight path, causing the photographs to be angled instead of straight down.

ii. Drift – Drift is a term used in aerial photography that refers to the deviation of the flight path from its intended course. It can occur due to various factors such as wind, navigation errors, or mechanical issues with the aircraft. The drift can cause the aerial photographs to have a noticeable curvature and affect the accuracy of the images. It is important to take drift into consideration when planning a flight for aerial photography and to minimize it as much as possible for accurate results.

**Describe the Radial Line Methods of Plotting**

The Radial Line Methods of Plotting is a method used to plot aerial photographs on a map. The method involves drawing radial lines from the camera center to the ground control points, which are located on the ground and their positions are known. The intersections of these radial lines with the ground control points are used to determine the scale and orientation of the aerial photograph.

The method involves the following steps:

- Mark the camera center and the ground control points on the aerial photograph.
- Draw radial lines from the camera center to the ground control points.
- Plot the ground control points on the map using their known coordinates.
- Project the radial lines onto the map using the same scale as the ground control points.
- The intersections of the radial lines with the ground control points are used to determine the scale and orientation of the aerial photograph on the map.

The Radial Line Methods of Plotting is an efficient way of plotting aerial photographs on a map as it requires only a few ground control points. However, it has the limitation that the ground control points must be distributed evenly on the photograph and their positions must be accurately known.

**Define the following terms: i. Depth Perception ii. Angle of Parallax iii. Stereoscopic Fusion iv. Parallax Difference**

i. Depth Perception

Depth perception refers to the ability of an observer to perceive the three-dimensional structure of an object or a scene by combining information from both eyes to determine the relative distances of objects in the scene. This allows the observer to judge the relative distances of objects in the scene and understand the spatial relationships between objects.

ii. Angle of Parallax

The angle of parallax refers to the angle between two lines of sight from two points, such as the observer’s eyes, to a point in the scene. This angle is used to measure the relative distances of objects in the scene and is used in determining depth perception.

iii. Stereoscopic Fusion

Stereoscopic fusion refers to the process by which the brain combines the images from two eyes to create a single three-dimensional image. The brain uses the difference in the images from each eye, known as the parallax difference, to judge the relative distances of objects in the scene and create a three-dimensional representation.

iv. Parallax Difference

The parallax difference refers to the difference in the position of an object as seen by the two eyes. This difference is used by the brain to judge the relative distances of objects in the scene and create a three-dimensional representation.

**Classify the Clue to Depth Perception**

“Classifying the Clues to Depth Perception” refers to identifying and categorising the various ways in which the human brain can determine the depth and distance of objects in our surroundings. Some of the most commonly recognized clues to depth perception include:

- Binocular cues: These are cues that require the use of both eyes to determine depth, such as stereoscopic vision and the angle of convergence of the eyes.
- Monocular cues: These are cues that can be used with one eye, such as size and position in the visual field, overlapping, linear perspective, and shading.
- Motion cues: These are cues that rely on the relative motion of objects in our field of view, such as the velocity and direction of objects, as well as their distance and size.
- Accommodation cues: These are cues that rely on the focusing of the eye’s lens, such as the changing focus of the lens when looking at objects at different distances.
- Perspective cues: These are cues that depend on the relative position and orientation of objects, such as the relative size of objects and their position in the visual field.

Each of these cues provides valuable information to the human brain, which combines them to form a comprehensive understanding of the three-dimensional world around us. Understanding the various clues to depth perception is crucial for a variety of fields, including psychology, neuroscience, and the visual arts.

**Describe the Purpose of Stereoscope and its types**

A stereoscope is an optical instrument used to view two-dimensional images as three-dimensional objects. It works by using two slightly offset images of the same scene, which are then merged by the brain into a single three-dimensional image. Stereoscopes were first developed in the 19th century and were popularly used to view stereo cards, which were a popular form of entertainment at the time.

There are several types of stereoscopes, including the following:

- View-Master: This is a handheld device that uses reels of stereo cards to display 3D images. It is a popular toy for children and is still in use today.
- Stereo Camera: This is a camera that takes two slightly offset images of the same scene, which can then be viewed using a stereoscope. Stereo cameras were popular in the 19th and early 20th centuries.
- Virtual Reality Headset: This is a modern version of the stereoscope that uses computer-generated images and head tracking to create a fully immersive 3D experience. Virtual reality headsets are used for gaming, simulations, and other applications.
- Stereoscopic Displays: These are displays that use multiple projectors or a special screen to present 3D images to the viewer. Stereoscopic displays are used in a variety of applications, including scientific visualisation, medical imaging, and entertainment.

In conclusion, the purpose of a stereoscope is to provide a 3D viewing experience by merging two offset images into a single image. There are several types of stereoscopes, including handheld devices, cameras, virtual reality headsets, and displays, each with their own unique applications and capabilities.

**Recall Algebraic definition of Parallax**

Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight. In other words, it is the apparent shift in the position of an object as seen from two different points. In mathematics, this phenomenon is represented by an algebraic definition.

The algebraic definition of parallax is expressed as:

Parallax = (d1 – d2) / d1

Where:

d1 is the distance between the first line of sight and the object being viewed

d2 is the distance between the second line of sight and the object being viewed

This formula calculates the fractional change in the position of the object as seen from the two lines of sight. It can be used to determine the distance to distant stars and galaxies by measuring their parallax against the background of more distant objects.

For example, if d1 = 10 units and d2 = 5 units, then the parallax would be (10 – 5) / 10 = 0.5 or 50%. This means that the apparent position of the object has shifted by 50% as seen from the two different lines of sight.

In conclusion, the algebraic definition of parallax is a mathematical expression that represents the apparent shift in the position of an object as seen from two different points. The formula (d1 – d2) / d1 can be used to determine the fractional change in position and is commonly used in astronomical measurements to determine distances to distant objects.

**Describe Parallax Equations for the Determination of Elevation and Ground Co-ordinates**

Parallax can be used to determine the elevation of an object and its ground coordinates. This is commonly done in surveying and mapping, where precise measurements of land features and elevations are necessary. Two equations are used for this purpose: the elevation parallax equation and the ground coordinate parallax equation.

Elevation Parallax Equation:

- This equation is used to determine the elevation of an object above the ground. It uses the concept of parallax to calculate the vertical distance between the object and the observer’s eye. The equation is as follows:

h = (H x d) / (H + h0)

Where:

h = elevation of the object above the ground

H = height of the observer’s eye above the ground

d = horizontal distance between the object and the observer’s eye

h0 = known height of the object above the ground

Ground Coordinate Parallax Equation:

- This equation is used to determine the ground coordinates of an object, such as its latitude and longitude. It uses the concept of parallax to calculate the horizontal distance between the object and the observer’s eye. The equation is as follows:

d = (H x h0) / (h0 + H)

Where:

d = horizontal distance between the object and the observer’s eye

H = height of the observer’s eye above the ground

h0 = known height of the object above the ground

In conclusion, the elevation parallax equation and the ground coordinate parallax equation are used to determine the elevation of an object and its ground coordinates, respectively. These equations use the concept of parallax to calculate the vertical and horizontal distances between the object and the observer’s eye, which are then used to determine the elevation and ground coordinates. These equations are commonly used in surveying and mapping for precise measurements of land features and elevations.

**Describe the Difference in Elevation by the Stereoscopic Parallax**

Stereoscopic parallax refers to the phenomenon of using two slightly offset views of an object to create a three-dimensional image. In surveying and mapping, this technique can be used to determine the difference in elevation between two points on the ground.

The process works by taking two photographs of the same scene from slightly different perspectives. These two images are then viewed through a stereoscope, which creates the illusion of a three-dimensional image. The difference in elevation between two points on the ground can be determined by comparing the relative position of the two points in the two images.

The difference in elevation can be calculated using the elevation parallax equation. This equation uses the concept of parallax to calculate the vertical distance between the object and the observer’s eye. The equation is as follows:

h = (H x d) / (H + h0)

Where:

h = elevation of the object above the ground

H = height of the observer’s eye above the ground

d = horizontal distance between the object and the observer’s eye

h0 = known height of the object above the ground

In conclusion, the stereoscopic parallax technique is a way of using two slightly offset views of an object to create a three-dimensional image. In surveying and mapping, this technique can be used to determine the difference in elevation between two points on the ground. The difference in elevation can be calculated using the elevation parallax equation, which uses the concept of parallax to calculate the vertical distance between the object and the observer’s eye.